1. INTRODUCTION

The importance of supersonic flow to a wide variety of flow processes. In research development, flight and applied science is well known. Efficient pressure recovery is a dominant consideration in establishing the design and power requirements of jets. Many objects may encounter in supersonic flow fields with the requirement of providing efficient supersonic properties. Flying articles require high and well controlled pressure recovery for stable operation and reliable performance that can be examined by supersonic flow. Military aircraft jet engines have noise characteristics much louder than civilian aircraft due to their very high exhaust velocities. The high intensity noise generated by these heated subsonic or supersonic jets is a health hazard to ground crews. This has led to a need for reduction of jet noise by developing noise suppression mechanisms that include new nozzle design concepts such as chevrons, corrugations, bevelled nozzles, or other non-axisymmetric geometries. The present study investigates the details of the properties of both heated and heat simulated jets, using a combination of experimental measurements and Computational Fluid Dynamic (CFD) simulations. Experiments performed with cold, pure air jets and with Nitrogen-air mixtures highlight the effects of simulated heat on the jet flow properties. Numerical results with cold and heated pure air jets as well as Nitrogen-air mixture jets are used to assess the validity of the Nitrogen addition to properly simulate heat as well as validate a model.

1. 1 OBJECTIVE

To design and fabricate a supersonic free jet. And the free jet will be operated at different pressure and the calculations are made between the chamber pressure and pressure in the nozzle exit using basic equations and the formulas. A comprehensive comparison of the supersonic open free jet is made between theoretical results and the experimental results.

1. ) The main objective of this project is to design and fabricate a supersonic free jet.

2. ) To design a supersonic nozzle up to mach 2. 4.

3. ) Using nitrogen gas the flow in the supersonic free jet is made at different pressures.

4. ) Using supersonic pitot tube the stagnation pressure is measured.

5. ) The calculations are made between the chamber pressure and the pressure in the nozzle exit using basic equations and formulas.

6. ) Finally a comprehensive comparison of the supersonic free jet is made between theoretical results and the experimental results.

2. LITERATURE SURVEY

2. 1 Previous Studies on Free jets

Jet flows have a wide range of applications in the engineering field and have been a subject of study for centuries. The use of jets as a means of propulsion can be dated back to the first century A. D., when the Greek engineer Hero of Alexandria invented the first steam engine known as the aeolipile. This invention directed trapped steam through a pair of nozzles in order to spin a sphere very rapidly. Normally, we are mainly concerned with flows that are slow enough that they may be treated as incompressible. We now consider flows in which the velocity approaches or even exceeds the speed of sound and in which density changes along streamlines cannot be ignored. Such flows are common in aeronautics and astrophysics. For example, the motion of a rocket through the atmosphere is faster than the speed of sound in air. in other words, it is basic concept of supersonic study. Therefore if we transform in to the frame of the rocket the flow of air past the rocket is also a type of free jet in supersonic condition. When the flow speed exceeds the speed of sound in some reference frame, it is not possible for a pressure pulse to travel upstream in that frame and change the direction of the flow. However, if there is a solid body in the way (e. g. a rocket or aircraft), the flow direction must change.

Nozzles were also used by the Chinese in the 11th century with the invention of the rocket. Then with the invention of the first turbojet engine by Frank Whittle in the 1980s, jet propulsion introduced a way of reaching speeds before unimaginable by man.

Research on the structure of turbulent free jets by KrzywoblockiThe formation of a free jet is common to applications that involve exhaust plumes from propulsion systems, vents in high pressure systems, injection of

gas into liquids, and many others. Although seeming relatively simple, circular free jets involve complex phenomena such as turbulent mixing, shocks, heat transfer coupling, and other compressibility effects. To aid in understanding these phenomena many studies have been performed on a wide range of jet flows. For the present study, the formation and decay of ax symmetric under expanded free jets issuing from a circular convergent nozzle were of considerable importance. A significant amount of research on the structure of turbulent free jets was conducted in the 2002s. Krzywoblocki provides an in-depth review of studies on the decay of subsonic jets issuing from round nozzles into a quiescent medium. Additionally, through the work of Anderson and Johns, Seddon and Haverty, and Owen and Thornhill, analytical and semi-empirical methods for determining jet characteristics of subsonic jets were developed. These studies provided an understanding of the flow within the core region of a subsonic jet.

Jet stability by HammittAs rocket propulsion became more widely utilized, studies on the development and decay of under expanded jets began in the early 1985s. Love et al. Studied the strength and location of the initial shock structure of axisymmetric free jets. Jet stability and sound generation studied by Hammitt provided further insight into the flow field associated with under expanded sonic jets. It was not until the 1995’s that the decay and spreading rates associated with both subsonic and sonic jets were characterized. Donaldson and Snedeker used pitot and static pressure probes to develop velocity profiles and spreading and decay characteristics for a subsonic jet, a moderately under expanded sonic jet, and a highly under expanded sonic jet. This investigation provided the first characterization of the reflecting shock structure associated under expanded jets and quickly became an important reference for the majority of studies on free jets that followed.

Investigation on supersonic jets from convergent divergent nozzles by A. mohamad et al. There have been many studies for the nozzle and characteristics of free jet flow. One of the studies had been conducted by A. Mohamad and A. Hamed (2003) to investigate on supersonic jets from convergent divergent nozzles with rectangular cross section experimental. The purpose is to test the jet spread rate at different nozzle pressure ratio. From experiment, the results indicate that the rectangular supersonic jet spread rate is greater along the minor axis and increase with the nozzle pressure ratio. Schlieren photographs are presented for over-expanded rectangular jets in quiescent atmosphere to show the effect of nozzle pressure ratio on the shock structure and jet mixing. The results indicate the mixing rate is high along the

jet’s minor axis at higher nozzle pressure ratios, but decreases as the nozzle pressure ratio is reduced. In over- expanded rectangular particle-laden jets, the shock strength was found to decrease as the nozzle pressure ratio was reduced.

