Last Updated: 7/10/2018
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 those
described below. Click on the title
for the writeup.
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.
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 duct 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.
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 program implementing this
project are included in Heat Transfer
Today.
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 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.
