Abstract
The use of crossed-wire probes to measure simultaneously the instantaneous stream-wise and normal velocities in supersonic turbulent flows has enabled researchers to investigate the characteristics of organized structures more fully. This paper examines both the practical aspects of using crossed-wire probes in supersonic flow and several methods of converting the resulting signals into useful quantities. Three small perturbation methods are compared in a Mach 2.9 boundary layer, and it is shown that the higher-order terms neglected in the traditional first-order perturbation analysis can alter the instantaneous velocity signals. This is particularly true for regions of intense streamwise mass flux fluctuations. A fourth method, which calculates the instantaneous flow angle directly from the inclined-wire formulation of King's Law, is introduced and discussed. While this method is potentially more accurate than the small perturbation techniques, it is more sensitive to parameter drift during the period between the wire calibration and actual testing.
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Abbreviations
- A, B, C :
-
sensitivities in the second-order expansion for e′
- D, F E :
-
anemometer voltage
- e′ :
-
anemometer voltage fluctuation
- G :
-
function containing angular dependence of anemometer voltage
- G′, G″ :
-
first and second derivatives of G with respect to φ
- k m :
-
longitudinal mass flux sensitivity
- k mv :
-
transverse mass flux sensitivity
- L :
-
intercept of King's Law
- M :
-
slope of King's Law, Mach number
- n :
-
Ling's Law exponent
- p :
-
pressure
- R Tu :
-
temperature-velocity correlation
- T :
-
temperature
- u, v :
-
instantaneous velocities in the streamwise and transverse directions
- u′, v′ :
-
fluctuating components of u and v
- φ :
-
instantaneous flow angle
- ψ :
-
angle of inclined wire with respect to the probe axis
- ξ :
-
function which relates k m to k mv
- ϱ :
-
density
- (ϱu):
-
instantaneous streamwise mass flux
- (ϱu)′:
-
fluctuating streamwise mass flux
- δ :
-
boundary layer thickness
- γ :
-
= 1.4, ratio of specific heats for air
- τ :
-
Reynolds shear stress, — \( - \bar \rho \overline {u'v'} \)
- x :
-
long-time average of x
- wall:
-
wall value
- 0:
-
tunnel stagnation value
- rms:
-
root-mean-square value
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Donovan, J.F., Spina, E.F. An improved analysis method for cross-wire signals obtained in supersonic flow. Experiments in Fluids 12, 359–368 (1992). https://doi.org/10.1007/BF00193881
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DOI: https://doi.org/10.1007/BF00193881