Dominique Laurence

Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach

The stability and accuracy of three methods which enforce either a divergence-free velocity field, density invariance, or their combination are tested here through the standard Taylor-Green and spin-down vortex problems. While various approaches to incompressible SPH (ISPH) have been proposed in the past decade, the present paper is restricted to the projection method for the pressure and velocity coupling. It is shown that the divergence-free ISPH method cannot maintain stability in certain situations although it is accurate before instability sets in. The density-invariant ISPH method is stable but inaccurate with random-noise like disturbances. The combined ISPH, combining advantages in divergence-free ISPH and density-invariant ISPH, can maintain accuracy and stability although at a higher computational cost. Redistribution of particles on a fixed uniform mesh is also shown to be effective but the attraction of a mesh-free method is lost. A new divergence-free ISPH approach is proposed here which maintains accuracy and stability while remaining mesh free without increasing computational cost by slightly shifting particles away from streamlines, although the necessary interpolation of hydrodynamic characteristics means the formulation ceases to be strictly conservative. This avoids the highly anisotropic particle spacing which eventually triggers instability. Importantly pressure fields are free from spurious oscillations, up to the highest Reynolds numbers tested.

LES, coarse LES, and transient RANS comparisons on the flow across a tube bundle

Abstract The cross-flow in a staggered tube bundle is computed with an LES and a transient Reynolds stress transport model (RSTM) in 2D and 3D, with two levels of grid refinement. The numerical method is based on a finite volume approach on unstructured grids using a collocated arrangement for all the unknowns. It is shown that the LES results on the fine mesh are comparable to a DNS and experiments and reasonable agreement is still achieved with a coarse mesh. The RSTM also produced satisfactory results in 3D but showed no advantage over the LES when the grid was coarsened. The 2D RSTM, which produced strong vortex shedding, was found to be physically unreasonable.

Large eddy simulation of a forward–backward facing step for acoustic source identification

The feasibility of using a commercial CFD code for large eddy simulation (LES) is investigated. A first test on homogeneous turbulence decay allows a fine-tuning of the eddy viscosity with respect to the numerical features of the code. Then, a flow over forward–backward facing step at Reynolds number Reh ¼ 1:7 � 10 5 is computed. The results found show good agreement with the new LDA data of Leclercq et al. [Forward backward facing step pair: aerodynamic flow, wall pressure and acoustic characterization. AIAA-2001-2249]. The acoustic source term, recorded from the LES and to be fed into a following acoustic propagation simulation, is found to be largest in the separation from the forward step. The source terms structures are similar to the vortical structures generated at the front edge of the obstacle and advected downstream. Structures generated from the backward step rapidly break down into smaller scale structures due to the background turbulence. 2003 Published by Elsevier Science Inc.

Inhomogeneity and anisotropy effects on the redistribution term in Reynolds-averaged Navier-Stokes modelling

A channel flow DNS database at Re τ = 590 is used to assess the validity of modelling the redistribution term in the Reynolds stress transport equations by elliptic relaxation. The model assumptions are found to be globally consistent with the data. However, the correlation function between the fluctuating velocity and the Laplacian of the pressure gradient, which enters the integral equation of the redistribution term, is shown to be anisotropic. It is elongated in the streamwise direction and strongly asymmetric in the direction normal to the wall, in contrast to the isotropic, exponential model representation used in the original elliptic relaxation model. This discrepancy is the main cause of the slight amplification of the energy redistribution in the log layer as predicted by the elliptic relaxation equation. New formulations of the model are proposed in order to correct this spurious behaviour, by accounting for the rapid variations of the length scale and the asymmetrical shape of the correlation function. These formulations do not rely on the use of so-called ‘wall echo’ correction terms to damp the redistribution. The belief that the damping is due to the wall echo effect is called into question through the present DNS analysis.

Modeling near-wall effects in second-moment closures by elliptic relaxation

The elliptic relaxation method for modeling near-wall turbulence via second-moment closures (SMC) is compared to direct numerical simulation (DNS) data for channel flow at Reτ=395. The agreement for second-order statistics, and the terms in their balance equation is quite satisfactory, confirming that essential kinematic effects of the solid boundary on near-wall turbulence are accurately modeled by an elliptic operator. Additional viscous effects, immediately next to the surface, can be added via Kolmogoroff scales. In combination, elliptic relaxation and Kolmogorov scaling provide a general formulation to extend high Reynolds number SMC to wall-bounded flows. This formulation was easily applied to the nonlinear Craft-Launder and Speziale-Sarkar-Gatski (SSG) pressure-strain models. It is observed that the boundary conditions of the relaxation operator dominate the homogeneous pressure-strain model in the near-wall region. While looking at high-Reynolds number channel flows, it was found necessary to modify the effect of the relaxation operator throughout the log-layer by accounting for gradients of the turbulent lengthscale; this brings the velocity gradient into perfect agreement with the von Karman constant. The final form of the model based on the SSG homogeneous closure was then successfully applied to rotating channel flows, including relaminarization. The paper merges and updates two contributions by the five authors to the 10th Turbulent Shear Flow Conference.

