Quantification of errors in large-eddy simulations of a spatially-evolving mixing layer

A stochastic approach based on generalized Polynomial Chaos (gPC) is used to quantify the error in Large-Eddy Simulation (LES) of a spatially-evolving mixing layer flow and its sensitivity to different simulation parameters, viz. the grid stretching in the streamwise and lateral directions and the subgrid scale model constant ($C_S$). The error is evaluated with respect to the results of a highly resolved LES (HRLES) and for different quantities of interest, namely the mean streamwise velocity, the momentum thickness and the shear stress. A typical feature of the considered spatially evolving flow is the progressive transition from a laminar regime, highly dependent on the inlet conditions, to a fully-developed turbulent one. Therefore the computational domain is divided in two different zones (\textit{inlet dependent} and \textit{fully turbulent}) and the gPC error analysis is carried out for these two zones separately. An optimization of the parameters is also carried out for both these zones. For all the considered quantities, the results point out that the error is mainly governed by the value of the $C_S$ constant. At the end of the inlet-dependent zone a strong coupling between the normal stretching ratio and the $C_S$ value is observed. The error sensitivity to the parameter values is significantly larger in the inlet-dependent upstream region; however, low error values can be obtained in this region for all the considered physical quantities by an ad-hoc tuning of the parameters. Conversely, in the turbulent regime the error is globally lower and less sensitive to the parameter variations, but it is more difficult to find a set of parameter values leading to optimal results for all the analyzed physical quantities

Modeles pratiques de catalyse a la paroi pour les calculs d'ecoulements hypersoniques

Dans cette etude on s'interesse a la modelisation physique des phenomenes de catalyse se produisant a la paroi d'un obstacle plonge dans un ecoulement hypersonique. On se propose en particulier, d'etudier et d'analyser les modeles presentes dans la litterature traitant de ce sujet. Cette recherche bibliographique a pour but d'etudier la possibilite d'implementer des modeles de catalyse de complexite croissante dans des codes de simulation numerique d'ecoulements hypersoniques reactifs. On presente tout d'abord un modele d'interaction binaire avec accomodation complete de l'energie dans lequel les termes de production des especes a la paroi ont fonctions de coefficients de recombinaison. Ces coefficients expriment la probabilite qu'un atome incident a la paroi se recombine. On decrit aussi differentes methodes (analytiques et empiriques) pour la determination des coefficients de recombinaison, pour l'oxygene et l'azote. On presente ensuite un modele des phenomenes de catalyse considerant un schema reactionnel heterogene a la paroi. On s'interesse enfin a l'implementation de ce modele dans un code de simulation numerique d'ecoulements hypersoniques qui repose sur une formulation mixte elements-finis/volumes-finis

A Preconditioned implicit Roe's scheme for barotropic flows: towards simulation of cavitation phenomena

The discretisation of the Euler equations for a barotropic state law is considered. An upwind scheme based on the definition of a Roe's type matrix is first obtained for this particular hyperbolic problem. A low Mach number asymptotic study is performed both in the continuous and discrete case showing that the discrete solution admits pressure fluctuations in space much larger than those of the exact one. This is the same kind of behaviour observed for the case of a polytropic state law. A preconditioning is then applied such that the obtained discrete formulation has an asymptotic behaviour in agreement with the continuous case. A linearised implicit scheme is defined using the properties of the Roe matrix instead of the first-order homogeneity of the flux function which is not satisfied here. The implicit formulation is also extended to the preconditioned scheme. All the proposed ingredients are validated in the case of a quasi 1-D nozzle flow of a cavitating liquid

Investigation of the steady engulfment regime in a three-dimensional T-mixer

The steady engulfment regime in a fully three-dimensional micro T-mixer is investigated. This regime is of significant interest for applications since it implies high mixing between the flow streams entering the device. Direct numerical simulations are first used to characterize this regime. In particular, the main vortical structures typical of the engulfment regime and their effects on mixing are investigated. Three-dimensional linear stability analysis is successively applied to the characterization of the instability leading to the engulfment regime. The critical Reynolds number and the global unstable mode are first computed for a configuration characterized by fully-developed inlet velocity conditions. The sensitivity of this instability to a generic modification of the base flow is then investigated, thanks to the computation of the mode adjoint to the direct unstable one. Finally, this kind of analysis is specialized to investigate the effect of a perturbation of the velocity distribution at the inlet of the T-mixer. Sensitivity analysis shows that non-fully developed inlet velocity conditions lead to an increase of the critical Reynolds number. More generally, the sensitivity maps can be used for the design of control strategies aimed at promoting or inhibiting the engulfment. An example is provided for a control based on blowing/suction through the mixer walls

Control of the turbulent flow in a plane diffuser through optimized contoured cavities

A passive control strategy, which consists in introducing contoured cavities in solid walls, is applied to a plane asymmetric diffuser at a Reynolds number that implies fully-turbulent flow upstream of the diffuser divergent part. The analysed reference configuration, for which experimental and numerical data were available, is characterized by an area ratio of 4.7 and a divergence angle of 10 degrees. A large zone of steady flow separation is present in the diffuser without the introduction of the control. One and two subsequent contoured cavities are introduced in the divergent wall of the diffuser and a numerical optimization procedure is carried out to obtain the cavity geometry that maximizes the pressure recovery in the diffuser and minimizes the flow separation extent. The introduction of one optimized cavity leads to an increase in pressure recovery of the order of 6.9% and to a significant reduction of the separation extent, and further improvement (9.6%) is obtained by introducing two subsequent cavities in the divergent wall. The most important geometrical parameters are also identified, and the robustness of the solution to small changes in their values and in the Reynolds number is assessed. The present results show that the proposed control strategy, previously tested in the laminar regime, is effective also for turbulent flows at higher Reynolds numbers. As already found for laminar flow, the success of the control is due both to a virtual geometry modification of the diffuser and to a favourable effect of the cavities in reducing the momentum losses near the wall

Connection between base drag, separating boundary layer characteristics and wake mean recirculation length of an axisymmetric blunt-based body

The variation of the base drag of an axisymmetric bluff body caused by modifications of the boundary-layer separating at the sharp-edged contour of its base is analysed through different numerical simulations, and the results are compared with those of a previous experimental investigation. Variational MultiScale Large-Eddy Simulations (VMS-LES) are first carried out on the same nominal geometry and at the same Reynolds number of the experiments. Subsequently, Direct Numerical Simulations (DNS) are performed at Reynolds numbers that are roughly two orders of magnitude lower, in order to investigate on the sensitivity of the main findings to the Reynolds number. The results of experiments, VMS-LES and DNS simulations show that an increase of the base pressure - and thus a decrease of the base drag - may be obtained by increasing the boundary layer thickness before separation, which causes a proportional increase of the length of the mean recirculation region behind the body. In spite of the different setups, Reynolds numbers and turbulence levels in the experiments and numerical simulations, in all cases the base pressure is found to be directly proportional to the length of the mean recirculation region, which is thus a key index of the base drag value. In turn, the recirculation length seems to be connected with the location of the incipient instability of the detaching shear layers, which can be moved downstream by an increase of the thickness of the separating boundary layer and upstream by an increase of the turbulence level