Experimental determination of the free-stream disturbance field in a short-duration supersonic wind tunnel

The free-stream disturbance field in a short-duration supersonic wind tunnel is investigated at a nominal Mach number of Ma=2.54. A specially designed constant-temperature anemometer is used to be able to draw a complete fluctuation diagram within one wind tunnel run (testing time: 120 ms). It is shown that the disturbance field is dominated by acoustic waves radiated from the turbulent boundary layer on the nozzle and the sidewalls, like in conventional supersonic wind tunnels. The acoustic field appears to be composed of highly localized shivering Mach waves superimposed on a background of eddy Mach waves.Abbreviations  a constant in the thermal conductivity/temperature power law of air: k/k_r=(T/T_r)^a (dimensionless) - b constant in the viscosity/temperature power law of air: /_r=(T/T_r)^b (dimensionless) - Be bandwidth (Hz) - A, B constants in the wire heat transfer relation (Eq. (7), dimensionless) -   (dimensionless) - c_p specific heat at constant temperature (kJ/kg K) - c_v specific heat at constant volume (kJ/kg K) -  boundary layer thickness (m) - D function of the overheat ratio (dimensionless) - e anemometer output voltage (V) - _F end-loss attenuation factor for mass flow sensitivity (dimensionless) - _G end-loss attenuation factor for total temperature sensitivity (dimensionless) -  recovery factor (dimensionless) - f frequency (Hz) - f₁ normalized frequency (dimensionless) - F anemometer nondimensional sensitivity to mass flow fluctuations (dimensionless) - G anemometer nondimensional sensitivity to total temperature fluctuations (dimensionless) - F_AC F×F (dimensionless) - G_AC G×G (dimensionless) - f,g functions in the wire heat transfer relation (Eq. (7), dimensionless) -  c_p/c_v (dimensionless) - k thermal conductivity of air (W/m K) - k_r thermal conductivity of air at temperature T_r (W/m K) - k anemometer sensitivity to total temperature fluctuations (V/K) - l Mach rhombus half-length (Fig. 1, m) - Ma Mach number (dimensionless) -  viscosity of air (kg/m·s) - _r viscosity of air at temperature T_r (kg/m·s) - n constant in the wire heat transfer relation (Eq. (7), dimensionless) - Nu Nusselt number (dimensionless) - p pressure (Pa) - p₀ stagnation pressure (Pa) - r –F/G (dimensionless) - R unit Reynolds number (1/m) - Re Reynolds number (dimensionless) -  correlation coefficient between mass flow and total temperature fluctuations (dimensionless) -  density (kg/m³) - T time span (s) - T₀ total temperature (K) - T_r reference temperature (K) - T_w hot wire temperature (K) -  overheat ratio: =(T_w–T₀)/T₀ (dimensionless) -  –<e>/G (%) - u x-component of the flow velocity (m/s) - u_s source velocity at acoustic origin (m/s) - u inviscid velocity at acoustic origin (m/s) - x wind tunnel axis (Fig. 1, m)Symbols  x̄ temporal mean value of a fluctuating quantity x - x fluctuating part of x: x=x–x̄ - x_RMS^' root mean square of x - <x> x_RMS^'/x̄ - (X) relative uncertainty of a random variable X

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