Bernardus J. Geurts

Inverse modeling for Large-Eddy simulation

Approximate higher order polynomial inversion of the top-hat filter is developed with which the turbulent stress tensor in large-eddy simulation can be consistently represented using the filtered field. Generalized (mixed) similarity models are proposed which improved the agreement with the kinetic energy transfer to small scales. These similarity models are analyzed for random periodic signals and the ensemble averaged spectra of the turbulent stress tensor and the corresponding models are compared.

Simulation techniques for spatially evolving instabilities in compressible flow over a flat plate

In this paper we present numerical techniques suitable for a direct numerical simulation in the spatial setting. We demonstrate the application to the simulation of compressible flat plate flow instabilities. We compare second and fourth order accurate spatial discretization schemes in combination with explicit multistage time stepping for the simulation of the 2D Navier-Stokes equations. We consider Mach numbers 0.5 and 4.5. In the vicinity of the outflow boundary, an efficient buffer domain treatment is introduced, which is suitable in conjunction with an explicit time integration scheme. This treatment requires only a short buffer domain to damp wave reflections at the outflow boundary. Results for the instability of Tollmien-Schlichting (T-S) waves are compared with two instability theories, linear stability theory (LST) and linear parabolized stability equations (PSE). The growth rates of T-S waves for parallel base flow at both Mach numbers compare well with LST results. Moreover, the growth rates of T-S waves for nonparallel base flow compare well with results obtained by solving the PSE at Mach number 0.5. The second order discretization scheme requires, however, considerably higher grid resolution than the fourth order method to achieve accurate results. High amplitude disturbances were also considered to activate nonlinear terms. The nonlinearity strongly affects the form of the T-S waves and the growth rate of the disturbances. The results obtained here support the use of these numerical techniques in flow simulations with increasing complexity such as flat plate flow simulations up to the turbulent regime and with separation regions in 3D. The results also encourage the use of perturbations derived from the compressible PSE as inlet perturbations for nonparallel flow.

Mixing efficiency in turbulent shear layers

The mixing efficiency in a turbulent mixing layer is quantified by monitoring the surface area of level sets of scalar fields. The Laplace transform is applied to numerically calculate integrals over arbitrary level sets using a new, locally exact quadrature method. With this method an accurate and efficient evaluation of the evolving mixing efficiency can be achieved, which allows us to quantify the increased complexity of the flow during transitional and turbulent flow. The analysis includes both direct and large-eddy simulation and can be used to assess the suitability of specific subgrid parametrizations in relation to predicting mixing efficiency. Several subgrid models are incorporated in the comparison, for example the Bardina scale similarity model, the dynamic eddy-viscosity model and the dynamic mixed model. For accurate predictions, dynamic models are favoured. It is observed that the ratio between LES filter width Δ and grid-spacing h has a considerable influence; a ratio Δ/h of four appears s...

Interacting errors in large-eddy simulation: a review of recent developments

The accuracy of large-eddy simulations is limited, among others, by the quality of the subgrid parameterisation and the numerical contamination of the smaller retained flow structures. We review the effects of discretisation and modelling errors from two different perspectives. We first show that spatial discretisation induces its own filter and compare the dynamic importance of this numerical filter to the basic large-eddy filter. The spatial discretisation modifies the large-eddy closure problem as is expressed by the difference between the discrete ‘numerical stress tensor’ and the continuous ‘turbulent stress tensor’. This difference consists of a high-pass contribution associated with the specific numerical filter. Several central differencing methods are analysed and the importance of the subgrid resolution is established. Second, we review a database approach to assess the total simulation error and its numerical and modelling contributions. The interaction between the different sources of error is shown to lead to their partial cancellation. From this analysis one may identify an ‘optimal refinement strategy’ for a given subgrid model, discretisation method and flow conditions, leading to minimal total simulation error at a given computational cost. We provide full detail for homogeneous decaying turbulence in a ‘Smagorinsky fluid’. The optimal refinement strategy is compared with the error reduction that arises from grid refinement of the dynamic eddy-viscosity model. The main trends of the optimal refinement strategy as a function of resolution and Reynolds number are found to be adequately followed by the dynamic model. This yields significant error reduction upon grid refinement although at coarse resolutions significant error levels remain. To address this deficiency, a new successive inverse polynomial interpolation procedure is proposed with which the optimal Smagorinsky constant may be efficiently approximated at a given resolution. The computational overhead of this optimisation procedure is shown to be well justified in view of the achieved reduction of the error level relative to the ‘no-model’ and dynamic model predictions.

Turbulence modification and heat transfer enhancement by inertial particles in turbulent channel flow

We present results of direct numerical simulation of turbulence modification and heat transfer in turbulent particle-laden channel flow and show an enhancement of the heat transfer and a small increase in the friction velocity when heavy inertial particles with high specific heat capacity are added to the flow. The simulations employ a coupled Eulerian-Lagrangian computational model in which the momentum and energy transfer between the discrete particles and the continuous fluid phase are fully taken into account. The effect of turbophoresis, resulting in an increased particle concentration near a solid wall due to the inhomogeneity of the wall-normal velocity fluctuations, is shown to be responsible for an increase in heat transfer. As a result of turbophoresis, the effective macroscopic transport properties in the region near the walls differ from those in the bulk of the flow. To support the turbophoresis interpretation of the enhanced heat transfer, results of simulations employing no particle-fluid coupling and simulations with two-way coupling at considerably lower specific heat, or considerably lower particle concentration are also included. The combination of these simulations allows distinguishing contributions to the Nusselt number due to mean flow, turbulent fluctuations and explicit particle effects. We observe an increase in Nusselt number by more than a factor of two for heavy inertial particles, which is the net result of a decrease in heat transfer by turbulent velocity fluctuations and a much larger increase in heat transfer stemming from the mean temperature difference between the fluid and the particles close to the walls.

