Laminar Throughflow of Varying-Quality Steam Between Corotating Disks

Abstract

A local analysis was made of the laminar throughflow between corotating disks of a Newtonian vapor containing liquid droplets. Such a flow is of practical interest in multiple-disk turbomachinery, and specifically is a model of a two-phase, single component flow (saturated vapor - saturated liquid steam) which would arise in geothermal applications of a multiple-disk turbine. Local mass conservation and momentum equations for the vapor and droplet fields were used, as well as mass conservation and energy equations for a single droplet. The vapor-droplet interaction was modeled by a drag force based on the well-known drag coefficients for flow past spheres. The governing equations were reduced to parabolic form by order-of-magnitude arguments to allow a marching-type solution. The nonlinear partial differential equations were replaced by nonlinear finite-difference equations, which were linearized. The resulting system of linear algebraic equations was solved directly. Various results are presented, including results for a set of flow parameters which are close to those applicable for multiple-disk turbines operating on geothermal steam.