Vibrational effects on convection in a square cavity at zero gravity. (Q2767790)

This is a numerical study of natural convection in a two-dimensional square cavity vibrating sinusoidally parallel to the applied temperature gradient in a zero-gravity field. The full Navier-Stokes equations coupled with the energy equation are presented in non-dimensional form, and these equations are then expressed in terms of stream function \(\psi\) and vorticity function \(\zeta\). These equations are solved subject to specified boundary conditions. The solution procedure is based on a finite difference Crank-Nicholson algorithm with second-order accuracy in time. The governing parameters are the Prandtl number \(\text{Pr}= 7.1\), the vibration Rayleigh number Ra based on acceleration amplitude and varied from \(1.0\times 10^4\) to \(1.0\times 10^5\), and dimensionless angular frequency \(\omega\) varied from \(1.0\times 10^5\) to \(1.0\times 10^3\). In the tested range, time evolutions exhibit synchronous, \(1/2\)-subharmonic and non-periodic responses, and flow patterns are characterized mainly by one- or two-cell structures.NEWLINENEWLINE The authors find that flow-regime diagrams based on periodicity reveal that convection becomes more stable as \(\omega\) increases or Ra decreases, and that convection is almost synchronous with the forced acceleration except for a \(1/2\)-subharmonic-response regime and two non-periodic-response regimes, some parts of which are isolated among synchronous regimes. It is also found that the flow regime based on flow patterns reveals that, for Ra larger than about \(5\times 10^4\), the convection tends to become more complex. Moreover, it is shown that the influence of gravity is essential even at relatively large values of Ra, if one compares the obtained zero-gravity flow regimes with previous results for non-zero-mean gravity. It should be mentioned that the presented flow behaviour is sometimes much more complicated than one would have expected on the basic of a constant-gravity field, or a modulating gravity field with even small non-zero-mean component.