Breakdown of large-scale circulation in turbulent rotating convection

Turbulent rotating convection in a cylinder is investigated both numerically and experimentally at Rayleigh number Ra=109 and Prandtl number σ=6.4. In this letter we discuss two topics: the breakdown under rotation of the domain-filling large-scale circulation (LSC) typical for confined convection, and the convective heat transfer through the fluid layer, expressed by the Nusselt number. The presence of the LSC is addressed for several rotation rates. For Rossby numbers Ro1.2 no LSC is found (the Rossby number indicates relative importance of buoyancy over rotation, hence small Ro indicates strong rotation). For larger Rossby numbers a precession of the LSC in anticyclonic direction (counter to the background rotation) is observed. It is shown that the heat transfer has a maximal value close to Ro=0.18 being about 15% larger than in the non-rotating case Ro=∞. Since the LSC is no longer present at this Rossby value we conclude that the peak heat transfer is independent of the LSC.

Dynamic inverse modeling and its testing in large-eddy simulations of the mixing layer

We propose new identities for dynamic subgrid modeling in large-eddy simulation involving an explicit filter and its inverse. Exact defiltering of a class of numerical realizations of the top-hat filter is developed. The approach is applied to large-eddy simulation of the temporal mixing layer. Smagorinsky’s model is adopted as base model and the results are compared to the standard dynamic eddy-viscosity model as well as to filtered DNS (direct numerical simulation) results. The difference between the results of the two models for the present application is found to be quite small. This is explained by performing a sensitivity analysis with respect to the dynamic coefficient, which hints towards a “self-restoring” response underlying the observed robustness of the physical predictions. Using DNS data the validity of the assumption that the model coefficients are independent of filter width is tested and found to favor the inverse modeling procedure. The computational effort of the dynamic inverse model is 15% smaller than of the standard dynamic eddy-viscosity model.

Mixing in manipulated turbulence

A numerical investigation of turbulent flow, subject to deterministic broadband forcing, is presented. Explicit forcing procedures are included that represent the simultaneous agitation of a wide spectrum of length scales, including both large scales and a band of much smaller scales. Such forcing induces a multiscale modulation of turbulent flow that is motivated by flow through complex objects and along irregular boundaries. Two types of forcing procedures are investigated; with reference to the collection of forced modes these procedures are classified as ‘constant energy’ or ‘constant-energy input rate’. It is found that a considerable modulation of the traditional energy cascading can be introduced with a specific forcing strategy. In spectral space, forcing yields strongly localized deviations from the common Kolmogorov scaling law, directly associated with the explicitly forced scales. In addition, the accumulated effect of forcing induces a significant non-local alteration of the kinetic energy including the spectrum for the large scales. Consequently, a manipulation of turbulent flow can be achieved over an extended range, well beyond the directly forced scales. Compared to flow forced in the large scales only, the energy in broadband forced turbulence is found to be transferred more effectively to smaller scales. The turbulent mixing of a passive scalar field is also investigated, in order to quantify the physical-space modifications of transport processes in multiscale forced turbulence. The surface area and wrinkling of level sets of the scalar field are monitored as measures of the influence of explicit forcing on the local and global mixing efficiency. At small Schmidt numbers, the values of surface area are mainly governed by the large-scale sweeping effect of the flow while the wrinkling is influenced mainly by the agitation of the smaller scales.

A boundary integral method for two-dimensional (non)-Newtonian drops in slow viscous flow

A boundary integral method for the simulation of the time-dependent deformation of Newtonian or non-Newtonian drops suspended in a Newtonian fluid is developed. The boundary integral formulation for Stokes flow is used and the non-Newtonian stress is treated as a source term which yields an extra integral over the domain of the drop. The implementation of the boundary conditions is facilitated by rewriting the domain integral by means of the Gauss divergence theorem. To apply the divergence theorem smoothness assumptions are made concerning the non-Newtonian stress tensor. The correctness of these assumptions in actual simulations is checked with a numerical validation procedure. The method appears mathematically correct and the numerical algorithm is second order accurate. Besides this validation we present simulation results for a Newtonian drop and a drop consisting of an Oldroyd-B fluid. The results for Newtonian and non-Newtonian drops in two dimensions indicate that the steady state deformation is quite independent of the drop-fluid. The deformation process, however, appears to be strongly dependent on the drop-fluid. For the non-Newtonian drop a mechanical model is developed to describe the time-dependent deformation of the cylinder for small capillary numbers.

Experimental and numerical investigation of turbulent convection in a rotating cylinder

The effects of an axial rotation on the turbulent convective flow because of an adverse temperature gradient in a water-filled upright cylindrical vessel are investigated. Both direct numerical simulations and experiments applying stereoscopic particle image velocimetry are performed. The focus is on the gathering of turbulence statistics that describe the effects of rotation on turbulent Rayleigh–Be nard convection. Rotation is an important addition, which is relevant in many geophysical and astrophysical flow phenomena.