Gas Dynamics-nozzles And Diffusers

Con--Div Diffuser Con Ø

Ø

With most present day aircraft engines, it is necessary to decelerate the air to subsonic velocity before passing it to the engine, this deceleration also increases the pressure of the incoming air. The deceleration is carried out in the diffuser. The deceleration potentially being shockshock-less at the design flight Mach number of the aircraft. In such a case the flow through the diffuser will be as shown in the following figure.

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Diffuser with different Inlet Mach number

M < Mdes

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Cont.. M > Mdes

n

Increase in Mach number will cause the Shock wave to be “swallowed” by the diffuser and the shock wave then settles in the divergent portion of the diffuser as shown in the above figure.

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Cont..

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Diffuser Performance

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Stagnation pressure ratio versus Mach number

P – Static Pr . Pt - Total Pr .

n

T otal Pr . Ratio is least sensitive to variations ofγ

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Cont..

T – Static Temp. Tt - Total Temp.

T/ Tt ratio relatively insensitive to variations in γ below M ≈ 0.8

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Cont.. Area ratio versus Mach number

Area ratio relatively insensitive to variations in γ below M ≈ 1.5

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Limitations of Gas tables 1.

2.

3.

4.

They do not show trends or the ‘big picture.’ There is almost always the need for interpolation. They display only one or at most a few values of γ. They do not necessarily have the required accuracy.

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Question 1 How to locate sonic state on the TT-s diagram? If the flow is subsonic, the sonic state will be below its static state. If the flow is supersonic, the sonic state will be above its static state.

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Question 2 A large supply chamber containing air at 6.0 atm and 300K is connected to a converging nozzle on the left side and a CC-D nozzle on the right side. Both nozzles share the same minimum passage area of 100 sq.cm. The CC-D nozzle has an exitexit-toto-throat area ratio of 1.2

Pamb

a) Let us consider the converging nozzle at the left and compare the pressure level at point A, C, and D.

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Cont..

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Cont..

b)

If the ambient pressure is reduced to 5.0 atm. What is the mass flow rate in the nozzle?

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Cont.. From the T emperature ratio Texit is Texit = 284.8 K

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Cont.. How much do we need to lower the ambient pressure to reach the choking point of this converging nozzle? For a converging nozzle, the ambient pressure has to be lower than 52.8% of the chamber pressure to choke the converging nozzle. This corresponds to an ambient pressure of Pamb ≤ 3.17 atm

If Pamb is lower than 3.17 atm, the exit plane pressure will not be the same as the ambient value (pressure mismatch). Pamb will keep staying at 3.17 atm. This is because no downstream pressure information can propagate upstream past the sonic point (exit plane). The flow within the nozzle becomes invariant once the sonic condition is attained at the exit.

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What is the mass flow rate at choking condition? For a con. nozzle the ambient pressure has to be lower than 52.8% of the chamber pressure to choke the con. Nozzle. This corresponds to an amb. Pr . of Pamb ≤ 3.17 atm. When Pamb = 3.17 atm, the Mach no. at the exit plane just reaches unity. From Isentropiv table at M = 1

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Let us consider CC-D nozzle on the right

n

n

n

If the ambient pressure is set at 5.0 atm, do you expect the mass flow rate in the C-D nozzle to be the same as that in the converging nozzle computed before? For this C-D nozzle case, we also need to check if the nozzle is choked at Pamb = 5.0 atm. The main difference between the C-D nozzle and the converging nozzle is that the choking pressure ratio is dependent on the exit-to-throat area ratio (not a universal constant anymore). With an area ratio of 1.20, we find from the isentropic flow table that the subsonic solution gives a pressure ratio

Hence, we conclude that - the ambient pressure is high enough that the flow is not choked - the flow remains subsonic within the C-D nozzle - ρexit, Mexit and Texit are the same as those in the converging nozzle case

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Cont.. Since the exit area is 1.20 times as large as that of the converging nozzle, we expect a 20 % increase in the mass flow rate. Hence, m.f.r is 12.96 kg/m3. How much do we need to lower the ambient pressure for the nozzle to operate at its first critical point? The first critical point corresponds to an isentropic, subsonic solution with Mach 1.0 flow at the throat. We obtain from the isentropic flow table that

What is the corresponding mass flow rate at the first critical point? Once this convergingconverging-diverging nozzle is choked at its first critical point, we know that Mach 1.0 is achieved at its minimum flow area, i.e. at the throat. We expect that same m.f.r as that of the converging nozzle choked case PDF created with pdfFactory trial version www.pdffactory.com

Cont.. At the design point (third critical) What is the ambient pressure? The third critical point corresponds to an isentropic, supersonic solution in the CC-D nozzle. For an area ratio of 1.20, we obtain a supersonic solution from the isentropic flow table Mexit = 1.534 This solution gives a pressure ratio Pamb/P0 = 0.25922, so Pamb = 1.55 atm Look back to our calculations: n

How do you compare the ambient pressure which is required to choke the converging and CC-D nozzle? Which one is higher? Can you explain it?

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Cont..

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Cont..

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Isentropic Nozzle flow

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1-D

Flow through constant area ducts

a) Adiabatic duct flow with Friction ( Fanno Flow) b) Duct flow with Heat Transfer and negligible friction ( Rayleigh Flow)

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