Existence and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system over moving domains

This dissertation concerns the well-posedness of the Navier-Stokes-Smoluchowski system. The system models a mixture of fluid and particles in the so-called bubbling regime. The compressible Navier-Stokes equations governing the evolution of the fluid are coupled to the Smoluchowski equation for the particle density at a continuum level. First, working on fixed domains, the existence of weak solutions is established using a three-level approximation scheme and based largely on the Lions-Feireisl theory of compressible fluids. The system is then posed over a moving domain. By utilizing a Brinkman-type penalization as well as penalization of the viscosity, the existence of weak solutions of the Navier-Stokes-Smoluchowski system is proved over moving domains. As a corollary the convergence of the Brinkman penalization is proved. Finally, a suitable relative entropy is defined. This relative entropy is used to establish a weak-strong uniqueness result for the Navier-Stokes-Smoluchowski system over moving domains, ensuring that strong solutions are unique in the class of weak solutions.

Energy Management of a Battery-Ultracapacitor Hybrid Energy Storage System in Electric Vehicles

Electric vehicle (EV) batteries tend to have accelerated degradation due to high peak power and harsh charging/discharging cycles during acceleration and deceleration periods, particularly in urban driving conditions. An oversized energy storage system (ESS) can meet the high power demands; however, it suffers from increased size, volume and cost. In order to reduce the overall ESS size and extend battery cycle life, a battery-ultracapacitor (UC) hybrid energy storage system (HESS) has been considered as an alternative solution. In this work, we investigate the optimized configuration, design, and energy management of a battery-UC HESS. One of the major challenges in a HESS is to design an energy management controller for real-time implementation that can yield good power split performance. We present the methodologies and solutions to this problem in a battery-UC HESS with a DC-DC converter interfacing with the UC and the battery. In particular, a multi-objective optimization problem is formulated to optimize the power split in order to prolong the battery lifetime and to reduce the HESS power losses. This optimization problem is numerically solved for standard drive cycle datasets using Dynamic Programming (DP). Trained using the DP optimal results, an effective real-time implementation of the optimal power split is realized based on Neural Network (NN). This proposed online energy management controller is applied to a midsize EV model with a 360V/34kWh battery pack and a 270V/203Wh UC pack. The proposed online energy management controller effectively splits the load demand with high power efficiency and also effectively reduces the battery peak current. More importantly, a 38V-385Wh battery and a 16V-2.06Wh UC HESS hardware prototype and a real-time experiment platform has been developed. The real-time experiment results have successfully validated the real-time implementation feasibility and effectiveness of the real-time controller design for the battery-UC HESS. A battery State-of-Health (SoH) estimation model is developed as a performance metric to evaluate the battery cycle life extension effect. It is estimated that the proposed online energy management controller can extend the battery cycle life by over 60%.