ME634A

Advanced Computational Fluid Dynamics

Credits:

  

 

3-0-0-0 (9 Credits)
 

Objective:

The primary objective of the course is to teach fundamentals of computational method for solving non-linear partial differential equations (PDE) primarily in complex geometry. The emphasis of the course is to teach CFD techniques for solving incompressible and compressible N-S equation in primitive variables, grid generation in complex geometry, transformation of N-S equation in curvilinear coordinate system and introduction to turbulence modellin.

Prerequisite:

Knowledge of undergraduate heat transfer and fluid mechanics, basic computational fluid dynamics.

Brief Syllabus:

Introduction: Finite difference (FDM) and Finite volume (FVM) methods, elliptic, parabolic and hyperbolic equations, Navier-Stokes (N-S) and energy equations, explicit and implicit methods, higher order schemes Solutions of simultaneous equations: iterative and direct methods, Gauss-Seidel iteration, CGS, Bi-CGSTAB and GMRES (m) matrix solvers, different acceleration techniques; Incompressible flow: N-S equation using explicit methods: MAC and SMAC (staggered and collocated grids), semi-implicit methods: SIMPLE and SIMPLER, projection method, higher order discretisations, Compressible Flow: solution of compressible N-S equation, finite volume formulations, geometric flexibility, Jameson's, MacCormack's, Steger and Warming schemes in FVM, flux splitting scheme and upwinding, different acceleration technique, multigrid method; Grid generation: grid generation using algebraic and partial differential equations; N-S equations in irregular geometry: transformation of N-S equation in curvilinear coordinate system, non-orthogonal grid, Uncertainty of numerical results: Sources of uncertainties, independence studies on grid, time-step, domain and initial condition. Turbulence modeling: scales of turbulence, concept of turbulence modeling, different eddy viscosity based models, introduction to large eddy simulation (LES) and direct numerical simulation (DNS).

Lecturewise Breakup (based on 50min per lecture)


I. Introduction: (3 Lectures)

    • Brief introduction of boundary layer flow, incompressible and compressible flows, finite difference and finite volume method, example of parabolic and hyperbolic systems and time discretization technique, explicit and implicit methods, upwind and central difference schemes, stability, dissipation and dispersion errors.

       

II. Solution of Simultaneous Equations: (4 Lectures)

      • point iterative/block iterative methods, Gauss-Seidel iteration (concept of central coefficient and residue, SOR), CGS, Bi-CGSTAB and GMRES (m) matrix solvers, different acceleration techniques.

III. Incompressible Flow: (11 Lectures)

      • Higher order upwind schemes: second order convective schemes, QUICK.

      • Solution of NS equations: Solution of incompressible N-S equation (Explicit time stepping, Semi–explicit time stepping).

      • SMAC method for staggered grid: Predictor - Corrector step, discretization of N-S and continuity equations, Pressure correction Poisson's equation, boundary conditions (no-slip, moving wall, slip boundary and inflow conditions), outflow (zero gradient/Orlanski) boundary conditions for unsteady flows, algorithm for the SMAC method, stability considerations for SMAC method.

      • Semi–implicit method (SIMPLE): Comparison with the SMAC and fully – implicit methods, algorithm for semi–implicit method, discussion on SIMPLE/SIMPLER and SIMPLEC. Discretization of governing equations and boundary conditions in FVM framework.

      • SMAC method for collocated grid: Pressure–velocity coupling, N- S equations on a collocated grid, concept of momentum interpolation to avoid pressure velocity decoupling, discretization of governing equations using the concept of momentum interpolation.

IV. FDE in complex geometries: (4 Lectures)

      • Transformation of governing equation in ξ η− plane, transformation of Laplace equation, introduction to geometrical parameters and the accuracy of the solution, basic facts about transformation, grid transformation on complex geometries. N-S equations in transformed plane, matrices and Jacobians.

V. Compressible Flow: (7 Lectures)

      • N-S and energy equations, properties of Euler equation, linearization.

      • Solution of Euler equation: Explicit and implicit treatment such as Lax-Wendroff, MacCormark, Beam and Warming schemes, Upwind schemes for Euler equation: Steger and Warming, Van Leer's flux splitting, Roe's approximate Riemann solver, TVD schemes.

      • Solution of N-S equations: MacCormack, Jameson algorithm in finite volume formulation and transformed coordinate system.

