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Boundary Conditions and Initial Value Lines for Unsteady Homentropic Flow Calculations

Published online by Cambridge University Press:  07 June 2016

W. A. Woods  and
H. Daneshyar
W. A. Woods
Affiliation:
University of Liverpool
H. Daneshyar
Affiliation:
Cambridge University
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Summary

A detailed discussion on the difference between an initial value line and a line characterised by a boundary condition has been presented. Two types of boundaries are described and illustrated. To examine each boundary, several different calculations have been performed for a straight pipe. The results of the numerical calculations are compared with an analytical solution. It is shown that known pressure and velocity at the pipe ends give the most accurate results. Comparisons are also made between several practical types of calculations which give similar findings. The use of time-dependent boundaries can lead to errors as large as 40 per cent in derived results. It is shown that good accuracy can be restored by converting the boundaries into initial value lines. It is concluded that in general no more than one time-dependent boundary should be used in any calculation. Finally it is demonstrated that errors are not revealed by means of pressure diagrams alone.

Type
Research Article
Information
Aeronautical Quarterly , Volume 21 , Issue 2 , May 1970 , pp. 145 - 162
Copyright
Copyright © Royal Aeronautical Society. 1970

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References

1. Courant, R. and Friedrichs, K. O. Supersonic flow and shock waves. Interscience Publishers, New York, 1948.Google Scholar
2. Shapiro, A. H. The dynamics and thermodynamics of compressible fluid flow. Ronald Press, New York, 1953.Google Scholar
3. Stanyukovich, K. P. Unsteady motion of continuous media. Pergamon Press, 1960.Google Scholar
4. Woods, W. A. Wave action in the exhaust system of a supercharged two-stroke cycle engine model. PhD. Thesis, University of Liverpool, 1957.Google Scholar
5. Smith, F. Theory of a two-stage hypervelocity launcher to give constant driving pressure at the model. Journal of Fluid Mechanics, Vol. 17, Pt. 1, pp. 113–125, 1963.CrossRefGoogle Scholar
6. Hoskin, N. E. Methods in computational physics. Vol. 3 p. 265. Academic Press, New York and London, 1964.Google Scholar
7. Benson, R. S., Garg, R. D. and Woollatt, D. A numerical solution of unsteady problems. International Journal of Mechanical Sciences, Vol. 6 p.117, 1964.CrossRefGoogle Scholar
8. Benson, R. S., Garg, R. D. and Woods, W. A. Unsteady flow in exhaust pipes with gradual or sudden changes in cross-section. Proceedings, Institution of Mechanical Engineers, Vol. 178, Pt. 3 p.1, 1963-4.Google Scholar
9. Benson, R. S., Woollatt, D. and Woods, W. A. Unsteady flow in simple branch systems. Proceedings, Institution of Mechanical Engineers, Vol. 178, Pt. 3 p. 24, 1963-4.Google Scholar
10. Manning, J. R. Computerised method of characteristics calculations for unsteady pneumatic line flows. American Society of Mechanical Engineers, Journal of Basic Engineering, 1968.Google Scholar
11. Woods, W. A. Tests to examine high pressure pulse charging on a two-cycle Diesel engine. American Society of Mechanical Engineers, Paper 66-DGEP-4, pp. 1–16, 1966.Google Scholar
12. Woollatt, D. Unsteady flow in branched systems. Ph.D. Thesis, University of Liverpool, 1962.Google Scholar