A theoretical model for calculating particle trajectory in a vane-type separator

A vane-type separator has been successfully applied to gas-liquid and liquid-liquid separation. In order to evaluate the separation performance of the separator, a theoretical model for calculating the particle motion trajectory in the vane-type separator was developed. Firstly, the simplified steady incompressible Navier-Stokes equations were derived to acquire the equations of tangential velocity and axial velocity of continuous phase flow field. Then, the coefficients were determined by fitting the CFD results and it can be used to obtain the velocity at different swirler structure conditions. Further, the force analysis on the particle was conducted to develop the motion governing equations to predict the trajectory. The predicted separation lengths at different geometric swirl number conditions show a good agreement with the experimental results and its relative error is smaller than 3%. Besides, the effects of the key parameters including density difference, particle size and viscosity of the continuous phase on the separation length were investigated.