Vortex diodes are used as leaky nonreturn valves in applications, where it is desirable to avoid valves with moving parts. Despite their use in practice for several decades, no detailed analysis of the flow inside the vortex diodes is available. A strategy was derived for the CFD simulations of the vortical flow in diodes. A good agreement was seen between pressure drop (Delta P) across the inlet-outlet ports from CFD simulations, and the experimental data for five diode sizes. The simulations showed that in the reverse flow situation tangential velocity was dominant and resulted in conservation of angular momentum in the chamber until it reaches the axial exit port. This vortical motion induced a significant pressure drop (Delta P-r). The axial velocity gradient over the chamber cross-section helps in inducing relaminarization of the flow. In the forward flow mode, the fluid gets distributed radially over the chamber and exits through the tangential port, yielding low Delta P-f. The analysis showed that the performance of a diode is strongly affected by diode geometry, size, aspect ratio, nozzle configuration and Reynolds number. Among different configurations, the nozzles with entry port size equal to diode yielded higher diodicity. Simulations showed that using angle of divergence for diffuser sections of nozzles of the order of 7 degrees exhibited higher diodicity than smaller angles. It was also observed that at higher flow rates significantly higher diodicity was obtained using axial nozzles with larger radius of curvature for expander section. The modeling methodology and results presented will be useful for evolving better designs of vortex diodes.