Steffen Stolz

An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows

The approximate deconvolution model (ADM) for the large-eddy simulation of incompressible flows is detailed and applied to turbulent channel flow. With this approach an approximation of the unfiltered solution is obtained by repeated filtering. Given a good approximation of the unfiltered solution, the nonlinear terms of the filtered Navier–Stokes equations can be computed directly. The effect of nonrepresented scales is modeled by a relaxation regularization involving a secondary filter operation. Large-eddy simulations are performed for incompressible channel flow at Reynolds numbers based on the friction velocity and the channel half-width of Reτ=180 and Reτ=590. Both simulations compare well with direct numerical simulation (DNS) data and show a significant improvement over results obtained with classical subgrid scale models such as the standard or the dynamic Smagorinsky model. The computational cost of ADM is lower than that of dynamic models or the velocity estimation model.

The approximate deconvolution model for large-eddy simulations of compressible flows and its application to shock-turbulent-boundary-layer interaction

A formulation of the approximate deconvolution model (ADM) for the large-eddy simulation (LES) of compressible flows in complex geometries is detailed. The model is applied to supersonic compression ramp flow where shock-turbulence interaction occurs. With the ADM approach an approximation to the unfiltered solution is obtained from the filtered solution by a series expansion involving repeated filtering. Given a sufficiently good approximation of the unfiltered solution at a time instant, the flux terms of the underlying filtered transport equations can be computed directly, avoiding the need to explicitly compute subgrid-scale closures. The effect of nonrepresented scales is modeled by a relaxation regularization involving a secondary filter operation and a dynamically estimated relaxation parameter. Results of the large-eddy simulation of the turbulent supersonic boundary layer along a compression ramp compare well with filtered DNS data. The filtered shock solution is correctly predicted by the ADM pr...

High-pass filtered eddy-viscosity models for large-eddy simulations of transitional and turbulent flow

Classical fixed-coefficient eddy-viscosity models for large-eddy simulations (LES), e. g., the Smagorinsky [Mon. Weather Rev. 93, 99 (1963)] and the structure-function model [Metais and Lesieur, J. ...

Large-eddy simulation of spatial transition in plane channel flow

Spatial large-eddy simulations (LES) of forced transition in plane incompressible channel flow are presented and compared to temporal simulations. Using the fringe method, spectral Fourier discretization is employed also in the streamwise, spatially evolving flow direction. Various subgrid-scale (SGS) models are examined including the dynamic Smagorinsky model, high-pass filtered (HPF) eddy-viscosity models and the relaxation-term model (ADM-RT). The applicability of the fringe method in conjunction with SGS models is demonstrated. Good results are obtained even at rather low LES resolution at which a coarse-grid no-model calculation is inaccurate. The most accurate prediction of transitional flow structures is obtained using the ADM-RT model. For this model, a detailed comparison between spatial and temporal simulation results is given. A clear representation of the transitional flow structures by LES up to the multi-spike stage could be established. Our results also show that the SGS models behave similarly in temporal and spatial simulations, thus allowing us to perform SGS model testing with the more straightforward and inexpensive temporal approach. The same SGS models work well without any change also in the fully developed turbulent flow.

High-Pass Filtered Eddy-Viscosity Models for LES

In this contribution we propose high-pass filtering suitable for high-pass filtered (HPF) eddy-viscosity models, e.g. the Smagorinsky or (filtered) structure-function model, and investigate their influence on the results of large-eddy simulations of laminar, transitional and turbulent flows. High-pass filtering employed to the computational quantities prior to computation of the eddy-viscosity and/or strainrate in the subgrid-scale model allows for a good prediction of transitional and turbulent flows without using any ad-hoc adaptation. Of particular importance is that the sensitivity of the results to the model coefficient is considerably reduced compared with non-HPF models. Furthermore, the proposed high-pass filters enable the computation of the structure function in the filtered or HPF structure-function model in all spatial directions even for inhomogeneous flows, removing the arbitrariness of special treatment of selected (e.g. wall-normal) directions.

The Approximate Deconvolution Model for Compressible Flows: Isotropic Turbulence and Shock-Boundary-Layer Interaction

A formulation of the approximate deconvolution model (ADM) for the large-eddy simulation of flows in complex geometries is detailed and applied to compressible turbulent flows. The paper considers two different issues. First, we study the feasibility of low-order schemes with ADM for large-eddy simulation. As test case compressible decaying isotropic turbulence is considered. Results obtained with low-order finite difference schemes and a pseudospectral scheme are compared with filtered well-resolved direct numerical simulation (DNS) data. It is found that even for low-order schemes very good results can be obtained if the cutoff wavenumber of the filter is adjusted to the modified wavenumber of the differentiation scheme. Second, we consider the application of ADM to large-eddy simulation of the turbulent supersonic boundary layer along a compression ramp, which exhibits considerable physical complexity due to the interaction of shock, separation, and turbulence in an ambient inhomogeneous shear flow. The results compare very well with filtered DNS data and the filtered shock solution is correctly predicted by the ADM procedure, demonstrating that turbulent and non-turbulent subgrid-scales are properly modeled. We found that a computationally expensive shock-capturing technique as used in the DNS was not necessary for stable integration with the LES.

