ME631A

Viscous Flow Theory

Credits:


3L0T0L0D (9 Credits)



Course Content:
Introduction: stressdeformation relation, vector and tensor, vorticity and circulation, derivation of NavierStokes equations; Exact solutions: Couette flow, HagenPoiseuille flow, Stokes problems; Complex variable and Potential flow, Twodimensional boundary layer: Blassius solution, KármánPohlhausen method, effect of pressure gradient, separation and control, Waltz’sQuadrature formula; Flow instability: concept of smallperturbations, linearized stability of parallel viscous flows, OrrSommerfeld equation; Turbulent boundary layers: Reynolds stress tensor, energy cascade, mixing length hypothesis, universal law of wall, fully developed turbulent flow through a pipe and channel, power law and effect of wall roughness; Compressible flow: condition of compressibility, subsonic, supersonic and hypersonic flows, shock and Mach waves, shockboundary layer interactions; Special topics: Transition and turbulence, fluidsolid interaction, freesurface flow, biofluids, nonNewtonian flows, CFD and Measurements (optional and limited to any one).
Lecturewise Breakup (based on 50min per lecture):
I. Introduction: (3 Lectures)

Fluid Properties, Definition of Continuum, Examples of Viscous Flow Phenomena, Laminar and Turbulent Flow, Vector and Tensor notation, Lagrangian/Eulerian Methods, Streamline, Path line, Streak line, Material Derivative and acceleration, Strain Rate, Translation, Rotation and Distortion of Fluid Element, Vorticity and Circulation.
II. Fundamental Equations of Viscous Flow: (5 Lectures)

Conservation of Mass, Momentum and Energy, Finite Volume Approach, Derivation of Continuity Equation: conservative and non conservative form, Derivation of NavierStokes (NS) equations for Compressible Flow, Stokes Hypothesis. Incompressible form of NS equations.
III. Exact Solutions: (7 Lectures)

Parallel Flow in a Straight Channel, Couette Flow, Lubrication Theory, HagenPoiseuille Flow, Unsteady Parallel Flow, Stokes Problems, Similarity Solution and Creeping Flow, Complex variable and Potential flow.
IV. Boundary Layer Theory: (6 Lectures)

Derivation of 2D Boundary Layer Equations, Displacement, Momentum and Energy Thickness, Order of Magnitude Analysis, Shape Factor, MomentumIntegral Approach, Boundary Layer Separation, Effect of Pressure Gradient, Boundary Layer Control by Suction and Blowing, Blassius Solution of Boundary Layer Equation, KármánPohlhausen Method for NonZero Pressure Gradient, Holsten and Bohlen Method (Modified Pohlhausen Method), Waltz’sQuadrature Formula and Example Problems.
V. Flow Instability: (4 Lectures)

Instability, Concept of SmallPerturbations, Linearized Stability of Parallel Viscous Flows, OrrSommerfeld Equation, Neutral Stability Curve, Boundary Layer Transition qver a Flat Plate.
VI. Turbulent Boundary Layers: (6 Lectures)

Introduction to Turbulent Flows, Features of Turbulence, Energy Cascade, Mean and Fluctuating Components, Derivations of Reynolds Averaged NavierStokes Equations, Reynolds Stress Tensor, Turbulent Boundary Layer Equations, Eddy Viscosity and Mixing Length Hypothesis, Universal Law of Wall, Laminar Sublayer, Power Law for Turbulent Boundary Layer, Skin Friction Coefficient, Turbulent Boundary Layer with Pressure Gradient, Quadrature Formula and Example Problems.
VII. Internal Flows: (3 Lectures)

Fully Developed Turbulent Flow through a Pipe and Channel, Use of Log Law and Power Law, Derivation of Coefficient of Friction for Turbulent Pipe Flow, Moody Diagram, Hydrodynamic Smooth and Rough Pipe and Example Problems.
VIII. Compressible Flows: (5 Lectures)

Introduction and Definition, Limiting Condition of Compressibility, Subsonic, Supersonic and Hypersonic Flows, Mach Angle, Propagation of Small Disturbances, Formation of Shock, Shock Waves, Normal Shock Relations, Oblique Shock, Compression and Expansion Waves, Reflection and Interaction of Shocks, Expansion Waves, ShockBoundary Layer Interactions and Example Problems.
IX. Special Topics: (3 Lectures)

Transition and turbulence, fluidsolid interaction, freesurface flow, biofluids and nonNewtonian flows, CFD and Measurements (optional and limited to any one topic).
