Simulation of Hypersonic Shock/Turbulent Boundary-Layer Interactions Using Shock-Unsteadiness Model

Pasha, Amjad Ali; Sinha, Krishnendu

doi:10.2514/1.57044

Cited by 7 publications

(19 citation statements)

References 14 publications

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“…Application of the shock-turbulence modification, like the model proposed by Sinha et al (2003), show that the majority of the effect is localized at the separation shock. The separation location is better predicted by the modification, and this results in an improved flow topology and shock structure (Pasha & Sinha 2008, 2012.…”

Section: Application To Shock-boundary Layer Interactionsmentioning

confidence: 93%

“…The mean flow Mach number and the local shock inclination angle can be obtained from a RANS solution. The shock-normal Mach number and its variation across the boundary layer can thus be computed; see previous work by Sinha et al (2005) and Pasha & Sinha (2008, 2012. On the other hand, the level of temperature fluctuations in a boundary layer and its correlation with the velocity fluctuations is not readily available in a RANS computation.…”

Section: Application To Shock-boundary Layer Interactionsmentioning

confidence: 99%

“…been validated for several supersonic and hypersonic applications (Sinha, Mahesh & Candler 2005;Pasha & Sinha 2008, 2012. The mean flow variables are initialized to a hyperbolic tangent profile centred at the DNS shock location.…”

Section: Effect Of Entropy Fluctuationsmentioning

confidence: 99%

“…It directly influences the extent of flow separation, and therefore determines the topology of shocks and expansion waves generated by the separation bubble. See, for example, the simulation of an oblique shock impinging on a turbulent boundary layer by Pasha & Sinha (2008) and hypersonic cone-flare configurations by Pasha & Sinha (2012). Accurate prediction of the flow topology is essential to obtain the correct variation of surface properties.…”

Section: Introductionmentioning

confidence: 99%

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Evolution of enstrophy in shock/homogeneous turbulence interaction

Sinha

2012

J. Fluid Mech.

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Interaction of turbulent fluctuations with a shock wave plays an important role in many high-speed flow applications. This paper studies the amplification of enstrophy, defined as mean-square fluctuating vorticity, in homogeneous isotropic turbulence passing through a normal shock. Linearized Navier-Stokes equations written in a frame of reference attached to the unsteady shock wave are used to derive transport equations for the vorticity components. These are combined to obtain an equation that describes the evolution of enstrophy across a time-averaged shock wave. A budget of the enstrophy equation computed using results from linear interaction analysis and data from direct numerical simulations identifies the dominant physical mechanisms in the flow. Production due to mean flow compression and baroclinic torques are found to be the major contributors to the enstrophy amplification. Closure approximations are proposed for the unclosed correlations in the production and baroclinic source terms. The resulting model equation is integrated to obtain the enstrophy jump across a shock for a range of upstream Mach numbers. The model predictions are compared with linear theory results for varying levels of vortical and entropic fluctuations in the upstream flow. The enstrophy model is then cast in the form of k-equations and used to compute the interaction of homogeneous isotropic turbulence with normal shocks. The results are compared with available data from direct numerical simulations. The equations are further used to propose a model for the amplification of turbulent viscosity across a shock, which is then applied to a canonical shock-boundary layer interaction. It is shown that the current model is a significant improvement over existing models, both for homogeneous isotropic turbulence and in the case of complex high-speed flows with shock waves.

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Section: Application To Shock-boundary Layer Interactionsmentioning

confidence: 93%

Section: Application To Shock-boundary Layer Interactionsmentioning

confidence: 99%

Section: Effect Of Entropy Fluctuationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Evolution of enstrophy in shock/homogeneous turbulence interaction

Sinha

2012

J. Fluid Mech.

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“…13 The computed shock/expansion wave patterns and shock-shock interaction match experimental data closely. 14,15 Due to its potential, the shock-unsteadiness model has been used widely 16,17 and is being developed further in recent works. 11,18,19 The variable P r T model, in conjunction with the shock-unsteadiness k-ω model, is found to reproduce the experimental data of Schulein 20 well for Mach 5 oblique shock impinging cases.…”

Section: Introductionmentioning

confidence: 99%

Variable turbulent Prandtl number model applied to hypersonic shock/boundary-layer interactions

Roy

Sinha

2018

2018 Fluid Dynamics Conference

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Interaction of shock waves with turbulent boundary-layers can enhance the surface heat flux dramatically. Reynolds-averaged Navier-Stokes simulations based on constant turbulent Prandtl number often give grossly erroneous heat transfer predictions in SBLI flows. This is due to the fact that the underlying Morkovin's hypothesis breaks down in the presence of shock waves; thus, the turbulent Prandtl number can not be assumed to be a constant. In our recent work (Roy, Pathak and Sinha,AIAA 2017), we developed a new variable turbulent Prandtl number model based on linearized Rankine-Hugoniot conditions applied to shock-turbulence interaction. The turbulent Prandtl number is a function of the shock strength and we proposed a shock function to identify the location and strength of shock waves. The shock function also simulates the post-shock ralaxation of the turbulent heat flux, akin to that observed in canonical shock-turbulence interaction. In this work, we extend the variable turbulent Prandtl number model for hypersonic flows by considering the influence of upstream total temperature fluctuation on turbulent heat flux. The model is combined with the well-validated shock-unsteadiness k-ω model and is used to study eight test cases involving shock/boundary-layer interactions at Mach numbers ranging from 5 to 11. Comparison with experimental data shows significant improvement in the surface heat transfer rate in the interaction region. The shock function is also used to propose a robust form of the existing shock-unsteadiness k-ω model that simplifies the numerical implementation enormously. NomenclatureP r T Turbulent Prandtl number P k Production term of turbulent kinetic energy S ij Symmetric part of mean strain rate tensor S ii Mean dilatation b 1 Shock-unsteadiness damping parameter A uT Correlation between temperature and velocity fluctuations r Density ratio c f Skin friction co-efficient q w Wall heat flux, W/cm 2 δ 0 Boundary-layer thickness upstream of interaction, m k Turbulent kinetic energy, m 2 /s 2 ω Specific dissipation rate of turbulent kinetic energy, s -1 ξ t Instantaneous shock speed, m/s ψ Shock function Subscript ∞ Free-stream condition

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Research on grid‐dependence of neural network turbulence model

Song

Zhang

Sun

et al. 2022

Numerical Methods in Fluids

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Turbulence machine learning based on deep neural network has become a research hotspot in turbulence modeling. Although most turbulence models have strict requirements on grid dependence, there are few analyses on grid dependence on the coupling of models and equations. In this article, a neural network turbulence model is constructed for the flow around airfoil with high Reynolds number, and the effects of wall‐normal grid spacing on the calculation accuracy are studied. The results show that compared with the traditional differential equation turbulence model, the neural network turbulence model can break through the limitation of y+ < 1 and relax the requirement of the normal density of the boundary layer grid while ensuring the accuracy.

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Simulation of Hypersonic Shock/Turbulent Boundary-Layer Interactions Using Shock-Unsteadiness Model

Cited by 7 publications

References 14 publications

Evolution of enstrophy in shock/homogeneous turbulence interaction

Evolution of enstrophy in shock/homogeneous turbulence interaction

Variable turbulent Prandtl number model applied to hypersonic shock/boundary-layer interactions

Research on grid‐dependence of neural network turbulence model

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