| The laminar flow of viscoplastic fluids in eccentric annuli between two pipes has been investigated numerically. Three distinct flow conditions have been modeled, namely, inner and outer pipe is fixed, when the flow is due to imposed axial pressure gradient, inner pipe having an axial motion in the absence of any imposed pressure gradient, and, inner pipe having a rotational motion in the presence of an axial pressure gradient. Viscoplastic fluids falls under the general category of a non-Newtonian fluid characterized by a yield stress which must be exceeded before significant deformation can occur. This, along with the shear rate dependent viscosity of a non-Newtonian fluid, makes the numerical analysis of a viscoplastic fluid system complicated. The rheology of the fluid must be properly understood for successful modeling of the flow system. The shape of the annuli is arbitrary so that modeling of a partial blockage is possible. A finite difference numerical scheme employing non-orthogonal boundary fitted coordinates have been used in this study. An exponential rheological model valid for both the yielded as well as the unyielded regions of the flow is used in the computation. The computed result is validated against published analytical and experimental result whenever available. Results indicate that the flow field for a viscoplastic fluid is vastly different from that of a typical Newtonian fluid. The flow behavior index has a profound impact on the flow. The characteristic plug flow region is found to be present where applicable. The effect of axial pressure gradient, axial and rotational speed of the inner cylinder, eccentricity and blockage height have been investigated and presented herein. |
