Supersonic Rectangular Over-Expanded Jets of Single and Two-Phase Flows

Supersonic Rectangular Over-Expanded Jets of Single and Two-Phase Flows A. Mohamed* and A. Hamed Department of Aerospace Engineering & Engineering Mechanics University of Cincinnati, Cincinnati, Ohio T. Lehnig Vice President and Director of Engineering and Operations Coldjet Inc., Cincinnati, Ohio ISABE 2003-1119 Abstract An experimental investigation was conducted to study supersonic jets from convergent divergent nozzles with rectangular cross section. The flow regimes and shock structure in the plume was characterized for jets in quiescent atmosphere at over-expanded conditions. Schlieren pictures of the jets are presented to show the shock structure and jet spread rate at different nozzle pressure ratios. LDV measurements are presented for the jet flow field and the centerline velocity decay. The results indicate that the rectangular supersonic jet spread rate is greater along the minor axis and increases with the nozzle pressure ratio. The individual shock cell length, as well a, the total number of shock cells within the jet plume were found to increase with nozzle pressure ratio. In two-phase rectangular jets of gas and dispersed solid particles the shock strength was found to attenuate with increased particle loading. Introduction Recent interest in rectangular supersonic jets is motivated by the need to reduce plume length and acoustically excited structural loads in the exhaust systems of high performance aircrafts. Semi-periodic *Doctoral student Professor, Fellow AIAA Member AIAA shock structures form in the jet plumes of these vehicles during low speed flight when the convergent divergent nozzles operate at off design conditions. These shock cells affect the jet velocity and temperature decay as well as the jet spread rate and its acoustic field. A number of studies presented experimental results for the centerline jet velocity decay and spread rate of subsonic rectangular jets. Sfier [1] studied air jets issuing from rectangular channels and slots in quiescent atmosphere. The results demonstrated that the jet growth rate in terms of the 50% velocity spread was greater in the direction of the minor axis. Sfier also presented experimental results for the axial variation of the mean velocity, longitudinal and lateral turbulence intensity and turbulence shear stress profiles and compared them to twodimensional jets. Lazanova and Shanov [2] conducted an experimental investigation to study the effect of rectangular jet aspect ratio on subsonic jet velocity and turbulence intensity. Experimental data obtained from 50 m/sec jets for aspect ratios between three and ten indicated that jet spreading rate in higher in the direction of the minor axis and that the crossover point of the jet half width moved downstream with increased aspect ratio. They also presented the axial variations in jet entrainment, axial jet momentum, and centerline turbulence intensity. By computing separately the mass

flow in four triangular sections from the center to each of the four rectangular jet sides, Lazanova and Shanov determined that the entrainment in the quadrants containing the long sides were double that in the quadrant containing the short side which confirms the more intensive spread of the jet in the minor plane. They also investigated the turbulence intensity patterns and the establishment of similarity velocity after distances greater than forty times the hydraulic diameter from the nozzle exit plane. Krothapalli et al. [3] studied the mixing of incompressible rectangular jets for aspect ratios between 5.5 and 16.7 up to axial distances 115 times the jet exit width (small nozzle dimension). Their results demonstrated similarity in both the mean velocity and shear stress profile in the plane along the minor axis beyond 30 times the width. Experimental investigations of rectangular high-speed jets also indicated higher jet spread rate in the plane of the minor axis. Von Glahn s experimental studies [4,5,6,7] of rectangular and circular high-speed subsonic jets in quiescent surroundings confirmed that the spread rate of rectangular jets in the direction of the minor axis is greater than in circular jets with the same area equivalent diameter. Von Glahn [6] developed correlations for the plume centerline velocity decay and 50% velocity spread variation with the axial distance in terms of the jet aspect ratio (AR), jet Mach number, and jet to ambient temperature ratio. The correlations were compared to the data for AR 6 rectangular jets at 0.784 Mach number and for a heated Mach 1.045 jet. He gave a different set of correlations in each of the three jet regions, namely, the initial mixing region, the transitional region, and the fully mixed region. He also included flight effects in the correlations based on velocity measurements of jets from rectangular nozzles in secondary streams. Seiner [8] compared the measured centerline velocity decay and acoustic efficiency of unheated jets for circular and rectangular nozzles with the same area equivalent diameter. The results for these Mach 0.857 shock free jets demonstrated the high mixing capability and beneficial noise reduction of rectangular nozzle exit geometry. A drastic reduction in the potential core length of the rectangular jet was reported compared to the equivalent circular jet. Seiner [8] reported a less drastic reduction in the core length of a Mach 1.52 fully expanded elliptic jet to 5.2 equivalent diameters, as compared to a 7.8 round jet [9]. Seiner [8] also presented phaseaveraged Schlieren photos of supersonic elliptic jets at fully expanded and overexpanded conditions. While the Mach 1.52 fully expanded elliptic jet mixing layers experienced similar growth rate along the major and minor axes, the shock structure in the jet plume greatly enhanced the jet spreading rate along the minor axis in the case of the over-expanded elliptic jet. Several experimental and analytical studies of under-expanded jets have been reported in the literature. Adamson and Nicholls [10] proposed a simple one-dimensional model to calculate the boundaries and distance of the first shock disk from the nozzle exit. They reported good agreement between the computed results and existing experimental data [11,12]. Pao and Abdolhamid [13] computed the flow fields of supersonic under-expanded circular and elliptic jets using different turbulence models and compared the computed first shock cell length with the experimental results for Mach 2 circular jet [14]. Grenville et al. [15] used a laser-based imaging method in a wall-adaptive wind tunnel to define the outer

