Assessment of a high-order shock-capturing central-difference scheme for hypersonic turbulent flow simulations

High-speed turbulent flows are encountered in most space-related applications (including exploration, tourism and defense fields) and represent a subject of growing interest in the last decades. A major challenge in performing high-fidelity simulations of such flows resides in the stringent requirements for the numerical schemes to be used. These must be robust enough to handle strong, unsteady discontinuities, while ensuring low amounts of intrinsic dissipation in smooth flow regions. Furthermore, the wide range of temporal and spatial active scales leads to concurrent needs for numerical stabilization and accurate representation of the smallest resolved flow scales in cases of under-resolved configurations. In this paper, we present a finite-difference high-order shock-capturing technique based on Jameson's artificial diffusivity methodology. The resulting scheme is ninth-order-accurate far from discontinuities and relies on the addition of artificial dissipation close to large gradients. The shock detector is slightly revised to enhance its selectivity and avoid spurious activations of the shock-capturing term. A suite of test cases ranging from 1D to 3D configurations (namely, shock tubes, Shu-Osher problem, isentropic vortex advection, under-expanded jet, compressible Taylor-Green Vortex, supersonic and hypersonic turbulent boundary layers) is analysed in order to test the capability of the proposed numerical strategy to handle a large variety of problems, ranging from calorically-perfect air to multi-species reactive flows. Results obtained on under-resolved grids are also considered to test the applicability of the proposed strategy in the context of implicit Large-Eddy Simulations

Finite-rate chemistry effects in turbulent hypersonic boundary layers: a direct numerical simulation study

The influence of high-enthalpy effects on hypersonic turbulent boundary layers is investigated by means of direct numerical simulations (DNS). A quasi-adiabatic flat-plate air flow at free-stream Mach number equal to 10 is simulated up to fully-developed turbulent conditions using a five-species, chemically-reacting model. A companion DNS based on a frozen-chemistry assumption is also carried out, in order to isolate the effect of finite-rate chemical reactions and assess their influence on turbulent quantities. In order to reduce uncertainties associated with turbulence generation at the inlet of the computational domain, both simulations are initiated in the laminar flow region and the flow is let to evolve up to the fully turbulent regime. Modal forcing by means of localized suction and blowing is used to trigger laminar-to-turbulent transition. The high temperatures reached in the near wall region including the viscous and buffer sublayers activate significant dissociation of both oxygen and nitrogen. This modifies in turn the thermodynamic and transport properties of the reacting mixture, affecting the first-order statistics of thermodynamic quantities. Due to the endothermic nature of the chemical reactions in the forward direction, temperature and density fluctuations in the reacting layer are smaller than in the frozen-chemistry flow. However, the first- and second-order statistics of the velocity field are found to be little affected by the chemical reactions under a scaling that accounts for the modified fluid properties. We also observed that the Strong Reynolds Analogy (SRA) remains well respected despite the severe hypersonic conditions and that the computed skin friction coefficient distributions match well the results of the Renard-Deck decomposition extended to compressible flows

Direct Numerical Simulation of a hypersonic boundary layer in chemical non-equilibrium

The influence of high-enthalpy effects in hypersonic, spatially developing boundary layers is investigated by means of direct numerical simulations. The flow of a reacting mixture of nitrogen and oxygen over a flat plate at Mach 10, previously investigated in the literature using linear stability theory (LST), is simulated using a compu-tational domain encompassing the laminar, transitional and turbulent regimes. Transition is triggered by forcing Mack’s second mode through suction and blowing at the wall. In the laminar region, the solution matches reasonably well the locally self-similar profiles, computed under chemical non-equilibrium assumptions. Strong dissociation phenomena are observed, due to the high temperatures reached close to the (uncooled) plate surface. The transitional regime is investigated by means of modal analysis. Despite the significant chemical activity, the results confirm the classical transition scenario for high-Mach number boundary layers, for which the second-mode resonance is the main mechanism responsible for turbulent breakdown. In the turbulent region, first- and second-order statistics reveal that chemical reactions do not modify significantly dynamic quantities such as velocity and Reynolds stress profiles, but greatly affect thermal properties, due to their endothermic nature. For the configuration at hand, chemical dissociation is slower than the characteristic time-scale of the flow, and the peak of chemical activity is located in the viscous sublayer, leading to mild modifications of the turbulent field compared to a frozen-chemistry model

A high-order scheme for the numerical simulation of high-enthalpy hypersonic flows

