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Axisymmetric Minimum Length Nozzle Design Tool

version 1.0.2 (181 KB) by Ludovico Fossà
Computes the contour of the divergent section of an axisymmetric minimum length nozzle for a perfect gas (irrotational flow).


Updated 15 Jan 2021

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This function computes the divergent section of an axisymmetric minimum length nozzle for a perfect gas (inviscid, compressible, irrotational flow). The kernel and transition regions are computed using the axisymmetric method of the characteristics. A normal sonic line is assumed at the throat.
The function requires as input:
- the exit Mach number (>1, supersonic);
- the heat capacity ratio (gamma=cp/cv);
- the number of characteristics (integer >0) in the linear kernel region;
- the number of characteristics (integer >0) in the compressed region downstream of the throat (x=0). When equal to one, the compression region is not resolved;
- the exponent of the power-law that defines the characteristics in the compressed region;
- maximum tolerance (residuals)
- aspect ratio of the mesh in the transition region (usually close to 1)
The function outputs a non-dimensional plot. Lengths are normalized to the throat radius. The code stores the coordinates of the contour points in a .txt file.

The code is based on the following references:
[1] J.D. Anderson. Modern Compressible Flow: With Historical Perspective. Aero-
nautical and Aerospace Engineering Series. McGraw-Hill Education, 2003 (Library of Congress CN: 2002067852)
[2] B. M. Argrow and G. Emanuel. Comparison of Minimum Length Nozzles. Journal of Fluids Engineering, 110(3):283-288, 09 1988.
[3] Kuno Foelsch. The analytical design of an axially symmetric Laval nozzle for a
parallel and uniform jet. Journal of the Aeronautical Sciences, 16(3):161-166,
[4] Ying-Nien Yu. A summary of design techniques for axisymmetric hypersonic
wind tunnels. Technical report, NATO - Science and Technology Organization,

Cite As

Ludovico Fossà (2021). Axisymmetric Minimum Length Nozzle Design Tool (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (2)

Ludovico Fossà

Hello Ibrahim, I wrote a function called area_mach_nozzle.m which I sometimes used to check and compare the results. However, the line you're referring to should be commented. If it is uncommented, please comment it. The function area_mach_nozzle.m is not necessary to run the program. Hope this helps!
However, I'll "clean" the code and remove commented lines in the next update. Thanks for reaching out!

ibrahim zengin

Is it only compatible with matlab 2020b version? When I open it with 2017 version, it doesn't see the area_mach function as defined. Is it because I am opening it with 2017?

MATLAB Release Compatibility
Created with R2020b
Compatible with R2020b
Platform Compatibility
Windows macOS Linux

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