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Compressible Flow: Supersonic Wind Tunnels
Aerospace Engineering, International School of Engineering (ISE) Academic year : 2013-2014 (January – May, 2014)
Jeerasak Pitakarnnop , Ph.D.
[email protected] [email protected]
March 29, 2014 Aerodynamics II 1
How to generate Mach 2.5 flow?
March 29, 2014 Aerodynamics II 2
High pressure supplied
require a large reservoir which
is costly. Shock free expansion pe = pB
More efficient way with less cost!
March 29, 2014 Aerodynamics II 3
Normal shock is the strongest shock which
create huge loss.
Extremely difficult to hold the shock exactly at the exit of the duct. Test SecPon
When introduce a test model, complex shock wave will form, the normal shock wave could not exist is such flow.
Final SoluPon – Oblique Shock Diffuser
March 29, 2014 Aerodynamics II 4
The waves propagate downstream and
interacts with the shock in the diffuser Large p0 or small pB
(vacuum) or combinaPon of both
At,2At,1
=p0,1p0,2
Ex1: Supersonic Wind Tunnel
• For the preliminary design of a Mach 2 supersonic wind tunnel, calculate the raPo of the diffuser throat area to the nozzle throat area.
March 29, 2014 Aerodynamics II 5
EX2: Exhaust Nozzle • Consider a rocket engine burning hydrogen and oxygen; the combusPon chamber temperature and pressure are 3517 K and 25 atm, respecPvely. The molecular weight of the chemically reacPng gas in the combusPon chamber is 16, and γ = 1.22. the pressure at the exit of the convergent-‐divergent rocket nozzle is 1.174 x 10-‐2 atm. The area of the throat is 0.4 m2. Assuming a calorically perfect gas and isentropic flow, calculate: – The exit Mach no. – The exit velocity – The are of the exit – The mass flow through the nozzle
March 29, 2014 Aerodynamics II 6
EX3: Convergent-‐Divergent Nozzle
• Consider the flow through a convergent-‐divergent duct with an exit-‐to-‐throat area raPo of 2. The reservoir pressure is 1 atm, and the exit pressure is 1 atm, and the exitpressure is 0.95 atm. Calculate the Mach nos. at the throat and at the exit.
March 29, 2014 Aerodynamics II 7
EX4: Convergent-‐Divergent Nozzle
• Consider a convergent-‐divergent duct with an exit-‐to-‐throat area raPo of 1.6. Calculate the exit-‐to-‐reservoir pressure raPo required to achieve sonic flow at the throat, but subsonic flow everywhere else.
March 29, 2014 Aerodynamics II 8
EX5: Convergent-‐Divergent Nozzle
• Consider a convergent-‐divergent nozzle with an exit-‐to-‐throat area raPo of 3. A normal shock wave is inside the divergent porPon at a locaPon where the local area raPo is A/At = 2. Calculate the exit-‐to-‐reservoir pressure raPo.
March 29, 2014 Aerodynamics II 9
Shock LocaPon – IteraPve SoluPon
• Assume shock locaPon (As/At) • Calculate pressure raPo (pe/pi) • Check whether pe/pi is agree with the specified value or not.
• If not, assume another As/At
• Repeat unPl accurate pe/pi is found.
March 29, 2014 Aerodynamics II 10
pi
pe
pt,s1 pt,s2 At
A*s1 A*s2
Ae
Normal Shock
Throat
Shock LocaPon – Direct SoluPon
March 29, 2014 Aerodynamics II 11
pi
pe
pt,s1 pt,s2 At
A*s1 A*s2
Ae
Normal Shock
Throat
Me2 = −
1γ −1
+1
γ −1( )2+2
γ −12
γ +1"
#$
%
&'
γ+1γ−1"
#$
%
&' pt,eAe
*
peAe
"
#$
%
&'
2
• From given pressure and area, calculate Me
• Then calculate total pressure across the shock
• Ms1 could be determined from total pressure across the shock.
• As/At can be found from Ms1.
EX6: Convergent-‐Divergent Nozzle
• Consider a convergent-‐divergent nozzle with an exit-‐to-‐throat area raPo of 3. The inlet reservoir pressure is 1 atm and the exit staPc pressure is 0.5 atm. For this pressure raPo, a normal shock will stand somewhere inside the divergent porPon of the nozzle. Calculate the locaPon of the shock wave using – A trial-‐and-‐error soluPon – The exact soluPon
March 29, 2014 Aerodynamics II 12
