Last Updated: 1/15/2010
University of Virginia
School of Engineering
Department of Mechanical & Aerospace Engineering
Computational Fluid
Dynamics & Heat Transfer I/Projects
Spring 2010 Projects
Much of the course will focus on six or seven programs which students will be expected to develop and submit. Generally a subroutine or section of the code will be provided as a start, but by and large the student will be independently writing the majority of the program. All students will emerge from this course as good scientific/technical programmers. Projects may include:
- Superposition of Elementary Solutions. Students
are given functions for one or two of the four elementary functions and
will write the others. The streamfield due to the superposition of several
combinations of the elementary solutions will be computed on a rectangular
mesh and a plot of the computed values will be made using a contouring
package. A major goal of this assignment is to familiarize students with
whatever software
package they plan to use for the rest of the semester.
Heat
Transfer in a Self-similar Boundary Layer. Students will be given a VBA
program for a 4th order Runge-Kutta solution of the Blasius equation.
With the velocity distribution from that solution, they will solve the
energy equation in the boundary layer both with dissipation (aerodynamic
heating) and without. Another Excel/VBA program demonstrating the direct
solution of the resulting tridiagonal system of linear equations will be
provided. Detailed implementation instructions are given in
"pdf" form on the Heat Transfer Today
CD
Panel
Method for Ideal Flow Over an Airfoil. Students will implement the
vortex panel method for a 2-D airfoil. Some coding of geometric quantities
will be supplied. An Excel workbook that
generates and plots the coordinates for a particular airfoil will be
provided or the student may design his or her own shape. An online source
of coordinate data for over a thousand airfoils is also
available. The system of linear equations may be solved using subroutines
from the Linpack or Lapack
collection. The students will plot the computed pressure coefficient
versus position on the airfoil for several angles of attack and may want
to plot the streamlines as well. A
highly developed version of this 2-D panel method calculation created by a
former student and which includes the effects of boundary layers, a
separation criterion and capability for the user to design an airfoil to
meet his or her performance specifications may be downloaded from his website.
Solution of
Elliptic Equations. Students will solve for the velocity profile for
Hagen-Poiseuille flow in an oddly-shaped
cross-section and determine the resulting friction factor. This
problem may then be extended to handle non-Newtonian fluids. A simple
pointwise iterative method will be used initially, and students will be
encouraged to try one of the more advanced techniques for solving the
system of linear equations resulting from the discretization of elliptic
equations; sample implementations of several will be provided.
- Grid
Generation for Odd Geometries. Students will generate a
computational grid for an airfoil or other odd geometry using elliptic
methods. Some of the coding will be provided, and the elliptic equations
will be solved using an iterative method. The boundary-fitted grid will be
plotted. A DRAFT version of a
highly interactive workbook that uses elliptic methods (both Laplace and Poisson)
to generate a grid for a symmetric nozzle may be downloaded here.
- Thermal Entry Length Problem. Assuming a fully developed
(parabolic) laminar velocity profile in a cylindrical pipe, students will
solve for the temperature distribution resulting from a sudden change in
the wall thermal boundary condition. This parabolic problem results in a
tridiagonal system of equations at each axial location along the pipe,
which may be solved using an algorithm provided. The local Nusselt Number
(non-dimensional convective heat transfer coefficient) will be computed as
a function of the axial coordinate. Thorough implementation instructions
(for both laminar and turbulent flows) and a complete VB-6 program
implementing this project are included in Heat
Transfer Today.
- Driven Cavity Problem. This standard test problem of viscous
flow in a rectangular region driven by a sliding upper surface will be
solved using a time-marching, primitive variable (i.e., pressure, velocity
components) method. This problem involves both parabolic and elliptic
equations, and the algorithm is typical of
methods commonly used for low speed flows. The resulting velocity field
will be plotted, either as velocity vectors or as streamlines.
- Two-D Incompressible, Viscous, Buoyancy-Induced Flow in a Saturated
Porous Matrix. This final project involves a coupled system, including
one non-linear partial differential equation. The primitive variable
algorithm we will implement is typical of those embedded in commercial CFD
software. Thorough implementation instructions and a complete VB-6 program
implementing this project are included in Heat
Transfer Today. Equally complete instructions for completing the
same project using the alternative vorticity-streamfunction formulation
and for the closely-related problem of Rayleigh-Benard convection are
included as appendices on the HTT CD-Rom.