Turbulent heat transfer predictions using the –f model on unstructured meshes

Abstract Durbins three transport equation model, the so-called v 2 –f model, has been implemented in an industrial finite element code, N3S, developed at the research and development department of Electricite de France, enabling the use of unstructured meshes. Validations by comparison with other codes have been performed in the cases of the channel flow at Reτ=395, and the backward-facing step at Re=5100. The test case of the 2D periodic ribbed-channel flow has then been computed, without heat transfer at ReH=37,200, and with a constant heat flux imposed at the ribbed-wall at ReH=12,600. The results obtained show the ability of the model to predict accurately the enhancement of heat transfer due to the ribs, which is of primary interest for industrial applications.

New low-reynolds-number k-ε model including damping effect due to buoyancy in a stratified flow field

Abstract A new k-e model which includes damping effect on vertical turbulent transport due to thermal stratification is proposed. The proposed model was tested by application to two kinds of two-dimensional thermally stratified flow fields. One is a high-Reynolds-number open channel flow, and the other is a low-Reynolds-number flowfield within an enclosure. The new model also includes low-Reynolds-number treatment which is effective not only in the vicinity of the wall, but also apart from the wall. With the aid of this new low-Reynolds-number treatment, the proposed k-e model becomes applicable to a flowfield which includes both turbulent area and pseudo-laminar area caused by thermal stratification. The agreement between the results given from the new k-e model and the experimental results was rather good.

Optimal Unstructured Meshing for Large Eddy Simulations

An attempt is made to provide a criterion for optimal unstructured meshing for LES from the knowledge of different turbulence lengthscales. In particular, the performance of a grid based on the Taylor microscales for turbulent channel flow, is investigated, with the final view of facilitating an a priori determination of the mesh resolution required for LES. The grid dictated by the Taylor microscales is more cubical in the centre of the domain than the typical empirical LES grids. Furthermore, it is as fine in the spanwise direction as it is in the wall normal direction. Empirical LES grids, currently widely used, have a very fine (approximately four times finer) wall normal resolution and a coarse (about twice as course) streamwise resolution as compared to a grid based on the Taylor microscales. A remarkable feature is that the mean velocity and streamwise component of fluctuating velocity (classically over-predicted in coarse grid LES) and the wall normal fluctuating velocity are well reproduced on the new grid. The attempt of building an unstructured LES grid based on the Taylor microscale has been found very successful. However, as the Reynolds number is increased this sort of requirement might be excessive and eventualy a criterion such as one tenth of the integral lengthscale could be sufficient.

Les in a U-Bend Pipe Meshed by Polyhedral Cells

Large Eddy Simulation of an incompressible fluid in a straight pipe with a circular cross-section is investigated with a Finite Volume (FV) method based on polyhedral cells, using synthetic turbulence at the inlet. Results of this non-periodic simulation are quite accurate after 2 diameters from the inlet, showing that the structures are self-sustainable. The method is then extended to a flow in a 180° U bend pipe with circular cross-section, using an original automatic and boundary-layer-adapting meshing technique. This configuration, or a more convoluted version of it, is often encountered in industry (e.g. in car engines, air-conditioning, etc) and could not be regularly and smoothly meshed by cylindrical grids. The Reynolds number based on the bulk velocity and the hydraulic diameter is in both cases equal to 54,700. Comparisons are made with the experimental results from Azzola et al. (1986). Success of the simulation is mostly due to the excellent properties of the FV scheme on polyhedral cells. The fact that lines connecting cell centres are nearly orthogonal to the cell faces ensures that the numerical scheme is virtually free from any numerical diffusion. This was demonstrated on an array of 2-D inviscid vortices which are self sustained without loss of intensity.

Modeling the response of turbulence subjected to cyclic irrotational strain

Using a second moment closure, analytical solutions for homogeneous turbulence subjected to periodic compression-dilatation strains show that both the characteristic turbulence frequency and turbulence kinetic energy eventually decay, irrespective of the initial turbulence level, anisotropy of the stress field, or Reynolds number. The eddy-viscosity models give erroneous results because of the artificial positive generation of turbulence energy during both the compression and expansion phase. The first observation results from the phase lag between periodic strain rate and stresses introduced by the exact production term in the second moment closure, whereas the eddy-viscosity model synchronizes the stresses with the strain rate, resulting in an overestimation of turbulence generation. The above findings are illustrated by analytical solutions, as well as by numerical solutions of in-cylinder turbulence, using the k−e eddy-viscosity and the second-moment closure models. The analysis and simulations support the conjecture that turbulence submitted to cyclic strains should always finally decay.