A volume element model (VEM) for energy systems engineering

Abstract

This work presents a simplified modeling and simulation approach for energy systems engineering that is capable of providing quick and accurate responses during system design. For that, the laws of conservation are combined with available empirical and theoretical correlations to quantify the diverse types of flows that cross the system and produce a simplified tridimensional mathematical model, namely a volume element model (VEM). The physical domain of interest is discretized in space, thus producing a system of algebraic and ODEs with respect to time, whose solution delivers the project variables spatial distribution and dynamic response. In order to illustrate the application of the VEM in energy systems engineering, three example problems are considered: (i) a regenerative heat exchanger; (ii) a power electronic building block (PEBB); and (iii) a notional all-electric ship. The same mathematical model was used to analyze problems (ii) and (iii), that is, the thermal management of heat-generating equipment packaging. In the examples, the converged mesh had a total of 20, 2000, and 7725 volume elements. The third problem led to the largest simulation, which for steady-state cases took between 5 and 10 min of computational time to reach convergence and for the ship dynamic response 50 min (i.e., 80,000 s of real time). The regenerative heat exchanger model demonstrated how VEM allowed for the coexistence of different phases (subsystems) within the same volume element. The thermal management model was adjusted and experimentally validated for the PEBB system, and it was possible to perform a parametric and dynamic analysis of the PEBB and of the notional all-electric ship. Therefore, because of the observed combination of accuracy and low computational time, it is expected that the model could be used as an efficient tool for design, control, and optimization in energy systems engineering.