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Register a new userOn a Simple and Effective Thermal Open Boundary Condition for Convective Heat Transfer Problems
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We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary will not cause an ``energy-like temperature functional to increase over time, irrespective of the state of flow on the open boundary. It is effective in coping with thermal open boundaries even in flow regimes where strong vortices or backflows are prevalent on such boundaries, and it is straightforward to implement. Extensive numerical simulations are presented to demonstrate the stability and effectiveness of our method for heat transfer problems with strong vortices and backflows occurring on the open boundaries. Simulation results are compared with previous works to demonstrate the accuracy of the presented method.
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A conjugate heat transfer (CHT) immersed boundary (IB and CHTIB) method is developed for use with laminar and turbulent flows with low to moderate Reynolds numbers. The method is validated with the canonical flow of two co-annular rotating cylinders at $Re=50$ which shows second order accuracy of the $L_{2}$ and $L_{infty}$ error norms of the temperature field over a wide rage of solid to fluid thermal conductivities, $kappa_{s}/kappa_{f} = left(9-100right)$. To evaluate the CHTIBM with turbulent flow a fully developed, heated, turbulent channel $left(Re_{u_{tau}}=150text{ and } kappa_{s}/kappa_{f}=4 right)$ is used which shows near perfect correlation to previous direct numerical simulation (DNS) results. The CHTIB method is paired with a momentum IB method (IBM), both of which use a level set field to define the wetted boundaries of the fluid/solid interfaces and are applied to the flow solver implicitly with rescaling of the difference operators of the finite volume (FV) method (FVM).
We numerically study the Rayleigh-Benard (RB) convection in two-dimensional model emulsions confined between two parallel walls at fixed temperatures. The systems under study are heterogeneous, with finite-size droplets dispersed in a continuous phase. The droplet concentration is chosen to explore the convective heat transfer of both Newtonian (low droplet concentration) and non-Newtonian (high droplet concentration) emulsions, the latter exhibiting shear-thinning rheology, with a noticeable increase of viscosity at low shear rates. It is well known that the transition to convection of a homogeneous Newtonian system is accompanied by the onset of steady flow and time-independent heat flux; in marked contrast, the heterogeneity of emulsions brings in an additional and previously unexplored phenomenology. As a matter of fact, when the droplet concentration increases, we observe that the heat transfer process is mediated by a non-steady flow, with neat heat-flux fluctuations, obeying a non-Gaussian statistics. The observed findings are ascribed to the emergence of space correlations among distant droplets, which we highlight via direct measurements of the droplets displacement and the characterisation of the associated correlation functions.
We present results of interface-resolved simulations of heat transfer in suspensions of finite-size neutrally-buoyant spherical particles for solid volume fractions up to 35% and bulk Reynolds numbers from 500 to 5600. An Immersed Boundary-Volume of Fluid method is used to solve the energy equation in the fluid and solid phase. We relate the heat transfer to the regimes of particle motion previously identified, i.e. a viscous regime at low volume fractions and low Reynolds number, particle-laden turbulence at high Reynolds and moderate volume fraction and particulate regime at high volume fractions. We show that in the viscous dominated regime, the heat transfer is mainly due to thermal diffusion with enhancement due to the particle-induced fluctuations. In the turbulent-like regime, we observe the largest enhancement of the global heat transfer, dominated by the turbulent heat flux. In the particulate shear-thickening regime, however, the heat transfer enhancement decreases as mixing is quenched by the particle migration towards the channel core. As a result, a compact loosely-packed core region forms and the contribution of thermal diffusion to the total heat transfer becomes significant once again. The global heat transfer becomes, in these flows at volume fractions larger than 25%, lower than in single-phase turbulence.
Lattice Boltzmann Method(LBM) has achieved considerable success on simulating complex flows. However, how to impose correct boundary conditions on the fluid-solid interface with complex geometries is still an open question. Here we proposed a velocity interpolation based bounce-back scheme where the ideas of interpolated bounce-back and non-equilibrium extrapolation are combined. The proposed scheme is validated by several well-defined benchmark cases. It is shown that the proposed scheme offers a better accuracy at high Reynolds number and less dependency on solids positions which may crucial in many engineering and science applications.
We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function approach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal convection in side-heated convection cell, which is heated from one vertical side and cooled from the other vertical side; while the other is turbulent thermal convection in Rayleigh-Benard convection cell, which is heated from the bottom and cooled from the top. In side-heated convection cell, steady results of hydrodynamic quantities and Nusselt numbers are presented at Rayleigh numbers of $10^6$ and $10^7$, and Prandtl number of 0.71, where the mesh sizes are up to $257^3$; in Rayleigh-Benard convection cell, statistical averaged results of Reynolds and Nusselt numbers, as well as kinetic and thermal energy dissipation rates are presented at Rayleigh numbers of $10^6$, $3times 10^6$, and $10^7$, and Prandtl numbers of 0.7 and 7, where the nodes within thermal boundary layer are around 8. Compared with existing benchmark data obtained by other methods, the present LB model can give consistent results.
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