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Unsteadiness of the shock wave structure in attached and separated compression ramp flows

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Abstract

Wall pressure fluctuations have been measured upstream of the corner-line in several two dimensional, adiabatic, compression ramp flows. The nominal freestream Mach number was 3 and the Reynolds number, based on boundary layer thickness, was 1.4 million. The measurements show that the shockwave structure is unsteady in both separated and attached flows, resulting in a region in which the wall pressure signal is intermittent. Statistical properties of this intermittent region, and of the separated flow, are presented and correlated with results from other studies.

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Abbreviations

C f :

skin friction coefficient

D :

blunt fin leading edge diameter

f :

frequency (Hz)

G(f):

power spectral density = \(\mathop {lim}\limits_{\Delta f \to 0} \frac{1}{{(\Delta f)}}\left[ {\frac{{lim}}{{T_{ \to \infty } }} \frac{1}{T} \int\limits_0^T {P_w^2 } (t,f,\Delta f)dt} \right]\)

L s :

streamwise length of shock motion

L sep :

length of separated flow

M :

Mach number

n :

number of data points used to calculated π w , σp w , etc.

P w :

instantaneous wall pressure

P w (t, f, Δf):

portion of P w (t) in the frequency range from f to Δf

π w :

mean wall pressure = \(\frac{1}{n} \sum\limits_{i = 1}^n {P_{w_i } }\)

q :

dynamic pressure

r :

recovery factor

t :

time

T :

signal observation time

Re :

Reynolds number

U :

velocity

X :

streamwise distance measured from the ramp corner (Fig. 1)

ΔX :

distance from interaction start to separation

α:

ramp angle (degrees)

α3 :

skewness coefficient = \(\frac{{\frac{1}{n} \sum\limits_{i = 1}^n {(P_{w_i } } - \bar P_w )^3 }}{{\sigma p_w^3 }}\)

α4 :

flatness coefficient = \(\frac{{\frac{1}{n} \sum\limits_{i = 1}^n {(P_{wi} } - \bar P_w )^4 }}{{\sigma p_w^4 }}\)

σ:

boundary layer thickness

σ* :

boundary layer displacement thickness

γ:

intermittency (Eq. 2)

σp w :

wall pressure standard deviation \( = \left[ {\sum\limits_{i = 1}^n {(P_{w_i } } - \bar P_w ){\raise0.5ex\hbox{$\scriptstyle 2$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle n$}} - 1} \right]^{ 1/2}\)

θ:

boundary layer momentum deficit thickness

aw :

adiabatic wall

e :

at boundary layer edge

m :

maximum

0:

just upstream of interaction start

w :

at the wall

∞:

undisturbed freestream conditions

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Authors and Affiliations

  1. Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, 78712-1085, Austin, Tex., USA

    D. S. Dolling

  2. Mechanical and Aerospace Engineering Department, Princeton University, New Jersey, USA

    C. T. Or

Authors
  1. D. S. Dolling
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  2. C. T. Or
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Dolling, D.S., Or, C.T. Unsteadiness of the shock wave structure in attached and separated compression ramp flows. Experiments in Fluids 3, 24–32 (1985). https://doi.org/10.1007/BF00285267

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