Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-13T06:37:42.110Z Has data issue: false hasContentIssue false
  • English
  • Français

Quantifying non-linearity in planar supersonic potential flows

Published online by Cambridge University Press:  18 January 2017

M.-C. Meijer ,
L. Dala  and
L. Dala
M.-C. Meijer*
Affiliation:
University of Pretoria, Department of Mechanical and Aeronautical Engineering, Pretoria, South Africa
L. Dala
Affiliation:
University of Pretoria, Department of Mechanical and Aeronautical Engineering, Pretoria, South Africa
L. Dala
Affiliation:
Council for Scientific and Industrial Research, Aeronautics Systems, Pretoria, South Africa
*
mariuscmeijer@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

An analysis is presented which allows the engineer to quantitatively estimate the validity bounds of aerodynamic methods based in linear potential flows a-priori. The development is limited to quasi-steady planar flows with attached shocks and small body curvature. Perturbation velocities are parameterised in terms of Mach number and flow turning angle by means of a series-expansion for flow velocity based in the method of characteristics. The parameterisation is used to assess the magnitude of non-linear term-groupings relative to linear groups in the full potential equation. This quantification is used to identify dominant nonlinear terms and to estimate the validity of linearising the potential flow equation at a given Mach number and flow turning angle. Example applications include the a-priori estimation of the validity bounds for linear aerodynamic models for supersonic aeroelastic analysis of lifting surfaces and panels.

Type
Research Article
Information
The Aeronautical Journal , Volume 121 , Issue 1237 , March 2017 , pp. 372 - 394
Copyright
Copyright © Royal Aeronautical Society 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Dowell, E.H. and Bliss, D.B. New look at unsteady supersonic potential flow aerodynamics and piston theory, AIAA JJournal, 2013, 51, (9), pp 2278–2281. doi: 10.2514/1.J052088 Google Scholar
2. Jameson, A. Re-engineering the design process through computation, J Aircr, 1999, 36, (1), pp 36–50.CrossRefGoogle Scholar
3. Meijer, M.-C. and Dala, L. On the validity range of piston theory, 16th International Forum on Aeroelasticity and Structural Dynamics, 28 June - 2 July 2015, Saint Petersburg, Russia.Google Scholar
4. Donov, A.E. A flat wing with sharp edges in a supersonic stream, 1956, Washington, DC.Google Scholar
5. Cole, J.D. Acceleration of slender bodies of revolution through sonic velocity, 1954, Pasadena, CA.Google Scholar
6. Hilton, W.F. Limitations of the use of Busemann’s second-order supersonic aerofoil theory, 1952, London.Google Scholar
7. Busemann, A. Aerodynamic lift at supersonic speeds, Luftfahrtforschung, 1935, 12, (6), pp 210–220.Google Scholar
8. Anderson, J.D. Fundamentals of Aerodynamics, 5th ed, 2011, McGraw-Hill, London, UK, p 641.Google Scholar
9. Pai, S.-I. Introduction to the Theory of Compressible Flow, 1959, D. Van Nostrand Company, London, UK, p 52.Google Scholar
10. Mascitti, V.R. A closed-form solution to oblique shock-wave properties, J Aircr, 1969, 6, (1), p 66.Google Scholar
11. Van Dyke, M.D. A study of second-order supersonic flow theory, 1952, Washington, DC.Google Scholar