design, fabrication, and realization of a supersonic wind tunnel for educational...

International Journal of Mechanical Engineering Education 37/4

Design, fabrication, and realization of a supersonic wind tunnel for educational purposesMohammed K. Ibrahima (corresponding author), A. F. Abohelwab and Galal B. Salemc

a Lecturer, Aerospace Engineering Department, Faculty of Engineering, University of Cairo, Giza, 12613 EgyptE-mail: [email protected] Assistant Professor, Aerospace Engineering Department, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, JapanE-mail: [email protected] Industrial Engineering Consultant, 88 Ramsis-2, Nasr City, Cairo, Egyptc Chairman and Professor, Aerospace Engineering Department, School of Engineering, University of Cairo, Giza 12613, Egypt

Abstract The supersonic wind tunnel is an indispensable facility for basic education in any course that covers compressible fl ows and one of the main pillars of any aerodynamic laboratory. The introduction of a supersonic wind tunnel at the aerodynamics laboratory of the Aerospace Engineering Department at Cairo University had often been postponed and was hindered by a lack of funds for the purchase of foreign equipment and expertise. Thoughts therefore turned to building such facility instead of buying it, substituting high-tech and complex foreign equipment for locally produced equipment, and ‘thinking out of the box’ to make the most use of available resources, even when this led to some unconventional applications. An extensive scheme for the design, fabrication, and realization of a multi-Mach number (M = 1.5, 2, and 2.5) supersonic wind tunnel for laboratory experiments is proposed in this paper. The proposed scheme is simple, detailed and multi-level; it starts by utilizing one-dimensional isentropic fl ow theory for the conceptual design phase and makes full use of computational fl uid dynamics at the detailed design phase. This ensured that we had a working design before we embarked on the manufacture of any components, which would have been costly to modify had there been any design error. A parametric study has been carried out for a number of design parameters, using numerical simulations. After the design and fabrication, a number of successful standard textbook experiments, for Mach number 2, were carried out as validation for the proposed scheme. The results showed good agreement with the theoretical predictions.

Keywords compressible fl ow; wind tunnel testing; supersonic fl ow; computational fl uid dynamics; isentropic fl ow; method of characteristics; shock waves

Notation

m mass fl ow rateA cross-sectional areaa speed of soundM Mach numberp pressureR gas constantT temperatureu, v Cartesian perturbed velocity components

Supersonic wind tunnel 287


V fl ow velocityx, y Cartesian coordinatesβ shock wave angleγ specifi c heat ratioΦ velocity potential functionϕ′ small perturbation potential functionρ densityθ cone semivertex angle�i unit vector in the x-direction�j unit vector in the y-direction

Subscripts1 condition upstream of normal shock wave2 condition downstream of normal shock wavee nozzle exit conditiono stagnation condition

Superscripts* critical condition at which M = 1` perturbation component normalized by critical speed of sound∼ full velocity components = a + u or a + v

Introduction

Supersonic wind tunnels have been used for research, development, and teaching for more than fi ve decades. Aerodynamics, propulsion, and acoustic testing are some of their main uses. The tunnel consists of a nozzle block, test section, and a diffuser. Details on various aspects of the supersonic wind tunnel and its components can be found in texts by Anderson [1, 2]. The problems encountered in supersonic wind tunnel design and operation include a high pressure ratio at the start of supersonic fl ow in the test section, insuffi cient supply of dry air, wall interference effects, and the need to use fast instrumentation for intermittent measurements. Starting a super-sonic wind tunnel is a critical issue in the tunnel design. Non-startup of the tunnel can be due to either insuffi cient area of the diffuser throat to allow the startup shock to pass through, or an insuffi cient pressure ratio between tunnel entry and exit.

An extensive scheme for the design, fabrication, and realization of an intermittent blow-down supersonic wind tunnel for laboratory experiments is proposed in this paper. Special attention was given to startup and the transient performance of the tunnel.

