Axial Flow Compressor Mean Line Design

Axial Flow Compressor Mean Line Design

Niclas Falck

February 2008 Master Thesis

Division of Thermal Power Engineering Department of Energy Sciences

Lund University, Sweden

© Niclas Falck 2008

ISSN 0282-1990 ISRN LUTMDN/TMHP—08/5140—SE Printed in Sweden Lund 2008

Preface

This master thesis has been conducted at the division of Thermal Power Engineering, department of Energy Science, Lund University, Sweden.

This experience has been very educational in terms of modeling and computing thermal energy devices. This thesis has been about axial flow compressors, but the approach and methodic that I have implemented in this thesis will also be useful in my future career as an Engineer regardless of branch.

I want to thank my supervisor Magnus Genrup for his support and expertise in the field of turbomachinery.

I also want to thank the rest of the department of Energy Science, especially my fellow master thesis workers, for an enjoyable time here in Lund.

Abstract

The main objective in this thesis is creating a method on how one can model an axial flow compressor. The calculation used in this thesis is based on common thermodynamics and aerodynamics principles in a mean stream line analyses. Calculations based on one stream line i.e. one dimension, is a good first start to model a compressor. Most of the correlations and thermodynamics are based on one stream line, or they can be modified to work on one stream line.

By just a handful of design specifications an accurate model can be generated. These specifications can be mass flow, rotational speed, number of stages, pressure ratio etc. The pressure ratio is also the one parameter that the calculation aims to satisfy. If the calculation results in a pressure ratio that is not what was specified in the beginning an adjustment must be made on one parameter. In this case the stage load coefficient is selected. By changing the stage loading coefficient and keeping the other parameters constant the pressure ratio will vary. This is done in an iterative process until the pressure ratio is converged.

The purposes of modeling compressors based on correlations and thermodynamics and not model them in a CFD (Computational Fluid Dynamics) simulation program at once is that it takes a long time for a calculation to converge in a CFD program. Finding better correlations and methods on how one can model a compressor will result in fewer hours fine tuning them in advanced fluid dynamic programs and hence same time and not to mention money.

1

Content

Nomenclature .................................................................................................................. 4

Introduction ..................................................................................................................... 6

1 Background .................................................................................................................. 7

1.1 Gas turbine .............................................................................................................. 7

1.2 Compressor ............................................................................................................. 8

1.3 Stagnation property ................................................................................................. 9

2 Compressor Fundamentals ....................................................................................... 11

2.1 Compressor operation ........................................................................................... 11

2.2 Blade to Blade Flow path ...................................................................................... 12

2.3 Rothalpy ................................................................................................................ 13

2.4 Compressor Losses ................................................................................................ 14

2.4.1 Profile-loss ..................................................................................................... 15

2.4.2 Endwall-loss ................................................................................................... 15

2.5 Blade geometry ..................................................................................................... 16

2.6 Dimensionless Parameters .................................................................................... 16

2.6.1 Stage load coefficient ..................................................................................... 17

2.6.2 Stage flow coefficient ...................................................................................... 17

2.6.3 Stage reaction ................................................................................................. 17

2.6.4 de Haller number ............................................................................................ 17

2.6.5 Pressure rise coefficient ................................................................................. 18

2.7 Efficiency .............................................................................................................. 18

2.7.1 Isentropic efficiency ........................................................................................ 18

2.7.2 Polytropic efficiency ....................................................................................... 19

2.7 Operating Limits ................................................................................................... 20

3 Methods of Calculation ............................................................................................. 22

3.1 State properties ...................................................................................................... 22

3.2 Incidence and Deviation ........................................................................................ 22

3.2.1 Incidence Angle .............................................................................................. 23

Content Axial Flow Compressor Mean Line Design

2

3.2.2 Deviation Angle .............................................................................................. 26

3.3 Diffusion Factor and Diffusion Ratio .................................................................... 28

3.4 Losses .................................................................................................................... 30

3.4.1 Profile loss model ........................................................................................... 30

3.4.2 Endwall loss model ......................................................................................... 31

3.4.3 Total loss ......................................................................................................... 31

3.5 Pitch Chord ratio .................................................................................................... 32

3.5.1 Diffusion Factor Method ................................................................................. 33

3.5.2 Hearsey Method .............................................................................................. 33

3.5.3 McKenzie Method ........................................................................................... 33

3.6 Stall/Surge ............................................................................................................. 33

4 Calculation procedure ................................................................................................ 39

4.1 Input parameters .................................................................................................... 39

4.1.1 Main specification ........................................................................................... 40

4.1.2 Detailed specification ..................................................................................... 41

4.1.3 Inlet specification ............................................................................................ 41

4.2 Parameter variations throughout the compressor .................................................. 41

4.3 Calculation limitations ........................................................................................... 42

4.3.1 Mean stream line analyses .............................................................................. 42

4.3.2 Convergence criteria’s .................................................................................... 43

4.4 Structure of the calculation .................................................................................... 44

4.4.1 Module 0 ......................................................................................................... 44

4.4.2 Module 1 ......................................................................................................... 44

4.4.3 Module 2 ......................................................................................................... 45

4.4.4 Module 3 ......................................................................................................... 46

4.5 Newton-Rhapson Method ...................................................................................... 47

5 Calculation process .................................................................................................... 48

5.1 Module 0, Inlet geometry ...................................................................................... 48

5.2 Module 1, Rotor-inlet ............................................................................................ 50

5.3 Module 2, Rotor-outlet/stator-inlet ........................................................................ 53

5.3.1 Module 2.1 start .............................................................................................. 53

5.3.2 Module 2.1 end ................................................................................................ 55

5.3.3 Module 2.2 start .............................................................................................. 55

Axial Flow Compressor Mean Line Design Content

3

5.3.4 Module 2 end .................................................................................................. 57

5.4 Module 3, Stator-outlet ......................................................................................... 58

5.4.1 Module 3.1 start .............................................................................................. 58

5.4.2 Module 3.1 end ............................................................................................... 59

5.4.3 Module 3.2 start .............................................................................................. 59

5.4.4 Module 3 end .................................................................................................. 61

5.5 Outlet Guide Vane, OGV ...................................................................................... 61

5.6 Blade angles calculation ........................................................................................ 64

6 Result ........................................................................................................................... 65

7 LUAX-C ...................................................................................................................... 69

7.1 Structure of the program ....................................................................................... 69

7.2 User Guide to LUAX-C ........................................................................................ 70

References ...................................................................................................................... 76

Appendix ........................................................................................................................ 77

A, polynomial coefficients for the graphs ................................................................... 77

B, MATLAB script for the calculations ...................................................................... 78

B.1 Main Calculation .............................................................................................. 78

B.2 Inlet geometry calculation ................................................................................ 96

B.3 Pitch chord ratio ............................................................................................... 97

B.4 Diffusion Factor and Diffusion Ratio ............................................................... 98

B.5 Compressor losses ............................................................................................. 99

B.6 Blade angles .................................................................................................... 100

Appendix C ............................................................................................................... 102

4

Nomenclature

Symbol Unit Description a [m/s] Speed of sound A [m2] Area cp [kJ/kgK] Specific heat at constant pressure cv [kJ/kgK] Specific heat at constant volume c [m] Chord C [m/s] Absolute velocity C [m/s] Tangential absolute velocity Cm [m/s] Meridional velocity Cp [-] Static pressure rise coefficient DF [-] Diffusion factor Deq [-] Equivalent diffusion ratio h [kJ/kg] Static enthalpy h0 [kJ/kg] Stagnation enthalpy H [m] Blade height i [°] Incidence I [-] Rothalpy m [kg/s] Massflow Ma [-] Mach-number N [rev/s] Rotational speed p [bar] Static pressure p0 [bar] Stagnation pressure r [m] Radius R [J/kgK] Gas constant s [kJ/kg] entropy S [m] Staggered spacing t [m] Maximum blade thickness T [K] Static temperature T0 [K] Stagnation temperature U [m/s] Blade velocity W [m/s] Relative velocity W [m/s] Tangential relative velocity

Axial Flow Compressor Mean Line Design Nomenclature

5

Symbol Unit Description [°] Angle between absolute velocity and axial direction [°] Angle between relative velocity and axial direction [°] Stagger angle [°] Deviation [m] Endwall clearance [%] Efficiency [-] Heat capacity ratio, Isentropic exponent Heat conductivity [Kg/m2] Density [m2/s] Kinematic viscosity Pressure loss coefficient [°] Camber angle [-] Stage load coefficient [-] Stage flow coefficient

6

Introduction

The development of gas turbines has in the recent years come a long way. Serious development began during the Second World War with the key interest of shaft power, but attention was shortly transferred to the turbojet engine for aircraft propulsion. The gas turbine began to compete successfully in other fields in the mid 1950s, since then it has made a successful impact in an increasing variety of applications.

When combining a gas turbine with a heat recovery steam generator the heat, that otherwise would be wasted from the gas turbine outlet, can be extracted. Together with a conventional steam generator this will form a combined cycle. The efficiency of a combined cycle power plant is far better than regular gas turbine power plants.

The question is than, how could we improve the efficiency of a gas turbine? One can either focus on the compressor, the combustion chamber or the turbine. In this thesis the compressor, especially the axial flow compressor, will be investigated.

When designing a new compressor, a good start is to create a base design for the compressor. By just a handful of design specifications an accurate model can be generated. The modelling techniques used are based on combinations of thermodynamic and aerodynamic correlations. This base design will make up for about 60-70 % of the finished design. In this first stage in designing a new compressor, designs that would not work or have pore efficiency can be avoided.

Further on in the process powerful CFD (Computational Fluid Dynamics) simulation programs are being used. A CFD calculation takes a long time and hence cost a lot of money. The solution to cutting down the number of simulations is then to make the base design more accurate.

7

1 Background

1.1 Gas turbine A gas turbine consists mainly by three components, the compressor, the combustion chamber and the turbine, see Figure 1.1. The compressor is one a part of the entire gas turbine, but never the less, an important and probably the most complicated component to design in an aerodynamic point of view.

The working fluid enters an inlet duct and continues to the compressor. The compressor pressurises the fluid and will also lead to an increase in temperature. Depending on the application it can either have a radial or an axial design depending on mass flow and pressure ratio. After the compressor, the pressure of the working fluid will have increased to 15-30 bar, even above 40 in aero engines, and will have a temperature of about 500°C.

By combustion of fuel in the combustion chamber, energy is added to the working fluid. A gas turbine is very flexible in terms of what sort of fuels can be used. The working fluid which now has a temperature of about 1200-1450°C enters the last stage in the process, the turbine. Here the fluid expands and thus transferring its energy to the turbine blade in form of mechanical work. The turbine is connected to the compressor by a shaft and this lead the mechanical work from the turbine to the compressor. If the gas turbine is to be used in a multi-shaft configuration, the work provided by the turbine will just be enough to drive the compressor otherwise a load can be connected like a pump, a propeller or a generator.

Compressor Turbine

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1 Background Axial Flow Compressor Mean Line Design

10

The stagnation enthalpy will not change through a duct if there is no heat or work done to the system. Flows through nozzles or diffusers usually satisfy these conditions, and any changes in the fluid velocity will create a change in the static enthalpy of the fluid. Substituting the enthalpy with temperature instead results in the following expression

or

(1.2)

Cp represents the specific heat value for the fluid for an ideal gas. T0 is called stagnation (or total) temperature. The term V2/2Cp is called the dynamic temperature and corresponds to the temperature rise during an adiabatic process.

The pressure a fluid obtains when brought to rest is called stagnation pressure, P0. For ideal gases with constant specific heats, P0 is related to the static pressure of the fluid by,

represents the specific heat ratio, Cp/Cv.

12

Figure 1.5, Steady flow of a fluid through an adiabatic duct

11

2 Compressor Fundamentals

2.1 Compressor operation A typical axial flow compressor consists of a series of stages; each stage has a row of moving rotor blades followed by a row of stator blades which is stationary, see Figure 2.1. The rotor blades accelerates the working fluid thus gaining energy, this kinetic energy is then converted into static pressure by decelerating the fluid in the stator blades. The process is then repeated as many times as necessary to get the required pressure ratio. The number of stages in a compressor is important especially when the engine will be used in an aircraft. The main reason is that too many stages will result in an increase in weight and a large core engine length. For land based gas turbines the main reason is the cost, which will increase when adding more stages. Some different compressors used in aircrafts are shown in Table 2.1, and here one can see how compressor improvement has come along over the years.

Engine Date Thrust Pressure Stages [kN] ratio Avon 1958 44 10 17 Spey 1963 56 21 17 RB-211 1972 225 29 14 Trent 1995 356 41 15

Table 2.1, Compressor evolution, aircraft engine

Figure 2.1, Cross-section view over a compressor flow path

2 Compressor Fundamentals Axial Flow Compressor Mean Line Design

12

As discussed earlier all the power is absorbed in the rotor and the stator transforms the kinetic energy which has been absorbed by the rotor into an increase in static pressure. The stagnation temperature remains constant throughout the stator since there is no work feed into the fluid. Figure 2.2 shows a sketch of a typical compressor stage.

The stagnation pressure rise occurs wholly in the rotor, but in practice, there will be some losses in the stator due to fluid friction which will result in a decrease in stagnation pressure. There are also some losses in the rotor and the stagnation pressure rise will be less than of an isentropic compression.

2.2 Blade to Blade Flow path To get a clear picture in how a compressor works, blade to blade flow path analysis is the most fundamental part. The velocity components of the working fluid can be expressed in two velocity vectors, absolute and relative velocity. The fluid enters the rotor with an absolute velocity, C1, and has an angle, 1, from the axial direction. Combining the absolute velocity with the blade speed, U, gives the relative velocity, W1,with its angle 1. The mechanical energy from the rotating rotors will be transferred to the working fluid. This energy absorption will increase the absolute velocity of the fluid. After leaving the rotor the fluid will have a relative velocity, W2, with an angle,

2, determined by the blade outlet angle. The fluid leaving the rotor is consequently the air entering the stator where a similar change in velocity will occur. Here the relative

p1

p01

p2

p03

p3

p02

T03´

T2

T01

T1

T02, T03

Temperature, T

Entropy, s

321

RS

Figure 2.2, Compressor stage and T-s diagram

Axial Flow Compressor Mean Line Design 2 Compressor Fundamentals

13

velocity, W2, will be diffused and leaving the stator with a velocity, C3, at an angle, 3.Typically the velocity leaving the stator will be the same as the velocity entering the rotor in the next row, C3 = C1 and 3 = 1. By creating so called “velocity triangles”, see Figure 2.3, will make it easier to visualize the change of velocities and angles in a compressor stage [1].

2.3 Rothalpy

The work, W, is expressed as the enthalpy change. For adiabatic machines the heat flux, Q, is zero. Introducing the Euler equation and expanding the stagnation enthalpy gives after rearrangement.

Consider the left-hand side, expanding C22 as C 2

2 + Cx22 + CR2

2 and then expressing the absolute tangential velocity in terms of that in the moving frame of reference C 2 = W 2 + U2. After some manipulation to the left-hand side of the equation one obtains.

This can then be used for obtaining the difference between the inlet and outlet.

U

W1 C1

Ca1

1 1

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15

The individual losses are lumped into profile- and endwall-losses. These pressure losses are dependent on a numerous parameters which include tip clearance, blade aspect ratio, pitch chord ratio, thickness chord ratio, Mach number and Reynolds number. The different loss models are based on mid radius and will be modelled individually for the rotor/stator.

2.4.1 Profile-loss Profile-losses are based on the effect of blade boundary layer growth (including separated flow) and wakes through turbulent and viscous dissipation. The effect of these losses is an increase of entropy due to the heat developed by the mechanical energy within the boundary layers. This results in a stagnation pressure loss [3].

2.4.2 Endwall-loss In addition to the losses which arise from the blade surfaces, i.e. profile losses, additional losses generated on the end walls. These are often called “secondary losses” which arises from end-wall boundary layer build up, secondary flow and tip clearance. When a flow that is parallel but non-uniform in velocity and density is made to follow a curved path, the result is a three-dimensional motion with velocity normal to the overall flow direction. Cross-flow of this type is referred as “secondary flow”. A good analogy of this is a simple teacup. When stirring the tea in a teacup, the tea leafs will move towards the center of the cup driven by the secondary flow.

The formation, development, diffusion and dissipation of these vortices as well as the kinetic energy in secondary velocities generate secondary flow losses. Somewhere between 50-70% of the losses may come from endwall losses, depending of the type of turbo machinery [3].


16

2.5 Blade geometry

1 Relative air inlet angle b1 Blade inlet angle 2 Relative air outlet angle b2 Blade outlet angle

Stagger angle Camber angle

i Incidence angle, 1 - b1Deviation angle, 2 - b2

c Chord length S Staggered spacing t Maximum thickness

Solidity, c/s

Table 2.2, Cascade notation

2.6 Dimensionless Parameters Introducing a set of dimensionless parameters will give a useful guidance in designing a compressor stage. These dimensionless performance parameters define the performance of a single stage in a compressor.

1

b1

2

b2

W1

Profile

W2

C

S

Camber line

t

Figure 2.5, Cascade notation


17

2.6.1 Stage load coefficient The total enthalpy rise through a rotor blade row is expressed by the well-known Euler turbine equation, i.e.

(2.2)

where H is the total enthalpy rise through the rotor. It is often useful to introduce dimensionless stage performance parameters for a “repeating” stage, i.e. the rotor-inlet (station 1) and the stator-outlet (station 3) from the previous stage has identical velocity diagrams. Then, the stage load coefficient, , can be defined as

(2.3)

2.6.2 Stage flow coefficient The stage flow coefficient, , is defined as followed.

(2.4)

This expresses the ratio between the meridional velocity and the blade velocity. A high stage flow coefficient indicated a high flow through the stage relative to the blade velocity. A low whirl velocity change in a stage would also indicate a high stage flow coefficient and vice versa [1].

2.6.3 Stage reaction The stage reaction, R, is defined as the fraction of the rise in static enthalpy in rotor compared to the rise in stagnation enthalpy throughout the entire stage.

(2.5)

If a compressor stage would have a stage reaction of 1.0 or 100%, the rotor would do all of the diffusion in the stage. Similar if the stage reaction is 0 than the stator will do all of the diffusion of the working fluid. It is never good to have either a stage reaction of 1.0 or 0. The literature, reference 1, suggest that a stage reaction about 0.5 i.e. the diffusion is equally divided between the two blade rows. But in practice a higher stage reaction is preferred. Increasing the stage reaction results in a decrease in whirl prior to the rotor. A smaller whirl will create a larger relative inlet velocity to the rotor row, at a constant Cp, and hence make it easier for the rotor to increase the static pressure.

2.6.4 de Haller number In most compressor stages both the rotors and the stators are designed to diffuse the fluid, and hence transform its kinetic energy into an increase in static enthalpy and static pressure. The more the fluid is decelerated, the bigger pressure rise, but boundary layer growth and wall stall is limiting the process. To avoid this, de Haller proposed that the


18

overall deceleration ratio, i.e. W2/W1 and C2/C3 in a rotor and stator respectively, should not be less than 0.72 (historic limit) in any row [1].

