24-Simulation of Transition


Numerical Simulation of Hypersonic transition to turbulence within the NSMB CFD solver

Vos1, A. Marouf 2 and Y. Hoarau 2 1 CFS Engineering,

1 EPFL Innovation Park, Batiment A, 1015 Lausanne, Switzerland

2Université de Strasbourg, Icube laboratory, Mechanical Department, 67000 Strasbourg, France


The Navier Stokes Multi Block (NSMB [1]) solver is developed in a consortium of different companies and universities in Switzerland, France and Germany. From the start the solver was designed to be used for hypersonic flow simulations, and it has been used in a large variety of ESA and EU funded space projects, among them the IXV (including the postflight analysis) and the RETALT (Re-usable Launchers) projects.

To facilitate the mesh generation for complex geometries NSMB employs the chimera method was well as the patch grid method. For hypersonic flows a bow shock adaption procedure is available. The ALE (Arbitrary Lagrangian Eulerian) approach is available for moving grids as well as for moving bodies simulations. A large variety of numerical schemes as well as turbulence models are available in the solver.

In this work the NSMB solver is used to simulate two test-case of flow with transition to turbulence :

  1. The sphere at Mach 4.5 and 10 with wall heat flux measurements performed by Mielke [2] at ISL
  2. The hypersonic axisymmetrical compression ramp flow of Lugrin & al [3,4]

In both cases an automatic mesh adaptation is used to refine the grid in the shock areas. The grid before refinement are presented on the figure 1.

The numerical simulation is based on the use of two turbulence models, namely the Spalart-Almaras QCR 2020 [5] and the Menter k-ω SST [6], combined with four transition models :

  1. The γ-Reθ two equation model of Langtry and Menter [7]
  2. The γ one equation model of Langtry and Menter & al [8]
  3. The algebraic model of Cakmakcioglu & al [9]
  4. The algebraic model of Menter & al [10]


visualisation of the axisymmetrical grid for the sphere at Mach 4.5 and Re=2E6

Figure 1.a : visualisation of the axisymmetrical grid for the sphere at Mach 4.5 and Re=2E6


visualisation of the axisymmetrical grid for the compression ramp at Mach 5

Figure 1.b : visualisation of the axisymmetrical grid for the compression ramp at Mach 5



  • Hoarau, Y., Pena, D., Vos, J. B., Charbonnier, D., Gehri, A., Braza, M., Deloze, T., and Laurendeau, E., 2016. Recent Developments of the Navier Stokes Multi Block (NSMB) CFD solver, 54th AIAA Aerospace Sciences Meeting, 2016, AIAA Paper 2016-2056.
  • Mielke. Wärmestromdichtemessung an Flugkörpern im Hyperschall-Hochenthalpie-Stoßwindkanal. Bachelorarbeit, Institut franco-allemand de recherches de Saint-Louis, Saint-Louis, September 2020
  • Lugrin, M., Beneddine, S., Leclercq, C., Garnier, E., & Bur, R. (2021). Transition scenario in hypersonic axisymmetrical compression ramp flow. Journal of Fluid Mechanics, 907, A6. https://doi.org/10.1017/jfm.2020.833
  • Lugrin, M., Nicolas, F., Severac, N. et al. Transitional shockwave/boundary layer interaction experiments in the R2Ch blowdown wind tunnel. Exp Fluids 63, 46 (2022). https://doi.org/10.1007/s00348-022-03395-9
  • Rumsey, C. L., Carlson, J.-R., Pulliam, T. H., and Spalart, P. R., “Improvements to the Quadratic Constitutive Relation Based on NASA Juncture Flow Data,” AIAA Journal, Vol. 58, No. 10, 2020, pp. 4374-4384, https://doi.org/10.2514/1.J059683.
  • R. Menter. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8):1598–1605, August 1994. https://doi.org/10.2514/3.12149
  • B. Langtry and F. R. Menter. Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes. AIAA Journal, 47(12):2894–2906, 2009
  • R. Menter, Pavel E P. Smirnov, Tao Liu, and Ravikanth Avancha. A one-equation local correlation-based transition model. Flow, Turbulence and Combustion, 95:583–619, 2015
  • C. Cakmakcioglu, O. Bas, R. Mura, and U. Kaynak. A Revised One-Equation Transitional Model for External Aerodynamics. AIAA AVIATION 2020 FORUM, 2020
  • Menter, F.R., Matyushenko, A., Lechner, R. et al. An Algebraic LCTM Model for Laminar–Turbulent TransitionPrediction. Flow Turbulence Combust 109, 841–869 (2022). https://doi.org/10.1007/s10494-022-00336-8