Computational confirmation of an abnormal Mach reflection wave configuration

Abstract

For the Mach reflection ͑MR͒ of symmetric shock waves of opposite families, only the wave configuration of an overall Mach reflection ͑oMR͒ consisting of two direct Mach reflections ͑DiMR+ DiMR͒ is theoretically admissible. For asymmetric shock waves, an oMR composed of a DiMR and an inverse Mach reflection ͑InMR͒ is possible if the two slip layers assemble a converging-diverging stream tube, while an oMR including two inverse Mach reflections ͑InMR + InMR͒ is absolutely impossible. In this paper, an overall Mach reflection configuration with double inverse MR patterns is computationally confirmed using the computational fluid dynamics technique. The aerodynamic mechanism behind such an abnormal wave pattern is illustrated. Classical two-and three-shock theories are also applied for the theoretical analysis. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3073006͔The shock wave interactions have significant impacts on the performance and reliability of a supersonic/hypersonic aircraft or a winged space shuttle during its re-entry flight. The study on shock interactions can be traced back to 1878 when Ernst Mach found two well known shock wave reflection configurations: a regular reflection ͑RR͒ and a Mach reflection ͑MR͒, which consists of a Mach stem, an incident shock, a reflected shock, and a slip layer. von Neumann 1 introduced the criteria for the RR↔ MR transition of symmetric shock waves: the von Neumann and detachment criteria. Theoretically, MR is impossible below the former, while RR is inadmissible beyond the latter. Both RR and MR are admissible between the criteria. Related research can still be found in the recent literature. [2][3][4][5][6] In the present work, an abnormal MR configuration of asymmetric shock waves is computationally confirmed over a double-wedge geometry ͑Fig.

On the modified dispersion-controlled dissipative (DCD) scheme for computation of flow supercavitation

“…The primary principle of the scheme aims at removing non-physical oscillation across strong discontinuities by making use of the dispersion characteristics of the modified equation instead of adding artificial viscosity. The DCD scheme has also been applied successfully to chemically reacting flows for compressible multi-component mixtures [24] and flows with strong shock wave interactions [25,26]. Such mentioned applications have shown that the DCD scheme is fairly robust, computationally efficient, and capable of resolving strong discontinuities.…”

“…In the original DCD scheme [22,23], the Steger-Warming (SW) method was suggested to obtain the split fluxes e F AE or e G AE . For the gasdynamic flows with an ideal gas EOS, the method works well and very efficiently [24][25][26]. Based on the Steger-Warming method, the split flux for the flux vector, e F ¼ n x F þ n y G, in the computational space can be written as…”

On the numerical technique for the simulation of hypervelocity test flows

“…1 (right). The DCD scheme has been applied to simulate shock wave problems in inert or reacting flows [21][22][23][24][25][26][27]. However, serious spurious oscillation occurs when the original DCD scheme is used for the simulation of hypervelocity test flow in the detonation-driven expansion tube, JF-16 [13,14].…”

“…The DCD scheme, without any tunable parameters, avoids encountering the 'carbuncle' phenomena altogether even for the case of very strong shock wave. It has also been successfully applied to chemically reacting flows for compressible multi-component mixtures [21][22][23][24][25] and flows in the presence of strong shock wave interaction [26,27]. The mentioned applications have attested to the DCD scheme as fairly robust, computationally efficient, and capable of resolving strong discontinuities.…”

“…(11). The original DCD scheme is easy for programming and computationally cheap due to the aforementioned simplicity which has been used successfully in a series of applications [21][22][23][24][25][26][27] except the simulation of shockexpansion tube running at high enthalpy. For the updated DCD scheme, however, the flow variables used for calculating the eigenvectors and eigenvalues are different from those used for the unknown vector as can be seen from Eq.…”