For rotationally constrained convection, the Taylor–Proudman theorem enforces an organization of nonlinear flows into tall columnar or compact plume structures. While coherent structures in convection under moderate rotation are exclusively cyclonic, recent experiments for rapid rotation have revealed a transition to equal populations of cyclonic and anticyclonic structures. Direct numerical simulation (DNS) of this regime is expensive, however, and existing simulations have yet to reveal anticyclonic vortical structures. In this paper, we use a reduced system of equations for rotationally constrained convection valid in the asymptotic limit of thin columnar structures and rapid rotation to perform numerical simulation of Rayleigh–Bénard convection in an infinite layer rotating uniformly about the vertical axis. Visualization indicates the existence of cyclonic and anticyclonic vortical populations for all parameters examined. Moreover, it is found that the flow evolves through three distinct regimes with increasing Rayleigh number (Ra). For small, but supercritical Ra, the flow is dominated by a cellular system of hot and cold columns spanning the fluid layer. As Ra increases, the number density of these columns decreases, the up-and down-drafts within them strengthen and the columns develop opposite-signed ‘sleeves’ in all fields. The resulting columns are highly efficient at transporting heat across the fluid layer. In the final regime, lateral mixing plays a dominant role in the interior and the columnar structure is destroyed. However, thermal plumes are still injected and rejected from the thermal boundary layers. We identify the latter two regimes with the vortex-grid and geostrophic turbulence regimes, respectively. Within these regimes, we investigate convective heat transport (measured by the Nusselt number), mean temperature profiles, and root-mean-square profiles of the temperature, vertical velocity and vertical vorticity anomalies. For all Prandtl numbers investigated, the mean temperature saturates in a non-isothermal profile as Ra increases owing to intense lateral mixing.
In order to better understand the behavior of Lithium-ion batteries under mechanical abuse, a coupled modeling methodology encompassing the mechanical, thermal and electrical response is presented for predicting short circuit under external crush. The combined mechanical-electric-thermal response is simulated in a commercial finite element software LS-DYNA® using a representative-sandwich finite-element model, where electrical-thermal modeling is conducted after an instantaneous mechanical crush. The model includes an explicit representation of each individual component such as the active material, current collector, separator, etc., and predicts their mechanical deformation under quasi-static compression and indentation. Model predictions show good agreement with experiments: the fracture of the battery structure under anindentation test is accurately predicted. The electrical-thermal simulation predicts the current density and temperature distribution in a reasonable manner. Whereas previously reported models consider the mechanical response exclusively, we use the electrical contact between active materials following the failure of the separator as a criterion for short circuit. These results are used to build a lumped-representative sandwich model that is computationally efficient and captures behavior at the cell level without resolving the individual layers.
The safety behavior of lithium-ion batteries under external mechanical crush is a critical concern, especially during large scale deployment. We previously presented a sequentially coupled mechanical-electrical-thermal modeling approach for studying mechanical abuse induced short circuit. In this work, we study different mechanical test conditions and examine the interaction between mechanical failure and electrical-thermal responses, by developing a simultaneous coupled mechanical-electrical-thermal model. The present work utilizes a single representative-sandwich (RS) to model the full pouch cell with explicit representations for each individual component such as the active material, current collector, separator, etc. Anisotropic constitutive material models are presented to describe the mechanical properties of active materials and separator. The model predicts accurately the force-strain response and fracture of battery structure, simulates the local failure of separator layer, and captures the onset of short circuit for lithium-ion battery cell under sphere indentation tests with three different diameters.Electrical-thermal responses to the three different indentation tests are elaborated and discussed. Numerical studies are presented to show the potential impact of test conditions on the electrical-thermal behavior of the cell after the occurrence of short circuit.
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