Fluid Flow and Heat Transfer in a Lid-Driven Cavity Due to an Oscillating Thin Fin: Transient Behavior

A finite-volume-based computational study of transient laminar flow and heat transfer (neglecting natural convection) within a lid-driven square cavity due to an oscillating thin fin is presented. The lid moves from left to right and a thin fin positioned perpendicular to the right stationary wall oscillates in the horizontal direction. The length of the fin varies sinusoidally with its mean length and amplitude equal to 10 and 5 percent of the side of the cavity, respectively. Two Reynolds numbers of 100 and 1000 for a $Pr=1$ fluid were considered. For a given convection time scale $tconv,$ fin’s oscillation periods (τ) were selected in order to cover both slow $τ/tconv>1$ and fast $τ/tconv<1$ oscillation regimes. This corresponded to a Strouhal number range of 0.005 to 0.5. The number of the cycles needed to reach the periodic state for the flow and thermal fields increases as $τ/tconv$ decreases for both Re numbers with the thermal field attaining the periodic state later than the velocity field. The key feature of the transient evolution of the fluid flow for the case with $Re=1000$ with slow oscillation is the creation, lateral motion and subsequent wall impingement of a CCW rotating vortex within the lower half of the cavity. This CCW rotating vortex that has a lifetime of about 1.5τ brings about marked changes to the temperature field within a cycle. The dimensionless time for the mean Nusselt numbers to reach their maximum or minimum is independent of the frequency of the fin’s oscillation and is dependent on the distance between the oscillating fin and the respective wall, and the direction of the primary CW rotating vortex. The phase lag angle between the oscillation of the fin and the mean Nusselt number on the four walls increases as the distance between the fin and the respective wall increases.