In order to further improve the cooling performance of a water-collecting box (WCB) for the high temperature exhaust gas in an engine exhaust system, a numerical simulation was performed to explore the effect of swirl intensity on the heat and mass transfer between the hot exhaust gas and the water droplets. The Eulerian-Lagrangian method and the discrete phase model were used in the three-dimensional simulation of the cross-flow spray cooling in the WCB. The swirl number was theoretically derived at a certain section of the vortex chamber in the WCB. The analytical swirl number was obtained using an analytical formula and was compared with the numerical solution. The results indicate that the swirling flow in the vortex chamber is strong and that the analytical swirl number agrees well with the numerical solution. A “barrier” is formed in the exhaust chamber, and the effective motion distance of the water droplets in the upstream zone of the “barrier” are longer than that of the droplets in the downstream zone. Raising the swirl intensity of gas flow will enhance the mix of two phases, and the effective motion distances and the evaporating time of the droplets will be prolonged. In order to enhance the spray cooling effect, the initial location where the water droplets enter the gas stream should be in the upstream zone of the “barrier”.