(2.6)

2.6.5 Pressure rise coefficient Another parameter is the pressure rise coefficient.

(2.7)

If axial velocity is assumed constant and the working fluid is assumed to be incompressible, then the pressure rise coefficient can also be expressed as a function of the deHaller number. This is done by applying Bernoulli’s principle.

(2.8)

2.7 Efficiency The term efficiency finds very wide application in turbo machinery. For all machines or stages, efficiency is defined as.

There are several different ways of evaluating efficiency and these reveal different information. Two of the most widely used efficiencies are the isentropic efficiency and the polytropic efficiency.

2.7.1 Isentropic efficiency The isentropic efficiency can be expressed as the ratio between enthalpy change in an ideal compressor and the actual enthalpy change. An ideal compressor which is both adiabatic and reversible cannot alter the entropy of the gas flowing through it. These types of compressors are usually referred to as isentropic. Since there will be some


19

losses which generates an entropy rise, the actual work into the compressor will differ from an ideal one. The efficiency can then be described as,

(2.9)

The subscript s denotes entropy held constant. Figure 2.6 shows a typical schematic diagram over a reversible adiabatic compression.

The constant pressure lines in the T-S diagram, Figure 2.6, have a slope proportional to the temperature and diverge as the temperature increases. For a given pressure rise the work input needed is greater for the later stages in a compressor, this because the temperature is higher and also that the work input required by the later stages is raised because of the previous stages. The isentropic efficiency therefore gets lower as the overall pressure ratio is increased. To cope with this problem, another efficiency the so-called polytropic or small-stage efficiency may be used instead [2].

2.7.2 Polytropic efficiency The definition of polytropic efficiency is as follows.

By applying Gibbs law and the relationship between temperature and enthalpy it can be rewritten so it depends on temperatures and pressures instead.

2s2

1

p01

p02

Entropy S

Temperature T

Figure 2.6, isentropic compression


20

Integrating the expression on pressure, p leads to the following equation.

(2.10)

One can also assume that the specific heat capacity is constant, which is not the case in this thesis. If this is assumed, the following expression can be found [2].

(2.11)

2.7 Operating Limits There are mainly two phenomena that can cause a compressor to break down, rotating stall and surge. Gas turbines, for example, may encounter severe performance and durability problems if the compressor is not able to avoid stall and surge. In preliminary designs there is a need for reliable methods for computing the compressors stall margin capability. This because it is difficult to correct and change the compressor stall margin after its basic design has been chose.

In a typical compressor it is normal that if the mass flow is reduced the pressure rise increases. At a certain point in an operating range the pressure rise is at its maximum, in a further reduction in mass flow will lead to an abrupt and definite change in flow pattern in the compressor. This change in flow pattern is known as surge and can cause the flow to start oscillating backwards and forwards, and after a while the compressor will break down. A mild version of surge causes the operating point to orbit around the point of maximum pressure rise. An audible burble is a clear indicator when the compressor is on the limit of the more severe surge [2].

The other phenomena that one should be looking for is stall. If the mass flow is reduced the axial velocity will, according to the continuity equation, also decrease. This will increase the air inlet angle and, due to the difference in air inlet angle and blade inlet angle, create incidence. With an increasing incidence angle the flow will eventually separate from the surface at the trailing edge. The separation will grow with a further


21

increase of incidence angle, and finally cover the whole upper blade. This phenomenon is called stall, and will change the performance of a compressor drastically.

Rotating stall means that the stall is moved from one blade to another and an uninformed pattern will occur, see Figure 2.7. The annulus then contains regions of stalled flow, usually referred as “cells”, and regions of unstalled flow. Rotating stall is a mechanism which allows the compressor to adapt to a mass flow which is too small. Instead of trying to share the limited flow over the whole annulus the flow is shared unequally, so that some areas have a larger mass flow than other. The overall mass flow remains constant but the local mass flow varies as the rotating cell passes the point of observation. The cells always rotate in the direction of the rotor. Part-span cells very often rotate at close to 50 percent of the rotor speed, full-span cells usually rotate more slowly in the range of 20-40 percent. Full-span cells extend axially through the whole compressor while part-span cells can exist in a single blade row [2].

Full-span stall Part-span stall

Cell

Unstalledflow

Figure 2.7, Different types of rotating stall

22

3 Methods of Calculation

3.1 State properties In order to calculate the state of a fluid, an approach according to the Gibbs-Dalton is used. The model used is the NASA SP-273, and by integration, the enthalpy and entropy are known. The specific heat is expressed as fifth order polynomial.

The reference values are set to zero at 101.325 kPa and 273.15 K. as seen in the equations above.

As seen in the equation above, the temperature and the pressure must be known if the entropy and enthalpy are to be found. If let say that the enthalpy and the temperature are known instead, an iterative process is needed since the specific heat value is expressed as a fifth order polynomial. This iterative procedure uses the standard Newton method, see chapter 4.5 “Newton Rhapson Method”. Introduction of other property libraries are straightforward, as long as they are semi-perfect (specific heat only a function of temperature) [11].

3.2 Incidence and Deviation There are several different methods on how to get the blade angles in a cascade. In this thesis, one method is used to calculate the angles based on a number of input variables. Howard, see reference 4, has put together a number of correlations and equations based on Johnsen and Bullock (1965), which commonly is referred to as NASA SP-36 correlations. These correlations are largely based on low speed cascade test; he also introduces some correlations for advanced transonic compressor blades by Köning, et al (1996), but this will not be taken in consideration in this thesis.

Axial Flow Compressor Mean Line Design 3 Methods of Calculation

23

3.2.1 Incidence Angle Incidence is the difference between the inlet blade angel and the inlet flow angle. As the fluid flows towards the leading edge it will experience “induced incidence”. There is one pressure surface and one suction surface at a given blade. This different of pressure will change the ingoing flow angle as it approaches the leading edge, see Figure 3.1.

By performing experimental tests on a given cascade, the incidence can be established. This incidence angle is referred as reference incidence.

When testing a given cascade at different inlet flow angles, the loss coefficient, ,varies with incidence. There will be an increase in both positive and negative incidence angles with a range of low values for . The pressure loss at twice the minimum loss will be the range in which the reference incidence will be located. Outside this range stall blade stall occurs. If this range of incidence is split in the middle, the point of reference incident angle will be found, see Figure 3.2.

Min. loss

2 xMin. loss

i/2 i/2

Incidence angle, i

Pressure loss,

Reference incidence angle

+_

Figure 3.1, induced incidence

Figure 3.2, Definition of reference incidence angle

3 Methods of Calculation Axial Flow Compressor Mean Line Design

24

The correlations for reference incidence angle are presented below:

(3.1)

Ksh and Kit are correction factors for blade shape and thickness respectively. Ksh differs whether the blade is a DCA, 65-Serie or a C-Series, see Table 3.1.

Ksh Blade type 0.7 DCA 1.0 65-Series 1.1 C-Series

Table 3.1, Shape factor, Ksh, for the calculation of incidence angle

(3.2)

i010 is the incidence angle based on 10% thick blades, see Figure 3.3. The variable nrepresents the incidence slope factor, see Figure 3.4.

(3.3)

(3.4)

In the polynomials above, 1 denotes the relative inlet flow angle for the rotor, and replaced by 2 for the stator.


25

Figure 3.3, reference incidence angle for profiles with zero camber with variations in solidity

Figure 3.4, slope factor, n, with variations in solidity

0 10 20 30 40 50 60 70 80-2

0

2

4

6

8

10

12

14

inci

denc

e, i 01

0

flow inlet angle [degree]

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

0 10 20 30 40 50 60 70 80-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

slop

e fa

ctor

, n


2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4


26

3.2.2 Deviation Angle Deviation angle is the difference between the blade angle from the trailing edge and the exit flow angle. It arises from a combination of two effects. Firstly the flow is decelerating on the suction surface and accelerating on the pressure surface as it approaches the trailing edge. A result from this is that the streamlines are diverging from the suction surface and converging towards the pressure surface so that the mean flow angle is less than the blade angle. This is an inviscid effect which increases in magnitude with the rate of diffusion and acceleration towards the trailing edge. Secondly the rapid boundary layer growth on the suction surface towards the trailing edge “pushes” the streamline away from the surface, contributing to the deviation [6].

A method to calculate the deviation angel is to use the classical Carter’s rule.

= deviation angle

mc = an empirical function of stagger angle,

= camber angle

= solidity

x = experimental factor (typical 2)

The deviation angle is dependent on both camber and stagger angle. This makes it quite difficult to calculate the deviation angle, therefore another approach is needed.

The deviation angle used in the calculation is based on the reference incidence angle and the structure looks very similar to that of the reference incidence angle.

(3.5)

Ksh is the same as for reference incidence but the correction factor for blade thickness is different.

(3.6)

010 is the deviation angle based on 10% thick blades, see Figure 3.5. The variable mrepresents the deviation slope factor, see Figure 3.6.

(3.7)


27

(3.8)

(3.9)

The modified slope factor, m, is different whether DCA, 65-series or C-Series is used.

65-series

(3.10)

DCA and C-series

(3.11)

Figure 3.5, zero camber deviation angle at iref with variations in solidity

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

devi

atio

n,

010


2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4

2.0

1.21.0

0.8

0.6

0.4


28

Figure 3.6, slope factor, m, with variations in solidity

3.3 Diffusion Factor and Diffusion Ratio The blade loading is usually assessed by the diffusion factor. This relates the peak velocity on the suction surface of the blade to the velocity at the trailing edge. Values of DF in excess of 0.6 are thought to indicate blade stall and values of 0.45 might be taken as a typical design choice. The ratio between maximum velocity and the outlet velocity is called the diffusion ratio [2].

There are several methods on how to calculate the diffusion ratio as well for the diffusion factor. Some of these correlations are presented below [4].

A simplified method on how to establish the diffusion ratio and the diffusion factor is.

(3.12)

(3.13)

Lieblein developed useful approximations for both diffusion ratio and diffusion factor. DF denotes the diffusion factor and Deq* the equivalent diffusion ratio. The derivation of the diffusion factor is based on the establishment of the velocity gradient on the

0 10 20 30 40 50 60 70 800.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

slop

e fa

ctor

, m


0.40.60.81.01.2

1.4

1.6

1.8

2.0

0.40.60.81.01.2

1.4

1.6

1.8

2.0

0.40.60.81.01.2

1.4

1.6

1.8

2.0

0.40.60.81.01.2

1.4

1.6

1.8

2.0

0.40.60.81.01.2

1.4

1.6

1.8

2.0

0.40.60.81.01.2

1.4

1.6

1.8

2.0

0.40.60.81.01.2

1.4

1.6

1.8

2.0

0.40.60.81.01.2

1.4

1.6

1.8

2.0

0.40.60.81.01.2

1.4

1.6

1.8

2.0


29

suction surface in terms of W1, W2 and Wmax in conjunction with results from cascade tests. From cascade tests it was deduced that the maximum velocity is

(3.14)

(3.15)

Koch and Smith modified the Lieblein approach and developed a more advanced correlation for the losses which allows for the factors maximum thickness to chord (t/c)and the Axial Velocity Density Ratio, i.e. AVDR.

(3.16)

where

(3.17)

(3.18)

(3.19)

and the density ratio between the passage throat to entry is


30

(3.20)

where Mx1 is the axial component of entry Mach number.

3.4 Losses 3.4.1 Profile loss model The profile-loss model used is a modified version of the two dimensional low speed correlation of Lieblein, see Figure 3.7. This correlation has been established for DCA aerofoils but is used for conventional circular arc aerofoils [8].

Figure 3.7, profile loss parameter with variation in Mach number

The profile-loss parameter is expressed as

(3.21)

where is the profile-loss coefficient.

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.60

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Equivalent diffusion ratio

Pro

file

loss

par

amet

er

1.00.70.3

1.00.70.3

1.00.70.3


31

3.4.2 Endwall loss model Again a correlation is used to determine the losses in the endwall. Based on a numerous sets of compressor data where the parameters, tip clearance, aspect ratio and mean line loading where systematically varied, Freeman was able to correlate these parameters, se Figure 3.8. To determine the loading on the blade, the diffusion factor where used [8].

Figure 3.8, endwall loss parameter with variation in tip clearance

As seen in the loss model created by Wright and Miller, the losses starts to increase rapidly as the diffusion factor approaches 0.45. A diffusion factor about 0.45 is a typical value for designing compressors.

The endwall-loss parameter is expressed as

(3.22)

where is the endwall-loss coefficient.

3.4.3 Total lossSummarizing the endwall-losses and profile-losses will give the total loss in the blade row.

From this the loss in stagnation pressure with respect to inlet dynamic pressure, p01 - p1,can be calculated [2].

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.650.02

0.04

0.06

0.08

0.1

0.12

0.14

Diffusion factor

End

wal

l los

s pa

ram

eter

0.10

0.07

0.04

0.020.00

0.10

0.07

0.04

0.020.00

0.10

0.07

0.04

0.020.00

0.10

0.07

0.04

0.020.00

0.10

0.07

0.04

0.020.00


32

Pressure losses in the blade row can be calculated, but it is preferred to express the losses in an entropy change instead. By applying Gibbs 2nd law, the pressure change can be expressed as a change in entropy instead.

By definition there is no enthalpy change, will be zero.

With help from the ideal gas law the following modification can be made.

After integration on the right hand side, the following expression can be found where 1 and 2 denoted the inlet and outlet conditions.

The final result will be as follow.

(3.23)

3.5 Pitch Chord ratio The pitch chord ratio is also known as the inverse of the solidity, , where the latter is used in the U.S. When determining the aerodynamic loading in a blade row the pitch chord ratio is an important parameter. A blade row with a low pitch chord ratio, high solidity, will probably have fewer blades in a blade row than one with a high stagger chord ratio. The aerodynamic loading will then be shared by less number of blades and thus the blade loading will increase. A higher aerodynamic loading will probably be nearer the surge/stall point than one with a lower aerodynamic load.

As for the Diffusion Factor, there are several methods on how to determine the pitch chord ratio.


33

3.5.1 Diffusion Factor Method The first method on how to calculate the pitch chord ratio is the same equation as for the diffusion factor, but instead of expressing it for the diffusion factor it will express the pitch chord ratio as a function of diffusion ratio instead.

(3.24)

3.5.2 Hearsey Method Hearsey uses an explicit loss correlation:

to produce the following relationship for minimum

(3.25)

where Dopt is the Diffusion Factor calculated using = opt. This correlation is based on profile losses only and underestimates the required solidity when shocks are expected.

3.5.3 McKenzie Method Another method is for determining the pitch chord ratio is taken from McKenzie, see reference 5. Here the pitch chord ratio is a function of the static pressure rise, Cp.

(3.26)

3.6 Stall/Surge When calculating on how near the each stage is to surge/stall a relationship is used created by Koch, see reference 9. By calculating the static pressure rise coefficient, Cp,based on pitchline dynamic head, and comparing it to the maximum static pressure rise, will give a good indication of how close the stage is towards stall. The maximum static pressure rise, Cp,max, is based on diffuser correlation modified by the influence of Reynolds number, tip clearance and axial spacing between blade rows. The correction factors for the static pressure rise coefficient are shown in Figures 3.10-3.13.

The static pressure rise coefficient and the maximum pressure rise coefficient are as followed.


34

(3.27)

Since there is a change in radius throughout the rotor, the factor (U22-U1

2)/2 will decrease static pressure rise. This decrease in static pressure rise will not put any more stress on the boundary layers because there will not be any further diffusion caused by the change in radius.

(3.28)

The effective dynamic pressure factor ef is described by Koch in the paragraph below.

“A parameter giving a quantitative measure of this flow coefficient/stagger angle effect, termed the effective dynamic pressure factor ef , was defined as the effective dynamic head divided by the pitchline free stream dynamic head. As indicated by the equation 3.29, the effective dynamic head was represented by a weighted average of the free stream dynamic head, the minimum possible dynamic head and the dynamic head at zero axial velocity. By trial and error, the best fit of the data was found to occur if the minimum dynamic head was weighted 2.5 times as heavily as the free stream head, and the head at zero axial velocity was weighted one half as heavily as the free stream head. The minimum dynamic head was set equal to the free stream value for vector triangles where ( + ) was greater than 90 deg., because in such a case the minimum possible dynamic head could only occur at axial velocities higher than the free stream value. Also, for vector triangles in which the upstream blade row turned the flow past the axial direction, the minimum dynamic head was not allowed to become less than the zero through-flow value, because in this case the mathematical minimum dynamic head could only occur at negative axial velocities.” [9]


35

Figure 3.9, diagram giving definition of the effective dynamic pressure factor, ef [9]

(3.29)

For the influences of Reynolds number, tip clearance and axial spacing between blade rows a set o graphs is used. These graphs were created by a numerous sets of tests in which different parameters were varied. The tests were performed with a General Electric low-speed multistage compressor and the blade geometry and clearance was systematically varied. These tests, plus some additional low speed experimental configurations, also provided data for the correction for Reynolds number and showed the effect of extreme values of stagger angle, flow coefficient and reaction [9].

Note that the value for the stage is determined by a weighted average value for the rotor and the stator.

g1

g2

L

U

U

C

W

Cmin

min90°

Rotor


36

The equations that will be presented are for the rotor but are applicable for the stator as well [4].

(3.30)

In the equation above Z denotes the number of blades in one row.

(3.31)

To determine the axial spacing between the rows, a guide rule can be used [10].

(3.32)

Figure 3.10, Correlation of stalling pressure rise data for baseline testing [9]

0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

CpD

Diffusion length/Exit passage width, L/g2


37

Figure 3.11, Effect of tip clearance on stalling pressure rise coefficient [9]

Figure 3.12, Effect of axial spacing on stalling pressure rise coefficient [9]

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

(Cp/C

pD)

Tip clearence/Average Pitchline Gap, /g

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.98

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

(Cp/C

pD)

Z

Normalized Axial Spacing, Z/s


38

Figure 3.13, Effect of Reynolds number on stalling pressure rise coefficient [9]

0.1 0.2 0.4 0.6 0.8 1 2 4 6 8 100.8

0.85

0.9

0.95

1

1.05(C

p/CpD

) Re

Reynolds Number x10-5, Re

39

4 Calculation procedures

4.1 Input parameters When designing a new compressor, a number of parameters must be chosen to specify the geometry and operating conditions for the compressor. There are numerous different combinations of parameters that could specify the compressor. The different input parameters, used in this thesis, are shown in table 4.1.

Main specification Type of compressor Mass flow Number of stages Pressure ratio Rotational speed Stage reaction Detailed specification Tip clearance, /c Aspect ratio, h/c Thickness chord ratio, t/cAxial velocity ratio, AVRBlockage factor, BLKDiffusion factor, DFStage Loading distribution Inlet specification Inlet flow angle, Stage flow coefficient, Hub tip ratio, rhub/rtip

Table 4.1, Input parameters for the calculations

4 Calculation procedures Axial Flow Compressor Mean Line Design

40

4.1.1 Main specification The geometry of a compressor can be categorised into 3 main designs types, a Constant Outer Diameter (COD), a Constant Mean Diameter (CMD) or a Constant Hub Diameter (CID), see Figure 4.1.

Figure 4.1, different compressor geometries

There are several different parameters that can specify a particular compressor. A number of these parameters will be presented and used for the calculation that will follow later on.

The first set of input parameters are based on the running conditions for the machine. These involve mass flow, rotational speed, pressure ratio and the number of stages.

