AFT Arrow Seminar Week of 22 May, 2017 - Prode AFT Fathom 7 and Arrow 4 8 Intro - Additional...

AFT Arrow SeminarWeek of 22 May, 2017

Introduction

Overview of Seminar

AFT ARROWA1. Overview of AFT ArrowA2. Fundamental Equations of Compressible FlowA3. Demonstration Problem - Determining Delivery ConditionsA4. Understanding Solution Control OptionsA5. AFT Arrow Hands-On ModelingA6. Troubleshooting AFT Arrow Models A7. The Five Primary WindowsA8. Pipe and Junction Details A9. Special TopicsA10. Verification of SolutionsA11. Using Scenario ManagerA12. Customizing Arrow and Using Databases A13. Introduction to AFT Arrow ModulesA14. More AFT Arrow Hands-On Modeling

Intro -

About Applied Flow Technology

Applied Flow Technology (AFT), founded in 1993, is a world leader in providing high quality software to analyze flows, pressures and transients in systems with pipes, pumps and valves

Customers in 70+ countries Representatives in 32 locations around the world

1

Intro -

AFT Fathom 9

Models incompressible network pipe systems Liquid and low velocity gas systems

Models open and closed systems Models systems that are pressure, gravity or pump driven Models heat transfer and system energy balance Offers broad range of innovative reporting features

Printed output is of report quality Offers customizable component and property databases

Cost calculations Rheological data handling to support non-Newtonian fluids

2

Intro -

AFT Fathom Add-On Modules

XTS eXtended Time Simulation Simulate dynamic behavior of systems over time Models infinite and open and closed finite tanks of constant and

varying cross section Supports user defined time and event transients of pumps, valves

and other components GSC Goal Seek & Control

Automatically determines input variables that will yield specified output values

Extends Fathoms control simulation capabilities to include remote sensing

SSL Settling Slurry simulation Simulates settling slurry behavior Simulates pump performance degradation

3

Intro -

AFT Arrow 6

Models compressible network pipe systems High to low velocity gas systems High to low pressures

Models open and closed systems Accurately models

Real gases Heat transfer Highly compressible (sonic and near sonic) systems

Balances flow and energy throughout the system Offers broad range of innovative reporting features Offers customizable component and property databases Includes high accuracy steam/water properties to ASME

4

Intro -

AFT Arrow Add-On Module

GSC Goal Seek & Control Automatically determines input variables that will yield specified

output values Extends Arrows control simulation capabilities to include remote

sensing

5

Intro -

AFT Impulse 6

Models waterhammer/surge flow in pipe networks Models system transients caused by

Sudden valve closures Pump startups and shutdowns including pump inertia effects Relief valve cracking Events defined within the system (e.g. flow, pressure, etc.)

Includes modeling of Control and relief valves, vacuum breaker valves, pumps,

accumulators and surge tanks Includes a steady-state solver to determine initial conditions Calculates unbalanced transient forces

Forces can be graphed or exported as Force/Time data files Can also import AFT Fathom models

6

Intro -

AFT Impulse Add-On Module

SSL Settling Slurry simulation Simulates settling slurry behavior Simulates pump performance degradation

7

Intro -

AFT Mercury 7AFT Titan 4

Models and designs network pipe systems Combines a powerful hydraulic solver and flexible graphical

interface with an advanced optimization engine Automatically selects best pipe and component sizes to minimize

initial or life cycle cost, size or weight using IntelliFlow

Ability to apply multiple constraints to pipes and junctions Cost optimization may include;

non-recurring costs (materials and installation) recurring costs (energy and maintenance) including time varying

cost (energy costs varying with time) Offers customizable engineering and cost databases Includes powerful modeling and output capabilities

of AFT Fathom 7 and Arrow 48

Intro -

Additional Software Products

Chempak Property Database Property database of ~700 fluids Ability to define static pre-mixtures Dynamic mixing capability in Arrow

Chempak Viewer 2.0 & Chempak Add-in (for Excel) Viewer allows use of Chempak as a stand alone application Add-in makes all of the Chempak functions accessible within an

Excel spreadsheet SteamCalc 2.0

High accuracy ASME steam/water library for Windows and Excel

9

Intro -

Product Applications

AFT products are being successfully applied to a broad range of industrial systems: Power generation systems Chemical and petrochemical systems Oil and gas production, transportation, refining and delivery Automotive systems Aerospace systems Air conditioning and refrigeration systems Pulp and paper processing Fire suppression Water and Wastewater treatment plant design Mining processing and support systems Municipal water distribution

10

Intro -

AFT Flow Expert Package

Provides consulting services beyond typical technical support requests on the installation, upgrade assistance, and functionality of AFT software.

Access to a consulting engineer assigned as your primary point of contact.

Package Options: Blocks of 5 hours, 10 hours and 20 hours Typical ways to use your hours:

Receive online training on specific topics of your choice Request help on model results interpretation Get a second opinion of your assumptions, modeling choices

and reports

11

Intro -

AFT Flow Expert Package (2)

Additional ways to use your hours: Have an expert double check your modeling input and point out

common modeling mistakes or suggest better ways to model the desired behavior

Receive guidance in how to model pumps and pump-system interaction, relief valves and relief systems, surge suppression equipment, slurry pipelines, system transients, and anything having to do with flow in pipe systems

Discuss with an expert alternative solutions for hydraulic problems

Help launch AFT software within your company and reduce your learning curve

Help new hires get acquainted with AFT software

12

A1. Overview of AFT Arrow

Overview of Seminar


Nomenclaturea sonic speed

A cross-sectional flow area of a pipe

C d discharge coefficientcp specific heat, constant pressure

cv specific heat, constant volume

D diameter of a pipe

e internal energy

f friction factor

F Force

F f Parameter in Section A2

F g Parameter in Section A2

F To Parameter in Section A2

F Parameter in Section A2

g gravitational constant

h internal convection coefficient

h enthalpy, static

ho enthalpy, stagnation

k thermal conductivity

K loss factor

L length of a pipem mass flow rate

M Mach Number

n constant

Nu Nusselt number

P pressure, static

Ph heated perimeter

Po pressure, stagnation

Pw wetted perimeter

Pr Prandtl number

q heat rate to a pipe

Q volumetric flow rate

q heat flux

r radius

r relaxation

R gas constant

Re Reynolds number

s fan speed

s entropy

T temperature, static

To temperature, stagnation

U overall heat transfer coefficient

v specific volume

NomenclatureV volume

V velocity

w work

x distance along pipe centerline

z elevation

Z compressibility factor

, , angle diameter ratio roughness specific heat ratio dynamic viscosity shear stress rotational velocity

Subscripts

1 location 1 in pipe

2 location 2 in pipe

i junction at which solution is sought

j junctions with pipes connecting to junction i

o stagnation infinity, far away, ambient

A1 -

AFT Arrow General Description

General purpose pipe network compressible flow analysis Drag-and-drop interface Calculates pressure drop, flow distribution and energy in pipe

networks Solves 5 equations for each pipe:

Continuity (Mass) Equation Momentum Equation Energy Equation Equation of State Mach Number

1

A1 -

AFT Arrow General Description (2)

Implements modified Newton-Raphson matrix method to solve network

Can model systems in any generalized configuration Open or closed systems Branching systems Looping systems

Can model sonic choking and heat transfer English and SI units supported

2

A1 -

Components That Can Be Modeled

Branching section (up to 25 pipes) Known pressure or flow boundaries Compressors and fans

Compressor/fan curves follow a polynomial equation Pressure and flow control valves Relief valves and check valves Heat exchanger pressure drop and heat transfer General fittings and components where the resistance curve

follows a polynomial relationship

3

A1 -

Engineering Limitations

No practical software limit to model size Flow is steady-state and one-dimensional No limit on number of fittings (i.e., additional losses) No limit on number of compressor/fans, control valves, etc. No limit on number of custom components, fluids or pipe

materials

4

A1 -

Arrow 6 Startup Window

5

A1 -

Primary Windows

The AFT Arrow modeling process flows through five Primary Windows Workspace Model Data Output Visual Report Graph Results

The Primary Windows offer a mixture and graphical and text-based features to assist in the modeling process

Tabbed Primary Windows allow for easier navigation Robust usage of dual monitors is supported

Can drag the Primary Window tabs into their own separate window

6

A1 -

Primary Window Process Flow

7

Graph Results

Visual Report

Workspace Output

Model Data

A1 -

Workspace

Multiple features available with Quick Access Panel Can pin Quick Access Panel to the Workspace or minimize with

thumbtack to allow for more Workspace area

8

These icons represent different components

This tool is used to draw new pipes

This tool will add annotation to the workspace

Minimize Quick Access Panel with thumbtack

Quick Access Panel

A1 -

Quick Access Panel Activate Modules

Ability to activate GSC, APS, and ANS Modules

9

A1 -

Workspace - Editing Features

Cut, copy, paste, delete, duplicate and undo features supported

Workspace can be sized to fit the model You can zoom out to see a larger area Objects can be selected as a group in several ways