edges of supersonic jets. They also presented computed results that predicted reductions in the jet core length in underexpanded and over-expanded jets with increased and decreased nozzle exit static pressure respectively. Krothapalli et al. [16], Gutmark et al. [17] and Zaman [18] conducted experimental studies of under expanded jets of symmetric and asymmetric cross sections. Their results indicate that the presence of shocks in the jet core further increased the spread rate along the minor axis compared to subsonic jets. Zaman [18] instantaneous schlieren pictures demonstrated that tabs spanning the narrow edges of the AR 3 rectangular nozzle weakened the shock/expansion structure, increased jet spreading along the minor axis, and reduced it along the major axis. Gutmark et al. [17] demonstrated transition to flapping mode at the minor axis plane for circular, elliptic, and AR 3 rectangular jets. The presented jet spread rate in the Mach 1-2.4 range demonstrated that the transition to the flapping mode with increased Mach number is abrupt in rectangular jets and more gradual in elliptic and circular jets. Tam [19] developed a linear shock cell model in which the mixing layer was approximated by a vortex sheet. Tam demonstrated that his linear model predictions of shock cell spacing agree with the experimental results of Powell [20] and Hammitt [21] for under expanded rectangular jets with aspect ratios greater than 4. His predications of screech tone frequencies based on the weakest link hypothesis [22] were in agreement with the experimental results of Krothapalli [16] and Powell [23]. A number of experimental and numerical studies were conducted to Investigate under-expanded circular jets of gas particle flows. Both Lewis et al. [24] and Sommerfeld [25] observed a forward shift in the Mach disk with increased particle loading. However, computational studies either predicted a rearward shift in the Mach disk location [26,27,28], or under predicted [25] the forward shift. Hamed et al. [29,30] conducted numerical simulations of gas-particle flows to determine the effect of particle loading in supersonic 2DCD nozzles. The computed results at over-expanded conditions with internal shocks in the nozzle [29], indicated that both shock strength and shock induced flow separation region are reduced with increased particle loading. Subsequently, the effects of particle sublimation and interphase energy exchange were included in the numerical simulations of CO 2 pellet-blasting nozzles [30]. The purpose of the present investigation is to characterize the shock structures in overexpanded rectangular jets plumes. Schlieren photographs are presented for overexpanded rectangular jets in quiescent atmosphere to show the effect of nozzle pressure ratio on the shock structure and jet mixing. The results indicate that the mixing rate is high along the jet s minor axis at the higher nozzle pressure ratios, but decreases as the nozzle pressure ratio is reduced. In over-expanded rectangular particle-laden jets, the shock strength was found to decrease as the nozzle pressure ratio was reduced. Experimental Method Experiments were carried out in a blow down facility with the jet discharging in the quiescent laboratory air. The air supplied by a compressor that pressurizes the ambient air up to 200 psig was filtered, dried and stored in a high-pressure reservoir consisting of 7

