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 22.5o 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)
first workbook includes worksheets for: (1) Isentropic flow with area change,
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.