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An Extension of One-Dimensional Theory to Inviscid Swirling Flow through Choked Nozzles

Published online by Cambridge University Press:  07 June 2016

P W Carpenter  and
N H Johannesen
P W Carpenter
Affiliation:
Department of the Mechanics of Fluids, University of Manchester
N H Johannesen
Affiliation:
Department of the Mechanics of Fluids, University of Manchester
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Summary

A method is presented for determining the swirling compressible flow through a nozzle, given conditions at a reference section. The principal assumption is that changes in the nozzle cross-sectional area are sufficiently gradual for the radial velocity component to be neglected at each section, i e, the usual assumption of one-dimensional compressible flow theory. This method is used to determine choked-flow conditions in the case where there is solid-body rotation at the throat for a range of swirl intensities with the ratio of the specific heats taking various values. Mass-flux coefficients and impulse functions are determined. Sonic surfaces, velocity profiles and other characteristics of interest are also presented. An approximate analysis valid for low swirl intensities is developed and analytical formulae are derived for most quantities of interest. The main conclusion of practical importance is that the introduction of swirl to compressible nozzle flows need not lead to a significant reduction in specific thrust. Further exploration of the possible effects of swirl on noise during the relatively short take-off and landing periods cannot therefore be ruled out on the grounds that swirl would lead to excessive thrust losses.

Type
Research Article
Information
Aeronautical Quarterly , Volume 26 , Issue 2 , May 1975 , pp. 71 - 87
Copyright
Copyright © Royal Aeronautical Society. 1975

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References

1 Gostintsev, Yu A et al On the structure of a supersonic swirling gas jet with underexpanded outflow (in Russian). Izv Akad Nauk SSSR, Mekh Zhidk Gaza, No 5, p 158, 1969.Google Scholar
2 Smith, R An investigation of supersonic swirling jets. Aeronautical Quarterly, Vol 24, p 167, 1973.Google Scholar
3 Mager, A Approximate solution of isentropic swirling flow through a nozzle. American Rocket Society Journal, Vol 31, p 1140, 1961.Google Scholar
4 Swithenbank, J Sotter, G Vortex generation in solid propellant rockets. AIAA Journal, Vol 2, p 1297, 1964.Google Scholar
5 Glick, R L Kilgore, M S Effect of specific-heat ratio on mass flow for swirling nozzle flow. Journal of Spacecraft and Rockets, Vol 4, p 1098, 1967.Google Scholar
6 Bastress, E K Interior ballistics of spinning solid-propellant rockets. Journal of Spacecraft and Rockets, Vol 2, p 455, 1965.Google Scholar
7 Manda, L J Spin effects on rocket nozzle performance. Journal of Spacecraft and Rockets, Vol 3, p 1695, 1966.Google Scholar
8 King, M K Comment on “Spin effects on rocket nozzle performance”. Journal of Spacecraft and Rockets, Vol 3, p 1812, 1966.CrossRefGoogle Scholar
9 Manda, L J Reply by author to M King. Journal of Spacecraft and Rockets, Vol 3, p 1813, 1966.Google Scholar
10 Hsu, C-T Mass blocking of swirling flow in nozzles. Journal of Spacecraft and Rockets, Vol 8, p 1232, 1971.Google Scholar
11 Lewellen, W S Burns, W J Strickland, H J Transonic swirling flow. AIAA Journal, Vol 7, p 1290, 1969.Google Scholar
12 Norton, D J Farquhar, B W Hoffman, J D An analytical and experimental investigation of swirling flow in nozzles. AIAA Journal, Vol 7, p 1992, 1969.Google Scholar
13 Gostintsev, Yu A The output characteristics of a nozzle issuing spiralling gas flow (in Russian). Izv Akad Nauk SSSR, Mekh Zhidk Gaza, No 4, p 153, 1969.Google Scholar
14 Caldonazzo, B Moti elicoidale simmetrici ad un asse di liquidi viscosi. Rendiconte del Reale Instituto Lombardo, Ser II, Vol 59, p 657, 1926.Google Scholar
15 King, W S On swirling nozzle flows. Journal of Spacecraft and Rockets, Vol 4, p 1404, 1967.Google Scholar
16 Hsu, C-T Swirling nozzle flow equations from Crocco’s relation. AIAA Journal, Vol 9, p 1866, 1971. (See also Vol 10, p 368, 1972.)Google Scholar
17 Moore, A W Transonic flows in nozzles of arbitrary shape and swirling flows in nozzles and jets. PhD thesis, University of Manchester, 1964.Google Scholar
18 Smith, R An investigation of the effects of swirl on some flows at transonic, supersonic and hypersonic speeds. PhD thesis, University of Manchester, 1971.Google Scholar
19 Hall, I M Transonic flow in two-dimensional and axially symmetric nozzles. Quarterly Journal of Mechanics and Applied Mathematics, Vol 15, p 487, 1962.Google Scholar
20 Boerner, C J Sparrow, E M Scott, C J Compressible swirling flow through convergent-divergent nozzles. Wärme- und Stoffübertragung, Vol 5, p 101, 1972.Google Scholar
21 Guderley, K G Breiter, M C Approximation for swirl flows in the vicinity of the throat of a Laval nozzle. Aerospace Research Laboratories Report ARL 70-0009, 1970.Google Scholar
22 Rychkov, A D Calculations of swirling outflow of an ideal gas in a Laval nozzle (in Russian). Izv Akad Nauk SSSR, Mekh Zhidk i Gaza, No 5, p 72, 1971.Google Scholar
23 Beltrami, E Considerazioni idrodinamiche. Rendiconte del Reale Instituto Lombardo, Ser II, Vol 22, p 121, 1889.Google Scholar
24 Batchelor, G K An Introduction to Fluid Dynamics. Cambridge University Press, 1967.Google Scholar
25 Truesdell, C The Kinematics of Vorticity. Indiana University Press, 1954.Google Scholar
26 Dunlap, R An investigation of the swirling flow in a spinning end-burning rocket. AIAA Journal, Vol 7, p 2293, 1969.Google Scholar
27 Long, R R Sources and sinks at the axis of a rotating liquid. Quarterly Journal of Mechanics and Applied Mathematics, Vol 9, p 387, 1956.Google Scholar
28 Guderley, K G Breiter, M C On the determination of optimum supersonic throat nozzles of given length for a flow with swirl: Numerical results. Aerospace Research Laboratories Report ARL 70-0161, 1970.Google Scholar
29 Guderley, K G Tabak, D On the determination of optimum supersonic thrust nozzles of given length for a flow with swirl: Theoretical part. Aerospace Research Laboratories Report ARL 66-0013, 1966.Google Scholar
30 Naumova, I N Shmyglevskii, Yu D Augmentation of nozzle thrust with swirling flow (in Russian). Izv Akad Nauk SSSR, Mekh Zhidk i Gaza, No 1, p 34, 1967.Google Scholar
31 Gostintsev, Yu A Iliukhin, V C Pokhil, P F Concerning a zone of reversed flow in strongly swirled supersonic gas flows and jets (in Russian). Inzhenerno-Fizicheskii Zhurnal, Vol 20, p 1036, 1971.Google Scholar