tanks with a total volume of 102 m 3. The total temperature was equal to that of the surrounding, and the total inlet pressure to the nozzle was controlled and maintained constant during the testing by a pressure regulator. A particle feeder was designed and manufactured to provide steady state flow of particles at pressures up to 150 psi. The particles were injected four meters upstream of the nozzle inlet to insure good mixing of the particles with the air. Visualization of the supersonic jet and shock structure was obtained by shadowgraph and Schlieren photography, with 100-watt mercury-vapor lamp as a continuous light source. Two 12 diameter parabolic mirrors with a focal length of 72 were arranged in the Z-shape configuration to redirect the light from the source through the test section and onto a screen. In the Schlieren arrangements, a knife-edge was placed at the focal point of the mirror and oriented horizontally. A two-component LDV system with conventional optics manufactured by Aerometrics Inc. was used in the present study. The blue wavelength (488nm) and green wavelength (514.5nm) lines from a 5-watt Spectra Physics argon-ion laser were used to create the LDV measurement volume. Velocities up to 570m/s could be measured using transmitting optics front lens with a focal length of 1000mm and a beam spacing of 32mm. The scattered laser light from the seeding particles in the test section was collected in the forward scattered mode by a 500mm (focal length) receiving lens situated 20 o off the forward scatter axis. The transmitting and receiving optics were mounted on two fixed tripods. Traversing the measuring volume throughout the flow-field was achieved by mounting the test nozzle on a computercontrolled 2D traverse mechanism. A twochannel Real-time Signal Analyzer (RSA) was used to process the LDV signal. Doppler frequency information from the signal analyzer was passed to a personal computer. Control of the RSA was managed by the personal computer via Data View (DV) software package. The software integrated the data acquisition process with the nozzle traversing mechanism, yielding automatic traversing capability during testing. The high-pressure particle feeder was used to seed the flow with 1-2µm diameter aluminum oxide particles. Results and Discussion The convergent divergent nozzle used in the current experimental study has an exit-tothroat area ratio of 2.79 for a design Mach number, M d of 2.5 and a design pressure ratio, NPR d, of 19.4. The rectangular cross section is 25.4mm x 4.92mm at the exit plane for an aspect ratio (AR) of 5.1. Tests were performed over a range of nozzle pressure ratios, NPR, between 4-9. The change in NPR was achieved by changing the inlet stagnation pressure to operate in the external over-expanded regime. Figure 1a and 1b show Schlieren photographs of the jet in the major and minor axis planes at different nozzle pressure ratios. The figure shows that the shock strength as well as the total number of shock cells in the jet plume decrease as the nozzle pressure ratio decreases. The visual jet spread rate along the minor axis is seen to decrease as the nozzle pressure ratio decreases. On the other hand, the visual jet width in the major plane does not exhibit noticeable spread, nor does it change with the nozzle pressure ratio. Sample contours of the axial jet velocity from LDV measurements in the major axis plane at NPR = 9, are presented in Fig. 2. The velocities are normalized by the speed

