Evaluation of Turbulence Models for the Air Flow in a Planar Nozzle
Main Article Content
Abstract
Keywords
Air flow, turbulence models, Shock wave, Static pressure, Planar nozzle, supersonic speed flujo de aire, modelos de turbulencia, onda de choque, presión estática, tobera plana, velocidad supersónica
References
[2] F. White, Viscous fluid flow. McGraw-Hill, 1991. [Online]. Available: http://bit.ly/2Wl4Htw
[3] H. Schlichting, Boundary-layer theory. McGraw-Hill classic textbook reissue series, 2016. [Online]. Available: http://bit.ly/2wh45Xk
[4] J. D. Anderson, Fundamentals of aerodynamics. McGraw-Hill series in aeronautical and aerospace engineering, 2001. [Online]. Available:
http://bit.ly/2YHGyeb
[5] F. White, Mecánica de fluidos. McGraw-Hill Interamericana de España S.L., 2008. [Online]. Available: http://bit.ly/2W4dHEd
[6] T. V. Karman, “The fundamentals of the statistical theory of turbulence,” Journal of the Aeronautical Sciences, vol. 4, no. 4, pp. 131–138, 1937. [Online]. Available: https://doi.org/10.2514/8.350
[7] J. Blazek, Computational fluid dynamics: principles and applications. Butterworth-Heinemann, 2015. [Online]. Available: http://bit.ly/2HRC7GM
[8] B. Andersson, R. Andersson, L. Håkansson, M. Mortensen, R. Sudiyo, B. van Wachem, and L. Hellström, Computational Fluid Dynamics Engineers. Cambridge University Press, 2012. [Online]. Available: http://bit.ly/2YLOcUR
[9] D. C. Wilcox, Turbulence modeling for CFD. DCW Industries, 2006. [Online]. Available: http://bit.ly/2K0NH5o
[10] C. Hunter, “Experimental, theoretical, and computational investigation of separated nozzle flows,” American Institute of Aeronautics and Astronautics, 1998. [Online]. Available: https://doi.org/10.2514/6.1998-3107
[11] G. P. Sutton and O. Biblarz, Rocket propulsion elements. John Wiley & Sons, 2001. [Online]. Available: http://bit.ly/2WkBGxT
[12] T.-H. Shih, J. Zhu, and J. L. Lumley, “A new reynolds stress algebraic equation model,” Computer Methods in Applied Mechanics and Engineering, vol. 125, no. 1, pp. 287–302, 1995. [Online]. Available: https://doi.org/10.1016/0045-7825(95)00796-4
[13] T. B. Gatski and C. G. Speziale, “On explicit algebraic stress models for complex turbulent flows,” Journal of Fluid Mechanics, vol. 254, pp. 59–78, 1993. [Online]. Available: https://doi.org/10.1017/S0022112093002034
[14] S. S. Girimaji, “Fully explicit and self-consistent algebraic reynolds stress model,” Theoretical and Computational Fluid Dynamics, vol. 8, no. 6, pp. 387–402, Nov 1996. [Online]. Available: https://doi.org/10.1007/BF00455991
[15] A. Balabel, A. Hegab, M. Nasr, and S. M. El-Behery, “Assessment of turbulence modeling for gas flow in two-dimensional convergent–divergent rocket nozzle,” Applied Mathematical Modelling, vol. 35, no. 7, pp. 3408–3422, 2011. [Online]. Available: https://doi.org/10.1016/j.apm.2011.01.013
[16] B. E. Launder and D. B. Spalding, Lectures in mathematical models of turbulence. Academic Press, London, New York, 1972. [Online]. Available: http://bit.ly/2Jz9rWt
[17] Y. S. Chen and S. Kim, “Computation of turbulent flows using extended k-" turbulence closure model,” NASA Contractor report. NASA CR-179204, Tech. Rep., 1987. [Online]. Available: http://bit.ly/2HNf6VA
[18] F.-S. Lien and G. Kalitzin, “Computations of transonic flow with the v2 ?f turbulence model,” International Journal of Heat and Fluid Flow, vol. 22, no. 1, pp. 53–61, 2001. [Online]. Available: https://doi.org/10.1016/S0142-727X(00)00073-4
[19] P. Durbin, “On the k ? " stagnation point anomaly,” International Journal of Heat and Fluid Flow, vol. 17, no. 1, pp. 89–90, 1996. [Online]. Available: http://bit.ly/2EsZSnV
[20] F. R. Menter, “Two equation eddy-viscosity turbulence models for engineering applications,” AIAA Journal, vol. 32, no. 8, pp. 1598–1605, 1994. [Online]. Available: https://doi.org/10.2514/3.12149
