The efficiency requirements for hydraulic pumps applied in automatic transmissions in future generations of automobiles will increase continuously. In addition, the pumps must be able to cope with multiphase flows to a certain extent. Given this background, a balanced vane pump (BVP), an internal gear pump (IGP) and a three-dimensional geared tumbling multi chamber (TMC) pump are analyzed and compared by a computational fluid dynamics (CFD) approach with ANSYS CFX and TwinMesh. Furthermore, test bench measurements are conducted to obtain experimental data to validate the numerical results. The obtained numerical results show a reasonable agreement with the experimental data. In the first CFD setup, the conveying characteristics of the pumps with pure oil regarding volumetric efficiencies, cavitation onset and pressure ripple are compared. Both the IGP and the BVP show high volumetric efficiencies and low pressure ripples whereas the TMC shows a weaker performance regarding these objectives. In the second CFD setup, an oil-bubbly air multiphase flow with different inlet volume fractions (IGVF) is investigated. It can be shown that free air changes the pumping characteristics significantly by increasing pressure and mass flow ripple and diminishing the volumetric efficiency as well as the required driving torque. The compression ratios of the pumps appear to be an important parameter that determines how the multiphase flow is handled regarding pressure and mass flow ripple. Overall, the BVP and the IGP show both a similar strong performance with and without free air. In the current development state, the TMC pump shows an inferior performance because of its lower compression ratio and therefore needs further optimization.