# Analysis of Cavity Corner Geometry Effect on Recirculation Zone Structure
## 3 Results and Discussion  
### Investigation of Flow Topology in the x-y Plane  
Flow topology in the x-y plane is represented as static pressure contours with flow velocity streamlines in Figure 6. Formation and dynamics of the recirculation zone depend on cavity geometry and Re. In general, recirculation zone length increases as Re increases. Depending on cavity geometry, the recirculation zone at Re = 10 exists in all cases except Ch3. The recirculation zone is the longest in Ch1, decreases in Ch4 and Ch2, and is absent in Ch3. Rounding of cavity bottom corners causes a lower pressure gradient; therefore, a weaker recirculation zone forms compared to the sudden cross-section changes in Ch1. In Ch3, due to rounded upper cavity corners and smooth transition from the channel to the cavity, streamlines follow cavity geometry smoothly and enter the cavity without separation. As Re increases (Re = 100), the recirculation zone becomes of comparable size and shape. Due to an increase of the main flow velocity, more kinetic energy is transferred to the recirculation zone, forcing it to grow. Yet in Ch3, the recirculation zone is still weakest. The pressure gradient is sufficient for the shear layer to separate; however, it is not sufficient for the recirculation zone to fill the entire cavity, thus reattachment is observed near the trailing wall. Because of the smaller recirculation zone, the main flow impingement occurs lower on the trailing wall compared to other cases. The impingement location matches the location of maximum pressure on the trailing cavity wall. Due to a shorter recirculation zone, maximum pressure values are distributed over a larger area on the trailing wall compared to other cases. As the cavity is filled with the recirculation zone, the separated shear layer bridges the cavity, and impingement occurs on the trailing wall edge. Additionally, flow topology changes are observed at Re = 1000. In this case, recirculation zones have reached their final shape and no longer depend on Re. The main difference from Re = 100 cases is the shift of vortex centre position to the vicinity of the trailing wall. In such flow, force is balanced between the main flow in the channel and the recirculation flow in the cavity. Concerning heat transfer enhancement in investigated geometries, Ch3 seems to be most promising due to the longest-lasting shear layer reattachment and the most unstable recirculation zone, especially at higher Re. Additionally, corner eddies (known as Moffat eddies) located between the leading cavity wall and the recirculation zone are formed in Ch1. The length of corner eddies is measured by the wall shear stress on the cavity bottom. The presence of corner eddies is due to an adverse pressure gradient behind the leading wall [14]. The minimum wall shear stress values are associated with the beginning and the end of the eddy. The distribution of wall shear on the  
Figure 4: Numerically and experimentally obtained velocity \(u\) profiles at Re = 100. Figure 5: Numerically and experimentally obtained velocity \(u\) profiles at Re = 1000. Ch1 bottom is given in Figure 7a. Note that the lengths of corner eddies in all investigated Re cases are tiny; therefore, they are not visible in Figure 6. In Ch1, the size of the corner eddy increases with increasing Re in similar manner to the main recirculation zone (Figure 7b). It is well known that fluid flow through a corner that is greater than 73.5\({}^{\circ}\) creates Moffat eddies [15]; therefore, corner eddies do not form for the rounded cavity corners (Ch2 and Ch4) (Figure 6). Additionally, corner eddies in Ch3 are absent due to gradually rounded corners--the adverse pressure gradient is insufficient for flow separation, and streamlines follow the corner geometry without forming recirculation zones. Figure 6: Static pressure contours and velocity streamlines in Ch1, Ch2 and Ch3 at Re = 10, 100 and 1000. Flow velocity \(u\) profiles in Ch1, Ch2 and Ch3 are given in Figures 8 and 9.