Last Updated: 11/19/07
University of Virginia
School of Engineering
Department of Mechanical & Aerospace Engineering
Computational Fluid
Dynamics & Heat Transfer I/Projects
Spring 2008 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.