Pope and Goin [3] provide an extensive reference for the testing of high-speed wind tunnels. Their design procedures are implemented in the present paper but are adapted by making use of computational fl uid dynamics (CFD) capabilities in the design loop to study the startup characteristics of the tunnel. This ensured that we had a working design before we embarked on the manufacture of any components, which would have been costly to modify had there been any design error. A para-

288 M. K. Ibrahim et al.


metric study was carried out for a number of design parameters using numerical simulations.

The proposed design scheme is divided into four stages. The fi rst is the conceptual design phase, which is based on a quasi one-dimensional fl ow analysis and makes assumptions which greatly reduce the number of calculations, while maintaining suffi cient accuracy for this stage of the design. The next phase is the preliminary design of the tunnel and involves accurate design of the nozzle contours and analysis of the fl ow using two-dimensional small-perturbation theory and the method of characteristics. Standard boundary layer correction procedures are also considered at this stage, when the aerodynamic design of the critical nozzle section is complete. To ensure that the results are accurate, comparison with numerical simulation results generated using commercial CFD code Fluent 6 (by Fluent Inc.) is carried out in the third stage. The numerical simulation capabilities are used to analyze the entrance problem and the transient effect of pressure build-up. The fi nal stage is the detailed design, that is, the ‘nuts and bolts’ of the actual wind tunnel.

Fig. 1 shows a detailed fl ow chart of the proposed design scheme. Various parts of the fl ow chart are presented in the subsequent sections. The fabricated tunnel underwent a series of standard textbook experiments that were designed to prove that the tunnel did achieve the required design Mach number. The results were compared with the most accurate data available and showed a good agreement.

Design of the supersonic wind tunnel

Conceptual designThe goal of the conceptual design is to select the most important dimensions of the tunnel and get a fair assessment of the expected specifi cations of the tunnel without getting involved in many complex calculations. Achieving the required pressure ratio is accomplished through one of two ways: a large vacuum can be created at the exit of the tunnel (this is known as an in-draft wind tunnel); or, a large reserve of pressurized gas can be created at the entrance of the wind tunnel (this is known as a blow-down wind tunnel). Due to the availability and local familiarity with air compressors as opposed to the rarity of vacuum pumps, a blow-down type was dic-tated for the present design. Furthermore, a restriction to the use of the two available tanks, of 1800-liter (1.8 m3) and 300-liter (0.3 m3) capacity, connected in series and pressurized at 10 bar, was also imposed on the present design.

The analysis was done with the following assumptions: (1) isentropic fl ow-through nozzle, (2) quasi-one-dimensional fl ow-through nozzle, (3) negligible transient effect (no build-up time), (4) nozzle throat choked, (5) tank discharges isentropically. Using these assumptions, an expression for the mass fl ow through the tunnel can easily be determined. The continuity equation can be written as:

�m T A M RT

T= ⎛

⎝⎜⎞⎠⎟

ρ γ ρρo o e e

e

o

e

o

(1)



Fig. 1 Detailed fl owchart for the proposed design scheme.



which can be written in terms of the exit Mach number:

�m T A M R M= +−⎛

⎝⎞⎠

⎛⎝

⎞⎠

− +−

ρ γ γγγ

o o e e e21

1

2

1

2 1

( )( )

(2)

Naturally, the mass fl ow rate is a key deciding factor in the running time of the tunnel; therefore, equation 2 needs to be examined carefully. The expression is a function of the stagnation conditions, the exit area and the exit Mach number. The stagnation pressure must be above a certain limit to ensure supersonic fl ow in the test section [1–5].

When a shock wave is present at the exit of the nozzle, the ratio of the stagnation pressure to the exit pressure can be written as:

P

P

P

P

P

P

P

P

P

Po

e

o o

e

= =1

1

2 1

1

(3)

where the subscripts 1 and 2 denote the conditions upstream and downstream of the shock wave, respectively. The exit conditions are considered to be identical to the downstream shock wave conditions. Equation 3 can be written in terms of exit Mach number as follows:

P

PM Mo

ee e= +

−⎛⎝

⎞⎠

⎛⎝

⎞⎠ +

−⎛⎝⎜

⎞⎠⎟

−( )⎛⎝⎜

⎞⎠⎟

−−

11

21

2

112 1 2

1γ γγ

γγ

(4)

