Computational Analysis of Transport Phenomena

24-618/24-428, Spring 2024

Satbir Singh

Simulation of turbulent flow in an engine

Lecture:

Day and Time: Mondays and Wednesdays, 10:00 AM - 11:50 AM
Location: DH 1112

Instructor Office Hours:

Time: Fridays, 1:00 - 2:00 PM
Location: SH 310

TA Office Hours:

Time: TBA
Location: TBA

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 7 weeks of the course will include lectures and simulation-based homework assignments. During last 7 weeks, teams of students will work on self-proposed or industry-contributed 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 high-performance 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 thermo-fluids 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, order-of-accuracy, 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 Navier-Stokes (NS) equations in dimensional and non-dimensional form, special cases of creeping and inviscid flows, iterative and non-iterative 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 non-dimensional 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 multi-component gas-phase diffusive and convective mass transport, introduction to relevant non-dimensional numbers, solution procedure for mass transport equation, computational assignment using CAE tool
--------------------------------------------------------------------- Chemical Source Terms in Transport Equations ---------------------------------------------------------------------
Week 5	Introduction to multi-component chemically reacting flows, multi-step chemistry mechanisms, calculation of production and destruction rates of chemical species as a system of ODEs, coupling of chemical reactions with energy and multi-component 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
--------------------------------------------------------------------- Midterm Exam ---------------------------------------------------------------------
Feb 28	Midterm exam
--------------------------------------------------------------------- Project Proposal Presentations ---------------------------------------------------------------------
Mar 13	A 15-minute presentation to the class by each team
--------------------------------------------------------------------- Computational Project ---------------------------------------------------------------------
Mar 18 - April 24	Team project in computational analysis using CAE tool, project proposal presentation, mid-project presentation, weekly meetings with TA and instructor
April 10	A 15-minute project update presentation to the class by each team
Final exam week	Final project presentation and submission of written report