VI. Grid system: (5 Lectures)

      • Historical aspects of the various grids, Body fitted grids in complex geometries, orthogonal grids, mapping functions, staggered/collocated and structured/unstructured, various methods of grid generations (Algebraic, Transfinite, Poisson equation methods).

VII. Uncertainty of numerical results: (2 Lectures)

      • Sources of uncertainties, studies on grid independence, time-step independence, domain independence, initial condition dependence.

VIII. Turbulence modelling: (4 Lectures)

      • Introduction to turbulence, scales of turbulence, Reynolds Averaged Navier Stokes (RANS) equation, closure problem, eddy viscosity model, k-ε and k-ω model, introduction to large eddy simulation (LES) and direct numerical simulation.

References:

    1. Computational Fluid Flow and Heat Transfer, Second Edition, K. Muralidhar,T. Sundararajan (Narosa), 2011.

    2. Computational Fluid Dynamics, Chung T. J., Cambridge University Press, 2003.

    3. Computational Fluid Dynamics, Tapan K. Sengupta, University Press, 2005

    4. Numerical Computation of Internal and External Flows, Hirch C., Elesvier 2007

    5. Numerical Heat Transfer and Fluid Flow, S. V. Patankar (Hemisphere Series on Computational Methods in Mechanics and Thermal Science)

    6. Essential Computational Fluid Dynamics, Zikanov. O., Wiley 2010.

    7. Computer Simulation of Flow and Heat Transfer, P. S. Ghoshdastidar (4th Edition, Tata McGraw-Hill), 1998.
 
 

ME639A

Liquid-Vapor Phase Change Technology

Credits:

  

 

3-0-0-0 (9 Credits)
 

Brief Syllabus:


Introduction:

  • Phase-change Thermo-physics, Equations of state, Phase diagrams, Phasestability and spinoidals, Interfacial tension, Free energy, Wetting and hysteresis.

Boiling and Condensation:

  • Homogeneous and heterogeneous nucleation, Pool and convective boiling, Critical Heat Flux, Film/dropwise condensation, Enhancement techniques.

Two-phase flow:

  • Flow patterns, Homogeneous and Separated flow model development.

Phase-change Technology (suggested topics):

  • Active and Passive systems, Design of conventional heat pipes, Micro heat pipes, Pulsating heat pipes, Capillary pumped loops/ Loop heat pipes, Gravity assisted thermosyphons/ Vapor chambers, Electronics thermal management, Space thermal management; Two-phase heat exchangers, Boilers/Evaporators and condensers for Nuclear/Power/RAC industry.

• Special topics (suggested topics):

  • Dynamic behavior of interfaces, Static and dynamic instabilities, Leidenfrost phenomena, Evaporation at interfaces, Marangoni effect, atomistic nucleation models, Accommodation coefficients, Molecular dynamics, phasechange under micro-gravity, Debris-bed cooling.

Experimental techniques:

  • Void fraction, Velocity and thermal field visualization, Surface tension, thermometry, Data analysis, application examples.

Lecturewise Breakup


I. Introduction: (2 Hours)

  • Introduction to phase change flow and heat transfer technology, Various industrial applications, Revision of Basic thermodynamics and heat transfer.

II. INTERFACIAL PHENOMENA & PHASE TRANSITIONS: (6 Hours)

  • Interfacial tension, wetting phenomenon and contact angles, Phase stability and nucleation.

III. BOILING AND CONDENSATION HEAT TRANSFER: (10 Hours)

  • Boiling Fundamentals, Homogeneous and heterogeneous nucleation, Pool Boiling and Convective Flow Boiling, Heat Transfer and CFH mechanisms, Enhancement techniques External and Internal condensation, Film condensation theory, Dropwise Condensation theory, Enhancement techniques.

IV. TWO PHASE FLOWS: (6 Hours)

  • Introduction to two-phase flows, Flow Patterns, Flow pattern Maps, Development of Homogeneous, Separated Flow and Drift Flux Models, Two-phase flow instabilities. [1 Lecture]

V. MEASUREMENT TECHNIQUES IN BOILING AND CONDENSATION: (2 Hours)

  • Void Fraction measurement techniques, Visualization techniques, Contact angle/Surface tension measurement, Conventional thermometry, Data reduction, Applications .

VI. APPLICATIONS OF PHASE CHANGE TECHNOLOGY: (8 Hours)

  • Boilers/Evaporators and Condensers for Nuclear/Power/RAC industry

  • Electronics thermal management

  • Gravity assisted thermosyphons/Vapor chambers.

