SUPERSONIC AERODYNAMIC
Principles and Experimental Methods
Date: 23 February 2009
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By: U.A. Bhat
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Supervisor: Dr. C. Lambert
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Aerospace Department, Coventry University, UK.
Summary Section 1 – Tools of Supersonic Aerodynamic Studies
This report looks at the principles of supersonic airflow over a surface. The report is divided Two of the most important experimental tools used for studying supersonic flow are a
three sections. In the first section the report look at some of the tools that are used for supersonic wind tunnel and Schlieren image systems.
studying supersonic aerodynamics. In the second section the report covers some basic
1.1 Supersonic Wind Tunnels
principles of supersonic flow. In the third section the report covers an analysis real
experiment for studying supersonic flow which uses the experimental tools and methods A wind tunnel is one of the most important and widely used tool used experimental work in
mentioned discussed in Section 1. This section will cover an analysis of the flow and aerodynamics. Wind tunnels are used to create an airflow in which small scale models of
compare it with the background theory discussed in Section 2. wings, aircrafts or other bodies can be placed for aerodynamic studies. Type and structure of
a wind tunnel depends on the type of airflow that needs to be analysed. Based on this the
wind tunnels are designed for subsonic, transonic, supersonic and hypersonic flow. Even
though some of the principles of design remain similar there are some key differences in the
designs. Figure 1.1a shows the layout of a supersonic wind tunnel. For a supersonic wind
tunnel many sections of the tunnel the speed is subsonic, and therefore the design for these
Figure 1.1a Layout of supersonic tunnel at Coventry University
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sections is similar to that for a subsonic section. But in addition to the big differences in M = Mach number
power requirements there are a number of special problems to be met, and various additional γ = ratio of specific heats for a gas (1.4 for air)
devices have to be incorporated into tunnel design. The main sections of a supersonic the
For any given liner, the area distribution is fixed and therefore the Mach number, a liner of
wind tunnel are: a) Compressed air supply, b) Settling Chamber, c) Contraction Cone and
different shape is required. This generally means substituting a new liner, but some tunnels
Liner, d) Working Section, e) Transition Cone and Diffuser. These are discussed below.
have liners with flexible walls, so that their shape, and hence the working section Mach
a) Compressed Air supply number, may be continuously varied, even while the tunnel is running.
As stated earlier the power requirements for a supersonic wind tunnel are very high. For this Some liners are single-sided,
reason these tunnels use compressed air that is stored in high pressure tanks. It is important i.e., one wall of the liner is
that the air entering the supersonic wind tunnel does not contain any moisture. For this plane, as indicated in Fig 1.1c.
purpose driers are used which dry the air by heating it or have chambers hydroscopic This makes the replacement of
substances (e.g. silica gel) one liner by another much easier
and cheaper, but it may be more Figure 1.1b Convergent – Divergent nozzle
b) Settling Chamber
difficult to achieve uniform
The function of settling chamber is to increase uniformity of flow and reduce turbulence. The flow. The working section Mach number is only achieved downstream of an oblique shock
flow in this section runs at subsonic speeds and therefore the design is similar to settling wave located across the tunnel and generated by the concavity of the liner wall (Clancy
chamber of a subsonic wind tunnel. 1975:368)
c) Contraction Cone and Liner
Supersonic tunnel use a convergent-divergent nozzle to accelerate the flow to supersonic
speeds. This is different compared to a subsonic wind tunnel in which increase in velocity is
achieved by increasing the blowing pressure. In a supersonic tunnel the flow is accelerated
subsonically to sonic speed at the throat, assuming that a sufficient pressure ratio has been
established, and then accelerated supersonically to the required Mach number in the working
Figure 1.1c A single-sided Liner.
section, which is a parallel-sided section immediately downstream of the nozzle, throughout
which they should remain effectively constant (see Fig 1.1b). The whole channel, nozzle and
working section, is called the liner of the tunnel. The relationship between the area ration and d) Working Section
Mach number is given by equation 1.1
The working section of a supersonic wind tunnel is always rectangular in cross-section. This
is different from subsonic wind tunnels which might have a rectangular, circular or elliptical
1 --- eq. 1.1
cross section. The main reasons for this are:
Where, A = Area of working section a) It is easier to construct nozzles of the required area distribution if the section is rectangular.