Evaluation of high pressure fuel valve nozzles using the method of characteristics and CFD by saangwon et al. Design and evaluation of high pressure fuel valve nozzles using the method of characteristics and CFD was studied by Saangwon, Charles and Allan(2003). The study is about the design fuel valve nozzles for natural gas engines that maximize the kinetic energy and momentum of the injected fuel and maintain a required mass flow rate. The nozzle design uses both the method of characteristics and computational fluid dynamics (CFD). Three types of nozzles were designed a converging-diverging nozzle, three conical nozzles and an aero spike nozzle.

Katanoda & et al. Have measured Pitot pressures in jets with Mach disc and compared that to numerical simulations. Under expanded jets has been the subject of many studies for a long time. The most often encountered ones issue from a convergent nozzle. Indeed, it is enough that the nozzle pressure ratio (henceforth NPR), defined as the ratio of upstream stagnation pressure to the ambient pressure, be above the critical value With the ratio of specific heats of the gas, and the jet is under expanded, the static Pressure at the nozzle exit being higher than the ambient. The pressure mismatch at the jet exit generates a quasi-periodic shock cell pattern. These flows present variety of practical applications. The pioneering studies mainly focused on then flow structure of highly under expanded flows, featuring a so called barrel shock and a large Mach disc. More detailed investigations of local mean value is taken by important flow variables, such as velocity, static pressure or Mach number, defined by the ratio of local velocity to local speed of sound, have been performed in the past. Donaldson & Snedecker and Hu McLaughlin have deduced velocity from static and Pitot pressure measurements. Norum & Seiner have led Extensive static pressure measurements on jet centerline in an attempt to link shock cell structure to shock associated noise. These measurements have been compared to mean flow simulations by Seiner et al. . Katanoda. have measured Pitot pressures in jets with Mach disc and compared that to numerical simulations. The Jet Age by prof. R. D. pehlke

The Jet Age, the 2001 Howe Memorial Lecture, Professor R. D. Pehlke highlighted the nature of processes integral to pneumatic steelmaking, spanning inceptive invention to the state-of-the-art and forward. The fundamentals of gas jet behaviour were emphasized and included the importance of coupled physics, chemistry and mechanics in between the gas and the molten slag and metal. The complete understanding of the transient heat, mass and momentum transfers in both top and bottom blowing systems is deceptively complex. Today, we continue to unearth new aspects about supersonic gas jets and how they interact with both gaseous ambient and molten targets. In the matter of top-blowing, a gas jet first passes through gaseous ambient prior to impacting liquid. A complete understanding of the former process is required to adequately define the latter. Accordingly, the subject of this paper is on supersonic gas jets interacting with gaseous ambient. The penetrability of a supersonic jet is a function of the entrainment and mixing rate with the ambient gas, which in turn depends on the temperature, composition and pressure, and also aerodynamic interactions (e. g., relative velocity). The difference between a reactive jet and a non-reactive jet is well acknowledged but not fully understood. The effect can be illustrated by examining the advent coherent jet technology. This technology employs an oxy-fuel flame, designed to shroud the supersonic jet to maximize the penetrability (i. e., delay mixing and spreading). The plots compare the axial(centerline) velocity profiles for flame shrouded jets and free jets (non shrouded), for oxygen and nitrogen at Mach 2, formed in ambient air. For the free jets, the profiles for oxygen and nitrogen coincide.

3. THEORIES

3. 1 Free jet theory

3. 2 Theory of nozzle with various conditions

3. 1 FREE JET THEORY

Besides the more conventional solid wall test sections the supersonic tunnel is sometime arranged so that the testing is done in a free jet either entirely open with no diffuser or as an enclosed free jet. In either case the flow leaving the nozzle exit is surrounding by still air with a turbulent mixing zone for a boundary surface and constant pressure as a boundary condition. The advantages that arise from the use of a free jet include.

1. The lessening of chocking and the consequent use of larger models than possible in a solid wall tunnel of the same nozzle exit diameter.

2. An improvement of access to the model.

3. In high temperature tunnels, a lessening of the window heating problem.

4. The starting and running compression ratio are nearly the same no over pressure to start is required.

The “price” of these above advantage is a usual increase of required compression ratio, and for the simple free jet, an enormous increase in noise. Usually, too, the flow quality is slightly poorer than in the solid wall tunnel. The open free jet is by far the easiest type of all to construct and is particularly useful in engine work where the engine may be directly linked to it, or simple immersed in it. In many instance a far large model can be tested than in a conventional solid wall test section. It is of interest to note the jet static pressure may be below ambient, a conditions not possible in supersonic flow. The starting pressure ratio will be approximately that corresponding to the normal shock in the test section, and the running ratio is about the same. The noise level from an open free jet is very serious and a tunnel with such a test section should not be planned for installation in populated areas unless it is to be very small.

The enclosed free jet avoids the noise problem and requires slightly less compression ratio than the open free jet. A model of the flow in the test chamber diffuser portion of a free jet wind tunnel has been deriving from theory and from experiments. The model may be describe the jet entering the test chamber because of mixing of the jet with the stagnant chamber air. Oblique shockwaves exist in the supersonic portion of the jet and are terminated by a strong shock wave system upstream of the diffuser throat. A very thick boundary layer exist between the supersonic jet and the wall of the contraction section of the diffuser. The flow passes through the reminder of the diffuser at subsonic speeds. With this flow configuration, the pressure at the diffuser at exit influences the pressure in the test chamber through flow upstream in the thick bounder layer. Increase in total pressure of the flow cause the normal shock to move downstream with the result that test chamber pressure to decreases.

