We numerically investigated steady axisymmetric flow through and around a porous disk with aspect ratio ($\chi$) ranging from 1 to 20, Reynolds number (Re) varying from 10 to 120, and Darcy number (Da) ranging from ${10}^{-6}$ to 1. The wake characteristics are presented in terms of the streamline patterns, the geometrical parameters as well as the occurrence of the recirculating wake. In particular, the bifurcation curves in the Re-Da parametric space can be collapsed onto approximately the same curve for all $\chi$ when the modified $\chi \text{Da}$ is used. Both $\chi$ and Da are demonstrated to be closely related to the drag and have similar effects on the flow behavior. The formation mechanism of recirculating wake at different $\chi$ is further discussed with respect to the base bleed quantified by the flow rate as well as the vorticity accumulation and decay.

• Received 29 January 2021
• Accepted 10 June 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.074101