Selecting the components by dragging the mouse over them Using the SHIFT key while clicking on the objects Using Select Flow Path on the Edit menu Using the Select Special tool on the Edit menu Using Groups / Select on the Edit menu Using the Select All feature

10

A1 -

Workspace Editing Features (2)

The Reference Flow Direction of a pipe can be changed The selected objects can be renumbered

Manually Renumber Automatic Renumber Wizard Renumber Increment

The Find tool will move the Workspace window to show a pipe or junction

11

A1 -

Workspace - Platform for Data Entry

All pipe and junction objects placed onto the Workspace are interactive

To open the Properties window for data entry, just double-click the graphical object Alternatively, you can select the object by clicking on it once and

then press the Enter key Or you can select the object by clicking on it once and then click

on the Open Pipe/Jct Window button on the Toolbar The Properties windows are the primary manner in which

component data is entered The Global Pipe Edit and Global Junction Edit window can

speed up data entry

12

A1 -

Workspace - Reporting

The Workspace image can be printed on printers and plotters Print Preview allows page customization

The image can be sized on the page A company logo and custom text can be added

13

A1 -

Model Data Window

Model Data is broken into three sections General Data Pipe Data Junction Data

Each section can be re-sized or collapsed allowing the user to focus on any of the sections

User can select all or portions of the Model Data Window content for printing Print format window allows customizing of content User can also select the font

14

A1 -

Model Data Window (2)

With a Workspace printout and the complete Model Data printout, the input can be printed in its entirety

Properties windows for data entry can be opened by double-clicking the far left column

15

A1 -

Output Window

The Output window is the primary vehicle for communicating the results of an analysis in text form

Output Window is broken into three sections General Results Pipe Results Junction Results


Each section contains tabs to permit quick viewing of output by type

16

A1 -

Output Window (2)

User can select all or portions of the Output Window content for printing Print format window allows customizing of content User can also select the font

User can sort output according to any of the columns for quick review of data extreme maximums and minimums

Output Window content is specified by Output Control Window

17

A1 -

Visual Report Window

Visual Report allows user to display input and output results together with pipe system image

18

A1 -

Graph Results Window

The Graph Results Window allows creation of full-featured Windows graphs

19

A2. Fundamental Eqns. of Compressible Flow

Overview of Seminar


A2 -

Introduction

AFT Arrow uses a modified Newton-Raphson Method to solve the flow distribution in a pipe network

This method is similar to that used in AFT Fathom, but more difficult to implement

There are no standard methods available to solve the full compressible flow equations for pipe networks

1

A2 -

Basic Laws of Incompressible Pipe Flow

Mass Conservation

Momentum Equation (Bernoulli, assuming incompressible)

The velocity (dynamic) pressure and static pressure can be combined into the total pressure, and the solution is then for total pressure Therefore, the momentum equation becomes

2

AVm =

lossPghVPghVP +++=++ 22

2212

11 21

21

lossoo PghPghP ++=+ 22,11,

A2 -

Law of Friction (Incompressible Flow)

Traditional method of friction loss calculation uses the Darcy-Weisbach friction factor, f

The friction factor is not a constant, but a function of the pipe wall characteristics and the Reynolds number

3

= 2

21 V

DLfPloss

A2 -

Law of Friction (Incompressible Flow) (2)

AFT Fathom uses the iterative Colebrook-White correlation for turbulent flow and the traditional laminar flow equation when laminar

Special friction models available for pulp and paper stock and crude oil

4

2

Re35.9log214.1

+=

fDf ( )4000Re >

Re64

=f ( )2300Re

A2 -

Modified Form for Law of Friction

Basic law (incompressible flow)

Substituting mass flow rate definition

Defining new term, where R is a pipe resistance

Bernoullis equation then becomes

5

= 2

21 V

DLfPloss

=

2

21

Am

DLfPloss

2mRPloss =

= 22

1AD

LfR

222,11, mRghPghP oo ++=+

A2 -

Balancing Mass at Branches

Applying law of mass conservation to a branching section

Substituting yields the following equation to be solved for every branch, i, (incompressible flow)

where sgn = 1 depending on flow direction

6

=

=n

jijm

10

( )( ) ( )=

=

++

n

j ij

ijiojoijiojo R

hhgPPhhgPP

1

5.0

,,,, 0sgn

A2 -

Balancing Mass at Branches (2)

The objective is to find all of the P values that satisfy the above equation applied to every branch

We will then have a solution for two unknowns: pressure at all junctions mass flow rate in all pipes

7

( )( ) ( )=

=

++

n

j ij

ijiojoijiojo R

hhgPPhhgPP

1

5.0

,,,, 0sgn

A2 -

Solving the Equations

We need to solve as many equations as there are flow splits All of the equations are non-linear AFT Fathom uses the Newton-Raphson Method to solve the

system of equations Newton-Raphson is an iterative method used to solve for roots of

equations

8

A2 -

Solving the Equations (2)

Initially the pipe flow rates are not known so an error, F, exists at each branch (incompressible flow)

The objective is to use the Newton-Raphson Method to drive all of the F errors to zero (within some tolerance)

9

( )( ) ( )=

=

++

n

ji

ij

ijiojoijiojo FR

hhgPPhhgPP

1

5.0

,,,,sgn

A2 -

The Newton-Raphson Method

The procedure for applying Newton-Raphson to a single equation is as follows:

1) Take a guess at the solution to function F2) Calculate an improved guess using the following equation:

3) Substitute the improved guess back into the above equation until the change in x is small

10

( )( )i

iii xF

xFxx'1

=+

x

F(x)

xi

F(xi)

xi+1

-F'(xi)

A2 -

Solving the System (Incompressible Flow) When applied to a system of equations with P as the

unknown, Newton-Raphson looks as follows

where P is the vector of pressures and JF is the Jacobian matrix of error function derivatives - both of a size, n, which is the number of branches (i.e., equations in the system)

=

no

n

o

n

o

n

nooo

nooo

F

PF

PF

PF

PF

PF

PF

PF

PF

PF

J

,2,1,

,

2

2,

2

1,

2

,

1

2,

1

1,

1

11

= FJPP Foldonewo1

,,

A2 -

Derivative Terms in Jacobian

The diagonal derivative terms in the Jacobian can be calculated analytically (incompressible flow)

The off-diagonal terms can also be calculated analytically (incompressible flow)

12

( )( ) ( )=

++=

n

j ij

ijiojoijiojoi R

hhgPPhhgPPF

1

5.0

,,,,sgn

( )( )=

+

=

n

jijiojo

iji

i hhgPPRP

F1

5.0

,,5.05.0

( )( ) 5.0,,5.05.0

+

=

ijiojoiji

i hhgPPRP

F

A2 -

Solving the Matrix (Incompressible Flow)

Rather than inverting the Jacobian matrix, it is usually faster to solve a linear system of equations as follows

We need to solve for the values in vector, z, that satisfy the above

13

= zPP oldonewo ,,

= FJz F1

= FzJ F

A2 -

Solving the Matrix (Incompressible Flow) (2) Use Gaussian Elimination to solve for z

By multiple substitutions, we progressively eliminate terms in JFand eventually obtain the identity matrix, where all terms are zero except the diagonal, which is unity

We then have the solution for z, which can be substituted back into the original equation at the top to improve our guess for all of the pressures in the pressure vector

14

= zPP oldonewo ,,

A2 -

Test Problem #1 (Incompressible Flow)P = 175 psiah = 0 feet

P = 200 psiah = 0 feet 1 2

3

4

P = 160 psiah = 0 feet

h = 0 feet

pipe 1 pipe 2

pipe 3pipe f L (ft) D (in) Fluid

1 0.0219 100 4 Water @ 70F2 0.0156 75 4 Water @ 70F3 0.0180 125 6 Water @ 70F

Jct P (psia)1 2002 1753 160In this test problem, pipe

resistances can be calculated based on known friction factor (shown in the table) 15

A2 -

Test Problem #1 (Incompressible Flow) (2) To start the solution, we

need to guess P4, so guess 180 psia

Note: All pressures here are stagnation 16

( )[ ]=

=

n

j ij

ijij R

PPPPF

1

5.0

sgn

( )[ ] ( )[ ] ( )[ ]5.0

43

4343

5.0

42

4242

5.0

41

4141 sgnsgnsgn

+

+

=

RPP

PPR

PPPP

RPP

PPF

1489.277=F5.0

435.043

5.0425.0

42

5.0415.0

41

5.05.05.0'

+

+

= PPR

PPR

PPR

F

6139.18' =F( )( )old

oldoldnew PF

PFPP'

=

A2 -

Test Problem #1 (Incompressible Flow) (3)