It is usually desirable to maintain the test chamber pressure near the nozzle exit pressure to avoid strong shock or expansions as the jet leaves the nozzle. There is a limiting value of second throat area below which it is not possible to reduces the test chamber pressure to the value at the nozzle exit. However, if the second throat area can be made with very little effect on the tunnel operating efficiency, the second throat to nozzle exit area ratio of 1. 6 were found satisfactory for operation at Mach number of 2. 0 to 4. 3 with diffuser efficiency of varying from 0.62 at Mach 2.0 to 0.5 at Mach 4. 3. For these conditions, free jet lengths to about 2. 25 nozzle exit diameter had no apparent effect tunnel starting on tunnel operating efficiency for theoretical plot from relating the ratio of diffuser inlet to nozzle exit area ratio A1/A2 to the ratio of test chamber to nozzle exit pressure Pe/P1 the tunnel operating efficiency.

For the mode of operation of the enclosed free jet just described, the tunnel starting pressure ratio is less than the tunnel running pressure ratio in contrast to the solid wall tunnel. The reason is that the strong shock is not driven through the diffuser throat. The total pressure in the tunnel can be increased sufficiently to obtain sonic flow in the diffuser at a normal shock in the diverging diffuser. With this flow configuration the test chamber pressure remains essentially proportional to the nozzle exit pressure and the value of the proportion is dependent on diffuser throat area. As might be expected the test chamber pressure increase as the diffuser as throat area is decreased.

For the higher Mach number it is not essential to keep the test chamber pressure equal to the nozzle exit pressure. Disturbance resulting from pressure differences will have shallow angles and will no effect the flow in the centre portion of the jet for a considerable distance downstream of the nozzle exit. With this reasoning, experiment were made at Mach number of 5 and 6 in an axially s tunnel with diffuser throat areas less than the nozzle exit area. In these experiments it was found that tunnel operating efficiencies were greater than 100 per cent in some case. Also it was found that the tunnel operation was similar to the solid wall tunnel in that tunnel required less pressure ratio to run than to start. Result of these tests indicated that the free jet length should be no greater than 1.5 diameters.

3. 2 THEORY OF NOZZLE WITH VARIOUS CONDITIONS

It is important to realize that the statement supersonic velocity can be reached only if pe/p0

<0. 528 is the M* = at the throat). Thus, in the strict sense it should

be started that, a nozzle will have Mth =1 at throat only if pth /p0≤0. 528, and the

flow in the divergent portion of the nozzle will accelerate to increasing supersonic mach numbers only if p/pth<1, where p is the local static pressure in the divergent portion of the nozzle. The flow after choking at the nozzle throat will continue to accelerate to progressively higher supersonic mach numbers, in the divergent portion downstream of the throat, only if pe/pth<1. In other words, for the flow to accelerate, a favourable pressure gradient should exist. Therefore, for a convergent-divergent nozzle to experience supersonic flow from downstream of the throat up to the exist, the limiting pressure ratio pe/po required across the nozzle is dictated by the presence of normal shock at the exist. Thus, pe/po required to choke the flow at a nozzle throat can also be greater than the isentropic limiting pressure ratio of 0. 528(for ᵞ=1. 4).

Fig.1 Nozzle

A variety of flow fields can be generated in the convergent –divergent or laval nozzle by independently governing the back pressure downstream of the nozzle exit. Consider the flow through a laval nozzle. When pe=po, there will no flow through the nozzle. This small favourable pressure gradient will cause a flow through the nozzle at low subsonic speeds. The local mach number will increase continuously through the convergent portion of the nozzle, reaching a maximum at the throat. In other words, the static pressure will decrease continuously in the convergent portion of the nozzle, reaching the minimum at the throat, as shown by a curve ‘a’. Assume that pe is reduced further (pe2). Then pressure gradient will be stronger, flow acceleration will be faster, and variation of mach number and static pressure through the duct will be larger, as

shown by curve b. Similarly, if pe is reduced continuously, at some value of pe, the flow will reach sonic velocity at the throat, as shown by curve c. For this case, At = A*. Now, the sonic flow at the throat will expand further in the divergent portion of the nozzle as the supersonic flow if pe/pth < 1, and will decelerate as a supersonic flow as shown in the curve c, for pe3/pth>1.

The mass flow through the duct increases as pe decreases. This mass flow can be calculated by evaluating equation at the throat, m=ρth A th V th

mA

=ρV = constantA

. When pe is equal to pe3, where sonic flow is attained at the throat, ˙m=ρ ¿ A ¿a¿, also the mach number at the throat is unity; this is dictated by the equation. Hence the flow properties at the throat and indeed throughout the subsonic convergent section of the duct became frozen when pe<pe3 i. e. the subsonic flow in the convergent portion of the nozzle remains unaffected and the mass flow remains constant for pe<pe3 this condition for sonic flow at the throat is called chocked flow. For further reduction of pe below pe3, after the flow becomes chocked, the mass flow remains constant.

At this stage it is important to realize that the chocked mass flow rate m* is the maximum only for a given p0 and T0. However, when the stagnation pressure and temperature are altered, m* will have different maxima corresponding to every set of p0 and T0.

From the for going discussions it is clear that in the convergent portion of the duct flow remains unchanged for back pressures below pe3. But, in the divergent portion of the duct flow expands as a supersonic flow for pe<pe3.

However, pe should be adequately reduced to a specified low value, pec, for establishing isentropic expansion of flow throughout the divergent portion of the nozzle, resulting in shock-free supersonic flow; the variation in pressure such an isentropic expansion as shown by curve d in fig.

However, pe should be adequately reduced to a specified low value, pec, for establishing isentropic expansion of flow throughout the divergent portion of the nozzle, resulting in shock-free supersonic flow; the variation in pressure such an isentropic expansion as shown by curve d in fig.

Fig.2 Flow in a CD nozzle

For values of exit pressure between pec and pe3, a normal shock wave exists inside a divergent portion of the nozzle. The flow behind the normal shock is subsonic; hence the static pressure increases to pe4 at the exit. The normal shock moves downstream with decreases in pe below pe4 and will stand precisely at the exit when pe=pe5, where pe5 is the static pressure behind a normal shock at the designed mach number of the nozzle; this is shown in fig. When pe

is further reduced such that pec<pb<pe5, the flow inside the nozzle is fully supersonic and isentropic where pb, the pressure of the ambient atmosphere to which the flow is discharged is called back pressure.

