Solutal buoyancy has a large impact on the flow of the alloy phase composing the positive electrode in liquid metal batteries. During discharge solutal buoyancy creates a stabilizing stratification, during charge it creates a vigorous solutal convection. In this article we provide new physical understandings of the role of solutal buoyancy during both charge and discharge. In particular we find that during discharge the electrovortex mechanism is in general not strong enough to counter the stabilizing effect of solutal buoyancy, and therefore this mechanism cannot be used to mix the alloy as is sometimes suggested in the literature. We show that the mixing capability of a generic flow in the alloy phase can be estimated by comparing the typical flow magnitude U to two velocity scales: U p and U m . Below U p the flow cannot mix the alloy, and above U m the flow significantly opposes solutal buoyancy. Although we focus on Li||Pb-based batteries, these simple mixing criteria can be used during the discharging phase in other types of liquid batteries. We also present new, fully three-dimensional simulations of solutal convection during the charging cycle. These simulations suggest scaling laws for the magnitude of the convective flow, the time for the onset of solutal convection, and the typical inhomogeneity level in the alloy during charge. We propose physical arguments to explain these scaling laws.
Sheared velocity profiles pervade all wind‐turbine applications, thus making it important to understand their effect on the wake. In this study, a single wind turbine is modeled using the actuator‐line method in the incompressible Navier–Stokes equations. The tip vortices are perturbed harmonically, and the growth rate of the response is evaluated under uniform inflow and a linear velocity profile. Whereas previous investigations of this kind were conducted in the rotating frame of reference, this study evaluates the excitation response in the fixed frame of reference, thus necessitating a frequency transformation. It is shown that increasing the shear decreases the spatial growth rate in the upper half of the wake while increasing it in the lower half. When scaled with the local tip vortex parameters, the growth rate along the entire azimuth collapses to a single value for the investigated wavenumbers. We conclude that even though the tip‐vortex breakdown is asymmetric in sheared flow, the scaled growth rates follow the behavior of axisymmetric helical vortices. An excitation amplitude reduction by an order of magnitude extends the linear growth region of the wake by one radius for uniform inflow. In the sheared setup, the linear growth region is extended further in the top half than in the bottom half because of the progressive distortion of the helical tip vortices. An existing model to determine the stable wake length was shown to be in close agreement with the observed numerical results when adjusted for shear.
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