We have carried out numerical simulations of the thermal hydraulic behavior of a neutron spallation target where liquid metal lead-bismuth serves as both coolant and as a neutron spallation source. The target is one of three designs provided by the Institute of Physics and Power Engineering (IPPE) in Russia. This type of target is proposed for Accelerator-driven Transmutation of Waste (ATW) to eliminate plutonium from hazardous fission products. The thermal hydraulic behavior was simulated by use of a commercial CFD computer code called CFX. Maximum temperatures in the diaphragm window and in the liquid lead were determined. In addition the total pressure drop through the target was predicted. The results of the CFX analysis were close to those results predicted by IPPE in their preliminary analysis.