Title: ME 412 Numerical Methods in Thermal Science
1ME 412 Numerical Methods in Thermal Science
- S. P.Vanka
- Professor of Mechanical Engineering,
- UIUC, Illinois, USA
2IN MEMORIUM
- This lecture is dedicated to my mother who passed
away recently (Nov. 29th, 2011) at the age of 89
years
3What this course is about
- This course teaches you the basics of developing
and applying computational methods for solving
problems of fluid flow and heat transfer - It covers both fundamental theory and application
of the techniques to develop practical fluid flow
software. In addition, you will be also using one
of the commercial fluid flow software to solve an
industrially relevant flow problem
4Course Objectives
- To expose students to fundamentals of
computational fluid dynamics and heat transfer. - To make students confident of developing as well
as using software for computational fluid
dynamics. - To make students familiar with simulation of
complex fluid flows with complex boundary shapes
and boundary conditions.
5Course Administration
- Instructor S. P. Vanka 3011 MEL, 4-8388,
spvanka_at_uiuc.edu - Office hours M, W 3-5 pm
- Lectures 400 Engineering Hall, MWF 1-1150pm.
- Text Book No specific book, but the book by
Ferziger and Peric is worth purchasing and
reading. - Class notes will be distributed as appropriate.
6Course Organization
- Project based approach.
- Students will develop / use projects to learn and
apply CFD. - Each project can take two to three weeks
depending on complexity. - There will be a total of 6 projects that graduate
students need to complete. Undergraduate
students will not do the final project. One
student per project. Help will be given during
the projects. - Grade will be assigned based on successful
completion of the projects.
7My Pledge
- I will try to make the course interesting,
beneficial and intellectually challenging - I will explain the material to the best of my
ability and give you a clear perspective of the
fundamentals as well as the applications - I will make myself available to you for answering
questions and helping in the completion of
projects
8My expectations from you
- Regular attendance in the class
- Punctual submission of assignments
- Attention in the class
- Benefit from frequent interactions
- Ask any questions whenever needed
9Tentative List of Projects
- 1. Solution of two-dimensional unsteady heat
conduction equation - 2. Solution of two-dimensional steady heat
conduction equation - 3. Solution of scalar transport equation (with
convective terms) - 4. Boundary layer flow over a flat plate
- 5. Two-dimensional unsteady recirculating flow
- 6. Application of a commercial CFD code.
10Grading
- Grading will be based on the projects and one
presentation. - 5 projects will be worth 75 points 25 points for
final project presentation and report. - Final letter grade will be based on points scored
on a curve. - Each project should be accompanied by a report
and code/results from commercial code. - Help on projects will be provided during office
hours.
11Grading
- To balance course work loads and previous
academic experiences, for undergraduate students,
the projects will be based on use of a commercial
code (Fluent/Ansys). Graduate students should
write their own codes, and will be graded
separately. - Undergraduate students need not complete the
final project if they are enrolled for 3 credit
hours. The last project is worth 1 credit hr.
12Fluid Mechanics (Mechanics of Fluids)
- Statics and Dynamics
- Statics useful in estimating forces and stresses
on earthen dams, tankers, sluice gates, etc.
Relatively easy to compute. Based on pressure
variation with depth. - Dynamics may be the most complex branch of
science. Nonlinear interactions lead to complex
phenomena such as three-dimensionality, chaos and
turbulence.
13Fluid Flow is Omnipresent
- Pumping of blood by the heart
- Circulation of blood and nutrients in the body
- Convective mass exchange in various organs
- Water flow in piping systems and rivers, canals,
seas - Atmospheric circulations, weather patterns
- Combustion of gases, vehicle propulsion
- Space and aeronautics
- Chemical processing, heat transfer,
- Etc.
14(No Transcript)
15Example Demonstrations
- Light an incense stick and observe the rising
incense smoke. Observe the transition from a
smooth flow to a unsteady and eventually
turbulent flow - Watch the flow of water in a river with some
rocks. Observe the complex patterns behind the
rock, and the stagnation of flow ahead of the
rock - Light a match stick and observe the flame
- Mix a colored dye in a beaker of water and
observe the propagation of the dye and the small
structures
16Computational Fluid Dynamics (CFD)
- Complimentary technique to experimental fluid
dynamics and theoretical fluid dynamics - Has become attractive because of rapid
development of computing technology - Several advantages over real-life experiments
- Cost, Speed, Feasibility, Accessibility,
Convenience
17CFD-Issues
- Several important issues
- Accuracy
- Scale resolution
- Representation of all physical processes through
mathematical models - Code validation and uncertainty
- Is it only colorful fluid dynamics ?
18Governing Equations of Fluid Flow
19Complexities of Fluid Flows
- Multi-dimensional
- Steady / Transient
- Compressible / incompressible
- Chemically reacting
- Newtonian / Non-Newtonian
- May contain external forces (magnetic , electric
fields, surface tension, buoyancy, etc.)
