Abstract
Underexpanded, supersonic gas-particle jets were experimentally studied using the shadowgraph technique in order to examine the influence of the dispersed particles on the shape of the free jet and the structure of the imbedded shock waves. The particle mass loading at the nozzle exit was varied between zero and one, and two sizes of particles (i.e. spherical glass beads) with mean number diameters of 26 and 45 μm were used. It was found that the Mach-disc moves upstream towards the orifice with increasing particle loading. The laser light sheet technique was also used to visualize the particle concentration distribution within the particle jet and the spreading rate of the particle jet. Furthermore, the particle velocity along the jet centerline was measured with a modified laser-Doppler anemometer. These measurements revealed that the particles move considerably slower than the gas flow at the nozzle exit. This is mainly the result of the particle inertia, whereby the particles are not accelerated to sonic speed in the converging part of the nozzle.
In order to further explore the particle behavior in the free jet, numerical studies were performed by a combined Eulerian/Lagrangian approach for the gas and particle phases, including full coupling between the two phases. The numerical results showed that the application of different particle velocities at the nozzle exit as the inlet conditions, which were below the sonic speed of the gas phase has a significant influence on the free jet shape and the configuration of the shock waves. These results demonstrate that the assumption of equilibrium flow (i.e. zero slip between the phases) at the nozzle exit which has been applied in most of the previous numerical studies is not justified in most cases. Furthermore, the numerical calculations of the free jet shape and the particle velocity along the jet axis were compared with the measurements. Although correlations for rarefaction and compressibility effects in the drag coefficient were taken into account, the particle velocity along the center line was considerably overpredicted.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ashkenas H, Sherman FS (1966) The structure and utilization of supersonic free jets in low density wind tunnels. In: de Leeuw JH (ed) Rarefied gas dynamics. Vol. II. Academic Press, New York, pp 84–105
Carlson DJ, Hoglund RF (1964) Particle drag and heat transfer in rocket nozzles. AIAA J 2:1980
Chang I-S (1980) One- and two-phase nozzle flows. AIAA J 18:1455
Colella P, Glaz HM (1983) Efficient solution algorithm for the Riemann problem for real gases. LBL Report 15776
Cook CH (1986) On operator splitting for unsteady boundary value problems. J Comp Phys 67:472
Durst F, Zaré M (1975) Laser-Doppler measurements in two-phase flows. In: Buchhave B (ed) The accuracy of flow measurements by laser Doppler methods, proceedings of the LDA-Symposium, Copenhagen, 1975. LDA-Symposium, Skovlunde, Denmark, pp 403–429
Fuchs NA (1989) The mechanics of aerosols. Dover Publications, Inc., New York
Hayashi K, Branch MG (1980) Concentration, velocity and particles size measurements in gas-solid two-phase jets. AIAA Paper 80-0351R
Hayashi AK, Matsuda M, Fujiwara T, Arashi K (1988) Numerical simulation of gas-solid two-phase nozzle and jet flows. AIAA Paper 88-2627
Hjelmfelt AT, Mockros LF (1966) Motion of discrete particles in a turbulent fluid. Appl Sci Res 16:149
Ishii R, Umeda Y, Yuhi M (1989) Numerical analysis of gas-particle twophase flows. J Fluid Mech 203:475
Jarvinen PO, Draper JS (1967) Underexpanded gas particle jets. AIAA J 5:824
Kihm KD, Chigier N (1991) Effect of shock waves on liquid atomization of a two-dimensional airblast atomizer. Atomization and Sprays 1:113
Knudsen JG, Katz DL (1958) Fluid Mechanics and Heat Transfer. McGraw-Hill Book Company, New York, p 511
Lewis LH, Carlson DJ (1964) Normal shock location in underexpanded gas and gas-particle jets. AIAA J 2:776
Marble FE (1970) Dynamics of dusty gases. Annual Review in Fluid Mechanics 2:397
Nishida M, Abe S (1986) Numerical and experimental studies of lowdensity dusty-gas free jets. In: Boffi V, Cercignani C (ed) Proc. of the 15th Int. Symp. on Rarefied Gas Dynamics, Grado, Italy. B. G. Teuber, Stuttgart, pp 534–543
Rudinger G (1965) Some effects of finite volume on the dynamics of gasparticle mixtures. AIAA J 3:1217
Sommerfeld M (1985) The unsteadiness of shock waves propagating through gas-particle mixtures. Exper in Fluids 3:197
Sommerfeld M (1987a) Expansion of a gas/particle mixture in supersonic free jet flow. Zeitschrift Flugwissenschaft und Weltraumforschung 11:87
Sommerfeld M (1987b) Numerical simulation of supersonic two-phase gasparticle flows. In: Grönig H (ed) Shock tubes and waves, proceedings of the 16th international symposium on shock tubes and waves, Aachen, FRG, 1987. VCH, Weinheim New York, pp 235–241
Sommerfeld M (1990) The influence of solid particles on the structure of supersonic free jet flows. In: Kim YW (ed) Current topics in shock waves, proceedings of the 17th international symposium on shock waves and shock tubes, Bethlehem, Pensylvania, U.S.A., 1989. American Institute of Physics, New York, pp 745–750
Sommerfeld M (1991) Experimental and numerical studies on particle laden underexpanded free jets. In: Stock DE, Tsuji Y, Jurewicz JT, Reeks MW. Gautam M (eds) Gas-solid flows. ASME, FED 121:213
Sommerfeld M, Nishida M (1986) Dusty gas flows with shock waves. In: Oshima K (ed) Proceedings of the international symposium on comptutational fluid dynamics, Tokyo, Japan, 1985, Vol. II. Japan Society of Computational Fluid Dynamics, Tokyo, pp 470–480
Yoshida T, Takayama K (1990) Interaction of liquid droplets with planar shock waves. Trans ASME, J Fluids Eng 112:481
Author information
Authors and Affiliations
Additional information
This article was processed using Springer-Verlag TEX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.
Rights and permissions
About this article
Cite this article
Sommerfeld, M. The structure of particle-laden, underexpanded free jets. Shock Waves 3, 299–311 (1994). https://doi.org/10.1007/BF01415828
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01415828