Numerical analysis on initial development of longitudinal vortices over a heated horizontal plate in uniform downward flow. (May 2017) - Mitsuishi, Akihiko; Suzuki, Takashi; Kitamura, Kenzo
Highlights: Initial longitudinal vortices over a heated plate in uniform downward forced flow are successfully simulated. Determination of the spanwise pitch of the vortices is governed by characteristics of both forced and natural convection. The exponential growth rate of the relevant spanwise power is fully described by the modified Grashof and the Reynolds numbers. Abstract: Fluid flow and heat transfer from an upward-facing horizontal two-dimensional heated plate in uniform downward forced flow are analyzed by means of numerical simulation. We focus our attention to a case where the plate is heated so strongly that the effect of the buoyancy force is not negligible. The Reynolds number based on the plate length is 200 and 500, and the modified Grashof number ranges from 3 × 10 6 up to 1.5 × 10 8 . Assuming that the working fluid is air at room condition, the Prandtl number is kept at 0.71. Longitudinal vortices, discovered in the recent experimental study, are successfully simulated. Typical structures appear as pairs of counter-rotating vortices in the vicinity of the plate with hot fluid ejection in between. They are elongated over the whole plate and regularly allocated in spanwise direction with almost uniform height. Special attention is focused on initial formation of these structures. At the beginning, germs of the structures appear either at the center or on the edge of the plate one by one until the number of them reaches a certain value. The value is subject to the natural convection instability unless the radius of the relevant vortex becomes significantly smaller than the laminar boundary layer thickness of forced stagnation flow. Streamwise contiguity of the structure is established before the power of the relevant spanwise mode comes to a stage of exponential growth inside the boundary layer.