When the flow situation in the nozzle is said to be over expanded, since the pressure at the exit has expanded below the back pressure pe<pb. Conversely, when the situation is shown in fig. The nozzle is said to be under expanded, since the exit pressure is higher than the back pressure, pe>pb, and hence the flow experiences the additional expansion after leaving the nozzle.

Fig.3 Various conditions in nozzle

The results can be summarized as follows:

1. For pe1/p0<1, the flow is subsonic at the throat and so the divergent portion acts as a diffuser. This is the case of flow through venture.

2. For pe3/p0<1, the pressure at the throat p* and also M=1 at throat but, pe3/pth>1; therefore the divergent portion act as a diffuser and the flow does not become supersonic.

3. For pressure at the exit equal to pec, the flow expands isentropically in the nozzle and there is shock free supersonic flow in the divergent portion of the nozzle.

4. For pec/p0<pe/p0<pe3/p0, there will be supersonic velocity locally, but at the exit it cannot be supersonic, and so there will be a jump in static pressure at some section of the nozzle, i. e. there is a shock. Therefore, there is a certain backpressure pec, above which the cannot be supersonic flow at exit. Only below pec there can be shock free supersonic flow up to the exit.

The equations which are useful for calculating the cross sectional average properties inside a nozzle of a given shape are

P ₒP

=(1+ γ−12

M ²)γ /( γ−1 )

ρ ₒρ

=(1+ γ−12

M ²)1 / (γ−1)

T ₒT

=(1+ γ−12

M ²)¿¿

Therefore for a supersonic tunnel, it is necessary to have a separate nozzle for every test section mach number of interest.

4. DESIGN OF SUPERSONIC FREEJET SETUP

4. 1 CATIA MODEL OF THE SUPERSONIC FREEJET SETUP

Fig.4 Catia model

5. FABRICATION OF SUPERSONIC FREE JET

5. 1 EXPERIMENTAL SETUP

The supersonic flow originates from a high pressure nitrogen cylinder. Using hydraulic hose the setup is connected to the nitrogen cylinder and a pressure regulator is used to regulate the flow for different pressure from the nitrogen cylinder. The jet exhausts through a D= 15mm diameter CD nozzle. And the supersonic setup is fixed using caskets to prevent the leakage during the flow. And the setup consists of 3 meshes that are provided between the chamber. The meshes are mainly used for to make the flow uniform and to raise the stagnation pressure in the settling chamber. And the stagnation pressure is measured using the pressure gauge which is fixed near the nozzle inlet. So that we see the exact pressure inside the chamber and to ensure the safety of the setup. The high compressed gas in the chamber rushes through the CD nozzle inlet with high pressure and reaches the throat of the nozzle and the flow sonic M=1. And finally in the divergent section of the nozzle the flow reaches to supersonic speed M=1. 5. The out coming supersonic flow is measured using supersonic pitot tube which is connected to the U tube mercury manometer and it is controlled by the traverse mechanism.

Fig. 5 Schematic diagram of Supersonic free jet setup

5. 2 FABRICATION

Seamless tube is used for making settling chamber.

Seamless steel is used for making diffuser.

Mild steel is used for making nozzle and mesh.

Meshs are used to make the flow laminar and to stagnate with pressure.

Caskets are used to prevent the leakage from setup.

Hydraulic tubes are used to connect the setup from the gas cylinder.

Pressure regulator is used to the regulate the pressure in the settling chamber.

Pressure gauge is used to measure the pressure in the settling chamber.

5. 3 DIFFUSER

The main task of the diffuser is to convert the kinetic energy into pressure energy. This purpose is the same in all subsonic and supersonic tunnels with either free jet or closed test section, Due to the increasing kinetic energy in supersonic tunnels and the large driving power needed for operation, the efficiency of the pressure recovery is becoming more important.

The second task of the diffuser, which is confined only to supersonic wind tunnels with free jet test section, is the control of the air pressure in the test chamber, which, at supersonic velocity of the jet, is not necessarily equal to the pressure of the air stream in the exit cross section of the nozzle. To fulfill these two requirements, the diffuser is usually designed with adjustable throat cross section and adjustable walls, upstream and downstream from the throat, forming a reasonable aerodynamic shape.

In any case, the convergent part of the diffuser should act as a converted Laval nozzle decelerating the supersonic flow of the diffuser entrance to approximately sonic velocity in the throat and to subsonic in the diverging part.

Fig.6 Supersonic diffuser

5. 4 THE SETTLING CHAMBER

The settling chamber is usually a cylindrical shell, one diameter or more long, which accepts the air from the wide angle diffuser provides a length for settling to obtain uniform flow, provides screens for promoting uniformity of flow and for reducing turbulence in the air stream, and then exhausts into the subsonic portion(inlet) of the nozzle.

The static pressure in the settling chamber is higher than at any downstream point in the tunnel. However, it is normally considerably below that in the storage tanks or in the piping to the pressure regulator. Because it is economical, the settling chamber and downstream portions of the tunnel are usually designed for their normal operating pressures rather than the tank pressure. Because there is usually the possibility of a malfunction of a tunnel components which could result in excessive pressure in the settling chamber, such as the pressure regulator suddenly being fully opened with maximum pressure in the air storage tanks, the settling chamber normally consists of blow off stack.

If the flow spreader in the wide angle diffuser is properly designed, air will enter the settling chamber with a fairly uniform distribution. In most spreader designs the air enters through perforations and a finite distance will be required for the individual jets of air from the individual perforations to coalesce to form a uniform flow. However, turbulence of the flow emanating from the control valve or elsewhere will not be removed by the spreader. In fact, additional turbulence is almost certain to be induced by a perforated spreader. The importance of turbulence level is generally considered to decreases as the wind tunnel or jet speed increases into the transonic and supersonic range.

