A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity–based shock-capturing on cut cells

We present a higher-order cut cell immersed boundary method (IBM) for the simulation of high Mach number flows. As a novelty on a cut cell grid, we evaluate an adaptive local time stepping (LTS) scheme in combination with an artificial viscosity–based shock-capturing approach. The cut cell grid is optimized by a nonintrusive cell agglomeration strategy in order to avoid problems with small or ill-shaped cut cells. Our approach is based on a discontinuous Galerkin discretization of the compressible Euler equations, where the immersed boundary is implicitly defined by the zero isocontour of a level set function. In flow configurations with high Mach numbers, a numerical shock-capturing mechanism is crucial in order to prevent unphysical oscillations of the polynomial approximation in the vicinity of shocks. We achieve this by means of a viscous smoothing where the artificial viscosity follows from a modal decay sensor that has been adapted to the IBM. The problem of the severe time step restriction caused by the additional second-order diffusive term and small nonagglomerated cut cells is addressed by using an adaptive LTS algorithm. The robustness, stability, and accuracy of our approach are verified for several common test cases. Moreover, the results show that our approach lowers the computational costs drastically, especially for unsteady IBM problems with complex geometries.     

Simulation on the Effect of Brownian Motion on Nanoparticle Trajectories in a Pulsed Microplasma Cluster Source

We describe a simulation of the nanoparticle trajectories in a pulsed cluster beam source. Clusters, formed by condensation of atomic vapor in a helium bath, and considered here as rigid spheres having a diameter of 1.5nm, were tracked during their travel inside the source cavity, an aerodynamic lens, and a cylindrical nozzle. Steady state supersonic laminar flow of helium is considered in an axi-symmetric geometry aiming to simulate, within some limitations, the conditions under which cluster formation takes place in a pulsed microplasma cluster source. In spite of the unsteady nature of the pulsed source, the time scale characterizing particle motion in the flow field is significantly smaller than the characteristic time constant for the evolution of gas pressure in the source. For this reason, a steady simulation can shed some light on the understanding of processes governing nanoparticle motion in a pulsed vaporization source. The extent to which the Brownian diffusion can affect the particle extraction from the source is investigated. Simulations have shown that the Brownian motion perturbs the clusters from the trajectories dictated by the carrier gas and increases the rate of cluster deposition on the source internal walls. However, it does not hinder the aerodynamic focalization produced by the lens even in nano-size cluster regime. This result is qualitatively confirmed by experiment.     

对可压缩流体若干问题的讨论

根据气体幼力学中一维定常等熵等流的基本方程组,得出的一维定常等熵管流的速度变化与管截面变化关系式,定性一讨论了一维定常等熵管流的截面变化对气流速度的影响。     

Effect of the stagnation temperature on supersonic flow parameters: Application for air in nozzles

When the stagnation temperature of a perfect gas increases, the specific heats and their ratio do not remain constant any more and start to vary with this temperature. The gas remains perfect and its state equation always remains valid, except it will be called a calorically imperfect gas. The aim of this research is to develop the relations of the necessary thermodynamics and geometrical ratios and to study the supersonic flow at high temperature (lower than the threshold of dissociation). The results are found by the resolution of nonlinear algebraic equations and integration of complex analytical functions where the exact calculation is impossible. The dichotomy method is used to solve the nonlinear equation, and the Simpson algorithm is used for the numerical integration of the found integrals. A condensation of the nodes is used, since the functions to be integrated have a high gradient at the extremity of the interval of integration. A comparison is made with a calorifcally perfect gas to determine the error of this. An application is made for air in a supersonic nozzle. The text was submitted by the authors in English.     

Shocks in local supersonic zones

The results of numerical integration of the Euler equations governing two-dimensional and axisymmetric flows of an ideal (inviscid and non-heat-conducting) gas with local supersonic zones are presented. The subject of the study is the formation of shocks closing local supersonic zones. The flow in the vicinity of the initial point of the closing shock is calculated on embedded, successively refined grids with an accuracy much greater than that previously achieved. The calculations performed, together with the analysis of certain controversial issues, leave no doubt that it is the intersection of C ^?-characteristics proceeding from the sonic line inside the supersonic zone that is responsible for the closing shock formation.     

Experimental study of the reverse flow in the forward separation region in a pulsating flow around a spiked body

The flow with a free-stream Mach number M _∞ = 6 around a cylindrical body with a sharp spike is studied. The existence of a supersonic reverse flow for one of the phases of the pulsating flow regime is experimentally validated. A range of spike lengths is determined, which ensures a region of a supersonic reverse flow near the side surface of the spike. The time of existence of the supersonic reverse flow region is shown to be 0.15 of the period of pulsations if the spike length equals the model diameter. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 30–39, July–August, 2007.     

Large-Scale Streamwise Vortices in the Supersonic Part of a Permeable Nozzle

Large-scale streamwise vortices in the vicinity of a perforated wall in the supersonic part of the nozzle are studied. The governing effect of gas inflow through a perforated wall on origination and parameters of streamwise vortices is experimentally established.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 68–75, September–October, 2005.     

超声速气膜冷却中激波抑制的研究

针对激波破坏超声速气膜冷却的机理,本文提出了一种壁面开孔的结构,数值研究结果表明：一方面,壁面开孔的结构能使激波作用的区域壁面附近的压力分布较均匀,从而使近壁区的马赫数分布比不开孔的壁面要高,有利于超声速气膜冷却。同时在激波的作用下,冷却气体可以通过开孔壁面的孔进入槽道内,而在槽内的下游再从孔里流出,保护下游的壁面,这...     

On the choice of approximations in direct problems of nozzle design

Two problems are considered: the design of a supersonic nozzle with a uniform exit characteristic and the design of a subsonic nozzle part with a plane (straight) sonic line in the minimum cross section. It is shown how the choice of a nozzle profile approximation affects the direct solutions to variational gas dynamics problems. The nozzle profile is described by polynomials or splines (quadratic, cubic, rational). The varied variables are the profile’s expansion coefficients in terms of basis functions or the parameters to be interpolated. It is shown that a priori information on the monotonicity of the desired profile improves the efficiency of the solution.