The propagation of spherical and cylindrical shock waves in real gases

Abstract

Real gas and heat transfer effects are included in the solution of the blast wave resulting from a point or line explosion. Due to the extremely high temperatures, particularly at the beginning of shock propagation, the assumption of perfect gas is not valid. The equation of state takes into account the high temperature effects of vibration, dissociation, electronic excitation, and ionization, as well as the intermolecular forces at high pressures. The computation of the flow problem is carried out using the method of characteristics which has been modified to the effects of radiative and conductive heat transfer. The results show considerable deviation in the initial stages of the explosion from the perfect gas solution, in particular the temperature profiles and the thermodynamic state immediately behind the front.

Physics of meteor generated shock waves in the Earth’s atmosphere – A review

“…High temperatures (T ≥ 11,000 K) in the front shock layer (Anderson, 2006) (including the sonic and boundary region which will be defined shortly), along with densities and pressures that exceed that of the ambient air by several orders of magnitude (Bronshten, 1983), are instrumental in approximating meteor cylindrical shock waves as explosive line sources (e.g., Lin, 1954;Bennett, 1958;Sakurai, 1964;Jones et al, 1968;Plooster, 1968;Tsikulin, 1970). This approximation is valid as a large amount of energy is released per unit length in a finite cylindrical volume (Lin, 1954;Plooster, 1968;Tsikulin, 1970;ReVelle, 1974ReVelle, , 1976Steiner et al, 1994). The radius of a cylindrical region with the maximum meteor energy deposition per unit length is referred to as the characteristic or blast radius (R0) and can be expressed as: 0 = ( 0 / 0 ) 0.5 , where E0 is the energy deposited per unit path length (which in the case of a meteoroid is the same as the total aerodynamic drag per unit length) and p0 is the ambient pressure (e.g., Tsikulin, 1970;ReVelle, 1974ReVelle, , 1976Silber et al, 2015;Silber and Brown, 2019).…”

The Effects of Viscosity on the Structure of Shock Waves in a Non-Ideal Gas

“…Thus, the study of shock waves in a non-ideal gas is of great interest both from the mathematical as well as the physical point of view due to its applications in a variety of fields such as microfluids, nuclear science, geophysics, plasma physics, aerodynamics, astrophysics and interstellar medium structure. The contribution of Anisimov and Spiner [19], Steiner and Gretler [20], Kjellander et al [21], Anand [22][23][24] and many others is remarkable for the study of shock waves in non-ideal gaseous media. Wu and Roberts [25] and Roberts and Wu [26] studied the problem of a spherical implosion by considering a simplified form of Van der Waals' equation of state.…”

Time-Dependent Interaction Between Water at Supercritical Pressures and a Hot Surface

“…For example, the interpolation of water properties (this article) or the use of a real-gas equation of state (as in Ref. [6]) requires additional numerical procedures that increase the computation time and may cause convergence problems.…”

“…A general reference on the mathematical formulation involving real-gas effects is the review by Melnikoff and Plohr [5]. For example, Steiner and Gretler [6] studied the propagation of spherical and cylindrical shock waves in real gases. For the real-gas model, they used an equation of state in a general form, and in the numerical method, they relied on the method of characteristics.…”