Journal of Applied and Computational Mechanics

Prediction of the Supersonic Flow Base Pressure by Axisymmetric ‎Direct Numerical Simulation

Document Type : Research Paper

Authors

1 Udmurt Federal Research Center, Russian Academy of Science, Ural Branch, Izhevsk, 426067, Russia

2 Keldysh Institute of Applied Mathematics, Russian Academy of Science, Moscow, 125047, Russia

3 Kalashnikov Izhevsk State Technical University, Izhevsk, 426069, Russia

Abstract

Axisymmetric direct numerical simulation (DNS) has been carried out to predict supersonic base flow behavior. Substantially fine grid has been used to perform calculations for the flow with Reynolds number up to 106. Optimal grid resolution was established through test calculations for affordable run time and solution convergence determined by the vorticity value. Numerical scheme provides fourth-order approximation for dissipative, fifth-order for convective and second-order for unsteady terms of conservation equations. Reynolds Averaged Navier-Stokes (RANS) approach has been employed to obtain input flow profiles for DNS calculations. Series of calculations have been carried out for Mach number 1.5 with Reynolds numbers 104, 105, 106 and for Mach number 2.46 with Reynolds number 1.65×106. It has been found that local base pressure coefficient calculated by DNS is a bit overestimated in a zone close to symmetry axis in comparison with experiment while integrated base drag coefficient shows good agreement with experimental data and noticeably better than one obtained by RANS approach.