For controlling the distribution of the load between the rotor and the stator the stage reaction can be set. If this is not of importance, the outlet flow angle for the each stage must be set instead, more on this in chapter 4.3 “Calculation limitations”.

Axial Flow Compressor Mean Line Design 4 Calculation procedures

41

4.1.2 Detailed specification There are three main geometry specifications that will be used in this thesis, tip clearance chord ratio, thickness chord ratio and blade height chord ratio also known as “aspect ratio”. These three parameters specify the main geometry for the blades in the compressor.

If the axial velocity is set to be constant throughout the compressor, the blades at the end of the compressor will be very short and thus have higher losses and more susceptible to mechanical stresses. Setting the Axial Velocity Ratio will take this in consideration. As the fluid is working itself towards the end of the compressor, boundary layer growth starts to appear on the compressor housing. This will result in a narrower path for the fluid to flowing through. Introducing a Blockage Factor will account for this phenomenon. The stage load distribution is another parameter that can be set.

4.1.3 Inlet specification To be able to start the calculations for the compressor, certain dimensions and properties must be calculated first. By setting up different parameters that is only valid for the first row these dimensions and properties can be calculated. These inlet specifications consist of three parameters, inlet flow angle, stage flow coefficient and the hub radius tip radius ratio.

4.2 Parameter variations throughout the compressorCertain parameters in the compressor will vary in the compressor, namely:

Tip clearance, /c

Aspect ratio, h/c

Thickness chord ratio, t/c

Axial velocity ratio, AVR

Blockage factor, BLK

Diffusion factor, DF

Stage Loading distribution

A simple linear distribution for the parameters may, for simplicity, be used except for the stage loading. By setting the front and rear value for the different parameters a linear distribution is than created. The parameters can also be set for the rotor and the stator separately.


42

As for the blockage factor one can say that after a certain stage in the compressor the boundary layer growth will have settled. By studying several different calculations that have been made a conclusion can be made that at the 5th stage the boundary layer growth has been stabilized.

The stage load distribution throughout the compressor can be determined by setting the inlet value, the mean value and the outlet value. This will create a type of ramp function, see Figure 4.2 for an example how it can look. Using this type of ramp function gives more control over how the stage load is distributed. More advanced functions can be used or a customized distribution can be made as well, but for most cases this ramp function will be adequate.

Figure 4.2, stage load distribution over a compressor

4.3 Calculation limitations 4.3.1 Mean stream line analyses The calculations in this thesis are based on mean line stream analysis i.e. one dimension. The mean radius is used in the calculations to determine the blade speed. Normally when calculating with the mean line stream method, the mean radius will not change. But by changing the mean radius throughout one stage will give a more accurate design, see Figure 4.3. The mean radius will be kept constant in the space between rotor and stator as well for the space between each row. A change in radius in the space between each blade row won’t make a big difference in the end result. It is more crucial to have a change in radius in the blade them self since this will have a more noticeable effect.

stage

Distribution, %

100

80

90


43

4.3.2 Convergence criteria’s There are two main input parameters that the calculation must satisfy. These are the total pressure ratio, , and the stage reaction, R. To be able to have the desirable pressure ratio and stage reaction after the calculation is done, it is necessary to adjust some parameters. There are several parameters that can be chosen but two parameters have been selected, one for the pressure ratio and one for the stage reaction.

The pressure ratio is adjusted with help from the stage load coefficient. Another possibility is to adjust the deHaller number. It is easier to control the load on the compressor when designing it; this is why the stage load coefficient is selected as the adjustment parameter for the pressure ratio.

The stage reaction is strongly dependent on the flow angles in and out of each stage. This since the stage reaction is the ratio between the work done in the rotor and the work done in the entire stage. The work done is dependent on the enthalpy change and thus is dependent on the absolute velocity for the inlet and outlet at each stage. The absolute angle, , decides the absolute velocity. Changing the outlet angle, 3, will change the stage reaction on the next stage. This because the inlet angle of a stage is the same as for the outlet angle from the previous stage. The question “Why can not the inlet angle be adjusted?” seems relevant at this point. The inlet angle cannot be adjusted since this angle is the same as for the outlet angle from the previous stage. If this would be changed then it would not have the same value as for the outlet angle from the previous stage.

The calculation is divided into separate modules. This makes it easier to understand how it is all related. There are three main modules and these makes up for the calculation for one stage, see Figure 4.4. Each of these modules has sub modules in their self. In chapter 5 “Calculation process”, an entire stage is described on how this calculation is done.

rmean

Rotor Stator

Figure 4.3, variation in radius through a single stage


44

4.4 Structure of the calculation 4.4.1 Module 0 Before the calculation can begin the inlet geometry must be determined. In this module the axial velocity, tip radius, mean radius and hub radius are being calculated. This will make up for the overall design for the compressor, if it has a constant mean radius or some of the other designs.

Some of the input criterions will have variations throughout the compressor. In module 0 these variations are accomplished.

4.4.2 Module 1 The calculations at rotor-inlet are performed in module 1. In this module there is no need for approximations for certain values and hence no need for iteration procedures.

R = f( 3(i-1) )

i=1

i +1

R

Stage i

= f( )

Module 1

Module 2

Module 3

Module 0

Figure 4.4, structure over the iteration procedure for the whole compressor


45

4.4.3 Module 2 In this module the calculations at rotor-outlet/stator-inlet are performed. There are two parameters that must be approximated. The first is the entropy rise in the rotor. This must be known to be able to calculate the entropy at rotor-outlet. With this identified, the temperature and pressure can then be determined. The second approximation is the mean radius at rotor-outlet. There will be a change in radius throughout the rotor and to be able to determine the velocities, a radius must be known. In Figure 4.5 a more detailed view over this procedure is shown.

guess s2-1

guess rrms,2

rrms,2

s2 1

Module 2.1

Module 2.2

Module 1

Module 3

Module 2

Figure 4.5, structure over the iteration procedure for a rotor (module 2)


46

4.4.4 Module 3 In the last of the three main modules, the stator-outlet is computed. The same method as in module 2 is used, namely two parameters must be approximated. The two parameters are somewhat the same as for the rotor, the entropy rise throughout the stator and the mean radius at stator-outlet, see Figure 4.6.

guess s3-2

guess rrms,3

rrms,3

s3 2

Module 3.1

Module 3.2

Module 2

Module 3

Figure 4.6, structure over the iteration procedure for a stator (module 3)


47

4.5 Newton-Rhapson Method Newton’s method (also called Newton-Rhapson method) for solving nonlinear equations is one of the most well-known and powerful procedures in all of numerical analysis methods. It always converges if the initial approximation is sufficiently close to the root, and it converges quadratically. Its only disadvantage is that the derivative f´(x)of the nonlinear function f(x) must be evaluated.

Newton’s method is illustrated graphically in Figure 4.7. Lets locally approximate f(x)by the linear function g(x), which is tangent to f(x), and find the solution g(x) = 0. That solution is then taken as the next approximation to the solution of f(x) = 0. The procedure is applied iteratively to convergence. Thus,

Solving the equation above for xn+1 with f (xn+1) = 0 yields.

This equation is applied repetitively until either one or both of the following convergence criteria are satisfied:

f(x)

g(x)

xn+1 xn

f(x)

x

Figure 4.7, Newton’s method [7]

48

5 Calculation process

5.1 Module 0, Inlet geometry To be able to solve the inlet geometry the inlet flow velocity, Cm, must be known. Since this velocity is unknown an iterative process must be used. By approximating the value of Cm, the density can be found. With help of mass continuity a new inlet flow velocity can be calculated. This value is then used to start over the calculation until converged, see Figure 5.1.

The first step is to get hold off the thermodynamic properties in the inlet of the compressor. The ambient pressure and temperature is known and from these the enthalpy and entropy can be found.

Now that the inlet properties are known, the iteration procedure can begin.

Axial Flow Compressor Mean Line Design 5 Calculation process

49

Start value Cm

Figure 5.1, structure over the iteration procedure for the inlet geometry (module 0)

5 Calculation process Axial Flow Compressor Mean Line Design

50

5.2 Module 1, Rotor-inlet When starting the calculation, the geometry from the inlet calculations is used.

Since the calculation for the entire stage will be repeated, the rotor-inlet conditions, i.e. station 1, will have the same velocity and radius as the stator-outlet, i.e. station 3, for the previous stage.

Now that the preferences for the rotor-inlet at the first stage are known the calculations can begin.

The first thing is to find out the entropy and the enthalpy for this station. From the ambient temperature and pressure the enthalpy and entropy can be found. If the calculations is not preformed on the first stage than the stagnation properties of the working fluid is taken from the previous stage.

Flow angles and velocities

To be able to find out the static properties of the working fluid the absolute velocity, C1,is necessary. With the help of the velocity diagrams, see Figure 5.2, the relative and the absolute velocity can be found, as well as the relative angle, 1.


51

Static properties

Now that the velocity is known, the static enthalpy can be calculated. And with help from the entropy other fluid dynamic properties like pressure, temperature, density etc. can be found.

To be able to move from the rotor-inlet towards the outlet of the rotor a relationship between these must be used. Since the rothalpy is constant throughout the rotor, makes the rothalpy useful when calculating the outlet of the rotor.

Further in to the calculations the relative Mach number and the axial Mach number will be used and since that the speed of sound, a1, is known these two Mach numbers can be calculated.

W1 C1

Cm1

1 1

C 1

Figure 5.2, velocity triangle for the rotor inlet


52

Relative properties

The dominating velocity that is acting on a rotor blade is the relative velocity, W1;therefore relative stagnation properties must be calculated. Instead of calculations based on the absolute velocity, C1, the relative velocity is used. The relative pressure and temperature are found out by the relative enthalpy and entropy.

Geometry

The blockage factor is here denoted as, BLK. The geometry is the same for the rotor-inlet as for the stator-outlet in the previous stage. A result of this is that the blockage factor should be the same for the rotor-inlet and the stator-outlet at the previous stage.

From the definition of the cross section area and the mean radius, the hub radius, the mean radius or the tip radius can be calculated depending if the compressor is of the type CID, CMD or COD.

Constant Mean Diameter, CMD


53

Constant Outer Diameter, COD

Constant Inner Diameter, CID

5.3 Module 2, Rotor-outlet/stator-inlet There are two separate modules in module 2. The first, 2.1, is for the calculation of the entropy rise in the rotor. The second, 2.2, calculates the mean radius at rotor-outlet. Both of these are iteration processes where an approximated value is first guessed and then a new value is calculated to adjust the approximated first value.

5.3.1 Module 2.1 start


The mean radius at rotor-outlet in unknown so a value for this must be approximates to be able to find out the blade speed. A new value for this will be calculated further on in the calculation.

Since a change in radius throughout the rotor is occurring a modification to the definition of the stage load coefficient must be made. A modification is made based on the blade velocity at the rotor-outlet.

The coefficient omega is the rotational speed in radians per second. By substituting this with the blade speed, U= r, following relation can be found.


54

The stage load coefficient is known and from this the tangential part of the absolute velocity, C 2, can be calculated.

Now that the tangential part of the absolute velocity is know the tangential part of the relative velocity, W 2, can be calculated. From this the absolute and relative velocities can be calculated and there angle.

Static properties

From the rothalpy calculation done previously on the rotor blade inlet, the static enthalpy at rotor blade outlet can now be calculated.

Due to the losses throughout the rotor passage, an increase in entropy will occur. This increase in entropy is used to calculate the entropy at the rotor-outlet, s2. The value of

W2 C2

Ca2

2 2

C 2

Figure 5.3, velocity triangle for the stator inlet


55

this entropy rise is just an approximation. A new value for this will be calculated further in to the calculations.

Stagnation properties

Geometry

Like for the inlet of the rotor the different radiuses is calculated with help from the area and the definition of the mean radius. This value is a new value for the one that was approximated in the beginning of module 2.1.

5.3.2 Module 2.1 end After the module 2.1 is completed a mean radius for the rotor-outlet has been calculated.

5.3.3 Module 2.2 start The calculation proceeds with the known rotor-outlet radius.


56

Rotor properties

An average value for the tip radius, mean radius and hub radius is used for calculating the height of the rotor blade. Since one of the input design parameters is the aspect ratio, i.e. H/c, the chord of the blade can also be calculated.

Reynolds number and AVDR are also calculated for the calculations that will follow. Reynolds number is based on the inlet velocity and viscosity at the inlet of the rotor. AVDR for the rotor is calculated because it is a definition that will be used when the equivalent diffusion ratio, Deq, will be determined.

Pitch chord ratio

The calculations for the pitch chord ratio, also known as pitch chord ratio, can be done based on either on the diffusion factor, the McKenzie method or on the Hearsey method. These different methods needs some input parameters and these are the same whether the method based on the diffusion factor is used or some of the other methods. The input parameters consist of the relative inlet and outlet flow angles, the different axial velocities and radiuses and also the diffusion factor. To get a deeper insight in how this calculation is performed see chapter 3.4 “Pitch chord ratio”.


57


When calculating the diffusion ratio a similar approach as the pitch chord ratio is used. The input parameters include apart from them in the pitch chord ratio calculation also the pitch chord ratio, thickness chord ratio, axial velocity density ratio and the Mach number based on the axial velocity at rotor-inlet, see chapter 3.2 “Diffusion Factor and Diffusion Ratio”.

Rotor losses

The last step in the rotor is to calculate entropy rise due to the losses throughout the rotor. In the beginning of the rotor calculation a good approximation was made for the entropy rise. This must be corrected by calculating a true entropy rise. To see more in detail on how this calculation is made see chapter 3 “Losses”.

5.3.4 Module 2 end At this point the geometry of the rotor is fully defined and the calculation can now proceed to the stator.


58

5.4 Module 3, Stator-outlet As for the rotor, the stator calculation is divided into two sub modules, 3.1 and 3.2.

5.4.1 Module 3.1 start


The same method is applied for the stator-outlet as for the stator-inlet when calculating the different velocities. Here the absolute velocity is the only one that is interesting since there is no relative velocity. The deHaller number is calculated based on the inlet and outlet velocity of the rotor.

Static properties

There is no work done to the working fluid in the stator. This results in a constant stagnation enthalpy throughout the stator passage. From this the static enthalpy can be calculated based on the absolute velocity, C3.

As for the rotor, an approximation for the entropy rise must be made for the stator. This will give the entropy at the stator-outlet. Later on in the calculation an accurate entropy rise will be calculated.

From the entropy and the enthalpy, the fluid dynamic properties of the working fluid can be found for the stator-outlet.


59


Geometry

Like for the rotor-inlet and the stator-inlet the different radiuses is calculated with help from the area and the definition of the mean radius. This value of the radius at stator-outlet is then used to update the approximated value at the beginning of the calculation of the stator-outlet.

5.4.2 Module 3.1 end The calculation can now proceed now that the radius at stator-outlet is known.

5.4.3 Module 3.2 start The calculation can now proceed, now that the radius at stator-outlet in known.

Stator properties

As for the rotor an average value for the tip radius, mean radius and hub radius is used for calculating the height of the rotor blade.


60

The Reynolds number is based on the inlet velocity, C2, and viscosity, 2, for the stator. AVDR for the stator is yet again based on the density and axial velocity for the stator-inlet and stator-outlet respectively.

Pitch chord ratio


Stator losses


61

5.4.4 Module 3 end The entire stage is now fully defined. This process is then repeated for the remaining stages.

The next step in the calculation is to calculate the outlet guide vane.

5.5 Outlet Guide Vane, OGV An outlet guide vane, OGV, is an extra stator after the compressor. Its main purpose is to turn the flow so the whirl component decreases or gets eliminated. When entering the combustion chamber one wants a smooth and controlled flow with no disturbances. The calculation for the outlet guide vane is similar to the stator in the compressor.


If zero whirl is desirable then the axial velocity at the last stator-outlet is equal to the absolute velocity at the OGV outlet.

Static properties

As before the stagnation enthalpy at the OGV outlet is equal to the stagnation enthalpy at the outlet of the last stator. And again an entropy rise must me approximated since this is unknown and is necessary for further calculations.

3C3

COGV

Figure 5.4, velocity triangle for the outlet guide vane


62


Geometry

An approximation is used for the OGV radiuses. This approximation is that the radiuses at the last stator-outlet are the same as for the OGV radiuses.


63

Pitch chord ratio


Outlet guide vane losses

The entire compressor is now fully computed and the pressure ratio and the stage reaction have converged. The next step is to determine the blade angles for the rotor row and stator row.


64

5.6 Blade angles calculation To be able to calculate the blade angles an iteration procedure is needed, like the ones used in previous calculations. In this case the camber angle is estimated. With this the incidence and deviation angles can then be found. From the incidence and deviation angle a new camber angle is calculated. This is then repeated until converged, see Figure 5.5.

One can argue whether this iteration is necessary since it is possible to explicit solve the camber angle. This approach was chosen for having flexibility for other types of correlations, like “Carter’s rule”, see chapter 3.12 “Deviation angle”. This method requires the stagger angle to be known, hence the iteration is necessary.

guess

Figure 5.5, structure over the iteration procedure for the blade angles

65

6 Results

In this chapter a compressor is calculated and the results analyzed. In the following tables, the input parameters are specified.

The compressor that will be calculated has a constant mean line design with a mass flow of 122 kg/s. The desirable pressure ratio is 20 and it has 15 stages. A stage reaction of 0.55 is also set as one of the input variables.

Main specification Type of compressor CMD Mass flow 122 Number of stages 15 Pressure ratio 20 Rotational speed 6600 Stage reaction 0.55

Table 6.1, input parameter example for the main specifications

The detailed specifications are listed below in table 6.2. Here the diffusion factor is set constant throughout the compressor, both for the rotors and the stators. The thickness chord ratio and tip clearance are also set constant.

Detailed specification First stage Last stage Tip clearance, /c 0.02 0.02 0 0 Aspect ratio, h/c 2.5 1 3.5 1 Thickness chord ratio, t/c 0.06 0.06 0.06 0.06 Axial velocity ratio, AVR 0.99 0.98 0.99 0.98 Diffusion factor, DF 0.45 0.45 0.45 0.45 First stage 5th stage Blockage factor, BLK 0.98 0.88

Table 6.2, input parameter example for the detailed specifications

As for the loading, the first blade rows have the highest stress. Further in to the compressor the stress on the blades will decrease.

6 Results Axial Flow Compressor Mean Line Design

66

First stage Middle stage Last stage Stage Loading distribution 1.0 0.9 0.8

Table 6.3, input parameter example for the stage loading distribution

The inlet air angle is set to 15 degrees and it has a hub tip ratio of 0.50. The stage flow coefficient for the inlet is set to 0.65.

Inlet specification Inlet flow angle, 15 Stage flow coefficient, 0.65 Hub tip ratio, rhub/rtip 0.50

Table 6.4, input parameter example for the inlet specifications

After the calculations have finished a graph over the blade geometry can be constructed, see Figure 6.1. In this graph the total length of the compressor can be estimated and also the variation of the radii. Here one can clearly see that it is a constant mean radius design as it was designed to be. The red colour indicates that it is a rotor and for the stators a blue colour.

Figure 6.1, example of the compressor geometry for a given set of input parameters

There are two efficiencies that can be calculated, polytropic and isentropic efficiency. These efficiencies and other interesting results are shown in table 6.5.