of sound, a o, based on the measured nozzle inlet stagnation temperature, while the distance is normalized by the nozzle minor axis width, h. The measurements were obtained up to x/h=16.6 on an 81 41 mesh by traversing the nozzle in 2mm increments in both vertical and horizontal directions. The corresponding centerline velocity variation along the nozzle axis is shown in Fig. 3. The centerline velocity decay is reproduced in a log-log plot in Fig. 4. One can see that the decay rate approaches the classical x -1 line past the shock cell zone. The distance from the jet exit to the first shock intersection with the jet centerline, L 1 and the average distance between subsequent shock intersections with the jet centerline, L S, as determined from the Schlieren photographs at the different nozzle pressure ratios are presented in Fig. 5. Both first and subsequent shock cell length are seen to increase with increased NPR. The shock cell length was also found to increase with nozzle pressure ratio in underexpanded jets [31, 17]. The rate of increase was dependant on the nozzle design Mach number [31], and on the shape of the jet cross section [17]. The rate was higher for elliptic and highest for rectangular jets, compared to circular jets of the same equivalent diameter [17]. Test results were obtained for two-phase rectangular jets at different particle loading ratios. Long grain rice, was used to simulate the cylindrical shaped CO 2 pellets in Coldjet s blasting nozzles. The material density, mean diameter and length of the particles are 750 kg/m 3, 1.5mm, and 5mm respectively. A particle separator was placed downstream from the jet to collect the suspended particles. Schlieren photographs of the jet at different particle loading ratios are shown in Fig. 6 for NPR=9.0. The photographs clearly show that as the particle loading increases, the shock strength as well as the number of shock cells decreases. Shock attenuation was also predicted in the case of internal shocks in a 2DCD nozzle operating at NPR much less than the design value [29]. Acknowledgements This work was sponsored by NSF Grant CTS-9812837. The authors would like to acknowledge the valuable help of Prof. S. M. Jeng, and to thank Mr. R. DiMicco for his support. References 1. Sfeir, A.A., The Velocity and Temperature Fields of Rectangular Jets, International Journal of Mass Transfer, Vol. 19, pp. 1289-1297, 1975. 2. Lozanova, M., and Stankov, P., Experimental Investigation on the Similarity of a 3D Rectangular Turbulent Jet, Experiments in Fluids, Vol. 24, pp. 470-478, 1998. 3. Krothapalli, A., Baganoff, D., and Karamcheti, K., On the Mixing of a Rectangular Jet, Journal of Fluid Mechanics, Vol. 107, pp 201-220, 1981. 4. Von Glahn, U.H., Correlation of Flight Effects on Centerline Velocity Decay for Cold- Flow Acoustically Excited Jets, NASA TM- 83502, 1983. 5. Von Glahn, U.H., On Some Flow Characteristics of Conventional and Excited Jets, AIAA Paper No. 84-0532, NASA TM- 83503, 1984. 6. Von Glahn, U.H., Rectangular Nozzle Plume Velocity Modeling for Use in Jet Noise Prediction, AIAA Paper No. 89-2357, Proceedings of the 25th Joint Propulsion Conference, Monterey, CA, 1989.

7. Von Glahn, U.H., Secondary Stream and Excitation Effects on Two-Dimensional Nozzle Plume Characteristics, AIAA Paper No. 87-2112, NASA TM-89813, 1987. 8. Seiner, J.M., Fluid Dynamics and Noise Emission Associated with Supersonic Jets, Studies in Turbulence, eds. Gatski, T.B., Sarkar, S. and Speziale, C.G., Springer- Verlag 1992. 9. Nagamatsu, H. and Horvay, G., Supersonic Jet Noise, AIAA Paper No. 70-237, 1970. 10. Adamson, T.C., and Nicholls, J.A., On the Structure of Jets from Highly Underexpanded Nozzles Into Still Air, Journal of Aerospace Sciences, pp. 16-25, January 1959. 11. Love, E.S., and Grigsby, C.E., Some Studies of Axi-symmetric Free Jets Exhausting from Sonic and Supersonic Nozzles into Supersonic Streams, NACA, RML54L31, 1955. 12. Owen, P.L., and Thornhill, C.K., The Flow in an Axially-Symmetric Supersonic Jet from a Nearly Sonic Orifice into Vacuum, A. R. C. Technical Report, R and M 2616, 1952. 13. Pao, S.P., and Abdol-Hamid, K.S., Numerical Simulation of Jet Aerodynamics Using the Three-Dimensional Navier-Stokes Code PAB3D, NASA Technical Paper 2596, 1996. 14. Love, E.S., Grigsby, C.E., Lee, L.P., and Woodling, M.J., Experimental and Theoretical Studies of Axi-symmetric Free Jets, NACA, TR R6-6, 1959. 15. Grenville, S.D., Favaloro, S.C., and Henbest, S.M., Experimental and Numerical Studies of Compressible Axisymmetric Free Shear-Layers, AIAA Paper No. A99-34265, 1999. 16. Krothapalli, A., Hsia, Y., Baganoff, D., and Karamcheti, K., The role of screech tones on the mixing of an underexpanded rectangular jet, Journal of Sound and Vibration, Vol. 106, pp. 119-143, 1986. 17. Gutmark, E., Shadow, K.C., and Bicker, C.J., Near Acoustic Field and Shock Structure of Rectangular Supersonic Jets, AIAA Journal, Vol. 28, No. 7, pp. 1164-1170, 1990. 18. Zaman, K.B.M., Spreading Characteristics of Compressible Jets from Nozzles of Various Geometries, Journal of Fluid Mechanics, Vol. 383, pp. 197-228, 1999. 19. Tam, C.K.W., The Shock-Cell Structures and Screech Tone Frequencies of Rectangular and Non-Axisymmetric Supersonic Jets, J. of Sound and Vibration, Vol. 121, No. 1, pp. 135-147, 1988. 20. Powell, A., On the noise emanating from a two-dimensional jet above the critical pressure, Aeronautical Quarterly, Vol. 4, pp. 103-122, 1953. On the. 21. Hammitt, A.G., The oscillation and noise of an overpressure sonic jet, Journal of Aerospace Sciences, Vol. 28, pp. 673-680, 1961. 22. Tam, C.K.W., Seiner, J.M., and Yu, J.M., Proposed relationship between broadband shock associated noise and screech tones, Journal of Sound and Vibration, Vol. 110, pp. 309-321, 1986. 23. Powell, A., On the mechanism of choked jet noise, Proceedings of the Physical Society, Section B66, pp. 1039-1056, 1953. 24. Lewis, L.H. and Carlson, D.J., Normal Shock Location in Under-Expanded Gas and Gas-Particle Jets, AIAA Journal, Vol. 2, pp. 776-777, 1964. 25. Summerfeld, M. Experimental and Numerical Studies on Particle Laden Underexpanded Free Jets, Proceedings of the fourth International Symposium on Gas-Solid

