Investigation of a Gas Flow with Solid Particles in a Supersonic Nozzle

Abstract

A two-phase flow with high Reynolds numbers in the subsonic, transonic, and supersonic parts of the nozzle is considered within the framework of the Prandtl model, i.e., the flow is divided into an inviscid core and a thin boundary layer. Mutual influence of the gas and solid particles is taken into account. The Euler equations are solved for the gas in the flow core, and the boundary-layer equations are used in the near-wall region. The particle motion in the inviscid region is described by the Lagrangian approach, and trajectories and temperatures of particle packets are tracked. The behavior of particles in the boundary layer is described by the Euler equations for volume-averaged parameters of particles. The computed particle-velocity distributions are compared with experiments in a plane nozzle. It is noted that particles inserted in the subsonic part of the nozzle are focused at the nozzle centerline, which leads to substantial flow deceleration in the supersonic part of the nozzle. The effect of various boundary conditions for the flow of particles in the inviscid region is considered. For an axisymmetric nozzle, the influence of the contour of the subsonic part of the nozzle, the loading ratio, and the particle diameter on the particle-flow parameters in the inviscid region and in the boundary layer is studied.Key words: two-phase flow, viscous flow in the nozzle, numerical methods.Introduction. Various gas-particle flows were studied in a number of papers where the gas flow was described by the full Navier-Stokes equations, Euler equations, and boundary-layer equations. The Eulerian approach is commonly used to study the behavior of particles, with all particle parameters being averaged over an elementary volume. A more recent trend is to use the Lagrangian approach where the parameters of each particle or a particle packet are computed.The flow in the boundary layer on a flat plate with a shock wave passing along the plate was considered in [1-3]. The gas motion was described by the equations of a compressible laminar boundary layer, and the motion of particles was computed by the Euler equations. Velocity and temperature profiles for the gas and particles were presented. Outa et al.[3] compared the numerical results with their own experiments conducted with glass spheres and found that particles 50 µm in diameter are concentrated near the boundary-layer edge. Saurel et al. [4] used the Euler equations for the gas and particles. It was shown that the equations for particles are degenerate hyperbolic equations, and a special numerical method was proposed to solve them. Results of computations of the flow in a curved channel with injection of particles through the side wall were presented. In [5,6], the gas flow was computed with the use of the full Navier-Stokes equations. The two-phase flow in a shock tube was studied with allowance for the lifting force for particles.An unsteady problem for a two-phase flow behind a shock wave passing through a dusty gas in a compression corner was considered in [7]. ...

Numerical analysis of supersonic gas-dynamic characteristic in laser cutting

“…dA entry (15) The thrust is mainly determined by the pressure and velocity. In the process of laser cutting, the hole is very small, so the thrust of the cross-section area is replaced by the axial thrust in the present discussion.…”

“…On the contrary, turbulent underexpanded jets and their impingement on a plate have been extensively studied because of their wide range of applications [13][14][15][16].…”