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General Information
Instructor
Juan R. Cebral
Email: jcebral@gmu.edu
Phone: 703-993-4078
Prerequisites
CSI 700, CSI 780, or permission of instructor.
Description
This course covers basic and advanced fluid dynamics. Fluid dynamics is a fundamental area of physical sciences and represents a theoretical building block in the understanding of Computational Fluid Dynamics (CFD) models and techniques. The goals of this course are:
- Provide a basic understanding of the governing equations describing fluid motion.
- Analyze the dynamic levels of approximation carried out to simplify the governing equations.
- Describe some of the mathematical techniques used to obtain analytical solutions.
- Analyze several analytical solutions in order to gain insight into basic flow patterns.
- Study in greater detail a fluid dynamics topic through a project focused on biofluids.
Bibliography
- Batchelor, "Introduction to Fluid Dynamics", Cambridge University Press, 1967.
- Kundu, "Fluid Mechanics", Academic Press, 2002.
- Schlichting, "Boundary Layer Theory", McGraw-Hill, 1968.
- Landau & Lifshitz, "Fluid Mechanics", Pergamon Press, 1987.
- Mazumdar, "Biofluid Mechanics", 1997.
Syllabus
1-Introduction
Continuous Hypothesis
Stress Tensor
Hydrostatics
Kinematics
2-Governing Equations
Mass Conservation
Material Derivatives and Conservation Laws
Momentum Conservation
Newtonian Fluids
Navier-Stokes Equations
Energy Conservation
Bernoulli's Equation
Full Set of Equations
3-Dimensional Analysis
Pi Theorem
Incompressibility: Mach Number
Similarity: Reynolds Number
Parameters of Incompressible Flows
Parameters of Compressible Flows
4-Incompressible Laminar Viscous Flows
Couette Flows
Poiseuille Flows
Unsteady Laminar Flows
Flows with Small Reynolds Number
Flows with Large Reynolds Number
Effects of Increasing the Reynolds Number
5-Turbulent Flows
Reynolds Experiment
Theory of Stability
Reynold Stresses
Incompressible Turbulence Flows
Turbulence Models
6-Boundary Layer Flows
Laminar Boundary Theory
Separation
Turbulent Boundary Layers
7-Levels of Approximations
Navier-Stokes Equations
Reynolds Average Navier-Stokes Equations
Euler Equations
Small Disturbance Approximation
Potential Flows
8-Potential Flows
Laplace's Equation
Elementary Solutions: sources, sinks, vortices
Method of Images
Separation of Variables
Complex Potential
Airfoil Theory
9-Biofluids (Slides available here)
Cardiovascular System
Blood Rheology
Blood Flow Models
Computational Hemodynamics
Image-Based Modeling of Biofluids
Problems
Class Notes
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