Setting the exit Mach number to the desired Mach number, the minimum required stagnation pressure or settling chamber pressure can be obtained to generate a super-sonic fl ow in the test section. From a practical standpoint, the actual stagnation pressure should be above this value, in order to overcome the viscous effects which arise during startup of the tunnel. Raising the stagnation pressure above the minimum required would increase the stagnation conditions, thereby increasing the mass fl ow rate, and would have a negative effect on the running time. The presence of a regula-tor to hold the pressure at around this threshold therefore increases the running time; this will be seen quantitatively below. Due to the assumption of isentropic tank dis-charge, the stagnation conditions in equation 2 can be fully determined using a time marching technique, and if a regulator is used it will be assumed that the regulator works through a throttling process.

The remaining two parameters (Ae and Me) are the two design parameters on which a certain degree of optimization must be carried out. It is of interest to see the running time variations with these two parameters. Very simply, the running time is the time taken for the tanks to reach the minimum threshold pressure. In order to perform the running time calculations with and without a regulator, some basic assumptions must be made. These are: (1) the fl ow from the tank to the settling chamber is adia-batic; (2) the pressure in the settling chamber is mainly governed by the regulator performance (if a regulator is present); (3) the opening of the valve is assumed to lead to a linear pressure rise (within a prescribed short period, say 1 s) in the settling



chamber until the stagnation pressure set by the regulator is obtained. Where there is no regulator, the stagnation pressure in the settling chamber will continue to rise until it is equal to the tank pressure minus the pressure losses between the tank and the settling chamber. Constant running time contour lines are shown in Fig. 2 with and without a regulator.

By examining the two graphs in Fig. 2, it is noted that the optimal running time for given test section area occurs around Mach numbers 1.75–2.5. It can be also noted that choosing a test section area of 25 cm2 will give a constant mass fl ow rate (with regulator) of 0.1 kg/s, which is just within the range of commercially available regulators. On this basis, the selected Mach numbers will be in the range 1.75–2.5 with a test section area of 42 mm × 60 mm, which will give a running time of around 6 s without a regulator and 15 s with a regulator.

It can be seen that the presence of a regulator more than doubles the running time. Although this is obviously highly desirable, a regulator that would allow such a high mass fl ow would be very expensive. Alternatively, the running time could be increased by connecting the available 8000-liter (8 m3) tank to the two tanks men-tioned above; this tank is capable of withstanding a pressure of 10 bar. This increases the running time to 35 seconds without a regulator. The cost of pressurizing these three tanks, with a total volume of 10.1 m3, will be an issue, as a high-power com-pressor is needed to achieve this. The two tanks of capacities 1.8 m3 and 8 m3 are connected in such a way that enables either of them to be bypassed, hence control-ling the running time.

Preliminary designThe goal of the preliminary design phase is to determine the fl ow distribution through the nozzle and test section. This analysis is based on the method of charac-teristics, an accurate and well tested way to achieve a working design for a super-sonic nozzle.

To initiate the method of characteristics, some initial data points are needed. There are many different ways of obtaining these, but in the present paper one of the most

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Tes

t sec

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Mac

h nu

mbe

r

Test section area (cm2)5 15 20 25 30

1.5

2

2.5

3

3.5

(a) (b)

5

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5

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Tes

t sec

tion

Mac

h nu

mbe

r

Test section area (cm2)5 15 20 25 30

1.5

2

2.5

3

3.5

Fig. 2 Running time in seconds versus test section size and Mach number: (a) with regulator’ (b) without regulator.



accurate ways, which involves some complicated mathematics and time-consuming computations of the transonic region of the nozzle throat, was chosen [6]. The benefi t of this method is that it provides a means for judging the effect of the radius of cur-vature upstream of the throat (the subsonic portion of the nozzle) and at the throat itself. The transonic analysis is based on a solution of the small-perturbation poten-tial (equation 5):

