Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T15:01:09.612Z Has data issue: false hasContentIssue false
  • English
  • Français

A General One-Dimensional Theory of Compressible Inviscid Swirling Flows in Nozzles

Published online by Cambridge University Press:  07 June 2016

P W Carpenter
P W Carpenter*
Affiliation:
University of Exeter
Get access

Summary

An approximate analytical method is presented for determining the swirling compressible flow through a nozzle. The method is developed from the techniques introduced by Carpenter and Johannesen. It is perfectly general in that the swirl distribution need not be specified a priori but the radial gradients of the stagnation enthalpy and entropy are assumed to be small. The principal assumption is that changes in the nozzle cross-sectional area are sufficiently gradual and smooth for the radial velocity component to be neglected at each section, i e the usual assumption of one-dimensional compressible flow theory. Analytical expressions are derived for various flow characteristics, e g mass-flux coefficient, impulse function and back-pressure ratio required for choking. The analytical results are compared to numerical results for two main classes of swirling flows. On the whole the analytical results are found to be good approximations for moderate swirl levels. The approximate numerical method is found to be reasonably successful at predicting flow reversal at the nozzle wall. The main result is that a swirl parameter is found such that, with the sole exception of the free-vortex case, the mass-flux-coefficient data for all swirling flows investigated collapse onto a single curve.

Type
Research Article
Information
Aeronautical Quarterly , Volume 27 , Issue 3 , August 1976 , pp. 201 - 216
Copyright
Copyright © Royal Aeronautical Society. 1976

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

1 Carpenter, P W Johannesen, N H An extension of one-dimensional theory to inviscid swirling flow through choked nozzles. Aeronautical Quarterly, Vol 26, p 71, May 1975.Google Scholar
2 Chernyi, G G Swirling now of a compressible gas in ducts (in Russian). Izvestia Akademiya Nauk SSSR, Otdel Tekh Nauk No 6, p 55, 1956.Google Scholar
3 Lewellen, W S Burns, W J Strickland, H J Transonic swirling flow. AIAA Journal, Vol 7, p 1290, 1969.Google Scholar
4 Slavianov, N N Theoretical investigation of swirling flow for an ideal gas through a Laval nozzle (in Russian). Izvestia Akademiya Nauk SSSR, Mekh Zhidk Gaza No 6, p 85, 1973.Google Scholar
5 Hsu, C T DeJoode, A D Inviscid swirling flows through a choked nozzle. AIAA Journal, Vol 11, p 1564, 1973.Google Scholar
6 Mager, A Approximate solution of isentropic swirling flow through a nozzle. American Rocket Society Journal, Vol 31, p 1140, 1961 Google Scholar
7 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
8 Chigier, N A Chervinsky, A Experimental investigation of swirling vortex motion in jets. Journal of Applied Mechanics, ASME Transactions, Vol 34E, p 443, 1967.Google Scholar
9 Maier, P Untersuchung isothermer drallbehafteter Freistrahlen. Forschung, Vol 34, p 133, 1968.Google Scholar
10 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
11 Dunlap, R An investigation of the swirling flow in a spinning end-burning rocket. AIAA Journal, Vol 7, p 2293, 1969.Google Scholar
12 Rychkov, AD Calculations of the swirling outflow of an ideal gas in a Laval nozzle (in Russian). Izvestia Akademiya Nauk SSSR, Mekh Zhidk Gaza No 5, p 72, 1971.Google Scholar