17

Pj=4 Mpipe=1 Mpipe=2 Mpipe=3 F F'Iteration1234567

180.0000 115.3464 -78.9048 -313.5906 -277.1489 -18.6139165.1106 152.3476 110.9691 -158.5207 104.7960 -23.3027169.6078 142.1903 81.9409 -217.3503 6.7810 -21.2485169.9269 141.4418 79.4792 -220.9305 -0.0095 -21.3129169.9265 141.4429 79.4827 -220.9255 0.0000 -21.3128169.9265 141.4429 79.4827 -220.9255 0.0000 -21.3128169.9265 141.4429 79.4827 -220.9255 0.0000 -21.3128

P (psia), M (lbm/s)

A2 -

Whats Special About Compressible Flow? Compressible flow is defined as fluid flow where density

changes are significant Changing density has several important ramifications

Velocity changes in a pipe Velocity change is generally non-linear

Density depends on temperature so that flow is coupled to energy equation

Accelerating flow is limited to sonic velocity, thus sonic choking can become a dominant characteristic of the system

Sonic choking may occur in multiple locations

18

)( AVm =

A2 -

Whats Special About Compressible Flow? (2) All governing equations are strongly coupled

An accurate solution must address all aspects of the gas flow Pipe networks introduce an order of magnitude complexity

into compressible flow analysis

19

A2 -

Possible Methods of Analysis

Use incompressible flow methods Inherently inaccurate Large safety margins required Engineer is never sure of analysis results Sonic choking glossed over

Use simplified compressible flow pressure drop correlations Crane manual isothermal flow equation (Eqn. 1-6) , Weymouth,

Panhandle, etc. Thermal and real gas effects are ignored Cannot extend method to pipe networks Large safety margins required Engineer is never sure of analysis results Sonic choking glossed over

20

A2 -

Possible Methods of Analysis (2)

Use iterative spreadsheet or in-house software Usually based on simplified correlations Usually assumes ideal gas behavior and ideal energy process

(adiabatic or isothermal) Time consuming to use and difficult to interpret results Often developed by non-specialists in compressible flow

21

A2 -

Basic Problems With Traditional Methods

Engineer is never sure of analysis results Gases frequently are not ideal Gases frequently are not isothermal or adiabatic

In many cases engineers believe their analysis is better than it really is

Sheer quantity of important variables means that important data can be easily overlooked

Low quality analysis leads to higher costs and reduced safety Over-design costs more during construction & over the life-cycle Safe operation of design is jeopardized if analysis is not properly

performed Parallel flow pipe networks cannot be properly

analyzed22

A2 -

AFT Arrow Approach to Compressible Flow Solve all governing equations simultaneously Include all thermal and real gas effects Balance mass and energy throughout the network

Implement special flow and energy balance iterative methods Offer several solution methods to increase flexibility Encapsulate powerful solution method in an easy-to-use

graphical Windows interface

23

A2 -

Governing Equations of Compressible Flow Equations for each pipe

[1] Mass:

[2] Momentum:

[3] Energy:

[4] Equation of State:

[5] Mach Number:

d dVV

+ = 0

P Z RT=

MVZRT

=

dP VfD

dx VdV+ + =12

02 gdz+

m d h V q+

=

12

2 + gz

24

A2 -

Governing Equations of Compressible Flow (2) Equations for each junction

25

[6] Balance Mass:

[7] Balance Energy:

mijj

n

=

=1

0

m h Vij ij ijj

n

+

=

=

1

202

1

0

1

,

1

===

npipes

j

ijc

ngases

c

m

[8+] Balance Species:

A2 -

Stagnation vs. Static Properties

The static properties are the true thermodynamic properties: pressure, temperature, density, enthalpy, etc.

The stagnation properties are those that combine the thermodynamic properties with the fluid dynamic effects

Classic example is a pitot tube that is normal to the flow or pointed directly into flow

Static Pressure Stagnation Pressure

26

A2 -

Stagnation vs. Static Properties (2)

Compressible flow calculations are greatly aided by using stagnation properties Effects of flow area changes are inherently taken care of

In incompressible flow, the stagnation pressure is the static plus dynamic pressure

27

2

21 VPPo +=

A2 -

Stagnation vs. Static Properties (3)

In compressible flow the relationship is more complicated It can be shown that the incompressible case is a simplification

while the compressible case is the true equation

28

+= 2

211 M

TTo

( )12

211

+=

MPPo

2

2Vhho +=

A2 -

AFT Arrows Solution Methods

AFT Arrow offers six solution methods altogether Two methods are "lumped" methods

Lumped Adiabatic Lumped Isothermal These are not as accurate but solve much faster Cannot model heat transfer Cannot model elevation changes (usually this is not very

important)

29

A2 -

AFT Arrows Solution Methods (2)

Four methods are marching methods Length March Mach Number March Two hybrid methods based on these two These four methods are highly accurate but have longer run

times Can accurately model heat transfer, elevation changes and

rotating systems

30

A2 -

AFT Arrows Solution Methods (3)

The two lumped methods use traditional handbook methods to solve a single pipe

Mach Number March method is a marching method that is optimized for sonic and near sonic systems

Length March method is a marching method that works well at all velocities, but is not as accurate or reliable as Mach Number March method at near-sonic conditions

For many systems all six methods will work fine and will give similar results

31

A2 -

These methods have closed form solutions and can be found in textbooks

Adiabatic flow equation and integrated solution

Isothermal flow equation and integrated solution

20 24

22

12

11

1 dMMM

MdxDfL M

M

+

=

+

+

++

=

21

22

22

21

22

21

211

211

ln2

1111

M

M

M

M

MMDfL

( ) 20 4

22

1

1 dMM

MdxDfTL M

M

=

=2

1

22

21

22

21

ln

1

M

M

M

M

M

DfLT

Lumped Adiabatic & Isothermal - Single Pipe

32

A2 -

Length March: Single Pipe

Using substitution and calculus, the following equation can be derived:*

Integration of the above yields:

In this approach, each distance step, x2, allows calculation of a new P0,2 .

The solution is obtained by marching down each pipe until x2 = L.

33

+++=

2 sin2 ZRT

dxgdZ

dZDfdx

TdTM

PdP

o

o

o

o

( ) ( )

+++= 1212

1

2

1

2

1,

2,2

1,2,sinlnlnln

2exp

TZRxxg

Dxxf

ZZ

TTMPP

o

ooo

* See AFT Arrow Help System topic Length March Method for complete derivation

Flow

1 2

A2 -

Mach Number March: Single Pipe

Using substitution and calculus, the following equation can be derived:*

where:

34

Flow

1 20sin2

2=

+ gf

o

oT ZRT

dxgFDfdxFdF

ZdZ

TdTF

M

dMo

F f = 2

22

12

11

M

MM

+

FTo =( )

2

22

12

111

M

MM

++

=( )

2

22

12

111

M

MM

+

F F g = 2

2

12

112

M

M

+

* See AFT Arrow Help System Topic Mach Number March Method for complete derivation

A2 -

Mach Number March: Single Pipe (2)

Integration of the above yields:*

By selecting a target Mach number M2 for each step, one can march down a pipe to calculate the corresponding x2 distance.

35

+

+

+=sin

lnlnlnln12

12

21

22

121

2

gf

o

oTo

TZRgF

DfF

FZZ

T

TF

M

M

xx

Flow

1 2

* See AFT Arrow Help System Topic Mach Number March Method for complete derivation

A2 -

Tying Things Together - Solving Networks To solve the network, energy and mass flow must balance at

each branching section AFT Arrow employs a modified Newton-Raphson method to

solve the mass flow balance Solves the non-linear flow equations using matrix techniques Similar to incompressible network solution method

Energy equation is linear and is solved by multiple substitution and iteration method

36

A2 -

Compressible Flow Solution Difficulties

Not possible to analytically calculate the derivative terms Pressure drop also depends on energy transfer Velocity and friction factors vary along pipe Negative pressures cannot be allowed Sonic choking Result is that AFT Arrow has to iterate much more than AFT

Fathom, leading to significantly longer run times

37

A2 -

Taking Care of Details

Sonic choking is accounted for by constant checking of Mach Numbers

Flow can choke at: A flow restriction (e.g., orifice) A flow expansion (area increase) The end of a pipe as it exits the system (endpoint choking)

Sonic choking is heavily influenced by friction effects and thermal effects AFT Arrow accounts for these effects when it solves the

equations simultaneously When flow is choked, special iterative techniques are

employed to converge on flow and pressure solutions

38

A2 -

Convergence

When the change in pressures, flow rate and temperature decrease to some small amount, the calculation is converged

Different criteria can be applied for identifying convergence Percentage change in result Absolute change in result

We will cover convergence in a later section

39

A2 -

Flow Rate and Enthalpy Updates

After the pressure solution is obtained a new flow solution and enthalpy are calculated

The new flows and enthalpies are then compared against the old flows and enthalpies

If the flow or enthalpy change too much it is updated and the pressure solution repeated

This whole procedure is repeated until flow, enthalpy and pressure updates are small

If mixing is modeled, a concentration update is also performed

40

A2 -

Solver Flow Chart

RecalculateConcentrations *

Start

RecalculateEnthalpies

Solve Junction Pressures

Yes

> Max Iterations ?Converged ? EndYesNo

No

> Max Iterations ?Converged ?No No

Yes

Return

Recalculate Mass Flow Rates


No

Yes

Update Flow Losses and Compressors

RecalculateEnthalpies

RecalculateConcentrations *


No

Yes Yes

* A concentration balance is performed only if dynamic mixing is modeled. If not, the Solver passes through this block.

