# Hypersonic interference heating in the vicinity of surface protuberances

## 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

### References

- Arrington JP (1968) Heat transfer and pressure distributions due to sinusoidal distortions on a flat plate at Mach 20 in helium. NASA TN D-4907Google Scholar
- Bertram MH, Wiggs MM (1963) Effect of surface distortions on the heat transfer on a wing at hypersonic speeds. AIAA J 1(6):1313–1319CrossRefGoogle Scholar
- Chapman DR, Kuehn DM, Larson KH (1958) Investigation of separated flows in supersonic and subsonic streams with emphasis on the effects of transition. NACA 1356Google Scholar
- Coleman HW, Lemmon EC (1973) The prediction of turbulent heat transfer and pressure on a swept leading edge near its intersection with a vehicle. AIAA 73-677Google Scholar
- Davis SR (2008) Ares I-X flight test—the future begins here. AIAA paper 2008-7806Google Scholar
- Eckert ERG (1956) Engineering relations for heat transfer and friction in high-velocity laminar and turbulent boundary layer flows over surfaces with constant pressure and temperature. Trans ASME 78(6):1273–1283Google Scholar
- Elfstrom GM (1971) Turbulent separation in hypersonic flow. I.C. Aero Report 71-16Google Scholar
- Estruch D (2009) Hypersonic interference aerothermodynamics. PhD thesis, Department of Aerospace Sciences, Cranfield University, Bedford, UKGoogle Scholar
- Estruch D, Lawson NJ, MacManus DG, Garry KP, Stollery JL (2008) Measurement of shock wave unsteadiness using a high-speed schlieren system and digital image processing. Rev Sci Instrum 79(12):126108–126108-3Google Scholar
- Estruch D, Lawson NJ, Garry KP (2009a) Application of optical measurement techniques to supersonic and hypersonic aerospace flows. ASCE J Aero Eng 22(4):383–395CrossRefGoogle Scholar
- Estruch D, Lawson NJ, MacManus DG, Garry KP, Stollery JL (2009b) Schlieren visualization of high-speed flows using a continuous LED light source. J Vis 12(4):289–290CrossRefGoogle Scholar
- Estruch D, MacManus DG, Richardson DP, Lawson NJ, Garry KP, Stollery JL (2009c) Experimental study of unsteadiness in supersonic shock-wave/turbulent boundary-layer interactions with separation. Aero J (in press)Google Scholar
- Fay JA, Riddell FR (1958) Theory of stagnation point heat transfer in dissociated air. J Aero Sci 25(2):73–85MathSciNetGoogle Scholar
- Guoliang M, Guiqing J (2004) Comprehensive analysis and estimation system on thermal environment, heat protection and thermal structure of spacecraft. Acta Astron 54(5):347–356CrossRefGoogle Scholar
- Hakkinen RJ, Greber I, Trilling L (1959) The interaction on an oblique shock wave with a laminar boundary layer. NASA Mem 2-18-59WGoogle Scholar
- Holden MS (1964) Heat transfer in separated flow. PhD thesis, Imperial College, UKGoogle Scholar
- Hung FT, Clauss JM (1980) Three-dimensional protuberance interference heating in high-speed flow. AIAA-80-0289Google Scholar
- Hung F, Patel D (1984) Protuberance interference heating in high-speed flow. In: Proceedings of the 19th thermophysics conference. AIAA-84-1724Google Scholar
- Jones RA (1964) Heat-transfer and pressure investigation of a fin-plate interference model at a Mach number of 6. NASA TN D-2028Google Scholar
- Kuehn DM (1959) Experimental investigation of the pressure rise required for the incipient separation of turbulent boundary layers in two-dimensional supersonic flow. NASA Memo 1-21-59WGoogle Scholar
- Lakshmanan B, Tiwari SN, Hussaini MY (1988) Control of supersonic intersection flowfields through filleting and sweep. In: Proceedings of the 1st national fluid dynamics congress, Cincinanati, Ohio, Part 2, pp 746–759Google Scholar
- Meador WE, Smart MK (2005) Reference enthalpy method developed from solutions of the boundary-layer equations. AIAA J 43(1):135–139CrossRefGoogle Scholar
- Needham DA (1963) Progress report on the Imperial College hypersonic gun tunnel. Report 118Google Scholar
- Needham DA, Stollery JL (1966a) Hypersonic studies of incipient separation and separated flows. Aeronautical Res Council paper ARC 27752 January 1966Google Scholar
- Needham DA, Stollery JL (1966b) Boundary layer separation in hypersonic flow. AIAA 66-455Google Scholar
- Nestler DE (1985) The effects of surface discontinuities on convective heat transfer in hypersonic flow. AIAA Paper 85-0971Google Scholar
- Neumann RD, Hayes JR (1981) Protuberance heating at high Mach numbers, a critical review and extension of the database. AIAA 81-0420Google Scholar
- Olivier H (2009) Thin film gauges and coaxial thermocouples for measuring transient temperatures. SWL, RWTHGoogle Scholar
- Price EA, Stallings RL (1967) Investigation of turbulent separated flows in the vicinity of fin-type protuberances at supersonic Mach numbers. NASA TN D-3804Google Scholar
- Prince SA (1995) Hypersonic turbulent interaction phenomena and control flap effectiveness. MSc thesis, Cranfield University, Bedford, UKGoogle Scholar
- Rogers GFC, Mayhew YR (1980) Engineering thermodynamics work and heat transfer. Longman Scientific & Technical, John Wiley, New YorkGoogle Scholar
- Schultz DL, Jones TV (1973) Heat-transfer measurements in short-duration hypersonic facilities. AGARD-AG-165Google Scholar
- Simmons JM (1995) Measurement techniques in high-enthalpy hypersonic facilities. Exp Therm Fluid Sci 10(4):454–469CrossRefGoogle Scholar
- Stainback PC (1969) Effect of unit Reynolds number, nose bluntness, angle of attack, and roughness on transition on a 5° half-angle cone at Mach 8. NASA TN D-4961Google Scholar
- Sterret JR, Emery JC (1960) Extension of boundary layer separation criteria to a Mach number of 6.5 by utilizing flat plates with forward facing steps. NASA TN D-618Google Scholar
- Sterret JR, Morrissete EL, Whitehead AH Jr, Hicks RM (1967) Transition fixing for hypersonic flow. NASA TN D-4129Google Scholar
- Stollery JL, MacManus DG, Estruch D (2008) Hypersonic research and its application to a real vehicle. Seminar presentationGoogle Scholar
- Vannahme M (1994) Roughness effects on flap control effectiveness at hypersonic speeds. MSc thesis, Cranfield University, Bedford, UKGoogle Scholar
- Wang SF, Ren ZY, Wang Y (1998) Effects of Mach number on turbulent separation behaviours induced by blunt fin. Exp Fluids 25:347–351CrossRefGoogle Scholar
- Wang XY, Yuko J, Motil B (2009) Ascent heating thermal analysis on the spacecraft adaptor (SA) fairings and the interface with the crew launch vehicle (CLV). NASA TM-2009-215474Google Scholar
- Weinstein LM (1970) Effects of two-dimensional sinusoidal waves on heat transfer and pressure over a flat plate at Mach 8. NASA TN D-5937Google Scholar
- White FM (2006) Viscous fluid flow, 3rd edn. McGraw Hill, New YorkGoogle Scholar