Supersonic Wind Tunnels ●
Why do we need supersonic wind tunnels ?
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Types of common wind tunnels (I) Blowdown wind tunnels (open-loop) which uses high-pressure gas storage tanks for feeding the supersonic nozzle & the test section.
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(II) Continuous-duty wind tunnels (closed-loop) which basically use a compressor and heat exchanger. They are used where long testing times are required ?. The main parts of the closed-loop wind tunnels are: 1) supersonic nozzle......to get M>1 2) test section.........for testing purposes 3) supersonic diffuser.......to reduce stagnation pressure loss and accordingly compressor power required to make up for steady state losses 4) Compressor.......to start up & overcome all steady-state losses. 5) Heat exchanger.....to cool the air that is heated by the compressor
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Nozzle
Diffuser M>1
M>1
M<1
M=1
M>1
Test section
M<1
M=1
M<1
M<1
Compressor
Heat Exchanger
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Wind Tunnel Startup Sequence M<1 M<1
M<1
M<1
M<1
(a) Initial Startup: Power is just applied to compressor & flow is subsonic through the entire wind tunnel loop
M<1 M=1
M<1
M<1
M<1
(b) First Throat Sonic: Increase of compressor power leads to flow choking at the minimum area, the flow subsonic elsewhere
M>1 M<1 M=1
M<1
M<1
M<1
(c) Shock in Diverging Section: Additional increase of compressor power leads to supersonic flow in the diverging & a N.S. there
*
(A )x
M>1
(A*)y
M<1 M=1
x y
M=1
M<1
M<1
(d) Shock in Test Section Entrance: Further increase of compressor power leads eventually to a shock at nozzle exit (test section entrance)
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At this point, some notes are due: 1. Stagnation pressure loss is maximum when shock wave is in the test `section ? 2. Diffuser throat must be larger than the nozzle throat ?. Hint: recall the isentropic relation of the maximum mass flow rate per unit area, which suggests that:
p ox A*x p oy A*y M>1
(A*)x M>1
M>1
M=1
M>1
M<1
M<1
(e) Shock Swallowed: Any further increase of a compressor power leads to moving the shock into the converging section of the diffuser. But, the shock can not remain there ? (why?) and moves through the throat where it is said: "The Shock is Swallowed" Note that, P0 becomes the same for both throats ? (why ?)
(A*)x M>1
M>1
M=1
M>1
M<1
M=1
M<1
M<1
(f) Shock-free Deceleration with Variable-area Diffuser Throat ?: Realizing that P0 is the same for both throats, so (1) Adjust the diffuser throat area to the same value as the nozzle throat (2) Increase back pressure to move shock backward until it disappears in the diffuser throat
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(A*)x M>1
M>1
M>1
M<1
M=1 M<1
M<1 (g) Shock in diffuser throat (Fixed-area throat): Increasing back pressure (reducing compressor power) gradually till the shock is placed in the diffuser throat
(where the lowest Mach number and minimum Stagnation pressure loss ?)
Note: For both diffusers, variable-area and fixed-area throats, it is suggested that the shock wave be placed slightly downstream of the diffuser throat. This is because some fluctuations are always present in the flow ??.
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T-s diagram of The most unfavorable starting conditions & The best operating conditions for Supersonic wind tunnel The most unfavorable starting conditions (shock in test section)
ox
x y
*x M>1
oy
*y
M<1
M>1
M<1
M<1
M=1
M=1
M<1
M<1
Shock
The best operating conditions for a fixed-area diffuser (shock in diffuser throat)
ox
x
*x M>1
oy2
x2 y2
M>1
M>1
M<1
M=1 M<1
M<1
Shock
T * Path of states when shock is in test section is: ox - x - y - *y - oy
p ox To
p oy 2
ox oy2
poy
oy py
y y2
Tx* Ty* Ty*2
*x
* Path of states when shock is in diffuser throat is: ox - x - x2 - y2 - oy2
*y
Nozzle
Test section
x2
px
Diffuser
x
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Example: A continuous-duty supersonic wind tunnel is to be designed. The test section specifications are a Mach number of 2, a static pressure of 40 kPa, a static temperature of 250 K, and an area of 0.5 m2 . Determine the stagnation conditions required upstream of the test section, the mass flow rate required, and the throat area required. During the startup process, what is the maximum stagnation pressure loss across the shock system ?, sketch this process on the T-s diagram. If a constant-area diffuser is used, what is the minimum diffuser throat area?. If a variable area-diffuser is used, explain the startup sequence required to achieve shock-free operation. M=2 A=0.5m2 p=40 kPa T=250 K
Test section
Heat Exchanger
Compressor
(A*)x
x y
M=2
M>1
M<1
M=1 Shock
Fixed-area diffuser steady-state operating conditions (Shock in diffuser throat)
(A*)y=(A*)x
(A*)x
M=2 M=1
M<1
M=1
Variable-area diffuser steady-state operating conditions (Shock-free deceleration) 56
Required: pox & Tox A*x max m po max (pox poy ) when shock is in test section A*y
Solution: enter M=2
A A*x 1.6875
read
p p ox 0.1278
Isentropic tables
T To 0.5556
A*x 0.5 1.6875 0.2963 m 2 , pox 40 0.1278 313 kPa , To 250 0.5556 450 K max 0.04042 & m
A*x pox 176.7 kg/s To
Note: Max. stagnation pressure loss is when shock is in the test section, enter M=2
read Normal S.W. tables
p omax p ox p oy 83.36 kPa A*y A*x pox poy A*y 0.2963 1 0.7209 A*y 0.411 m 2
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poy pox 0.7209
Maximum stagnation pressure loss during startup process (shock in test section)
ox
x y
*x M>1
oy
*y
M<1
M>1
M<1
M<1
M=1
M=1
M<1
Shock
T
p ox To
M<1
poy
ox
oy py
y
Tx* Ty*
*x *y
px x
s If a variable area diffuser is used, * throat must initially be 0.411 m2 * power is increased till shock is swallowed * diffuser is, then, reduced to first throat (0.2963 m2) and at the same time back pressure is increased to place shock in diffuser throat. Ultimately, a shock-free operation will be attained.
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