Most high speed wind tunnels are designed with screens in the settling chamber to promote flow uniformity and to reduce the turbulence level before the air expanded through the nozzle. Sometimes turbulence may be caused by screens and it is recommended that several low pressure drop screens are preferable to single high-pressure drop screen. This is the practice normally followed in blow down tunnel design.

The characteristic of flow in the tunnels is that the magnitude of velocity fluctuations in the settling chamber will remain essentially constant during the expansion of air through the nozzle.

The settling chamber should be designed for flow velocities no greater than 80 to 100 feet per second. If possible, the lowest velocity in the settling chamber should be no less than about 10 feet per second. Convection currents can become a problem any time, there are significant differences between the air temperature in the settling chamber and the walls of the settling chamber, which is not usually in blow down tunnels.

The settling chamber should be designed for easy removal or for easy access to its interior, since the screens will require some maintenance. It will have a provision for a connection to a pressure port because the velocity head will be negligible. The settling chamber should also have a provision for measuring total air temperatures. Pressure and temperature measurements should, of course be made downstream of the screens.

The settling chamber and wide angle diffuser should be designed according to the pressure vessel code and should have hydraulic pressure check at 150 per cent of the design pressure. The pressure check will require blind flanges for the individual components or of the assembly. It will also require fittings for filling with water and bleeding off air.

Fig.7 Settling chamber with dial gage

5. 4 DIFFUSER AND SETTLING CHAMBER DESIGN

Fig.8 Diffuser and settling chamber design in catia

6. SUPERSONIC NOZZLE DESIGN

The supersonic nozzle consists of a subsonic portion which accelerates the settling chamber flow up to sonic speed, and a supersonic portion which further accelerates the flow and finally delivers it as uniform stream to the test section. Considering first the subsonic portion, we find that it is exceedingly difficultly to accelerate the settling chamber flow without having some areas of deceleration near the walls which tend to thicken the boundary layer undesirably. Usually this effect is neglected by nozzle designers, apparently without serious harm, and one of three completely arbitrary procedures is used to determine the subsonic shape.

1. Draw a smooth curve of mach number against nozzle length from settling chamber mach number to M =1. 0, and to compute the correct area ratio. (the reason for not drawing the area curve directly is that the extra step yields a much more gradual curve than intuition would normally indicate. )

2. Draw an arc of 5h* where h* is the height of the sonic throat. 3. Use the curve made by an ellipse having the major axis equal to the throat

height and the minor axis equal to one-half throat height. A 45-deg line is then faired from settling chamber to the ellipse.

In the usual case of fairing from a round settling chamber to a rectangular section at the sonic point (nozzle throat), about twenty control stations should be used. In actual construction the subsonic portion of the nozzle should end at M=0. 9 below to avoid a joint at the sonic station, and whatever joint finally evolves should cause a step of no more than 0. 001inch. For designing the portion of the nozzle between the throat and the test section, the method of characteristics is normally used. An outline of the steps are required in the design of a two dimensional nozzle by the method of characteristics will be given. Note that use of the method oh characteristics requires dividing the diverging portion of the nozzle in to a series of straight section in order to define the characteristics lines and their reflections and cancellations. however, after the characteristics calculation have been completed, it is possible to obtain a smooth curve which, after allowance has been made for the boundary layer, is suitable for creating a uniform supersonic stream of a predetermined mach number. The general steps to take are as follows:

1. Read the turning angle γ for the desired mach number from the reference table and compute the maximum wall angle θ max from θ max= γ/2.

2. Since a nozzle symmetrical about a horizontal centre line will have symmetric flow, the problem is somewhat shortened if we design only the upper half. Hence we now draw figure the centerline OH and a very short horizontal section AB representing the downstream end of the subsonic portion.

3. Construct a smooth and arbitrary curve BCD that expands the minimum section to at some distance downstream. Both the distance downstream and the curve are unimportant expect in the way they effect the overall distance between the nozzle throat and the test section. In supersonic nozzles, this distance is usually in the range of 3 to 8 test section heights, with the lower values occurring at lower mach numbers.

4. Divide the curve in to equal straight sections to make an angle of not over 2 deg between each section. The shorter the test sections are, the greater accuracy, and of course, the greater the number of calculations. Steps smaller than/2 deg are probably unnecessary.

5. Construct the expansion waves and their reflection according to our previous work and the example that follow step 8.

6. Construct he section cancelling all the expansion waves. 7. Redraw the nozzle to an expanded vertical scale and fair a smooth

curve through the points of intersection of the waves with the wall. 8. Check the final result by comparing the area ratio of minimum to

final section with that of

¿¿

Fig. 9 CD nozzle design in catia

7. BASIC FORMULAE FOR SUPERSONIC CALCULATIONS

From our discussions so far it is easy to identify that the following are the important relations required for the supersonic flow calculations.

p1

p2=( ρ1

ρ2)

γ

=(T 1

T 2)

γγ−1

a= √γRT=20. 04 √T m/ s

γγ−1

pρ+ V 2

2=constant= γ

γ−1p t

ρt

Where pt and ρt are the stagnation pressure and density respectively

ρ ₒρ

=(1+ γ−12

M ²)1 / (γ−1)

P ₒP

=(1+ γ−12

M ²)γ /( γ−1 )

P2

P1=

(1+ γ−12

M 12)

(1+ γ−12

M 22)

γ / (γ−1)

T ₒT

=(1+ γ−12

M ²)Where p, ρ ,and T are the local pressure, density, and temperature, respectively and p1 and p2 are the pressures upstream and downstream of a normal shock.

