Jochen Fröhlich

Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions

High-resolution large-eddy simulation is used to investigate the mean and turbulence properties of a separated flow in a channel constricted by periodically distributed hill-shaped protrusions on one wall that obstruct the channel by 33% of its height and are arranged 9 hill heights apart. The geometry is a modification of an experimental configuration, the adaptation providing an extended region of post-reattachment recovery and allowing high-quality simulations to be performed at acceptable computing costs. The Reynolds number, based on the hill height and the bulk velocity above the crest is 10595. The simulated domain is streamwise as well as spanwise periodic, extending from one hill crest to the next in the streamwise direction and over 4.5 hill heights in the spanwise direction. This arrangement minimizes uncertainties associated with boundary conditions and makes the flow an especially attractive generic test case for validating turbulence closures for statistically two-dimensional separation. The emphasis of the study is on elucidating the turbulence mechanisms associated with separation, recirculation reattachment, acceleration and wall proximity. Hence, careful attention has been paid to resolution, and a body-fitted, low-aspect-ratio, nearly orthogonal numerical grid of close to 5 million nodes has been used. Unusually, the results of two entirely independent simulations with different codes for identical flow and numerical conditions are compared and shown to agree closely. Results are included for mean velocity, Reynolds stresses, anisotropy measures, spectra and budgets for the Reynolds stresses. Moreover, an analysis of structural characteristics is undertaken on the basis of instantaneous realizations, and links to features observed in the statistical results are identified and interpreted. Among a number of interesting features, a distinct ‘splatting’ of eddies on the windward hill side following reattachment is observed, which generates strong spanwise fluctuations that are reflected, statistically, by the spanwise normal stress near the wall exceeding that of the streamwise stress by a substantial margin, despite the absence of spanwise strain.

Investigation of wall-function approximations and subgrid-scale models in large eddy simulation of separated flow in a channel with streamwise periodic constrictions

Large eddy simulations are presented for the flow in a periodic channel segment, which is laterally constricted by hill-shaped obstructions on one wall, having a height of 33% of the unconstricted channel. The Reynolds number, based on channel height, is 21,560. Massive separation thus arises on the hills’ leeward sides, the length of which is about 50% of that of the periodic segment. After reattachment, the flow is allowed to recover over about 30% of the segment length before being strongly accelerated over the windward side of the next hill. The principal challenge of this flow arises from the separation on the curved hill surface and the fact that the reattachment point, and hence the whole flow, are highly sensitive to the separation process. Simulations were performed with three grids, six subgrid-scale models and eight practices of approximating the near-wall region in simulations on the two coarser grids. These were supported by wall-resolved and wall-function simulations for fully-developed channel flow. The principal objective is to identify the sensitivity of the predictive accuracy to resolution and modelling issues. Coarse-grid simulations are judged by reference to data derived from two independent highly-resolved simulations obtained over identical meshes of close to 5 million nodes. Similarly, coarser-grid simulations were also performed with the two codes to enhance confidence in the results. The principal message emerging from the simulations is that grid resolution, especially in the streamwise direction around the mean separation position, has a very strong influence on the reattachment behaviour and hence the whole flow. This has serious implications for even more challenging high-Reynolds-number cases in which separation occurs from gently curved surfaces. The near-wall treatment, including the details of the numerical implementation of the wall laws, is also shown to be influential, most prominently on the coarsest grid. The application of the no-slip conditions at the wall at which separation occurs is found to cause substantial errors, especially in conjunction with poor streamwise resolution, even if the wall-nearest grid nodes are within the semi-viscous sublayer, in the range 5≲y+≲15. The sensitivity to subgrid-scale modelling is shown to be more modest, with those models returning relatively low subgrid-scale viscosity giving the closest accord with the highly-resolved simulation.

A framework for predicting accuracy limitations in large-eddy simulation

The accuracy of large-eddy simulations is limited, among other things, by the quality of the subgrid parametrization and the numerical contamination of the smaller retained flow structures. We characterize the total simulation error in terms of the “subgrid-activity” s, which measures the relative turbulent dissipation rate (0⩽s⩽1) and the “subgrid resolution” r. This analysis is applied to turbulent mixing of a “Smagorinsky fluid” using a finite volume discretization of fourth order accuracy. On fixed coarse grids, i.e., at constant computational cost, the total simulation error decreases monotonically with filter width Δ for large s while for smaller s the total error may even increase with decreasing Δ. The corresponding modeling- and spatial discretization-error contributions are quantified at various resolutions.

An improved immersed boundary method with direct forcing for the simulation of particle laden flows

An efficient approach for the simulation of finite-size particles with interface resolution was presented by Uhlmann [M. Uhlmann, An immersed boundary method with direct forcing for the simulation of particulate flows, J. Comput. Phys. 209 (2005) 448-476.]. The present paper proposes several enhancements of this method which considerably improve the results and extend the range of applicability. An important step is a simple low-cost iterative procedure for the Euler-Lagrange coupling yielding a substantially better imposition of boundary conditions at the interface, even for large time steps. Furthermore, it is known that the basic method is restricted to ratios of particle density and fluid density larger than some critical value above 1, hence excluding, for example, non-buoyant particles. This can be remedied by an efficient integration step for the artificial flow field inside the particles to extend the accessible density range down to 0.3. This paper also shows that the basic scheme is inconsistent when moving surfaces are allowed to approach closer than twice the step size. A remedy is developed based on excluding from the force computation all surface markers whose stencil overlaps with the stencil of a marker located on the surface of a collision partner. The resulting algorithm is throughly validated and is demonstrated to substantially improve upon the original method.

