Pressure curves for compressible flow with slip through constricted cylinders

Salahaldeen Rabba

doi:10.32920/ryerson.14649126.v1

Abstract

<p>The goal of this research is to determine more accurate pressure curves for compressible flow with slipthrough cylinders that have a local constriction. Existing analyses for compressible flow with slip througha local constriction linearize the pressure gradient equation, and higher-order derivatives are dropped as well. The equation to be developed as part of this research retains quadratic pressure gradient terms. The corresponding solution for the pressure gradient is found following existing analysis in the literature for incompressible, no-slip flow, and subsequently the pressure is found using numerical integration. Results are compared to those from the linearized pressure gradient equation to see the extent of the improvement. Results are also assessed and compared to pressure and density curves available in the literature for some specific constrictions. Improvements may be obtained when the second-order derivatives are kept as well inthe pressure gradient equations, which can be assessed and analyzed in the same context. Pressure curves are assessed in different idealized flow geometries including the Gaussian model, a cosinu-soidal model, and a smooth piece-wise polynomial model. In each case the pressure is found, and hence alsothe density. A range of Reynolds numbers, degrees of constriction, length of the constriction, compressibilityand slip are considered. Density curves are separately compared to existing particle-based results obtained from a stochastic particle dynamics using multiparticle collision dynamics. </p>

Highlights

IntroductionWhen blood vessels are constricted blood flow through those vessels becomes restricted
The extensive quantitative analysis helps estimating the significant effects of the severity of the stenoses, effecting blood pressure and density
This Thesis is organized as follows: In Chapter 2 we provide the Fluid Dynamics background that is required for our analytical results as well as the mathematical forms for the various flow geometries considered in our later assessment of the pressure curves

Summary

Introduction

When blood vessels are constricted blood flow through those vessels becomes restricted. A mathematical model is developed analytically to study the flow characteristics of blood through an artery in the presence of stenosis (constriction). The flow mechanism in the stenosed artery is subjected to a pulse-pressure-gradient. Fluid dynamics has a wide range of applications, including calculating forces and momentum, and determining the mass flow rate of liquids through cylinders. The solution to a fluid dynamics problem typically involves calculating various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space. These will play a key role in our approach in deriving the pressure gradient equation and analysing the pressure and density curves. The study of flow geometry of the constriction can be described by the bell-shaped Gaussian distribution profile.

Objectives

Discussion

Conclusion