A high-order shock-capturing finite-difference scheme for scale-resolving numerical simulations of hypersonic high-enthalpy flows, involving thermal non-equilibrium effects, is presented. The suitability of the numerical strategy for such challenging configurations is assessed in terms of accuracy and robustness, with special focus on shock-capturing capabilities. The approach is demonstrated for a variety of thermochemical non-equilibrium configurations

Direct Numerical Simulation of hypersonic boundary layers in chemical non-equilibrium

The influence of high-temperature effects on compressible wall-bounded turbulence is investigated by means of a direct numerical simulation of a hypersonic, chemically out-of-equilibrium, turbulent boundary layer. The analysis aims at assessing the effects of chemical reactions on turbulence, also by comparing the results with those of a frozen flow. We will present a detailed analysis of the turbulent statistics and near-wall dynamics; the validity of some classical scalings and Reynolds analogy will also be discussed

Direct numerical simulation of hypersonic turbulent boundary layers with thermochemical non-equilibrium effects

Les effets de haute température survenant lors des vols hypersoniques ont un impact sur les performances aérodynamiques d'un véhicule. En outre, la transition d'un régime laminaire à un régime turbulent peut se produire dans des conditions de vol réelles et est une préoccupation majeure. Tous ces phénomènes ont lieu dans la couche limite qui se développe sur le fuselage du véhicule. La prédiction du couplage bidirectionnel de la turbulence compressible et des processus thermochimiques déclenchés par la haute température est un sujet partiellement inexploré.Dans ce travail, le comportement des couches limites de plaques planes dans des conditions hypersoniques est examiné, au moyen de simulations numériques directes (SND). Des configurations avec parois adiabatiques et refroidies sont étudiées, du régime laminaire au régime entièrement turbulent. L’air est modélisé comme un mélange réactif à cinq espèces, dans le but final d'étudier l'effet de la chimie et de la relaxation vibrationelle des couches limites turbulentes fortement compressibles. On constate que l'activité chimique a un impact sur les propriétés de transport, les les grandeurs thermodynamiques et les fluctuations turbulentes, lorsque la température est suffisamment élevée pour déclencher une dissociation significative de l'oxygène moléculaire. Dans le cas d'un léger découplage entre les temps caractéristiques de l'écoulement et de la thermochimie, on constate que les corrélations classiques des quantités turbulentes sont en accord avec les résultats obtenus pour les gaz à bas Mach. Le transport turbulent redistribue les espèces chimiques et entretient le non-équilibre thermique. Les fluctuations de vitesse jouent un rôle majeur dans le mélange des gaz chauds et froids, ce qui conduit à des décalages de l'énergie vibrationelle par rapport à sa valeur d'équilibre; les quantités moyennes et fluctuantes thermodynamiques sont affectées par ce mécanisme.High-temperature effects arising in hypersonic flights have a major impact on aerodynamic performance of a vehicle. In addition, transition from a laminar to a turbulent regime may occur in real flight conditions and represents a major concern. All these phenomena take place in the boundary layer developing on the vehicle fuselage. The accurate prediction of the two-way coupling of wall-bounded compressible turbulence and thermochemical processes triggered by the high temperature at stake is a subject partially unexplored.In this work, the behavior of spatially evolving flat-plate boundary layers in hypersonic conditions is inspected by means of Direct Numerical Simulations (DNS), ensuring no uncertainties deriving from deficiencies of turbulence closure models. Adiabatic and wall-cooled configurations are investigated, from the laminar up to the fully turbulent regime. A five-species air mixture model is considered, with the final aim of studying the effect of finite-rate chemistry and vibrational relaxation on high compressible turbulent flows. It is found that chemical activity has an impact on transport properties, thermal fields and turbulent fluctuations, when the temperature is high enough to trigger significant molecular oxygen dissociation. In the case of slight decoupling between characteristic times of flow and thermochemistry, classical correlations of turbulent quantities are found to be in accordance with the results obtained for low-Mach gases. Turbulent transport is found to redistribute chemical species and to sustain thermal nonequilibrium. Velocity fluctuations have indeed a major role in the mixing of hot and cold gases, which lead to the excitation of all energetic modes and lags in the vibrational energy with respect to its equilibrium value; accordingly, thermal mean and fluctuating quantities are affected by this mechanism

Simulations numériques directes de couches limites turbulentes hypersoniques avec des effets thermochimiques de non-équilibre

