Showing papers by "Bart Merci published in 2000"

Computational Treatment of Source Terms in Two-Equation Turbulence Models

Abstract: The source terms in turbulence models require careful treatment to obtain a stable discretization. The choice between implicit and explicit treatment has to be made. This can be done either on the basis of individual terms or on the basis of the exact Jacobian of the source terms. A comparison of both methods shows that the latter is generally applicable and superior to the first, approximate method with respect to convergence speed. This comes from the possibility of using the multigrid technique with the exact method, whereas this is not always possible with the approximate method. In principle, for robustness a time-step restriction for the source terms has to be introduced to prevent the turbulence quantities from becoming negative or infinitely large. An approximation of the appropriate time step is calculated. Practical results, however, indicate that the time-step restriction is not always necessary. Different two-equation turbulence models are investigated confirming the generality of the approach

Realizable eddy-viscosity turbulence models in turbulent reacting flows.

Abstract: The quality of two-equation eddy-viscosity models is studied for non-premixed turbulent gas combustion in an axisymmetric co-flow burner. Non-linear extensions of low-Reynolds versions of two-equation turbulence models have been made. Both k − e and k −ω based turbulence models are studied. First order non-linearity in the constitutive law for the Reynolds stresses has been introduced on the basis of realizability. Realizability is obtained by introducing a dependency of the eddy-viscosity on local flow velocity gradients. The main advantage of non-linear eddy-viscosity models is that they describe the flowfield more accurately than their linear counterparts without rather 'ad hoc' adjustments of model constants. Differences between results from high-and low-Reynolds versions are small in the cases studied. Results are presented for an axisymmetric free jet, followed by results for an inert mixing jet. Finally, results for reacting jet are given. The realizable models always provide the best results.

Treatment of All Speed Flows and High Aspect Ratios in CFD Applications

Abstract: An AUSM (Advection Upstream Splitting Method) based discretization method, using an explicit third-order discretization for the convective part, a line-implicit central discretization for the acoustic part and for the diffusive part, has been developed for incompressible and low speed compressible Navier-Stokes equations. The lines are chosen in the direction of the gridpoints with shortest connection. The semi-implicit line method is used in multistage form because of the explicit third-order discretization of the convective part. Multigrid is used as acceleration technique. Due to the implicit treatment of the acoustic and the diffusive terms, the stiffness otherwise caused by high aspect ratio cells is removed. Low Mach number stiffness is treated by a preconditioning technique. To ensure physical correct behaviour of the discretization for vanishing Mach number, extreme care has been taken. For vanishing Mach number, stabilization terms are added to the mass flux. Pressure and temperature stabilization terms are necessary. The coefficients of these terms are chosen so that correct scaling with Mach number is obtained. A blend of the low speed algorithm with the original AUSM algorithm developed for high speed applications has been constructed so that the resulting algorithm can be used at all speeds.

A finite volume method for viscous compressible flows in low and high speed applications

Abstract: An AUSM (Advection Upstream Splitting Method) based discretization method, using an explicit third-order discretization for the convective part, a line-implicit central discretization for the acoustic part and for the diffusive part, has been developed for incompressible and low speed compressible flow. The lines are chosen in the direction of the gridpoints with shortest connection. The semi-implicit line method is used in multistage form because of the explicit third-order discretization of the convective part, Multigrid is used as an acceleration technique. Due to the implicit treatment of the acoustic and the diffusive terms, the stiffness otherwise caused by high aspect ratio cells is removed. Low Mach number stiffness is treated by a preconditioning technique. To ensure physically correct behaviour of the discretization for vanishing Mach number, extreme care has been taken. For vanishing Mach number, stabilization terms are added to the mass flux. Pressure and temperature stabilization terms are necessary. The coefficients of these terms are chosen so that correct scaling with Mach number is obtained. A blend of the low speed algorithm with the original AUSM algorithm developed for high speed applications has been constructed so that the resulting algorithm can be used at all speeds.

Application of Multigrid in Two-Equation Turbulence Modelling

Abstract: Source terms in two-equation turbulence models require special attention with respect to numerical stability. They can be treated explicitly or implicitly, depending on the Jacobian of the source terms. A fundamental study is carried out to find the appropriate numerical treatment, allowing the use of the multigrid technique. Different low-Reynolds turbulence models are investigated (k — e and k — ω based models). Convergence rates are compared for different test cases (flat plate flow, backward-facing step flow). A comparison is made between solving all the equations in a coupled way and decoupling the NS-subsystem from the turbulence subsystem. Convergence rates are comparable. A comparison between the use of V-and W-cycles shows comparable convergence rates, too.