8. AREA MACH NUMBER RELATION

¿¿

Fig.10 Area relation curve

9. FABRICATION OF SUPERSONIC NOZZLE DESIGN

Fig.11 Catia model of nozzle

10. RUNNING TIME OF FLOW IN THE FREE JET FLOW

Blow down supersonic wind tunnels are usually operated with either constant dynamic pressure (q) or constant mass flow rate(m). For constant operation the only control necessary is a pressure regulating value (PRV) that holds the stagnation pressure in the storage tank falls according to the polytropic process with the polytropic index n=1. 4 for short duration runs with thermal mass in the tank.

For constant mass flow run the stagnation temperature and pressure in the settling chamber must be held constant. For this either a heater or a thermal mass external to the storage tank is essential. The addition of heat energy to the pressure energy in the storage tank results is longer running time of the tunnel.

Another important consequence of this heat addition is that the constant settling chamber temperature of the constant mass run keeps the test section Reynolds number at a constant value.

For calculating the running time of a tunnel we make the following assumption

1. Expansion of the gas in the storage tank is polytropic

2. Gas temperature in the storage tank is held constant with a heater.

3. Gas pressure in the settling chamber is kept constant with a pressure regulating valve.

4. No heat is lost in the pipelines from the storage tank to the test section.

5. Expansion of the gas from the settling chamber to the test section is isentropic.

6. Test section speed is supersonic.

The mass flow rate m through the tunnel, as given by

m=(1. 4 / RT )1 /2 MptA(1+0. 2 M 2 )3

Where M is the test section Mach number and p stagnation pressure, T stagnation temperature respectively are the pressure and temperature in settling chamber.

We know that for supersonic flows it is convenient to calculation the mass flow rate with nozzle throat conditions. At the throat M=1. 0 and became

m=0. 0404 pA¿

√T t

The value of the gas constant used in the above equation is R=287m2/(s2K) which is the gas constant for air.

The product of the mass flow rate and run time gives the change of mass in the storage tank. Therefore,

Mt=(ρi−ρf )Vt

Where Vt is the tank volume and ρiand ρf are the initial and final densities in the tank, respectively the running time is obtained as

t = (ρi−ρf )m Vt

Arranging the above equation, we get

t =24. 728√TtPt

VtA ¿ ρi(1−

ρf

ρi)for polytropic expansion of air in

the storage tank we can write

ρf

ρi=( p f

p i)

1n

Where subscripts I and f denote the initial and final condition in the tank respectively. Substitution of the above relation then the result in time t

t=0.086V t

A¿√T t

T i

p i

p t [1−( Pf

Pi )1n ]

With Vt in m3 this given the running time in seconds for the general case of blow down tunnel operation with constant mass flow condition, it is obvious that for t max the condition required is Pt minimum. At this stage we should realize that the above equation for running time has to be approached from a practical point of view and not from a purely mathematical point of view. Realizing this it can seen that the tunnel run does not continue until the tank pressure drops to the settling chamber stagnation pressure Pt but stops when the storage pressure reaches a value that is appreciably higher than Pt that is when Pf=Pt + ∆P. This ∆P is required to overcome the frictional and other losses in the piping system between the storage tank and the settling chamber. The value of ∆P varies from about 0. 1 Pt for very small mass flow runs to somewhere around 1. 0Pt for high mass flow runs.

11. DETERMINING THE MACH NUMBER

The mach number in the supersonic jets are usually obtained from close to the speed of sound up to M=1. 6 by measuring the static pressure in the section and total head in the settling chamber and using equation

P ₒP

=(1+ γ−12

M ²)γ /( γ−1 )

Above M=1. 6 is more accurate to use the pitot pressure in the test section with the total head in the stagnation chamber and required because the loss of head

above M=1. 6 yields a sufficient difference between the pitot pressure and the stagnation pressure for a useful ratio to be obtained. A further advantage is that the static pressure is a more difficult quantity to measure at best.

Although less accurate than the pitot pressure method at the higher mach numbers the measurement of the static pressure can also be used for determine the mach number as can the measurement of the shock wave angles from schlieren photographs or shadowgraphs.

Whereas mach numbers in near sonic and transonic tunnels are usually determined only on the tunnel centerline and the tunnel walls mach number in supersonic tunnels are usually obtained off the tunnel centerline as well. The reason is that much larger non uniformities of flow are possible in supersonic nozzles because they can be caused shock waves. An average flow mach number in the vicinity of a model is desired from testing and data reduction purpose and the cross sectional area survey will give a better average mach number than the centerline survey. If the centerline distribution is constant or varies gradually but continuously, the centerline survey is usually adequate. However, the characteristics of this distribution are not known when the calibration is started.

12. MEASURING THE FLOW CONTITION

12. 1 NITROGEN GAS PROPERTIES

12. 2 PITOT PRESSURE TUBE

12. 3 SUPERSONIC PITOT TUBE

12. 4 MEASURING STAGNATION PRESSURE

12. 5 DIAL TYPE PRESSURE GAUGE

12. 1 NITROGEN GAS PROPERTIES

Molecular weight: 28. 0134 g/mol

Liquid density (1. 013 bar at boiling point) : 808. 607 kg/m3

Critical temperature: -147 °C

Critical pressure: 33. 999 bar

Critical density: 314. 03 kg/m3

Gas density (1. 013 bar at boiling point): 4. 614 kg/m3

Gas density (1. 013 bar and 15 °C (59 °F)): 1. 185 kg/m3

Compressibility Factor (Z) (1. 013 bar and 15 °C (59 °F)) : 0. 9997

Specific gravity (air = 1) (1. 013 bar and 21 °C (70 °F)): 0. 967

Specific volume (1. 013 bar and 21 °C (70 °F)): 0. 862 m3/kg

12. 2 PITOT PRESSURES TUBE

Pitot pressures are measured by using a simple device called a pitot probe. The pitot probe is simply a tube and the tube end is facing into the airstream. The tube will normally have an inner and outer diameter ratio of ½ to ¾ and the length aligned with the airstream of 15 to 20 tube diameters. The pressure orifice is formed at the inside diameter of the tube end. It will be in sensitive to an angle of attack up to 10deg for an orifice diameter only up to 10percent of the outside diameter and up to 15deg for one 98per cent of its outside diameter. Calibration errors due to angle of attack and the hole size within the above ranges are much less than the actual flow deviation found in any reasonable tunnel.

