Weakly compressible flow through a cylinder with pressure-dependent viscosity and Navier-slip at the wall

作者：Regmi L P; Rohlf K^*

来源：European Journal of Mechanics - B: Fluids , 2016, 60: 13-23.

DOI：10.1016/j.euromechflu.2016.07.004

• Poiseuille flow
• Compressible flow
• Pressure-dependent viscosity
• Viscosity density parameter
• Navier-slip
• Perturbation methods

A perturbation solution is derived for weakly compressible force-driven flow through a cylinder of fixed cross-section, with pressure-dependent viscosity and Navier-slip at the wall. The compressibility number is used as the perturbation parameter and a solution is derived up to second order. The perturbation solution is used to assess changes in flow for different Reynolds numbers, Froude numbers, aspect ratios, compressibilities, pressure-dependent viscosities and slip values. The viscosity pressure dependence is controlled by compressibility and by a viscosity density parameter. The following results are found: the viscosity density parameter appears only at second-order for axial velocity, density and average volumetric flow rate, while at first order for pressure, average pressure drop and average Darcy friction factor; the volumetric flow rate decreases with increasing compressibility if forcing is small enough, increases with slip, and decreases with viscosity density parameter; the average Darcy friction factor and average pressure drop can increase with increasing compressibility if the viscosity density parameter is large enough. Although these results are as expected, the key contribution of this paper is the derivation of analytical expressions for the flow that incorporate the pressure dependence effects.

• 出版日期2016-12