41

A2 -

Known Flow Vs. Known Pressure Junctions At all system boundaries AFT Arrow must solve for either flow

or pressure User cannot specify both flow and pressure at the same point

because there would be nothing for AFT Arrow to solve Either the flow rate calculation or the pressure calculation

must be available to AFT Arrow

42

A3. Demo. Problem - Delivery System

Overview of Seminar


A3 -

Pipes

AFT Arrow uses two system constructs: pipes and junctions Pipes are conduits for steady-state, compressible, one-

dimensional fluid flow The mass flow rate through the entire length of the pipe is

always constant Volumetric flow rate is not constant!

Pipes have constant diameters but the fluid velocity is not constant

Each pipe must be connected to a junction on each end

1

A3 -

Pipes (2)

A pipe differs from a junction in that it has a reference positive flow direction To say a pipe has a flow rate of 1 lbm/sec is meaningless unless

the flow direction is specified. In cases where there is uncertainty about flow direction, you

do not need to specify the actual flow direction in a pipe AFT Arrow sorts out the true physical flow directions of the

system you define However, the pipe orientation is critical when using pressure-

dependent junctions like pumps and control valves

2

A3 -

Junctions

Junctions are connector points for pipes Junctions are elements at which flow and energy balances

are made Some junction types can only connect to one pipe while

others can connect with up to twenty five AFT Arrow provides a total of twenty standard junction types

3

A3 -

Junctions (2)

In addition to balancing flow and energy, junctions also influence the flow or pressure behavior of the system A tank junction applies a constant pressure at a location, and the

flow at a tank is free to adjust in whatever manner is consistent with the governing equations

An assigned flow junction applies a known flow rate at its location, allowing the pressure to adjust to that level dictated by the governing equations

The twenty standard junction types allow you to specify special kinds of irrecoverable pressure losses or fluid behavior

Junctions communicate with each other through the pipes connecting them

4

A3 -

Creating Objects

Pipe and junction objects are created using the Workspace Toolbox New pipes and junctions can also be derived from previous ones

by duplication Pipes are drawn on the Workspace Junctions are dragged from the Toolbox

5

A3 -

Creating Objects (2)

Pipe and junctions have default numbers assigned Users can reassign numbers Pipes numbers are displayed near the pipe center preceded by a

"P" Junction numbers are displayed over the junction icons

preceded by a "J" Pipes also have a direction arrow displayed with the number to

indicate the positive flow direction

6

A3 -

Moving Objects

The objects on the Workspace can be moved individually or as groups

To move an object, select it, drag it within the Workspace, and drop it in the desired location When an object is dragged off the existing Workspace area, the

Workspace is expanded accordingly The pipe object can be stretched by grabbing the handles at

the pipe endpoints and moving an endpoint to a new location

7

A3 -

Moving Objects (2)

To prevent accidental movement of objects, lock the objects on the Workspace The Lock feature is accessed from the Edit menu or the lock

button on the Toolbar. To group multiple objects for movement or other operations,

hold down the SHIFT key when selecting the objects Objects can also be selected by using the Selection Tool on

the Workspace Toolbar Click on the Workspace and drag the mouse to draw a box

around the objects Holding down the SHIFT key while drawing multiple boxes

permits multiple sets of grouped selections

8

A3 -

Connecting Pipes and Junctions

Pipes and junction objects can be placed anywhere on the Workspace

Remember that connectivity ONLY exists between junctions and pipes There are no junctions that connect to junctions, and no pipes

that connect to pipes The model connectivity you establish on the Workspace

remains only as long as you maintain the graphical objects in their current visual relationship to each other

The most certain way to maintain the connectivity of your model is to Lock the objects to the Workspace so they cannot be moved

9

A3 -

Connecting Pipes and Junctions (2)

To establish a connection between a junction and a pipe, the following three steps are required:

1) Graphically connect the objects on the Workspace (the pipe endpoint must terminate within the boundaries of a junction icon)

2) Enter data for the pipes through the Pipe Property window or globally

3) Enter data for the junctions through the Junction Property window or globally

10

A3 -

Editing Objects

The objects you place on the Workspace can be edited with the editing commands from the Edit menu or the Workspace Toolbar

Objects can be cut, copied, pasted, duplicated, and deleted These operations can be performed on individual objects or

on groups One level of undo is available for each editing operation

through the Edit menu

11

A3 -

Lay Out the Model

Open branching system Need to find the delivery conditions at J5, J6 and J7 Model looks as below

12

A3 -

Using the Checklist

The Checklist tracks the status of your model Communicates what items must be completed before you can

run the model

13

You can open the Checklist box from the Toolbar, View menu, or Quick Access Panel

A3 -

Using the Checklist (2)

The first item is always checked off because AFT Arrow assigns default Solution Control parameters The default Solution Control parameters work satisfactorily in

most cases The fourth item is disabled because no costs are applied by

default The fifth item may not be visible or may be disabled

depending on GSC module usage

14

A3 -

Checklist Quick Access Panel

Checklist status is available from Status Light on the Quick Access Panel

15

Status Light

A3 -

Using the Object Status Feature

Each pipe or junction object requires some minimum input data

Until each object has the required input, it is "undefined" The Show Object Status feature checks the required data for

each object and reports to the user which objects are and are not defined Undefined object numbers change color (to red by default) Right clicking on an object will display a listing of the input,

output, and undefined items for that object

16

A3 -

Using the Object Status Feature (2)

Show Object Status is toggled on and off from the Workspace Toolbar (flood light) or the View Menu

Show Object Status should be used selectively because it slows down the Workspace graphics if left in the ON state For large models, users should turn it ON only when needed

17

A3 -

Using Undefined Objects Window

Opened from the View menu, undefined pipes and junctions are displayed in lists

Click on a pipe or junction to see undefined properties

18

A3 -

Solution Control Windows

Solution Control Window is opened from the Analysis Menu or by clicking the Solution Control in the Checklist area of the Quick Access Panel.

This window gives user control of how the Solver behaves The default parameters are sufficient for the majority of

analyses

19

A3 -

Output Control Window

Output Control Window is opened from the Tools Menu or by clicking the Output Control icon on the Toolbar

Users can modify and keep Output Control formats for future use

20

A3 -

Output Control Window (2)

Output Control offers users control over the following items: The pipe and junction output parameters to be included in the

output The engineering units in which the output parameters will be

expressed The order in which the output parameters will appear The title appearing on the output report Reference information to keep with model Special summary reports The minimum number of significant digits to appear in the output

parameters Where to direct the output once it has been obtained and

formatting

21

A3 -

System Properties Window

System Properties Window is opened from the Analysis Menu or by clicking the Systems Properties on the Checklist in the Quick Access Panel

This window allows the user to select a fluid (or fluids) for use in the model With Chempak, static mixtures can be created The AFT Standard fluid database is customizable ASME Steam properties can be used

Other options include: Change the gravity level, atmospheric pressure, transition

Reynolds numbers, and STP conditions A rotational velocity can be specified here for modeling

turbomachinery22

A3 -

Cost Setting Window

Cost Calculations are enabled on the Analysis Menu Pump Energy Only or Full Cost Calculations can be calculated

Cost Settings Window is opened from the Analysis Menu or clicking the Specify Cost Settings on the Checklist in the Quick Access Panel when Cost Calculations are being calculated

Various costs can be calculated such as material, installation, and operation/energy

23

A3 -

Entering Pipe and Junction Data

Data for pipes and junctions are entered into Properties Windows

Properties Windows are opened either by double-clicking or single-click then pressing enter for the pipe or junction of interest Properties windows may also be opened by double clicking an

object within the Model Data and Output windows Data can also be entered through Global Edit Windows

24

A3 -

Input Data For Pipes

All pipes must have data for Length Diameter Roughness Heat transfer model

In addition, each pipe must have at least two connecting junctions

25

A3 -

Input Data For Junctions

All junctions must have Elevation data

Connecting pipes are assumed to travel linearly between junctions Sufficient number of connecting pipes

Number of connecting pipes is different for each junction type

There are twenty different junctions

26

A3 -

Data For Bend Junctions

Use standard elbow for all bend Bend junction K factors may depend on diameter Diameter is picked up from upstream pipe

All Bend junctions must have two connecting pipes

27

A3 -

Data For Tanks

Can have 1-25 connecting pipes For open systems do not select balance energy option Tank junctions maintain a constant stagnation pressure

