

Lecture:

Day and Time: Mondays and Wednesdays, 4:30  6:20 PM
Location: GHC 4211

Instructor Office Hours:

Time: TBD
Location: Scaife Hall (SH) 319

TA Office Hours:

Time: TBD
Location: TBD


Course Description:

In this course, students will develop basic understanding and skill sets to perform simulations of transport phenomena (mass, momentum, and energy transport) for engineering applications using a commercial CFD tool, learn to analyze and compare simulation results with theory or available data, and develop ability to relate numerical predictions to behavior of governing equations and the underlying physical system. First 8 weeks of the course will include lectures and simulationbased homework assignments. During last 7 weeks, teams of students will work on selfproposed or industrycontributed projects related to computational analysis of transport phenomena. In the project, students will learn to approach loosely defined problems through design of adequate computational mesh, choice of appropriate numerical scheme and boundary conditions, selection of suitable physical models, efficient utilization of available computational resources. Simulations for the project will be performed in Linux environment on highperformance computing (HPC) resources of the Pittsburgh Supercomputing Center (PSC). Training will be provided in the course to work in the Linux environment. Each team will communicate results of their project through multiple oral presentations and a final written report.

Prerequisites:

Undergraduate thermofluids courses

Reference books:

Transport Phenomena by Bird, Stewart, and Lightfoot
Computational Methods for Fluid Dynamics by Ferziger and Peric
Numerical Heat Transfer and Fluid Flow by S. V. Patankar

Grading:

Homework (40%)
Project (50%)
Midterm exam (10%)

Tentative Syllabus Outline:


Introduction to Finte Volume, Finite Element, and Finite Difference Methods


Week 1

Discretization of 2D general transport equation using FV, FE, and FD methods, explicit vs implicit time advancement, direct vs iterative solvers, solution residuals, programming assignment on implimentation of FD method in 2D


Numerics, Mesh, and Boundary Conditions


Week2

Numerical diffusion, modified wavenumber analysis, orderofaccuracy, numerical stabilization, computational assignment using CAE tool
Unstructured vs structured mesh, assessment of mesh quality, effect of element shape on accuracy and stability, false diffusion due to mesh alignment, types of boundary conditions, computational assignment using CAE tool


Momentum Transport in Laminar Flows


Week 3

Introduction to NavierStokes (NS) equations in dimensional and nondimensional form, special cases of creeping and inviscid flows, iterative and noniterative methods for numerical solution of NS equations (SIMPLE, PISO, FSM methods), computational assignment using CAE tool


Heat and Mass Transport in Laminar Flows


Week 4

Steady and unsteady heat condition equations, natural and forced convection in laminar flows, introduction to relevant nondimensional numbers, difficulties faced in numerical solution of energy equation, coupling of energy and momentum equations, computational assignment using CAE tool
Fick's law of mass diffusion, equations of change for multicomponent gasphase diffusive and convective mass transport, introduction to relevant nondimensional numbers, solution procedure for mass transport equation, computational assignment using CAE tool


Chemical Source Terms in Transport Equations


Week 5

Introduction to multicomponent chemically reacting flows, multistep chemistry mechanisms, calculation of production and destruction rates of chemical species as a system of ODEs, coupling of chemical reactions with energy and multicomponent mass transrpot equations


Introduction to Turbulent Flows and their Simulations


Week 6

Practical examples of turbulent flows, statistical description of turbulent flows, scales of turbulent motion, transition from laminar to turbulent flows, examples of free shear flows and wall flows, turbulence modelling approaches (RANS, LES, DNS), choice of an approach based on computational cost and relevant physics, examples of most commonly used turbulence models, computational assignment using CAE tool


Project Proposal Presentations


Feb 28

A 15minute presentation to the class by each team


Meshing Training


Mar 05

Meshing training and project help in MechE Computing Cluster


Midterm Exam


Mar 07

Midterm exam


Computational Project


Mar 12  May 02

Team project in computational analysis using CAE tool, project proposal presentation, midproject presentation, weekly meetings with TA and instructor

April 04

Meshing training and project help in MechE Computer Cluster

April 09

A 15minute project update presentation to the class by each team

Final exam week

Final project presentation and submission of written report



