Non-smooth Methods for Complementarity Formulations of Switched Advection-Diffusion Processes
Rankine cycle processes are widely established in process engineering for the recovery of energy from a source of exhaust heat, and have recently found novel use as a promising hybridization concept for heavy duty vehicles (in the following called an exhaust heat recovery (EHR) system) with power demands that exceed the capacities of hybrid electrical drivetrains by a wide margin. Characteristic for all such applications is an advection-diffusion process operated in a cyclic fashion in order to transfer exhaust heat energy by way of a boiler into a working fluid. This fluid is then expanded to harness mechanical energy that may possibly be converted to electrical energy in a second stage, while the fluid is fed back to the condenser by way of an evaporator and a pump. The dynamics of each of the four phases of a complete EHR system Rankine cycle constitutes an advection-diffusion process that can be modeled by instationary partial differential-algebraic equations (PDAE) in one or two spatial dimensions. The overall system is described by a switched PDAE and exhibits additional non-smoothnesses as the working fluid necessarily undergoes at least two phase changes. Due to the large scale of process models and due to significant perturbations of the process by external load-point changes on a time scale considerably smaller than the intrinsic time constant of the process, the switching behaviour is non-periodic and exhibits non-trivial patterns. Optimal operation of the transient behaviour is paramount to make the concept practically worthwhile, and is at the same time a highly challenging task for classical control concepts. Aim of the project is to develop efficient numerical methods for optimization of advection- diffusion processes described by large-scale instationary switched PDAES. These methods shall combine the state of the art in reduced approaches for PDE-constrained optimization with a novel idea for a decomposition approach to mixed-integer optimal control with combinatorial constraints, and shall be able to efficiently cope with the task of computing optimal switching structures and process trajectories.
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