Identification and analysis of coherent structures in the near field of a turbulent unconfined annular swirling jet using large eddy simulation

Large eddy simulations of incompressible turbulent flow in an unconfined annular swirling jet at Reynolds number 81500 are reported, based on the outer radius of the jet. The results are in excellent agreement with experimental data for mean flow, turbulent statistics, and power spectral densities of velocity fluctuations. Two dominant families of large-scale coherent structures are identified in the flow. Both are orthogonal to the mean three-dimensional streamlines, which suggests that they are formed as the result of a Kelvin-Helmholtz instability. Instantaneous vortex structures as well as different types of spectra and two-point correlations are presented to further elucidate the properties of the flow.

An adaptive two-dimensional wavelet-vaguelette algorithm for the computation of flame balls

This paper is concerned with the numerical simulation of two-dimensional flame balls. We describe a Galerkin-type discretization in an adaptive basis of orthogonal wavelets. The solution is represented by means of a reduced basis being adapted in each time step. This algorithm is applied to compute the evolution of circular and elliptic thermodiffusive flames. In particular, we study the influence of the Lewis number, the strength of radiative losses and of the initial radius. The results show different scenarios. We find repeated splitting of the flame ball which is studied in some detail, extinction after excessive growth and also obtain quasi-steady flame balls.

Large departures from Boussinesq approximation in the Rayleigh–Bénard problem

Flows involving natural convection are generally studied employing the Boussinesq approximation of the Navier–Stokes equations. This paper deals with large departures from this limit by considering the two‐dimensional, periodic Rayleigh–Benard problem as an example. The main effect investigated here is a strong variation in the density considered primarily as a function of temperature as it is accounted for by the low Mach number equations. Additionally, the effect of temperature‐dependent viscosity and heat conductivity is considered. Both types of departure are measured by the nondimensional temperature gradient. They destroy the midplane symmetry of the problem and lead to quantitative and qualitative changes of the flow, in particular in the bifurcation from the conduction state. The present study illustrates how three different approaches—by linear stability analysis, weakly nonlinear analysis, and direct simulation—permit the investigation of complementary aspects of the problem. The first is used t...

A simple wall-layer model for large eddy simulation with immersed boundary method

A wall-layer model is proposed for large eddy simulation of high Reynolds number turbulent flows in conjunction with immersed boundaries. The model is based on two main steps: the reconstruction of the velocity field at the first grid point off the immersed body and the modelization of the actual wall shear stress at the immersed boundary through imposition of a Reynolds averaged Navier–Stokes-like eddy viscosity obtained by means of analytical considerations. The model is tested in a turbulent plane channel flow with walls reproduced by immersed boundaries considering both Cartesian and curvilinear grids. Even with coarse and distorted grids the proposed methodology is able to reproduce accurately both first- and second-order turbulent statistics.

Large eddy simulation of a swirling transverse jet into a crossflow with investigation of scalar transport

The flow field of a turbulent jet emerging from a straight round pipe into a laminar crossflow is investigated by means of large eddy simulations. The concentration of a passive scalar, introduced with the jet, is calculated in order to quantify the mixing of the jet and the crossflow. In the jet, swirl is introduced by means of body forces and a range of jet swirl numbers from S = 0 up to S = 0.6 is studied. The impact of the jet swirl on the flow field, on the coherent structures, and on the mixing efficiency is investigated and quantified by means of various analyses. It is found that for all swirl numbers larger than zero a clear asymmetry appears in all quantities studied. Additional to the two hanging vortices at both sides of the jet a third vortex is introduced by the swirling pipe flow which interacts with the former. This feature is described in detail as it is not mentioned in the literature. For the strongest swirl investigated a recirculation zone near the jet exit is observed. Despite the asymmetry and even with a recirculation zone at the outlet, the counter-rotating vortex pair still exists in all cases in the downstream flow, where it entrains a large amount of crossflow fluid into the jet. The near field, however, is altered by the jet swirl in several respects. The jet more and more approaches the bottom wall with increasing swirl. As a result, the entrainment is gradually attenuated due to the larger blocking of the secondary flow by the wall. Increased swirl increases both the turbulent kinetic energy in the pipe and the vorticity of the average flow field near the jet exit, and thus stimulates the mixing in these regions. However, this stimulating effect is overwhelmed by the closer position of the jet trajectory to the wall of the channel with increasing swirl, which in turn reduces entrainment of fresh crossflow fluid into the jet. As a final result of these two competing effects, the overall mixing efficiency of a jet into a crossflow is merely unchanged with the addition of swirl. Various mixing indices, both spatial and temporal, are used for this analysis. Their respective advantages and disadvantages are discussed and detailed illustrations provide a sound understanding of their behavior.

Computation of decaying turbulence in an adaptive wavelet basis

Abstract The paper presents computations of decaying two-dimensional turbulence in an adaptive wavelet basis. At each time step the vorticity is represented by an adaptively selected set of wavelet functions which adjusts to the instantaneous distribution of vorticity. Essential features are the use of operator–adapted test functions and the adaptive evaluation of the convection term. The results of this new algorithm are compared to a classical Fourier method and a Fourier method supplemented with wavelet compression in each time step. They show that turbulent flows with a multitude of spatial scales can be computed with a reduced number of degrees of freedom. The investigation of diverse spectral and statistical criteria validates the wavelet approach.