The theoretical limit for wind turbine performance, the so-called Betz limit, arises from an inviscid, irrotational analysis of the streamtube around an actuator disk. In a wind farm in the atmospheric boundary layer, the physics are considerably more complex, encompassing shear, turbulent transport, and wakes from other turbines. In this study, the mean flow streamtube around a wind turbine in a wind farm is investigated with large eddy simulations of a periodic array of actuator disks in half-channel flow at a range of turbine thrust coefficients. Momentum and mean kinetic energy budgets are presented, connecting the energy budget for an individual turbine to the wind farm performance as a whole. It is noted that boundary layer turbulence plays a key role in wake recovery and energy conversion when considering the entire wind farm. The wind farm power coefficient is maximized when the work done by Reynolds stress on the periphery of the streamtube is maximized, although some mean kinetic energy is also dissipated into turbulence. This results in an optimal value of thrust coefficient lower than the traditional Betz result. The simulation results are used to evaluate Nishino’s model of infinite wind farms, and design trade-offs described by it are presented.
Intra-abdominal perivascular epithelioid cell tumors (PEComas) are rare mesenchymal tumors. Although no effective therapies have been agreed upon, mTOR inhibitors are currently being investigated as a potential therapy for this extremely rare tumor. We present a case of a 64-year-old male found to have a large intra-abdominal PEComa with multiple metastatic lesions in the liver. Patient underwent surgical resection of the primary lesion in the abdomen and sigmoid colon followed by adjuvant therapy with the mTOR inhibitor, sirolimus. Initial response was noted with a decrease in size and number of lesions found in the patient’s liver. After 8 months of therapy, restaging imaging showed disease progression in the liver lesions. Patient subsequently failed treatments with pazopanib, investigational therapy TAK-228 (Sapanisertib) and nivolumab and ipilimumab. Overall the patient died after 22 months of disease. PEComas generally follow a benign course. This case is a much rarer entity given the malignant features/outcome.
This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook (2007), Lele (2019), in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al. (2010), in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations (Tiwari et al., 2013). The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al. ( 2020), in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a fourequation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases.The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer-Meshkov instability of a copper-aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. This is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.
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