Surface Boundary Conditions for Hypersonic Flow Simulation

Jacob Needels

Prof. Juan J. Alonso

3^rd SU2 Conference

September 5-7, 2022

Motivation

• Hypersonic flows are characterized by high temperatures and large aerothermal loads
• Heat flux and wall temperature are important quantities of interest in hypersonic design problems
• Recent development effort within the SU2-NEMO community has focused on the simulation of flows in thermochemical nonequilibrium^1,2, allowing accurate prediction of
• Reacting flows
• Thermodynamic properties
• Transport properties
• But to predict heat loads and wall temperatures, accurate physical models at the surface boundary are also required

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Perfect Gas

Nonequilibrium

Mach 15.5 Cylinder in Cross-flow

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1. Maier, W.T., Needels, J.T., Garbacz, C., Morgado, F., Alonso, J.J., and Fossati, M., “SU2-NEMO: an open-source framework for high-mach nonequilibrium multi-species flows,” Aerospace, Vol. 8, No. 7, 2021, p. 193.
2. Economon, T.D., Palacios, F., Copeland, S.R., Lukaczyk, T.W., and Alonso, J.J., “SU2: An Open-Source Suite for Multiphysics Simulation and Design,” AIAA Journal, Vol. 54, No. 3, 2016, pp. 828–846. https://doi.org/10.2514/1.J053813.

Limitations of Heat Flux and Isothermal Wall Boundaries

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• Smoluchowski-Maxwell BC (Morgado) for rarefied flows, focus here on continuum
• Current SU2-NEMO wall boundaries can predict temperature for specified heat flux (HF wall) or cold wall heat flux for fixed temperature (isothermal wall)
• These neglect the fact that wall temperature and heat flux are coupled by physical processes
• A more complex treatment of the surface energy balance is required

Depth

Transient solution

10 seconds

Surface Energy Balance

• Heat flux into the surface is composed of multiple physical mechanisms of energy transport
• While full determination of in-depth response requires coupling with an in-depth material solver, the assumption of an insulated surface allows a good approximation of wall temperature and heat flux

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Vehicle Surface

4. Milos, F. S., and Rasky, D. J., “Review of numerical procedures for computational surface thermochemistry,” Journal of Thermophysics and Heat Transfer, Vol. 8, No. 1, 1994, pp. 24–34. https://doi.org/10.2514/3.497.

Catalytic Wall Boundary Condition

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Vehicle Surface

Q

Catalytic Wall Boundary Validation with HYMETS Arc Jet

• Validation against stagnation point heat flux measurements in Hypersonic Material Environmental Test System
• Slug calorimeters with different catalytic efficiencies

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5. Needels, J.T., Duzel, U., Hanquist, K.M., and Alonso, J.J., Sensitivity Analysis of Gas-Surface Modeling in Nonequilibrium Flows, 2022. https://doi.org/10.2514/6.2022-1636.

Catalytic Wall Boundary Validation with HYMETS Arc Jet

• Verification and validation against LeMANS surface heat flux profiles and experimental measurements (left) and surface heating profiles for various catalytic efficiencies (right)

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Radiative Equilibrium Wall Boundary

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Vehicle Surface

Radiative Equilibrium Wall Boundary condition

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• Perfect gas, laminar flow simulation
• Assessment of effect of emissivity values on different radiative equilibrium wall temperatures

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Effect of Temperature on Catalytic Wall Heat Flux

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Effect of Temperature on Catalytic Wall Heat Flux

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• Wall temperature has a strong effect on relative contribution of catalytic heating augmentation
• Larger wall temperature reduces wall temperature gradient, increases importance of catalytic reactions
• Demonstrates importance of coupling – radiative equilibrium wall temperature is ~2,000 K for this flight condition

~50%

Conclusions and Future Work

• Accurate prediction of surface temperature and heat flux in hypersonic flows requires the inclusion of relevant physics in the surface energy balance
• Initial results demonstrate the utility of catalytic and radiative equilibrium boundary conditions in obtaining accurate cold wall heat flux and wall temperature, respectively
• Future work will focus on continued model development and validation, including
• Continued verification and validation
• Inclusion of a non-charring ablation boundary condition
• Coupling of models to capture full suite of physics
• More efficient implementation in the SU2 solver class

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Thank you!