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.2

0.4

0.6

Axial Flow Compressor Mean Line Design 6 Results

67

Polytropic efficiency 91.80 % Isentropic efficiency 89.55 % Temperature rise 428.7 K Inlet Mach @ tip 1.08 Mass flow @ 3000 590.5 kg/s Compressor power 54.13 MW

Table 6.5, Results from the calculations

A graph can be drawn of the surge limit of each stage, see Figure 6.2. Studying the graph one can see that in stage number 2 there is a possibility of surge. Further in to the compressor the margin to surge increases. The limit to surge is strongly dependent to the diffusion factor. By decreasing the diffusion factor will result in a lower static pressure rise and hence increase the margin to surge. The diffusion factor is not something one can change by itself; it is dependent on several other factors. Pitch chord ratio, s/c, is the factor that has the most profound effect on the diffusion factor. If the pitch chord ratio is decreased, then the diffusion factor will also decrease, resulting in a lower static pressure rise, see Figure 6.3.

Figure 6.2, Koch surge limit for this compressor example

0 2 4 6 8 10 12 14 160.35

0.4

0.45

0.5

0.55

Stage

Sta

tic p

ress

ure

rise

coef

ficie

nt

Ch,max

Ch

6 Results Axial Flow Compressor Mean Line Design

68

Figure 6.3, Koch surge limit for this compressor example, with a change in pitch chord ratio

0 2 4 6 8 10 12 14 160.35

0.4

0.45

0.5

0.55

Stage

Sta

tic p

ress

ure

rise

coef

ficie

nt

Ch,max

Ch

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7 LUAX-C

7.1 Structure of the program In order to use these calculations for designing a preliminary design of a compressor a GUI, Graphic User Interface, was created. This interface was made in MATLAB and is called LUAX-C, Lund University Axial Flow Compressor.

The main calculation which calculates the whole compressor is divided into separate sub programs, each program takes care of one part of the calculation, for example the losses generated in the rotor/stator.

As discussed in chapter 4.1 “Input parameters”, a set of input parameters that specify the running conditions and geometry is needed for the calculations. These input parameters are placed in a text file. This because it is easier to make small and more specific changes in the input parameters this way and the text file is compatible with other computer programs as well. As for the input file, the result, output file, is also a text file. In this all the results from the calculations that could be of use for further study are displayed.

The communication between the GUI and the calculation and other post processing programs are done with a type of databases. There are three different databases that are generated by the main calculation.

STG

CompInfo

OGV

In the first one, “STG”, the information for each stage is saved. Some of this information can be the different velocities, angles, geometry etc. The second one, “CompInfo”, consists of all the information about the compressor, for example efficiency, power, mass flow, pressure ratio etc. The last one, “OGV”, consists of the information about the outlet guide vane.

After the calculation is finished and the database is created the data is transferred to the post processing. The post processing will create a text file which consists of all the results from the database. It will also send information to the GUI so different graphs and other demonstrations can be made to visualize the result.

7 LUAX-C Axial Flow Compressor Mean Line Design

70

Figure 7.1, Structure of LUAX-C

7.2 User Guide to LUAX-C In this chapter a quick walkthrough of the program is shown.

This program uses MATLAB as a platform so it is necessary to have MATLAB installed on the computer where the program will run from.

The first step is to change the “current directory” to the directory where LUAX-C is saved. This will help MATLAB to find the files and to have a place to save the output files. The main window consists of all the input parameters necessary to calculate an entire compressor, see Figure 7.1.

GUI

Inputfile Main

Sub 2

Sub 1

STGCompInfo

OGV

Resultfile

Post Process

Axial Flow Compressor Mean Line Design 7 LUAX-C

71

Figure 7.2, Main window in LUAX-C

Based on the filename chosen by the user, the program will create input and output files with the same file name.

Next step is to define what type of compressor one wants to design and the specifications of this compressor. Here the user can chose the number of stages, mass flow, pressure ratio and rotational speed. If the stage reaction is of importance, this can also be set. If not, the whirl angle of the stage needs to be set instead. These settings are the main specifications and the detailed specifications are as follows.

Tip clearance, /c

Aspect ratio, h/c

Thickness chord ratio, t/c

Axial velocity ratio, AVR

Blockage factor, BLK

Diffusion factor, DF

Stage Loading distribution


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All of these specifications are varied linearly throughout the compressor based on the inlet and outlet values.

After all the input parameters are specified, an input file must be created. By pressing “Create Data File”, the variations will be created and an input data file will be created. If one wish to specify these parameters for each blade row separately, this is possible by pressing “Open/Edit”, see Figure 7.2. This will open the input text file where it is possible to make the changes that one wants to do. Table 7.1 shows which row in the text file that represents which input parameter and the choices that can be made for each parameter. After this, the text file must be saved since this is the input file for the calculations.

Figure 7.3, input text file for LUAX-C


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Input parameter choice File name - Compressor Type CMD, COD, CID Ambient pressure bar Ambient temperature Celsius Number of stages - Mass flow kg/s Pressure ratio - Rotational speed rpm Stage reaction select stage reaction = 1, whirl angle = 0 Stage reaction whirl angle in degree s/c calculation method DF, McKenzie, Hearsay Alpha in degree PHI in - h/t in - Epsilon/c rotor - Epsilon/c stator - Aspect ratio rotor - Aspect ratio rotor - t/c rotor - t/c stator - Diffusion factor rotor - Diffusion factor stator - Axial velocity ratio rotor from 1.0 to 0.97 Axial velocity ratio rotor from 1.0 to 0.97 Blockage factor - PSI variation from 1.0 to 0.0

Figure 7.1, List of the different parameters in the input text file

Now it is time to run the program. By pressing “RUN” will initiate the calculations and it is important that the input file has been created. For each run the user must create the input file by pressing “Create Data File”.

When the program has finished calculating, which can take a while depending of the computer power and type of compressor, two graphs are shown, see Figure 7.4. The one above is a graph over how the geometry varies over the length of the compressor. The red blades represents the rotors and the blue ones the stators. The second graph shows the velocity diagrams over a particular stage. Here the user can chose which stage one wants to look at.


74

Figure 7.4, after the calculations has been finished

By pressing “Open Result File” will open the result file created by the program, see Figure 7.5. This file consists of all the data that the user may need when transferring it to another program like a CFD simulation program. In this result file, the performance of the compressor are shown and several other important parameters.

Figure 7.5, Result text file


75

If the user wishes to study the surge limits, this is done by pressing “Surge Graph”, see Figure 7.6. This opens a graph in which the user can see if the compressor is on the limit of surge on a particular stage. This surge graph is based on Koch which is discussed in this thesis.

Figure 7.6, Koch surge limit for this compressor example

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References

[1] Saravanamutto, HIH, Rogers, GFC och Cohen, H. Gas Turbine Theory Fifth Edition, Pearson Prentice Hall, 2001.

[2] Cumpsty, N.A. Compressor Aerodynamics, Krieger Publishing Company, 2004.

[3] Lakshminarayana, Budugur. Fluid Dynamics and Heat Transfer of Turbomachinery, Wiley-Interscience, John Wiley & Sons, 1996.

[4] Howard, J.H.G. Axial Fan and Compressor Modeling. 2001.

[5] McKenzie, A.B. Axial Flow Fans and Compressors, Ashgate Publishing Limited, 1997.

[6] Denton, J D. Cambridge Turbomachinery Course, Whittle Laboratory, Deparment of Engineering, University of Cambridge, 2004.

[7] Hoffman, Joe D. Numerical Methods for Engineers and Scientists, Marcel Dekker Inc.

[8] Wright, P I och Miller, D C. An Improved Compressor Performance Prediction Model, ACGI,DIC,Rolls-Royce, Derby, 1991.

[9] Koch, C.C. Stalling Preuusre Rise Capability of Axial Flow Compressor Stages, Aircraft Engine Group, General Electric Co., 1981.

[10] Walsh, P.P och Fletcher, P. Gas Turbine Performance, Blackwell Science, 1998.

[11] Genrup, Magnus. Degradation and Monitoring Tools for Gas and Steam Turbines, Doctoral Thesis, Department of Heat and Power Engineering, Lund Institute of Technology, Lund University, Sweden, 2005.

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Appendix

A, polynomial coefficients for the graphs A polynomial fitting method has been used to interpret the graphs that are used in this thesis for the calculations. The different coefficients for each polynomial for each figure are listed in the following tables.

a4 a3 a2 a1 a0-1.61839e-02 1.14774e-01 -2.66675e-01 2.62982e-01 -8.26097e-02 -2.08264e-02 1.48500e-01 -3.56939e-01 3.68490e-01 -1.30107e-01 -2.13465e-02 1.52219e-01 -3.66336e-01 3.78126e-01 -1.36535e-01

Table A.1, Polynomial coefficients for Figure 3.7

a4 a3 a2 a1 a02.32625e02 -3.14825e02 1.60855e02 -3.66895e01 3.23881e00 1.85224e02 -2.58533e02 1.36001e02 -3.18679e01 2.86933e00 2.48570e01 -2.03045e01 3.12191e00 1.04984e00 -2.00381e-01 4.61697e01 -6.61454e01 3.57996e01 -8.62635e00 8.18792e-01 1.36794e01 -1.92343e01 1.01622e01 -2.36201e00 2.38135e-01


a5 a4 a3 a2 a1 a01.7779e-03 -1.9627e-02 9.1688e-02 -2.5166e-01 4.9160e-01 7.6431e-02


a5 a4 a3 a2 a1 a0-5.35103e04 2.20418e04 -3.38124e03 2.42416e02 -1.00986e01 1.21683e00


a5 a4 a3 a2 a1 a05.1421e-01 -7.4519e-01 -2.2107e-01 9.6073e-01 -6.1567e-01 1.1191e00


Appendix Axial Flow Compressor Mean Line Design

78

For the interpretation of figure 3.13 a normal polynomial fitting was not feasible, instead a function of the type

was used.

a b c -101.8 -0.6767 1.041

Table A.5, coefficients for the function in Figure 3.11

B, MATLAB script for the calculations B.1 Main Calculation

% Main Calculation for the compressor

%#####################################################################%## ##%## Main Calculation ##%## ##%## (c) Niclas Falck and Magnus Genrup 2008 ##%## ##%## Lund University/Dept of Energy Sciences ##%## ##%#####################################################################

function [STG,CompInfo,OGV] = compressorcalculation(filename);

%################# Converts textfile to a matrix ##########################

CompInputdata = createInputFile(filename);

%###################### Numerical settings ##############################

RLX_REACT = 0.8; RLX_PR = 0.95;

%################### Import data from the input matrix ####################

N_stg = str2num(CompInputdata{5,1}); % number of stages in the compressor

PR_comp = str2num(CompInputdata{7,1}); % sets the desirable compressor ratio

P0_in = str2num(CompInputdata{3,1}); % absolute inlet pressureT0_in = str2num(CompInputdata{4,1})-273.15; % absolute inlet temperatureRPM = str2num(CompInputdata{8,1}); % revolutions per minute

for k=1:N_stg % massflow variation flow(k) = str2num(CompInputdata{6,k}); end

Alpha_in = str2num(CompInputdata{12,1}); PHI_in = str2num(CompInputdata{13,1}); HONT_in = str2num(CompInputdata{14,1}); % hub/tip

comp_type = CompInputdata{2,1}; SONC_type = CompInputdata{11,1}; set_REACT = str2num(CompInputdata{9,1});

if set_REACT == 1 for i=1:N_stg

Axial Flow Compressor Mean Line Design Appendix

79

REACT_stg(i) = str2num(CompInputdata{10,i}); % sets a fixed value of the degree of reation

endend

for i=1:N_stg

EPSONC_rtr(i) = str2num(CompInputdata{15,i}); %(blande end clearence)/chord EPSONC_str(i) = str2num(CompInputdata{16,i}); %(blande end clearence)/chord

AR_rtr(i) = str2num(CompInputdata{17,i}); %Aspect ratio (H/C) AR_str(i) = str2num(CompInputdata{18,i});

TONC_rtr(i) = str2num(CompInputdata{19,i}); % (T/C) TONC_str(i) = str2num(CompInputdata{20,i});

if strcmp(SONC_type,'Custom') == 0 % SONC is not set but is calculated instead DF_rtr(i) = str2num(CompInputdata{21,i}); DF_str(i) = str2num(CompInputdata{22,i});

else SONC_rtr(i) = str2num(CompInputdata{21,i}); SONC_str(i) = str2num(CompInputdata{22,i});

end

AVR_rtr(i) = str2num(CompInputdata{23,i}); % Axial Velocity Ratio AVR_str(i) = str2num(CompInputdata{24,i});

BLK_stg(i) = str2num(CompInputdata{25,i}); % Blockage Factor

PSI_variation(i) = str2num(CompInputdata{26,i}); %loading distributionend

%########################## Compressor inlet ##############################

[P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('PT',P0_in,T0_in,0,1);

Cp_in = Cp; rho_in = rho; Visc_in = Visc; kappa_in = kappa; a_in = a;

[r_rms_in, r_m_in, r_hub_in, r_tip_in] = Inletgeom(P0_in,T0_in,flow(1),RPM,HONT_in,PHI_in,Alpha_in,BLK_stg(1));

U_in = r_rms_in*pi*RPM/30; %blade speed based om RMS radiusCm_in = PHI_in*U_in; %meridional velocityC_in = Cm_in/cosd(Alpha_in); M_in = C_in/a_in; % inlet relative Mach #

U_tip_in = r_tip_in*pi*RPM/30;

M_tip_in = ((Cm_in^2+(U_tip_in-Cm_in*tand(Alpha_in))^2)^0.5)/a_in;

area_in = flow(1)/(Cm_in*rho_in);

%##########################################################################%########################## Pressure ratio iteration ######################%##########################################################################

if set_REACT == 1 for k=1:N_stg

Alpha3(k) = Alpha_in; % Init values for reaction iterationend

elsefor k=1:N_stg %

Alpha3(k) = str2num(CompInputdata{10,i}); % sets the whirl angles if the REACT is not set

endend

%########################## Start values for PSI ##########################

factor = 1.01;


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PSI = 0.4*PSI_variation; % Creates a variation of PSIPSI(2,:) = PSI*factor; % inorder to calculated the derative a second is needed

%########################## Start of iteration ##########################

n_PR = 0; PR_rel_error_level = 1; conv_PR = 0;

while conv_PR == 0 % Solves for correct pressure ratio

if abs(PR_rel_error_level) < 10^(-4) conv_PR = 1;

end

for j=1:2 %Second run for obtaining derivative

%##################################################################%###################### Reaction iteration ########################%##################################################################

REACT_rel_RMS_error = 1; n_REACT = 0; conv_REACT = 0;

while conv_REACT == 0

%############### Compressor meridional flowpath ###############for i=1:N_stg

if comp_type == 'CMD' r_rms(i) = r_rms_in(1);

elseif comp_type == 'CID' %Sets constant HUB radius throughout the compressor r_hub(i) = r_hub_in(1);

elseif comp_type == 'COD' %Sets constant TIP radius throughout the compressor r_tip(i) = r_tip_in(1);

end

%##########################################################%################## Station 1 Rotor inlet #################

if i==1 r_rms_1(i) = r_rms_in; Cm1(i) = Cm_in; Alpha1(i) = Alpha_in;

else r_rms_1(i) = r_rms_3(i-1); Cm1(i) = Cm3(i-1); Alpha1(i) = Alpha3(i-1);

end U1(i) = r_rms_1(i)*pi*RPM/30;

%################ Station 1 total properties ##############

if i==1 % The first stage P01(i) = P0_in; T01(i) = T0_in; [P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('PT',P01(i),T01(i),0,1); H01(i) = H; S01(i) = S; S1(i) = S;

else P01(i) = P03(i-1); T01(i) = T03(i-1); H01(i) = H03(i-1); S01(i) = S3(i-1); S1(i) = S3(i-1);

end

C_theta1(i) = Cm1(i)*tand(Alpha1(i)); W_theta1(i) = U1(i)-C_theta1(i); Beta1(i) = atand(W_theta1(i)/Cm1(i)); C1(i) = Cm1(i)/cosd(Alpha1(i)); W1(i) = Cm1(i)/cosd(Beta1(i));


81

%################# Station 1 static properties ############

H1(i) = H01(i)-(C1(i)^2)/2; % Static enthalpy at rotor inlet

[P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('HS',H1(i),S1(i),0,1); P1(i) = P; T1(i) = T; Cp1(i) = Cp; rho1(i) = rho; Visc1(i) = Visc; kappa1(i) = kappa; a1(i) = a;

MW1(i) = W1(i)/a1(i); % Station 1 relative Mach #

MCm1(i) = Cm1(i)/a1(i); % Relative inlet meridional Mach #

%############# Station 1 relative properties ##############

H01_rel(i) = H1(i)+ (W1(i)^2)/2; % Relative total enthalpy [P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('HS',H01_rel(i),S1(i),0,1); P01_rel(i) = P; T01_rel(i) = T;

I1(i) = H1(i)+(W1(i)^2)/2-(U1(i)^2)/2; % Station 1 rothalpy

%################### Station 1 geometry ###################

if i==1 area1(i) = flow(i)/(Cm1(i)*rho1(i)*BLK_stg(i));

else area1(i) = flow(i)/(Cm1(i)*rho1(i)*BLK_stg(i-1));

end

if comp_type == 'CMD' r_hub_1(i) = ((r_rms_1(i)^2)-(area1(i)/(2*pi)))^0.5; r_tip_1(i) =((r_rms_1(i)^2)+(area1(i)/(2*pi)))^0.5;

elseif comp_type == 'CID' r_hub_1(i) = r_hub(i); r_rms_1(i) = ((r_hub_1(i)^2)+(area1(i)/(2*pi)))^0.5; r_tip_1(i) =((r_rms_1(i)^2)+(area1(i)/(2*pi)))^0.5;

elseif comp_type == 'COD' r_tip_1(i) = r_tip(i); r_rms_1(i) = ((r_tip_1(i)^2)-(area1(i)/(2*pi)))^0.5; r_hub_1(i) = ((r_rms_1(i)^2)-(area1(i)/(2*pi)))^0.5;

end

height1(i) = r_tip_1(i)-r_hub_1(i); chord1(i) = height1(i)/AR_rtr(i);

%##########################################################%########### Station 2 Rotor Outlet/Stator inlet ##########

r_rms_2(i) = r_rms_1(i); % init value for r_rms_2

if i==1 dS21(i) = 5; % initial dS21

else dS21(i) = dS21(i-1); % initial dS21 value from previous rotor

end

%########## Entropy rise iteration for the rotor ##########

dS21_rel_error = 1; n_dS = 0; % Noff iteration steps

while abs(dS21_rel_error) > 10^(-4) % Outer loop solves for correct entropy rise

n_RMS = 0; % Noff iteration steps RMS_rel_error = 1;

while abs(RMS_rel_error) > 10^(-4) % Inner loop solves for correct exit radius


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Cm2(i) = Cm1(i)*AVR_rtr(i); U2(i) = r_rms_2(i)*pi*RPM/30; C_theta2(i) = PSI(j,i)*U2(i)+(r_rms_1(i)/r_rms_2(i))*C_theta1(i); % N.B. Based on delH/U2^2 W_theta2(i) = U2(i)-C_theta2(i); C2(i) = (Cm2(i)^2+C_theta2(i)^2)^0.5; W2(i) = (Cm2(i)^2+W_theta2(i)^2)^0.5; Alpha2(i) = atand(C_theta2(i)/Cm2(i)); Beta2(i) = atand(W_theta2(i)/Cm2(i));

dH_rtr(i) = W2(i)/W1(i); % Rotor deHaller #

%########## Station 2 static properties ###########

S2(i) = S1(i)+dS21(i);

