Reynolds Stress Modeling for Hypersonic Flows

Bosco, Arianna; Reinartz, Birgit; Müller, Siegfried; Brown, Melrose; Boyce, Russell

doi:10.1007/978-3-642-28968-2_23

Cited by 4 publications

(7 citation statements)

References 5 publications

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“…Figure 17 shows the pressure coefficient, 18) and the Stanton number [Eq. (17)] at the lower intake wall for two different adaptive level L 4 computation using different threshold values and the uniformly refined L 4 grid. The geometry of the intake is also shown.…”

Section: B Scramjet Intake: Two-dimensional Resultsmentioning

confidence: 99%

“…This class of models has not been widely used because of its decreased stability and the increased computational cost due to the presence of seven equations that describe turbulence. However, in an earlier study, the RSM was successfully used for the simulation of separated hypersonic boundary layer flow where common two-equations eddy viscosity models failed [17,18]. Thus far, complex three-dimensional computations with engineering applications have only been performed using the differential Reynolds stress model on block-structured, nonadaptive grids; in the current study, we will show its application to adaptive grids as well.…”

Section: Introductionmentioning

confidence: 93%

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Investigation of Hypersonic Intakes Using Reynolds Stress Modeling and Wavelet-Based Adaptation

et al. 2014

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The simulation of hypersonic flows is computationally demanding due to the large gradients of the flow variables at hand, caused both by strong shock waves and thick boundary or shear layers. The resolution of those gradients imposes the use of extremely small cells in the respective regions. Taking turbulence into account intensifies the variation in scales even more. Furthermore, hypersonic flows have been shown to be extremely grid sensitive. For the simulation of fully three-dimensional configurations of engineering applications, this results in a huge amount of cells and, as a consequence, prohibitive computational time. Therefore, modern adaptive techniques can provide a gain with respect to both computational costs and accuracy, allowing the generation of locally highly resolved flow regions where they are needed and retaining an otherwise smooth distribution. In this paper, an h-adaptive technique based on wavelets is employed for the solution of hypersonic flows. The compressible Reynolds-averaged Navier-Stokes equations are solved using a differential Reynolds stress turbulence model, well suited to predict shock-wave/ boundary-layer interactions in high-enthalpy flows. Two test cases are considered: a compression corner at 15 deg and a scramjet intake. The compression corner is a classical test case in hypersonic flow investigations because it poses a shock-wave/turbulent-boundary-layer interaction problem. The adaptive procedure is applied to a twodimensional configuration as validation. The scramjet intake is first computed in two dimensions. Subsequently, a three-dimensional geometry is considered. Both test cases are validated with experimental data and compared to nonadaptive computations. The results show that the use of an adaptive technique for hypersonic turbulent flows at high-enthalpy conditions can strongly improve the performance in terms of memory and CPU time while at the same time maintaining the required accuracy of the results. Nomenclature b ij= anisotropy tensor c p = specific heat at constant pressure, pressure coefficient D ij = diffusion tensor for the Reynolds stresses, m 2 ∕s 3 δ ij = Kronecker delta d = spatial dimension E = specific total energy, m 2 ∕s 2 H = total specific enthalpy, m 2 ∕s 2 II = second invariant of the anisotropy tensor k = turbulent kinetic energy, m 2 ∕s 2 L = maximum refinement level l = local refinement level M = Mach number M ij = turbulent mass flux tensor for the Reynolds stresses, m 2 ∕s 3 μ = molecular viscosity, kg∕m · s P ij = production tensor for the Reynolds stresses, m 2 ∕s 3 p = pressure, Pa p t = total pressure, Pa q i = component of heat flux vector, W∕m 2 q t k = turbulent heat flux, W∕m 2 R ij = Reynolds stress tensor, m 2 ∕s 2 Re = Reynolds number, 1∕m Res drop = averaged density residual at which the adaptations are performed ρ = density, kg∕m 3 S ij = strain-rate tensor, 1∕s St = Stanton number T = temperature, K T w = wall temperature, K T 0 = total temperature, K t = time, s U = local velocity, m∕s u i = velocity component, m∕s W ij...