γ φ φ φ+( ) ′ ′ − ′ =1 0x xx yy (5)

The derivatives of φ′ are the perturbations of the fl ow velocity around a certain value normalized by division by the speed of sound at the throat. The fl ow in the throat region is sonic with small perturbations; therefore, the velocity vector can be written as u = a* + u and v = v, where u and v represent the total velocity and u, v represent the perturbations in the x and y directions, respectively. Defi ne u′ and v′ as:

′ =uu

a* (6)

′ =vv

a* (7)

Hence

′ =φ φx

x

a* (8)

′ =φφy

a* (9)

The solution to equation 5 involves assuming a power series solution in y with the coeffi cient a function of x. For more details the reader is referred to [6]. Suffi ce it to say that the end result is a number of points in the throat region that are now fully defi ned, stretching from the wall to the centre line of the nozzle. The method of characteristics is then applied to the supersonic portion of the nozzle. This method is based on the following full potential equation:

1 12

02

2

2

2 2−⎛

⎝⎜⎞⎠⎟

+ −⎛⎝⎜

⎞⎠⎟

+ =Φ ΦΦ

ΦΦ Φ

Φxxx

yyy

x yxy

a a a (10)

where Φ is the full velocity potential such that:

Φ x u= � (11)

Φ y v= � (12)

V ui vj= +��

��

(13)

From the rules of differential mathematics:

d d d d dΦ Φ Φ Φ Φxx x

xx xyx

xy

y x y= ∂∂

+ ∂∂

= + (14)



d d d d dΦΦ Φ

Φ Φyy y

xy yyx

xy

y x y=∂∂

+∂∂

= + (15)

These can be treated as three equations in three unknowns, namely Φxx, Φyy and Φxy.

It is found that for certain values of

dydx

⎛⎝⎜

⎞⎠⎟

the solution is undefi ned. This fact can

be manipulated to solve for the fl ow fi eld, i.e., obtain the velocities, along certain lines known as characteristic lines. This method can also be used to obtain the wall contour, provided that the wall section between two adjacent points is assumed to be a straight line with an angle equal to half the fl ow tangent angle at the two points. The reader is referred to [1, 2, 6] for more details about the implementation of the method.

The procedure required for fl ow computations for a given contour of the nozzle based on the method of characteristics was programmed using Matlab. The computa-tion procedures can be summarized as follows: (1) nozzle contour determination based on the procedures outlined in reference [1]; (2) throat radius selection such that neither oblique shocks nor variation in exit condition occurs; (3) computation of the initial data line by solving equation 5; (4) computation of the points that do not depend on the nozzle contour points; (5) computation of the points resulting from the throat region and the initial data line; (6) computation of the fl ow-straight-ening portion of the nozzle. The end results of the above procedures are illustrated in Fig. 3 for exit nozzle Mach number = 2. Boundary layer correction of the nozzle contour was applied using a simplifi ed technique proposed in reference [3], which utilizes the Mach number distribution obtained from the method of characteristics. An approximate method presented in reference [7] for estimating boundary layer thickness in a two-dimensional nozzle with minimum calculations was used in the correction.

Results from the present method of characteristics are compared with the quasi-one-dimensional results for the Mach number distribution along the nozzle center line and are shown in Fig. 4. The results show good agreement.

0 0.02 0.04 0.06 0.08

−0.01

0

0.01

0.02

0.03

0.04

(a) (b)

1234567891011

y (m

)

x (m)

y (m

)

x (m)

Fig. 3 Results of method of characteristics for nozzle exit Mach number of 2: (a) characteristics lines; (b) Mach number contours.



Simulation using computational fl uid dynamics

In this section, the resulting nozzle profi le produced using the method of character-istics with boundary layer correction, presented above, is used as an input for com-mercial software Fluent 6 (by Fluent Inc.). A two-dimensional unsteady, laminar, segregated (implicit) Navier–Stokes solver is employed in the present computations. The resulting computations of the solver are used to ensure that the proposed nozzle contour will not affect the resulting Mach number distribution in the test section. The solver is used to study the effects of: entrance angle to the nozzle; the settling chamber–nozzle interaction; and diffuser design.

