CAPM vs. Bulk Flow - reliable and efficient prediction of forces and leakage for annular gaps in pumps

The interaction of rotor and casing is strongly influenced by the flow in annular gaps of pumps. State of the art in efficient prediction of forces and leakage at high Reynolds numbers are models based on the bulk flow theory (Childs, 1993). This bulk flow model omits viscous stress in the fluid and generally provides hydrodynamic variables only as sine/cosine functions over the gap circumference. Motivated by the uncertainty of the predictions caused by these approximations, a more physical model was developed in recent works at TU Darmstadt. The CAPM (clearance averaged pressure model) takes into account viscous friction, both laminar and turbulent, by means of ansatz functions for velocity profiles. The only inherent assumption is constant pressure over the gap height due to the small ratio of mean gap height to the radius of the rotor. Axial and circumferential coordinates are treated differentially, the radial coordinate is treated with integrals over gap height. Thus, the solver for the model is based on a two dimensional finite differencing scheme solving the complete nonlinear continuity, axial and circumferential momentum equations via a SIMPLEC algorithm. As yet, the implementation was validated extensively with hypothetical turbulent test cases by means of CFD (Lang, 2018). In the presented paper, suitable boundary conditions for the CAPM are described which allow for successful calculation of real application cases. Furthermore the CAPM is compared to a bulk flow model at typical operation conditions of media lubricated journal bearings where neither inertia nor viscous effects are negligible. Increasing differences of the predictions of the two models are seen for high eccentricities, high flow number and long annular gaps.