Simulation of Heat and Fluid Flow of a Highly Viscoelastic Fluid, Using a Spectral Method

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Steady-state laminar non-Newtonian fluid flows past an elliptic cylinder or past an ellipsoid of revolution and natural convectin f non-Newtonian fluid filled in the half of an elliptic cylinder are analyzed numericaly to clarify the highly viscoelastic behavior of plymer solutions. A second order fluid model is adopted as a constitutive equation ; in a two-dimensonal flow case the equations of motion lead to a similar, but slightly modified, equation to the vorticity transport equation for an incompressible Newtonian fluid, whereas in a three-dimensional case the situation is different from the two-dimensional case, being supplemented with the stress components. The system f equations in an unsteady form can be split into Fourier components, using Fourier components of a stream function and vorticity in a boundary-fitted conformal coordinate sstem. Then each component is discretized in a finite difference method for doubly-exponential grid spacing in time and space ; the resulting equations can be integrated with respect to time to get a steady-state solution. As a rsult, a large increase of a drag force and a large variation of streamlines due to fluid viscoelastcity is found at moderae Reynolds numbers of Grashf numbers for a variety of shapes.