*
A = Area of the throat
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b) The visualisation of the flow by optical methods involves the insertion of plane windows 1.2 Schlieren Image system
in the side of walls of the working section.
The light undergoes a change in direction due to change in its speed
C) When models are mounted in the working section, and tested, shock waves are generated as it travels from one medium to another. For example the light will
by the model. These are inevitably reflected by the tunnel walls, and it is imperative that the bend as it travels from air into water as can be seen in Figure 2.1.
reflected shocks should not stride the model. For this reason, at any given Mach number, the This property is known as refraction. Refraction also occurs within
shocking section must have a minimum height in relation to the model length or chord. This an inhomogeneous medium like air and is caused due to changing
would be impossible over the whole span of a two-dimensional model if the section were densities. The relationship between the refractive index of a medium
circular. (Clancy 1975:369) (such as air or other gases) and density is shown in equation 2.1 2.1 Refraction of light
e) Transition cone and Diffuser 1 --- eq. 2.1
The slowing down of air flow in a supersonic tunnel can be divided into two sections. The Where: n = refractive index of medium
first one is the transition cone where the flow is slowed down from supersonic to subsonic k = the Gladstone-Dale constant that depends on the light wavelength λ (=0.23 cm3/g of
speeds. The second section is the diffuser which the flow is reduced to the low speeds at visible light)
which the air is discharged into atmosphere or sent on its return circuit. The design of the and ρ = density of the medium.
second section is similar to a diffuser used for a subsonic tunnel.
Due to the changes being very small we are unable to see the effect with our naked eyes
however using a Schlieren imaging system we are able to visualize the density gradients.
One of the most popular applications is in supersonic/hypersonic flows. In this type of flows
there are important gradients of the density,
mainly across shock and expansion waves.
Through Schlieren technique these features can
be identified with great precision. This is
fundamental for the design of high – speed
vehicles, since their stability is strongly
dependent on the location of shock and
Fig. 2.2 Shock waves can be seen using Schlieren
expansion waves. (Jeronimo & Van Der
System
Haegen 2002)
Setup of Schlieren System
A simple Schlieren installation is depicted diagrammatically in Fig.2.3. Light from a source S
is collimated by a lens, so that a parallel beam passes through the working section of the wind
tunnel, is collected by another lens and brought to a focus at K, then passes through yet
another lens to project an image of the working section on to a screen. At the focus position,
K, a knife edge is introduced, which can be moved into or out of the beam to cut our some of
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or all of the light. When a model is introduced into the working section, its shadow appears 2 Principals of Supersonic flow
on the screen, and if the tunnel is now run, variation in density produces refraction of the Supersonic flow behaves very differently compared to subsonic flow. One of the main
light rays. Light passing through the region of positive density gradient normal to the knife differences is the way the flow behaves when it meets corners or passes through contacting
edge are cut off by the knife edge, and the corresponding area on the screen is darkened. Rays and expanding ducts. Understanding this behaviour of the supersonic flow will enable us to
passing through regions of negative density gradient in the working section are then deflected study how, when and where the shockwave and expansion waves are produce.
away from the knife edge,
2.1 Compressive Supersonic flow
In this section we will see how supersonic flow reacts when it meets a concave corner. A
concave corner can be a like small-angled wedge. One way of describing this kind of corner
is to say that if the flow were to go string on it would be interest the body as seen in Figure
2.1a
Fig 2.3 Setup for a simple Schlieren System (Clancy 1975:381)
so that more of these rays pass through the focus position, K, and the corresponding area on
the screen are lightened. Thus shock waves appear as dark lines, expansion regions as light
regions, on screen. If the knife edge were introduced into the beam from the opposite side,
this situation could be reversed, and the shock waves would appear as lighter lines. By
Figure 2.1a
moving the knife edge further into or out of the beam, the contrast,
and the general intensity of illumination, may be varied until an
The flow will in fact go straight on until it hits the shockwave which is formed by slowing up
optimum condition is achieved. Instead of being projected the
of the flow as a result of the point of the wedge being inserted in the flow, and the consequent
screen, the light beam may be projected directly on a photographic
converging of Mach Lines.
plate, and a photographic record made of the flow. (Clancy
1975:381) In this type of flow there will be an inclined or oblique shock wave. A shock wave oblique to
the flow causes both reduction in magnitude of the velocity and a change in its direction. The
The Schlieren system can be improved by using mirrors and extra
Fig 2.4 A setup of lenses flow after the corner is at a reduced velocity (though the velocity may still be supersonic), the
lenses to increase the distance that the light has to travel. An easier and knife edge for a
way of recording the images is by taking photographs of the screen. Schlieren System lines of flow are closer together, the pressure is higher, the density is higher (the air is
compressed, possibly quite appreciably), and the temperature is higher. The mach lines, at the
low speed, will be more steeply inclined to new surface.
