NUMERICAL INVESTIGATION OF FLOW-PROPERTY CHANGES ACROSS NORMAL SHOCK WAVES IN SUPERSONIC AIRFLOW

Author

Muskaan Banu , Bhavyashree M, Itika Sharma, Ayeesha MS, Anushree M, Khushwanth, S Kalyan Yadav

Abstract

 A normal shock wave is an irreversible compression phenomenon in which a supersonic stream is abruptly converted into a subsonic stream. The present report examines the changes in Mach number, static pressure, density, temperature, stagnation pressure and entropy for air represented as a calorically perfect gas with a constant specific-heat ratio of γ = 1.4. The governing relations are derived from conservation of mass, momentum and energy and are evaluated over an upstream Mach-number range extending from 1.2 to 3.5. The results show that stronger shocks produce larger increases in static pressure, density and temperature, while the downstream Mach number and stagnation-pressure recovery decrease. A detailed literature survey is included to place the one-dimensional normal-shock model in the wider context of classical gas dynamics, experimental shock studies, shock-wave/boundary-layer interaction, computational methods and aerospace applications. The ideal-gas calculation is intended as a transparent baseline for preliminary analysis and for comparison with more complex numerical or experimental work.

Keywords

Normal shock; compressible flow; supersonic aerodynamics; Mach number; stagnation pressure; entropy generation; shock-boundary-layer interaction.

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References

[1] Ames Research Staff, “Equations, Tables, and Charts for Compressible Flow,” NACA Report 1135, 1953. NASA Technical Reports Server: https://ntrs.nasa.gov/citations/19930091059.

[2] NASA Glenn Research Center, “Normal Shock Wave Equations,” Beginner’s Guide to Aeronautics. https://www.grc.nasa.gov/www/k-12/airplane/normal.html.

[3] J. D. Anderson, Jr., Modern Compressible Flow: With Historical Perspective, 3rd ed., McGraw-Hill, 2003.

[4] L. Davies and D. H. Edwards, “An experimental investigation of the reflected-shock pressure-time profiles for air, oxygen, nitrogen, argon, carbon dioxide and acetylene,” Journal of Fluid Mechanics, 1964.

[5] C. duP. Donaldson, “Effects of Interaction Between Normal Shock and Boundary Layer,” NACA, 1944.

[6] J. E. Green, “Interactions between shock waves and turbulent boundary layers,” Progress in Aerospace Sciences, vol. 11, pp. 235–340, 1970.

[7] G. G. Mateer, A. Brosh, and J. R. Viegas, “A normal shock-wave turbulent boundary-layer interaction at transonic speeds,” AIAA Paper 76-161, 1976.

[8] Y. Andreopoulos, J. H. Agui, and G. Briassulis, “Shock wave–turbulence interactions,” Annual Review of Fluid Mechanics, vol. 32, pp. 309–345, 2000.

[9] J. Delery, J. G. Marvin, and E. Reshotko, Shock-Wave Boundary-Layer Interactions, AGARDograph 280, NATO, 1986.

[10] P. M. Ligrani, E. S. McNabb, H. Collopy, M. Anderson, and S. M. Marko, “Recent investigations of shock wave effects and interactions,” Advances in Aerodynamics, vol. 2, article 4, 2020. https://doi.org/10.1186/s42774-020-0028-1.

[11] D. V. Gaitonde and M. C. Adler, “Dynamics of three-dimensional shock-wave/boundary-layer interactions,” Annual Review of Fluid Mechanics, vol. 55, pp. 291–321, 2023. https://doi.org/10.1146/annurev-fluid-120720-022542.

[12] K. Sabnis and H. Babinsky, “A review of three-dimensional shock wave–boundary-layer interactions,” Progress in Aerospace Sciences, 2023.

[13] T. Jana and M. Kaushik, “Survey of control techniques to alleviate repercussions of shock-wave and boundary-layer interactions,” Advances in Aerodynamics, vol. 4, article 27, 2022.

[14] J. D. Anderson, Jr., Hypersonic and High-Temperature Gas Dynamics, 2nd ed., AIAA, 2006.

[15] S. M. Yahya, Fundamentals of Compressible Flow with Aircraft and Rocket Propulsion, 4th ed., New Age International, 2011.

[16] E. Rathakrishnan, Gas Dynamics, 2nd ed., Prentice Hall of India, 2010.

[17] E. Rathakrishnan, Applied Gas Dynamics, Wiley, 2010.