[21] B. E. Launder, G. J. Reece, and W. Rodi, “Progress in the development of a reynolds-stress turbulence closure,” Journal of Fluid Mechanics, vol. 68, no. 3, pp. 537–566, 1975. [Online]. Available: https://doi.org/10.1017/S0022112075001814
[22] A. Toufique Hasan, “Characteristics of overexpanded nozzle flows in imposed oscillating condition,” International Journal of Heat and Fluid Flow, vol. 46, pp. 70–83, 2014. [Online]. Available: https://doi.org/10.1016/j.ijheatfluidflow.2014.01.001
[23] V. M. K. Kotteda and S. Mittal, “Flow in a planar convergent–divergent nozzle,” Shock Waves, vol. 27, no. 3, pp. 441–455, May 2017. [Online]. Available: https://doi.org/10.1007/s00193-016-0694-4
[24] M. Taeibi-Rahni, F. Forghany, and A. Asadollahi-Ghoheih, “Numerical study of the aerodynamic effects on fluidic thrust vectoring,” in Conference: International Congress Propulsion Engineering, At Kharkov, Ukrain, no. 8, 2015, pp. 27–34. [Online]. Available: http://bit.ly/2W1p6Ew
[25] E. Shimshi, G. Ben-Dor, A. Levy, and A. Krothapalli,“Asymmetric and unsteady flow separation in high mach number planar nozzle,” International Journal of Aeronautical Science & Aerospace Research (IJASAR), vol. 2, no. 6, pp. 65–80, 2015. [Online]. Available: https://doi.org/10.19070/2470-4415-150008
[26] R. Arora and A. Vaidyanathan, “Experimental investigation of flow through planar double divergent nozzles,” Acta Astronautica, vol. 112, pp. 200–216, 2015. [Online]. Available: https://doi.org/10.1016/j.actaastro.2015.03.020
[27] S. Zivkovic, M. Milinovic, N. Gligorijevic, and M. Pavic, “Experimental research and numerical simulations of thrust vector control nozzle flow,” The Aeronautical Journal, vol. 120, no. 1229, pp. 1153–1174, 2016. [Online]. Available: https://doi.org/10.1017/aer.2016.48
[28] E. Martelli, P. P. Ciottoli, M. Bernardini, F. Nasuti, and M. Valorani, “Delayed detached eddy simulation of separated flows in a planar nozzle,” in 7th European Conference for Aeronautics and aerospace Sciences, 2017. [Online]. Available: https://doi.org/10.13009/EUCASS2017-582
[29] O. Kostic, Z. Stefanovic, and I. Kostic, “Comparative cfd analyses of a 2d supersonic nozzle flow with jet tab and jet vane,” Tehnicki vjesnik, vol. 24, no. 5, pp. 1335–1344, 2017. [Online]. Available: https://doi.org/10.17559/TV-20160208145336
[30] S. Verma, M. Chidambaranathan, and A. Hadjadj, “Analysis of shock unsteadiness in a supersonic over-expanded planar nozzle,” European Journal of Mechanics - B/Fluids, vol. 68, pp. 55–65, 2018. [Online]. Available: https://doi.org/10.1016/j.euromechflu.2017.11.005
[31] D. C. Wilcox, “Reassessment of the scaledetermining equation for advanced turbulence models,” AIAA Journal, vol. 26, no. 11, pp. 1299–1310, 1988. [Online]. Available: https://doi.org/10.2514/3.10041
[32] K. Walters and D. Cokljat, “A threeequation eddy-viscosity model for reynoldsaveraged navier-stokes simulations of transitional flows,” Journal of Fluids Engineering, vol. 130, no. 12, p. 121401, 2008. [Online]. Available: https://doi.org/10.1115/1.2979230
[33] M. M. Gibson and B. E. Launder, “Ground effects on pressure fluctuations in the atmospheric boundary layer,” Journal of Fluid Mechanics, vol. 86, no. 3, pp. 491–511, 1978. [Online]. Available: https://doi.org/10.1017/S0022112078001251
[34] B. E. Launder, “Second-moment closure and its use in modeling turbulent industrial flows,” International Journal for Numerical Methods in Engineering, vol. 9, pp. 963–985, 1989. [Online]. Available: https://doi.org/10.1002/fld.1650090806
[35] Y. A. Cengel and J. M. Cimbala, Mecánica de fluidos, fundamentos y aplicaciones. McGraw-Hill, 2006. [Online]. Available: http://bit.ly/2X7THwU
[36] K. S. Abdol-Hamid, A. Elmiligui, C. A. Hunter, and S. J. Massey, “Three-dimensional computational model for flow in an over expanded nozzle with porous surfaces,” in Eighth International Congress of Fluid Dynamics & Propulsion, Cairo, Egypt, 2006. [Online]. Available: https://go.nasa.gov/2JY3QZe