Question

As a propulsion engineer, you are tasked with testing a turbojet engine to determine characteristics. The turbojet engine consists of a diffuser, compressor, combustion chamber, turbine and nozzle. Consider the following cases: its performance 2. Air approaches the diffuser of the turbojet engine with a pressure of 20 kPa at a Mach number of 2. A normal shock occurs at the inlet of the channel The exit to inlet area ratio is 3. Determine the following: a. The loss of total pressure b. The Mach number at the exit 3. Determine the diffuser efficiency if the shock is: a. At the inlet b. At the exit

Answer 1

Given data,

Inlet condition:

Pressure (P) = 20 kPa , Mach Number (M) = 2 , Specific heat ratio ($\gamma$) = 1.4

Exit condition:

Pressure (p) = ? , Mach Number (m) = ?

Now, as we know the standard formula for TurboJet engine,

Exit pressure

p /P = [ 2*$\gamma$*M² - ($\gamma$ - 1) ]/($\gamma$ + 1)

p = 20 * [ 2*1.4*2² - (1.4 - 1) ]/(1.4 + 1)

p = 90 kPa

So Total pressure loss = p - P = 90 - 20 = 70 kPa

Exit Mach number

m² = [ ($\gamma$ - 1)*M² + 2 ]/ [ 2*$\gamma$*M² - ($\gamma$ - 1)]

= [ (1.4 - 1)*2² + 2 ]/ [ 2*1.4*2² - (1.4 - 1)]

m = 0.58 <1 i.e sub sonic flow

Now Diffuser efficiency (n)

For subsonic flow , $\pi$ = 0.95

For Super sonic flow , $\pi$ = 0.85

At inlet , i.e. M = 2 (Supersonic flow)

n =  [ { 1 + 0.5* ($\gamma$ - 1)*M² } * $\pi$^{($\gamma$-1)/$\gamma$} - 1 ] / [0.5* ($\gamma$ - 1)*M² ]

=  [ { 1 + 0.5* (1.4 - 1)*2² } * 0.85^(1.4-1)/1.4 - 1 ] / [0.5* (1.4 - 1)*2² ]

n = 0.8875 = 88.75 %

At Exit , i.e. m = 0.58 (Supersonic flow)

n =  [ { 1 + 0.5* ($\gamma$ - 1)*m² } * $\pi$^{($\gamma$-1)/$\gamma$} - 1 ] / [0.5* ($\gamma$ - 1)*m² ]

=  [ { 1 + 0.5* (1.4 - 1)*0.58² } * 0.95^(1.4-1)/1.4 - 1 ] / [0.5* (1.4 - 1)*0.58² ]

n = 0.6827 = 68.27 %