Onset of Rayleigh-B,nard convection in cold water near its density maximum in vertical annular containers

A set of three-dimensional numerical simulations of Rayleigh-B,nard convection in cold water near its density maximum in vertical annular containers is performed with the aim of determining the critical Rayleigh number at the onset of convection and the primary flow patterns for different geometric dimensions and density inversion parameters. The Prandtl number of cold water is about 11.57. The annular container is heated from below and cooled from above. The inner and outer sidewalls are considered to be perfectly adiabatic. The results obtained show that the critical Rayleigh number at the onset of convection increases with increase in the density inversion parameter and the radius ratio and with decrease in the aspect ratio. When the radius ratio is small, the flow patterns in vertical annular containers are similar to those in cylindrical containers. At large radius ratios the flow pattern is relatively simple, with several convective rolls observable along the azimuthal direction and similar with those characteristic of Rayleigh-B,nard convection in the Boussinesq fluid. The stratified flow phenomenon is found to exist at moderate values of the density inversion parameter. The results are compared with those obtained in the Boussinesq fluid to reveal the effect of the density inversion parameter.