M. S. Ivanov

Transition between regular and Mach reflection of shock waves: new numerical and experimental results

Abstract. New numerical and experimental results on the transition between regular and Mach reflections of steady shock waves are presented. The influence of flow three-dimensionality on transition between steady regular and Mach reflection has been studied in detail both numerically and experimentally. Characteristic features of 3D shock wave configuration, such as peripheral Mach reflection, non-monotonous Mach stem variation in transverse direction, the existence of combined Mach-regular-peripheral Mach shock wave configuration, have been found in the numerical simulations. The application of laser sheet imaging technique in streamwise direction allowed us to confirm all the details of shock wave configuration in the experiments. Close agreement of the numerical and experimental data on Mach stem heights is shown.

Numerical Analysis of Shock Wave Reflection Transition in Steady Flows

Different aspects of the transition between regular and Mach reflections of strong shock waves in steady flows are numerically studied. Two approaches-kinetic (the direct simulation Monte Carlo method) and continuum (Euler equations)-are used to investigate the hysteresis phenomenon in the flow about two symmetrical wedges in two- and three-dimensional statements. The dependence of the final shock wave configuration on initial conditions, the transition from regular to Mach reflection by means of flow perturbations, and three-dimensional effects are examined. The three-dimensionality of the flow is shown to increase the angles of transition from regular to Mach reflection and back and to decrease the Mach stem height

On the use of chemical reaction rates with discrete internal energies in the direct simulation Monte Carlo method

The conventional chemical reaction models of the direct simulation Monte Carlo method developed with the assumption of continuous rotational or vibrational modes that are shown to exhibit systematic errors when used with discrete energy modes. A reaction model is proposed that is consistent with the use of discrete energy distributions of rotational and vibrational modes, and is equally applicable to diatomic and polyatomic systems. The sensitivity of the model to variations of different reaction rate parameters is examined. The revised chemical reaction model is then applied to the modeling of hypersonic flows over spacecraft in the Martian and Earth atmospheres.

Investigation of the hysteresis phenomena in steady shock reflection using kinetic and continuum methods

The problem of transition of planar shock waves over straight wedges in steady flows from regular to Mach reflection and back was numerically studied by the DSMC method for solving the Boltzmann equation and finite difference method with FCT algorithm for solving the Euler equations. It is shown that the transition from regular to Mach reflection takes place in accordance with detachment criterion while the opposite transition occurs at smaller angles. The hysteresis effect was observed at increasing and decreasing shock wave angle.

Measurements and simulation of orifice flow for micropropulsion testing

Numerical and experimental results for a rarefied gas expansion through a thin circular orifice are presented. The orifice flow was used as a calibration test for a torsional thrust stand designed to measure force levels from 10 - 6 to 10 - 3 N. Molecular nitrogen, argon, and helium at room temperature are used as test gases. The mass flux and thrust measurements are compared with the direct simulation Monte Carlo results for Knudsen numbers from 40 to 0.01 and plenum to facility background pressure ratios of 10 3 - 10 7 . Factors that affect the total propulsive force, such as jet backflow and facility background gas penetrating the jet, are analyzed. The measured and calculated mass flux and total propulsive force were found to agree well for Knudsen numbers less than 1.

Experiments on shock wave reflection transition and hysteresis in low-noise wind tunnel

Experiments on the transition between steady regular and Mach reflections of shock waves have been performed in a low-noise wind tunnel. Owing to a very low level of free-stream disturbances inherent in this facility, the hysteresis phenomenon has been observed in close agreement with theoretical predictions and results of the previous numerical simulations. When increasing the incident shock wave angle, regular reflection persists in most of the dual solution domain. Thus, the detachment criterion can be considered as a true one for the transition from regular to Mach reflection, and an earlier transition observed in many wind tunnel experiments is certainly caused by free-stream disturbances, which were present in those facilities.

Numerical Investigation of Shock-Reflection Phenomena in Overexpanded Supersonic Jets

The transition from regular to Mach reflection in a supersonic planar jet operating under overexpanded conditions has been studied numerically. First, inviscid computations are performed by the solution of Euler equations. The results demonstrate that a hysteresis phenomenon is observed as the jet/ambient pressure ratio decreases and increases, causing a change in the angle of incidence of the nozzle-lip shock and, as a consequence, the transition from regular to Mach reflection and back. The angles of forward and backward transitions are close to the theoretical detachment and von Neumann criteria, respectively. Furthermore, turbulent computations (by the use of an improved two-equation model) are conducted to investigate the transition in a more realistic situation

Flow-Mach-Number-Variation-Induced Hysteresis in Steady Shock Wave Reflections

Introduction TWO shock-wave-rex8fection conx8e gurations, regular rex8f ection (RR) andMach rex8f ection (MR), are possible in steady x8f ows.1 The RR and the MR consist of two and three shock waves, respectively.Two extreme angles of incidence are associatedwith the oblique rex8f ection of a shock wave. They are the von Neumann A and the detachment AD angles (AD >AN ). For a given x8f ow Mach number, A is the smallest angle of incidence for which an MR is theoretically possible, and AD is the largest angle of incidence for which an RR is theoretically possible. Consequently, an MR is impossible for A AD . For incident angles in the range A ·A ·A both RR andMR are theoretically possible. Consequently, the RR

Entropy considerations in numerical simulations of non-equilibrium rarefied flows

MR transition could take place at any angle of incidence A inside that range. The angle of incidence A is determined by the x8f ow Mach number M and wedge angle μw . Therefore, it is convenient to represent the detachment and von Neumann criteria in the (M; μw ) plane, as is shown in Fig. 1, where μ N w and μ D w , the wedge angles that correspond to the mentioned criteria, are shown for a perfect gas with a specix8e c heats ratio of ° D 1:4. The curves μ N w .M/ and μ D w .M / divide the plane into three domains: a domain in which only RR is theoreticallypossible, a domain in which only MR is theoretically possible, and a domain, known as the dual-solutiondomain, in which both RR and MR are theoreticallypossible.Note that the curve correspondingto μ N w reaches a maximum value of μ N w;max D 20:92 deg at M D 4:46. At large values of M , the curves corresponding to both μ N w and μ D w approachasymptoticvaluesequal to 17.96and 32.02deg, respectively.

Comparison of direct simulation Monte Carlo chemistry and vibrational models applied to oxygen shock measurements

Abstract Non-equilibrium rarefied flows are encountered frequently in supersonic flight at high altitudes, vacuum technology and in microscale devices. Prediction of the onset of non-equilibrium is important for accurate numerical simulation of such flows. We formulate and apply the discrete version of Boltzmann’s H -theorem for analysis of non-equilibrium onset and accuracy of numerical modeling of rarefied gas flows. The numerical modeling approach is based on the deterministic solution of kinetic model equations. The numerical solution approach comprises the discrete velocity method in the velocity space and the finite volume method in the physical space with different numerical flux schemes: the first-order, the second-order minmod flux limiter and a third-order WENO schemes. The use of entropy considerations in rarefied flow simulations is illustrated for the normal shock, the Riemann and the two-dimensional shock tube problems. The entropy generation rate based on kinetic theory is shown to be a powerful indicator of the onset of non-equilibrium, accuracy of numerical solution as well as the compatibility of boundary conditions for both steady and unsteady problems.