Leonhard Kleiser

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-resolution simulations of particle-driven gravity currents

Abstract High-resolution simulations are presented of particle-driven gravity currents in the lock-exchange configuration. The study concentrates on dilute flows with small density differences between particle-laden and clear fluid. Moreover, particles are considered which have negligible inertia, and which are much smaller than the smallest length scales of the buoyancy-induced fluid motion. For the mathematical description of the particulate phase a Eulerian approach is employed with a transport equation for the local particle-number density. The governing equations are integrated numerically with a high-order mixed spectral/spectral-element technique. In the analysis of the results, special emphasis is placed on the sedimentation of particles and the influence of particle settling on the flow dynamics. Time-dependent sedimentation profiles at the channel floor are presented which agree closely with available experimental data. A detailed study is conducted of the balance between the various components of the energy budget of the flow, i.e. the potential and kinetic energy, and the dissipative losses. Furthermore, the simulation results, along with a modified Shields criterion, are used to show that resuspension of sediment back into the particle-driven current is unlikely to occur in the cases considered. Two-dimensional (2D) and three-dimensional (3D) computations are compared which reveal that, for the present configuration, a 2D model can predict reliably the flow development at early times. However, concerning the long-time evolution of the flow, more substantial differences exist between 2D and 3D simulations.

Direct simulation of turbulent supersonic boundary layers by an extended temporal approach

The present paper addresses the direct numerical simulation of turbulent zero-pressure-gradient boundary layers on a flat plate at Mach numbers 3, 4.5 and 6 with momentum-thickness Reynolds numbers of about 3000. Simulations are performed with an extended temporal direct numerical simulation (ETDNS) method. Assuming that the slow streamwise variation of the mean boundary layer is governed by parabolized Navier–Stokes equations, the equations solved locally in time with a temporal DNS are modified by a distributed forcing term so that the parabolized Navier–Stokes equations are recovered for the spatial average. The correct mean flow is obtained without a priori knowledge, the streamwise mean-flow evolution being approximated from its upstream history. ETDNS reduces the computational effort by up to two orders of magnitude compared to a fully spatial simulation. We present results for a constant wall temperature T w chosen to be equal to its laminar adiabatic value, which is about 2.5 T ∞ , 4.4 T ∞ and 7 T ∞ , respectively, where T ∞ is the free-stream temperature for the three Mach numbers considered. The simulations are initialized with transition-simulation data or with re-scaled turbulent data at different parameters. We find that the ETDNS results closely match experimental mean-flow data. The van Driest transformed velocity profiles follow the incompressible law of the wall with small logarithmic regions. Of particular interest is the significance of compressibility effects in a Mach number range around the limit of M ∞ ≃ 5, up to which Morkovins hypothesis is believed to be valid. The results show that pressure dilatation and dilatational dissipation correlations are small throughout the considered Mach number range. On the other hand, correlations derived from Morkovins hypothesis are not necessarily valid, as is shown for the strong Reynolds analogy.

Mixing and dissipation in particle-driven gravity currents

Results are presented from a high-resolution computational study of particle-driven gravity currents in a plane channel. The investigation was conducted in order to obtain better insight into the energy budget and the mixing behaviour of such flows. Two- and three-dimensional simulations are discussed, and the effects of different factors influencing the flow are examined in detail. Among these are the aspect ratio of the initial suspension reservoir, the settling speed of the particles, and the initial level of turbulence in the suspension. While most of the study is concerned with the lock-exchange configuration, where the initial height of the suspension layer is equal to the height of the channel, part of the analysis is also done for a deeply submerged case. Here, the suspension layer is only one-tenth of the full channel height. Concerning the energy budget, a careful analysis is undertaken of dissipative losses in the flow. Dissipative losses arising from the macroscopic fluid motion are distinguished from those due to the microscopic flow around each sedimenting particle. It is found that over a large range of settling velocities and suspension reservoir aspect ratios, sedimentation accounts for roughly half of all dissipative losses. The analysis of the mixing behaviour of the flow concentrates on the mixing between interstitial and ambient fluid, which are taken to be of identical density. The former is assumed to carry a passive contaminant, whose dispersion with time is analysed qualitatively and quantitatively by means of Lagrangian markers. The simulations show the mixing between interstitial and ambient fluid to be more intense for larger values of the particle settling velocity. Finally, the question is addressed of whether or not initial turbulence in the suspension may exert a significant effect on the flow evolution. To this end, results from three simulations with widely different levels of initial kinetic energy are compared. While the initial turbulence level strongly affects the mixing within the current, it has only a small influence on the front velocity and the overall sedimentation rate.

