Question

What is the formula to compute the efficiency of diffusers?

(a) ηD = \(\frac {(\frac {p_{d_0}}{p_0})_{actual }}{(\frac {p_{0_2}}{p_{01}})_{normal \, shock \, at \, M_e}}\)

(b) ηD = \(\frac {(\frac {p_{d_0}}{p_0})_{actual }}{(\frac {p_{0_2}}{p_{01}})_{oblique \, shock \, at \, M_e}}\)

(c) ηD = \(\frac {(\frac {p_{0_2}}{p_{01}})_{normal \, shock \, at \, M_e}}{(\frac {p_{d_0}}{p_0})_{actual }}\)

(d) ηD = \(\frac {(\frac {p_{0_2}}{p_{01}})_{oblique \, shock \, at \, M_e}}{(\frac {p_{d_0}}{p_0})_{actual }}\)

This question was addressed to me in an international level competition.

My question is taken from Compressible Flow through Diffusers in section Compressible Flow through Nozzles, Diffusers and Wind Tunnels of Aerodynamics

Answer 1

Correct option is (a) ηD = \(\frac {(\frac {p_{d_0}}{p_0})_{actual }}{(\frac {p_{0_2}}{p_{01}})_{normal \, shock \, at \, M_e}}\)

The explanation is: The efficiency of diffuser is measured by the ratio of actual total pressure ratio \(\frac {p_{d_0}}{p_0}\)  to the total pressure ratio across hypothetical normal shock wave at test section Mach number \(\frac {p_{0_2}}{p_{01}}\).