In this paper an analytical model is presented for fluid couplings in aero-engine applications. It can be used to predict the performance of fully filled as well as partially filled couplings in terms of a transmitted torque. As such it will lead to a predictive tool for design purposes. The model makes use of toroidal coordinates. This allows for the assessment of the mass flux and angular momentum flux within the entire toroid halves, formed by the driving unit (pump) and driven unit (turbine). In previous work only the fluxes at the coupling plane (between pump and turbine) could be evaluated, since cylindrical coordinates were used. The Euler equations in toroidal coordinates are used to obtain approximate solutions for the 2D pressure field within these toroid halves. Assuming that the pressure within an air cavity of a partially filled coupling is constant, the air-oil interface, flow regime (annular, stratified) and fill status are obtained from contours of constant pressure. In previous work the pressure distribution is not considered, except in criteria for the flow regimes, based on the centrifugal and vortex head in the coupling plane. The analytical model is validated. It shows a good agreement with torque measurements on a fully filled coupling, after a Reynolds dependency for the power loss coefficients is introduced. It shows a reasonable, qualitative agreement with CFD simulations on a partially filled coupling, after the solution for the pressure distribution is corrected for the variable vortex speed and radial velocity component. The analytical approach is efficient compared to CFD, which is very expensive in terms of CPU times, in particular for the two-phase flow in partially filled fluid couplings.

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