Investigation of a Compression Corner at Hypersonic Conditions using a Reynolds Stress Model

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

doi:10.2514/6.2011-2217

Cited by 7 publications

(10 citation statements)

References 9 publications

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“…Hence, the number of cells stays nearly the same after the third and fourth adaptation. 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.…”

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: 92%

“…Pressure (left) and Stanton number (right) distribution for two adaptive grids with different threshold values, a uniform grid, and experimentally obained pressure measurements[18].…”

mentioning

confidence: 99%

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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: 92%

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

et al. 2014

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“…The computational grids are represented by block-structured parametric B-spline patches. All the key ingredients have been described in detail in the theses by Bramkamp [21], Lamby [22], and Müller [23], followed by numerous publications in which the solver has been extended and applied to a wide range of problems from subsonic to hypersonic flows, together with a thorough validation; for example, some recent publications are [24][25][26][27][28][29]. By now the QUADFLOW solver, as well as the underlying numerical methods, are well established.…”

Section: B Numerical Methodsmentioning

confidence: 98%

Investigation of Unsteady Edney Type IV and VII Shock–Shock Interactions

2016

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Edney type IV and type VII shock-shock interactions are complex hypersonic flow phenomena. They are characterized by a supersonic jet that reaches far into the flowfield. An experimental investigation of the inner jet structure is difficult, especially in cases where the jet is subject to high-frequency unsteady movements. The present paper provides insight into the jet structure and its movement by means of a highly resolved computational fluid dynamics analysis in thermochemical nonequilibrium that significantly exceeds the resolution of existing publications. Simulations of an Edney type IV interaction in nitrogen flow are presented. Advanced adaptation strategies allow for the identification and analysis of the mechanisms of the jet unsteadiness, resulting in a new classification of the unsteady flowfield behavior with respect to the periodic jet movement. This classification is based not only on wall quantities, but also on the core flowfield. The computations are supplemented by a grid sensitivity study. The second configuration is an Edney type VII interaction. This shock-shock interaction type was observed and defined in nitrogen flow by Yamamoto et al (Numerical Investigation of Shock/Vortex Interaction in Hypersonic Thermochemical Nonequilibrium Flow, Journal of Spacecraft and Rockets, Vol. 36, No. 2, 1999, pp. 240-246. The present results demonstrate that this interaction may also be observed in carbon-dioxide-dominated flow with a gas composition similar to the Martian atmosphere. The results provide insight into the jet structure of this less known interaction.

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“…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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Investigation of a Compression Corner at Hypersonic Conditions using a Reynolds Stress Model

Cited by 7 publications

References 9 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

Investigation of Unsteady Edney Type IV and VII Shock–Shock Interactions

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

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