Large-Eddy Simulation of Separated Flow in a Channel with Streamwise-Periodic Constrictions

Large-eddy simulations using the approximate-deconvolution subgrid-scale model of compressible flow in a channel with streamwise-periodic constrictions are performed at two Reynolds numbers of 2800 and 10,595. The goal of the study is the evaluation of this subgrid-scale model for massively separated flows. The Mach number was chosen as 0.2 to facilitate comparison with incompressible flow data. A relatively coarse structured grid and a finite-volume discretization employing a skew-symmetric fourth-order central scheme are used with a four-stage Runge-Kutta method for time integration. The results are compared to data from the literature obtained with incompressible direct numerical simulations, as well as highly resolved large-eddy simulations. Despite the chosen coarse resolution, good agreement of the statistical quantities and important flow features, such as separation and reattachment locations, is achieved. In contrast to previous works we also consider the flow properties at the straight upper wall. We introduce a new measure quantifying the time fraction of reverse flow along the wall. Furthermore, we analyze the energy density spectra of the velocity fluctuations and study the turbulence structure with Lumleys flatness parameter and realizability map. We also illustrate the vortex systems associated with the shedding and other instantaneous flow structures.

Evaluation of high-pass filtered eddy-viscosity models for large-eddy simulation of turbulent flows

Large-eddy simulations (LES) of incompressible homogeneous isotropic turbulence and turbulent channel flow are performed at moderate Reynolds numbers using high-pass filtered (HPF) eddy-viscosity models. This family of models computes the subgrid-scale (SGS) terms from a high-pass filtered velocity field using classical closure relations, e.g. the Smagorinsky or the structure–function model closure. Unlike the classical fixed-coefficient eddy-viscosity models, the HPF models are able to accurately describe the viscous sublayer of near-wall turbulence. Moreover, it has been shown recently that the HPF models are also capable of predicting transitional flows. Detailed results of energy and dissipation spectra are given for forced isotropic turbulence at microscale Reynolds number up to Re λ≈5500. For turbulent channel flow at friction Reynolds number Re τ≈590, results are presented for first- and second-order statistics as well as for the energy budget including the SGS terms. The overall performance of the HPF eddy-viscosity models is very good for both flow cases using a constant model coefficient. An empirical adaptation of the model coefficient to the cutoff wavenumber of the chosen high-pass filter is given. In contrast to classical eddy-viscosity models, the HPF models allow the prediction of backscatter effects, which are important for wall-bounded flows close to the walls.

Analysis of the SGS energy budget for deconvolution- and relaxation-based models in channel flow

The energy budget of subgrid-scale (SGS) models of deconvolution and relaxation type, e.g. the approximate deconvolution model (ADM), is analysed. Energy transfer properties of the deconvolution and the relaxation regularisation are computed individually. An alternative formulation of ADM based on one filter operation only is analysed and compared to a scale-similarity model with additional relaxation. Depending on the primary LES filter used, the model dissipation caused by the modification of the nonlinear terms drops to roughly one third of the total model dissipation, rendering the relaxation the dominant source of energy dissipation. Consequently, models based on a relaxation regularisation alone perform equally well. All models are exhibiting backscatter in the vicinity of the walls.

Relaxation-Term Models for LES of Transitional/Turbulent Flows and the Effect of Aliasing Errors

Subgrid-scale (SGS) models based on relaxation regularization are investigated for incompressible transitional and turbulent channel flow using a spectral method. The main focus is on a simple model formalism which can be used on very coarse LES grids. During the initial phase of transition, the models remain inactive as long as the flow is still well resolved on the coarse LES grid. During the late stages of transition and the following fully-turbulent phase the models provide necessary SGS dissipation. The connection of aliasing errors and SGS modelling is examined. Of particular importance is that SGS models based on relaxation regularization reduce the effects of aliasing errors, allowing to perform numerical simulations even without dealiasing and thus lowering the computational time significantly. Furthermore, the performance of the models is evaluated for different dynamic and non-dynamic model coefficients all showing good agreement with fully-resolved DNS.