A supersonic wind tunnel draws air from a reservoir at stagnation temperature and…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Thermal, Statistical & Complex Systems · The laws of thermodynamics

Signal Speeds in Fluids, Ch Steady compressible flow: energy, stagnation and the Mach number

Problem

A supersonic wind tunnel draws air from a reservoir at stagnation temperature

T_0 = 400\,\mathrm{K}

and stagnation pressure

p_0 = 700\,\mathrm{kPa}

, and expands it isentropically to a test section running at

M = 2.5

. A thin flat-plate model of chord

c = 0.15\,\mathrm{m}

is mounted in the test section at an angle of attack

\alpha = 4^\circ

to the flow. Treat air as an ideal gas with

\gamma = 1.4

and

R = 287.05\,\mathrm{J\,kg^{-1}\,K^{-1}}

, and treat the flow as steady, inviscid and isentropic outside the thin Mach waves shed by the model. ((a)) Find the static temperature

T_1

and static pressure

p_1

in the test section. ((b)) Find the sonic temperature

T^*

, sonic speed

c^*

, and limiting speed

u_{\max}

of an isentropic expansion from the reservoir at

T_0 = 400\,\mathrm{K}

. ((c)) Using supersonic thin-aerofoil theory, find the lift coefficient

C_L

, drag coefficient

C_D

, and lift-to-drag ratio

L/D

of the model, and hence the lift and drag per unit span it experiences in the test section.