Chris De Langhe

Determination of ϵ at inlet boundaries

Different methods for the determination of accurate values for the dissipation rate ϵ at the inlet boundary of a computational domain, are studied. With DNS data for a fully developed channel flow and pipe flow, it is shown that the method suggested by Rhee and Sung (2000), in which the k–ϵ turbulence model is used to compute both k and ϵ from a given velocity profile, is not reliable and can result in very poor results. The method is found to be extremely sensitive to the details of the imposed velocity profile. An alternative procedure is proposed, in which only the ϵ transport equation is employed, with given profiles for the mean velocity and the turbulence kinetic energy. This way, accurate and reliable profiles are obtained for ϵ. Another procedure, based on the turbulent mixing length, was suggested by Jones (1994). The problem. The problem is then shifted towards the determination of the mixing length at the inlet boundary of the computational domain. An expression for this mixing length is proposed in this paper, based on the mentioned DNS data. Finally, the method proposed by Rodi and Scheuerer (1985) is included for comparison reasons. The different procedures are first validated on the fully developed channel and pipe flow. Next, the turbulent flow over a backward‐facing step is considered. Finally, the influence of the inlet boundary condition for ϵ is illustrated in the application of a turbulent piloted jet diffusion flame.

Construction of explicit and implicit dynamic finite difference schemes and application to the large-eddy simulation of the Taylor-Green vortex

A general class of explicit and implicit dynamic finite difference schemes for large-eddy simulation is constructed, by combining Taylor series expansions on two different grid resolutions. After calibration for Re->~, the dynamic finite difference schemes allow to minimize the dispersion errors during the calculation through the real-time adaption of a dynamic coefficient. In case of DNS resolution, these dynamic schemes reduce to Taylor-based finite difference schemes with formal asymptotic order of accuracy, whereas for LES resolution, the schemes adapt to Dispersion-Relation Preserving schemes. Both the explicit and implicit dynamic finite difference schemes are tested for the large-eddy simulation of the Taylor-Green vortex flow and numerical errors are investigated as well as their interaction with the dynamic Smagorinsky model and the multiscale Smagorinsky model. Very good results are obtained.

Numerical simulation of heat transfer of turbulent impinging jets with two‐equation turbulence models

A numerical scheme that has already proved to be efficient and accurate for laminar heat transfer is extended for turbulent, axisymmetric heat transfer calculations. The extended scheme is applied to the steady‐state heat transfer of axisymmetric turbulent jets, impinging onto a flat plate. Firstly, the low‐Reynolds version of the standard k‐e model is employed. As is well known, the classical k‐e turbulence model fails to predict the heat transfer of impinging jets adequately. A non‐linear k‐e model, with improved e‐equation, yields much better results. The numerical treatment of the higher order terms in this model is described. The effect on the heat transfer predictions of a variable turbulent Prandtl number is shown to be small. It is also verified that the energy equation can be simplified, without affecting the results. Results are presented for the flow field and the local Nusselt number profiles on the plate for impinging jets with different distances between the pipe exit and the flat plate.

Intermittency based RANS bypass transition modelling

A transition model for describing bypass transition is presented. It is based on a two-equations k-ω model and a dynamic equation for intermittency factor. This intermittency factor is a multiplier of the turbulent viscosity computed by the turbulence model. Following a suggestion by Menter et al. (2002), the start of transition is computed based on local variables. The quality of the transition model, developed on flat plate test cases is illustrated on turbine cascades.

The dynamic procedure for accuracy improvement of numerical discretizations in fluid mechanics

In CFD computations, discretization or truncation errors should be small providing an acceptable level of accuracy. In this paper, an extension is made of the recently proposed LES formalism based on sampling operators. It is shown that the sampling-based dynamic procedure, in combination with an appropriate truncation error model, can be used as a technique to increase the numerical accuracy of a discretization. The technique is resemblant to the well-known Richardson extrapolation. The procedure is tested on a 1D convection-diffusion equation and a 2D lid-driven cavity at Re=400, using a finite difference method. Promising results are found.

Transition modelling with the SST turbulence model and an intermittency transport equation

In gas turbine engines, laminar-turbulent transition occurs. However, generally, the turbulence models to describe such transition results in too early and too short transition. Combining a turbulence model with a description of intermittency, i.e. the fraction of time the flow is turbulent during the transition phase, can improve it. By letting grow the intermittency from zero to unity, start and evolution of transition can be imposed. In this paper, a method where a dynamic equation of intermittency combining with a two-equation k-ω turbulence model is described. This intermittency factor is a premultiplicator of the turbulent viscosity computed by the turbulence model. Following a suggestion by Menter et al.[1], the start of transition is computed based on local variables.

Hybrid RANS-LES modelling with the renormalization group

A two-equation turbulence model that can adjust itself from RANS to LES regimes is constructed using the renormalization group. When the grid-spacing gets to coarse for LES, the model tends to a RANS model. In well-resolved regions the model results in a LES subgrid-model. The renormalization group procedure leads to transport-equations that are dependent on the filterwidth and contain no adjustable constants.Copyright

Quality assessment of dynamic finite difference schemes on the taylor-green vortex

The performance of a class of explicit and implicit dynamic finite difference schemes (Fauconnier et al. J. Comput. Phys., 228(6):1830–1861 (2009), J. Comput. Phys., Accepted (2009)) is investigated for the Large-Eddy Simulation of the three-dimensional Taylor-Green Vortex flow (Brachet et al. (1983)), in which the dynamic Smagorinsky model and the small-small multiscale Smagorinsky model are used. The numerical errors and the modeling errors and their interactions are investigated.

THE SAMPLING BASED DYNAMIC PROCEDURE FOR NUMERICAL DISCRETIZATION ENHANCEMENT

Recently, a new sampling formalism for Large Eddy simulation was proposed by Winckelmans et al. [1] and Knaepen et al.[2], which is a projection method for Navier-Stokes equations from continuum space to a discrete space, using a sampling operator instead of a filter operator. Since the sampling operator is not commutative with spatial derivatives, a closure term appears which represents the loss of information due to the projection on a discrete mesh. In e.g.[2] a Smagorinsky model was proposed that, by relying on a generalized dynamic procedure, succeeded in accounting for the subgrid scales. In this paper, we investigate the ability of this sampling based dynamic procedure, in combination with an appropriate model for the truncation error, to obtain higher-order numerical accuracy. Two such possible models are presented. Further, we show that Richardson extrapolation is a simplified formulation of this procedure.

Parametrizing Hybrid RANS-LES Approaches With The Renormalization Group

A two-equation turbulence model that can adjust itself from RANS to LES regimes is constructed using the renormalization group. When the grid-spacing gets too coarse for LES, the model tends to a RANS model. In well-resolved regions the model results in a LES subgrid-model. The renormalization group procedure leads to transport-equations that are dependent on the filterwidth and contain no adjustable constants.