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Section: B Scramjet Intake: Two-dimensional Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 93%

Investigation of Hypersonic Intakes Using Reynolds Stress Modeling and Wavelet-Based Adaptation

et al. 2014

View full text Add to dashboard Cite

show abstract

“…This class of models has not been widely used because of its decreased stability and the increased computational cost due to the presence of seven equations that describe turbulence. However, in an earlier study, the RSM was successfully used for the simulation of separated hypersonic boundary layer flow where common two-equations eddy viscosity models failed [16,17]. So far, complex three-dimensional computations with engineering applications have only been performed using the differential Reynolds stress model on block-structured, non-adaptive grids; in the current study, we will show its application to adaptive grids as well.…”

mentioning

confidence: 88%

Wavelet-based Adaptive Techniques Applied to Turbulent Hypersonic Scramjet Intake Flows

Frauholz,

Bosco,

Reinartz

et al. 2013

Preprint

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“…Krause implemented the transition model into our flow solver and developed correlations for hypersonic flows [3]. Now, within this paper we exchange the SST turbulence model with the RSM turbulence model which improves the numerical prediction of separated hypersonic boundary layer flow [6,7]. The hypersonic, in-house correlations within the transition model have to be calibrated for the RSM model.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Transition Prediction for Scramjets Using γ-Reθt Model Coupled to Two Turbulence Models

Frauholz

Reinartz

Müller

et al. 2015

Journal of Propulsion and Power

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Because of viscous interaction in hypersonic flows, the state of the boundary layer significantly influences possible shock-wave boundary-layer interaction as well as surface heat loads. Hence, for engineering applications, the efficient numerical prediction of the laminar-to-turbulent transition is a challenging and important task. Within the framework of the Reynolds-averaged Navier-Stokes equations, Langtry-Menter proposed the γ-Re θ t transition model using two transport equations for the intermittency and Re θ t combined with the shear stress transport turbulence model. The transition model contains two empirical correlations for the onset and length of transition. Langtry-Menter designed and validated the correlations for the subsonic and transonic flow regimes. For applications in the hypersonic flow regime, the development of a new set of correlations proved necessary. Within this paper, we propose a next step and couple the transition model with the Speziale-Sarkar-Gatski/Launder-Reece-Rodi ω Reynolds stress turbulence model, which we found to be well suited for scramjet intake simulations. First, we illustrate the necessary modifications of the Reynolds stress model and the hypersonic in-house correlations using a hypersonic flat plate test case. Next, the transition model is successfully validated for its use coupled to both turbulence models using a hypersonic double ramp test case. Regardless of the turbulence model, the transition model is able to correctly predict the transition process compared to experimental data. In addition, we apply the transition model combined with both turbulence models to three different fully three-dimensional scramjet intake configurations that are experimentally investigated in wind tunnel facilities. The agreement with the available experimental data is also shown. Nomenclature c p = specific heat at constant pressure, pressure coefficient, -D ij = diffusion tensor for Reynolds stresses, m 2 ∕s 3 E = specific total energy, m 2 ∕s 2 E γ = destruction term of γ transport equation, m∕s F length = transition length function, empirical correlation, -H = total specific enthalpy, m 2 ∕s 2 I = turbulent intensity,k = turbulent kinetic energy, m 2 ∕s 2 L = maximum refinement level,l = local refinement level, -M = Mach number, -M ij = turbulent mass flux tensor for Reynolds stresses, m 2 ∕s 3 P ij = production tensor for Reynolds stresses, m 2 ∕s 3 P γ = production term of γ transport equation, m∕s P θ t = production term of Re θt transport equation, m∕s p = pressure, Pa p t = total pressure, Pa q i = component of heat flux vector, W∕m 2 q t k = turbulent heat flux, W∕m 2 Re = Reynolds number, 1∕m Re θt = transition onset Reynolds number, -Re θ c = critical Reynolds number, empirical correlation, -Res drop = averaged density residual, at which adaptations are performed, -R ij = Reynolds stress tensor, m 2 ∕s 2 St = Stanton number, -T = temperature, K T w = wall temperature, K T 0 = total temperature, K t = time, s u i = velocity component, m∕s x i = Cartesian coordinates compon...

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Reynolds Stress Modeling for Hypersonic Flows

Cited by 4 publications

References 5 publications

Investigation of Hypersonic Intakes Using Reynolds Stress Modeling and Wavelet-Based Adaptation

Investigation of Hypersonic Intakes Using Reynolds Stress Modeling and Wavelet-Based Adaptation

Wavelet-based Adaptive Techniques Applied to Turbulent Hypersonic Scramjet Intake Flows

Transition Prediction for Scramjets Using γ-Reθt Model Coupled to Two Turbulence Models

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