Also maintain constant stagnation temperature for flow into system

28

A3 -

Data For Branches

Branches can have from 2-25 pipes No additional data is needed for branches

29

A3 -

Data For Assigned Flow

Assigned Flow junctions connect to one pipe only Allows you to define an inflow or outflow Requires fluid temperature, but only uses temperature for

inflows

30

A3 -

Inspecting Objects

The data in a pipe or junction can be reviewed quickly using the inspection feature

Inspecting is done by pressing down the right mouse button on the graphical pipe or junction

Inspecting is much quicker than opening the Properties Window Using the inspection window also does not clear the output

results as opening a Properties window can

31

A3 -

Inspecting Objects Quick Access Panel

Pipe and Junction input/output data can be viewed in Quick Access Panel Click the Property tab on Quick Access Panel Select a pipe or a junction on Workspace

32

Property Tab

A3 -

Model Data Window

The Model Data window is useful for reviewing the text input for the model All data can be printed out for documentation

Model Data can be accessed from the Model Data Primary Window tab or from the Window menu

Use the Model Data window to do a quick sanity check of the input Incorrect units or a typo become more obvious in Model Data

Double-clicking the far left column of the tables opens the appropriate Properties Window

33

A3 -

Running Models - Solution Progress Window When a model is complete, the Run command is enabled The model can be run by choosing Run from the Analysis

Menu or clicking the appropriate toolbar icon When a model is running, the Solution Progress Window

displays The Solution Progress Window shows the status of the

Solver's progress towards convergence

34

A3 -

Running Models - Solution Progress Window (2) The Solution Progress Window allows you to Cancel or Pause

the run so that Solution Control parameters can be modified Modifying Solution Control parameters during runtime may help

for difficult models When the solution converges, you are notified When you select View Output, you are immediately taken to

the Output Window

35

A3 -

Output Window

The Output Window displays text output for your model and is accessed from the Primary Window tabs or Window menu

The Output Control Window allows you to customize the content of the output


Each section may have multiple tabs to quickly view data by type

Print Format allows you to select the content of the printed report

36

A3 -

Output Window (2)

Transfer Results to Initial Guesses saves the current output results as the initial conditions Transfer Results to Initial Guesses may be accessed from the

Edit menu or the Output Toolbar (push pin) Warnings are placed into the General Results section

When warnings exist the text color is changed to red Sort allows you to sort the Output according to one the

columns Double-clicking the column header allows you to change the

units for that column

37

A3 -

Graph Results

Graphs are created with the Graph Results Window This window is one of the Primary Window tabs Graph Results can also be accessed from the Window menu

Various parameters can be graphed by clicking on the Select Graph Data button in the Graph Results window

The graph can be printed, copied to the clipboard, or saved to a file

The graph x-y data can be exported to a file or copied to the clipboard

38

A3 -

Visual Report

Visual Report allows you to see the results superimposed on the Workspace graphic This is one of the Primary Window tabs Visual Report can also be accessed from the Window menu

The Visual Report Control allows you to select the type of results you want to see

You can print the image at full size or fit it to a single page with Print Special

Text locations are automatically saved with the model

39

A3 -

Input for Demo 1

40

All pipes are Steel - ANSI, standard schedule (STD), standard friction dataGN2, Redlich-Kwong and Generalized Enthalpy, SolutionDefault Solution Control All elevations are zero

US

A3 -

Output for Demo 1

41

US

A3 -

Input for Demo 1

42

SI

All pipes are Steel - ANSI, standard schedule (STD), standard friction dataGN2, Redlich-Kwong and Generalized Enthalpy, SolutionDefault Solution Control All elevations are zero

A3 -

Output for Demo 1

43

SI

A4. Understanding Solution Control Options

Overview of Seminar


A4 -

Solution Control Window Summary

The Solution Control Window is opened from the Analysis Menu

Solution Control is one of the Checklist items Solution Control is required for every model

AFT Arrow provides robust Solution Control defaults Parameters that can be modified include solution method,

solution step size, tolerance, relaxation and maximum iterations

You can also keep track of the iteration history

1

A4 -

Solution Control Window Summary (2)

2

A4 -

Solution Control Window Summary (3)

3

A4 -

How To Use Solution Control

In general, the defaults provided by AFT Arrow are sufficient to guide a model to convergence Care should be taken to review output to ensure operating

conditions are consistent with solution method It is recommended you avoid changing the Solution Control

parameters unless you understand how to use them or it is recommended by AFT or a more experienced user The danger is that it is possible to modify the Solution Control

parameters in such a way that the model will converge on the wrong answer

We will cover different convergence strategies later in the seminar

4

A4 -

Solution Methods

The Length March method and Mach Number March method have been discussed previously

Arrow 6 offers two methods that are hybrids of the two basic methods Length March with Mach Number Limits Mach Number March with Length Limits

Arrow 6 also offers two lumped methods Lumped Adiabatic Lumped Isothermal

5

A4 -

Length March Method

The Length March method takes solution steps over equal length steps The user can specify steps either as number per pipe, or by

absolute length The Length March method solution for a single pipe looks as

follows: Note equal length steps

6

A4 -

Mach Number March Method

The Mach Number March method takes solution steps over equal Mach number steps This allows the solver to follow rapidly accelerating flow in pipes

The Mach Number March method solution for a single pipe looks as follows: Note how the distance steps shorten towards the end of the pipe

1 2 3 4 5 6 7 8 9 10 11 Note equal Mach number increments

7

A4 -

Hybrid Solution Methods

The two hybrid methods combine the best of the two basic solution methods They prevent length steps that are excessively large, as well as

Mach number increments that are excessively large The hybrid methods switch between the two basic methods

dynamically

8

A4 -

Hybrid Solution Methods (2)

9

Note how equal length increments are used until Point 6, then equal Mach number increments are used

A4 -

Default Solution Method

The default solution method is the Length March method (with two increments per pipe) with Mach Number increments limits

Note that this method uses two pipe sections on every pipe in the model, no matter how long

Using more sections per pipe causes longer run times

10

A4 -

Tolerance Summary

There are three tolerance inputs for the three variables (four if dynamic mixing is modeled) Pressure (at all junctions) Mass Flow Rate (in all pipes) Enthalpy (at all junctions) Concentration (at all junctions if dynamic mixing)

Each tolerance has four criteria to choose from Absolute Relative Either Absolute or Relative Both Absolute and Relative

11

A4 -

Tolerances and Convergence

When solution iterations are performed, the values of all junction pressures, enthalpies and pipe flow rates progress from the initial guesses (which are incorrect) to the true results (which satisfy the governing equations)

The solution method needs to have a criteria to decide when the results are good enough so it can stop iterating The tolerance values are the criteria the solution method

compares against to decide to stop iterating

12

A4 -

Tolerances and Convergence (2)

The best way to determine whether results are converged is to compare the results of the current iteration to those of the previous iteration If the results do not change appreciably then the true results

have been obtained Each iteration AFT Arrow does this check and when the

change in results for all the pipes and junctions is less than the specified tolerance, it considers the results converged

13

A4 -

The relative tolerance approach does the comparison of current vs. previous on a relative change (i.e., percentage change) basis

Relative tolerance is the AFT Arrow default because it is the

most robust AFT Arrow uses 0.0001 (i.e., 0.01%) as the

criteria for both pressure and flow

Relative Tolerance

( ) P P P

j new j old

j new

, ,

,

< TOL If (For All Junctions) Then

Convergence = True Else

Convergence = False End If

14

A4 -

This method is especially good for systems with highly different flow rates because each flow rate must converge to a percentage value only

One drawback of this method is if systems have zero or near zero flow rates

Relative Tolerance (2)

15

( ) P P P

j new j old

j new

, ,

,

< TOL If (For All Junctions) Then


Convergence = False End If

A4 -

The absolute tolerance approach does the comparison of current vs. previous on an absolute change basis (i.e., number of psi's)

Absolute tolerance has units associated with it

Absolute Tolerance

If (For All Junctions) Then


Convergence = False

End If

P P j new j old , , < TOL

16

A4 -

This method is good for systems with flows that are all of a similar magnitude

Typically, both tolerance settings will give (and should give) the same answer Usually relative tolerance is more efficient and reliable

Absolute Tolerance (2)

If (For All Junctions) Then


Convergence = False

End If

P P j new j old , , < TOL

17

A4 -

Tolerance Application:

Note that this convergence and tolerance is for pressure

(psia) -------------(lbm/s)------------- (lbm/s) (lbm/s/psia) --- (psia) P4 M1 M2 M3 F F' REL CHNG ABS CHNG 180.0000 115.3464 -78.9048 -313.5906 -277.1489 -18.6139 --- --- 165.1106 152.3476 110.9691 -158.5207 104.7960 -23.3027 9.0178E-02 1.4889E+01 169.6078 142.1903 81.9409 -217.3503 6.7810 -21.2485 2.6515E-02 4.4972E+00 169.9269 141.4418 79.4792 -220.9305 -0.0095 -21.3129 1.8780E-03 3.1913E-01 169.9265 141.4429 79.4827 -220.9255 0.0000 -21.3128 2.6127E-06 4.4398E-04 169.9265 141.4429 79.4827 -220.9255 0.0000 -21.3128 6.8205E-12 1.1590E-09 169.9265 141.4429 79.4827 -220.9255 0.0000 -21.3128 0.0000E+00 0.0000E+00

1 2 3 4 5 6 7

Iter #

18

A4 -

Solver Flow Chart

Recalculate Concentrations *

Start

Recalculate Enthalpies

Solve Junction Pressures

Yes

> Max Iterations ? Converged ? End Yes No

No

> Max Iterations ? Converged ? No No

Yes

Return

Recalculate Mass Flow Rates


No

Yes

Update Flow Losses and Compressors

Recalculate Enthalpies

Recalculate Concentrations *


No

Yes Yes

* A concentration balance is performed only if dynamic mixing is modeled. If not, the Solver passes through this block.

