Johannes G.M. Kuerten

Can turbophoresis be predicted by large-eddy simulation?

Direct numerical simulation (DNS) and large-eddy simulation (LES) of particle-laden turbulent channel flow, in which the particles experience a drag force, are performed. In this flow turbophoresis leads to an accumulation of particles near the walls. It is shown that the turbophoresis in LES is reduced, in case the subgrid effects in the particle equations of motion are ignored. To alleviate this problem an inverse filtering model is proposed and incorporated into the particle equations. The model is shown to enhance the turbophoresis in actual LES, such that a good agreement with the DNS prediction is obtained.

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.

Comparison of direct numerical simulation databases of turbulent channel flow at Re τ = 180

Direct numerical simulation (DNS) databases are compared to assess the accuracy and reproducibility of standard and non-standard turbulence statistics of incompressible plane channel flow at Re τ = 180. Two fundamentally different DNS codes are shown to produce maximum relative deviations below 0.2% for the mean flow, below 1% for the root-mean-square velocity and pressure fluctuations, and below 2% for the three components of the turbulent dissipation. Relatively fine grids and long statistical averaging times are required. An analysis of dissipation spectra demonstrates that the enhanced resolution is necessary for an accurate representation of the smallest physical scales in the turbulent dissipation. The results are related to the physics of turbulent channel flow in several ways. First, the reproducibility supports the hitherto unproven theoretical hypothesis that the statistically stationary state of turbulent channel flow is unique. Second, the peaks of dissipation spectra provide information on length scales of the small-scale turbulence. Third, the computed means and fluctuations of the convective, pressure, and viscous terms in the momentum equation show the importance of the different forces in the momentum equation relative to each other. The Galilean transformation that leads to minimum peak fluctuation of the convective term is determined. Fourth, an analysis of higher-order statistics is performed. The skewness of the longitudinal derivative of the streamwise velocity is stronger than expected (−1.5 at

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

y^{+}

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

=30). This skewness and also the strong near-wall intermittency of the normal velocity are related to coherent structures.

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

Ideal stochastic forcing for the motion of particles in large-eddy simulation extracted from direct numerical simulation of turbulent channel flow

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.

Statistics of spatial derivatives of velocity and pressure in turbulent channel 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.

Modeling the evaporation of sessile multi-component droplets

The motion of small particles in turbulent conditions is influenced by the entire range of length- and time-scales of the flow.At highReynolds numbers this range of scales is too broad for direct numerical simulation (DNS). Such flows can only be approached using large-eddy simulation (LES), which requires the introduction of a sub-filter model for the momentum dynamics. Likewise, for the particle motion the effect of sub-filter scales needs to be reconstructed approximately, as there is no explicit access to turbulent sub-filter scales. To recover the dynamic consequences of the unresolved scales, partial reconstruction through approximate deconvolution of the LES-filter is combined with explicit stochastic forcing in the equations of motion of the particles. We analyze DNS of high-Reynolds turbulent channel flow to a priori extract the ideal forcing that should be added to retain correct statistical properties of the dispersed particle phase in LES. The probability density function of the velocity differences that need to be included in the particle equations and their temporal correlation display a striking and simple structure with little dependence on Reynolds number and particle inertia, provided the differences are normalized by their RMS, and the correlations expressed in wall units. This is key to the development of a general “stand-alone” stochastic forcing for inertial particles in LES.

Low-Reynolds-number flow over partially covered cavities

Statistical profiles of the first- and second-order spatial derivatives of velocity and pressure are reported for turbulent channel flow at Re τ = 590. The statistics were extracted from a high-resolution direct numerical simulation. To quantify the anisotropic behavior of fine-scale structures, the variances of the derivatives are compared with the theoretical values for isotropic turbulence. It is shown that appropriate combinations of first- and second-order velocity derivatives lead to (directional) viscous length scales without explicit occurrence of the viscosity in the definitions. To quantify the non-Gaussian and intermittent behavior of fine-scale structures, higher-order moments and probability density functions of spatial derivatives are reported. Absolute skewnesses and flatnesses of several spatial derivatives display high peaks in the near wall region. In the logarithmic and central regions of the channel flow, all first-order derivatives appear to be significantly more intermittent than in isotropic turbulence at the same Taylor Reynolds number. Since the nine variances of first-order velocity derivatives are the distinct elements of the turbulence dissipation, the budgets of these nine variances are shown, together with the budget of the turbulence dissipation. The comparison of the budgets in the near-wall region indicates that the normal derivative of the fluctuating streamwise velocity (∂u ′/∂y) plays a more important role than other components of the fluctuating velocity gradient. The small-scale generation term formed by triple correlations of fluctuations of first-order velocity derivatives is analyzed. A typical mechanism of small-scale generation near the wall (around y + = 1), the intensification of positive ∂u ′/∂y by local strain fluctuation (compression in normal and stretching in spanwise direction), is illustrated and discussed.