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Compressible swirling flow through convergent-divergent nozzles

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Abstract

The effects of swirl on the rate of mass flow and on the velocity field in the throat region of axi-symmetric nozzles are studied analytically and experimentally. In the analytical phase, methods are developed for treating either the direct or the inverse problem for flow in de Lavai and annular nozzles, taking account of either weak or strong swirl. The experiments were performed in an annular nozzle, with swirl being imparted to the flow by adjustable vanes situated upstream of the test section.

The analytical results facilitated an examination of the effects of swirl strength, distribution of swirl, and nozzle geometry. The rate of mass flow was found to decrease with increasing swirl strength. The mass flow results were well correlated by a swirl strength parameter evaluated at the throat, with swirl type and geometry being of secondary importance. Another effect of swirl was to shift the sonic line upstream of the geometric nozzle throat. The experimentally determined mass flow results were in agreement with the analytical predictions. Also, all of the qualitative characteristics of the local flow field measurements were reproduced by the analytical results.

Zusammenfassung

Der Einfluß einer Wirbelkomponente auf den Massenfluß und das Geschwindigkeitsfeld in dem Gebiet um den engsten Querschnitt von zylindersymmetrischen Düsen wird analytisch und experimentell untersucht. In dem analytischen Teil werden Methoden zur Behandlung sowohl des direkten als auch des inversen Problems der Strömung in Laval- und ringförmigen Düsen entwickelt, für entweder eine schwache, oder eine starke Wirbelkomponente. Die Experimente sind mit einer ringförmigen Düse durchgeführt worden, wobei die Rotation der Strömung durch verstellbare Flügel stromaufwärts der Versuchskammer erzeugt worden ist.

Die analytischen Ergebnisse erleichtern die Untersuchungen des Einflusses von Wirbelstärke, Verteilung des Wirbels und der Düsengeometrie. Die Ergebnisse zeigen, daß der Massenfluß abnimmt mit zunehmender Stärke der Wirbelkomponente. Die resultierenden Werte für den Massenfluß können gut durch einen Wirbelstärkenparameter korreliert werden, der für den engsten Querschnitt der Düse entwickelt wird. Die Art des Wirbels und die Düsengeometrie ist von untergeordneter Bedeutung. Ein weiterer Effekt der Wirbelkomponente ist die Verschiebung der Fläche, wo die Strömung die Machzahl 1 erreicht, in eine Position stromaufwärts der Stelle des geringsten Querschnitts. Die experimentell bestimmten Massenflüsse stimmen mit den theoretisch vorhergesagten überein. Ebenso sind alle qualitativen Merkmale der lokalen Strömungsfeldmessungen durch die analytischen Resultate reproduziert worden.

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Abbreviations

A:

cross sectional area

a:

sound speed

a* :

critical speed

H2 :

ratio,ρ *a*/pq

h:

enthalpy

h0 :

stagnation enthalpy

M* :

dimensionless velocity magnitude, (ũ2 + v2 + w2)1/2/a*

m:

ratio of mass flow with and without swirl

\(\widehat{\dot m}\) :

mass flow parameter, Eq. (61)

P:

proportionality function, Eq. (48)

p:

static pressure

q:

velocity vector in r, z plane, Eq. (50)

R:

radius of curvature of nozzle wall at geometrical throat

R:

dimensionless radius of curvature, Eq. (10)

r, rw, r* :

radial coordinate, wall radius, throat radius

r, rw :

dimensionless radial coordinate and wall radius, Eq. (10)

S:

swirl parameter, Eq. (60)

Ŝ:

swirl parameter, Eq. (61)

s:

entropy

T:

absolute temperature

ũ, v, w:

velocity components in radial, tangential, and axial directions

u, v, w:

dimensionless velocity components, Eq. (10)

x:

stream function, Eq. (47)

z:

axial coordinate

z:

dimensionless axial coordinate, Eq. (10)

γ :

ratio of specific heats

η, ξ :

scaled coordinates, Eq. (51)

'S :

generalized velocity potential, Eq. (48)

ρ :

density

ρ * :

density corresponding to a*

ψ :

stream function

R:

reference streamline

References

  1. Boerner, C. J.: Compressible Swirling Flow through Nozzles. Ph.D. Thesis, Dec. 1970, University of Minnesotta, Minneapolis, Minn.

