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CHE521 ADVANCED FLUID FLOW

Course Objectives

At the end of the course students should be able to

• Develop basic equations of fluid flow through vector/tensor operations
• Obtain general solutions for creeping flows via eigenfunction expansions
• Apply regular and singular perturbations for pulsatile flow
• Solve steady shear flow problems involving non-Newtonian fluids through generalized Newtonian model
• Use linear viscoelastic constitutive models and interpret their physical significance for material characterization
• Apply nonlinear viscoelastic models to obtain relations for material functions

Course Content

Inviscid fluid, Euler equation, Bernoulli equation, Kelvin's theorem, irrational motion, Stoke's stream function, vorticity; analytical and numerical solutions of Navier-Stokes equation; creeping flow equation, introduction to lubrication theory; vorticity transport equation, laminar boundary layers, turbulent boundary layers; introduction to turbulence.

Course Learning Outcomes

• Vector/tensor manipulations, index notation, Reynold’s transport theorem, continuity equation
• Properties of stress tensor, Cauchy stress equation, mechanical and thermal energy balances, constitutive equations
• Navier-Stokes equations, steady and unsteady unidirectional flows, scaling terms in the Navier-Stokes equations
• Creeping flows, linearity of Stokes equations, streamfunctions, general solutions via eigenfunction expansions
• Regular and singular perturbations for pulsatile flow, lubrication theory, Reynold’s equation, slider block and cylinder problems
• Shear flow with viscous dissipation, concept of viscoelasticity and Deborah number. Shear-rate dependent viscosity in steady shear flow
• Invariant properties of tensors. Generalized Newtonian fluid models. Measurement of steady shear viscosity: Couette and cone-and-plate rheometers. Analytical solutions for generalized Newtonian fluids in simple shear flows
• Definition of normal stress differences in steady shear flows. Analysis of observable effects of normal stresses. Measurement of normal stress differences with cone-and-plate rheometers
• Linear viscoelastic properties: The complex modulus and complex viscosity. Linear viscoelastic constitutive equations: The Maxwell, Jeffreys and Kelvin models in differential and integral form
• Linear viscoelasticity with multiple relaxation times. Empiricisms for relating the linear viscoleastic properties to steady shear viscosity and normal stress differences: The Cox-Merz rule and Laun’s rule
• Limitations of linear viscoelastic models. Commonly observed “funy flow phenomena” in viscoelastic liquids. The need for nonlinear constitutive equations