Effect of apex and attack angles to horseshoe vortex formed around a pyramid obstacle

Abstract

The effect of apex and attack angles to the flow around a pyramid obstacle was investigated with flow visualization and laser Doppler velocimetry. The flow visualization was performed by dye injection and electrolytic etching methods. The Reynolds number based on the height of the pyramid is 600. The apex angle, 2α, is in the range of 15 through135 degrees, and the attack angle,γ, is 0 and 45 degrees. It seems like the flow in upstream region of the pyramid is divided into two patterns; two and four vortex systems. The height of the primary vortex of horseshoe vortices takes a maximum value around 2α=90 degree for γ=0 degree, but 2α=45 degree for γ=45 degree. The height for γ=45 degree is lower compared with the result for γ=0 degree. The dependency on 2α and γ of the additional stain rate due to the obstacle can be formulated with the spanwise component of fluid velocity along the obstacle surfaces and the streamwise projected base width. The maximum vorticity, |Ω|_maxδ^*_us /U_∞ where U_∞ is free stream velocity and δ^*_us is the displacement thickness near the upstream separation point, of the primary vortex varies depending on the magnitude of the vortex stretching due to the additional strain rate multiplied by time scale that the fluid passes through the obstacle. The vortex system is two vortices for |Ω|_maxδ^*_us /U_∞ <1.5, and four vortices for |Ω|_maxδ^*_us /U_∞ >1.5.