High-temperature effects arising in hypersonic flights have a major impact on aerodynamic performance of a vehicle. In addition, transition from a laminar to a turbulent regime may occur in real flight conditions and represents a major concern. All these phenomena take place in the boundary layer developing on the vehicle fuselage. The accurate prediction of the two-way coupling of wall-bounded compressible turbulence and thermochemical processes triggered by the high temperature at stake is a subject partially unexplored.In this work, the behavior of spatially evolving flat-plate boundary layers in hypersonic conditions is inspected by means of Direct Numerical Simulations (DNS), ensuring no uncertainties deriving from deficiencies of turbulence closure models. Adiabatic and wall-cooled configurations are investigated, from the laminar up to the fully turbulent regime. A five-species air mixture model is considered, with the final aim of studying the effect of finite-rate chemistry and vibrational relaxation on high compressible turbulent flows. It is found that chemical activity has an impact on transport properties, thermal fields and turbulent fluctuations, when the temperature is high enough to trigger significant molecular oxygen dissociation. In the case of slight decoupling between characteristic times of flow and thermochemistry, classical correlations of turbulent quantities are found to be in accordance with the results obtained for low-Mach gases. Turbulent transport is found to redistribute chemical species and to sustain thermal nonequilibrium. Velocity fluctuations have indeed a major role in the mixing of hot and cold gases, which lead to the excitation of all energetic modes and lags in the vibrational energy with respect to its equilibrium value; accordingly, thermal mean and fluctuating quantities are affected by this mechanism.Les effets de haute température survenant lors des vols hypersoniques ont un impact sur les performances aérodynamiques d'un véhicule. En outre, la transition d'un régime laminaire à un régime turbulent peut se produire dans des conditions de vol réelles et est une préoccupation majeure. Tous ces phénomènes ont lieu dans la couche limite qui se développe sur le fuselage du véhicule. La prédiction du couplage bidirectionnel de la turbulence compressible et des processus thermochimiques déclenchés par la haute température est un sujet partiellement inexploré.Dans ce travail, le comportement des couches limites de plaques planes dans des conditions hypersoniques est examiné, au moyen de simulations numériques directes (SND). Des configurations avec parois adiabatiques et refroidies sont étudiées, du régime laminaire au régime entièrement turbulent. L’air est modélisé comme un mélange réactif à cinq espèces, dans le but final d'étudier l'effet de la chimie et de la relaxation vibrationelle des couches limites turbulentes fortement compressibles. On constate que l'activité chimique a un impact sur les propriétés de transport, les les grandeurs thermodynamiques et les fluctuations turbulentes, lorsque la température est suffisamment élevée pour déclencher une dissociation significative de l'oxygène moléculaire. Dans le cas d'un léger découplage entre les temps caractéristiques de l'écoulement et de la thermochimie, on constate que les corrélations classiques des quantités turbulentes sont en accord avec les résultats obtenus pour les gaz à bas Mach. Le transport turbulent redistribue les espèces chimiques et entretient le non-équilibre thermique. Les fluctuations de vitesse jouent un rôle majeur dans le mélange des gaz chauds et froids, ce qui conduit à des décalages de l'énergie vibrationelle par rapport à sa valeur d'équilibre; les quantités moyennes et fluctuantes thermodynamiques sont affectées par ce mécanisme

Simulations numériques directes de couches limites turbulentes hypersoniques avec des effets thermochimiques de non-équilibre

