Abstract
This article presents correlations for indirect measurement of skin friction inside a laminar separation bubble induced by hypersonic shock-boundary layer interaction (SBLI) on a flat plate. The correlations, based on parameters that are known to influence the SBLI region, were developed using exhaustive numerical and analytical studies. Experiments were conducted in a hypersonic shock tunnel at Mach 8.6 (±0.22) to measure surface heat-flux and pressure in the zone of SBLI on a flat plate, which were then used to supplement and validate the correlations. The data predicted by the correlations agreed reasonably well with that of exact solutions. The case studies contained non-reacting air, behaving as a perfect gas on a flat surface.
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Abbreviations
- C :
-
Chapman–Rubesin parameter
- C p :
-
pressure coefficient, \( 2p/\left( {\rho_{\infty } V_{\infty }^{2} } \right) \)
- c p :
-
specific heat at constant pressure (J/(kg-K)
- C f :
-
skin friction coefficient, \( 2\tau /\left( {\rho_{\infty } V_{\infty }^{2} } \right) \)
- C h :
-
Stanton number, \( q_{w} /\left( {\rho_{\infty } V_{\infty } \left( {h_{ad} - h_{w} } \right)} \right) \)
- h :
-
enthalpy (J/kg)
- h ad :
-
adiabatic-wall enthalpy (J/kg), had = T0 × cp × \( \sqrt {Pr} \) = T0 × 1005 × \( \sqrt {0.71} \)
- L sb :
-
length of separation bubble
- M :
-
Mach number
- p :
-
pressure (N/m2)
- Pr :
-
Prandtl number
- q:
-
heat flux (W/m2)
- r:
-
reattachment point
- s:
-
separation point
- Re :
-
Reynolds number
- T :
-
temperature (K)
- T * :
-
reference temperature (K), \( T^{*} = T_{\infty } \left( {1 + 0.032M_{\infty }^{2} + 0.58\left( {\frac{{T_{w} }}{{T_{\infty } }} - 1} \right)} \right) \)
- V :
-
velocity (m/s)
- \( x_{0} \) :
-
distance from leading edge where shock meets the flat plate in inviscid case
- \( \gamma \) :
-
specific heat ratio
- \( \delta_{0}^{*} \) :
-
displacement thickness of undisturbed flat-plate boundary layer at \( x_{0} , \) \( \delta_{0}^{*} = 0.664 \times \frac{\gamma - 1}{2} \times \frac{{M_{\infty }^{2} x_{0} }}{{\sqrt {Re_{{x_{0} }} } }} \times \left( {1 + 2.60\frac{{T_{w} }}{{T_{0} }}} \right) \) for weak viscous interaction
- θ :
-
flow turn-angle on the shock generator (wedge angle) (deg.)
- µ :
-
coefficient of dynamic viscosity (N-s/m2)
- ρ :
-
density (kg/m3)
- τ :
-
shear stress (N/m2)
- \( \bar{\chi } \) :
-
viscous interaction parameter
- SBLI:
-
shock-boundary layer interaction
- e :
-
boundary-layer edge property
- I:
-
shock-shear layer interaction point, shown in figure 4
- p :
-
pressure-plateau region
- r :
-
re-attachment point
- s :
-
separation (initiation) point
- w :
-
wall property
- x :
-
property at distance ‘x’ from leading-edge of flat plate
- ∞ :
-
freestream condition
- 0:
-
total condition
- *:
-
evaluated at reference temperature, T*
References
Meloy J, Griffin J, Sells J, Chandrasekharan V, Cattafesta L N and Sheplak M 2011 Experimental verification of a MEMS based skin friction sensor for quantitative wall shear stress measurement. AIAA Paper 2011-3995
Vasudevan B 2005 Measurement of skin friction at hypersonic speeds using fiber-optic sensors. AIAA Paper 2005-3323
Bowersox R D W, Schetz J A, Chadwick K and Deiwert S 1995 Technique for direct measurement of skin friction in high enthalpy impulsive scramjet flowfields. AIAA Journal 33: 1286–1291
Novean M G, Schetz J A and Bowersox R D W 1997 Direct measurements of skin friction in complex supersonic flows. AIAA Paper 97-0394
Holden M S 1978 A study of flow separation in regions of shock wave-boundary layer interaction in hypersonic flow. In: 11th Fluid and Plasma Dynamics Conference, pp. 1169–1190
Kelly G M, Simmons J M and Paull A 1992 Skin-friction gauge for use in hypervelocity impulse facilities. AIAA Journal 30: 844–845
van Driest E R 1952 Investigation of laminar boundary layer in compressive fluids using the Crocco method. NACA Technical Note 2597
Goyne C P, Stalker R J and Paull A 2003 Skin-friction measurements in high-enthalpy hypersonic boundary layers. Journal of Fluid Mechanics 485: 1–32
Meritt R J, Schetz J A, Marineau E C, Lewis D R and Daniel D T 2017 Direct skin friction measurements at Mach 10 in a hypervelocity wind tunnel. Journal of Spacecraft and Rockets 54: 871–882
Schülein E 2006 Skin-friction and heat flux measurements in shock/boundary-layer interaction flows. AIAA Journal 44: 1732–1741
Anderson J D Jr. 2006 Hypersonic and High-Temperature Gas Dynamics. 2nd edn. AIAA, Virginia, pp. 261–374
John B and Kulkarni V 2014 Numerical assessment of correlations for shock wave boundary layer interaction. Computers and Fluids 90: 42–50
John B, Kulkarni V N and Natarajan G 2014 Shock wave boundary layer interactions in hypersonic flows. International Journal of Heat and Mass Transfer 70: 81–90
Sahoo N, Saravanan S, Jagadeesh G and Reddy K P J 2006 Simultaneous measurement of aerodynamic and heat transfer data for large angle blunt cones in hypersonic shock tunnel. Sadhana 31: 557–581
Knauss H, Roediger T, Bountin D A, Smorodsky B V, Maslov A A and Srulijes J 2009 Novel sensor for fast heat-flux measurements. Journal of Spacecraft and Rockets 46: 255–265
Moore F K 1961 On local flat-plate similarity in the hypersonic boundary layer. Journal of the Aerospace Sciences 28: 753–762
Chapman D R, Kuehn D M and Larson H K 1958 Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition. NACA Technical Report 1356
Coleman H W and Steele W G 2009 Experimentation, Validation and Uncertainty Analysis for Engineers. 3rd edn. Wiley, New Jersey, pp. 61–81
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Kshetrimayum, M., Irimpan, K.J. & Menezes, V. Skin friction estimation on a surface under shock-boundary layer interaction. Sādhanā 45, 195 (2020). https://doi.org/10.1007/s12046-020-01437-8
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DOI: https://doi.org/10.1007/s12046-020-01437-8