Flow dynamics in the radial-annular cavity of turbomachines

This paper considers the problem of modeling a rotational flow in the radial-annular cavity of turbo machines with fixed walls. This case corresponds to the boundary conditions of the supply channel for a radial centripetal turbine. In the presented model, the flow is conventionally divided into radial and circumferential movement. The radial component of the velocity is determined by the mass flow rate from the continuity equation, the circumferential component is formed by the tangential channel supply. The main equation in the integration is the equation of the change in the momentum for the flow in the form of the Euler equation. In the case of the circumferential component of the velocity, the angular momentum law is used, assuming the potentiality of the flow and the constancy of the angular momentum within the integration step. As a result of the transformations of the motion equations, differential equations for the radial, circumferential component of velocity and static pressure are obtained, which represent a certain system of three equations in three unknowns. The system of equations allows integration under known boundary conditions at the inlet; as a result of integration, it is possible to obtain the field of distributions of velocities and pressures along the radius of the radial-annular cavity. The results of the study can be used in modeling the circumferential and radial forces on the rotor (impeller) of turbo machines.