  • Conventional heat pipes

  • Micro heat pipes

  • Capillary pumped loops/ Loop heat pipes

  • Micro two-phase heat exchangers

VII. SPECIAL TOPICS/ Term Paper presentation: (4 Hours)

  • For example: Marangoni effect, microscale phenomena, atomistic models for nucleation, physically/chemically textured surfaces, fabrication/integration techniques, contact resistance, instabilities, surface roughness characteristics, boiling on porous media, Reactor debris cooling, Transport effects, dynamic behavior of interfaces and etc.

References:

  1. Liquid Vapor Phase Change Phenomena , by Van P. Carey (Taylor & Francis)

  2. Heat Pipe Science and Technology, Amir Faghri (Taylor and Francis)

  3. One Dimensional Two-Phase Flow , G. B. Wallis (McGraw Hill)

  4. Heat Transfer Characteristics in Boiling and Condensation, Karl Stephan (Springer)

  5. Convective Boiling And Condensation , Collier John (Oxford Engineering Science)

  6. Two-phase Flow and Heat Transfer, P. B. Whalley (Oxford Engineering Science)

  7. Heat Pipe Technology and Applications, J. P. Peterson (John Wiley & Sons)

  8. Heat Transfer – A practical approach, Yunus Cengel (Tata McGraw Hill)

  9. Heat Transfer – Incropera and Dewitt, John Wiley and Sons
 

ME643A

Combustion

Credits:

  

 

3-0-0-0 (9 Credits)
 

Course Content:


Introduction, review of thermodynamics, adiabatic flame temperature, chemical equilibrium, chemical kinetics, steady-state approximation, partial equilibrium, mass transfer, conservation equations and transport properties, laminar premixed flame, flame speed, ignition, quenching, flammability limits and stability, laminar non-premixed flame, conserved scalar concept, estimation of flame height, burning rate for a single droplet, turbulent premixed flames, Borghi diagram, flame height for turbulent nonpremixedflames, liftoff and blowout phenomena, flame stabilizationin turbulent flows, Soot and NOxformation in premixed and nonpremixed combustion.

Lecturewise Breakup (considering the duration of each lecture is 50 minutes)


I. Introduction: (2 Lectures)

  • Practical applications of combustion, motivation to study combustion, definition of combustion.

  • Classifications of fundamental combustion phenomena,challenges and approach to our study.

II. Combustion and thermochemistry: (6 Lectures)

  • Review of thermodynamics: extensive/intensive properties, equation of state, calorific equations of state, ideal gas mixture, latent heat of vaporization.

  • The first law of thermodynamics, concept of stoichiometry, heat capacity, standard enthalpy of formation.

  • Adiabatic flame temperature for constant pressure and constant volume systems.

  • Chemical equilibrium, the second law of thermodynamics, Gibbs function, Complex systems.

  • Equilibrium products of combustion, concepts of full equilibrium.

  • Water-gas equilibrium, effect of pressure on equilibrium.

III. Chemical kinetics and reaction mechanism: (5 Lectures)

  • Global and elementary reactions, molecularity and order, elementary reaction rates.

  • Bimolecular reactions and collision theory, other elementary reactions.

  • Rates of multistep mechanisms, Arrhenius law, relation between rate coefficients and equilibrium constants.

  • Steady-state approximation, unimolecular reactions.

  • Chemical time scale, partial equilibrium.

IV. Introduction to mass transfer: (2 Lectures)

  • Fick's law of diffusion, molecular basis of diffusion (kinetic theory of gases), species conservation for a reactive system.

  • The Stefan problem, liquid-vapor interface boundary conditions, droplet evaporation.

V. Conservation equations and transport properties: (4 Lecture)

  • Derivation of species conservation equation for a reactive system.

  • Integral and differential form of a general conservation equation.

  • Derivation of energy conservation for a reactive system, Shvab-Zeldovich form.

  • Transport properties: thermal conductivity, viscosity, mass and thermal diffusivity.

VI. Laminar premixed flame: (5 Lectures)

  • Physical description, flame speed and thickness, Bunsen burner, simplified analysis of a premixed flame.

  • Factors influencing flame thickness and velocity.

  • Ignition, ignition delay time for hydrocarbons, spark ignition.

  • Flame quenching, estimation of quenching distance, flammability limits.

  • Flame stabilization, flame extinction, flashback and lift off

VII. Laminar nonpremixed flame : (4 Lectures)

  • Physical description of jet diffusion flame, counterflow diffusion flame

  • Concept of a conserved scalar, mixture fraction, conservation of mixture fraction.