Effect of nozzle entrance angleAn accurate picture of the divergent part of the nozzle, the throat radius and the majority of the convergent part of the nozzle is available after the above design stages. Computations using two-dimensional laminar Navier–Stokes solver are carried out to select the entrance angle to the nozzle as well as to ensure that the viscous effect will not affect the Mach number in the test section. The entrance angle of the convergent part of the nozzle is an important issue for Mach numbers other than 2 (e.g., 1.5 and 2.5), from the point of view of the interchangeability of the nozzle insert. This is because each Mach number will require a different nozzle insert profi le. Therefore, one must ensure that various nozzle profi les will work for the same entrance angle. Three entrance angles are selected for this study: 30°, 45°, and 60°, measured from the upstream nozzle center line. Grids were constructed for each case using Gambit software. For an entrance angle of 30°, a total of 5460 points in the domain were used (60 points in the stream direction and 91 points in the radial direction). More grid points were used for other cases. Fig. 5 illustrates the grids used for the computations.

From the computations, shown in Fig. 6, it was found that the 60° entrance angle produced the most uniform Mach number in the test section, as well as the lowest loss, which in turn increases the running time. In addition, the 60° entrance angle is

0 0.02 0.04 0.06 0.080

0.5

1

1.5

2

2.5

Mac

h nu

mbe

r

Axial distance, x (m)

Quasi-one-dimensional flowCenter lineWallCross-section (Average)

Fig. 4 Computed Mach number distribution by method of characteristics and one-dimensional fl ow theory, for nozzle exit Mach number of 2.



Fig. 5 Generated computational grids used for (a) 30°, (b) 45°, and (c) 60° nozzle entrance angles.



a good compromise for all the desired test section Mach numbers, specifi cally 1.5, 2 and 2.5, from the construction point of view. With this in mind, the entrance angle was set at 60°.

One of the great advantages of having a two-way approach to the more detailed aerodynamic design is that it gives us the opportunity to compare results obtained by the method of characteristics and the presented numerical simulation, as shown in Fig. 7. The results are very encouraging and give one the confi dence to move on to the detailed mechanical design of the wind tunnel.

Settling chamber interactionHaving selected the 60° entrance angle, the problem was then expanded to include the settling chamber in the computations, to detect what, if any, effect it would have. The present settling–nozzle area ratio is about 13. The effective length of the present settling chamber is twice length of the nozzle plus test section combined. Fig. 8

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0.5

1

1.5

2

2.5

(a) (b)M

ach

num

ber

Axial distance, x (mm)

30o

45o

60o

1.7 1.8 1.9 2 2.10

5

10

15

20

25

30

35

Hei

ght f

rom

cen

ter

line

(mm

)

Mach number

30o

45o

60o

Fig. 6 Mach number distribution for various test section entrance angles: (a) nozzle centerline–Mach number distribution; (b) test section–Mach number distribution.

0 20 40 60 800

0.5

1

1.5

2

2.5

Cen

terl

ine

Mac

h nu

mbe

r

Axial distance, x (mm)

Method of characteristicsNumerical Simulation

Fig. 7 Centerline–Mach number distribution for both the method of characteristics and a two-dimensional Navier–Stokes simulation for a 60° entrance nozzle angle.



shows the grid at selected grid lines used for the settling chamber–nozzle system computations. A relatively small number of grid points, about 11,700 points, is used to obtain the unsteady solution within an acceptable time.

The effect of the settling chamber is seen to be negligible, and even the predicted losses in running time due to pressure build-up in the settling chamber were not of major concern. This is probably because there is no regulator and when the valve is opened the tank pressure of 10 bar quickly expands to fi ll the volume of the settling chamber. The settling time is less than 2 s in the present computations. (The settling time is the time required for the Mach number to reach the design Mach number in the test section.) Fig. 9 shows the steady Mach number distribution in the settling chamber–nozzle system. The opening time of the valve is ignored in the present computation; that is, the tank pressure is imposed directly at the settling chamber inlet boundary. To ensure the fl ow uniformity, full perforated cone at the convergent part of the settling chamber and two screens at both the start and end of the constant area part of the settling chamber are installed in the fabricated tunnel.