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Acknowledgements:

• SU2-NEMO WG:
• Strathclyde: Fábio Morgado, Catarina Garbacz, Prof. Marco Fossati
• Stanford: Wally Maier
• Univ. of Arizona: Umran Düzel, Ozgur Tumuklu, Prof. Kyle Hanquist
• VKI: Michele Capriati, Dr. Thierry Magin
• AFOSR

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Questions?

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Contact:

Email: jneedels@stanford.edu

Group Website: https://adl.stanford.edu/people/jacob-needels

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References

1. Maier, W.T., Needels, J.T., Garbacz, C., Morgado, F., Alonso, J.J., and Fossati, M., “SU2-NEMO: an open-source framework for high-mach nonequilibrium multi-species flows,” Aerospace, Vol. 8, No. 7, 2021, p. 193.
2. Economon, T.D., Palacios, F., Copeland, S.R., Lukaczyk, T.W., and Alonso, J.J., “SU2: An Open-Source Suite for Multiphysics Simulation and Design,” AIAA Journal, Vol. 54, No. 3, 2016, pp. 828–846. https://doi.org/10.2514/1.J053813.
3. Brandis, A.M., Johnston, C.O., “Characterization of Stagnation-Point Heat Flux for Earth Entry”, AIAA Aviation Forum, 2014. https://doi.org/10.2514/6.2014-2374.
4. Milos, F. S., and Rasky, D. J., “Review of numerical procedures for computational surface thermochemistry,” Journal of Thermophysics and Heat Transfer, Vol. 8, No. 1, 1994, pp. 24–34. https://doi.org/10.2514/3.497.
5. Needels, J.T., Duzel, U., Hanquist, K.M., and Alonso, J.J., Sensitivity Analysis of Gas-Surface Modeling in Nonequilibrium Flows, 2022. https://doi.org/10.2514/6.2022-1636.
6. Scoggins, J., and Magin, T., “Development of Mutation++: Multicomponent Thermodynamic and Transport Properties for Ionized Plasmas written in C++,” 2014. doi:10.2514/6.2014-2966.
7. Chatzigeorgis, G. B., Turchi, A., Viladegut, A., Chazot, O., Barbante, P. F., and Magin, T., “Development of catalytic and ablative gas-surface interaction models for the simulation of reacting gas mixtures,” 23rd AIAA Computational Fluid Dynamics Conference, 2017. doi:10.2514/6.2017-4499.
8. Splinter, S.C., Bey, K.S., Gragg, J.G., and Brewer, A.R., “Comparative Measurements of Earth and Martian Entry Environments in the NASA Langley HYMETS Facility,” 49th AIAA Aerospace Sciences Meeting, Orlando, FL, 2011. doi:10.2514/6.2011-1014.
9. Scalabrin, L.C., “Numerical Simulation of Weakly Ionized Hypersonic Flow over Reentry Capsules,” Ph.D. thesis, University of Michigan, 2007.
10. Duzel, U., Schroeder, O. M., Zhang, H., and Martin, A., “Numerical Simulation of an Arc Jet Test Section,” Journal of Thermophysics and Heat Transfer, 2019, pp. 1–11. doi:10.2514/1.t5722.

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Backup

Ballistic Entry Aerothermodynamics

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3. Brandis, A.M., Johnston, C.O., “Characterization of Stagnation-Point Heat Flux for Earth Entry”, AIAA Aviation Forum, 2014. https://doi.org/10.2514/6.2014-2374.

Navier-Stokes Equations for Flows in Thermochemical Nonequilibrium

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