Session: 11-19-01: Methods in Computational Heat Transfer and Their Applications

Paper Number: 145318

145318 - Evaluation of Multi-Dimensional Optimization Methods for Maximizing Segmented Thermoelectric Unicouple Performance 

To further enable future NASA deep-space and sub-surface missions, the use of alternative radioisotopes (e.g., Am-241, Cm-244, Po-210, Sr-90), heat source configurations (e.g., General Purpose Heat Source in the STEP-1 and STEP-2 configurations, Compact Heat Source, etc.), and thermoelectric materials (e.g., CE-TEC (La_3−xTe₄ and 14-1-11 Zintl), skutterudites, and PbTe/TAGs, etc.) comprising a radioisotope thermoelectric generator (RTG) either in the MOD-1 or MOD-2 set-up, piques interest. The evaluation of alternative designs that meet electrical and/or thermal performance requirements necessitates improved methods of RTG design and optimization. There are several independent design variables that can constitute the design space, including the aforementioned and thermoelectric converter geometry, such as n- and p- type cross-sectional areas (A_n and A_p) and high temperature segment lengths, total unicouple height, externally applied load resistance (R_load), desired output voltage, and expected cold-side temperature. Naive search methods are computationally intractable, and the imposition of system response constraints nullifies simple optimization methods (e.g., gradient-based algorithms, such as hill climb and particle swarm). Prior work compared optimization methods over a representative design space (R_load, A_n and A_p, and length fractions), and identified methods that decreased computational time, as measured by number of solver calls. This work expands upon prior studies by accounting for the solution space shape, and identifying exploitable trends that allow for the use of faster methods, such as Multi-dimensional (MD) Section Search (SS), Nested Section Search (NSS), and Grid Search (GS) schemes. MD SS was done three ways, considering a 5D-SS, a 4D+1D-NSS and a 2D+2D+1D-NSS. The GS was paired with Successive Refinement (SR) and then SR and NSS simultaneously. The results and computational time of MD SS, NSS, GS+SR and GS+SR-NSS optimization methods were compared to and benchmarked against known global solutions and number of solver calls (N_calls), respectively. With the use of these methods, N_calls can be reduced by six orders of magnitude while remaining within 1.0% relative difference from the "true" solution, as determined from an exhaustive parametric study. Using pure GS+SR methods, the largest attainable speedup (N_calls of the exhaustive parametric study per N_calls of the proposed method) was 154,787; GS+SR methods are the most robust and have the least deviation from the "true" solution. MD SS methods failed to find a design configuration within 1% of the "true" solution. Using NSS methods, the maximum speedup obtained was 552,827; these methods are highly sensitive to the SS fraction and the shape of the design. Combining GS and NSS methods, the GS+SR-NSS method had a maximum speedup of 316,185. With the demonstration and validation of less computationally expensive optimization methods, it is possible to identify additional mission satisfying RTG designs. Furthermore, using these methods, multiple designs that meet design requirements were found, some with more favorable geometries and operating points (i.e., fewer number of unicouples requires and lower segment interfacial temperatures).

Presenting Author: Caroline Lehrer University of Pittsburgh

Presenting Author Biography: Caroline is an Undergraduate Student Researcher in the Mechanical Engineering and Materials Science department at the University of Pittsburgh. Caroline's research is focused on developing and implementing multi-dimensional optimization methods to expedite trade studies of Radioisotope Thermoelectric Generators.

Authors:

Caroline Lehrer University of Pittsburgh
Shane Riley University of Pittsburgh
Carter Gassler University of Pittsburgh
Cara Rossetti University of Pittsburgh
Jean-Pierre Fleurial Jet Propulsion Laboratory, California Institute of Technology
Michael Durka Jet Propulsion Laboratory, California Institute of Technology
Bill Nesmith Jet Propulsion Laboratory, California Institute of Technology
Matthew Barry University of Pittsburgh