Numerical prediction of separated flows

Abstract

Upwind and central difference schemes for laminar and turbulent flows over a step in a two-dimensional channel are compared with each other and with experiment. Vorticity u and stream function (I are used as dependent variables and it is shown that an upwind difference method can give predictions which agree with experiment for high Reynolds number flows. The numerical implementation of the boundary conditions is found critically to determine the solutions obtained. Explicit prescription of $ and w at the inlet leads to incorrect values of the inlet velocity component perpendicular to the flow and a solution that does not agree with experiment. Experimental evidence is not available at low Reynolds numbers, but it is found that upwind differences give recirculation zones 8 per cent shorter and 8 per cent less intense than the more conventional conditionally stable central difference method.The distribution of the false diffusion effect in the upwind scheme is considered. and it is shown by use of a simple example that previous statements as to possible minimization of this effect are not generally true.The difficulty of determining the pressure distribution from the vorticity and stream function model is analysed and illustrated.Further, turbulent separated flows are seen to contain regions where two-dimensional time-dependent flow does not exist, and conventional theories do not give good results. + Now at Admiralty Marine Technology Establishment, Teddington, Middx., U.K.

Split, Characteristic Based Semi-Implicit Algorithm for Laminar/Turbulent Incompressible Flows

“…A general observation by earlier investigators is that while oscillation free results could be obtained with upwinding for laminar flow problems, for turbulent predictions, upwinding could lead to an underprediction of such quantities as turbulent kinetic energy and reattachment lengths. 20 We find that this assertion is not generally true and that the present algorithm yields good results also in the turbulent regime. The problems dealt with in the present work to address the above issues include laminar flow over a backward facing step, laminar flow in a lid-driven cavity and turbulent flow over a backward facing step.…”

Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

“…An example of the type of mesh used to solve the equations is shown in Figure 5(b). In Figure 6, the horizontal velocity, u, shows the comparison with the experimental results of Briard [30] and Atkins [31]. Figure 7 shows the comparison of the turbulence kinetic energy, k, from the same experimental results.…”

“…Thus, u i can be defined as a vector from the ith-dimensional Krylo6 subspace, denoted [30] and Atkins [31] for the backward facing step at Re= 3025.…”

Computational fluid flow in two dimensions using simple T4/C3 element

“…It should be pointed out that this formulation did not use the upwinding technique to suppress the wiggles, while the local Reynolds number (Re= (u c × l c )/w, in which u c and l c are local characteristic velocity and length respectively) was increased. Convergence is defined by the specification that the maximum relative error is less than 0.01 and this criterion is acceptable when numerical results are compared with experimental data or other simulations [9][10][11][12][13][14].…”