[18] NASA Glenn Research Center, “Oblique Shock Waves,” Beginner’s Guide to Aeronautics. https://www.grc.nasa.gov/www/k-12/airplane/oblique.html.

[19] R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience, 1948.

[20] H. W. Liepmann and A. Roshko, Elements of Gasdynamics, Wiley, 1957.

[21] A. H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow, Vols. I–II, Ronald Press, 1953.

[22] M. J. Zucrow and J. D. Hoffman, Gas Dynamics, Vol. I, Wiley, 1976.

[23] P. A. Thompson, Compressible-Fluid Dynamics, McGraw-Hill, 1972.

[24] W. H. J. Sutton and A. G. S. Sutton, Rocket Propulsion Elements, 9th ed., Wiley, 2017.

[25] R. W. Zucker and O. Biblarz, Fundamentals of Gas Dynamics, 2nd ed., Wiley, 2002.

[26] J. F. Clarke and M. McChesney, The Dynamics of Real Gases, Butterworths, 1964.

[27] J. D. Anderson, Computational Fluid Dynamics: The Basics with Applications, McGraw-Hill, 1995.

[28] C. Hirsch, Numerical Computation of Internal and External Flows, Vol. 2, Wiley, 1990.

[29] R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002.

[30] E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, 3rd ed., Springer, 2009.

[31] P. L. Roe, “Approximate Riemann solvers, parameter vectors, and difference schemes,” Journal of Computational Physics, vol. 43, pp. 357–372, 1981.

[32] B. van Leer, “Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method,” Journal of Computational Physics, vol. 32, pp. 101–136, 1979.

[33] A. Harten, “High resolution schemes for hyperbolic conservation laws,” Journal of Computational Physics, vol. 49, pp. 357–393, 1983.

[34] P. L. Roe, “Characteristic-based schemes for the Euler equations,” Annual Review of Fluid Mechanics, vol. 18, pp. 337–365, 1986.

[35] J. L. Steger and R. F. Warming, “Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods,” Journal of Computational Physics, vol. 40, pp. 263–293, 1981.

[36] A. Jameson, W. Schmidt, and E. Turkel, “Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes,” AIAA Paper 81-1259, 1981.

[37] S. K. Godunov, “A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics,” Matematicheskii Sbornik, vol. 47, pp. 271–306, 1959 (English translation).

[38] P. D. Lax, “Weak solutions of nonlinear hyperbolic equations and their numerical computation,” Communications on Pure and Applied Mathematics, vol. 7, pp. 159–193, 1954.

[39] R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems, 2nd ed., Interscience, 1967.

[40] P. Colella and P. R. Woodward, “The piecewise parabolic method (PPM) for gas-dynamical simulations,” Journal of Computational Physics, vol. 54, pp. 174–201, 1984.

[41] P. Woodward and P. Colella, “The numerical simulation of two-dimensional fluid flow with strong shocks,” Journal of Computational Physics, vol. 54, pp. 115–173, 1984.

[42] G. A. Sod, “A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws,” Journal of Computational Physics, vol. 27, pp. 1–31, 1978.

[43] D. S. Balsara, “Divergence-free adaptive mesh refinement for magnetohydrodynamics,” Journal of Computational Physics, vol. 174, pp. 614–648, 2001.

[44] D. S. K. Yee, “A class of high-resolution explicit and implicit shock-capturing methods,” NASA TM-89464, 1987.

[45] D. Knight, H. Yan, A. G. Panaras, and A. Zheltovodov, “Advances in CFD prediction of shock wave turbulent boundary layer interactions,” Progress in Aerospace Sciences, vol. 39, pp. 121–184, 2003. https://doi.org/10.1016/S0376-0421(02)00069-6.

[46] D. Ranjan, J. Oakley, and R. Bonazza, “Shock-bubble interactions,” Annual Review of Fluid Mechanics, vol. 43, pp. 117–140, 2011. https://doi.org/10.1146/annurev-fluid-122109-160744.

[47] G. Ben-Dor, Shock Wave Reflection Phenomena, 2nd ed., Springer, 2007.

[48] G. Ben-Dor, Shock Wave Reflection Phenomena, Springer, 1992.

[49] J. D. Anderson, “A history of aerodynamics and its impact on high-speed flight,” Cambridge University Press, 1997.

[50] R. J. Goldstein (ed.), Fluid Mechanics Measurements, 2nd ed., Taylor & Francis, 1996.

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