I2(i) = I1(i); %I.e. constant rothalpy through a rotor

H2(i) = I2(i)-(W2(i)^2)/2+(U2(i)^2)/2;

[P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He] = state('HS',H2(i),S2(i),0,1); P2(i) = P; T2(i) = T; Cp2(i) = Cp; rho2(i) = rho; Visc2(i) = Visc; kappa2(i) = kappa; a2(i) = a;

MC2(i) = C2(i)/a2(i); % Absolute inlet Mach #

MCm2(i) = Cm2(i)/a2(i); % Relative inlet meridional Mach #

%############# Station 2 relative properties ##############

H02_rel(i) = H2(i)+ (W2(i)^2)/2; % Relative total enthalpy [P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('HS',H02_rel(i),S2(i),0,1); P02_rel(i) = P; T02_rel(i) = T;

%########### Station 2 total properties ###########

H02(i) = H2(i)+(C2(i)^2)/2; % Exit total enthalpy [P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He] = state('HS',H02(i),S2(i),0,1); P02(i) = P; T02(i) = T;

%################ Station 2 geometry ##############

area2(i) = flow(i)/(Cm2(i)*rho2(i)*BLK_stg(i)); if comp_type == 'CMD'

r_hub_2(i) = ((r_rms_2(i)^2)-(area2(i)/(2*pi)))^0.5; r_tip_2(i) =((r_rms_2(i)^2)+(area2(i)/(2*pi)))^0.5; r_rms_2_new(i) = r_rms_2(i);

elseif comp_type == 'CID' r_hub_2(i) = r_hub(i); r_rms_2_new(i) = ((r_hub_2(i)^2)+(area2(i)/(2*pi)))^0.5; r_tip_2(i) =((r_rms_2_new(i)^2)+(area2(i)/(2*pi)))^0.5;

elseif comp_type == 'COD' r_tip_2(i) = r_tip(i); r_rms_2_new(i) = ((r_tip_2(i)^2)-(area2(i)/(2*pi)))^0.5; r_hub_2(i) = ((r_rms_2_new(i)^2)-(area2(i)/(2*pi)))^0.5;

end height2(i) = r_tip_2(i)-r_hub_2(i); chord2(i) = height2(i)/AR_rtr(i);

RMS_rel_error = r_rms_2_new(i)/r_rms_2(i) - 1; r_rms_2(i)= r_rms_2_new(i);

n_RMS = n_RMS+1; if n_RMS > 50 %Emergency break

RMS_rel_error = 0; warning('RMS radius Convergence Error');

end


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end % End of RMS loop

%################## Rotor geometry #################### r_rms_rtr(i) = (r_rms_1(i)+r_rms_2(i))/2; r_hub_rtr(i) = (r_hub_1(i)+r_hub_2(i))/2; r_tip_rtr(i) =(r_tip_1(i)+r_tip_2(i))/2; HONT_rtr(i) = r_hub_rtr(i)/r_tip_rtr(i); height_rtr(i) = r_tip_rtr(i)-r_hub_rtr(i); chord_rtr(i) = height_rtr(i)/AR_rtr(i);

Re_rtr(i) = W1(i)*chord_rtr(i)/Visc1(i); % Reynolds number

%## Rotor Pitch-to-chord ratios and diffusion factors # rel_ang_in = Beta1(i); rel_ang_out = Beta2(i);

AVDR_rtr(i) = rho2(i)*Cm2(i)/(rho1(i)*Cm1(i)); % Axial Velocity Density Ratio for the rotor

if strcmp(SONC_type,'Custom')==0 [SONC,SONC_Hearsey,SONC_McKenzie] = SONC1(rel_ang_in,rel_ang_out,Cm1(i),Cm2(i),r_rms_1(i),r_rms_2(i),DF_rtr(i));

if strcmp(SONC_type,'DF') SONC_rtr(i) = SONC;

elseif strcmp(SONC_type,'Hearsey') SONC_rtr(i) = SONC_Hearsey;

elseif strcmp(SONC_type,'McKenzie') SONC_rtr(i) = SONC_McKenzie;

endend

[DF_lbl,Deq_star_lbl,Deq,Deq_star_ks] = Deq_star1(rel_ang_in,rel_ang_out,Cm1(i),Cm2(i),r_rms_1(i),r_rms_2(i),SONC_rtr(i),TONC_rtr(i),AVDR_rtr(i),MCm1(i)); DF_lbl_rtr(i) = DF_lbl; Deq_star_lbl_rtr(i) = Deq_star_lbl; Deq_rtr(i) = Deq; Deq_star_ks_rtr(i) = Deq_star_ks;

[Mcrit_Hearsey,Mcrit_Sch] = MCRIT1(rel_ang_in,rel_ang_out,Cm1(i),SONC_rtr(i),TONC_rtr(i),kappa1(i)); Mcrit_Hearsey_rtr(i) = Mcrit_Hearsey; Mcrit_Sch_rtr(i) = Mcrit_Sch;

%################# Rotor entropy rise #################

[OMEGA_p,OMEGA_ew, K_Re] = WRTMLR(DF_lbl_rtr(i),Deq_rtr(i),dH_rtr(i),rel_ang_out,MW1(i),AR_rtr(i),EPSONC_rtr(i),Re_rtr(i)); K_Re_rtr(i) = K_Re; % Correction factor for Reynolds number OMEGA_p_rtr(i) = OMEGA_p; OMEGA_ew_rtr(i) = OMEGA_ew; OMEGA_rtr(i) = OMEGA_p+OMEGA_ew; OMEGA_rtr(i) = OMEGA_rtr(i)*K_Re;

dP21(i) = OMEGA_rtr(i)*(P01_rel(i)-P1(i)); % Total pressure drop dS21_new(i) = -R*log(1-(dP21(i))/P01(i)); % updated value of S_2 - S_1

dS21_rel_error = dS21_new(i)/dS21(i) - 1; dS21(i) = dS21_new(i);

n_dS = n_dS+1; if n_dS > 20 %Emergency break

dS21_rel_error = 0; warning('entropy rise Convergence Error on rotor');

endend % End of entropy loop

%###################### Station 3 Stator Outlet ###############

r_rms_3(i) = r_rms_2(i);

dS32(i) = dS21(i); % initial guess value dS32_rel_error = 1; n_dS = 0; % Noff iteration steps

while abs(dS32_rel_error) > 10^(-4) % Solves for correct entropy rise


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n_RMS = 0; % Noff iteration steps RMS_rel_error = 1;

while abs(RMS_rel_error) > 10^(-4) Cm3(i) = Cm2(i)*AVR_str(i);

if i == N_stg Alpha3(i) = Alpha3(i-1);

end

C_theta3(i) = Cm3(i)*tand(Alpha3(i));

C3(i) = Cm3(i)/cosd(Alpha3(i));

dH_str(i) = C3(i)/C2(i); % Stator deHaller #

%########### Station 3 static properties ##########

H03(i) = H02(i); % Constant total enthalpy through the stator H3(i) = H03(i)-(C3(i)^2)/2; S3(i) = S2(i)+dS32(i); [P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('HS',H3(i),S3(i),0,1); P3(i) = P; T3(i) = T; Cp3(i) = Cp; rho3(i) = rho; Visc3(i) = Visc; kappa3(i) = kappa; a3(i) = a;

MC3(i) = C3(i)/a3(i);% Absolute inlet Mach #

MCm3(i) = Cm3(i)/a3(i);% Relative inlet meridional Mach #

%############ Station 3 total properties ##########

[P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('HS',H03(i),S3(i),0,1); P03(i) = P; T03(i) = T;

%################ Station 3 geometry ##############

area3(i) = flow(i)/(Cm3(i)*rho3(i)*BLK_stg(i));

if comp_type == 'CMD' r_hub_3(i) = ((r_rms_3(i)^2)-(area3(i)/(2*pi)))^0.5; r_tip_3(i) =((r_rms_3(i)^2)+(area3(i)/(2*pi)))^0.5; r_rms_3_new(i) = r_rms_3(i);

elseif comp_type == 'CID' r_hub_3(i) = r_hub(i); r_rms_3_new(i) = ((r_hub_3(i)^2)+(area3(i)/(2*pi)))^0.5; r_tip_3(i) =((r_rms_3_new(i)^2)+(area3(i)/(2*pi)))^0.5;

elseif comp_type == 'COD' r_tip_3(i) = r_tip(i); r_rms_3_new(i) = ((r_tip_3(i)^2)-(area3(i)/(2*pi)))^0.5; r_hub_3(i) = ((r_rms_3_new(i)^2)-(area3(i)/(2*pi)))^0.5;

end

height3(i) = r_tip_3(i)-r_hub_3(i); chord3(i) = height3(i)/AR_str(i);

RMS_rel_error = r_rms_3_new(i)/r_rms_3(i) - 1; r_rms_3(i) = r_rms_3_new(i);

n_RMS = n_RMS+1; if n_RMS > 50 %Emergency break

RMS_rel_error = 0; warning('RMS radius Convergence Error');

endend % End of RMS loop

%################### Stator geometry ##################

area_str(i) = (area2(i)+area3(i))/2; r_rms_str(i) = (r_rms_2(i)+r_rms_3(i))/2;


85

r_hub_str(i) = ((r_rms_str(i)^2)-(area_str(i)/(2*pi)))^0.5; r_tip_str(i) =((r_rms_str(i)^2)+(area_str(i)/(2*pi)))^0.5; HONT_str(i) = r_hub_str(i)/r_tip_str(i); height_str(i) = r_tip_str(i)-r_hub_str(i); chord_str(i) = height_str(i)/AR_str(i);

Re_str(i) = C2(i)*chord_str(i)/Visc2(i); % Reynolds number

%# Stator Pitch-to-chord ratios and diffusion factors #

rel_ang_in = Alpha2(i); rel_ang_out = Alpha3(i);

AVDR_str(i) = rho3(i)*Cm3(i)/(rho2(i)*Cm2(i));% Axial Velocity Density Ratio for the stator

if strcmp(SONC_type,'Custom')==0 [SONC,SONC_Hearsey,SONC_McKenzie] = SONC1(rel_ang_in,rel_ang_out,Cm2(i),Cm3(i),r_rms_2(i),r_rms_3(i),DF_str(i));

if strcmp(SONC_type,'DF') SONC_str(i) = SONC;

elseif strcmp(SONC_type,'Hearsey') SONC_str(i) = SONC_Hearsey;

elseif strcmp(SONC_type,'McKenzie') SONC_str(i) = SONC_McKenzie;

endend

[DF_lbl,Deq_star_lbl,Deq,Deq_star_ks] = Deq_star1(rel_ang_in,rel_ang_out,Cm2(i),Cm3(i),r_rms_2(i),r_rms_3(i),SONC_rtr(i),TONC_str(i),AVDR_str(i),MCm2(i)); DF_lbl_str(i) = DF_lbl; Deq_star_lbl_str(i) = Deq_star_lbl; Deq_str(i) = Deq; Deq_star_ks_str(i) = Deq_star_ks;

[Mcrit_Hearsey,Mcrit_Sch] = MCRIT1(rel_ang_in,rel_ang_out,Cm2(i),SONC_str(i),TONC_str(i),kappa2(i)); Mcrit_Hearsey_str(i) = Mcrit_Hearsey; Mcrit_Sch_str(i) = Mcrit_Sch;

%################## Stator entropy rise ###############

[OMEGA_p, OMEGA_ew, K_Re] = WRTMLR(DF_lbl_str(i),Deq_str(i),dH_str(i),rel_ang_out,MC2(i),AR_str(i),EPSONC_str(i),Re_str(i)); K_Re_str(i) = K_Re; % Correction factor for Reynolds number OMEGA_p_str(i) = OMEGA_p; OMEGA_ew_str(i) = OMEGA_ew; OMEGA_str(i) = OMEGA_p+OMEGA_ew; OMEGA_str(i) = OMEGA_str(i)*K_Re;

dP32(i) = OMEGA_str(i)*(P02(i)-P2(i)); % P0_3 - P0_2 dS32_new(i) = -R*log(1-(dP32(i))/P02(i)); %S_3 - S_2

dS32_rel_error = dS32_new(i)/dS32(i) - 1; dS32(i) = dS32_new(i);


dS21_rel_error = 0; warning('entropy rise Convergence Error on stator');

end

end % End of entropy loop

end % for all stages

%##############################################################%############### outlet guide vane, OGV #######################

dS_OGV = dS32(N_stg); % initial guess value dS_OGV_rel_error = 1; n_dS = 0; % Noff iteration steps

while abs(dS_OGV_rel_error) > 10^(-4) % Solves for correct entropy rise


86

AVR_OGV = 1.0; Cm_OGV = Cm3(N_stg)*AVR_OGV; C_OGV = Cm_OGV;

%########### OGV static properties ##########

H0_OGV = H03(N_stg); % Constant total enthalpy through the OGV H_OGV = H0_OGV-(C_OGV^2)/2; S_OGV = S3(N_stg)+dS_OGV; [P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('HS',H_OGV,S_OGV,0,1); P_OGV = P; T_OGV = T; Cp_OGV = Cp; rho_OGV = rho; Visc_OGV = Visc; kappa_OGV = kappa; a_OGV = a;

MCm_OGV = Cm_OGV/a_OGV; MC_OGV = C_OGV/a_OGV;% Absolute inlet Mach #

dH_OGV = C_OGV/C3(N_stg);

%############ OGV total properties ##########

[P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('HS',H0_OGV,S_OGV,0,1); P0_OGV = P; T0_OGV = T;

%############ OGV geometry ##########

r_rms_OGV = r_rms_3(N_stg); r_tip_OGV = r_tip_3(N_stg); r_hub_OGV = r_hub_3(N_stg); HONT_OGV = r_hub_OGV/r_tip_OGV; height_OGV = r_tip_OGV-r_hub_OGV; chord_OGV = height_OGV/AR_str(i);

Re_OGV = C_OGV*chord_OGV/Visc_OGV; % Reynolds number

rel_ang_in = Alpha3(N_stg); rel_ang_out = 0;

AVDR_OGV = rho_OGV*Cm_OGV/(rho3(N_stg)*Cm3(N_stg));% Axial Velocity Density Ratio for the stator

if strcmp(SONC_type,'Custom')==0 [SONC_OGV,SONC_OGV_Hearsey,SONC_OGV_McKenzie] = SONC1(rel_ang_in,rel_ang_out,Cm3(N_stg),Cm_OGV,r_rms_3(N_stg),r_rms_OGV,DF_str(N_stg));

if strcmp(SONC_type,'DF') SONC_OGV = SONC_OGV;

elseif strcmp(SONC_type,'Hearsey') SONC_OGV = SONC_OGV_Hearsey;

elseif strcmp(SONC_type,'McKenzie') SONC_OGV = SONC_OGV_McKenzie;

endelse

SONC_OGV = SONC_str(N_stg); end

[DF_lbl,Deq_star_lbl,Deq,Deq_star_ks] = Deq_star1(rel_ang_in,rel_ang_out,Cm3(N_stg),Cm_OGV,r_rms_3(N_stg),r_rms_OGV,SONC_OGV,TONC_str(N_stg),AVDR_OGV,MCm_OGV); DF_lbl_OGV = DF_lbl; Deq_star_lbl_OGV = Deq_star_lbl; Deq_OGV = Deq; Deq_star_ks_OGV = Deq_star_ks;

[Mcrit_Hearsey,Mcrit_Sch] = MCRIT1(rel_ang_in,rel_ang_out,Cm3(N_stg),SONC_OGV,TONC_str(N_stg),kappa3(N_stg)); Mcrit_Hearsey_OGV = Mcrit_Hearsey; Mcrit_Sch_OGV = Mcrit_Sch;

%################## OGV entropy rise ###############


87

[OMEGA_p,OMEGA_ew, K_Re] = WRTMLR(DF_lbl_OGV,Deq_OGV,dH_OGV,rel_ang_out,MC3(N_stg),AR_str(N_stg),EPSONC_str(i),Re_OGV); K_Re_OGV = K_Re; % Correction factor for Reynolds number OMEGA_p_OGV = OMEGA_p; OMEGA_ew_OGV = OMEGA_ew; OMEGA_OGV = OMEGA_p+OMEGA_ew; OMEGA_OGV = OMEGA_OGV*K_Re;

dP_OGV = OMEGA_OGV*(P03(N_stg)-P3(N_stg)); % P0_3 - P0_3 dS_OGV_new = -R*log(1-(dP_OGV)/P03(N_stg)); %S_OGV - S_3

dS_OGV_rel_error = dS_OGV_new/dS_OGV - 1; dS_OGV = dS_OGV_new;


dS_OGV_rel_error = 0; warning('entropy rise Convergence Error on stator');

end

end % End of entropy loop for OGV

if set_REACT == 1

%#### Calculates the degree of reaction and the slope #####

for k=1:N_stg REACT(k) = (H2(k)-H1(k))/(H03(k)-H01(k)); REACT_slope(k) = Cm1(i)/U1(i)*AVR_rtr(i)*pi/(180*cosd(Alpha3(k))^2);

end

%############### Calculates new Alpha3 values #############

for k=2:N_stg REACT_error(k) = REACT(k)-REACT_stg(k); REACT_rel_error(k) = REACT_stg(k)/REACT(k)-1; Alpha3(k-1) = Alpha3(k-1)+REACT_error(k)/REACT_slope(k)*RLX_REACT;

end

%############### Evaluate RMS error for reaction ##########

REACT_rel_RMS_error = 0;

for k=1:N_stg REACT_rel_RMS_error = REACT_rel_RMS_error+REACT_rel_error(k)^2;

end

if abs(REACT_rel_RMS_error) < 10^(-4) conv_REACT = 1; % the itertation has converged

end

n_REACT = n_REACT+1; if n_REACT > 50 %Emergency break

REACT_rel_RMS_error = 0; warning('REACT Convergence Error');

end

else conv_REACT = 1;

for k=1:N_stg REACT_stg(k) = (H2(k)-H1(k))/(H03(k)-H01(k));

endend

end

%####################### End of REACT loop ########################%##################################################################

PR(j) = P0_OGV/P01(1); % calculates the pressure ratio

%################ breaks the pressure ratio loop ##################

if conv_PR == 1 break


88

end

end % end of the "two" calculations for obtaining derivative

%############## calculates the PR slope if not converged ##############

if conv_PR == 0 PR_slope = (PR(1)-PR(2))/(mean(PSI(1,:))-mean(PSI(2,:))); % the numerical derivative dPR/dPSI

PR_rel_error_level = PR_comp/PR(1)-1; PR_error_level = PR_comp-PR(1);