High-temperature effects arising in hypersonic flights have a major impact on aerodynamic performance of a vehicle. In addition, transition from a laminar to a turbulent regime may occur in real flight conditions and represents a major concern. All these phenomena take place in the boundary layer developing on the vehicle fuselage. The accurate prediction of the two-way coupling of wall-bounded compressible turbulence and thermochemical processes triggered by the high temperature at stake is a subject partially unexplored.In this work, the behavior of spatially evolving flat-plate boundary layers in hypersonic conditions is inspected by means of Direct Numerical Simulations (DNS), ensuring no uncertainties deriving from deficiencies of turbulence closure models. Adiabatic and wall-cooled configurations are investigated, from the laminar up to the fully turbulent regime. A five-species air mixture model is considered, with the final aim of studying the effect of finite-rate chemistry and vibrational relaxation on high compressible turbulent flows. It is found that chemical activity has an impact on transport properties, thermal fields and turbulent fluctuations, when the temperature is high enough to trigger significant molecular oxygen dissociation. In the case of slight decoupling between characteristic times of flow and thermochemistry, classical correlations of turbulent quantities are found to be in accordance with the results obtained for low-Mach gases. Turbulent transport is found to redistribute chemical species and to sustain thermal nonequilibrium. Velocity fluctuations have indeed a major role in the mixing of hot and cold gases, which lead to the excitation of all energetic modes and lags in the vibrational energy with respect to its equilibrium value; accordingly, thermal mean and fluctuating quantities are affected by this mechanism.Les effets de haute température survenant lors des vols hypersoniques ont un impact sur les performances aérodynamiques d'un véhicule. En outre, la transition d'un régime laminaire à un régime turbulent peut se produire dans des conditions de vol réelles et est une préoccupation majeure. Tous ces phénomènes ont lieu dans la couche limite qui se développe sur le fuselage du véhicule. La prédiction du couplage bidirectionnel de la turbulence compressible et des processus thermochimiques déclenchés par la haute température est un sujet partiellement inexploré.Dans ce travail, le comportement des couches limites de plaques planes dans des conditions hypersoniques est examiné, au moyen de simulations numériques directes (SND). Des configurations avec parois adiabatiques et refroidies sont étudiées, du régime laminaire au régime entièrement turbulent. L’air est modélisé comme un mélange réactif à cinq espèces, dans le but final d'étudier l'effet de la chimie et de la relaxation vibrationelle des couches limites turbulentes fortement compressibles. On constate que l'activité chimique a un impact sur les propriétés de transport, les les grandeurs thermodynamiques et les fluctuations turbulentes, lorsque la température est suffisamment élevée pour déclencher une dissociation significative de l'oxygène moléculaire. Dans le cas d'un léger découplage entre les temps caractéristiques de l'écoulement et de la thermochimie, on constate que les corrélations classiques des quantités turbulentes sont en accord avec les résultats obtenus pour les gaz à bas Mach. Le transport turbulent redistribue les espèces chimiques et entretient le non-équilibre thermique. Les fluctuations de vitesse jouent un rôle majeur dans le mélange des gaz chauds et froids, ce qui conduit à des décalages de l'énergie vibrationelle par rapport à sa valeur d'équilibre; les quantités moyennes et fluctuantes thermodynamiques sont affectées par ce mécanisme

Assessment of a high-order shock-capturing central-difference scheme for hypersonic turbulent flow simulations

International audienceHigh-speed turbulent flows are encountered in most space-related applications (including exploration, tourism and defense fields) and represent a subject of growing interest in the last decades. A major challenge in performing high-fidelity simulations of such flows resides in the stringent requirements for the numerical schemes to be used. These must be robust enough to handle strong, unsteady discontinuities, while ensuring low amounts of intrinsic dissipation in smooth flow regions. Furthermore, the wide range of temporal and spatial active scales leads to concurrent needs for numerical stabilization and accurate representation of the smallest resolved flow scales in cases of under-resolved configurations. In this paper, we present a finite-difference high-order shock-capturing technique based on Jameson’s artificial diffusivity methodology. The resulting scheme is ninth-order-accurate far from discontinuities and relies on the addition of artificial dissipation close to large gradient flow regions. The shock detector is slightly revised to enhance its selectivity and avoid spurious activations of the shock-capturing term. A suite of test cases ranging from 1D to 3D configurations (namely, perfect-gas and chemically reacting shock tubes, Shu–Osher problem, isentropic vortex advection, under-expanded jet, compressible Taylor–Green Vortex, supersonic and hypersonic turbulent boundary layers)is analyzed in order to test the capability of the proposed numerical strategy to handle a large variety of problems, ranging from calorically-perfect air to multi-species reactive flows. Results obtained on underresolved grids are also considered to test the applicability of the proposed strategy in the context of implicit Large-Eddy Simulations

Numerical investigation of hypersonic turbulent boundary layers with high-temperature effects

A hypersonic turbulent boundary layer over a flat plate is numerically investigated. The large Mach number and temperature values in the freestream (M e = 12.48 and T e = 594.3 K, respectively) lead to a high-enthalpy regime and to the occurrence of thermochemical non-equilibrium effects. Vibrational relaxation phenomena are shown to be predominant with respect to chemical activity. In this context, high-fidelity results obtained by means of a Direct Numerical Simulation (DNS) are used as a benchmark to assess the quality of a Large-Eddy Simulation (LES) performed with a coarser wall-resolved grid. The wall-adapting local eddy viscosity approach is selected as sub-grid scale (SGS) model. The LES strategy is shown to capture the mean and fluctuating dynamic fields in the fully turbulent region quite satisfactorily, whereas transition to turbulence is slightly anticipated with respect to DNS. Both the chemical and vibrational source terms are evaluated with the filtered aerothermochemical quantities, resulting in an overestimation of the translational-vibrational energy exchange and an underestimation of dissociation chemical production rates. These results shed light on the necessity of developing more accurate closure models for the source terms, the SGS turbulence-thermochemistry interactions being important for the configuration under investigation