Diffuser designDespite extensive literature surveys, no conclusive method for designing a diffuser was found. Phrases such as ‘art more than science’ and ‘by previous experience’

Fig. 8 Grid used for settling chamber–nozzle system computations.

Fig. 9 Mach number distribution from numerical simulations throughout the settling chamber–nozzle system, for a Mach number of 2 in the nozzle exit.



were commonplace in nearly all the literature reviewed. It was decided to try several types of diffuser and determine which offered the best effects. After several attempts, no diffuser was found to be acceptable. The resulting increase in the required stagna-tion pressure was seen as far too high a price to pay. Also, it became clear that a regulator would not be within the fi nancial capabilities of the current research. This meant that for a run of long duration, the diffuser would be raising the pressure when the stagnation pressure was already above that which would give an exit pressure above the ambient. This would have resulted in expanding fl ows outside the wind tunnel and a greatly increased noise level. It was decided to use a divergent diffuser with an angle of 15° for the present wind tunnel. The precaution of having a second throat before the diffuser, larger than the nozzle throat, with the model installed, was considered in the current wind tunnel design to ensure a stable fl ow in the test section.

Detailed design

The important factors for the detailed design are: (1) to keep the design as simple as possible; (2) to maximize the safety factor for the critical components like glass to about 5 (the test section glass window is a critical part of the tunnel and is used for fl ow visualization using the schlieren technique); (3) to use available commercial steel for construction of most of the tunnel components; (4) to conduct stress analysis of each component before manufacturing using commercial software (Nastran); (5) to allow easy assembly and disassembly of the test section and model section; (6) to install a quick-acting valve to pass the fl ow from the tanks to the settling chamber within 1 s or less. For safety reasons, a circuit was built to prohibit opening the quick-acting valve without switching on a warning alarm before operation in the fabricated tunnel.

In the following section, a brief description of the test section assembly and the model section assembly is presented.

Test section assemblyThe test section assembly comprises mainly the nozzle section, which has the wooden nozzle contour as determined by the preliminary design. The wooden surface in contact with the fl ow was hardened and smoothed using a special paint. The contour is encased in a sturdy metal frame and contains a glass covering over the test section as well as various pressure taps for measurements during experimen-tation. From the point of view of applied stresses and strength analysis, the glass is the only truly critical component and is designed using the procedure set out in [3]. Fig. 10 shows the resulting assembly.

Model support and diffuser assemblyThe model support assembly serves as the supporting section for the strut, which in turn holds the sting on which the model is fi xed. It is most important that the cross-section through which the fl ow passes does not fall below a certain level, in order to allow the passage of the normal shock during startup operations. Due to this, the



model section is a compromise between the fl ow requirements and the structural integrity of the strut and sting. The model section assembly serves also as the dif-fuser for the present wind tunnel design. Fig. 11 shows the resulting model support and diffuser assembly.

Fig. 10 (a) Components of the test section (note that there are two of each); (b) photograph of the assembled test section.

Fig. 11 (a) Components of the model support and diffuser assembly; (b) photograph of model support and diffuser section.



Testing and discussion

After the complete design and fabrication of the wind tunnel, a few simple experi-ments were carried out to ensure that it worked properly. The fi rst test simply involved measuring the pressure in the settling chamber (the stagnation pressure) and the pressure in the test section at various time intervals. The ratio of these two pressures is enough to give us the Mach number we need. The fi rst test was carried out without any model in the test section, to rule out any model interference in our results. The total storage capacity was 2100 liters (2.1 m3) pressurized to 9 bar (gauge pressure). The results are illustrated in Fig. 12, together with the curves pre-dicted for isentropic fl ow. At fi rst glance, the results look very promising; however, the divergence of the predicted results from the theory towards the end of the run needs to be examined in order to rule out any serious design fl aw in the wind tunnel. This might have contributed to the deviation of the real fl ow from the isentropic fl ow as well as the response of the gauges at low pressures. It was noticed that the surfaces of the wind tunnel underwent severe cooling, and hence the air must have

