Large Eddy Simulation of complex sidearms subject to solar radiation and surface cooling

Large Eddy Simulation (LES) is used to model two lake sidearms subject to heating from solar radiation and cooling from a surface flux. The sidearms are part of Lake Audrey, NJ, USA and Lake Alexandrina, SA, Australia. The simulation domains are created using bathymetry data and the boundary is modelled with an Immersed Boundary Method. We investigate the cooling and heating phases with separate quasi-steady state simulations.     

Unsteady natural convection boundary-layer flow along a vertical isothermal plate in a linearly stratified fluid with Pr>1

In this study, the unsteady natural convection boundary-layer flow along an impulsively heated vertical isothermal plate immersed in a stably stratified semi-infinite ambient fluid is explored using scaling analysis and direct numerical simulation. Scaling relations are obtained for the thermal and velocity boundary layer thicknesses, the boundary layer velocity, the development time and the Nusselt number, in terms of the Rayleigh and Prandtl numbers and the stratification parameter. The scaling results are validated using the numerical simulations.     

Long-term behavior of cooling fluid in a vertical cylinder

The long-term behavior of cooling an initially quiescent isothermal Newtonian fluid in a vertical cylinder by unsteady natural convection with a fixed wall temperature has been investigated in this study by scaling analysis and direct numerical simulation. Two specific cases are considered. Case 1 assumes that the fluid cooling is due to the imposed fixed temperature on the vertical sidewall whereas the top and bottom boundaries are adiabatic. Case 2 assumes that the cooling is due to that on both the vertical sidewall and the bottom boundary whereas the top boundary is adiabatic. The long-term behavior of the fluid cooling in the cylinder is well represented by T_a(t), the average fluid temperature in the cylinder at time t, and the average Nusselt number on the cooling boundary. The scaling analysis shows that for both cases θ_a(τ) scales as , where θ_a(τ) is the dimensionless form of T_a(t), τ the dimensionless time, A the aspect ratio of the vertical cylinder, Ra the Rayleigh number, and C a proportionality constant. A series of direct numerical simulations with the selected values of A, Ra, and Pr (Pr is the Prandtl number) in the ranges of 1/3 ? A ? 3, 6 × 10⁶ ? Ra ? 6 × 10¹⁰, and 1 ? Pr ? 1000 have been carried out for both cases to validate the developed scaling relations, and it is found that these numerical results agree well with the scaling relations. These numerical results have also been used to quantify the scaling relations and it is found that C = 1.287 and 1.357 respectively for Case 1 and 2 with Ra, A and Pr in the ranges of 1/3 ? A ? 3, 6 × 10⁶ ? Ra ? 6 × 10¹⁰, and 1 ? Pr ? 1000.     

Boundary layer instability of the natural convection flow on a uniformly heated vertical plate

Direct numerical simulation is employed to investigate the two-dimensional boundary layer instability of a natural convection flow on a uniformly heated vertical plate submerged in a homogeneous quiescent environment. A Boussinesq fluid with Prandtl numbers of Pr = 0.733 (air) and 6.7 (water), in the local Rayleigh number range 0 ? Ra_x ? 2.4 × 10¹⁰, is studied. Controlled low amplitude numerical disturbances introduced into the base flow excite unstable travelling waves, with the resulting waves tracked and analyzed as they travel up the boundary layer. The numerical simulation readily reproduced what is predicted by the parallel linear stability theory for the two dimensional mode relatively short wave spectrum, but not for some parts of the long wave spectrum. Critical Rayleigh numbers have been obtained separately for both the temperature and velocity signals using the numerical results, and shown to be in good agreement with each other provided the data is renormalized using the boundary layer scalings of Sparrow and Greg [1]. It has been shown that the disturbance behavior depends on the Prandtl and Rayleigh numbers, the excitation frequency and to a lesser extent the prescribed thermal coupling at the plate.     

The Reynolds and Prandtl number dependence of weak fountains

The effect of the Prandtl number (Pr) and the Reynolds number (Re) on the behaviour of weak laminar axisymmetric and plane fountains has been studied using dimensional and scaling analyses and direct numerical simulation. For Fr 1.0 and assuming viscous effects are important, the analysis shows that for both the axisymmetric and plane fountains, y_mFrRe^–1/2, where Fr is the Froude number defined at the fountain source and y_m is the non-dimensionalized fountain height. These scalings are also valid for the non-dimensionalized fountain width. The analyses also shows _msFr², where _ms is the non-dimensionalized time scale for the fountain flow in the fountain core to reach steady state, and using this time scale y_TFr(RePr)^–1/2, where y_T is the non-dimensionalized thickness of the temperature layer on the symmetry axis over which the fountain fluid temperature changes from the inlet value to that of the ambient fluid. All these scalings have been quantified by the direct numerical simulations, hence confirming in certain ranges the phenomenological scaling obtained in this paper. The financial supports from the National Natural Science Foundation (grant numbers 19872059 and 10262003) and Yunnan Province of the People's Republic of China to W. Lin and the Australian Research Council are gratefully acknowledged.     

VERY WEAK FOUNTAINS IN A HOMOGENEOUS FLUID

The behaviour of very weak axisymmetric and plane fountains formed by the discharge of denser fluids upwards into large containers containing a homogeneous fluid of lower density has been studied by dimensional analysis and direct simulations. For very weak fountains, the momentum fluxes are negligible compared with the buoyancy fluxes and the flows are governed by the balance between the buoyancy and the viscosity. Dimensional analysis shows that the fountain height, fountain width, thickness of the temperature layer on the symmetry axis, and the times for the fountain flow in the fountain core to reach steady state and for the temperature layer to be fully developed are scaled by the Froude, Reynolds, and Prandtl numbers. These scalings have been validated and quantified by direct numerical simulations.