**Last Updated: 6/14/2018**

**Solution of Blasius Equation ****(Updated: 3/2/2018)**

This
workbook performs a numerical solution of the Blasius equation for flow in a
laminar, self-similar, flat plate boundary layer. The Runge-Kutta
integration scheme and shooting algorithm used to solve this third-order,
non-linear, ordinary differential equation were taken from *An Introduction
to Computational Fluid Mechanics* by C.Y. Chow and embellished with Excel
graphics. In the 5/11/04 version tabulated results from a classical source (Howarth's results as reported in Schlicting)
were added for comparison with the current solution.

**Advection
of a Passive Scalar in One and Two Dimensions ****(Updated: 3/20/2018) **

This
workbook is intended for use as demonstrations in an introductory course in Computational Fluid Dynamics
and Heat Transfer at the introductory graduate and advanced undergraduate
level. It consists of two sheets. On the first one the user can select one of
five separate differencing schemes for the transient, one-dimensional advection
equation and input the Courant number. Numerical diffusion and dispersion are
vividly illustrated as the initially-square wave is advected
across the plot. Differencing schemes included are simple upwind, weighted
upwind, Quick (third order), Flux-corrected Transport (FCT) and Total Variation
Diminishing (TVD).

The second sheet demonstrates use of the upwind and weighted
upwind schemes in two dimensions. A cone representing a passive scalar is advected for one orbit in a velocity field corresponding to
solid body rotation. The resulting distribution is plotted at 22.5^{o}
intervals so as to give the effect of animation.

**Projectile Motion with Air Resistance ****(Updated: 3/14/2018) **

**Elliptic
Grid Generation ****(Updated:
3/20/2018) **

**One-Dimensional Compressible Flows
****(Updated: 3/14/2018) **

This
first workbook includes worksheets for: (1) Isentropic flow with area change,
(2)

The
second workbook is for oblique, planar shocks. The user will have to become familiar
with Excel’s Solver Add-in in order to use this workbook.

**Vortex Panel Method (Updated:
3/6/2018) **

This
workbook implements the vortex panel method for a lifting airfoil. It closely follows the algorithm
in Kuethe and Chow (1986).

**Vortex Motion above a Runway ****(Updated: 3/6/2018) **

This spreadsheet is an Excel/VBA translation
of a Fortran program from C.Y.Chow's *An
Introduction to Computational Fluid Mechanics*. The program tracks the
motion of wingtip vortices and shows their motion as induced by each other and
influenced by the nearby ground and the ambient crosswind. The user can change
the crosswind speed, wingspan, mass of the aircraft and aircraft velocity and
watch the impact on the subsequent motion of the vortices. The simple model
includes no dissipation of the vortices, but it is well
known that trailing vortices may be long-lived and dangerous to following
aircraft.

**1976 U.S. Standard
Atmosphere ****(Updated:
3/20/2018) **

This
spreadsheet calculates the temperature, pressure and density corresponding to
the 1976 U.S. Standard Atmosphere. The user can input any altitude and the
three values are returned. Plots like that seen below for temperature are
provided for pressure and density as well. The basics are covered in this slide show.

**One-dimensional Wave Equation ****(Updated: 4/3/2018) **

This
spreadsheet applies a 3-time-level differencing scheme to the one-dimensional,
linear wave equation. The user can watch the time dependence of the wave as a
function of spatial position or can see the complete transient as a function of
space and time as seen in the contour plot below. The user can choose the
Courant number to give an exact solution, a solution demonstrating numerical
dispersion or a solution demonstrating a numerical instability. The algorithm
is from *An Introduction to Computational Fluid Mechanics* by C.Y. Chow.

**Velocity Triangles for Turbomachinery
****(New 6/4/2018) **

This spreadsheet uses vectors available in
Excel’s drawing tools for the numerical/graphical analysis of a single
stage of an axial flow compressor.
You merely need to set up array of four cells holding the x and y coordinates
of the head and tail of each vector you wish to display.

**HTTdemosub.xlsm
A spreadsheet demonstrating a lot of features of Excel and VBA (Updated
3/7/2018) **

** **This one includes buttons, scrollbars,
functions, subroutines, named ranges and even narration.

**General Reference on Use of
VBA with Excel (VBAPrimer.pdf) – Updated
6/4/2018:**

Ribando,
R.J., "An Excel/Visual Basic for Applications (VBA) Primer," *Computers
in Education Journal*, Vol. VIII, No. 2, April-June 1998, pp. 38-43. A
version of this article updated for Excel 2007 and newer may be found here.

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