Summary
A one-dimensional unsteady gas flow induced by an impulsive motion of a piston is studied by using a method of characteristics. The flow pattern in the nonisentropic flow region has been determined along particle paths emerging from the front shock into the region and along the positive characteristics emerging from the piston. The analytical solution obtained here enables us to determine the locations of the moving shock boundaries. It is found that the solution, which is also numerically computed and graphically presented, provides a good beginning toward the exact description of shock dynamics.
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References
Friedrichs, K. O.: Formation and decay of shock waves. Commun Pure Appl Math 1 (1948) 211–245
Pillow, A. F.: The formation and growth of shock waves in the one-dimensional motion of a gas. Proc Camb Phil Soc. 45 (1949) 558–586
Lighthill, M. J.: Energy distribution behind decaying shocks. The Phil Mag 41 (1950) 1101–1128
Whitham, G. B.: Linear and non-linear waves. New York: Wiley 1974
Lighthill, M. J.: Higher approximations in aerodynamic theory. Princeton: Princ. Univ. Press 1960
Mahony, J. J.: A critique of shock-expansion theory. J Aero Sci 22 (1955) 673–680
Meyer, R. E.; Ho, D. V.: Notes on nonuniform shock propagation. J Acoust Soc Am 35 (1963) 1126–1132
Sachdev, P. L.; Venkataswamy-Reddy, A.: Some exact solutions describing unsteady plane gas flows with shocks. Quart Appl Math 40 (1983) 249–272
Sharma, R. R.; Sharma, V. D.; Pandey, B. D.; Shukla P.: Approximate and numerical solutions of a gaseous flow with shocks. Quart J Mech Appl Math 46 (1993) 141–152
Ustinov, M. D.: Approximate solution to nonself-similar problem of motion of a piston after an impact. Izv. Akad. Nauk SSSR, Mech. zhid. i gaza 2 (1982) 167–171
Pert, G. J.: Self-similar flows with uniform velocity gradient and their use in modeling the free expansion of polytropic gases. J Fluid Mech 100 (1980) 257–277
Poslavskii, S. A.: A new class of exact solutions with shock waves in gas dynamics. PMM 49 (1985) 752–757
Sharma, V. D.; Ram, R.; Sachdev, P. L.: Uniformly valid analytical solution to the problem of a decaying shock wave. J Fluid Mech 185 (1987) 153–170
Sirovich, L.; Chong, T. H.: Approximate solution in gasdynamics. Phys Fluids 23 (1980) 1291–1295
Chong, T. H.; Sirovich, L.: Numerical integration of the gasdynamic equations. Phys Fluids 23 (1980) 1296–1300
Lewis, T. S.; Sirovich, L.: Approximate and exact numerical computation of supersonic flow over an airfoil. J Fluid Mech 112 (1981) 265–282
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Sharma, R.R., Pandey, B.D. & Sharma, P. The analytical solution of an unsteady gas flow with shocks. Arch. Appl. Mech. 67, 158–166 (1997). https://doi.org/10.1007/s004190050108
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DOI: https://doi.org/10.1007/s004190050108