zbMATH — the first resource for mathematics

Periodic state of fluid flow and heat transfer in a lid-driven cavity due to an oscillating thin fin. (English) Zbl 1188.76199
Summary: Results of a computational study of periodic laminar flow and heat transfer in a lid-driven square cavity due to an oscillating thin fin are presented. The lid moves from left to right and a thin fin is positioned normal to the right stationary wall. The length of the fin varies sinusoidally with its mean length and amplitude equal to 10% and 5% 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 \((t_{conv})\), fin’s oscillation periods \((\tau )\) were selected in order to cover both slow \((TR = \tau /t_{conv} > 1)\) and fast \((\tau /t_{conv} < 1)\) oscillation regimes, covering a Strouhal number range of 0.005-0.5. The periodic flow field for the case with \(Re = 1000\) and TR = 10 is distinguished by the creation, lateral motion and subsequent wall impingement of a CCW rotating vortex within the lower half of the cavity. Periodic flow and thermal fields of the other nine cases studied were not as varied. Phase diagrams of the stream function and temperature vs. fin’s length clearly exhibit the synchronous behavior of the system. Amplitude of fluctuations of the kinetic energy and temperature are very intense near the fin. As the fin oscillates slower, a greater portion of the cavity exhibits intense fluctuations. For slow to moderate oscillations, the maximum value of \(K_{amp}\) is observed to be greater for \(Re = 1000\) in comparison to \(Re = 100\). For fast oscillations, this behavior is reversed. The maximum values of the amplitude of fluctuations of temperature increase monotonically as the fin oscillates slower. The maximum values of \(\theta _{amp}\) are greater for \(Re = 1000\) compared to \(Re = 100\). The amplitude of fluctuations of the mean Nusselt number on four walls increase as the fin oscillates slower.

76D05 Navier-Stokes equations for incompressible viscous fluids
76M12 Finite volume methods applied to problems in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
Full Text: DOI