    Google Scholar 

  2. Norton, D. J., Farquhar, B. W., Hoffman, J. B.: An Analytical Investigation of the Fluid Mechanics of Rotating Flows in Rocket Motors. TM-67-7, Oct. 1967, Jet Propulsion Center, Purdue University, Lafayette, Ind.

    Google Scholar 

  3. Norton, D. J., Farquhar, B. W., Hoffman, J. B.: An Analytical and Experimental Investigation of Swirling Flow in Nozzles. F-67-9, Oct. 1967, Jet Propulsion Center, Purdue University, Lafayette, Ind.

    Google Scholar 

  4. Lewellen, W. S., Burns, W. J., Strickland, H. J.: Transonic Swirling Flow. AIAA Journal 7, No. 7 (1969) 1290/1297.

    Google Scholar 

  5. King, W. S.: On Swirling Nozzle Flows. Journal of Spacecraft and Rockets 4, No. 10 (1967) 1404/1405.

    Google Scholar 

  6. Manda, L.: Spin Effect on Rocket Nozzle Performance. Journal of Spacecraft and Rockets 3, No. 12 (1966) 1695/1696.

    Google Scholar 

  7. King, M. K.: Comment on Spin Effect on Rocket Nozzle Performance. Journal of Spacecraft and Rockets 3, No. 12 (1966) 1812/1813.

    Google Scholar 

  8. Bastress, E. K.: Interior Ballistics of Spinning Solid Propellant Rockets. Journal of Spacecraft and Rockets 2, No. 3 (1965) 455/457.

    Google Scholar 

  9. Hall, M. G.: The Structure of Concentrated Vortex Cores. In Progress in Aeronautical Sciences, D. Küchemann, ed., Vol. 7, Pergamon Press, Oxford (1966) 53/110.

    Google Scholar 

  10. Mager, A.: Approximate Solution of Isentropic Swirling Flow through a Nozzle. ARS Journal 31, No. 8 (1961) 1140/1148.

    Google Scholar 

  11. Binnie, A. M.: The Passage of a Perfect Fluid through a Critical Cross Section or Throat. Proceedings of the Royal Society of London, Vol. A197 (1949) 545/555.

    Google Scholar 

  12. Farquhar, B. W.: An Experimental Investigation of Swirling Flow in Nozzles. Ph.D. Thesis, June 1968, Purdue University, Lafayette, Ind.

    Google Scholar 

  13. Kliegel, J. R., and Quan, V.: Convergent-Divergent Nozzle Flows. AIAA Journal 6, No. 9 (1968) 1728/1754.

    Google Scholar 

  14. Hopkins, D. F., Hill, D. E.: Effect of Small Radius of Curvature on Transonic Flow in Axisymmetric Nozzles. AIAA Journal 4, No. 8 (1966) 1337/1343.

    Google Scholar 

  15. Hopkins, D. F., Hill, D. E.: Transonic Flow in Unconventional Nozzles. AIAA Journal 6, No. 5 (1968) 838/842.

    Google Scholar 

  16. Rouse, H., Hassan, M. M.: Cavitation-free Inlets and Contractions. Mechanical Engineering 71 (1949) 213/216.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Konstruktions-Abteilung A, Farbenfabriken Bayer AG, Leverkusen

    C. J. Boerner

  2. Department of Mechanical Engineering, University of Minnesota, 55455, Minneapolis, Minnesota

    E. M. Sparrow & C. J. Scott

Authors
  1. C. J. Boerner
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  2. E. M. Sparrow
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  3. C. J. Scott
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Additional information

Publication from the Heat Transfer Laboratory, University of Minnesota, Minneapolis, Minnesota.

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Boerner, C.J., Sparrow, E.M. & Scott, C.J. Compressible swirling flow through convergent-divergent nozzles. Warme- und Stoffubertragung 5, 101–115 (1972). https://doi.org/10.1007/BF01438411

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  • DOI: https://doi.org/10.1007/BF01438411

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