Flows, ASME FED-Vol. 121, pp. 213-220, 1991. 26. Summerfeld, M., and Nishida, M., Dusty Gas Flows with Shock Waves, Proceedings of the International Symposium on Computational Fluid Dynamics, Ed. K. Oshima, pp. 470-480, 1986. 27. Hayashi, A.K., Matsuda, M., Fujiwara, T., and Arashi, K., Numerical Simulation of Gas-Solid Two-Phase Nozzle and Jet Flow, AIAA Paper 88-2627, 1988. 28. Ishii, R., Umeda, Y., and Yuhi, M., Numerical Analysis of Gas-Particle Two- Phase Flows, J. Fluid Mechanics, Vol. 203, pp. 475-515, 1989. 29. Hamed, A., Mesalhy, O., Shock Wave Attenuation in Gas Particle Flows, Paper No. 921, Proceedings of the ICMF-2001, May 27- June 1, New Orleans, LA, 2001. 30. Hamed, A., Mesalhy, O., and Lehnig, T, Gas-Particle Flows in CO 2 Pellet-Blasting Nozzles, XV ISOABE Conference, Sept. 2-7, 2001, Bangalore, India. 31. Seiner, J.M., Advances in High Speed Jets, AIAA Paper 84-2275, 1984.

NPR=9.0 NPR=8.5 NPR=8.0 NPR=7.5 NPR=7.0 Major axis plane Minor axis plane Figure 1a. Schlieren photographs of a rectangular jet at different nozzle pressure ratios (7.0-9.0).

NPR=6.0 NPR=5.5 NPR=5.0 NPR=4.5 Major axis plane NPR=4.0 Minor axis plane Figure 1b. Schlieren photographs of a rectangular jet at different nozzle pressure ratios (7.0-9.0).

Figure 2. Axial velocity contours (NPR=9.0). Figure 3. Jet centerline velocity variation (NPR=9.0).

Figure 4. Jet centerline velocity decay (NPR=9.0) L 1 L s L s Figure 5. Effect of nozzle pressure ratio on shock cell length.

Particle loading = 0% Particle loading = 12% Particle loading = 15% Particle loading = 30% Particle loading=60% Figure 6. Schlieren photographs of rectangular jet at different particle loadings (NPR=9.0).