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Supersonic flow most commonly compressed through a shock wave, and at the leading edge It should be noted that although the change at the expansion wave is gradual when compared
of a wing, or the nose of a body, or at the mouth of a contacting duct, there is – as at this with compared with that at a shock wave, it still takes place over a very short time and
wedge – no gradual change of pressure as with subsonic flow, but a sudden raise in pressure, distance compared with subsonic flow. (Kermode 2006:348)
density and temperature, and a sudden fall in velocity. This type of flow is called
The new velocity and the angles at which the waves are formed can be calculated using
compressive flow. (Kermode 2006:347)
Prandtl-Mayer expression. For the experiment in Section 3 an online calculator is used to find
The angle of the shockwave and the change in velocity can be calculated using form the the new Mach number.
speed of flow before the shock and the deflection angle. And easier way to do this is by
2.3 Flow over a Double wedge
looking at a table of compressible flow which has got most of the variables already calculated
at different Mach numbers and deflection angles. Figure 2.3a shows a double wedge model. As can be seen from the Figure, a double wedge
will has got both concave and convex corners. This means that at the concave corners on the
2.2 Supersonic Expansive Flow
leading edge and the trailing edge a shock wave will be produced at supersonic speeds. On
Supersonic flow also acts differently when it meets at a convex corner, i.e. one at which, if the other hand at the concave corner a Mach wave expansion will be produced.
the flow were to go straight on it would get farther away from surface. Fig 2.2 shows a
convex corner. As can be seen from the Figure the supersonic airflow is free to expand. This
it does, becoming more rarefied, i.e. decreasing in density in the decreased pressure and the
lines of flow are therefore farther apart, and the temperature also falls as is usually in an
expanding flow. The velocity on the other hand increases. Another fundamental difference
which is illustrated in the Figure is dotted lines indicated the slopes of the two Mach Lines,
the first one for the velocity of flow before the corner and the second one after the corner.
The second one is at a more acute angle to the new surface than the first one is to the original
surface, i.e. that the angle between the mach lines is greater that the change of angle of the
Figure 2.3a Double Wedge
surface. This is because the velocity after the corner is greater that before the corner. More
The Mach wave expansion will always be generated on the centre corners but whether a
important than this is to notice that between the mach lines the flow changes gradually on a
shock wave or a expansion wave is produced at the leading and trailing edges depends on the
cured path, not suddenly as at a shock wave because the Mach Lines no longer converge but
angle of attack and the wedge angle.
on the contrary then now diverge
Table 2.3 shows the three condition and the resulting waves for a positive angle of attack
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Table 2.3
Top leading Bottom leading Top Trailing Bottom Trailing Table 2.4
edge edge edge edge Top leading Bottom leading
α >δ Expansion Strong Shock Strong Shock Expansion edge edge
waves wave wave waves α >δ Expansion Strong Shock
α =δ No waves Strong Shock Strong Shock No waves waves wave
wave wave α =δ No waves Strong Shock
α [23 Jan 2009]
Kermode, A.C. (2006) 11th edn. ed. by Barnard, R.H. & Philpott, D.R. Machanics of Flight.
Harlow: Pearson Education Limited
Clancy, L.J. (1975) Aerodynamics. London: Pitman Publishing Limited
Chris (n. d.) Prandtl-Meyer calculator [online] available from
[21 Feb 2009]
Virginia Tech Department of Aerospace and Ocean Engineering (n. d.) Compressible
Aerodynamics Calculator [online] available from
[21 Feb 2009]
Seel, M.W.R. (1998) Tables for Compressible Flow of Dry Air
Software used
Gimps 2 – Image editing software
Digimizer – Image measurement and analysis software
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