Thermal lattice boltzmann simulation of diffusion/ forced convection using a double mrt model

The Lattice-Boltzmann method (LBM) is an alternative and flexible approach for computational fluid dynamics (CFD). Unlike many other direct numerical simulation (DNS) techniques, LBM is not solving the Navier-Stokes equations but is based on the kinetic theory and the discrete Boltzmann equation. LBM utilizes a Cartesian mesh and hence does not require a complex mesh derivation or a re-meshing in case of moving boundaries. Thermal LBM (TLBM) which is capable of solving thermal convection/diffusion problems relies on a set of two distribution functions, the so called double distribution function (DDF) approach; one for the fluid density and one for the internal energy. For the carried out numerical investigations a 3D TLBM framework is derived involving a multiple-relaxation-time (MRT) collision operator for both, the fluid and the temperature field which is yet not applied widely. Hydrodynamic and thermal boundary conditions are represented by interpolated bounce back schemes. The derived TLBM framework is applied to diffusion and convection-diffusion problems (e.g. forced convection) for plane and curved boundaries and is validated against analytical solutions, when available or compared to established correlations. The thermal MRT operator is further compared against an existing LBM model based on a thermal Bhatnagar-Gross-Krook (BGK) operator regarding accuracy and numerical stability. Averaged and local heat transfer coefficients are presented. The findings indicate that the double MRT framework with interpolated boundary conditions offers a highly accurate and efficient approach for the analysis of heat transfer problems especially for particle/fluid systems under detailed resolved flow

Modelling and simulation of the chondrocyte cell growth, glucose consumption and lactate production within a porous tissue scaffold inside a perfusion bioreactor

AbstractMathematical and numerical modelling of the tissue culture process in a perfusion bioreactor is able to provide insight into the fluid flow, nutrients and wastes transport, dynamics of the pH value, and the cell growth rate. Knowing the complicated interdependence of these processes is essential for optimizing the culture process for cell growth. This paper presents a resolved scale numerical simulation, which allows one not only to characterize the supply of glucose inside a porous tissue scaffold in a perfusion bioreactor, but also to assess the overall culture condition and predict the cell growth rate. The simulation uses a simplified scaffold that consists of a repeatable unit composed of multiple strands. The simulation results explore some problematic regions inside the simplified scaffold where the concentration of glucose becomes lower than the critical value for the chondrocyte cell viability and the cell growth rate becomes significantly reduced

A Ghost Fluid Approach for Thermal Lattice Boltzmann Method in Dealing with Heat Flux Boundary Condition in Thermal Problems with Complex Geometries

In this paper, the ghost fluid thermal lattice Boltzmann method is improved to properly impose the heat flux boundary condition on complex geometries [Khazaeli, R., S. Mortazavi and M. Ashrafizaadeh (2013). Application of a ghost fluid approach for a thermal lattice Boltzmann method, J. Comput. Phys. 250, 126– 140]. A double-population thermal lattice Boltzmann method is used to handle both the flow and temperature fields on a Cartesian grid and the boundary conditions are imposed using a ghost fluid method. The method is based on the decomposition of the unknown distribution functions into their equilibrium and non-equilibrium parts at every ghost point. The equilibrium parts are determined by performing an extrapolation of major quantities from the image points to the associated ghost points. The bounce-back scheme is then used to determine the non- equilibrium parts. The method benefits from some features such as easy implementation and second order accuracy. The method is applied to simulate natural convection within annuluses with different shapes and boundary conditions,. The obtained results are generally in a good agreement with those predicted by other numerical efforts