19

A4 -

Relaxation Overview

Relaxation slows the amount of flow rate change allowed by the solution Relaxation is like a damping factor that smoothens the convergence

process while also slowing the process Relaxation is applied to the flow rate and pressure update for all pipes, i

Relaxation is always greater than zero and less than or equal to one Relaxation of 1 is the same as no relaxation Relaxation of 0 would never update the flow rates

A relaxation of 1 is fastest Arrow will automatically reduce flow relaxation if dictated by the solution

progress Flow relaxation less than 0.01 is almost never required If you relaxation values -

For flow, typical settings for highly non-linear models are 0.1 or 0.05 For pressure, never use anything other than 0.5 or 1

m m m m ( ) , , , , r i new i new i old i old = + p r p p p i new p i new i old i old , , , , ( ) = +

20

A4 -

Relaxation Application

Calculate the new flow rates for several values of relaxation Relaxation Old Flow Rate (lbm/s)

Ideal New Flow Rate (lbm/s)

New Flow Rate (lbm/s)

1 10 20 20 0.5 10 20 15 0.2 10 20 12 0.1 10 20 11

0.05 10 20 10.5 0 10 20 10

21

A4 -

The Solution Progress Window (which displays while the Solver is running) communicates the maximum out of tolerance junction pressure, junction enthalpy and pipe mass flow rate

Junction pressures are solved first and the pipe flow rates and junction enthalpies are updated

Completing the Picture on Tolerance

22

A4 -

Using Transfer Results to Initial Feature

The Output Window has a feature called Transfer Results to Initial

This features takes the current results and transfers them to the initial guess for each pipe and junction

This makes the model run much faster in the future Transfer Results to Initial can be always enabled with the

Output Control window

23

A4 -

Maximum Global Iterations

The Maximum Iterations parameters restricts the total number of iterations for the Solver to calculate

The Maximum Global Iterations can be as high or as low as you want - it has no effect on the behavior of the Solver

The purpose of this parameter is to keep the Solver from searching forever for a solution it cannot obtain

Most models will converge within 50000 iterations, which is the default

24

A4 -

Maximum Local Iterations

Maximum Local Iterations should usually be left at 500 It can be changed to as high as 2000 in certain cases

Local Iterations are those iterations Arrow performs when it marches down a specific pipe

When marching down a pipe Arrow will iterate on all of the local solution parameters to make them consistent with each other for the step size

In certain cases Arrow cannot drive all of the local solution parameters to convergence within the desired local tolerance

25

A4 -

Maximum Local Iterations (2)

If no limit is set on this process, Arrow will get stuck in an infinite loop To make sure this does not happen, Arrow checks the local

iteration loop counter against the Maximum Local Iterations set in Solution Control

When the local counter reaches the limit, Arrow will warn the user and offer several options

26

A4 -

Local Iteration Control

If a local iteration problem occurs on the final iteration, AFT Arrow keeps a record of the problem and automatically retries the iteration (up to 3 times by default)

If the local iteration problem happens and it is not the final iteration, AFT Arrow ignores it It will not affect the solution because it is not the final iteration This happens frequently inside the Solver and the

user will never see it

27

A4 -

Local Iteration Control (2)

28

If a local iteration problem happens three times in a row, AFT Arrow displays convergence and then adds a warning to the output IF the value is more than 50 (by default) times greater than the tolerance

If the Error Value is far above the Tolerance, the answer is not reliable If it is only slightly out of

tolerance, this is usually not a problem

A5. AFT Arrow Example Models

Overview of Seminar


A5 -

Introduction to Scenario Manager

The Scenario Manager allows you to keep variants of a model all with the same model

The types of changes that can be made are very broad Junctions can be turned on and off to evaluate different

operating conditions Pipe and junction data can be varied to parametrically evaluate

competing designs You can build an existing system as your base model then add to

the system to evaluate expansion possibilities on the existing system

You can easily evaluate different working fluids by setting them up as different children scenarios

1

A5 -

Introduction to Scenario Manager (2)

Scenarios are created, manipulated, and loaded using the Scenario Manager window

The Scenario Manager can be opened from the Tools menu in the Workspace window, the Scenario Manager button on the toolbar, or Quick Access Panel

2

From Quick Access Panel

A5 -

Build Model of Nitrogen Transfer System

Hands-on problem #1 (TEST1.ARO - "Length March 2 Segments" Scenario) - Find flow rate through pipe

SolutionControl NotDefaultLengthMarch,2segmentsGN2IdealGasReferenceEnthalpy

Po =225psiaTo =100FEl =0


1

2

pipe1

US

3

L = 200 ftSteel - ANSI3 in., STD (Sch. 40)Adiabatic

A5 -

Modify Test Model #1 for Real Gases

Modify model to use real gas features, Redlich-Kwong and Generalized Enthalpy ("Real Gas" Scenario) - Find flow rate through pipe



1

2

pipe1L = 200 ftSteel - ANSI3 in., STD (Sch. 40)Adiabatic

SolutionControlLengthMarch,2segmentsGN2RedlichKwongGeneralizedEnthalpy

US

4

A5 -

Modify Test Model #1 for More Sections

Change number of pipe sections ("Length March 10 Segments" Scenario) - Find flow rate through pipe



1

2

pipe1

SolutionControlLengthMarch,10segmentsGN2RedlichKwongGeneralizedEnthalpy

US

5


A5 -

Modify Test Model #1 Solution Method

Change solution method to Mach March method ("Mach March Step 0.01" Scenario) - Find flow rate through pipe



1

2

pipe1

SolutionControlMachMarch,.01incrementsGN2RedlichKwongGeneralizedEnthalpy

US

6


A5 -


Change solution method to Arrow defaults (Length March to Mach March transition) - Find flow rate through pipe



1

2

pipe1

SolutionControlLengthMarchwithMachNumberLimits,2segments&0.01incrementsGN2RedlichKwongGeneralizedEnthalpy

US

7


A5 -

Modify Test Model #1 - Add Heat Transfer

Change model so that ambient temperature is 20F, no insulation and external convection coefficient is 100 Btu/Hr-ft2-R ("Heat Transfer" Scenario) Use Default Length March with Mach Number Limits

How does this affect the flow rate? What was the flow rate prediction error from the original

calculation?Eqn.State Enthalpy SolutionMethod Increment FlowrateIdeal Reference LengthMarch 2 20.20RK General LengthMarch 2 20.29RK General LengthMarch 10 20.73RK General MachMarch 0.01 20.74

Heat/RK General MachMarch 0.01 21.26RK General Default 0.01 20.74

US

8

A5 -

Graph Results

Use Graph Results to see how velocity changes along the pipe for the Heat Transfer scenario

US

9

A5 -

Size Helium Storage Tank

It is required to supply two systems with at least 2.5 lbm/s of helium (each) at a minimum 100 psia stagnation pressure

A single line runs from your tank for 1000 feet and then splits into two lines each 500 feet long. These two lines supply the two demand points. All pipe is steel - ANSI, 4 inch, schedule 40.

The lines are well insulated and thus heat transfer can be neglected to ambient

Elevation changes can be neglected

10

US

A5 -

Size Helium Storage Tank (2)

The system must function on hot and cold days, with the design ambient temperatures at 30 F for cold days and 100 F for hot days

The helium supply vessel will be outside, and thus will always be at the ambient temperature

What minimum (stagnation) pressure must the storage tank be designed to guarantee adequate supply year round?