At this point we may make the classification that an open-ended tube facing into the airstream always measures the stagnation pressure (a term identical in meaning to total head). Above M=1. 0 the shock wave is formed ahead of the tube means that is it sees not a free stream stagnation pressure but the stagnation pressure behind the normal shock. This new value is called pitot pressure and in modern terms implies a supersonic stream, although there is no error in calling the pressure so measured in the subsonic stream pitot pressure.

Pressures measured by pitot probes are influenced significantly by very low Re number based on the probe diameter. This effect is seldom a problem in supersonic tunnels, however because a reasonable- sized probe will usually have a Re number well above 500 or 1000, which is the range where trouble starts.

12. 3 SUPERSONIC PITOT TUBE DESIGN AND FABRICATION

Fig.12 Pitot tube

12. 4 MEASURING STATIC PRESSURES

Pressures in the supersonic flow are much difficult to measure than the pressure in the subsonic flow and the pitot pressure in the supersonic flow. The static pipe described for calibrating near sonic and transonic tunnels are rarely used because its presence in the tunnel will affect the flow in the test section. It changes the area ratio of the nozzle by subtracting from effective throat and the test section area, and it also interferes with expansion pattern required for the development of uniform flow.

The primary problem in the use of probes in the supersonic speeds is that any probe will have a shock wave at its forward end which causes the rise in the pressure. If the probe consists of a cone tip followed by a cylinder, the air passing the shoulder will be expanded to a pressure below static. Then as distance from the shoulder is increased, the pressure on the probe will approach the true static pressure on the stream.

Pressure measurements on a cone-cylinder probe with 7-deg included angle cone followed by a cylinder 30 diameter in length. These results show negligible errors in static pressure measurements for the orifice located at 10 diameters of the shoulder.

The another type of probe designed for the accurate measurement of static pressures over a large mach number range is designed. They were obtained by reference to a static pressure calculated from measured pitot and total pressure. Flow angularity during these tests was consequence, since the tunnel employed even flow. However it was found impossible to get consistent results until the

pitot probe mentioned above the static probe were mounted in the section on vertically moving support systems so that either could be moved into centerline calibration position without the tunnel shutdown and with little time interval between measurements evidently for the extreme accuracy being sought (of the order of 0. 001 per cent of q), minute tunnel changes due to controls or thermal expansion became significant. When mach number is to be determined from static pressure measurements, the total pressure of the stream is measured in the settling chamber simultaneously with the section static pressure. Therefore the static pressure is calculated from these two pressures and the relation

P ₒP

=(1+ γ−12

M ²)γ /( γ−1 )

Fig.13 Pitot tube setup at the end of nozzle

12. 5 DIAL-TYPE PRESSURE GAGES

The dial-type pressure gages is usually operated on the principle of bellows or a bourdon tube deflecting s a result of a pressure change and driving the needle on a dial through a mechanical linkage. Gages of this type of range in cost for a few dollars up, with cost being costly related to accuracy. Although gages of this type may be obtained with accuracies suitable for measuring the pressures, they are not extensively used for this purpose. Their primary use is for visual monitoring of pressures in the many plumbing circuits required for the usual tunnels.

Dial-type gages do have advantages over a manometer of being easier to read. Also, they can be obtained from pressure ranges well beyond those of the manometer. Their primary advantage is that they must be calibrated periodically to ensure that they continue to read correctly. Their second advantage is that manometers are cheaper when there is a large number of pressure to be read, and a third, as with manometers, is that they cannot be easily read electronically.

Fig.14 Dial gage used in settling chamber

13. Manometers

Manometers measure the difference between a known and unknown pressure by observing the difference in heights of two fluid columns. Two popular types of manometers a simple manometer consists of two vertical glass tubes joined together with U-tube connections at the bottom. Each tube has a linear scale attached to it, which is usually marked off in millimeters. The tubes are filled with a fluid until the fluid level in the tubes is at the middle of the adjacent scales. A reference pressure is applied at the top of one of the tubes and the pressure to be measured is applied at the top of the second tube. The height of the two columns of fluid will change until the difference between the height h is equal to the pressure to be measured in terms of fluid column height. The commonly applied reference pressure for this type of manometers is the atmospheric pressure.

However, in many cases the difference the atmospheric and measured pressure will represent a longer column of manometer fluid that can be accommodated by the tubes. In such cases, the only way to use the manometer is to adjust the reference pressure so that a smaller fluid column height will be reached. However, this method has the disadvantage of adding an intermediate

pressure measure. Instead of two separate scales for measuring the liquid levels at the two column of the U-tube manometer, a column scale fixed at the middle of the U-tube may also be used for measurement. In fact this has a specific advantage, because reading the fluid level in one of the tube of the U-tube is adequate for pressure management if the scale is marked with zero before measurement, in the case. With this arrangement, the measured column level in one tube will give the pressure to be measured when it is doubled. The multi tube manometer, operates on the same principle as the U-tube manometer. However, in this manometer a large cross-sectional area sump takes the place of the tube in the U-tube manometer, to which the reference pressure is applied. The sump level is used as the reference, and often a number of tubes are employed to form a multi tube manometer. The sump and tube manometer has the following advantages over the U-tube manometer.

It can be used for measuring more than one pressure at a time. The reference level can be adjusted so that only one scale needs to

be read instead of two, to determine the manometric fluid column height.

Demerits

They are not suitable for very high or low pressure measurements. They have very poor frequency response. A little dirt in a tube, a bubble in a line, or the presence of condensate

changing the fluid specific gravity can produce anomalous readings.

