Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

Abstract

The flow of a compressible fluid with slip through a cylinder with an asymmetric local constriction has been considered both numerically, as well as analytically. For the numerical work, a particle-based method whose dynamics is governed by the multiparticle collision (MPC) rule has been used together with a generalized boundary condition that allows for slip at the wall. Since it is well known that an MPC system corresponds to an ideal gas and behaves like a compressible, viscous flow on average, an approximate analytical solution has been derived from the compressible Navier-Stokes equations of motion coupled to an ideal gas equation of state using the Karman-Pohlhausen method. The constriction is assumed to have a polynomial form, and the location of maximum constriction is varied throughout the constricted portion of the cylinder. Results for centerline densities and centerline velocities have been compared for various Reynolds numbers, Mach numbers, wall slip values and flow geometries.

Modelling Compressible Blood Flow with Slip in a Constricted Rectangular Flow Domain

“…or theoretically ([3], [1], [24]) as an axisymmetrical cylindrical tube. For this thesis, a rectangular geometry is chosen to model the constriction instead of the cylindrical geometry.…”

“…The fluid dynamics of blood have been investigated analytically using idealized, smooth cylindrical geometries. The momentum integral equations have been solved using perturbation methods ( [21], [19]) and the Karman-Pohlhausen method ( [9], [24], [23], [1]). In the latter, the solution to the velocity profile is assumed to be of a polynomial form.…”

“…While [23] assumes a zero slip boundary condition, it was suggested by [16] to include slip velocity along the vessel wall. The role of slip was further investigated by ([14], [1], [20]). In [1], the role of slip was investigated with respect to an asymmetric constriction.…”

“…The role of slip was further investigated by ([14], [1], [20]). In [1], the role of slip was investigated with respect to an asymmetric constriction. In the Thesis by [20], the role of slip was investigated using a variety of smooth geometries.…”

“…However, [3] and [19] demonstrated that the pressure gradient is affected by the weakly compressible nature of blood. Recently, particle-based methods called Multi-particle Collision Dynamics (MPC) have become popular approaches to further study the fluid properties of blood ( [11], [3], [1]). MPC methods allows researchers to describe the individual interactions among particles suspended in the blood.…”