The annelid body wall generally comprises an outer layer of circular muscle fibres and an inner layer of longitudinal muscle fibres as well as parapodial and chaetal muscles. An investigation of Dysponetuspygmaeus (Chrysopetalidae) with confocal laser scanning microscopy showed that circular muscles are entirely absent. Further studies indicate that this feature is characteristic for all Chrysopetalidae. A scrutiny of the literature showed a similar situation in many other polychaetes. This lack of circular muscle fibres may either be due to convergence or represent a plesiomorphic character. Since circular muscles are very likely important for burrowing forms but not necessary for animals which proceed by movements of their parapodial appendages or cilia, this problem is also related to the question of whether the ancestral polychaete was epi‐ or endobenthic.
In this work, we continue to study the possibility of applying moment equations for strongly nonequilibrium flows by an example of the problem of the shock wave structure in a monatomic gas in a wide range of Mach numbers for various models of molecular interaction. The object of the study is the so-called regularized 13-moment Grad's system (R13). First time, both linear and nonlinear versions of this system of equations were considered for the problem at such wide range of parameters. The Godunov method with increased accuracy is used as a numerical tool for solving the R13 system. The numerical results for the R13 system are analyzed by using data obtained by the Direct Simulation Monte Carlo (DSMC) method, experimental data, and analytical results. As a whole, the R13 system provides an adequate description of the shock wave structure in a wide range of Mach numbers. For Mach numbers around 2, good agreement with experimental and DSMC results is observed for both linear and nonlinear versions of the system. For high Mach numbers, the result strongly depends on the molecular interaction model used: shock wave structure predictions of the nonlinear R13 system are better for Maxwell molecules and worse for hard spheres as compared to the linear version. Particular attention in this work is paid to studying nonmonotonicity of the total temperature profile (temperature overshoot) in the structure of a strong shock wave. It is shown that the moment equations correctly predict the existence of the temperature overshoot. At the same time, the solution of the moment equations overpredicts the temperature overshoot at least two-fold for Mach number M = 8, and the nonlinear version of the R13 system yields a better result for this parameter than the linear version. C 2015 AIP Publishing LLC. [http://dx.
Articles you may be interested inInternal energy relaxation in shock wave structure Phys. Fluids 25, 126102 (2013); 10.1063/1.4837275 Study of the shock wave structure by regularized Grad's set of equations AIP Conf.
The spatial structure of radiation of a surface sliding discharge with a duration of ~ 300 ns (plasma sheet) in inhomogeneous supersonic air flows including oblique shock wave in a discharge chamber of shock tube was experimentally investigated. The flows were created behind plane shock waves with Mach numbers 2.8-4.2; flow Mach numbers were 1.30-1.60. The flow in the discharge chamber included an oblique shock wave generated by the interaction of a supersonic flow with a small obstacle, and then reflected from the upper wall of the discharge chamber. In this case, the shock wave interacted with the boundary layer of the supersonic flow, which formed on the streamlined wall. A surface sliding discharge with a length of 100 mm and 30 mm wide was initiated on a streamlined surface at a certain moment in time. The discharge current, emission spectra, and spatial characteristics of the radiation under various conditions of discharge initiation were obtained and analyzed in experiments. The time dependence of geometry of the discharge glow region was obtained by digital processing of discharge images in flows. CFD simulation was performed to determine the shock-wave structure of the flow in the channel with an obstacle under experimental conditions. The comparison of experimental data with the results of numerical calculation of the supersonic flow field was done. It was shown that the spatial distribution of radiation from a surface sliding discharge visualizes the low density areas and the separation zone formed under the interaction of an oblique shock wave with a boundary layer.
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