Fig.15 Mercury manometer

14. VELOCITY AND MACH NUMBER FROM PRESSURE MEASUREMENTS

For an incompressible flow, velocity V can be calculated from the measured total and static pressures, using the Bernoulli equation

p0−p=1/2 ρV 2

For compressible flows, Mach number M is one of the most important parameters. From the measured pressures, the flow Mach number may be obtained using the pressure Mach number relations which are well established.

If the flow at the measuring point experiences only isentropic changes, its stagnation pressure may be assumed to be the same as the reservoir pressure p0. A measurement of the static pressure p alone is necessary to compute the mach number using the isentropic relation,

P ₒP

=(1+ γ−12

M ²)γ /( γ−1 )

This relation is applicable to both subsonic and supersonic flows, and is used for obtaining the Mach number distribution along an aerodynamic surface, using surface static pressure holes, and for flow field Mach number, using a static probe.

In an isentropic supersonic flow, the local Mach number can be computed using the pitot pressure measured by a pitot probe. But we know that a detached shock will be formed at the nose of the probe when it is placed in supersonic stream. therefore, what the probe measures is the total pressure behind the shock and not the actual total pressure of the stream. Also, we know that the portion of the detached shock(also called bow shock)ahead of the probe nose can be approximated as a normal shock. therefore, the flow mach number can be calculated, using the normal shock relation,

p01

p02=( 2 γ

γ+1M1

2− γ−1γ+1 )

1(γ−1) ( γ +1

2M 2)

γγ−1

Where p01 is the reservoir pressure which is same as the total pressure of the stream in an isentropic flow, and p02 is the pressure measured by the pitot probe. in flow fields where the reservoir condition are not known, as in the case of

measurement from an aircraft, it is not possible to use any of the above two equations to obtain the Mach number, because it is necessary to know both the static and total pressures for using them. In subsonic flow, the pitot pressure measured is the actual total pressure, and the mach number can be obtained from above equation once the static pressure is known. But in supersonic flows, the measured pitot pressure p02 is the total pressure behind the normal shock at the probe nose, and not the actual total pressure of the flow. therefore, to eliminate the actual total pressure p0 (or p01), resulting in

PPO2

=( 2 γ

γ+1M 1

2− γ−1γ+1 )

1(γ−1)

( γ +12

M 12)

γ /( γ−1 )

This equation is popularly known as the Rayleigh supersonic pitot formula. In this equation both pressures involved are measurable in supersonic streams.

15. MEASURING THE FLOW IN JET CORE LENGTH

15. 1 Distance 0. 5mm from the nozzle exit

15. 2 Distance 1. 0mm from the nozzle exit

15. 3 Distance 1. 5mm from the nozzle exit

15. 4 Tabulations

15. 5 Calculations

16. COMPUTATIONAL FLUID DYNAMICS ANALYSIS

16. 1 CATIA MODEL

16. 2 MESHING THE CATIA MODEL

16. 3 FLUENT ANALYSIS

17. VARIOUS CONTOUR GRAPHS

17. 1 MACH NUMBER CONTOUR

17. 2 PRESSURE CONTOUR

17. 3 DENSITY CONTOUR

18. COMPARING THE EXPERIMENTAL AND COMPUTATIONAL RESULT

19. CONCLUSION

20. REFERANCE JOURNALS

1.Tanna, H. K., Dean, P.D., and Fisher, M. J., “The Inuence of Temperature on Shock-Free Supersonic Jet Noise”.

2. Lau, J., ”Effects of Exit Mach Number and Temperature on Mean-Flow and Turbulence Characteristics in Round Jets”.

3. Doty, M. J., and McLaughlin, D. K, \Acoustic and Mean Flow Measurements of High Speed Helium Air Mixture Jets,"International Journal of Aeroacoustics, Vol 2, No. 3, 2003, pp293-334.

4. Papamoschou, D, “Acoustic Simulation of Coaxial Hot Air Jets Using Cold Helium-Air Mixture Jets”.23, No. 2, March-April 2007, pp. 375-381

5.Kuo, C. -W.Veltin, J., and McLaughlin, D. K., “Acoustic Measurements of Models of Military Style Supersonic Nozzle Jets," 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition, AIAA-2009-18,2009

6. 32. Woodmansee, M. A. & Dutton, J. C., “Experimental measurements of pressure,temperature, and density in an underexpanded sonic jet flowfield,” 30th AIAFluid Dynamics Conference, A99-33660, 1999

7.Schlichting, H. and Gersten, K., “Boundary layer theory," Springer, 2003

8.Lau, J., Morris, P. J., Fisher. M. J., \Measurements in Subsonic and Supersonic Free Jets," Journal of Fluid Mechanics, Vol. 93, 1979, pp. 1-27 pp. 193-218.

9. Yoder, D. A., Georgiadis, N. J., and O'Gara, M. R. \Frozen Chemistry Effects on Nozzle Performance Simulations," 38th Fluid Dynamics Conference and Exhibit, 23-26 June, Seattle, Washington, AIAA 2008-3909, 2008.

10. Donaldson, C. D. &Snedeker, R. S., “A study of free jet impingement. Part 1. Mean properties of free and impinging jets,” Journal of Fluid Mechanics, vol. 45,part 2, pp. 281-319, 1971

11. Krzywoblocki, M. Z., Jet Propulsion, vol. 26, pp. 760-779, 1956

13. Anderson, A. R., & Johns, F. R., Jet Propulsion, vol. 25, pp. 13-15, 1955

14. Love, E. S., Grigsby, C. E., Lee, L. P., & Woodling, M. J., “Experimental and theoretical studies of axisymmetric free jets,” NASA TR, R-6, 1959

15. Dash, S. M., Wolf, D. E., & Seiner, J. M., “Analysis of turbulent underexpanded nozzles SCIPVIS,” AIIAA Journal, vol. 23, No. 4, 1984