Numerical simulation of the fuel-oil cooling in the sunken Prestige tankerFrancesc Xavier Grau 要約This paper presents and discusses the predictions of the cooling rates of the fuel-oil contained in the tanks of the sunken Prestige tanker. These predictions were obtained through the numerical simulation of the time-evolution of the natural convection flow in the tanks and through the solution of the simplified macroscopic thermal energy balances. The physical model of the problem consists in a two-dimensional cross section of the tanker with two tanks. Initially the fuel-oil is considered to be at rest and at constant temperature (T_{i}=50 °C) and the temperature of the external walls is set constant through the cooling process (T_{w}=2.6°C). The conventional Boussinesq approximation is adopted. The strong viscosity dependence on temperature of the fuel-oil (μ=500 Pa·s at T=3.1°C μ=0.85 Pa·s at T=50°C) is considered as well. The initial high Rayleigh (Ra≈10^{13}) and Prandtl (Pr≈10^{8}) numbers involved and the overall duration of the cooling process, which is of order of months, impose severe computational requirements for the numerical simulation of the complete time evolution in terms of grid sizes, time-step and total integration time. The numerical simulation shows that during the initial cooling period (t<45 days) the flow is highly unsteady (10^{10}≥Ra≥10^{13}) and it is mainly governed by the interaction of the vertical boundary layers developed near the vertical walls of the tanks and the unstable stratification imposed near the top horizontal walls. The flow has a broadband of length scales that range from the thin thermal boundary layers of several millimeters of thickness to the large-scale recirculations of order of the dimensions of the tanks. The macroscopic thermal energy balances underpredict by about 7°C the averaged temperatures of the numerical simulation when the conventional correlations of natural convection flows for high Prandtl number fluids are used to compute the convective heat fluxes through the walls. These temperature differences are reduced down to 3°C using the heat transfer coefficients predicted by the numerical simulation. |
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