Shyam S. Chikatamarla

Lattice Boltzmann method for direct numerical simulation of turbulent flows

We present three-dimensional direct numerical simulations (DNS) of the Kida vortex flow, a prototypical turbulent flow, using a novel high-order lattice Boltzmann (LB) model. Extensive comparisons of various global and local statistical quantities obtained with an incompressible-flow spectral element solver are reported. It is demonstrated that the LB method is a promising alternative for DNS as it quantitatively captures all the computed statistics of fluid turbulence.

ENTROPIC LATTICE BOLTZMANN SIMULATION OF THE FLOW PAST SQUARE CYLINDER

Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier–Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena at the kinetic level might provide an efficient tool for large scale simulations. Indeed, a particular variant of this approach, known as the entropic lattice Boltzmann method (ELBM), has shown that an efficient coarse-grained simulation of decaying turbulence is possible using these approaches. The present work investigates the efficiency of the entropic lattice Boltzmann in describing flows of engineering interest. In order to do so, we have chosen the flow past a square cylinder, which is a simple model of such flows. We will show that ELBM can quantitatively capture the variation of vortex shedding frequency as a function of Reynolds number in the low as well as the high Reynolds number regime, without any need for explicit sub-grid scale modeling. This extends the previous studies for this set-up, where experimental behavior ranging from Re~O(10) to Re≤1000 was predicted by a single simulation algorithm.1–5

Entropic multirelaxation lattice Boltzmann models for turbulent flows.

We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014)] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows.

Entropic lattice Boltzmann method for simulation of thermal flows

A new thermal entropic lattice Boltzmann model on the standard two-dimensional nine-velocity lattice is introduced for simulation of weakly compressible flows. The new model covers a wider range of flows than the standard isothermal model on the same lattice, and is computationally efficient and stable.

Simulation of binary droplet collisions with the entropic lattice Boltzmann method

The recently introduced entropic lattice Boltzmann method (ELBM) for multiphase flows is extended here to simulation of droplet collisions. Thermodynamically consistent, non-linearly stable ELBM together with a novel polynomial equation of state is proposed for simulation large Weber and Reynolds number collisions of two droplets. Extensive numerical investigations show that ELBM is capable of accurately capturing the dynamics and complexity of droplet collision. Different types of the collision outcomes such as coalescence, reflexive separation, and stretching separation are identified. Partition of the parameter plane is compared to the experiments and excellent agreement is observed. Moreover, the evolution of the shape of a stable lamella film is quantitatively compared with experimental results. The end pinching and the capillary-wave instability are shown to be the main mechanisms behind formation of satellite droplets for near head-on and off-center collisions with high impact parameter, respectively. It is shown that the number of satellite drops increases with increasing Weber number, as predicted by experiments. Also, it is demonstrated that the rotational motion due to angular momentum and elongation of the merged droplet play essential roles in formation of satellite droplets in off-center collisions with an intermediate impact parameter.

Grad's approximation for moving and stationary walls in entropic lattice Boltzmann simulations

We introduce a new generalized wall boundary condition for the entropic lattice Boltzmann method (ELBM) that is capable of handling complex flow geometries including moving walls. The Grads ten moments approximation is employed to approximate the missing populations at the boundary nodes. The new boundary condition significantly improves accuracy, stability and sub-grid features of LBM and in particular of its entropic variant, ELBM. The proposed boundary condition is tested for a range of flows in two dimensions, including planar channel flow, Couette flow, flow past a circular cylinder and sedimenting circular particles. Further simulations involving complex geometries such as flapping wing and transversely oscillating cylinder demonstrate superior stability and accuracy of the new wall boundary condition.

Conjugate heat transfer with the entropic lattice Boltzmann method.

A conjugate heat-transfer model is presented based on the two-population entropic lattice Boltzmann method. The present approach relies on the extension of Grads boundary conditions to the two-population model for thermal flows, as well as on the appropriate exact conjugate heat-transfer condition imposed at the fluid-solid interface. The simplicity and efficiency of the lattice Boltzmann method (LBM), and in particular of the entropic multirelaxation LBM, are retained in the present approach, thus enabling simulations of turbulent high Reynolds number flows and complex wall boundaries. The model is validated by means of two-dimensional parametric studies of various setups, including pure solid conduction, conjugate heat transfer with a backward-facing step flow, and conjugate heat transfer with the flow past a circular heated cylinder. Further validations are performed in three dimensions for the case of a turbulent flow around a heated mounted cube.

Drops bouncing off macro-textured superhydrophobic surfaces

Recent experiments with droplets impacting a macro-textured superhydrophobic surfaces revealed new regimes of bouncing with a remarkable reduction of the contact time. We present here a comprehensive numerical study that reveals the physics behind these new bouncing regimes and quantify the role played by various external and internal forces that effect the dynamics of a drop impacting a complex surface. For the first time, three-dimensional simulations involving macro-textured surfaces are performed. Aside from demonstrating that simulations reproduce experiments in a quantitative manner, the study is focused on analyzing the flow situations beyond current experiments. We show that the experimentally observed reduction of contact time extends to higher Weber numbers, and analyze the role played by the texture density. Moreover, we report a non-linear behavior of the contact time with the increase of the Weber number for application relevant imperfectly coated textures, and also study the impact on tilted surfaces in a wide range of Weber numbers. Finally, we present novel energy analysis techniques that elaborate and quantify the interplay between the kinetic and surface energy, and the role played by the dissipation for various Weber numbers.

Grid refinement for entropic lattice Boltzmann models

We propose a multidomain grid refinement technique with extensions to entropic incompressible, thermal, and compressible lattice Boltzmann models. Its validity and accuracy are assessed by comparison to available direct numerical simulation and experiment for the simulation of isothermal, thermal, and viscous supersonic flow. In particular, we investigate the advantages of grid refinement for the setups of turbulent channel flow, flow past a sphere, Rayleigh-Bénard convection, as well as the supersonic flow around an airfoil. Special attention is paid to analyzing the adaptive features of entropic lattice Boltzmann models for multigrid simulations.

Lattice Kinetic Theory in a Comoving Galilean Reference Frame

We prove that the fully discrete lattice Boltzmann method is invariant with respect to Galilean transformation. Based on this finding, a novel class of shifted lattices is proposed which dramatically increases the operating range of lattice Boltzmann simulations, in particular, for gas dynamics applications. A simulation of vortex-shock interaction is used to demonstrate the accuracy and efficiency of the proposed lattices. With one single algorithm it is now possible to simulate a broad range of applications, from low Mach number flows to transonic and supersonic flow regimes.