TEST2.ARO (Hot and Cold Scenarios)

11

US

A5 -

Model Control Valve

Model flow control valve (TEST3.ARO, Base Scenario) Steam flow Use steam properties from AFT Standard Use real gas and real enthalpy models Inlet (stagnation) pressure is 250 psia at 425 F Exit (stagnation) pressure is 150 psia (assume 425F - this

temperature at the discharge will not be used) Pipe is horizontal Pipe is uninsulated 450 feet long and Standard Schedule (40)

steel - ANSI

12

US

A5 -

Model Control Valve (2)

Model flow control valve (TEST3.ARO, Base Scenario): contd Ambient temperature is 60F External heat transfer coefficient is 10 Btu/hr-ft2-F (same as

Btu/hr-ft2-R) Minimum pressure drop is 20 psid across valve Required flow rate is 5 lbm/s Assume valve is in the middle

Find minimum pipe size if valve is in middle of pipe Do the results change if the valve is not in the middle?

13

US

A5 -


Fluids in the AFT Standard database do not have saturation line data It is not possible to evaluate condensation Chempak fluids and the ASME Steam data do have saturation

line data Use steam data from the Chempak database to evaluate

whether condensation will occur. Does it? TEST3.ARO - "Chempak - No Insulation" Scenario

14

US

A5 -


To prevent condensation one can add insulation. The selected insulation has a thermal conductivity of 0.1 Btu/hr-ft-R

Insulation thickness of 0.25, 0.5 and 1.0 inch are being considered. Will they work? If so, which is best?

Is the control valve pressure drop still acceptable? TEST3.ARO - "Insulation XX inch" Scenarios

15

US

A5 -

Answers to Problems

TEST2 T-hot needs 265 psia (stagnation) T-cold needs 250 psia (stagnation) Requirement is thus 265 psia

TEST3, Use 3 inch pipes, which gives a stagnation pressure drop of 26.30 psid Results change if valve is not in middle (less pressure drop

available as valve is moved towards pipe inlet)

16

US

A5 -

Answers to Problems (2)

TEST3 with Chempak Condensation begins in pipe 1 before the control valve The previous sizing calculation is thus invalid

TEST3 with insulation Insulation of 0.5 or 1 inch prevents condensation. The 0.25 inch

does not. With 0.5 inch insulation the control valve pressure drop is 22.29

psid using 3 inch pipe With 1 inch insulation the control valve pressure drop is 21.67

psid using 3 inch pipe Use 0.5 inch insulation

17

US

A5 -

Build Model of Nitrogen Transfer System

Hands-on problem #1 (TEST1 (SI).ARO - "Length March 2 Segments" Scenario) - Find flow rate through pipe

SolutionControl NotDefaultLengthMarch,2segmentsGN2IdealGasReferenceEnthalpy

Po =1600kPaTo =40CEl =0meters


1

2

pipe1

L=60metersSteel ANSI3in.,Sch.40.(7.8cmID)Adiabatic

18

SI

A5 -

Modify Test Model #1 for Real Gases

Modify model to use real gas features, Redlich-Kwong and Generalized Enthalpy ("Real Gas" Scenario) - Find flow rate through pipe



1

2

pipe1

L=60metersSteel ANSI3in.,Sch.40(7.8cmID)Adiabatic

SolutionControlLengthMarch,2segmentsGN2RedlichKwongGeneralizedEnthalpy 19

SI

A5 -

Modify Test Model #1 for More Sections

Change number of pipe sections ("Length March 10 Segments" Scenario) - Find flow rate through pipe



1

2

pipe1


SolutionControlLengthMarch,10segmentsGN2RedlichKwongGeneralizedEnthalpy 20

SI

A5 -


Change solution method to Mach March method ("Mach March Step 0.01" Scenario) - Find flow rate through pipe



1

2

pipe1


SolutionControlMachMarch,.01incrementsGN2RedlichKwongGeneralizedEnthalpy 21

SI

A5 -


Change solution method to Arrow defaults (Length March to Mach March transition) - Find flow rate through pipe



1

2

pipe1


SolutionControlLengthMarchwithMachNumberLimits,2segments&0.01incrementsGN2RedlichKwongGeneralizedEnthalpy

22

SI

A5 -

Modify Test Model #1 - Add Heat Transfer

Change model so that ambient temperature is -7.0 C, no insulation and external convection coefficient is 570 W/m2-K ("Heat Transfer" Scenario) Use Default Length March with Mach Number Limits

How does this affect the flow rate? What was the flow rate prediction error from the original

calculation?Eqn.State Enthalpy SolutionMethod Increment FlowrateIdeal Reference LengthMarch 2 9.290RK General LengthMarch 2 9.332RK General LengthMarch 10 9.522RK General MachMarch 0.01 9.526Heat/RK General MachMarch 0.01 9.771RK General Default 0.01 9.526

23

SI

A5 -

Graph Results

Use Graph Results to see how velocity changes along the pipe for the Heat Transfer scenario

24

SI

A5 -

Size Helium Storage Tank

It is required to supply two systems with at least 1.1 kg/s of helium (each) at a minimum 700 kPa stagnation pressure

A single line runs from your tank for 300 meters and then splits into two lines each 150 meters long. These two lines supply the two demand points. All pipe is steel - ANSI, 4 inch (10.2 cm ID), schedule 40.

The lines are well insulated and thus heat transfer can be neglected to ambient

Elevation changes can be neglected

25

SI

A5 -

Size Helium Storage Tank (2)

The system must function on hot and cold days, with the design ambient temperatures at -1.0 C for cold days and 40 C for hot days

The helium supply vessel will be outside, and thus will always be at the ambient temperature

What minimum (stagnation) pressure must the storage tank be designed to guarantee adequate supply year round?

TEST2 (SI).ARO (Hot and Cold Scenarios)

26

SI

A5 -

Model Control Valve

Model flow control valve (TEST3 (SI).ARO, Base Scenario) Steam flow Use steam properties from AFT Standard Use real gas and real enthalpy models Inlet (stagnation) pressure is 1725 kPa at 220 C Exit (stagnation) pressure is 1050 kPa (assume 220C - this

temperature at the discharge will not be used) Pipe is horizontal Pipe is uninsulated 140 meters long and Standard Schedule (40)

steel - ANSI

27

SI

A5 -


Model flow control valve (TEST3 (SI).ARO, Base Scenario) contd Ambient temperature is 16C External heat transfer coefficient is 57 W/m2-K Minimum pressure drop is 140 kPa across valve Required flow rate is 2.25 kg/s Assume valve is in the middle

Find minimum pipe size if valve is in middle of pipe Do the results change if the valve is not in the middle?

28

SI

A5 -


Fluids in the AFT Standard database do not have saturation line data It is not possible to evaluate condensation Chempak fluids and the ASME Steam data do have saturation

line data Use steam data from the Chempak database to evaluate

whether condensation will occur. Does it? TEST3 (SI).ARO - "Chempak - No Insulation" Scenario

29

SI

A5 -


To prevent condensation one can add insulation. The selected insulation has a thermal conductivity of 0.2 W/m-K

Insulation thickness of 0.5, 1.25 and 2.5 cm are being considered. Will they work? If so, which is best?

Is the control valve pressure drop still acceptable? TEST3 (SI).ARO - "Insulation XX cm" Scenarios

30

SI

A5 -

Answers to Problems

TEST2 (SI) T-hot needs 1778 kPa (stagnation) T-cold needs 1675 kPa (stagnation) Requirement is thus 1778 kPa

TEST3 (SI), Use 3 inch (7.8 cm ID) pipes, which gives a stagnation pressure drop of 168.2 kPa Results change if valve is not in middle (less pressure drop

available as valve is moved towards pipe inlet)

31

SI

A5 -

Answers to Problems (2)

TEST3 (SI) with Chempak Condensation begins in pipe 1 before the control valve The previous sizing calculation is thus invalid

TEST3 (SI) with insulation Insulation of 1.25 or 2.5 cm prevents condensation. The 0.5 cm

does not. With 1.25 cm insulation the control valve pressure drop is 141.7

kPa using 3 inch pipe With 2.5 cm insulation the control valve pressure drop is 135.4

kPa using 3 inch pipe Use 1.25 cm insulation

32

SI

A6. Troubleshooting AFT Arrow Models

Overview of Seminar


A6 -

Getting the Right Results

There are a number of modeling problems AFT sees frequently

This section offers numerous strategies and suggestions for approaching modeling problems

1

A6 -

0

2

4

6

8

10

12

0 50 100 150 200

Flow (ft3/sec)

Pres

sure

(psi

d)

0

2

4

6

8

10

12

0 50 100 150 200

Flow (ft3/sec)

Pres

sure

(psi

d)

Compressor/Fan Curves

AFT Arrow allows you to use compressor/fan curves up to fourth order

Quadratic compressor/fan curves always reach a zero head value

Third or fourth order compressor/fan curves may not reach the zero head axis

This is a problem because the compressor/fan curve may start increasing This will cause problems for

the Solver 2BAD!

