Calculation of the Time-Averaged Flow in Squirrel-Cage Blowers by Substituting Blades With Equivalent Forces

Radial fans of the squirrel-cage type are used in various industrial applications. The analysis of such fans via computational fluid mechanics can provide the overall fan performance coefficients, as well as give insights into the detailed flow field. However, a transient simulation of a 3D machine using a sliding grid for the rotating blades still requires prohibitively large computational resources, with CPU run times in the order of months. To avoid such long simulation times, a faster method is developed in this paper. Instead of solving the transient Navier–Stokes equations, they are first averaged over one impeller rotation, and then solved for the mean flow since only this flow is of practical interest. Due to the averaging process, the blades disappear as solid boundaries, but additional equation terms arise, which represent the blade forces on the fluid. An innovative closure model for these terms is developed by calculating forces in 2D blade rows with the same blade geometry as the 3D machine for a range of flow parameters. These forces are then applied in the 3D machine, and the resulting 3D time-averaged flow field and performance coefficients are calculated. The 3D flow field showed several characteristic features of squirrel-cage blowers, such as a cross-flow pattern through the fan at low flow coefficients, and a vortexlike flow pattern at the fan outlet. The 3D fan performance coefficients showed an excellent agreement with experimental data. Since the 3D simulation solves for the mean flow, it can be run as a steady-state problem with a comparatively coarse grid in the blade region, reducing CPU times by a factor of about 10 when compared to a transient simulation with a sliding grid. It is hoped that these savings in computational cost will encourage other researchers and industrial companies to adopt the new method presented here.