I. E. Ivanov

Study of the shock wave structure by regularized Grad’s set of equations

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 s...

Study of the shock wave structure by regularized Grad's set of equations

This study is devoted to the analysis of applicability of moment equations to the shock wave structure problem in a wide range of Mach numbers. A modification of original Grads 13-moment set of equations, so-called regularized Grads set of equations (R13), is taken as a mathematical model. The numerical method for this set is formulated as a variant of the explicit high-order Godunov scheme with linear reconstruction of flow parameters. The degree of applicability of moment equations is determined by comparisons with Direct Simulation Monte Carlo (DSMC) predictions. Numerical results for hard sphere molecules show that the R13 set of equations describes well the internal structure of the shock wave in a wide range of Mach numbers. Nevertheless, R13 set significantly overpredicts the overall temperature overshoot (about 3 times for M=8), which is apparently related to nonlinearity of the dependence of the product of the transverse temperature component and density on normalized density.

Application of moment equations to the mathematical simulation of gas microflows

An approach to the simulation of moderately rarefied gas flows in a transition zone is developed. The applicability of the regularized Grad 13-moment (R13) equations to the numerical simulation of a transition flow between the continual and free-molecular gas flow regimes is explored. For the R13 equations, a numerical method is proposed that is a higher order accurate version of Godunov’s explicit method. A numerical procedure for implementing solid-wall boundary conditions is developed. One- and two-dimensional test problems are solved, including the shock wave structure and the Poiseuille flow in a plane channel. The possibility of applying the R13 equations to the simulation of plane channel and jet flows in a transition regime is explored. To this end, the flow in a square cavity generated by the motion of one of the walls is studied and the operation of the Knudsen pump is analyzed.

2D numerical simulation of gas flow interaction with a solid wall by regularized Grad's set of equations

This study is devoted to the two-dimensional numerical simulation of gas flow in the transition regime with solid wall interaction. The regularized 13-moment Grads set of equations (R13) [1,2] was chosen as a mathematical model. A variant of explicit high order Godunov-type scheme with linear flow parameter reconstruction is used for the numerical solution of this set of equations. Numerical method for wall boundary conditions is based on Newtons iterative method suggested here. Couette and Poiseuille flows and lid-driven cavity flow were solved as test examples with this numerical scheme.

Numerical simulation of separated flow in nozzle with slots

A mathematical model and a high-resolution numerical method for numerical simulation of turbulent separated flow in convergent–divergent nozzles are presented. A comparison between numerical calculations and experimental data for plane and axi-symmetric nozzles shows an efficiency and a reasonable accuracy of a numerical code based on the proposed model. A detailed computational study of separated nozzle flows has been conducted for nozzles with one or two circular slots. The possibility for increasing in thrust efficiency is shown under ground conditions due to decreasing of overexpanded flow zone.

An Approach for Delaunay Tetrahedralization of Bodies with Curved Boundaries

Problem of tetrahedral meshing of three-dimensional domains whose boundaries are curved surfaces is wide open. Traditional approach consists in an approximation of curved boundaries by piecewise linear boundaries before mesh generation. As the result mesh quality may deteriorate. This paper presents a technique for Delaunay-based tetrahedralization in which a set of constrained facets is formed dynamically during face recovery and mechanisms for mutual retriangulation of the curved faces and the tetrahedralization are suggested. The proposed algorithm is constructed in such a way that a facet that was once added in the set of constrained facets is never split into small triangles. It allows retaining the high quality of surface mesh in the tetrahedralization, because during boundary recovery the surface mesh on the curved faces and the tetrahedralization are refined conjointly.

Shock-wave structure formation by nanosecond discharge in helium

We have experimentally studied and numerically simulated the shock-wave flow that arises as a result of the development of a system of microchannels of pulsed sliding surface discharge in helium at low pressure. Using numerical simulations based on a solution of the system of regularized Grad equations (R13) and Navier-Stokes equations, results obtained for various Knudsen numbers are compared and it is shown that the influence of rarefaction on the discharge-plasma-induced shock-wave flow is manifested in a transient regime at Kn = 10−1.

The development of turbulence behind a shock wave front moving in an inhomogeneous region

We have studied the formation of vortex structures and the development of turbulence behind the front of a shock wave with Mach number M = 1.5–3.0 moving along a near-wall gas layer excited by a nano-second pulsed transverse surface discharge within 40–500 μs after initiation. Schlieren images of the flow are compared to the results of two-dimensional numerical simulations based on the Navier-Stokes equations and a pulsed energy deposition model.

Investigation of the Interaction of a Shock Wave with the Zone of a Pulsed Surface Discharge in a Rectangular Channel

This study concerns the effect of the zone of a plane surface energy deposition on a gas-dynamic flow with a shock wave of M = 2.3–2.7 in a channel with a rectangular cross section. The source of the pulsed energy is a distributed sliding nanosecond discharge that develops in an approximately 1-mm-thick layer on a surface of 100 × 30 mm2. The results of a 3D numerical simulation of the problem on the basis of the Navier-Stokes equations for a compressed gas are presented and compared with the experimental shadow images.

Pulsed action on a shock wave in the case of self-localized high-current surface discharge in front of the shock-wave front

The directional use of plasmas produced by localized surface discharges seems to be rather efficient for correcting supersonic high-enthalpy flows. This is true under the condition of rapid conversion of the discharge-current energy to the translational energy of gas molecules. The frequency-periodic regime of the energy supply is the most efficient for the quasi-stationary local action on discontinuities, the boundary layer, and flow-separation zones [1]. Based on the concept of electric actuators, we offer to directly transform the energy of the electric-current arising in the case of flows around surfaces to the energy of gas molecules. This action on the boundary layer is rather efficient in subsonic regimes of flows around surfaces [2, 3]. The interest in controlling characteristics of transonic and supersonic flows around various structural elements with the use of an external energy supply results in searching for intense sources of the corresponding energy action. The intensity of the energy-contribution source can be estimated as the ratio of the energy absorbed by the gas per pulse to the total enthalpy of the incident flow in the source volume.