  • Functional dependencies under various conditions: cold mixing, complete and infinitely fast reaction, chemical equilibrium condition, finite rate chemistry

  • Analytical solutions for flame height.

VIII. Droplet evaporation and combustion : (4 Lectures)

  • Applications, simple model of droplet evaporation

  • Simple model for burning droplet, burning rate constant and droplet lifetime.

  • Droplet burning in convective environments

  • Real-world effects on droplet burning rate.

IX. Turbulent Reactive Flows: (6 Lectures)

  • Applications of turbulent premixed flames, turbulent flame speed

  • Structure andcharacteristics of turbulent premixed flame.

  • Different regimes of turbulent premixed flame

  • Applications of turbulent nonpremixed flames, estimation of flame height using scaling laws for turbulent diffusion flames.

  • Liftoff and blowout phenomena in turbulent jet flames.

  • Various flame stabilization mechanism in turbulent flows.

X. Pollutant emissions: (2 Lectures)

  • Effects of NOx and Soot, quantification

  • Combustion generated emission and control measures.

References:

  1. An Introduction to Combustion: Concepts and Applications, S. R. Turns, McGraw-Hill Science/Engineering/Math; 3 edition (January 24, 2011)

  2. Combustion by I. Glassman, Academic Press; 4 edition (September 8, 2008)

  3. Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation, J. Warnatz, U. Mass and R. W. Dibble, Springer; 4th edition (November 9, 2010)
 

ME647A

Introduction to Turbulent Flows

Credits:

  

 

3-0-0-0 (9 Credits)
 

Course Content:


The primary objective of the course is to teach fundamentals of turbulent flows, an important topic in fluid dynamics. The course coverage includes: Statistical representation of turbulent flows, energy cascade, Kolmogorov hypothesis, free shear and wall-bounded flows apart from introduction to turbulence modelling and experiments.

Prerequisites:


Knowledge of heat transfer, fluid mechanics and viscous flow theory.

Brief Syllabus


Introduction: Origin of turbulence, irregularity, diffusivity, three-dimensional motions, dissipation, wide spectrum, length scales; Statistical Description of Turbulence: Probability density, moments, correlations, integral micro scales, homogeneous and isotropic turbulence, Kolmogorov hypothesis, energy cascade, turbulence spectra; Turbulent Transport: Reynolds decomposition, turbulent stresses, Reynolds equations, mixing-length model, dynamics of turbulence; Free Shear Flows: Mixing layer, turbulent wakes and jets, grid turbulence; Wall-bounded Turbulent Flows: Channel and pipe flows, Reynolds stresses, turbulent boundary layer equations, logarithmic-law of wall; Introduction to turbulence modelling and experimental methods

Lecturewise Breakup (considering the duration of each lecture is 50 minutes)


I. Introduction: (3 Lectures)

  • Nature of turbulent flows, irregularity, diffusivity, threedimensional motions, dissipation, wide spectrum, origin of turbulence, eddy motions and length scales.

II. Statistical Description of Turbulence: (7 Lectures)

  • Random nature of turbulence,distribution function, probability density, moments, correlations, Taylor's hypothesis, integral micro scales, homogeneous and isotropic turbulence,Kolmogorov hypothesis, scales of turbulence, energy cascade, turbulence spectra..

III. Turbulent Transport of Moment and Heat: (6 Lectures)

  • Reynolds decomposition, turbulent stresses, vortex stretching, Reynolds equations, mixing-length model, Reynolds' analogy, dynamics of turbulence.

IV. Free Shear Flows: (6 Lectures)

  • Mixing Layer, Turbulent Wakes and Jets, Grid Turbulence.

V. Wall-Bounded Turbulent Flows: (6 Lecture)

  • Channel and pipe flows, Reynolds stresses, turbulent boundary layer equations, logarithmic-law of walls, turbulent structures.

VI. Turbulence Modelling: (6 Lectures)

  • Introduction, eddy-viscosity hypothesis, algebraic model, k-ε and k-ω model, Reynolds-stress model, near-wall treatment,iIntroduction to LES and DNS.

VII. Experimental Methods: (5 Lectures)

  • Introduction, hot wire anemometry, uncertainty analysis and laser doppler anemometry.

References:

  1. Turbulent Flows, Stephen B. Pope, Cambridge University Press

  2. A First Course in Turbulence, H. Tennekes and J. L. Lumley, MIT Press