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

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Abstract

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.

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Notes

  1. A similar approach was recently followed by Comte-Bellot and Sarma (2001) with a constant voltage anemometer (CVA) in a supersonic boundary layer.

  2. This is equivalent to assuming that G depends only on τ, which is sufficient for the present purpose.

  3. This value is close to the average pressure fluctuation at x/l=0.76: (<p>)0.76=(<p>EMW)0.76=0.130%.

  4. The boundary layer thickness was computed with the code of Harris and Blanchard (1982) assuming laminar–turbulent transition at the nozzle throat. The computational results agree very well with measurements at the nozzle output.

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: μ/μ r=(T/T r)b (dimensionless)

Be :

bandwidth (Hz)

A, B :

constants in the wire heat transfer relation (Eq. (7), dimensionless)

α :

\( \left( {1 + {{\gamma - 1} \over 2}Ma^2 } \right)^{ - 1} \) (dimensionless)

c p :

specific heat at constant temperature (kJ/kg K)

c v :

specific heat at constant volume (kJ/kg K)

δ :

boundary layer thickness (m)

D :

function of the overheat ratio (dimensionless)

e :

anemometer output voltage (V)

ε F :

end-loss attenuation factor for mass flow sensitivity (dimensionless)

ε G :

end-loss attenuation factor for total temperature sensitivity (dimensionless)

η :

recovery factor (dimensionless)

f :

frequency (Hz)

f 1 :

normalized frequency (dimensionless)

F :

anemometer nondimensional sensitivity to mass flow fluctuations (dimensionless)

G :

anemometer nondimensional sensitivity to total temperature fluctuations (dimensionless)

F AC :

ε F ×F (dimensionless)

GAC :

ε G ×G (dimensionless)

f,g :

functions in the wire heat transfer relation (Eq. (7), dimensionless)

γ :

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 θ :

anemometer sensitivity to total temperature fluctuations (V/K)

l :

Mach rhombus half-length (Fig. 1, m)

Ma :

Mach number (dimensionless)

μ :

viscosity of air (kg/m·s)

μ r :

viscosity of air at temperature Tr (kg/m·s)

n :

constant in the wire heat transfer relation (Eq. (7), dimensionless)

Nu :

Nusselt number (dimensionless)

p :

pressure (Pa)

p 0 :

stagnation pressure (Pa)

r :

−F/G (dimensionless)

R :

unit Reynolds number (1/m)

Re :

Reynolds number (dimensionless)

\( R_{{\rho u,T_{0} }} \) :

correlation coefficient between mass flow and total temperature fluctuations (dimensionless)

ρ :

density (kg/m3)

T :

time span (s)

T 0 :

total temperature (K)

T r :

reference temperature (K)

T w :

hot wire temperature (K)

τ :

overheat ratio: τ=(T w−ηT 0)/T 0 (dimensionless)

Θ :

−<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)

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

ε(X):

relative uncertainty of a random variable X

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Acknowledgements

This work was performed within the Partial Project TPC5 of the Special Research Group SFB259, established at Stuttgart University and financed by the German Research Foundation (DFG). The authors are grateful to Dr. Boris Smorodsky for his computation of the nozzle boundary layer thickness, and to Karl-Heinz Laicher and Manfred Giess for their expert technical assistance.

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  1. J. Weiss

    Present address: ALSTOM (Switzerland) Ltd., Brown Bovery Strasse 7, 5401, Baden, Switzerland

Authors and Affiliations

  1. Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, 70550, Stuttgart, Germany

    J. Weiss, H. Knauss & S. Wagner

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Correspondence to J. Weiss.

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Weiss, J., Knauss, H. & Wagner, S. Experimental determination of the free-stream disturbance field in a short-duration supersonic wind tunnel. Exp Fluids 35, 291–302 (2003). https://doi.org/10.1007/s00348-003-0623-z

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