%##################### Calculates new PSI values ######################

for i=1:N_stg PSI(1,i) = PSI(1,i)+PR_error_level/PR_slope*RLX_PR; % calculate new PSI numbers PSI(2,i) = PSI(1,i)*factor;

end

n_PR = n_PR+1; if n_PR>20 % Emergency break

PR_error_level = 0; warning('Pressure ratio Convergence Error');

endend

end

%####################### End of PR loop ################################%##########################################################################

pressure_ratio = P_OGV/P01(1);

%########################## Blade angles ##################################

for i = 1:N_stg

spacing_rtr(i) = chord_rtr(i)*SONC_rtr(i); diameter_rtr(i) = 2*pi*r_rms_rtr(i); numb_blades_rtr(i) = diameter_rtr(i)/spacing_rtr(i); numb_blades_rtr(i) = ceil(numb_blades_rtr(i));

spacing_str(i) = chord_str(i)*SONC_str(i); diameter_str(i) = 2*pi*r_rms_str(i); numb_blades_str(i) = diameter_str(i)/spacing_str(i); numb_blades_str(i) = ceil(numb_blades_str(i));

%############################## Rotor angles ########################## rel_ang_in = Beta1(i); rel_ang_out = Beta2(i); SONC = SONC_rtr(i); TONC = TONC_rtr(i); M = MW1(i);

[incidence_angle,deviation_angle,camber_angle,attack_angle,stagger_angle,blade_angle_in,blade_angle_out] = Bladeangles(rel_ang_in,rel_ang_out,SONC,TONC,M); incidence_angle_rtr(i) = incidence_angle; deviation_angle_rtr(i) = deviation_angle; camber_angle_rtr(i) = camber_angle; attack_angle_rtr(i) = attack_angle; stagger_angle_rtr(i) = stagger_angle; blade_angle_in_rtr(i) = blade_angle_in; blade_angle_out_rtr(i) = blade_angle_out;

%########################### Stator angles ############################ rel_ang_in = Alpha2(i); rel_ang_out = Alpha3(i); SONC = SONC_str(i); TONC = TONC_str(i); M = MC2(i);

[incidence_angle,deviation_angle,camber_angle,attack_angle,stagger_angle,blade_angle_in,blade_angle_out] = Bladeangles(rel_ang_in,rel_ang_out,SONC,TONC,M); incidence_angle_str(i) = incidence_angle; deviation_angle_str(i) = deviation_angle; camber_angle_str(i) = camber_angle;


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attack_angle_str(i) = attack_angle; stagger_angle_str(i) = stagger_angle; blade_angle_in_str(i) = blade_angle_in; blade_angle_out_str(i) = blade_angle_out;

%########################### Tip-housing angle ########################

tip_angle_rtr(i) = atand((r_tip_1(i)-r_tip_2(i))/(chord_rtr(i)*cosd(stagger_angle_rtr(i)))); tip_angle_str(i) = atand((r_tip_2(i)-r_tip_3(i))/(chord_str(i)*cosd(stagger_angle_str(i))));

end

%##################### Blade angles for the OGV ###########################

spacing_OGV = chord_OGV*SONC_OGV; diameter_OGV = 2*pi*r_rms_OGV; numb_blades_OGV = diameter_OGV/spacing_OGV; numb_blades_OGV = ceil(numb_blades_OGV);

rel_ang_in = Alpha3(N_stg); rel_ang_out = 0; SONC = SONC_OGV; TONC = TONC_str(N_stg); M = MC3(N_stg); [incidence_angle,deviation_angle,camber_angle,attack_angle,stagger_angle,blade_angle_in,blade_angle_out] = Bladeangles(rel_ang_in,rel_ang_out,SONC,TONC,M); incidence_angle_OGV = incidence_angle; deviation_angle_OGV = deviation_angle; camber_angle_OGV = camber_angle; attack_angle_OGV = attack_angle; stagger_angle_OGV = stagger_angle; blade_angle_in_OGV = blade_angle_in; blade_angle_out_OGV = blade_angle_out;

%########################## Misc. properties ##############################

Power=0; %Resetting stage power summation

for i=1:N_stg

%####################### static pressure rise #########################

Cp_rtr(i) = (P2(i)-P1(i))/(P01_rel(i)-P1(i)); Cp_str(i) = (P3(i)-P2(i))/(P02(i)-P2(i));

%######################### Stage pressure ratio #######################

PR_stg(i) = P03(i)/P01(i);

%###################### Accumulated pressure ratio ####################

PR_acc(i) = P03(i)/P01(1);

%######################### Stage temp increase ########################

dT0_stg(i) = T03(i)-T01(i);

%#################### Polytropic stage efficiency #####################

[P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('PT',1,T03(i),0,1); aa = S; % a dummie variable [P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('PT',1,T01(i),0,1); bb = S; % a dummie variable poly_eff_stg(i) = R*log(P03(i)/P01(i))/(aa-bb);

%################# Accumulated polytropic efficiency ##################

[P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('PT',1,T03(i),0,1); aa = S; % a dummie variable [P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('PT',1,T01(1),0,1); bb = S; % a dummie variable


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poly_eff_acc(i) = R*log(P03(i)/P01(1))/(aa-bb);

%###################### Isentropic stage efficiency ###################

P = P03(i); S = S01(i); [P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('PS',P,S,0,1); H03s = H; % the isentropic enthalpy isen_eff_stg(i) = (H03s-H01(i))/(H03(i)-H01(i));

%##################### Stage flow coefficient #########################

PHI_stg(i) = (Cm1(i)+Cm2(i))/(U1(i)+U2(i));

%####################### Compressor Power ############################

Power=Power+flow(i)*(H03(i)-H01(i))/1000;

end

%############################ Stall and Surge #############################%##########################################################################

for i =1:N_stg

%##################### constants/variables ######################

% staggered spacing g_rtr = pi*r_rms_rtr(i)*(cosd(blade_angle_in_rtr(i))+cosd(blade_angle_out_rtr(i)))/numb_blades_rtr(i); g_str = pi*r_rms_str(i)*(cosd(blade_angle_in_str(i))+cosd(blade_angle_out_str(i)))/numb_blades_str(i);

g = (W1(i)^2*g_rtr + C2(i)^2*g_str)/(W1(i)^2+C2(i)^2); % average value of g in the stage

% L/g2, L is meanline length of circular-arc profile LONG2_rtr = (1/SONC_rtr(i))/(cosd(blade_angle_out_rtr(i))*cosd(camber_angle_rtr(i)/2)); LONG2_str = (1/SONC_str(i))/(cosd(blade_angle_out_str(i))*cosd(camber_angle_str(i)/2));

LONG2 = (W1(i)^2*LONG2_rtr + C2(i)^2*LONG2_str)/(W1(i)^2+C2(i)^2); % average value of L/g2 in the stage

% endwall space epsilon_rtr = EPSONC_rtr(i)*chord_rtr(i); epsilon_str = EPSONC_str(i)*chord_str(i);

epsilon = (W1(i)^2*epsilon_rtr + C2(i)^2*epsilon_str)/(W1(i)^2+C2(i)^2);

% epsilon/g EPSONG = epsilon/g;

%Reynolds number Re = (W1(i)^2*Re_rtr(i) + C2(i)^2*2*Re_str(i))/(W1(i)^2+C2(i)^2);

% axial spacing axial_spacing_rtr = 0.2*chord_rtr(i); axial_spacing_str = 0.2*chord_str(i);

axial_spacing = (W1(i)^2*axial_spacing_rtr + C2(i)^2*axial_spacing_str)/(W1(i)^2+C2(i)^2); dZ = axial_spacing;

%staggered spacing s_rtr = spacing_rtr(i); s_str = spacing_str(i);

s = (W1(i)^2*spacing_rtr(i) + C2(i)^2*spacing_str(i))/(W1(i)^2+C2(i)^2); dZONS = dZ/s; % dZ/s

%################## F_ef #################


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% rotor U_in = U1(i); C_in = C1(i); W_rtr_in = W1(i);

if (Alpha1(i)+Beta1(i)) >= 90 V_min = C1(i)*sind(Alpha1(i)+Beta1(i));

else V_min = C1(i);

end F_ef_rtr = (1+2.5*V_min^2+0.5*U_in^2)/(4*C_in^2);

% stator U_in = U2(i); C_in = C2(i); V_str_in = C2(i);

if (Alpha2(i)+Beta2(i)) >= 90 V_min = C2(i)*sind(Alpha2(i)+Beta2(i));

else V_min = C2(i);

end F_ef_str = (1+2.5*V_min^2+0.5*U_in^2)/(4*C_in^2);

% average F_ef(i) = (W1(i)^2*F_ef_rtr + C2(i)^2*F_ef_str)/(W1(i)^2+C2(i)^2);

%######################## ChD ###############################

x = LONG2;

%polynomial coefficients coeff_Ch_D = [0.001777942251246 -0.019627519528419 0.091687954954062 -0.251659185450453 0.491601357182957 0.076431045899622];

Ch_D(i) = 0;

for j=1:6 Ch_D(i) = Ch_D(i)+coeff_Ch_D(j)*(x)^(6-j); % evaluate the polynomial

end

%######################## (Ch/ChD)_eps ###############################

x = EPSONG; % epsilon/g

%polynomial coefficients coeff_Ch_eps = [-53510.30317191636 22041.80905688297 -3381.24369820182 242.41566524838544 -10.098550480478846 1.216825975980701];

Ch_eps(i) = 0;

for j=1:6 Ch_eps(i) = Ch_eps(i)+coeff_Ch_eps(j)*(x)^(6-j); % evaluate the polynomial

end

%######################## (Ch/ChD)_dZ ###############################

x = dZONS; % dZ/S

%polynomial coefficients coeff_Ch_dZ = [0.514206502798114 -0.745186356821405 -0.221066436780794 0.960732185823537 -0.615664604922058 1.119049824148622];

Ch_dZ(i) = 0;

for j=1:6 Ch_dZ(i) = Ch_dZ(i)+coeff_Ch_dZ(j)*(x)^(6-j); % evaluate the polynomial


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end

%######################## (Cp/CpD)_Re ###############################

x = Re;

% coefficients a = -107.8; b = -0.6767; c = 1.041;

Ch_Re(i) = a*x^b+c;

%##################################################

Ch_max(i) = F_ef(i)*Ch_D(i)*Ch_Re(i)*Ch_dZ(i)*Ch_eps(i);

%#################### Ch #####################

kappa_mean = (kappa1(i)+kappa3(i))/2; Cp_mean = (Cp1(i)+Cp3(i))/2;

aa = Cp_mean*(T1(i)+273.15)*((P3(i)/P1(i))^((kappa_mean-1)/kappa_mean)-1); bb = (U2(i)^2-U1(i)^2)/2; cc = (W1(i)^2+C2(i)^2)/2;

Ch(i) = (aa-bb)/cc;

omega(i) = Ch(i)/Ch_max(i);

end

%########################## Polytropic efficency ##########################

P_ref = 1; % a reference pressure for the calculation[P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('PT',P_ref,T03(N_stg),0,1);aa = S; % a dummie variable[P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('PT',P_ref,T01(1),0,1);bb = S; % a dummie variable

poly_eff = R*log(P03(N_stg)/P01(1))/(aa-bb);

%########################## Isentropic efficency ##########################

P = P3(N_stg); S = S3(1); [P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('PS',P,S,0,1);H2s = H; % the isentropic enthalpy

isen_eff = (H2s-H1(1))/(H3(N_stg)-H1(1));

%############################# Compressor cost ############################

mean_diameter = r_rms_1(1)+r_rms_3(N_stg);

comp_cost = 1.13*2625*(N_stg^1.155 * PR_comp^0.775 * mean_diameter^0.489 + 14.25);

%########################### Compressor Length ############################

Comp_length = 0;

for i=1:N_stg

Comp_length = Comp_length + chord_rtr(i)*cosd(stagger_angle_rtr(i)); Comp_length = Comp_length + chord_rtr(i)*0.2; Comp_length = Comp_length + chord_str(i)*cosd(stagger_angle_str(i)); Comp_length = Comp_length + chord_str(i)*0.2;

endComp_length = Comp_length - chord_str(N_stg)*0.2;

Comp_angle = atand((r_tip_1(1)-r_tip_3(N_stg))/Comp_length);

%############ Creates a structure of a properties and values #############


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CompInfo.comp_name = CompInputdata{1,1}; CompInfo.type = comp_type; CompInfo.P0_in = P0_in; CompInfo.T0_in = T0_in; CompInfo.PR_comp = PR_comp; CompInfo.N_stg = N_stg; CompInfo.RPM = RPM; CompInfo.Alpha_in = Alpha_in; CompInfo.PHI_in = PHI_in; CompInfo.HONT_in = HONT_in; CompInfo.poly_eff = poly_eff; CompInfo.isen_eff = isen_eff; CompInfo.comp_cost = comp_cost; CompInfo.area_in = area_in; CompInfo.M_tip_in = M_tip_in; CompInfo.Power = Power; CompInfo.Comp_length = Comp_length; CompInfo.Comp_angle = Comp_angle;

OGV.Cm = Cm_OGV; OGV.C = C_OGV; OGV.H0 = H0_OGV; OGV.H = H_OGV; OGV.S = S_OGV; OGV.P = P_OGV; OGV.T = T_OGV; OGV.Cp = Cp_OGV; OGV.rho = rho_OGV; OGV.Visc = Visc_OGV; OGV.kappa = kappa_OGV; OGV.a = a_OGV; OGV.P0 = P0_OGV; OGV.T0 = T0_OGV; OGV.MCm = MCm_OGV; OGV.MC = MC3(N_stg); OGV.dH = dH_OGV; OGV.r_rms = r_rms_OGV; OGV.r_tip = r_tip_OGV; OGV.r_hub = r_hub_OGV; OGV.HONT = HONT_OGV; OGV.height = height_OGV; OGV.chord = chord_OGV; OGV.Re = Re_OGV; OGV.SONC = SONC_OGV; OGV.DF_lbl = DF_lbl_OGV; OGV.Deq_star_lbl = Deq_star_lbl_OGV; OGV.Deq = Deq_OGV; OGV.Deq_star_ks = Deq_star_ks_OGV; OGV.Mcrit_Hearsey = Mcrit_Hearsey_OGV; OGV.Mcrit_Sch = Mcrit_Sch_OGV; OGV.OMEGA_p = OMEGA_p_OGV; OGV.OMEGA_ew = OMEGA_ew_OGV; OGV.numb_blades = numb_blades_OGV; OGV.incidence_angle = incidence_angle_OGV; OGV.deviation_angle = deviation_angle_OGV; OGV.camber_angle = camber_angle_OGV; OGV.attack_angle = attack_angle_OGV; OGV.stagger_angle = stagger_angle_OGV; OGV.blade_angle_in = blade_angle_in_OGV; OGV.blade_angle_out = blade_angle_out_OGV;

for i = 1:N_stg

STG(i).Alpha1 = Alpha1(i); STG(i).Alpha2 = Alpha2(i); STG(i).Alpha3 = Alpha3(i); STG(i).Beta1 = Beta1(i); STG(i).Beta2 = Beta2(i); STG(i).C1 = C1(i); STG(i).C2 = C2(i); STG(i).C3 = C3(i); STG(i).W1 = W1(i); STG(i).W2 = W2(i); STG(i).Cm1 = Cm1(i); STG(i).Cm2 = Cm2(i);


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STG(i).Cm3 = Cm3(i); STG(i).U1 = U1(i); STG(i).U2 = U2(i); STG(i).C_theta1 = C_theta1(i); STG(i).C_theta2 = C_theta2(i); STG(i).C_theta3 = C_theta3(i); STG(i).W_theta1 = W_theta1(i); STG(i).W_theta2 = W_theta2(i); STG(i).MW1 = MW1(i); STG(i).MC2 = MC2(i); STG(i).Mcrit_Hearsey_rtr = Mcrit_Hearsey_rtr(i); STG(i).Mcrit_Sch_rtr = Mcrit_Sch_rtr(i); STG(i).Mcrit_Hearsey_str = Mcrit_Hearsey_str(i); STG(i).Mcrit_Sch_str = Mcrit_Sch_str(i); STG(i).a1 = a1(i); STG(i).a2 = a2(i); STG(i).a3 = a3(i); STG(i).kappa1 = kappa1(i); STG(i).kappa2 = kappa2(i); STG(i).kappa3 = kappa3(i); STG(i).Cp1 = Cp1(i); STG(i).Cp2 = Cp2(i); STG(i).Cp3 = Cp3(i); STG(i).rho1 = rho1(i); STG(i).rho2 = rho2(i); STG(i).rho3 = rho3(i); STG(i).visc1 = Visc1(i); STG(i).visc2 = Visc2(i); STG(i).visc3 = Visc3(i); STG(i).P1 = P1(i); STG(i).P2 = P2(i); STG(i).P3 = P3(i); STG(i).P01 = P01(i); STG(i).P02 = P02(i); STG(i).P03 = P03(i); STG(i).T1 = T1(i); STG(i).T2 = T2(i); STG(i).T3 = T3(i); STG(i).T01 = T01(i); STG(i).T02 = T02(i); STG(i).T03 = T03(i); STG(i).H1 = H1(i); STG(i).H2 = H2(i); STG(i).H3 = H3(i); STG(i).H01 = H01(i); STG(i).H02 = H02(i); STG(i).H03 = H03(i); STG(i).S1 = S1(i); STG(i).S2 = S2(i); STG(i).S3 = S3(i); STG(i).S01 = S1(i); STG(i).S02 = S2(i); STG(i).S03 = S3(i); STG(i).EPSONC_rtr = EPSONC_rtr(i); STG(i).EPSONC_str = EPSONC_str(i); STG(i).SONC_rtr = SONC_rtr(i); STG(i).SONC_str = SONC_str(i); STG(i).HONT_rtr = HONT_rtr(i); STG(i).HONT_str = HONT_str(i); STG(i).TONC_rtr = TONC_rtr(i); STG(i).TONC_str = TONC_str(i); STG(i).AR_rtr = AR_rtr(i); STG(i).AR_str = AR_str(i); STG(i).chord_rtr = chord_rtr(i); STG(i).chord_str = chord_str(i); STG(i).height_rtr = height_rtr(i); STG(i).height_str = height_str(i); STG(i).DF_rtr = DF_lbl_rtr(i); STG(i).DF_str = DF_lbl_str(i); STG(i).Deq_rtr = Deq_rtr(i); STG(i).Deq_str = Deq_str(i); STG(i).Deq_star_lbl_rtr = Deq_star_lbl_rtr(i); STG(i).Deq_star_lbl_str = Deq_star_lbl_str(i); STG(i).Deq_star_ks_rtr = Deq_star_ks_rtr(i); STG(i).Deq_star_ks_str = Deq_star_ks_str(i); STG(i).dH_rtr = dH_rtr(i); STG(i).dH_str = dH_str(i);


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STG(i).dS_rtr = dS21(i); STG(i).dS_str = dS32(i); STG(i).area1 = area1(i); STG(i).area2 = area2(i); STG(i).area3 = area3(i); STG(i).Re_rtr = Re_rtr(i); STG(i).Re_str = Re_str(i); STG(i).r_tip_1 = r_tip_1(i); STG(i).r_tip_2 = r_tip_2(i); STG(i).r_tip_3 = r_tip_3(i); STG(i).r_hub_1 = r_hub_1(i); STG(i).r_hub_2 = r_hub_2(i); STG(i).r_hub_3 = r_hub_3(i); STG(i).r_rms_1 = r_rms_1(i); STG(i).r_rms_2 = r_rms_2(i); STG(i).r_rms_3 = r_rms_3(i);

