Grid Convergence Property of Three-Dimensional Measurement-Integrated Simulation for Unsteady Flow behind a Square Cylinder with Karman Vortex Street

The purpose of this study was to clarify grid convergence property of three-dimensional measurement-integrated (3D-MI) simulation for a flow behind a square cylinder with Karman vortex street. Measurement-integrated (MI) simulation is a kind of the observer in the dynamical system theory by using CFD scheme as a mathematical model of the system. In a former study, two-dimensional MI (2D-MI) simulation with a coarse grid system showed a fairly good result in comparison with a 2D ordinary (2D-O) simulation, but the results were degraded with grid refinement. In this study, 3D-MI simulation and three-dimensional ordinary (3D-O) simulation were performed with three grid systems of different grid resolutions, and their grid convergence properties were compared. As a result, all 3D-MI simulations reproduced the vortex shedding frequency identical to that of the experiment, and the flow fields obtained were very close, within 5% difference between the results, while the results of the 3D-O simulations showed variation of the solution under convergence. It is shown that the grid convergence property of 3D-MI simulation is monotonic and better than that of 3D-O simulation, whereas those of 2D-O and 2D-MI simulations for streamwise velocity fluctuation are divergent. The solution of 3D-MI simulation with a relatively coarse grid system properly reproduces the basic three-dimensional structure of the wake flow as well as the drag and lift coefficients.

基于STAR-CCM+的船体周围流体流动数值分析及验证结果

In this paper,numerical analyses of fluid flow around the ship hulls such as Series 60,the Kriso Container Ship(KCS),and catamaran advancing in calm water,are presented.A commercial computational fluid dynamic(CFD)code,STAR-CCM+is used to analyze total resistance,sinkage,trim,wave profile,and wave pattern for a range of Froude numbers.The governing RANS equations of fluid flow are discretized using the finite volume method(FVM),and the pressure-velocity coupling equations are solved using the SIMPLE(semi-implicit method for pressure linked equations)algorithm.Volume of fluid(VOF)method is employed to capture the interface between air and water phases.A fine discretization is performed in between these two phases to get a higher mesh resolution.The fluid-structure interaction(FSI)is modeled with the dynamic fluid-body interaction(DFBI)module within the STAR-CCM+.The numerical results are verified using the results available in the literatures.Grid convergence studies are also carried out to determine the dependence of results on the grid quality.In comparison to previous findings,the current CFD analysis shows the satisfactory results.

Numerical study on ship-generated unsteady waves based on a Cartesian-grid method

The added resistance of a ship in waves can be related to ship-generated unsteady waves.In the present study,the unsteady wave-pattern analysis is applied to calculate the added resistance in waves for two modified Wigley models using a Cartesian-grid method.In the present numerical method,a first-order fractional-step method is applied to the velocity-pressure coupling in the fluid domain,and one of volume-of-fluid(VOF)methods is adopted to capture the fluid interface.A ship is embedded in a Cartesian grid,and the volume fraction of the ship inside the grid is calculated by identifying whether each grid is occupied by liquid,gas,and solid body.The sensitivity to the location of measuring position of unsteady waves as well as the number of solution grids is examined.The added resistance computed by direct pressure integration and wave pattern analysis is compared with experimental data.In addition,nonlinear characteristics of the added resistance in waves are investigated by detailed analyses of unsteady flow field and resulting wave pattern.

Accuracy analysis of gradient reconstruction on isotropic unstructured meshes and its effects on inviscid flow simulation

The accuracy of gradient reconstruction methods on unstructured meshes is analyzed both mathematically and numerically.Mathematical derivations reveal that,for gradient reconstruction based on the Green-Gauss theorem(the GG methods),if the summation of first-and-lower-order terms does not counterbalance in the discretized integral process,which rarely occurs,second-order accurate approximation of face midpoint value is necessary to produce at least first-order accurate gradient.However,gradient reconstruction based on the least-squares approach(the LSQ methods)is at least first-order on arbitrary unstructured grids.Verifications are performed on typical isotropic grid stencils by analyzing the relationship between the discretization error of gradient reconstruction and the discretization error of the face midpoint value approximation of a given analytic function.Meanwhile,the numerical accuracy of gradient reconstruction methods is examined with grid convergence study on typical isotropic grids.Results verify the phenomenon of accuracy degradation for the GG methods when the face midpoint value condition is not satisfied.The LSQ methods are proved to be at least first-order on all tested isotropic grids.To study gradient accuracy effects on inviscid flow simulation,solution errors are quantified using the Method of Manufactured Solutions(MMS)which was validated before adoption by comparing with an exact solution case,i.e.,the 2-dimensional(2D)inviscid isentropic vortex.Numerical results demonstrate that the order of accuracy(OOA)of gradient reconstruction is crucial in determining the OOA of numerical solutions.Solution accuracy deteriorates seriously if gradient reconstruction does not reach first-order.