Chart1

10

9.95

9.8

9.55

9.2

8.75

8.2

7.55

6.8

5.95

5

3.95

2.8

1.8

1.2

1

1.2

1.8

2.8

4.2

6

Flow (ft3/sec)

Pressure (psid)

Sheet8

Pointx (feet)Mass Flow (lbm/sec)Velocity (feet/sec)Mach #P Stag. (psia)P Static (psia)T Stag. (deg. F)T Static (deg. F)H Stag. (Btu/lbm)H Static (Btu/lbm)fRho Static (lbm/ft3)

102.10648343.8560.22404110096.6032540.317530.781310.699308.3370.01935960.23449500.2240411

210.05072.10648359.0380.23404195.982492.4316540.316529.919310.699308.1240.01935950.22457980.1005070.2340410.959824

318.842.10648374.1990.24404192.305788.6005540.316529.021310.699307.9020.01935950.21548060.18840.2440410.923057

426.56472.10648389.3390.25404188.929585.0696540.316528.087310.699307.6710.01935950.20710110.2656470.2540410.889295

533.38472.10648404.4580.26404185.819881.8049540.316527.118310.699307.4320.01935950.19935950.3338470.2640410.858198

639.43132.10648419.5550.27404182.947578.7771540.316526.113310.699307.1830.01935940.19218610.3943130.2740410.829475

744.81292.10648434.6280.28404180.287575.9612540.316525.073310.699306.9260.01935940.1855210.4481290.2840410.802875

849.61992.10648449.6770.29404177.818273.3357540.316523.998310.699306.660.01935940.17931210.4961990.2940410.778182

953.92772.10648464.7020.30404175.520870.8816540.316522.888310.699306.3860.01935930.17351470.5392770.3040410.755208

1057.82.10648479.7010.31404173.37968.5827540.316521.743310.699306.1030.01935930.16808930.5780.3140410.73379

1161.29082.10648494.6740.32404171.378566.4246540.316520.564310.699305.8120.01935920.16300160.6129080.3240410.713785

1264.44592.10648509.6190.33404169.506564.3946540.316519.351310.699305.5120.01935920.15822120.6444590.3340410.695065

1367.30472.10648524.5370.34404167.75262.4815540.317518.105310.699305.2040.01935910.15372140.6730470.3440410.67752

1469.90092.10648539.4260.35404166.10560.6755540.317516.825310.699304.8880.01935910.14947840.6990090.3540410.66105

1572.26372.10648554.2860.36404164.556758.9677540.318515.511310.699304.5630.01935910.1454710.7226370.3640410.645567

1674.41832.10648569.1170.37404163.099357.3503540.318514.165310.699304.230.0193590.14168030.7441830.3740410.630993

1776.38682.10648583.9160.38404161.725855.8162540.319512.786310.699303.8890.0193590.13808940.7638680.3840410.617258

1878.18842.10648598.6840.39404160.429854.359540.32511.374310.699303.5410.01935890.13468320.7818840.3940410.604298

1979.83992.10648613.4190.40404159.205752.9731540.321509.93310.699303.1840.01935880.13144780.7983990.4040410.592057

2081.35612.10648628.1220.41404158.048251.6532540.322508.455310.699302.8190.01935880.12837090.8135610.4140410.580482

2182.75022.10648642.7910.42404156.952750.3948540.323506.948310.699302.4470.01935870.12544130.8275020.4240410.569527

2284.03352.10648657.4260.43404155.91549.1935540.324505.409310.699302.0670.01935870.12264890.8403350.4340410.55915

2385.21652.10648672.0260.44404154.931348.0456540.326503.84310.699301.6790.01935860.11998430.8521650.4440410.549313

2486.30812.10648686.5910.45404153.998146.9475540.328502.24310.699301.2840.01935860.11743910.8630810.4540410.539981

2587.31662.10648701.1190.46404153.112145.8959540.329500.61310.699300.8820.01935850.11500560.8731660.4640410.531121

2688.24922.10648715.610.47404152.270544.888540.331498.95310.699300.4720.01935840.11267670.8824920.4740410.522705

2789.11242.10648730.0640.48404151.470543.921540.333497.26310.699300.0540.01935840.11044590.8911240.4840410.514705

2889.91212.10648744.480.49404150.709742.9925540.335495.541310.699299.630.01935830.10830730.8991210.4940410.507097

2990.65352.10648758.8570.50404149.985842.1001540.338493.793310.699299.1980.01935820.10625530.9065350.5040410.499858

3091.34142.10648773.1940.51404149.296741.2419540.34492.017310.699298.760.01935810.1042850.9134140.5140410.492967

3191.982.10648787.4920.52404148.640640.4157540.343490.212310.699298.3140.01935810.10239160.91980.5240410.486406

3292.57332.10648801.7490.53404148.015539.6199540.346488.379310.699297.8610.0193580.10057090.9257330.5340410.480155

3393.12482.10648815.9650.54404147.4238.8527540.349486.519310.699297.4020.01935790.09881870.9312480.5440410.4742

3493.63762.10648830.1390.55404146.852438.1127540.352484.631310.699296.9360.01935780.09713150.9363760.5540410.468524

3594.11482.10648844.2710.56404146.311337.3983540.355482.717310.699296.4640.01935770.09550560.9411480.5640410.463113

3694.55882.10648858.3590.57404145.795436.7082540.359480.776310.699295.9850.01935770.0939380.9455880.5740410.457954

3794.97222.10648872.4050.58404145.303536.0413540.363478.809310.699295.4990.01935760.09242570.9497220.5840410.453035

3895.35722.10648886.4060.59404144.834435.3963540.367476.816310.699295.0070.01935750.09096570.9535720.5940410.448344

3995.71572.10648900.3630.60404144.387134.7721540.371474.798310.699294.5090.01935740.08955560.9571570.6040410.443871

4096.04972.10648914.2750.61404143.960634.1677540.375472.755310.699294.0050.01935730.08819290.9604970.6140410.439606

4196.36092.10648928.1420.62404143.553933.5823540.38470.687310.699293.4950.01935720.08687530.9636090.6240410.435539

4296.65082.10648941.9620.63404143.166233.0148540.384468.595310.699292.9790.01935710.08560060.9665080.6340410.431662

4396.92092.10648955.7370.64404142.796732.4645540.389466.479310.699292.4570.0193570.0843670.9692090.6440410.427967

4497.17252.10648969.4640.65404142.444631.9306540.395464.339310.699291.9290.01935690.08317240.9717250.6540410.424446

4597.40682.10648983.1430.66404142.109131.4123540.4462.177310.699291.3960.01935680.08201510.9740680.6640410.421091

4697.62492.10648996.7750.67404141.789730.909540.406459.991310.699290.8570.01935670.08089350.9762490.6740410.417897

4797.8282.106481010.3590.68404141.485630.4199540.412457.784310.699290.3120.01935660.07980590.978280.6840410.414856

4898.0172.106481023.8930.69404141.196329.9446540.418455.554310.699289.7620.01935650.0787510.980170.6940410.411963

4998.19272.106481037.3790.70404140.921329.4824540.425453.303310.699289.2070.01935630.07772720.9819270.7040410.409213

5098.35612.106481050.8150.71404140.6629.0327540.431451.03310.699288.6470.01935620.07673340.9835610.7140410.4066

5198.50782.106481064.2010.72404140.411828.5951540.438448.737310.699288.0810.01935610.07576820.9850780.7240410.404118

5298.64872.106481077.5370.73404140.176428.1691540.446446.423310.699287.5110.0193560.07483050.9864870.7340410.401764

5398.77932.106481090.8210.74404139.953327.7541540.453444.09310.699286.9360.01935590.07391920.9877930.7440410.399533

5498.90032.106481104.0550.75404139.742127.3498540.461441.736310.699286.3560.01935570.07303310.9890030.7540410.397421

5599.01232.106481117.2370.76404139.542426.9558540.469439.364310.699285.7710.01935560.07217140.9901230.7640410.395424

5699.11592.106481130.3670.77404139.353826.5716540.477436.972310.699285.1820.01935550.07133310.9911590.7740410.393538

5799.21142.106481143.4450.78404139.17626.1969540.486434.562310.699284.5880.01935540.07051720.9921140.7840410.39176

5899.29952.106481156.4710.79404139.008625.8313540.495432.134310.699283.9890.01935520.0697230.9929950.7940410.390086

5999.38042.106481169.4440.80404138.851325.4746540.504429.689310.699283.3870.01935510.06894950.9938040.8040410.388513

6099.45482.106481182.3630.81404138.703925.1263540.514427.226310.699282.780.01935490.06819610.9945480.8140410.387039

6199.52292.106481195.2290.82404138.56624.7861540.524424.746310.699282.1690.01935480.0674620.9952290.8240410.38566

6299.5852.106481208.0410.83404138.437424.4539540.534422.25310.699281.5540.01935

AFT Arrow Seminar Week of 22 May, 2017 - Prode AFT Fathom 7 and Arrow 4 8 Intro - Additional...

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Transcript of AFT Arrow Seminar Week of 22 May, 2017 - Prode AFT Fathom 7 and Arrow 4 8 Intro - Additional...