Jörn Sesterhenn

A characteristic-type formulation of the Navier–Stokes equations for high order upwind schemes

Abstract We propose a formulation of the three-dimensional Navier–Stokes equations, which expresses the inviscid part of the equations as a decomposition into several plane waves which are aligned with the numerical grid. The resulting equations are very well suited to numerical solution using compact high order upwind schemes. Boundary conditions and blockwise decomposition of the computational domain are particularly straightforward. Such advantages make the formulation attractive, even when using central or pseudospectral differencing methods. Numerical examples are presented.

Turbulent supersonic channel flow

The effects of compressibility are studied in low Reynolds number turbulent supersonic channel flow via a direct numerical simulation. A pressure-velocity-entropy formulation of the compressible Navier-Stokes equations which is cast in a characteristic, non-conservative form and allows one to specify exact wall boundary conditions, consistent with the field equations, is integrated using a fifth-order compact upwind scheme for the Euler part, a fourth-order Pade scheme for the viscous terms and a third-order low-storage Runge-Kutta time integration method. Coleman et al fully developed supersonic channel flow at M?=?1.5 and Re?=?3000 is used to test the method. The nature of fluctuating variables is investigated in detail for the wall layer and the core region based on scatter plots. Fluctuations conditioned on sweeps and ejections in the wall layer are especially instructive, showing that positive temperature, entropy and total temperature fluctuations are mainly due to sweep events in this specific situ...

Turbulent mixing in temporal compressible shear layers involving detailed diffusion processes

Direct numerical simulations (DNS) of temporally evolving weakly compressible shear layers with gradients of species and temperature have been performed to investigate the influence of detailed diffusion processes on turbulent mixing. As an exact modeling of the mixing process is a prerequisite of correct combustion prediction, this study aims at exploring the necessity of considering detailed diffusion processes of active scalars. The results comprise a demonstration of the strength of the Soret and Dufour effect and of their impact on the scalar and temperature gradients. The erroneous assumption of a spatially and temporally constant Schmidt number, equal for all species, is discussed. Furthermore, the scalar dissipation rate which is responsible for the smoothening of scalar fluctuations in the smallest scales is investigated. As this quantity is controlling the molecular mixing, it is clear that an influence on it by detailed diffusion processes has a direct impact on the chemical reaction and heat r...

Linear interaction of a cylindrical entropy spot with a shock

The interaction of a cylindrical element of hot or cold gas (the “entropy spot”) with a shock wave is considered. An exact solution in the limit of weak spot amplitudes is elaborated, using the linear interaction analysis theory and the procedure of decomposition proposed by Ribner (Technical Report No. 1164, NACA, 1953). The method is applied to an entropy spot with a Gaussian profile. Results are presented for a wide range of shock Mach numbers, with a special interest at M1=2. The resulting vorticity field consists of a pair of primary counter-rotating vortices, as well as a pair of secondary vortices of opposite sign and weaker amplitude. An expression for the circulation in half a plane is derived and compared to existing results. The pressure field consists of a cylindrical acoustic wave which propagates away from the transmitted spot and an evanescent nonpropagative field confined behind the shock. For a hot spot, the cylindrical wave is a rarefaction wave on its forward front and a compression wav...

Flux-vector splitting for compressible low Mach number flow

Abstract Several problems are encountered when calculating low Mach number flow. We illustrate them from different points of view and investigate two flux-vector splittings designed for this type of flow. Both splittings are applied to a quasi-1-D nozzle flow, using the explicit as well as a semi-implicit and the implicit Euler scheme with a finite-volume upwind formulaton. Results at low and very low Mach numbers are compared with calculations using Roes scheme. A von Neumann stability analysis is carried out for the more promising scheme based on a convection pressure splitting.

Instabilities in compressible attachment–line boundary layers

The hydrodynamic stability of the weakly compressible attachment–line boundary layer, with a sweep Mach number ranging from 0.1 to 1.3, is studied using a temporal compressible direct numerical simulation. A flow impinging non-normally onto an infinitely extended flat plate was computed. This complements the study of Hall et al. [Proc. R. Soc. London, Ser. A 395, 229 (1984)] who investigated the linear stability of an incompressible attachment–line boundary layer under the assumption of Gortler–Hammerlin perturbation modes. In the present work, the base flow is modeled starting from the incompressible swept Hiemenz flow. Using Rayleigh-Jansen Mach number expansions, we obtain a family of base flows parameterized with the sweep Mach number ranging from 0.1 to 1.3. The Reynolds number of the simulation is higher than the incompressible critical Reynolds number, and the plate is adiabatic. Small purely vortical stochastic perturbations are inserted in the boundary layer and followed in time. For Mach numbers...

Direct Numerical Simulation of Turbulent Compressible and Incompressible Wall-Bounded Shear Flows

Active research in turbulent compressible flow dates back to the fifties and was mainly driven by the aim to make flight at supersonic speeds possible. Considerable progress in measuring such flows and in predicting them numerically was achieved since then. Yet, a lot more has to be understood about the physics of compressible turbulence, especially what effects of compressibility due to turbulent fluctuations (intrinsic compressibility effects) is concerned. During the last decade direct numerical simulation (DNS) has made valuable contributions in this direction.

LES of Turbulent Low Mach Number Shear Layers with Active Scalars Using Explicit Filtering

Performing Large Eddy Simulations (LES) at moderate Reynolds numbers with active scalars and detailed molecular transport mechanisms is quite complicated as they are fully coupled with the flow field and influence it directly for example via density gradients resulting from varying mass fractions. The use of the explicit filtering method (EFM) is especially attractive due to its simplicity: The Navier-Stokes and species transport equations in the original DNS formulation are solved on the LES grid and the resulting flow fields are explicitly low-pass filtered in a specific way after each time step. No heuristic or physical subgrid models are used. Up to now, the EFM has been successfully applied to compressible turbulent channel flows [2]. In this work, it is tested for turbulent shear layers in order to find out how it performs in the presence of active scalars. The first section of the paper describes the inert shear layer configuration and the parameters of the simulations. In addition, the EFM is briefly explained. The method is tested qualitatively and quantitatively in the next section by comparing LES results with results from Direct Numerical Simulations (DNS). The last part of the paper is dedicated to the application of the EFM to reacting shear layers with infinitely fast chemistry.

Preconditioning and flux vector splitting for compressible low Mach number flow

We tested five explicit methods to solve the quasi 1D Euler equations for compressible low Mach number flow through a Laval nozzle. All of them converge similarly slowly to the steady state, although at least the preconditioning methods and the semi-implicit flux vector splitting were expected to perform better. The reason is probably due to the use of reflecting boundary conditions. For low Mach number flow, the error in pressure of the flux vector splitting methods is lower than that of Roes scheme.

DNS of Compressible Inert and Infinitely Fast Reacting Mixing Layers

This paper deals with the effects of heat release and compressibility on temporally evolving, turbulent mixing layers. Direct Numerical Simulations (DNS) of such layers at two different convective Mach numbers are performed with and without combustion which allows to study the effects of heat release and compressibility separately and combined. It is shown that both, compressibility and heat release, dampen the turbulence activity and lead to a reduced growth of the mixing layer. Alterations in pressure fluctuations are a main reason for the changes. The effects of compressibility are not as strong in the reacting mixing layer as in the inert one. A significant difference between the inert and the reacting mixing layers at high convective Mach number is that entropic density fluctuations prevail over the acoustic ones when reaction takes place while both contribute to nearly equal parts in the non-reacting compressible flow.