# Analysis of Cavity Corner Geometry Effect on Recirculation Zone Structure
## 1 Introduction  
Research of fluid dynamics in channels with sudden expansion and contraction is common due to its simple geometry and complex physics, including widely known phenomena such as Taylor-Gortler vortices, corner and longitudinal vortices, the complex transition from laminar to turbulent flow, complex heat exchange processes, etc. Moreover, these phenomena have practical application, such as in aeronautics, automobile aerodynamics, and other industrial applications. It is generally agreed to classify channels with sudden expansion and contraction into three types: open-type cavity (\(L/h_{1}<10\)), transitional-type cavity (\(10<L/h_{1}<13\)) and closed-type cavity (\(L/h_{1}>13\)) [1]. Numerical and experimental investigations of fluid dynamics in open-type cavities are frequent in fluid dynamics research; therefore, many studies have been performed to deepen the fundamental knowledge of separated flow dynamics. [PERSON] and [PERSON] [2] employed the lattice Boltzmann method to investigate vortex structure in a two-dimensional, lid-driven open-type cavity with a wide range of cavity length-to-depth ratios (\(L/h_{1}\)) and Reynolds numbers (Re). The study focused on vortex structure, revealing that when \(L/h_{1}\leq 1\), vortex structure is strongly dependent on Re. When Re \(\leq 100\), the cavity is filled with a large vortex alongside a pair of bottom corner vortices. As Re increases further, the sizes of the bottom vortices start to differ. However, when \(L/h_{1}<1\), the number of vortices formed in the cavity increases with further \(L/h_{1}\) decreases and Re increase. Another study of flow visualization in an open-type cavity was performed by [PERSON] et al. [3]. The study was focused on flow visualization in the moderate Reynolds number range (1150-10,670) and varying cavity length-to-step-height ratio (\(L/h_{1}=0.5\)-2) of the shear-layer driven cavity. Analysis revealed that shear-layersecondary instabilities do not cause 3D developments, and that a secondary vortex in the upstream part of the cavity is linked to instability of the main vortex when \(L/h_{1}=2\). It is well known that studies of flow dynamics are inherent from heat transfer studies since heat exchange heavily relies on recirculation zone dynamics. Heat transfer has already been deeply analyzed in open-type cavities. [PERSON] and [PERSON] [3] investigated heat transfer in flow driven by natural convection with ambient fluid in open-type, partially closed cavities with length-to-depth ratio \(L/h_{1}=1\). The study showed that Nusselt number (Nu) depends on Rayleigh number (Ra), aspect ratio and aperture position. Additionally, the study showed that inclination angle had a nonlinear effect on heat transfer. A similar study was performed by [PERSON] and [PERSON] [4], where natural convection heat transfer in open-type cavities with a discrete heat source was investigated. The authors determined the optimal position of a discrete heater and its dependence on Ra. Further, the influence of geometrical parameter changes was determined on Ra and Nu by investigating various aspect ratios of the channel. It was shown that Ra is a decreasing function of the cavity aspect ratio, and that Nu is an increasing function of Ra. [PERSON] et al. [5] studied the effects of shape, wall temperature, cavity opening ratio and inclination on convective loss in open-type cavities. The study showed that the highest convective loss is observed in a hemispherical open-type cavity with opening ratios of 0.25 and 0.5. Additionally, the study showed that convective loss could be decreased by inclining the channel. The highest convective loss was observed at 0\({}^{\circ}\) inclination (horizontal channel) and the lowest at 90\({}^{\circ}\) (vertical channel). [PERSON] et al. [6] investigated mixed convection in a trapezoidal open-type cavity with a heat source of different lengths fixed to the bottom wall.