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Fig. 12 Pressures and test section conditions during a run: (a) tank total pressure; (b) settling chamber total pressure; (c) test section static pressure;

(d) test section Mach number.



absorbed considerable amounts of heat. This would lead to a departure from the isentropic assumption and may explain the divergence of the results. After this fi rst test, various models (i.e., cones with varying cone angles and a blunt body) were inserted in the test section and the shock waves emanating from the bodies photo-graphed using the schlieren system.

Fig. 13 shows the resulting schlieren photographs and Fig. 14 shows the measured shock wave angles from the different cones compared with the isentropic prediction presented in [8]. Again, the results look promising; however, the results from the 20° and 60° cones are far less impressive than those for the 40° cone. Horizontal alignment of the sting with model is performed manually and this may explain the discrepancy in the results.

Conclusion and further work

An extensive scheme for design, fabrication, and testing of an intermittent blow-down supersonic wind tunnel for the purpose of teaching the basics of compressible fl ow experiments is presented in this paper. The proposed scheme makes use of CFD capabilities in the design loop. This ensured that we had a working design before we embarked on the manufacture of any components, which would have been costly

Fig. 13 Schlieren photos for a blunt body and cones of various semivertex angles: (a) bow shock wave due to blunt body; (b) oblique shock wave due to 60° cone; (c) oblique shock wave due to 40° cone; (d) oblique shock wave due to 20° cone.



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10

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30

40

50

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70

80

90

Shoc

k w

ave

angl

e (d

eg.)

Cone semivertex angle (deg.)

TheoryPresent experiment

Fig. 14 Comparison of measured and theoretical prediction for Mach 2 shock wave angle for model cones of different cone angles.

to modify had there been any design error. A parametric study was carried out for the nozzle entrance angle and an angle of 60° resulted in a uniform Mach number distribution in the test section compared with the other angles studied in the present work. The fabricated tunnel then underwent a series of tests that were designed to prove that the tunnel did achieve the required Mach number. The results were com-pared with the most accurate data available and comparisons showed good agree-ment. The diffuser design needs to be explored in detail in order to reduce the air exit velocity from the tunnel, which in turn could reduce the aerodynamically pro-duced sound.

Acknowledgements

The authors would like to acknowledge Mr Shaady S. Abdel-Meguid, Mr Moham-med I. El-Dessoky, Mr Mohammed M. Zein, and Mr Mohammed S. Hussein for their valuable technical support during the development and construction of the present facility. The present supersonic facility would not have been possible without the generous fi nancial and technical support from the Faculty of Engineering, Cairo University, Egyptian Railways, Garage Equipment Centre, and PICO Industrial Co., represented by Eng. Hamdy Rashad, the managing director.

References

[1] J. D. Anderson, Fundamentals of Aerodynamics, 2nd edn (McGraw-Hill, New York, 1991).[2] J. D. Anderson, Modern Compressible Flow with Historical Perspective, 3rd edn (McGraw-Hill,

New York, 2003).[3] A. Pope and K. Goin, High Speed Wind Tunnel Testing (Krieger, Malabar, FL, 1965).[4] A. H. Shapiro, The Dynamics and Thermodynamics of Compressible Flow, vols 1, 2 (John Wiley

Sons, New York, 1953).



[5] A. Saad Michael, Compressible Fluid Flow, 2nd edn (Prentice Hall, New York, 1993).[6] Maurice J. Zucrow and Joe D. Hoffman, Gas Dynamics (John Wiley and Sons, New York, 1976).[7] Maurice Tucker, Approximate Calculation of Turbulent Boundary-Layer Development in Compress-

ible Flow (NACA, TN 2337, 1951).[8] Ames Research Staff, Equations, Tables, and Charts for Compressible Flow, Technical Report 1135

(NACA Ames, 1953).

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design, fabrication, and realization of a supersonic wind tunnel for educational...

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