Title: Pressure curves for compressible flows with slip through asymmetric local constrictions

Authors: Salahaldeen Rabba; Katrin Rohlf

Addresses: Department of Electrical and Computer Engineering, Ryerson University, Toronto, ON, Canada ' Department of Mathematics, Ryerson University, Toronto, ON, Canada

Abstract: A second-order nonlinear differential equation is derived for the pressure of a compressible flow with slip at the wall through a constricted cylinder. The ideal gas equation of state is used, and the Karman-Pohlhausen method is utilised to derive the pressure differential equation from the Navier-Stokes equations of motion for a Newtonian viscous fluid. The solution for pressure is determined numerically and assessed in various flow geometries. This work is an extension of existing assessments in that nonlinear terms are kept in the differential equation for pressure, as well as second-order derivative terms. Additionally, wall slip and compressibility are incorporated in the equations, as well as geometries that are asymmetric with respect to the location of maximum constriction.

Keywords: pressure; gradient; compressible; stenosis; Navier-Stokes; slip; Karman-Pohlhausen; asymmetric; nonlinear; constriction.

DOI: 10.1504/IJANS.2018.097324

International Journal of Applied Nonlinear Science, 2018 Vol.3 No.1, pp.21 - 40

Received: 16 Nov 2016
Accepted: 05 Mar 2017
Published online: 15 Jan 2019 *

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