Thermal Convection in a Tilted Rectangular Cell with Aspect Ratio 0.5

Thermal convection in a three-dimensional tilted rectangular cell with aspect ratio 0.5 is studied using direct nu- merical simulations within both Oberbeck-Boussinesq （OB） approximation and strong non-Oberbeck-Boussinesq （NOB） effects. The considered Rayleigh numbers Ra range from 105 to 107, the working fluid is air at 30OK, and the corresponding Prandtl number Pr is 0.71. Within the OB approximation, it is found that there exist multiple states for Ra = 105 and hysteresis for Ra = 106. For a relatively small tilt angle/3, the large-scale circulation can either orient along one of the the vertical diagonal planes （denoted by Ma mode） or orient parallel to the front wall （denoted by Mp mode）. Which of the two modes transports heat more efficiently is not definitive, and it depends on the Rayleigh number Ra. For/Ta = 107 and β = 0°, the time-averaged flow field contains four rolls in the upper half and lower half of the cell, respectively, Md and Mp modes only developing in tilted cells. By investigating NOB effects in tilted convection for fixed/Ta = 106, it is found that the NOB effects on the Nusselt number Nu, the Reynolds number Re and the central temperature Tc for different β ranges are different. NOB effects can either increase or decrease Nu, Re and Tc when β is varied.

Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile

Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis.A high order spectral element method with the matrix-free pseudo-arclength technique is used for the steady-state solution and numerical continuation.The complex flow patterns beyond the symmetry-breaking at Re≈320 are presented by a bifurcation diagram for Re<2500.The results of stable symmetric and asymmetric solutions are consistent with those reported in literature,and a new unstable asymmetric branch is obtained besides the stable branches.A novel hysteresis phenomenon is observed in the range of 2208<Re<2262,where two pairs of stable and two pairs of unstable asymmetric steady solutions beyond the stable symmetric state coexist.The vortices near the sidewall appear when the Reynolds number increases,which correspond to the bifurcation of topology structure,but not the bifurcation of Navier-Stokes equations.The hysteresis is proposed to be the result of the combined mechanisms of the competition and coalescence of secondary vortices.

Heat transfer and plume statistics in turbulent thermal convection with sparse fractal roughness

Rough-surface Rayleigh-Benard convection is investigated using direct numerical simulations in two-dimensional convection cells with aspect ratioГ=2.Three types of fractal roughness elements,which are marked as nl,n2 and n3,are constructed based on the Koch curve and sparsely mounted on both the plates,where n denotes the level of the roughness.The considered Rayleigh numbers Ra range from 10^(7)to 10^(11)with Prandtl number Pr=1.Two regimes are identified for cases nl,n2.In Regime I,the scaling exponentsβin the effective Nusselt number Nu vs Ra scaling Nu~Ra^(β)reach up to about 0.4.However,when Ra is larger than a critical value Ra_(c),the flow enters RegimeⅡ,with p saturating back to a value close to the smooth-wall case(0.3).Rac is found to increase with increasing n,and for case n3,only Regime I is identified in the studied Ra range.The extension of Regime I in case n3 is due to the fact that at high Ra,the smallest roughness elements can play a role to disrupt the thermal boundary layers.The thermal dissipation rate is studied and it is found that the increasedβin Regime I is related with enhanced thermal dissipation rate in the bulk.An interesting finding is that no clear convection roll structures can be identified for the rough cases,which is different from the smooth case where well-organized convection rolls can be found.This difference is further quantified by the detailed analysis of the plume statistics,and it is found that the horizontal profiles of plume density and velocity are relatively flattened due to the absence of clear convection rolls.

Accelerating CFD simulation with high order finite difference method on curvilinear coordinates for modern GPU clusters

A high fidelity flow simulation for complex geometries for high Reynolds number(Re)flow is still very challenging,requiring a more powerful HPC system.However,the development of HPC with traditional CPU architecture suffers bottlenecks due to its high power consumption and technical difficulties.Heterogeneous architecture computation is raised to be a promising solution to the challenges of HPC development.GPU accelerating technology has been utilized in low order scheme CFD solvers on the structured grid and high order scheme solvers on unstructured meshes.The high-order finite difference methods on structured grids possess many advantages,e.g.,high efficiency,robustness,and low storage.However,the strong dependence among points for a high-order finite difference scheme still limits its application on the GPU platform.In the present work,we propose a set of hardware-aware technology to optimize data transfer efficiency between CPU and GPU,as well as communication efficiency among GPUs.An in-house multi-block structured CFD solver with high order finite difference methods on curvilinear coordinates is ported onto the GPU platform and obtains satisfying performance with a speedup maximum of around 2000x over a single CPU core.This work provides an efficient solution to apply GPU computing in CFD simulation with specific high order finite difference methods on current GPU heterogeneous computers.The test shows that significant accelerating effects can be achieved for different GPUs.