Session: 06-06 Heat Pumps-II

Paper Number: 152774

A Comparative Study of Component Surrogate Model Approximation for Holistic, Multi-Disciplinary Optimization of High Temperature Heat Pumps 

Industrial high temperature heat pumps are a key technology to electrify process heat demand.  In order to exploit the full potential of this technology, the thermodynamic cycle needs be designed to meet specific process requirements. The heat pumps performance strongly depends on the efficiency of the components like turbomachines and heat exchangers, which are additionally highly interactive in closed cycles. The design process is a challenging task as many disciplines and design steps need to be considered. In a sequential design procedure, the thermodynamic cycle is optimized without detailed knowledge about the component performance and as a consequence it is impossible to find the overall optimal configuration. Multi-disciplinary optimization (MDO) approaches for holistic heat pump design have proven to be superior to conventional sequential design but can largely increase the complexity and computational cost of the optimization problem. This is mainly caused by the high numerical effort of detailed physical modeling to simulate aerodynamics or heat transfer for component analysis.  In holistic optimization approaches a high number of simulations can occur in nested design processes. For this reason, surrogate models to approximate component analyses are necessary to reach a faster evaluation compared to physical models.  This allows for more flexibility in setting up the optimization structure with the overlying challenge to find the best suitable combination of architecture, regression method and optimization algorithms to minimize function evaluations.

This paper focuses on the comparison of different surrogate model approaches to approximate the analysis of multi-stage compressor aerodynamics and heat transfer as well as pressure drop in shell and tube heat exchangers. Local and global models for Gaussian process regression, linear regression and radial basis functions are applied for different sizes of training datasets. Model quality and approximation error are compared as well as the numerical effort for training and evaluation in optimizations.  Their individual suitability for MDO is demonstrated for a holistic optimization structure to design a reversed Brayton cycle heat pump. The designs of three heat exchangers and an axial compressor are optimized simultaneously with the thermodynamic cycle. It can be shown that the computational effort of the holistic heat pump optimization is significantly decreased, which enables optimization architectures with nested component designs. Gaussian process surrogate models are able to predict the complex functional output of the component analyses and can be applied for holistic heat pump optimization. Moderate databases with less than 200 training samples are sufficient to reach high global model accuracy for heat exchanger predictions with 8-10 design parameters. High dimensional compressor design with 35 design parameters is more challenging but sufficient accuracy can be achieved with a maximum amount of 1500 sample points. Evaluation of the optimized designs shows good agreement with the simulations and thereby little exploitation by the optimizer.  The overall function evaluations to simulate the component configurations are significantly decreased using surrogate models, which in perspective allows the optimization strategy to be applied for more detailed component designs.

The results of this work contribute to the overall objective of this research, which is to orchestrate the optimization with regard to structure and surrogate model training. The latter will be performed with adaptive refinement during runtime of the optimization process in future work.

Presenting Author: Jens Gollasch German Aerospace Center (DLR)

Presenting Author Biography: - studied mechanical engineering at the Leibniz University in Hannover (Germany) with focus
on energy technology and on aerodynamic simulations of axial turbomachines
- motivation to work on the development of technologies that contribute to the transition of our
energy system
- research associate at the Institute of Low-Carbon Industrial Processes (German Aerospace
Center, DLR) since 02/2020
- The research focus is on holistic optimization concepts that integrate component design with the design of thermodynamic cycles
- The present work shows results for optimization strategies that use surrogate models to predict the functional output of component analyses

Authors:

Jens Gollasch German Aerospace Center (DLR)
Michael Lockan German Aerospace Center (DLR)