Numerical Simulation of Flow Separation in a Thrust Optimized Parabolic Nozzle

Document Type : Research Article

Authors

1 Department of Aerospace Engineering, Ferdowsi University, Mashhad, Iran

2 Space Transportation Research Institute, Iranian Space Research Center, Tehran, Iran

Abstract

Complex flow separation in thrust optimized parabolic nozzles in the over-expanded condition is one of the challenging issues of many numerical investigations. The correct estimation of a thrust optimized parabolic nozzle performance extremely depends upon the accurate estimation of the onset of flow separation. Literature review indicates that conventional Reynolds-averaged Navier–Stokes turbulence models have a significant error in predicting the onset of flow separation in these types of nozzles due to the overestimating of turbulent kinetic energy production. Recently proposed generalized k-omega has made it possible to rectify numerical simulations based on governing physics and using limited experimental results. In the present study, the flow physics in the LEA_TOC nozzle has been investigated with the numerical simulation approach. At the first, the significant error of conventional Reynolds-averaged Navier–Stokes turbulence models is shown to simulate flow separation in this type of problem. Then, the generalized k-omega parameters are modified based on the limited experimental result of the LEA_TOC nozzle, and the ability of this model has been evaluated to estimate the flow physics under different pressure ratios. Numerical investigations show that generalized k-omega has a high capability for accurately estimating the onset of flow separation at a wide range of nozzle pressure ratios. Applying the corrected generalized k-omega has resulted in an improvement of about 30% in the estimation of the onset of separation in the over-expanded LEA_TOC nozzle compared to the k-ω-SST model.

