Abstract

<p>The goal of this research is to analyze the effect of blood flow through expansions by using the Karman-Pohlhausen method. The Karman-Pohlhausen method has previously been used in several research works to analyze the flow through constrictions. In this Thesis, the effect of different flow parameters (Reynolds number, compressibility, and slip) on pressure, pressure gradient, centerline velocity, and on wall shear stress are analyzed. Our results show that the pressure gradient curves are most affected by increasing Reynolds number and compressibility, as well as for smaller slip values (ws0). Furthermore, the scaled centerline velocity was least affected by varying Reynolds and Mach numbers, whereas changes are observed in centerline velocity curves for different slip values. The wall shear stress was essentially unchanged by the Reynolds numbers, compressibility range and slip values considered in this Thesis.</p>

Highlights

  • It has been reported in the literature that smoking, hypertension and male sex are strong risk factors for the development of abdominal aortic aneurysms (AAAs)

  • We plot the solution curves for various Reynolds numbers, compressibility and slip values, keeping the values of other parameters fixed such as z1 = 6m, l1 = 4m, l2 = 1m, R0 = 0.1m, δ = 0.05m, ρ0 = 1050kg/m3, μ = 0.0035kg/ms, whereas the values for W0, g0 and kB T m are determined from the relations described below

  • In order to study the effect, solution curves were obtained for various Reynolds numbers, compressibility (Mach numbers) and slip values

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Summary

References vii

4.1 Pressure curves in piecewise polynomial geometry with ws0 = 0.04, l1 = 4, l2 = 1, R0 = 0.1, 4.2 Pressure gradient curves in piecewise polynomial geometry with ws0 = 0.04, l1 = 4, l2 = 1, 4.3 Centerline velocity curves in piecewise polynomial geometry with ws0 = 0.04, l1 = 4, l2 = 1, 4.4 Wall shear stress curves in piecewise polynomial geometry with ws0 = 0.04, l1 = 4, l2 = 1, 4.5 Pressure curves in piecewise polynomial geometry with ws0 = 0.04, l1 = 4, l2 = 1, R0 = 0.1, 4.6 Pressure gradient curves in piecewise polynomial geometry with ws0 = 0.04, l1 = 4, l2 = 1, 4.7 Pressure curves in piecewise polynomial geometry with Re0 = 200, l1 = 4, l2 = 1, R0 = 0.1, 4.8 Pressure gradient curves in piecewise polynomial geometry with Re0 = 200, l1 = 4, l2 = 1, 4.9 Scaled centerline velocity curves in piecewise polynomial geometry with Re0 = 200, l1 = 4, 4.10 Wall shear stress curves in piece-wise polynomial geometry with Re0 = 200, l1 = 4, l2 = 1, ix

Introduction
Governing Equations
Dimensionless quantities
Derivation of integrated z-momentum equation
Differential equation for pressure
Upstream Properties
Flow geometry
Piecewise polynomial geometry
Effect of Reynolds number
Effect of compressibility
Effect of slip
Conclusion and Future work
Constant flow rate

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