Unstructured High-Resolution Method For Calculation Of Unsteady Flow And Heat Transfer

In nature and engineering flow problems, the unsteadiness is a basic characteristic of the problems. And the unstructured grid is an effective measure to compute flow in complex geometries. In this paper, we carry out the calculations of unsteady flow and heat transfer based on the unstructured high-resolution method.First, the energy equation and the standard k-ε turbulence model were added to an in-house high-resolution code, which was for calculation of laminar flows using unstructured finite volume method with selection of high order schemes. The procedure was validated by calculating natural convection in enclosures and turbulent flow over a heated backward facing step. For comparison, these cases were also computed by a commercial software package, the FLUENT, using the same meshes. The results obtained by the present procedure agreed well with the benchmark solutions. For the FLUENT, however, worse agreements with the benchmark solutions were obtained. These confirmed the high resolution of the numerical procedure.On the basis of the steady state program, we carried out a second-order fractional-step method for calculation of unsteady flows using cell centered unstructured grids. The momentum interpolation method was applied to eliminate the spurious pressure oscillations which might occur in non-staggered grid system. For temporal discretization, the Crank-Nicolson’s scheme was applied to both convection and diffusion terms.On the other hand, the QUICK scheme was employed to evaluate the convection flux and the central-difference was used to calculate the diffusion. The procedure was validated by calculating the decaying-vortex problem, the flow over circular cylinder, an oscillatory lid driven cavity flow and flow after a blunt body. The results well agreed with the benchmark numerical solutions or experimental data. The temporal convergence index showed that the resolution for the calculated unsteady results was higher than second-order.The paper presents a high-resolution method for calculation of unsteady flow and heat transfer in complex area implemented on unstructured grid. It provides the foundation for high precision calculation of unsteady flow and heat transfer, further development of the high accuracy algorithm of unstructured grid.