STG(i).incidence_angle_rtr = incidence_angle_rtr(i); STG(i).deviation_angle_rtr = deviation_angle_rtr(i); STG(i).camber_angle_rtr = camber_angle_rtr(i); STG(i).attack_angle_rtr = attack_angle_rtr(i); STG(i).stagger_angle_rtr = stagger_angle_rtr(i); STG(i).turning_rtr = Beta1(i)-Beta2(i); STG(i).blade_angle_in_rtr = blade_angle_in_rtr(i); STG(i).blade_angle_out_rtr = blade_angle_out_rtr(i);

STG(i).incidence_angle_str = incidence_angle_str(i); STG(i).deviation_angle_str = deviation_angle_str(i); STG(i).camber_angle_str = camber_angle_str(i); STG(i).attack_angle_str = attack_angle_str(i); STG(i).stagger_angle_str = stagger_angle_str(i); STG(i).turning_str = Alpha2(i)-Alpha3(i); STG(i).blade_angle_in_str = blade_angle_in_str(i); STG(i).blade_angle_out_str = blade_angle_out_str(i); STG(i).tip_angle_rtr = tip_angle_rtr(i); STG(i).tip_angle_str = tip_angle_str(i); STG(i).spacing_rtr = spacing_rtr(i); STG(i).numb_blades_rtr = numb_blades_rtr(i); STG(i).spacing_str = spacing_str(i); STG(i).numb_blades_str = numb_blades_str(i);

STG(i).PR = PR_stg(i); STG(i).PR_acc = PR_acc(i); STG(i).React = REACT_stg(i); STG(i).PSI = PSI(1,i); STG(i).PHI = PHI_stg(i); STG(i).dT0 = dT0_stg(i); STG(i).dS = dS21(i)+dS32(i); STG(i).OMEGA_p_rtr = OMEGA_p_rtr(i); STG(i).OMEGA_ew_rtr = OMEGA_ew_rtr(i); STG(i).OMEGA_p_str = OMEGA_p_str(i); STG(i).OMEGA_ew_str = OMEGA_ew_str(i); STG(i).poly_eff = poly_eff_stg(i); STG(i).poly_eff_acc = poly_eff_acc(i); STG(i).isen_eff = isen_eff_stg(i); STG(i).flow = flow(i); STG(i).Ch = Ch(i); STG(i).Ch_max = Ch_max(i); STG(i).omega = omega(i); end


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B.2 Inlet geometry calculation % Inlet geometry calculation

%#####################################################################%## ##%## Inlet geometry ##%## ##%## (c) Niclas Falck and Magnus Genrup 2008 ##%## ##%## Lund University/Dept of Energy Sciences ##%## ##%#####################################################################

function[r_rms_rtr,r_m_rtr,r_hub_rtr,r_tip_rtr]=Inletgeom(P0,T0,flow,RPM,HONT,PHI,alpha1,BLK)

%##########################################################################% Inlet state

[P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV,y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('PT',P0,T0,0,1);H0 = H; S0 = S;

%##########################################################################% Main calculation

Cm = 0.6*a; %Initial velocity guess

RLX = 0.15; %dampingrel_error_Cm = 1; n = 0; %Noff iteration steps

while abs(rel_error_Cm) > 10^(-3) %Solves for correct velocity Cm_old = Cm; C = Cm_old/cosd(alpha1); H = H0-C^2/2;

[P, T, H, S, Cp, rho, Visc, lambda, kappa, R, a, crit, FARsto, LHV, y_SO2, y_H2O, y_CO2, y_N2, y_O2, y_Ar, y_He]=state('HS',H,S0,0,1);

area = flow/(Cm_old*rho*BLK); r_tip_rtr = (area/(pi*(1-HONT^2)))^0.5; %tip radius r_hub_rtr = HONT*r_tip_rtr; %hub radius r_m_rtr = (r_tip_rtr+r_hub_rtr)/2; %mean radius r_rms_rtr=((r_hub_rtr^2+r_tip_rtr^2)/2)^0.5; %RMS radius U_m = 2*r_m_rtr*pi*RPM/60; %blade speed based om mean radius U_rms = 2*r_rms_rtr*pi*RPM/60; %blade speed based om RMS radius

Cm = PHI*U_rms; %Updated meridional velocity

rel_error_Cm = Cm/Cm_old-1;

Cm = Cm+(Cm_old-Cm)*RLX; %damping

n = n+1; if n>20 %Emergency break

rel_error_Cm = 0; warning('Velocity Cm Convergence Error');

endend


97

B.3 Pitch chord ratio % Pitch-to-chord ratio

%#####################################################################%## ##%## Pitch-to-chord ratio ##%## ##%## (c) Niclas Falck and Magnus Genrup 2008 ##%## ##%## Lund University/Dept of Energy Sciences ##%## ##%#####################################################################

function[SONC,SONC_Hearsey,SONC_McKenzie] = SONC1(rel_ang_in,rel_ang_out,Cm_in,Cm_out,r_in,r_out,DF);

rel_vel_in = Cm_in/cosd(rel_ang_in); rel_vel_out = Cm_out/cosd(rel_ang_out);

dH = rel_vel_out/rel_vel_in; Cpi = 1-dH^2;

C_theta_in = Cm_in*tand(rel_ang_in); C_theta_out = Cm_out*tand(rel_ang_out);

SONC = (DF-1+dH)*rel_vel_in*(r_in+r_out)/abs(r_in*C_theta_in-r_out*C_theta_out);

%##################### Hearsey solidity method ###########################

% The Hearsey method is taken from Concepts ETI's "Practical Compressor % Aerodynamic Design", page 44, eq 44.

DF_opt = 0.45; %Init guessj = 0; error_str = 1;

while error_str > 0.00001 DF_opt_old = DF_opt; SOL_opt = (8.861805*abs(r_in*C_theta_in-r_out*C_theta_out)/(rel_vel_in*(r_in+r_out)))*DF_opt_old^0.436794; DF_opt = 1-dH+abs(r_in*C_theta_in-r_out*C_theta_out)/((r_in+r_out)*SOL_opt*rel_vel_in); error = abs(DF_opt/DF_opt_old-1); j = j+1;

if j>20 error_str = 0;

endend

SONC_Hearsey = 1/SOL_opt;

%##################### McKenzie solidity method ###########################

% The McKenzie method is taken from "Axial Flow Fans and Compressors -% Aerodynamic Design and Performance", figure 4.3 on page 32.

SONC_McKenzie = 9*(0.567-Cpi);


98

B.4 Diffusion Factor and Diffusion Ratio % Diffusion ratios

%#####################################################################%## ##%## Diffusion ratios ##%## ##%## (c) Niclas Falck and Magnus Genrup 2008 ##%## ##%## Lund University/Dept of Energy Sciences ##%## ##%#####################################################################

function[DF_lbl,Deq_star_lbl,Deq,Deq_star_ks]=Deq_star1(rel_ang_in,rel_ang_out,Cm_in,Cm_out,r_in,r_out,SONC,TONC,AVDR,Max)

% rel_ang_in=55.77;% rel_ang_out=39.66;% Cm=167.64;% SONC=1/1.11;% TONC=0.06;% Max=167.64/346.97

rel_vel_in = Cm_in/cosd(rel_ang_in); rel_vel_out = Cm_out/cosd(rel_ang_out);

dH = rel_vel_out/rel_vel_in; %DeHaller

C_theta_in = Cm_in*tand(rel_ang_in); C_theta_out = Cm_out*tand(rel_ang_out);

gamma = (r_in*C_theta_in-r_out*C_theta_out)*2*SONC/(rel_vel_in*(r_in+r_out));

% Lieblein diffusion factor

DF_lbl = 1-dH+abs(gamma)/2;

% Lieblein equivalent diffusion ratio

Deq_star_lbl = 1/dH*(1.12+0.61*SONC*(cosd(rel_ang_in))^2*(tand(rel_ang_in)-tand(rel_ang_out)));

% Equivalent diffusion ratio

Deq = (1-dH+(0.1+TONC*(10.116-36.15*TONC))*gamma)/dH+1;

% Koch & Smith diffusion ratio

Ap_star = (1-0.4458*TONC/(SONC*cosd((rel_ang_in+rel_ang_out)/2)))*(2+1/AVDR)/3; rho_ratio = 1-(Max^2/(1-Max^2))*(1-Ap_star-0.2445/SONC*gamma*sind(rel_ang_in));

Deq_star_ks = 1/dH*(1+0.7688*TONC+0.6024*abs(gamma))*((sind(rel_ang_in)-0.2445/SONC*gamma)^2+(cosd(rel_ang_in)/(Ap_star*rho_ratio)))^0.5;


99

B.5 Compressor losses %Wright & Miller Compressor Loss Model

%#####################################################################%## ##%## Wright & Miller Compressor Loss Model ##%## ##%## (c) Niclas Falck Magnus Genrup 2008 ##%## ##%## Lund University/Dept of Energy Sciences ##%## ##%#####################################################################

function[OMEGA_p,OMEGA_ew, K_Re]=WRTMLR(DF,DR,dH,rel_ang_out,rel_Mach_in,HONC,EPSONC,Re)

%############################ Profile losses ##############################

M_array = [0.3 0.7 1]; %the different Machnumbers for each polynomial

%%%%%%%%%%%%%%%%%%%%%%% polynomial coefficients %%%%%%%%%%%%%%%%%%%%%%%%%%%

Coeff_Y2 = [-8.26097e-02 2.62982e-01 -2.66675e-01 1.14774e-01 -1.61839e-02 -1.30107e-01 3.68490e-01 -3.56939e-01 1.48500e-01 -2.08264e-02 -1.36535e-01 3.78126e-01 -3.66336e-01 1.52219e-01 -2.13465e-02];

%%%%%%%%%%%%%%%%%%%%%%%%%%% main calculation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Yp2_array = [0 0 0];

for i=1:3

for j=1:5 Yp2_array(i) = Yp2_array(i)+Coeff_Y2(i,j)*(DR)^(j-1); %calculates each segment/degree of the polynomial

end

end

LP_p = interp1(M_array,Yp2_array,rel_Mach_in,'linear','extrap'); %interpolates for the value of M

OMEGA_p = LP_p*2*dH^2*(1/cosd(rel_ang_out));

%############################ Endwall losses ##############################

EPSONC_array = [0.1 0.07 0.04 0.02 0]; %the different epsilon/c for each polynomial

% %%%%%%%%%%%%%%%%%%%%%%%%polynomial coefficients %%%%%%%%%%%%%%%%%%%%%%%%%

Coeff_Y1 = [3.23881e00 -3.66895e01 1.60855e02 -3.14825e02 2.32625e02 2.86933e00 -3.18679e01 1.36001e02 -2.58533e02 1.85224e02 -2.00381e-01 1.04984e00 3.12191e00 -2.03045e01 2.48570e01 8.18792e-01 -8.62635e00 3.57996e01 -6.61454e01 4.61697e01 2.38135e-01 -2.36201e00 1.01622e01 -1.92343e01 1.36794e01];

%%%%%%%%%%%%%%%%%%%%%%%%%%%%% main calculation %%%%%%%%%%%%%%%%%%%%%%%%%%%%

Yp_array = [0 0 0 0 0];

for i=1:5

for j=1:5 Yp_array(i) = Yp_array(i)+Coeff_Y1(i,j)*(DF)^(j-1); %calculates each segment/degree of the polynomial

end

if Yp_array(i) > 0.14 %checks if the value is to high Yp_array(i) = 0.14;

end

end


100

LP_ew = interp1(EPSONC_array,Yp_array,EPSONC,'linear','extrap'); %interpolates for the value of EPSONC

OMEGA_ew = LP_ew*dH^2*(1/HONC);

%%%%%%%%%%%%%%%%%%%% Correction for the Reynolds number %%%%%%%%%%%%%%%%%%%

if Re < 10^5 K_Re = 489.8*(Re^-0.5); elseif Re > 10^6 K_Re = 1; else K_Re = 13.8*(Re^-0.19); end

B.6 Blade angles % Blade angles

%#####################################################################%## ##%## Blade angles ##%## ##%## (c) Niclas Falck and Magnus Genrup 2007 ##%## ##%## Lund University/Dept of Energy Sciences ##%## ##%#####################################################################

function[incidence_angle,deviation_angle,camber_angle,attack_angle,stagger_angle,blade_angle_in,blade_angle_out] = Bladeangles(rel_ang_in,rel_ang_out,SONC,TONC,M)

blade = 'DCA';

turning = rel_ang_in-rel_ang_out;

%###################### Minimum loss incidence #########################%#########################################################################

%########################### i_0 ###############################

i_0_10 = (0.0325-0.0674/SONC)+(-0.002364+0.0913/SONC)*rel_ang_in+(1.64e-5-2.38e-4/SONC)*rel_ang_in^2;

K_i_t = -0.0214+19.17*TONC-122.3*TONC^2+312.5*TONC^3;

if blade == 'DCA' K_sh = 0.7; elseif blade == 'NACA65' K_sh = 1.0; elseif blade == 'NTGEC' K_sh = 1.1; end

%####################### Mach # correction #######################

del_i_M = 10*(M-0.7);

%########################## Camber influence ##########################

n = (-0.063+0.02274/SONC)+(-0.0035+0.0029/SONC)*rel_ang_in-(3.79e-5+1.11e-5/SONC)*rel_ang_in^2;

%###################### Deviation@i = i_ref #########################%#########################################################################

del_0_10 = (-0.0443+0.1057/SONC)+(0.0209-0.0186/SONC)*rel_ang_in+(-0.0004+0.00076/SONC)*rel_ang_in^2;

K_del_t = 0.0142+6.172*TONC+36.61*TONC^2;


101

%####################### Camber influence ##########################

if blade == 'DCA' m_prime = 0.249+7.4e-4*rel_ang_in-1.32e-5*rel_ang_in^2+3.16e-7*rel_ang_in^3; elseif blade == 'NACA65' m_prime = 0.17-3.33e-4*(1.0-0.1*rel_ang_in)*rel_ang_in; elseif blade == 'NTGEC' m_prime = 0.249+7.4e-4*rel_ang_in-1.32e-5*rel_ang_in^2+3.16e-7*rel_ang_in^3; end

b = 0.9655-2.538e-3*rel_ang_in+4.221e-5*rel_ang_in^2-1.3e-6*rel_ang_in^3;

m = m_prime*SONC^b;

%####################### Camber iteration ##########################

camber = 1.2*(turning); %Start value

z = 0; rel_error_level = 1;

while rel_error_level > 0.0001; camber_old=camber; i_ref = K_i_t*K_sh*i_0_10-1+del_i_M+n*camber_old; del_ref = K_del_t*K_sh*del_0_10+m*camber_old;

rel_blade_ang_in = rel_ang_in-i_ref; rel_blade_ang_out = rel_ang_out-del_ref;

camber = rel_blade_ang_in-rel_blade_ang_out;

rel_error_level = abs(camber/camber_old-1);

z=z+1; if z > 10

rel_error_level = 0; end

error(z) = rel_error_level; end

camber_angle = camber; incidence_angle = i_ref; deviation_angle = del_ref; blade_angle_in = rel_blade_ang_in; blade_angle_out = rel_blade_ang_out; stagger_angle = rel_ang_in - camber_angle/2; attack_angle = rel_ang_in - stagger_angle;


102

Appendix C A result file from the program LUAX-C based on the input parameters set in chapter 6 “Result” are shown on the following pages.

----------------------------------------------

| LUAX-C |

| Version 1.0 |

| Niclas Falck & Magnus Genrup |

| 2008 |

----------------------------------------------

Name: Comp

_________________________________________________________________________________________________________________________________________________

12-Feb-2008 13:37:58

Type: Contstant Mean Radius

Pressure ratio: 20

Number of stages: 15

Inlet massflow: 122 kg/s

Rotational speed: 6600 rpm

Ambient pressure: 1 bar

Ambient temperature: 15 C

===== Compressor Performance =====

=================================================================================================================================================

Polytropic efficiency: 91.80 %

Isentropic efficiency: 89.55 %

Temperature rise: 428.7 K

Inlet Mach @ tip: 1.08

massflow @ 3000: 590.5 kg/s

specific massflow: 231.4 kg/(s m^2)

Compressor cost: 676000 €

Compressor power: 54.13 MW

===== Koch Surgelimit =====

Stage 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ch 0.381 0.410 0.408 0.406 0.406 0.412 0.419 0.425 0.431 0.435 0.435 0.436 0.437 0.439 0.448

Ch_max 0.391 0.404 0.406 0.407 0.410 0.419 0.428 0.438 0.447 0.455 0.459 0.464 0.472 0.481 0.502

Ch/Ch_max 0.974 1.015 1.006 0.999 0.990 0.985 0.978 0.971 0.964 0.956 0.948 0.939 0.927 0.912 0.892

===== STAGE 1 =====

=================================================================================================================================================

PR REACT Flow PSI PHI dT0 dS ------Efficiencies------ --------Surge (Koch)------

Poly Isen acc.Poly Ch Ch_max Ch/Ch_max

1.420 0.550 122 0.391 0.647 32.872 8.031 0.926 0.922 0.926 0.381 0.391 0.974

point ------radius------- ------------------Velocities-------------- ----Angles----

tip rms hub U Cm C W C_theta Alpha Beta

1 0.528 0.421 0.274 290.70 188.95 195.62 305.51 50.630 15.000 51.794

2 0.513 0.421 0.300 290.70 187.07 249.03 225.71 164.392 41.309 34.027

3 0.507 0.421 0.310 N/A 185.19 201.15 N/A 78.519 22.961 N/A

point ---Pressure--- --Temperatures-- ----Enthalpy---- Entropy Cp Kappa rho Visc a

Total Static Total Static Total Static

1 1.013 0.797 14.85 -4.19 14.923 53.270 -4.211 1004.481 1.400 1.032 1.776e-005 328.93

2 1.451 1.018 47.72 16.90 47.993 58.867 16.984 1005.306 1.400 1.222 1.595e-005 341.53

3 1.438 1.147 47.72 27.62 47.993 61.301 27.762 1005.827 1.400 1.327 1.512e-005 347.75

deHaller DF Deq --------Deq*-------- Loss Coefficients --------Mach------ H/C S/C T/C H/T

Lieblein Koch/Smith Endwall Profile relative critical

rotor 0.739 0.450 1.648 1.707 1.858 0.0114 0.0215 0.929 0.892 2.500 1.014 0.060 0.552

stator 0.808 0.367 1.488 1.583 1.650 0.0070 0.0209 0.729 0.888 3.500 1.495 0.060 0.598

Nr.blades --------------------------Blade angles-------------------------

inlet outlet incidence deviation camber stagger turning

rotor 28.000 54.542 24.696 -2.748 9.332 29.846 36.871 17.767

stator 31.000 49.051 5.853 -7.742 17.108 43.198 19.710 18.348

===== STAGE 2 =====

=================================================================================================================================================



