Abstract
Cost is equally important to power density or efficiency for the adoption of waste heat recovery thermoelectric generators (TEG) in many transportation and industrial energy recovery applications. In many cases, the system design that minimizes cost (e.g., the $/W value) can be very different than the design that maximizes the system’s efficiency or power density, and it is important to understand the relationship between those designs to optimize TEG performance-cost compromises. Expanding on recent cost analysis work and using more detailed system modeling, an enhanced cost scaling analysis of a waste heat recovery TEG with more detailed, coupled treatment of the heat exchangers has been performed. In this analysis, the effect of the heat lost to the environment and updated relationships between the hot-side and cold-side conductances that maximize power output are considered. This coupled thermal and thermoelectric (TE) treatment of the exhaust waste heat recovery TEG yields modified cost scaling and design optimization equations, which are now strongly dependent on the heat leakage fraction, exhaust mass flow rate, and heat exchanger effectiveness. This work shows that heat exchanger costs most often dominate the overall TE system costs, that it is extremely difficult to escape this regime, and in order to achieve TE system costs of $1/W it is necessary to achieve heat exchanger costs of $1/(W/K). Minimum TE system costs per watt generally coincide with maximum power points, but preferred TE design regimes are identified where there is little cost penalty for moving into regions of higher efficiency and slightly lower power outputs. These regimes are closely tied to previously identified low cost design regimes. This work shows that the optimum fill factor F opt minimizing system costs decreases as heat losses increase, and increases as exhaust mass flow rate and heat exchanger effectiveness increase. These findings have profound implications on the design and operation of various TE waste heat recovery systems. This work highlights the importance of heat exchanger costs on the overall TEG system costs, quantifies the possible TEG performance-cost domain space based on heat exchanger effects, and provides a focus for future system research and development efforts.
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Abbreviations
- A :
-
Total heat exchanger area (m2)
- A TE :
-
One n-type + p-type TE element area, TE couple area (m2)
- \(C^{\prime\prime}\) :
-
TE material area-dependent manufac-turing costs ($/m2)
- \(C^{\prime\prime\prime}\) :
-
TE material volumetric-dependent costs ($/m3)
- C HX,C :
-
Cold heat exchanger cost coefficient [$/(W/K)]
- C HX,H :
-
Hot heat exchanger cost coefficient [$/(W/K)]
- C p :
-
Exhaust flow specific heat (J/kg K)
- F :
-
TEG fill factor
- F opt :
-
Optimum TEG fill factor
- G :
-
TE system total cost per output power ($/W)
- I :
-
Electrical current (A)
- k :
-
Thermal conductivity of TE material (W/m K)
- K C :
-
TE system cold-side conductance (W/K)
- K exh :
-
Exhaust conductance (= \(\dot{m}C_{\rm{p}}\varepsilon\)) (W/K)
- K H :
-
Effective hot-side conductance (W/K)
- K HX :
-
Additional hot-side thermal conductance (W/K)
- K TE :
-
TE module thermal conductance (W/K)
- \({K_\parallel}\) :
-
Parallel leakage thermal conductance (W/K)
- L TE :
-
TE element length (m)
- \(\dot{m}\) :
-
Mass flow rate of exhaust (kg/s)
- N :
-
Number of TE couples
- P :
-
TE power output (W)
- Q :
-
Heat input from exhaust (W)
- Q C :
-
Heat rejected (W)
- Q H :
-
TE hot-side thermal input (W)
- Q loss :
-
Parasitic thermal loss at heat exchanger/TE interfaces (W)
- \({Q_\parallel}\) :
-
Parallel leakage heat (W)
- R :
-
TE module electrical resistance (Ω)
- S pn :
-
Junction seebeck coefficient (= S p − S n) (V/K)
- T 1 :
-
TE hot-side junction temperature (K)
- T 2 :
-
TE cold-side junction temperature (= T cold) (K)
- T C :
-
Cold sink temperature (K)
- T exh :
-
Hot source (exhaust) temperature (K)
- T H :
-
Hot heat exchanger temperature (K)
- T m :
-
Mean junction temperature (T 1 + T 2)/2 (K)
- U :
-
Overall heat exchanger heat transfer coefficient (W/m2 K)
- UA h :
-
Overall hot-side heat exchanger conductance (W/K)
- Z* :
-
Optimum thermoelectric module figure␣of merit [= S 2pn /(R*K TE)] (1/K)
- ε :
-
Heat exchanger effectiveness
- η Total :
-
Total TE system efficiency
- η TE :
-
TE module efficiency
- ρ :
-
Material electrical resistivity [= (ρ p + ρ n)/2] (Ω m)
- σ :
-
Heat loss fraction (= Q loss /Q)
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Acknowledgements
This work was carried out under NASA Space Act Agreement No.43-17508, a contract between NASA and General Motors with funding from the U.S. Department of Energy, at the Jet Propulsion Laboratory, California Institute of Technology, under a contract to the National Aeronautics and Space Administration.
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Hendricks, T.J., Yee, S. & LeBlanc, S. Cost Scaling of a Real-World Exhaust Waste Heat Recovery Thermoelectric Generator: A Deeper Dive. J. Electron. Mater. 45, 1751–1761 (2016). https://doi.org/10.1007/s11664-015-4201-y
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DOI: https://doi.org/10.1007/s11664-015-4201-y