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[1] J. O¨ stlund, B. Muhammad-Klingmann, Supersonic flow separation with application to rocket engine nozzles, Appl. Mech. Rev., 58(3) (2005) 143-177.
[2] G.P. Sutton, O. Biblarz, Rocket propulsion elements, John Wiley & Sons, 2016.
[3] G. Rao, Approximation of optimum thrust nozzle contours, ARS J., 30 (1960) 561.
[4] L. Nave, G. Coffey, Sea level side loads in high-area-ratio rocket engines, in:  9th propulsion conference, 1973, pp. 1284.
[5] A. Shams, S. Girard, P. Comte, Numerical simulation of shock-induced separated flows in overexpanded rocket nozzles, Progress in Flight Physics, 3 (2012) 169-190.
[6] E. Martelli, L. Saccoccio, P. Ciottoli, C. Tinney, W. Baars, M. Bernardini, Flow dynamics and wall-pressure signatures in a high-Reynolds-number overexpanded nozzle with free shock separation, Journal of Fluid Mechanics, 895 (2020).
[7] N. Fouladi, M. Farahani, A. Mirbabaei, Performance evaluation of a second throat exhaust diffuser with a thrust optimized parabolic nozzle, Aerospace science and technology, 94 (2019) 105406.
[8] C.-L. Chen, S. Chakravarthy, C. Hung, Numerical investigation of separated nozzle flows, AIAA journal, 32(9) (1994) 1836-1843.
[9] S. Deck, A.T. Nguyen, Unsteady side loads in a thrust-optimized contour nozzle at hysteresis regime, AIAA journal, 42(9) (2004) 1878-1888.
[10] A. Shams, P. Comte, S. Girard, G. Lehnasch, M. Shahab, 3D unsteady numerical investigation of an overexpanded thrust optimized contour nozzle, in:  6th European Symposium on Aerothermodynamics for Space Vehicles, 2009, pp. 90.
[11] P. Reijasse, F. Bouvier, P. Servel, Experimental and numerical investigation of the cap-shock structure in over expanded thrust-optimized nozzles,  (2002).
[12] J. Ostlund, M. Jaran, Assessment of turbulence models in overexpanded rocket nozzle flow simulations, in:  35th Joint Propulsion Conference and Exhibit, 1999, pp. 2583.
[13] C. Pilinski, A. Nebbache, Flow separation in a truncated ideal contour nozzle, Journal of Turbulence, 5(1) (2004) 014.
[14] R. Stark, B. Wagner, Experimental flow investigation of a truncated ideal contour nozzle, in:  42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2006, pp. 5208.
[15] H. Luedeke, Axisymetric investigasion of the VAC S6 short nozzle with forced external fluctuation, in: Proceedings of the ATAC-FSCD workshop, Noordwijk, The Netherlands, 2007.
[16] A. Hadjadj, Y. Perrot, S. Verma, Numerical study of shock/boundary layer interaction in supersonic overexpanded nozzles, Aerospace science and technology, 42 (2015) 158-168.
[17] S. Sarkar, Modeling the pressure-dilatation correlation, Institute for computer applications in science and engineering, 1991.
[18] A. Yaravintelimath, B. Raghunandan, J.A. Moríñigo, Numerical prediction of nozzle flow separation: Issue of turbulence modeling, Aerospace Science and Technology, 50 (2016) 31-43.
[19] A. Nebbache, Separated nozzle flow, Comptes Rendus Mécanique, 346(9) (2018) 844-854.
[20] N. Fouladi, M. Farahani, Numerical investigation of second throat exhaust diffuser performance with thrust optimized parabolic nozzles, Aerospace Science and Technology, 105 (2020) 106020.
[21] F.R. Menter, A. Matyushenko, R. Lechner, Development of a generalized k-ω two-equation turbulence model, in:  Symposium der Deutsche Gesellschaft für Luft-und Raumfahrt, Springer, 2018, pp. 101-109.
[22] F. Menter, R. Lechner, A. Matyushenko, Best practice: generalized k-ω two-equation turbulence model in ANSYS CFD (GEKO), Technical Report, ANSYS,  (2019) 27.
[23] A.T. Nguyen, H. Deniau, S. Girard, T. Alziary de Roquefort, Unsteadiness of flow separation and end-effects regime in a thrust-optimized contour rocket nozzle, Flow, Turbulence and Combustion, 71(1) (2003) 161-181.
[24] M. Frey, G. Hagemann, Restricted shock separation in rocket nozzles, Journal of Propulsion and Power, 16(3) (2000) 478-484.
[25] G. Hagemann, M. Frey, W. Koschel, Appearance of restricted shock separation in rocket nozzles, Journal of Propulsion and Power, 18(3) (2002) 577-584.
[26] E. Martelli, F. Nasuti, M. Onofri, Numerical calculation of FSS/RSS transition in highly overexpanded rocket nozzle flows, Shock Waves, 20(2) (2010) 139-146.
[27] N. Fouladi, A. Mohamadi, H. Rezaei, Numerical investigation of pre-evacuation influences of second throat exhaust diffuser, Fluid Mechanics and Aerodynamics, 5(2) (2017) 55-69.
[28] E. Mohammadi, N. Fouladi, A. Madadi, Design and Analysis of Gas Ejector in High Altitude Test Facility, Amirkabir Journal of Mechanical Engineering, 52(11) (2019) 3015-3032.
[29] N. Fouladi, M. Hataminasab, S. Afkhami, Numerical Analysis of Cross Section Time Variation Effects of the Supersonic Exhaust Diffuser, Amirkabir Journal of Mechanical Engineering, 53(3) (2021) 7-7.
[30] D.C. Wilcox, Turbulence modeling for CFD, DCW industries La Canada, CA, 1998.
[31] N. Fouladi, A. Mohamadi, H. Rezaei, Numerical design and analysis of supersonic exhaust diffuser in altitude test simulator, Modares Mechanical Engineering, 16(8) (2016) 159-168.
[32] H.-W. Yeom, S. Yoon, H.-G. Sung, Flow dynamics at the minimum starting condition of a supersonic diffuser to simulate a rocket’s high altitude performance on the ground, Journal of Mechanical Science and Technology, 23(1) (2009) 254-261.
[33] S. Sankaran, T.N. Satyanarayana, K. Annamalai, K. Visvanathan, V. Babu, T. Sundararajan, CFD analysis for simulated altitude testing of rocket motors, Canadian Aeronautics and Space Journal, 48(2) (2002) 153-162.
[34] R. Manikanda Kumaran, T. Sundararajan, D. Raja Manohar, Simulations of high altitude tests for large area ratio rocket motors, AIAA journal, 51(2) (2013) 433-443.
[35] D.C. Wilcox, Formulation of the kw turbulence model revisited, AIAA journal, 46(11) (2008) 2823-2838.
[36] F. Menter, Zonal two equation kw turbulence models for aerodynamic flows, in:  23rd fluid dynamics, plasmadynamics, and lasers conference, 1993, pp. 2906.
[37] Y.-K. Jung, K. Chang, J.H. Bae, Uncertainty Quantification of GEKO Model Coefficients on Compressible Flows, International Journal of Aerospace Engineering, 2021 (2021).
[38] S. Sarkar, L. Balakrishnan, Application of a Reynolds stress turbulence model to the compressible shear layer, in:  21st Fluid Dynamics, Plasma Dynamics and Lasers Conference, 1990, pp. 1465.
[39] C. Allamaprabhu, B. Raghunandan, J. Morinigo, Improved prediction of flow separation in thrust optimized parabolic nozzles with FLUENT, in:  47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2011, pp. 5689.
[40] Vulcan 2+ NE, TN, CFD Simulations," Prog. Nr. SV NT 114 0000E2026, VOLVO Internal Report, 2000, Issue Date2000-09-26
[41] M. Herbert, R. Herd, Boundary-layer separation in supersonic propelling nozzles,  (1964).