20Computational Methodologies
- Finite-Difference Methods (x)
- Finite Volume Methods (x)
- Finite Element Methods (x)
- Spectral Methods (x)
- Spectral Element Methods (x)
- Vortex Methods
- Boundary Element Methods
- Lattice Boltzmann Methods (x)
21Finite Difference Method
- Each derivative in the differential equation is
first expressed in the form of a relation
(stencil) between discrete values of the variable
on a grid (rectangular, curvilinear, triangular,
etc.) - The discrete equations for each derivative are
derived using Taylor series expansions of the
continuous variable
22Finite Difference Method
- The accuracy of the solution depends on how the
expansion is truncated - The error is determined by the leading term that
has been truncated (first order, second-order,
fourth order schemes are commonly used) - Stability and convergence are important
requirements of the finite difference method
23Finite Volume Method
- Finite Volume Method is based on conservation
principles. Each relevant dependent variable is
conserved over discrete volumes. For example,
mass, momentum per unit mass, energy, species,
are conserved quantities, which are expressed as
balances over discrete control volumes
24Finite Volume Method
- The finite volume method can be seen as directly
related to how the basic governing equations were
initially derived. The discrete relations also
assume some polynomial variation of variables
between the locations where they are computed - The quantities computed by the finite volume
method are cell averages not point values
25Finite Difference / FVM
- Both finite difference method and finite volume
method satisfy the governing equation at each
discrete location / control volume to the level
of solution accuracy - The error in the discrete solution from the
continuous solution is a combination of
discretisation error and solution error
26Evolution of Computing Power
Since the 1950s computing power has increased
dramatically. In 1968, I used the IBM 1620
computer, which probably was slower than a hand
held calculator of current time. Input was
typically through punched cards and output was in
paper. Most computers were at data centers, and
one had to pay for computing power in real
dollars. The availability of personal computers
and the graphics based use made the computers
more user friendly and powerful. Simultaneously,
the chip in the computer has continually become
more powerful
27Evolution of Computing Power
Advances in processor speed are correlated well
with Moores law by which processor speed doubles
every 18 months. This has happened until now, but
can be challenged in future due to heating
considerations Another advance in computing speed
has been the development of parallel computers.
Consider networking hundreds of small computers
to make one big calculation. Each small computer
performs calculations on limited data and then
exchanges results with other processors. The end
result is an increase in computational speed
equivalent to number of processor times the
single processor speed
28Evolution of Computing Power
Personal Computers can perform calculations at a
few GFLOPS (Giga Floating Point
Operations) Networked PCs can increase the
performance ten fold or more NCSA has clusters
that can deliver teraflop speeds We are now
expecting Peta Flops from a recently funded NSF
center (Blue Waters) Simultaneously we now have
significant increases in RAM (random access
memory)
29Advances in Scientific Visualization
In my graduate school days, I had to make plots
by hand by joining the dots by a French curve,
trace them on transparent paper by India ink,
and then copy into a thesis. There were no color
printers, CDs, USB devices or WYSIWYG screens. In
current days, you have LCD screens on your
computers, beautiful animation software, and
inexpensive color printers, storage devices,
etc. THE FUTURE IS YET TO COME !!!
30Selection of GRID
Several types of grids can be used Cartesian
(x-y-z) grids Triangular / quadrilateral/tetrahed
ral elements Curvilinear grids Grid-less
(meshless) methods do not need a grid Vortex
methods also do not need a grid Accuracy depends
on the type of grid (grid quality) and the number
of mesh points/elements Mesh generation time is
usually quite large for a complex industrial
problem
31Selection of Numerical Parameters
The numerical parameters are Steady or time
marching algorithm Time of integration and time
step Numerical relaxation parameters Number of
iterations, parameters in the solvers Turbulence
constants, and constants in the combustion
model
32Some Examples
33Natural Convection in Enclosures
Velocity vectors and temperature contours for
natural convection in a square cavity, (a) Ra
104. and (b). Ra 105
34Natural Convection in Enclosures
(b)
(a)
Velocity vectors and temperature contours for
natural convection in a square cavity with a
cylinder, (a). Pr 0.71, Ra 105. and (b).
Pr 0.71, Ra 106
35Three Dimensional Natural Convection
Natural convection in a "green house" with bottom
wall maintained at T 1.0 and all other walls
at T 0. Vector color corresponds to fluid
temperature.
36- Rayleigh-Taylor instabilities (Re1024)
Density contours
37Buoyancy-Induced Mixing in Tilted Channel
38Mixing in a Curved Duct
39Mixing in a Curved Duct
40Turbulent Flow in a Circular Pipe, Re (tau) 400
40
41Instantaneous Fields in a Square Duct
41
42Lagrangian Particle Tracking
St 5.0
St 0.3
St 0.1
43Wavy Channel Flow
- Rush et al. (1999) observed mixing and heat
transfer characteristics of developing flow in
serpentine and wavy channels
44Wavy Channel Flow
- Stone and Vanka (1999) numerically simulated
developing flow and heat transfer in a wavy
channel.
45Some Good Websites
http//www.cfd-online.com/ http//www.cfd-online.c
om/Wiki/Codes http//www.fluent.com/ http//www.la
nl.gov/orgs/t/t3/codes.shtml Google CFD