VuCalc is based on a program of the same name written by Tom Benson of NASA Glenn as an aid to making calculations in compressible fluid dynamics. There are six screens, each of which performs a different class of calculations.
| Isentropic Flow | Oblique Shock | Rayleigh Flow |
| Normal Shock | Standard Atmosphere | Fanno Flow |
The isentropic flow page enables the user to calculate
the total temperature ratio, total pressure ratio,
total density ratio, area ratio, Mach angle and
Prandtl-Meyer function for any Mach number.
In addition, the values of any one of these quantities
may be specified and VuCalc will solve for the corresponding
Mach number and the remaining quantities.
Screen Shot
The ratios of downstream to upstream values of various
quantities may be computed for any Mach number.
As with the isentropic flow page, the value of any flow
parameter may be specified and VuCalc will calculate the
corresponding Mach number and all other quantities.
Screen Shot
The oblique shock problem has an additional degree of freedom
in specifying the problem.
In this case, the user supplies the upstream Mach number and one
of the following variables: ramp angle, wave angle,
total pressure ratio, static pressure ratio, temperature ratio,
density ratio or downstream Mach number.
The other variables will then be computed and displayed.
Of course, there are many cases for which there is no
solution with an attached shock.
Screen Shot
A flight condition in the standard atmosphere is specified by the
altitude and Mach number.
For these conditions, the values of velocity, temperature, density,
pressure, speed of sound, unit Reynolds number, viscosity,
dynamic pressure are computed and displayed.
SI or US units may be used for input.
When switching between SI and US units, the previous case is
remembered and the appropriate values are shown for the other
set of units.
Screen Shot
The flow condition known as Rayleigh Flow assumes
that the flow is in a constant-area duct without friction
but with heat transfer.
This type of flow turns out to be a good approximation of
heat exchangers and of constant-area combustion chambers
such as is typical of gas turbines.
Typical tables of Rayleigh Flow show ratios of various
thermodynamic flow quantities at a given Mach number to the
value of this same quantity at a Mach number of 1.0 with
the flow modified by heat transfer without friction.
Typical quantities are static temperature, total temperature,
static pressure, total pressure, density, and velocity.
As on the other pages, one may select a given value of any
flow parameter and command VuCalc to compute the coressponding
Mach number as well as the remaining flow parameters.
Screen Shot
Fanno flow assumes flow in a constant-area duct with friction
but without heat transfer.
As on the other pages, one may select a given value of any
flow parameter and command VuCalc to compute the coressponding
Mach number as well as the remaining flow parameters.
Screen Shot
The program may be used as supplied, but because the source code is included, the functions that compute the flow quantities are available for inclusion in your own computing projects. The flow ratios in terms of Mach number are straightforward codings of the equations in NACA Report 1135 or any gas dynamics textbook. The inverse relations can sometimes be solved by algebraic manipulation, but must be computed by numerical root finding in others.
There is a similar
calculator
developed by
William Devenport of Virginia Tech.
Instead of being a Windows application (like VuCalc),
it is a Java applet that runs in your web browser, provided you
have a Java-enabled browser.
There is an interesting
supersonic airfoil page written by Evgeni Kudriavitski
that uses the oblique shock and Prandtl-Meyer expansion
functions to compute the inviscid aerodynamic force on a
wedge airfoil with attached shocks. It is very instructive to
reshape the wing or change the angle of attack and watch the
pressures and forces recompute. This is implemented as a
java applet and runs on your browser. He has made the applet
available for download, so you can run the applet even
if you are not connected to the web.
You may
download a copy (PDF, 12.9 MB) of NACA Report 1135 on Equations, Charts and
Tables for Compressible Flow
Go to the page of references for the Compressible Flow Calculator program.