Keywords

Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Compton III, W.B., Effect on Base Drag of Recessing the Bases of Conical Afterbodies at Subsonic and Transonic Speeds, NASA Technical Note D-4821, 1968.
[2] Sahu, J, Nietubicz, C.J, Steger, J.L., Navier-Stokes Computations of Projectile Base Flow with and without Mass Injection, AIAA Journal, 23(9), 1985, 1348-1355.
[3] Sahu, J., Drag Predictions for Projectiles at Transonic and Supersonic Speeds, Memorandum Report BRL-MR-3523, 1986.
[4] Rollstin, L., Measurement of In-Flight Base Pressure on an Artillery-Fired Projectile, AIAA Paper 87-2427, 1987.
[5] Fasel, H.F., Sandberg, R.D., Simulation of Supersonic Base Flows: Numerical Investigations Using DNS, LES and URANS, Report ARO Grant No. DAAD190210361, 2006.
[6] Sandberg, R.D., Fasel, H.F., Direct Numerical Simulations of Transitional Supersonic Base Flows, AIAA Journal, 44(4), 2006, 848-858.
[7] Reddy, D.S.K., Sah, P., Sharma, A., Prediction of Drag Coefficient of a Base Bleed Artillery Projectile at Supersonic Mach number, Journal of Physics: Conference Series, 2054, 2021, 012013.
[8] Aziz, M., Ibrahim, A., Riad, A., Ahmed, M.Y.M., Live Firing and 3D Numerical Investigation of Base Bleed Exit Configuration Impact on Projectile Drag, Advances in Military Technology, 17(1), 2022, 137–152.
[9] Chapman, D.R., An Analysis of Base Pressure at Supersonic Velocities and Comparison with Experiment, NACA Technical Note 2137, 1950.
[10] McCoy, R.L., MC DRAG – A Computer Program for Estimating the Drag Coefficients of Projectiles, Technical Report ARBRL-TR-02293, 1981.
[11] Karpov, B.G., The Effect of Various Boattail Shapes on Base Pressure and Other Aerodynamic Characteristics of a 7-Caliber Long Body of Revolution at M=1.70, Report No. 1295 US Army Ballistic Research Laboratory, 1965.
[12] Mair, W.A., Reduction of Base Drag by Boat-Tailed Afterbodies in Low-Speed Flow, Aeronautical Quarterly, 20(4), 1969, 307-320.
[13] Sahu, J., Heavey, K.R., Numerical Investigation of Supersonic Base Flow with Base Bleed, AIAA Paper 95-3459, 1995.
[14] Mathur, T., Dutton, J.C., Velocity and Turbulence Measurements in a Supersonic Base Flow with Mass Bleed, AIAA Journal, 34(6), 1996, 1153-1159.
[15] Kubberud, N., Øye, I.J., Extended Range of 155mm Projectile Using an Improved Base Bleed Unit, Simulations and Evaluation, 26th International Symposium, DEStech Publications, 2011, 549-560.
[16] Kayser, L.D., Base Pressure Measurements on a Projectile Shape at Mach Numbers from 0.91 to 1.20, Memorandum Report ARBLR-MR-03353, 1984.
[17] Forsythe, J.R., Hoffmann, K.A., Cummings, R.M., Squires, K.D., Detached-Eddy Simulation with Compressibility Corrections Applied to a Supersonic Axisymmetric Base Flow, Journal of Fluids Engineering, 124(4), 2002, 911-923.
[18] Simon, F., Deck, S., Guillen, P., Sagaut, P., Reynolds-Averaged Navier-Stokes/Large-Eddy Simulations of Supersonic Base Flow, AIAA Journal, 44(11), 2006, 2578-2590.
[19] Garbaruk, A., Shur, M., Strelets, M., Travin, A., Supersonic Base Flow, in: DESider – A European Effort on Hybrid RANS-LES Modelling, W. Haase, M. Braza, A. Revell (Eds.), Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Springer, Vol.103, 2009, 197-206.
[20] Shin, J.R., Choi, J.Y., DES Study of Base and Base-Bleed Flows with Dynamic Formulation of DES Constant, AIAA Paper 2011-662, 2011.
[21] Luo, D., Yan, C., Wang, X. Computational Study of Supersonic Turbulent-Separated Flows Using Partially Averaged Navier-Stokes Method, Acta Astronautica, 107, 2015, 234–246.
[22] Jung, Y.K., Chang, K., Bae, J.H. Uncertainty Quantification of GEKO Model Coefficients on Compressible Flows, International Journal of Aerospace Engineering, 2021, 2021, 1‑17.
[23] Herrin, J.L., Dutton, J.C., Supersonic Base Flow Experiments in the Near Wake of a Cylindrical Afterbody, AIAA Journal, 32(1), 1994, 77–83.
[24] Reedy, T.M., Elliott, G., Dutton, J.C., Lee, Y., Passive Control of High-Speed Separated Flows Using Splitter Plates, AIAA Paper 2011-484, 2011.
[25] Sandberg, R.D., Stability Analysis of Axisymmetric Supersonic Wakes Using Various Basic States, Journal of Physics: Conference Series 318, 2011, 032017.
[26] Givoli, D., Non-Reflecting Boundary Conditions, Journal of Computational Physics, 94, 1991, 1-29.
[27] Sanderberg, R.D., Fasel, H.F., Numerical Investigation of Transitional Supersonic Axisymmetric Wakes, Journal of Fluid Mechanics, 563, 2006, 1-41.
[28] Menter, F.R., Zonal Two-Equation k-w Turbulence Model for Aerodynamic Flow, AIAA Paper 1993-2906, 1993.
[29] Lipanov, A.M., Kisarov, Yu.F., Klyuchnikov, I.G., Theoretical Investigation of Parameters for Turbulent Subsonic Flows in Compressible Media: Method and Certain Results, Doklady Physics, 44(6), 1999, 380-384.
[30] Karskanov, S.A., Lipanov, A.M., On Critical Reynolds Numbers in Plane Channels with a Sudden Expansion at the Entry, Computational Mathematics and Mathematical Physics, 50(7), 2010, 1195-1204.
[31] Jiang, G.S., Shu, C.W., Efficient Implementation of Weighted ENO Schemes, Journal of Computational Physics, 126(1), 1996, 202–228.
[32] Shu, C.W., High Order ENO and WENO Schemes for Computational Fluid Dynamics, High-Order Methods for Computational Physics, Lecture Notes in Computational Science and Engineering, 9, 1999, 439-582.
[33] Gottlieb, S., Shu, C.W., Total Variation Diminishing Runge-Kutta Schemes, Mathematics of Computation, 67, 1998, 73–85.
[34] Lipanov, A.M., Karskanov, S.A., Galactic Structures in a Viscous Gas Flow in a Channel, Mathematical Models and Computer Simulations, 11(2), 2019, 168–175.
[35] Pope, S.B., Turbulent Flows, Cambridge University Press, 2000.
[36] Menter, F.R., Kuntz, M., Langtry, R., Ten Years of Industrial Experience with the SST Turbulence Model, in: Turbulence Heat and Mass Transfer 4, Hanjalic, K., Nagano, Y., Tummers, M.J. (Eds.), Begell House, New York, 2003.
Journal of Applied and Computational Mechanics
Volume 9, Issue 3
July 2023
Pages 739-748