Interaction between axial and annular jets leaving a cylindrical cavity and an incoming supersonic gas flow

Abstract

Many researchers have studied pressure pulsations that arise in jets, separated flows, and bottom flows. Certain investigations devoted to oscillatory processes in Hartmann resonators were discussed in [1]. Such processes have been modeled by the method of coarse particles, the Chudov-Roslyakov finite-difference scheme, the Godunov-Kolgan scheme, and other methods.In an experiment conducted in [2], stable pressure pulses were obtained in a supersonic flow past a hollow cylindrical body (cylinder) with its open end facing the incoming flow. In [3], the experimental data obtained in [2] was compared with results calculated on the basis of kinetically consistent difference schemes. Good agreement was obtained with the experimental data within the region of Reynolds numbers Re~ _> 105, where the effect of Rer on the main characteristics of the process (mean shock-wave decay, amplitude of shock-wave pulsations, period of oscillation, standard deviations of the pressure pulsations) is negligible.Here, we use the Godunov method to examine the problem of the supersonic flow of an inviscid gas past hollow cylindrical bodies. It is shown numerically that it is possible to control oscillatory flow regimes by the injection of gas from the bottom of the cavity.1. We will examine the flow of an ideal gas with the Mach number M~. = 3.7 about a cylinder (Fig. 1). The geometric characteristics of the cylinder (//D = 1.6, 6/D = 0.04) are the same as in [2, 3].The equations of gas dynamics are as follows in the cylindrical coordinate system [4] Opr (gpur Opvr ot +--g~ + 0--7 -=0,where p is pressure; p is density; u and v are components of the velocity vector along x and r (we assume that the component associated with the angle ~o is equal to zero); e is the total energy of a unit mass of the gas; t is time. The system is closed by the equation of state of an ideal gas. The quantities were converted to dimensionless form as follows:r=~D/2, x=s t=tD/2aoo, a=aaoo, u = ftaoo, v = ~aoo, P = PPoo, P = ~pooa~ (a~. is sonic velocity in the incoming flow and D is the diameter of the cylinder (see Fig. 1)).Kharkov Aviation Institute, 310111 Kharkov.

Numerical and Experimental Investigation of Cylinder Cavity Flows

“…4), the mesh points distribution were set to be uniform. The calculations were performed using the same finite-difference scheme as that employed in references [3], [9], and [13]. Some computational results in this investigation are generated using the numerical method with modified finite-difference Godunov's scheme based on the deforming meshes [14][15][16].…”

“…It is well known that supersonic flow around bodies with cavities located on the nose is accompanied by pulsation [1][2][3]. A forward-facing cavity may be regarded as a resonance tube.…”

“…Flow stabilization by jet injection from the cavity bottom is discussed in previous work [3]. Control and manipulation of the pulsation process by energy deposition due to the influence of a pulse laser is considered as well [6][7][8][9].…”