Numerical Simulation Of Two-dimensional Rotating Flow In Square Cavity Based On Spin Model Of Turbulence

Two-dimensional numerical simulation based on the spin model of turbulence iscarried out in this paper for the incompressible fluid flow in square cavity, andcompared with that of classical theory—the Navier-Stokes (N-S) equations.According to the N-S equations, the inner fluid just rotates as a rigid body with therotating square cavity. But the spin model of turbulence predicts such a flow hasnontrivial property and instability.Herein we deduce the source item of complementary acceleration and the tinyspin source item in the rotating frame bases, and obtain the governing equations forall field components. Their general form is obtained after non-dimensional treatmentof the governing equations. Meanwhile we get the non-dimensional parameterscontrolling this flow. The discrete representation of the general form is obtained atstaggered grid with the Finite Volume Method. We calculate them using theSIMPLEC method, which is a revision of the original SIMPLE method. The discreteschemes of convective term are dealt with deferred correction method of quadraticupwind interpolation of convective kinematics (QUICK). We solve it by thetwo-dimensional TDMA iteration process and deal with boundary condition by themethod of Block finally.The program used in our simulation is based on the FAST-2D program, andaltered on the need of our governing equations. The cases we calculate are as follows:Case 1 is the case of Navier-Stokes (N-S) equations that the convergence to theconvergence to the rotating of rigid body no matter how its angular velocity andviscosity change.Case 2 is of flow with invariable viscosity and the change in Reynolds number.Case 3 is of flow with invariable angular velocity and the change in Reynoldsnumber.Case 4 is of flow with invariable Reynolds number and the change in angularvelocity.By analyzing the calculated results, we can obtain the following conclusions. According to the spin model, the cohesion of fluid is not so strong to make the fluidrotate as a rigid body with the solid boundary. The rotating boundary must inducemicroscale dissipative eddy in fluid. Such eddy evolves unsteady and organizestopological defects (vortex intensity) chequered with positive and negative near thesolid wall. These orientation singularities in fluid are sensitive to velocity disturbancewhich is ubiquitous in real flow, and stimulates the amplification of disturbance tolarge scale vortex motion. However, it needs experimental evidence to validatewhether the phenomenon is in good agreement with real flow.