The exchanges between a recirculating flow and its external main flow were determined by numerical simulation in the range of Froude number, from Fr = 0.2 to 4.5, much higher than any of the previous studies. We used a well-calibrated WENO scheme to capture the shock waves while maintaining the numerical stability of the computation. The momentum-exchange coefficient was found to reduce with the Froude number. The mass-exchange coefficient, however, is observed to have a sudden jump at the Froude number of Fr ≃ 3 associate with the formation of the shock waves within the recirculating region.