Energy transfer in numerically simulated wall‐bounded turbulent flows

Using velocity fields obtained in direct numerical simulations of turbulent convection and of turbulent channel flow, the energy transfer process among lateral scales of motion in these low Reynolds number flows is analyzed. In all cases the energy is transferred most effectively between scales of similar size. As a result, the subgrid‐scale energy transfer is caused almost exclusively by interactions between resolved scales and subgrid scales characterized by wave numbers not greater than twice the cutoff wave number. The scale dependence of forward and inverse energy transfers contributing to the total subgrid‐scale eddy viscosity is discussed. The local energy transfer between small scales is strongly affected by the nonlocal interactions characterized by a scale separation greater than a factor of 2 in wave number. However, the direct energy transfer between scales satisfying this condition is one order of magnitude less than the local energy transfer between scales of similar size.

The Late Stages of Transition to Turbulence in Channel Flow

The late stages of transition, from the ?-vortex stage up to turbulence, are investigated by postprocessing data from a direct numerical simulation of the complete K-type transition process in plane channel flow at a Reynolds number of 5000 (based on channel half-width and laminar centreline velocity). The deterministic roll-up of the high-shear layer that forms around the ?-vortices is examined in detail. The new vortices arising from this process are visualized by plotting three-dimensional surfaces of constant pressure. Five vortices are observed, with one of these developing into a strong hairpin-shaped vortex. Interactions between the different vortices, and between the two channel halves, are found to be important. In the very last stage of transition second-generation shear layers are observed to form and roll up into new vortices. It is postulated that at this stage a sustainable mechanism of wall-bounded turbulence exists in an elementary form. The features which are locally present include high wall shear, sublayer streaks, ejections and sweeps. Large-scale energetic vortices are found to be an important part of the mechanism by which the turbulence spreads to other spanwise positions. The generality of the findings are discussed with reference to data from simulations of H-type and mixed-type transition

Subgrid‐scale energy transfer in the near‐wall region of turbulent flows

Direct numerical simulation databases of turbulent channel and pipe flow have been used in order to assess the energy transfer between resolved and unresolved motions in large‐eddy simulations. To this end, the velocity fields are split into three parts: a statistically stationary mean flow, the resolved, and the unresolved turbulent fluctuations. The distinction between the resolved and unresolved motions is based on the application of a cutoff filter in spectral space. Within the buffer layer a backward transfer of averaged kinetic energy from subgrid to grid‐scale turbulent motions has been found to exist, which is primarily caused by subgrid‐scale stresses aligned with the mean rates of strain. Such reverse transfer generally cannot be described by the simple eddy‐viscosity‐type subgrid models usually applied in large‐eddy simulations. The use of a conditional averaging technique revealed that the reverse transfer of energy within the near‐wall flow is strongly enhanced by coherent motions, such as th...

Small particles in homogeneous turbulence: Settling velocity enhancement by two-way coupling

The gravitational settling of an initially random suspension of small solid particles in homogeneous turbulence is investigated numerically. The simulations are based on a pseudospectral method to solve the fluid equations combined with a Lagrangian point-particle model for the particulate phase (Eulerian-Lagrangian approach). The focus is on the enhancement of the mean particle settling velocity in a turbulent carrier fluid, as compared to the settling velocity of a single particle in quiescent fluid. Results are presented for both one-way coupling, when the fluid flow is not affected by the presence of the particles, and two-way coupling, when the particles exert a feedback force on the fluid. The first case serves primarily for validation purposes. In the case with two-way coupling, it is shown that the effect of the particles on the carrier fluid involves an additional increase in their mean settling velocity compared to one-way coupling. The underlying physical mechanism is analyzed, revealing that t...

Large-Eddy Simulation of Shock-Turbulence Interaction

The approximate deconvolution model (ADM) for large-eddy simulation (LES) is adapted for use with a central fourth-order finite volume (Jameson-type) scheme widely applied for aerodynamics calculations of industrial interest. With ADM, an approximation of the unfiltered solution is obtained by repeated filtering, and given a good approximation of the unfiltered solution the nonlinear terms of the filtered Navier‐Stokes equation are computed directly. The effect of scales not represented on the numerical grid is modeled by a relaxation regularization involving a secondary filter operation and a relaxation parameter. The supersonic turbulent boundary layer along a compression ramp at a freestream Mach number of M =3 and a Reynolds number (based on free-stream quantities and the mean momentum thickness at inflow) of Reθ = 1685 is computed to evaluate the ability of ADM to represent discontinuities and turbulent flow regions. It was observed that a unified modeling of discontinuities and turbulence required a local adaptation of the secondary filter used for the relaxation regularization. The LES results are compared with corresponding filtered direct-numerical-simulation (DNS) data. Very good agreement between the filtered DNS and the LES is observed for the mean, fluctuating, and averaged wall quantities.