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An extension of the compound flow theory with friction between the streams and at the wall

Published online by Cambridge University Press:  02 December 2024

Jan Van den Berghe Open the ORCID record for Jan Van den Berghe [Opens in a new window] ,
Miguel A. Mendez Open the ORCID record for Miguel A. Mendez [Opens in a new window]  and
Yann Bartosiewicz Open the ORCID record for Yann Bartosiewicz [Opens in a new window]
Jan Van den Berghe*
Affiliation:
von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, 1640 Sint-Genesius-Rode, Belgium Institute of Mechanics, Materials, and Civil Engineering (iMMC), Université catholique de Louvain (UCLouvain), 1348 Louvain-la-Neuve, Belgium
Miguel A. Mendez
Affiliation:
von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, 1640 Sint-Genesius-Rode, Belgium
Yann Bartosiewicz
Affiliation:
Institute of Mechanics, Materials, and Civil Engineering (iMMC), Université catholique de Louvain (UCLouvain), 1348 Louvain-la-Neuve, Belgium
*
†Email address for correspondence: [email protected]
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Abstract

Compound flows consist of two or more parallel compressible streams in a duct and their theoretical treatment has gained attention for the analysis and modelling of ejectors. Recent works have shown that these flows can experience choking upstream of the geometric throat. While it is well known that friction can push the sonic section downstream of the throat, no mechanism has been identified yet to explain its displacement in the opposite direction. This study extends the existing compound flow theory and proposes a one-dimensional (1-D) model, including friction between the streams and the duct walls. The model captures the upstream and downstream displacements of the sonic section. Through an analytical investigation of the singularity at the sonic section, it is demonstrated that friction between the streams is the primary driver of upstream displacement. The 1-D formulation is validated against axisymmetric Reynolds averaged Navier–Stokes simulations of a compound nozzle for various inlet pressures and geometries. The effect of friction is investigated using an inviscid simulation for the isentropic case and viscous simulations with both slip and no-slip conditions at the wall. The proposed extension accurately captures the displacement of the sonic section, offering a new tool for in-depth analysis and modelling of internal compound flows.

JFM classification

Compressible Flows: Gas dynamics Wakes/Jets: Shear layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1000 , 10 December 2024 , A85
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Agnone, A.M. 1971 Comment on “Choked flow: a generalization of the concept and some experimental data”. AIAA J. 9 (4), 768.CrossRefGoogle Scholar
Beans, E.W. 1970 Computer solution to generalized one-dimensional flow. J. Spacecr. Rockets 7 (12), 1460–1464.CrossRefGoogle Scholar
Bernstein, A., Heiser, W.H. & Hevenor, C. 1967 Compound-compressible nozzle flow. J. Appl. Mech. 34, 548–554.CrossRefGoogle Scholar
Clark, L. 1995 Application of compound flow analysis to supersonic ejector-mixer performance prediction. In 33rd Aerospace Sciences Meeting and Exhibit. AIAA Paper 95-0645.CrossRefGoogle Scholar
Fage, E. 1976 Apparent subsonic choking in dual-stream nozzles. AIAA J. 14 (5), 681–683.CrossRefGoogle Scholar
Grazzini, G., Mazzelli, F. & Milazzo, A. 2016 Constructal design of the mixing zone inside a supersonic ejector. Intl J. Heat Technol. 34 (S1), S109–S118.CrossRefGoogle Scholar
Hedges, K.R. & Hill, P.G. 1974 Compressible flow ejectors: part II—flow field measurements and analysis. Trans. ASME J. Fluids Engng 96 (3), 282–288.CrossRefGoogle Scholar
Hoge, H.J. & Segars, R.A 1965 Choked flow-a generalization of the concept and some experimental data. AIAA J. 3 (12), 2177–2183.CrossRefGoogle Scholar
Kracik, J. & Dvorak, V. 2023 Effect of wall roughness on secondary flow choking in supersonic air ejector with adjustable motive nozzle. Intl J. Heat Fluid Flow 103, 109168.CrossRefGoogle Scholar
Lamberts, O., Chatelain, P., Bourgeois, N. & Bartosiewicz, Y. 2018 The compound-choking theory as an explanation of the entrainment limitation in supersonic ejectors. Energy 158, 524–536.CrossRefGoogle Scholar
Menter, F. 1993 Zonal two equation kw turbulence models for aerodynamic flows. In 23rd Fluid Dynamics, Plasmadynamics, and Lasers Conference. AIAA Paper 93-2906.Google Scholar
Metsue, A., Debroeyer, R., Poncet, S. & Bartosiewicz, Y. 2021 An improved thermodynamic model for supersonic real-gas ejectors using the compound-choking theory. Energy 238, 121856.CrossRefGoogle Scholar
Otis, D.R. 1976 Choking and mixing of two compressible fluid streams. Trans. ASME J. Fluids Engng 98 (2), 311–317.CrossRefGoogle Scholar
Papamoschou, D. 1993 Model for entropy production and pressure variation in confined turbulent mixing. AIAA J. 31 (9), 1643–1650.CrossRefGoogle Scholar
Papamoschou, D. 1996 Analysis of partially mixed supersonic ejector. J. Propul. Power 12 (4), 736–741.CrossRefGoogle Scholar
Pearson, H., Holiday, J.B. & Smith, S.F. 1958 A theory of the cylindrical ejector propelling nozzle. J. R. Aeronaut. Soc. 62, 746–751.CrossRefGoogle Scholar
Restrepo, J. & Simões-Moreira, J.R. 2022 Viscous effects on real gases in quasi-one-dimensional supersonic convergent divergent nozzle flows. J. Fluid Mech. 951, A14.CrossRefGoogle Scholar
Shapiro, A.H. 1953 The Dynamics and Thermodynamics of Compressible Fluid Flow. Ronald.Google Scholar
Sutherland, W. 1893 LII. The viscosity of gases and molecular force. Lond. Edinb. Dubl. Phil. Mag. J. Sci. 36 (223), 507–531.CrossRefGoogle Scholar
Van Driest, E.R. 1951 Turbulent boundary layer in compressible fluids. J. Aeronaut. Sci. 18 (3), 145–160.CrossRefGoogle Scholar
Versteeg, H.K. 2007 An Introduction to Computational Fluid Dynamics the Finite Volume Method, 2/E. Pearson Education India.Google Scholar