Fluid Dynamics Course

Lesson 1 • Hydrostatics and Pressure Distribution

Derives pressure variation in static fluids and applies it to buoyancy and manometry. Provides the baseline for understanding pressure-driven flows.

Lesson 2 • Conservation Laws: Mass and Momentum

Derives the continuity equation and Euler momentum equation in integral and differential forms. Connects physical conservation principles to mathematical field equations.

Lesson 3 • Continuum Hypothesis and Kinematics

Introduces the continuum assumption and Lagrangian vs. Eulerian descriptions of motion. Links microscopic molecular behavior to macroscopic field variables.

Lesson 4 • Properties of Fluids

Covers density, viscosity, surface tension, and compressibility as intrinsic fluid properties. Establishes the physical vocabulary needed for all subsequent analysis.

Lesson 1 • Dimensional Homogeneity and Units

Reviews fundamental dimensions and enforces dimensional homogeneity in physical equations. Prepares students for systematic non-dimensionalization.

Lesson 2 • Key Dimensionless Parameters

Introduces Reynolds, Mach, Froude, Weber, and Strouhal numbers with physical interpretations. Links each parameter to dominant flow physics.

Lesson 3 • Buckingham Pi Theorem

Applies the Pi theorem to reduce governing variables into independent dimensionless groups. Students practice identifying repeating variables and forming Pi groups.

Lesson 1 • Creeping Flow and Low Reynolds Number

Analyzes Stokes flow regime where inertia is negligible relative to viscous forces. Covers Stokes drag on a sphere and lubrication theory fundamentals.

Lesson 2 • Exact Solutions of Navier-Stokes

Solves canonical viscous flow problems including Couette, Poiseuille, and Stokes flows. Builds physical intuition for velocity profiles and pressure gradients.

Lesson 3 • Stress Tensor and Constitutive Relations

Develops the viscous stress tensor and Stokes constitutive law for Newtonian fluids. Bridges kinematics to the momentum equation with viscous terms.

Lesson 4 • Vorticity Dynamics in Viscous Flows

Derives the vorticity transport equation and analyzes vorticity generation and diffusion. Connects viscous dissipation to rotational flow structures.

Lesson 1 • Pressure Gradient Effects and Separation

Examines how adverse pressure gradients cause boundary layer thickening and separation. Links separation to drag increase and stall phenomena.

Lesson 2 • Prandtl Boundary Layer Equations

Derives the boundary layer equations via order-of-magnitude scaling of Navier-Stokes. Establishes the thin-layer approximation valid at high Reynolds numbers.

Lesson 3 • Transition to Turbulence in Boundary Layers

Describes the laminar-to-turbulent transition process and the Tollmien-Schlichting instability mechanism. Identifies critical Reynolds numbers and transition prediction methods.

Lesson 4 • Integral Methods: von Karman Equation

Applies the von Karman momentum integral equation to approximate boundary layer growth. Enables engineering estimates without solving full PDEs.

Lesson 1 • Reynolds-Averaged Navier-Stokes Equations

Derives the RANS equations and identifies the Reynolds stress closure problem. Motivates the need for turbulence models in practical computations.

Lesson 2 • Turbulent Energy Cascade and Kolmogorov Scales

Explains Richardson's energy cascade and Kolmogorov's similarity hypotheses for small-scale turbulence. Defines the dissipation range and inertial subrange.

Lesson 3 • Engineering Turbulence Models

Surveys zero-equation, k-epsilon, and k-omega turbulence models with their assumptions and applicability. Guides model selection for different flow configurations.

Lesson 4 • Turbulent Boundary Layer Structure

Describes the inner and outer layer structure of turbulent boundary layers using wall units. Derives the log-law of the wall and wake region profiles.

Lesson 1 • Panel Methods for Arbitrary Bodies

Introduces source and vortex panel methods for numerically solving potential flow around arbitrary shapes. Connects analytical theory to computational aerodynamic tools.

Lesson 2 • Irrotational Flow and Velocity Potential

Defines irrotational flow and introduces the velocity potential and stream function. Establishes the Laplace equation as the governing equation for potential flow.

Lesson 3 • Conformal Mapping and Airfoil Theory

Uses Joukowski and Karman-Trefftz transformations to map cylinder solutions to airfoil geometries. Predicts lift and pressure distributions on thin airfoils.

Lesson 4 • Flow Over Cylinders and Spheres

Constructs flow over a cylinder by superposing doublet and uniform flow, then adds circulation. Derives the Kutta-Joukowski lift theorem.

Lesson 1 • Oblique Shocks and Expansion Waves

Extends shock analysis to oblique shocks and Prandtl-Meyer expansion fans. Enables analysis of supersonic flow over wedges and corners.

Lesson 2 • Fanno and Rayleigh Flow

Analyzes adiabatic flow with friction (Fanno) and frictionless flow with heat addition (Rayleigh). Applies these models to duct flows with real physical effects.

Lesson 3 • Normal Shock Waves

Derives Rankine-Hugoniot relations across normal shocks and analyzes entropy production. Applies shock relations to pitot tube measurements and diffuser design.

Lesson 4 • Isentropic Flow in Nozzles

Analyzes isentropic flow through converging and converging-diverging nozzles using area-Mach relations. Predicts choked flow conditions and design Mach numbers.

Lesson 1 • Finite Difference Methods

Applies finite difference discretization to diffusion and convection equations on structured grids. Covers explicit and implicit time-stepping schemes.

Lesson 2 • Turbulence and Mesh Resolution in CFD

Discusses RANS, LES, and DNS approaches in CFD with their mesh resolution requirements. Guides students in selecting appropriate simulation strategies for given flow problems.

Lesson 3 • Finite Volume Method

Discretizes conservation laws over control volumes to ensure local and global conservation. Introduces flux interpolation and gradient reconstruction techniques.

Lesson 4 • Pressure-Velocity Coupling

Addresses the incompressible flow pressure-velocity coupling problem using SIMPLE and related algorithms. Explains staggered and collocated grid arrangements.