1.363 0.550 122 0.381 0.634 31.965 6.857 0.928 0.925 0.927 0.410 0.404 1.015



1 0.507 0.421 0.310 290.70 185.19 201.15 281.63 78.519 22.976 48.885

2 0.500 0.421 0.321 290.70 183.34 263.59 209.48 189.374 45.927 28.927

3 0.494 0.421 0.332 N/A 181.51 198.32 N/A 79.917 23.752 N/A



1 1.438 1.147 47.72 27.62 47.993 61.301 27.762 1005.827 1.400 1.327 1.512e-005 347.75

2 1.978 1.379 79.69 45.23 80.219 65.556 45.480 1006.834 1.399 1.508 1.392e-005 357.71

3 1.960 1.605 79.69 60.19 80.219 68.158 60.553 1007.849 1.399 1.677 1.298e-005 365.95



rotor 0.744 0.450 1.645 1.713 1.836 0.0121 0.0221 0.810 0.892 2.390 0.985 0.060 0.627

stator 0.752 0.452 1.643 1.717 1.818 0.0071 0.0226 0.737 0.891 3.320 0.975 0.060 0.657



rotor 35.000 53.109 18.661 -4.224 10.266 34.448 31.661 19.957

stator 53.000 51.052 12.665 -5.125 11.087 38.387 26.734 22.175

===== STAGE 3 =====

=================================================================================================================================================



1.316 0.550 122 0.371 0.621 31.043 6.374 0.925 0.922 0.927 0.408 0.406 1.006



1 0.494 0.421 0.332 290.70 181.51 198.32 278.16 79.917 23.764 49.268

2 0.489 0.421 0.339 290.70 179.69 259.97 207.04 187.865 46.274 29.781

3 0.484 0.421 0.346 N/A 177.90 195.60 N/A 81.319 24.558 N/A



1 1.960 1.605 79.69 60.19 80.219 68.158 60.553 1007.849 1.399 1.677 1.298e-005 365.95

2 2.601 1.888 110.73 77.30 111.599 72.091 77.808 1009.200 1.398 1.875 1.206e-005 375.12

3 2.579 2.159 110.73 91.82 111.599 74.532 92.469 1010.518 1.397 2.059 1.133e-005 382.71



rotor 0.744 0.450 1.645 1.711 1.834 0.0126 0.0230 0.760 0.892 2.290 1.001 0.060 0.683

stator 0.752 0.453 1.644 1.717 1.818 0.0075 0.0233 0.693 0.891 3.140 0.988 0.060 0.705



rotor 39.000 54.290 19.164 -5.022 10.617 35.125 31.705 19.486

stator 59.000 52.069 13.198 -5.795 11.360 38.870 26.838 21.715

===== STAGE 4 =====

=================================================================================================================================================



1.279 0.550 122 0.361 0.609 30.106 5.959 0.922 0.919 0.926 0.406 0.407 0.999



1 0.484 0.421 0.346 290.70 177.90 195.60 274.75 81.319 24.566 49.648

2 0.480 0.421 0.351 290.70 176.12 256.41 204.71 186.360 46.618 30.644

3 0.476 0.421 0.357 N/A 174.36 192.99 N/A 82.728 25.378 N/A



1 2.579 2.159 110.73 91.82 111.599 74.532 92.469 1010.518 1.397 2.059 1.133e-005 382.71

2 3.324 2.493 140.84 108.42 142.135 78.205 109.261 1012.224 1.396 2.274 1.061e-005 391.19

3 3.298 2.810 140.84 122.49 142.135 80.492 123.513 1013.840 1.395 2.473 1.002e-005 398.21



rotor 0.745 0.450 1.644 1.708 1.832 0.0133 0.0239 0.718 0.892 2.180 1.020 0.060 0.724

stator 0.753 0.454 1.645 1.716 1.819 0.0080 0.0237 0.655 0.891 2.960 1.003 0.060 0.740



rotor 43.000 55.395 19.678 -5.747 10.966 35.717 31.789 19.003

stator 63.000 53.026 13.744 -6.407 11.634 39.282 26.977 21.240

===== STAGE 5 =====

=================================================================================================================================================



1.248 0.550 122 0.351 0.597 29.158 5.618 0.919 0.916 0.925 0.406 0.410 0.990



1 0.476 0.421 0.357 290.70 174.36 192.99 271.39 82.728 25.383 50.025

2 0.474 0.421 0.360 290.70 172.61 252.92 202.48 184.862 46.962 31.515

3 0.470 0.421 0.364 N/A 170.89 189.80 N/A 82.600 25.795 N/A



1 3.298 2.810 140.84 122.49 142.135 80.492 123.513 1013.840 1.395 2.473 1.002e-005 398.21

2 4.148 3.196 169.99 138.58 171.825 83.938 139.841 1015.880 1.394 2.703 9.446e-006 406.06

3 4.117 3.563 169.99 152.32 171.825 86.110 153.813 1017.784 1.393 2.915 8.970e-006 412.63



rotor 0.746 0.450 1.644 1.705 1.831 0.0140 0.0245 0.682 0.892 2.070 1.042 0.060 0.755

stator 0.750 0.460 1.656 1.724 1.830 0.0085 0.0243 0.623 0.892 2.790 0.991 0.060 0.767



rotor 46.000 56.448 20.189 -6.423 11.326 36.259 31.895 18.510

stator 68.000 53.722 14.152 -6.760 11.643 39.570 27.177 21.167

===== STAGE 6 =====

=================================================================================================================================================



1.231 0.550 122 0.351 0.585 29.028 5.282 0.919 0.916 0.924 0.412 0.419 0.985



1 0.470 0.421 0.364 290.70 170.89 189.80 269.27 82.600 25.797 50.608

2 0.467 0.421 0.368 290.70 169.18 250.50 199.63 184.734 47.517 32.061

3 0.464 0.421 0.372 N/A 167.49 186.69 N/A 82.477 26.218 N/A



1 4.117 3.563 169.99 152.32 171.825 86.110 153.813 1017.784 1.393 2.915 8.970e-006 412.63

2 5.102 4.017 199.02 168.34 201.516 89.345 170.142 1020.186 1.392 3.168 8.481e-006 420.14

3 5.066 4.445 199.02 182.00 201.516 91.393 184.088 1022.382 1.391 3.400 8.078e-006 426.41



rotor 0.741 0.450 1.647 1.709 1.834 0.0146 0.0246 0.653 0.892 1.960 1.009 0.060 0.782

stator 0.745 0.461 1.661 1.729 1.835 0.0090 0.0244 0.596 0.892 2.610 0.957 0.060 0.795



rotor 51.000 57.187 20.958 -6.579 11.103 36.229 32.494 18.547

stator 76.000 54.356 14.858 -6.839 11.360 39.498 27.768 21.298

===== STAGE 7 =====

=================================================================================================================================================



1.215 0.550 122 0.351 0.573 28.883 4.987 0.918 0.916 0.923 0.419 0.428 0.978



1 0.464 0.421 0.372 290.70 167.49 186.69 267.22 82.477 26.217 51.188

2 0.462 0.421 0.375 290.70 165.81 248.14 196.85 184.611 48.071 32.612

3 0.460 0.421 0.378 N/A 164.15 183.66 N/A 82.358 26.648 N/A



1 5.066 4.445 199.02 182.00 201.516 91.393 184.088 1022.382 1.391 3.400 8.078e-006 426.41

2 6.199 4.972 227.90 197.95 231.206 94.441 200.419 1025.112 1.389 3.674 7.660e-006 433.59

3 6.158 5.466 227.90 211.52 231.206 96.380 214.341 1027.564 1.388 3.926 7.315e-006 439.58



rotor 0.737 0.450 1.650 1.712 1.837 0.0152 0.0248 0.627 0.893 1.860 0.977 0.060 0.806

stator 0.740 0.461 1.665 1.733 1.839 0.0095 0.0245 0.572 0.892 2.430 0.923 0.060 0.817



rotor 57.000 57.864 21.748 -6.676 10.864 36.116 33.130 18.576

stator 83.000 54.932 15.583 -6.861 11.064 39.349 28.396 21.423

===== STAGE 8 =====

=================================================================================================================================================



1.202 0.550 122 0.351 0.562 28.727 4.740 0.918 0.916 0.923 0.425 0.438 0.971



1 0.460 0.421 0.378 290.70 164.15 183.66 265.24 82.358 26.644 51.765

2 0.457 0.421 0.380 290.70 162.51 245.86 194.14 184.492 48.624 33.166

3 0.455 0.421 0.383 N/A 160.89 180.69 N/A 82.244 27.083 N/A



1 6.158 5.466 227.90 211.52 231.206 96.380 214.341 1027.564 1.388 3.926 7.315e-006 439.58

2 7.450 6.073 256.63 227.39 260.896 99.274 230.672 1030.576 1.386 4.224 6.955e-006 446.47

3 7.402 6.638 256.63 240.86 260.896 101.120 244.572 1033.242 1.385 4.496 6.657e-006 452.21



rotor 0.732 0.450 1.653 1.716 1.840 0.0159 0.0249 0.603 0.893 1.750 0.945 0.060 0.827

stator 0.735 0.462 1.669 1.738 1.844 0.0102 0.0245 0.551 0.893 2.250 0.889 0.060 0.836



rotor 62.000 58.484 22.553 -6.719 10.613 35.931 33.800 18.599

stator 90.000 55.455 16.323 -6.830 10.759 39.131 29.059 21.542

===== STAGE 9 =====

=================================================================================================================================================



1.190 0.550 122 0.351 0.551 28.561 4.530 0.917 0.915 0.922 0.431 0.447 0.964



1 0.455 0.421 0.383 290.70 160.89 180.69 263.32 82.244 27.076 52.339

2 0.453 0.421 0.385 290.70 159.28 243.65 191.50 184.378 49.177 33.724

3 0.452 0.421 0.387 N/A 157.69 177.79 N/A 82.130 27.523 N/A



1 7.402 6.638 256.63 240.86 260.896 101.120 244.572 1033.242 1.385 4.496 6.657e-006 452.21

2 8.866 7.332 285.19 256.64 290.587 103.883 260.904 1036.483 1.383 4.818 6.345e-006 458.82

3 8.811 7.973 285.19 270.01 290.587 105.650 274.782 1039.318 1.382 5.111 6.086e-006 464.34



rotor 0.727 0.450 1.656 1.720 1.844 0.0168 0.0250 0.582 0.893 1.640 0.914 0.060 0.844

stator 0.730 0.462 1.674 1.743 1.849 0.0109 0.0245 0.531 0.893 2.070 0.856 0.060 0.852



rotor 68.000 59.053 23.369 -6.714 10.355 35.684 34.497 18.615

stator 96.000 55.925 17.077 -6.747 10.446 38.847 29.754 21.654

===== STAGE 10 =====

=================================================================================================================================================



1.180 0.550 122 0.351 0.540 28.390 4.338 0.916 0.914 0.922 0.435 0.455 0.956



1 0.452 0.421 0.387 290.70 157.69 177.79 261.47 82.130 27.513 52.910

2 0.450 0.421 0.389 290.70 156.11 241.50 188.94 184.264 49.729 34.286

3 0.449 0.421 0.390 N/A 154.55 175.76 N/A 83.715 28.456 N/A



1 8.811 7.973 285.19 270.01 290.587 105.650 274.782 1039.318 1.382 5.111 6.086e-006 464.34

2 10.458 8.759 313.58 285.70 320.277 108.296 291.115 1042.737 1.380 5.457 5.813e-006 470.70

3 10.397 9.475 313.58 298.83 320.277 109.989 304.830 1045.668 1.379 5.767 5.588e-006 475.95



rotor 0.723 0.450 1.659 1.724 1.847 0.0177 0.0251 0.563 0.894 1.540 0.884 0.060 0.859

stator 0.728 0.456 1.666 1.737 1.842 0.0117 0.0244 0.513 0.893 1.890 0.854 0.060 0.866



rotor 73.000 59.575 24.195 -6.665 10.091 35.380 35.220 18.623

stator 97.000 56.686 18.031 -6.958 10.425 38.655 30.401 21.272

===== STAGE 11 =====

=================================================================================================================================================



1.166 0.550 122 0.343 0.528 27.574 4.207 0.913 0.911 0.921 0.435 0.459 0.948



1 0.449 0.421 0.390 290.70 154.55 175.76 258.32 83.715 28.443 53.253

2 0.448 0.421 0.392 290.70 152.69 238.74 186.55 183.524 50.239 35.065

3 0.447 0.421 0.393 N/A 150.86 173.29 N/A 85.258 29.488 N/A



1 10.397 9.475 313.58 298.83 320.277 109.989 304.830 1045.668 1.379 5.767 5.588e-006 475.95

2 12.193 10.336 341.16 314.07 349.291 112.541 320.793 1049.134 1.377 6.128 5.354e-006 481.94

3 12.123 11.123 341.16 326.91 349.291 114.196 334.277 1052.101 1.376 6.453 5.159e-006 486.92



rotor 0.722 0.450 1.660 1.723 1.847 0.0190 0.0254 0.543 0.894 1.430 0.891 0.060 0.872

stator 0.726 0.458 1.669 1.738 1.846 0.0129 0.0248 0.495 0.894 1.710 0.854 0.060 0.877



rotor 74.000 60.238 24.895 -6.986 10.170 35.343 35.581 18.187

stator 97.000 57.396 19.109 -7.157 10.379 38.287 31.096 20.751

===== STAGE 12 =====

=================================================================================================================================================



1.154 0.550 122 0.335 0.515 26.769 4.095 0.909 0.908 0.921 0.436 0.464 0.939



1 0.447 0.421 0.393 290.70 150.86 173.29 254.88 85.258 29.473 53.709

2 0.446 0.421 0.394 290.70 148.75 235.63 183.80 182.741 50.855 35.972

3 0.445 0.421 0.395 N/A 146.67 170.40 N/A 86.751 30.622 N/A



1 12.123 11.123 341.16 326.91 349.291 114.196 334.277 1052.101 1.376 6.453 5.159e-006 486.92

2 14.064 12.058 367.93 341.70 377.629 116.669 349.869 1055.567 1.374 6.827 4.957e-006 492.58

3 13.985 12.914 367.93 354.23 377.629 118.291 363.111 1058.532 1.372 7.166 4.787e-006 497.32



rotor 0.721 0.450 1.660 1.722 1.848 0.0205 0.0258 0.523 0.894 1.320 0.895 0.060 0.881

stator 0.723 0.459 1.674 1.740 1.852 0.0143 0.0252 0.478 0.894 1.540 0.850 0.060 0.886



rotor 74.000 60.962 25.776 -7.253 10.196 35.187 36.116 17.738

stator 95.000 58.155 20.344 -7.300 10.277 37.810 31.950 20.233

===== STAGE 13 =====

=================================================================================================================================================



1.143 0.550 122 0.327 0.500 25.976 4.013 0.905 0.903 0.920 0.437 0.472 0.927



1 0.445 0.421 0.395 290.70 146.67 170.40 251.21 86.751 30.604 54.279

2 0.444 0.421 0.396 290.70 144.32 232.20 180.73 181.908 51.573 37.010

3 0.443 0.421 0.397 N/A 142.01 167.16 N/A 88.188 31.861 N/A



1 13.985 12.914 367.93 354.23 377.629 118.291 363.111 1058.532 1.372 7.166 4.787e-006 497.32

2 16.069 13.921 393.90 368.59 405.292 120.700 378.332 1061.958 1.371 7.552 4.611e-006 502.67

3 15.979 14.845 393.90 380.80 405.292 122.304 391.320 1064.890 1.369 7.903 4.462e-006 507.18



rotor 0.719 0.450 1.662 1.721 1.850 0.0223 0.0262 0.505 0.894 1.210 0.895 0.060 0.890

stator 0.720 0.461 1.678 1.743 1.858 0.0161 0.0256 0.462 0.894 1.360 0.842 0.060 0.893



rotor 73.000 61.752 26.836 -7.474 10.174 34.917 36.820 17.269

stator 90.000 58.962 21.737 -7.389 10.124 37.225 32.960 19.712

===== STAGE 14 =====

=================================================================================================================================================



1.133 0.550 122 0.319 0.484 25.195 3.952 0.900 0.899 0.919 0.439 0.481 0.912



1 0.443 0.421 0.397 290.70 142.01 167.16 247.34 88.188 31.840 54.960

2 0.443 0.421 0.397 290.70 139.45 228.51 177.42 181.019 52.390 38.185

3 0.442 0.421 0.398 N/A 136.94 163.64 N/A 89.577 33.210 N/A



1 15.979 14.845 393.90 380.80 405.292 122.304 391.320 1064.890 1.369 7.903 4.462e-006 507.18

2 18.199 15.922 419.10 394.72 432.278 124.655 406.170 1068.246 1.368 8.299 4.308e-006 512.25

3 18.097 16.909 419.10 406.61 432.278 126.256 418.889 1071.119 1.366 8.660 4.177e-006 516.53



rotor 0.717 0.450 1.663 1.721 1.852 0.0242 0.0266 0.488 0.894 1.110 0.892 0.060 0.896

stator 0.716 0.462 1.684 1.746 1.865 0.0185 0.0260 0.446 0.895 1.180 0.830 0.060 0.899



rotor 72.000 62.613 28.073 -7.653 10.112 34.540 37.690 16.775

stator 84.000 59.821 23.279 -7.431 9.931 36.542 34.119 19.180

===== STAGE 15 =====

=================================================================================================================================================



1.123 0.550 122 0.311 0.466 24.427 3.983 0.893 0.892 0.918 0.448 0.502 0.892



1 0.442 0.421 0.398 290.70 136.94 163.64 243.32 89.577 33.189 55.749

2 0.442 0.421 0.398 290.70 134.21 224.59 173.92 180.083 53.305 39.496

3 0.441 0.421 0.399 N/A 131.52 157.16 N/A 86.030 33.189 N/A



1 18.097 16.909 419.10 406.61 432.278 126.256 418.889 1071.119 1.366 8.660 4.177e-006 516.53

2 20.445 18.050 443.52 420.11 458.588 128.576 433.367 1074.383 1.365 9.064 4.043e-006 521.35

3 20.327 19.134 443.52 432.08 458.588 130.239 446.238 1077.276 1.364 9.446 3.923e-006 525.57



rotor 0.715 0.450 1.665 1.721 1.855 0.0266 0.0271 0.471 0.895 1.000 0.886 0.060 0.901

stator 0.700 0.486 1.735 1.790 1.916 0.0224 0.0269 0.431 0.896 1.000 0.715 0.060 0.903



rotor 69.000 63.546 29.479 -7.797 10.018 34.068 38.715 16.253

stator 87.000 59.314 24.486 -6.009 8.704 34.828 35.891 20.116

===== OUTLET GUIDE VANE=====

=================================================================================================================================================

------radius------- Velocities

tip rms hub Cm

0.441 0.421 0.399 131.52

---Pressure--- --Temperatures-- ----Enthalpy---- Entropy Cp Kappa rho Visc a


20.260 19.422 443.52 435.51 458.588 131.183 449.939 1078.105 1.363 9.541 3.896e-006 526.77



0.837 0.450 1.590 1.688 1.689 0.0289 0.0270 0.299 0.888 1.000 1.048 0.060 0.903

Nr.blades --------------------------Blade angles----------------

inlet outlet incidence deviation camber stagger

60.000 44.211 -17.624 -11.022 17.624 61.835 2.272

Axial Flow Compressor Mean Line Design

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