The applicability of quasi-steady theory to pressure statistics beneath roof-top vortices

During cornering winds, dual conical vortices form in the separated flow along the leading edges of flat roofs. These vortices cause the most extreme wind induced suction forces found anywhere on the building, so it is important to predict them accurately. The quasi-steady theory is commonly used to predict building surface pressures using upstream flow conditions. However, many studies have concluded that the quasi-steady theory should not be used in the separated flow regions of a building, because it underpredicts the peak and rms pressure coefficients, Cp∨ and Cprms. A wind tunnel study of a low-rise building is performed to examine why Cp∨ and Cprms are underpredicted. The study uses simultaneous pressure and velocity measurement to assess the basic assumption of quasi-steady theory in this situation, which is that an instantaneous change in wind direction (ω) will have the same effect on vortex position and strength as a long-term change in ω. This assumption is found to be valid only for wind angles of 45°±10°, and primarily for low-frequency changes in ω. This ought to actually result in an overprediction of Cp∨ and Cprms, as quasi-steady theory is shown to overestimate the effects of vortex motion due to lateral turbulence. However, the quasi-steady theory ignores the contributions to Cp∨ and Cprms from random vortex motion and random changes in vortex strength. The authors apply an analytical model of the vortex flow that links vortex behaviour to surface pressure to assess these contributions, and show that their absence results in the net underprediction of Cp∨ and Cprms, even when the quasi-steady theory is applied fully, with no linear simplifications.