# Hypersonic interference heating in the vicinity of surface protuberances

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- Accepted:

DOI: 10.1007/s00348-010-0844-x

- Cite this article as:
- Estruch, D., MacManus, D.G., Stollery, J.L. et al. Exp Fluids (2010) 49: 683. doi:10.1007/s00348-010-0844-x

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## Abstract

The understanding of the behaviour of the flow around surface protuberances in hypersonic vehicles is developed and an engineering approach to predict the location and magnitude of the highest heat transfer rates in their vicinity is presented. To this end, an experimental investigation was performed in a hypersonic facility at freestream Mach numbers of 8.2 and 12.3 and Reynolds numbers ranging from *Re*_{∞}/*m* = 3.35 × 10^{6} to *Re*_{∞}/*m* = 9.35 × 10^{6}. The effects of protuberance geometry, boundary layer state, freestream Reynolds number and freestream Mach numbers were assessed based on thin-film heat transfer measurements. Further understanding of the flowfield was obtained through oil-dot visualizations and high-speed schlieren videos. The local interference interaction was shown to be strongly 3-D and to be dominated by the incipient separation angle induced by the protuberance. In interactions in which the incoming boundary layer remains unseparated upstream of the protuberance, the highest heating occurs adjacent to the device. In interactions in which the incoming boundary layer is fully separated ahead of the protuberance, the highest heating generally occurs on the surface just upstream of it except for low-deflection protuberances under low Reynolds freestream flow conditions in which case the heat flux to the side is greater.

### List of symbols

- α
Protuberance deflection angle, degrees

- α
_{R} Coefficient of resistivity, K

^{−1}- δ
Boundary layer thickness with edge at

*U*= 0.99*U*_{∞}, m- μ
Dynamic viscosity, kg m

^{−1}s^{−1}- θ
Temperature relative to wall, =

*T*_{aw}−*T*_{w}- Ø
Diameter, m

- ρ
Density, kg m

^{−3}- \( \left( {\sqrt {\rho c_{p} k} } \right)_{g} \)
Thermal property of gauges, J K

^{−1}m^{−2}s^{−0.5}*c*_{p}Specific heat capacity at constant pressure, J kg

^{−1}K^{−1}*G*System gain, = 2.06 at 0.1–5 kHz signal frequency

*h*Protuberance height, m

*k*Thermal conductivity, W m

^{−1}K^{−1}*l*Characteristic linear dimension, m

*L*Separation length ahead of protuberance-plate junction, m

*M*Mach number

- Nu
Nusselt number, =

*StRe*Pr*p*Static pressure, Pa

*P*_{D}Drive pressure, Pa

*Pr*Prandtl number, assumed = 1

*q*Heat flux, \( = {{\left( {\sqrt {\rho c_{p} k} } \right)_{g} \overline{{V_{2} }} } \mathord{\left/ {\vphantom {{\left( {\sqrt {\rho c_{p} k} } \right)_{g} \overline{{V_{2} }} } {\left( {\alpha_{R} V_{1} G} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\alpha_{R} V_{1} G} \right)}} \), W m

^{−2}- r
Recovery factor, assumed = 1

*Re*Reynolds number, \( = {{\rho Ul} \mathord{\left/ {\vphantom {{\rho Ul} \mu }} \right. \kern-\nulldelimiterspace} \mu } \)

*Re*/*m*Reynolds number per unit length, \( = {{\rho U} \mathord{\left/ {\vphantom {{\rho U} \mu }} \right. \kern-\nulldelimiterspace} \mu } \)

*Re*_{L}Reynolds number based on L, \( = {{\rho_{\infty } U_{\infty } L} \mathord{\left/ {\vphantom {{\rho_{\infty } U_{\infty } L} {\mu_{\infty } }}} \right. \kern-\nulldelimiterspace} {\mu_{\infty } }} \)

*Re*_{x,k}Reynolds number based on x

_{k}, \( = {{\rho_{\infty } U_{\infty } x_{k} } \mathord{\left/ {\vphantom {{\rho_{\infty } U_{\infty } x_{k} } {\mu_{\infty } }}} \right. \kern-\nulldelimiterspace} {\mu_{\infty } }} \)*Re*_{y,cl}Reynolds number based on y

_{cl}, \( = {{\rho_{\infty } U_{\infty } y_{cl} } \mathord{\left/ {\vphantom {{\rho_{\infty } U_{\infty } y_{cl} } {\mu_{\infty } }}} \right. \kern-\nulldelimiterspace} {\mu_{\infty } }} \)*St*Stanton number, \( = {q \mathord{\left/ {\vphantom {q {\left[ {\rho_{\infty } U_{\infty } c_{p} \theta } \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {\rho_{\infty } U_{\infty } c_{p} \theta } \right]}} \)

*t*Time, s

*T*Static temperature, K

*U*Axial velocity, m s

^{−1}*V*_{1}Initial voltage across gauge, V

- \( \overline{{V_{2} }} \)
Average output voltage of integrated signal across effective run duration, V s

^{−0.5}*W*Protuberance width, m

*x*Longitudinal distance, m

*y*Lateral distance from centreline, m

*z*Normal distance from flat plate, m

### Subscripts

- ∞
Freestream conditions

- *
Reference value

*aw*Adiabatic wall

*cl*Relative to centreline

*e*Conditions at boundary layer edge

*h*Based on protuberance height

*i*Incipient conditions

*k*Relative to protuberance leading edge

*le*Relative to flat plate leading edge

*o*Total or stagnation conditions

*s*Shock wave

*u*Undisturbed conditions at protuberance location

*w*Conditions on the wall

*x*Based on local values