Using the constant properties model for accurate performance estimation of thermoelectric generator elements

Ponnusamy, Prasanna; Boor, Johannes de; Müller, Eckhard

doi:10.1016/j.apenergy.2020.114587

Cited by 35 publications

(47 citation statements)

References 38 publications

(68 reference statements)

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“…The constants used to define the model materials were obtained using the spatial averages (SpAv; for electrical and thermal resistivity) at a current density corresponding to the maximum efficiency of the real material and the temperature average (TAv; for the Seebeck coefficient). The SPAv and TAv of a

-dependent quantity p for a hot side temperature

and a cold side temperature

are given by [ 1 , 12 , 18 , 25 ]

where

and

are the length of the TE leg. The exact efficiency using

-dependent properties was obtained using the 1D solution algorithm developed in [ 18 ] by calculating

…”

Section: Methods Results and Discussionmentioning

confidence: 99%

“…Depending on the slope ratio of

and

, the efficiency discrepancy due to Joule heat asymmetry,

, will vary considerably between different materials and may change sign from case to case, as observed in [ 18 ].…”

Section: Methods Results and Discussionmentioning

confidence: 99%

“…A very good approximation of the actual

profile and hence the SpAv of

and

in accordance with a real material can be calculated in a straightforward way from the T -dependent properties without using an iterative solution [ 18 ] for

This may considerably simplify the estimation of appropriate SpAvs as CPM property values.

can be obtained analytically from the CPM case,

from a integration of the Fourier equation and

and from a 1TD

model by a single integration.…”

Section: Appendix A1 Note From Section 21mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In a previous study [ 18 ], on the physically appropriate choice of averages in the CPM, we highlighted that spatial averages (SpAv) for resistivities (electrical and thermal) and temperature averaging (TAv) for the Seebeck coefficient are essential for a meaningful CPM estimate. However, there is still a remaining deviation due to unconsidered local redistribution of internal heat release or absorption and of thermal conduction in the CPM, which is linked to a change in the T profile T ( x ) [ 1 , 12 , 18 , 19 ]. Here, we will analyze the individual heat contributions exemplarily for six representative thermoelectric materials that we considered previously [ 18 ] plus PbTe [ 20 ], as this is one of the best TE materials in practice and shows an especially large deviation between CPM and exact results.…”

Section: Introductionmentioning

confidence: 99%

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Discrepancy between Constant Properties Model and Temperature-Dependent Material Properties for Performance Estimation of Thermoelectric Generators

Ponnusamy

Boor

Müller

2020

Entropy

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The efficiency of a thermoelectric (TE) generator for the conversion of thermal energy into electrical energy can be easily but roughly estimated using a constant properties model (CPM) developed by Ioffe. However, material properties are, in general, temperature (T)-dependent and the CPM yields meaningful estimates only if physically appropriate averages, i.e., spatial averages for thermal and electrical resistivities and the temperature average (TAv) for the Seebeck coefficient (α), are used. Even though the use of αTAv compensates for the absence of Thomson heat in the CPM in the overall heat balance, we find that the CPM still overestimates performance (e.g., by up to 6% for PbTe) for many materials. The deviation originates from an asymmetric distribution of internally released Joule heat to either side of the TE leg and the distribution of internally released Thomson heat between the hot and cold side. The Thomson heat distribution differs from a complete compensation of the corresponding Peltier heat balance in the CPM. Both effects are estimated quantitatively here, showing that both may reach the same order of magnitude, but which one dominates varies from case to case, depending on the specific temperature characteristics of the thermoelectric properties. The role of the Thomson heat distribution is illustrated by a discussion of the transport entropy flow based on the α(T) plot. The changes in the lateral distribution of the internal heat lead to a difference in the heat input, the optimum current and thus of the efficiency of the CPM compared to the real case, while the estimate of generated power at maximum efficiency remains less affected as it is bound to the deviation of the optimum current, which is mostly <1%. This deviation can be corrected to a large extent by estimating the lateral Thomson heat distribution and the asymmetry of the Joule heat distribution. A simple guiding rule for the former is found.

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-dependent quantity p for a hot side temperature

and a cold side temperature

are given by [ 1 , 12 , 18 , 25 ]

where

and

are the length of the TE leg. The exact efficiency using

-dependent properties was obtained using the 1D solution algorithm developed in [ 18 ] by calculating

…”

Section: Methods Results and Discussionmentioning

confidence: 99%

“…Depending on the slope ratio of

and

, the efficiency discrepancy due to Joule heat asymmetry,

, will vary considerably between different materials and may change sign from case to case, as observed in [ 18 ].…”

Section: Methods Results and Discussionmentioning

confidence: 99%

“…A very good approximation of the actual

profile and hence the SpAv of

and

in accordance with a real material can be calculated in a straightforward way from the T -dependent properties without using an iterative solution [ 18 ] for

This may considerably simplify the estimation of appropriate SpAvs as CPM property values.

can be obtained analytically from the CPM case,

from a integration of the Fourier equation and

and from a 1TD

model by a single integration.…”

Section: Appendix A1 Note From Section 21mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Discrepancy between Constant Properties Model and Temperature-Dependent Material Properties for Performance Estimation of Thermoelectric Generators

Ponnusamy

Boor

Müller

2020

Entropy

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Efficiency Measurement and Modeling of a High‐Performance Mg₂(Si,Sn)‐Based Thermoelectric Generator

et al. 2022

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Mg2(Si,Sn) is an attractive material class due to its excellent thermoelectric (TE) properties, its eco‐friendly constituents, its low mass density, and its low price. A lot of research has been done on optimizing its TE properties; however, works on its use in thermoelectric generators (TEG) are scarce. Herein, the first conversion efficiency measurement of a functional, fully Mg2(Si,Sn)‐based TEG, approaching a maximum value of 4% for an applied ΔT = 375 °C, is shown. A maximum power density of 0.9 W cm−2 (related to the cross‐sectional area of the TE legs) at ΔT=375 °C is also reported, which is among the highest performance of silicide‐based modules reported in literature. Efficiency measurements can be tricky due to the uncertainty of heat flow measurement and parasitic heat losses; therefore, assessing the measurement reliability by confronting it to theoretical calculations is necessary. TEG device simulation in a constant property model is used to compare measured data to expected values and a good match is found (<1% deviation for current at maximum power, <4% difference for maximum power output, deviation within measurement uncertainty range for heat flows and efficiency). The significant discrepancy between measurement and calculations of the inner electrical resistance reveals room for improvement. Cracks form due to thermally induced mechanical stress, which dramatically increase the inner electrical resistance. It is shown that by avoiding those cracks, the maximum power output and conversion efficiency of the TEG could be improved by 30%.

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Interlaboratory Testing for High‐Temperature Power Generation Characteristics of a Ni‐Based Alloy Thermoelectric Module

et al. 2020

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Standardization of metrology for thermoelectric generator modules (TEMs) is a necessary step toward industrialization of thermoelectric applications. Unspecified uncertainty budgets of the widely used custom‐built characterization facilities seem insufficient to validate technological developments, industrial benchmarks, or allow sound conclusions in scientific studies. Particularly, works on high‐temperature TEM have to be supported by suitable characterization techniques. This shall accelerate progress toward product releases for thermoelectric energy conversion. Herein, a Ni‐based alloy TEM is reported, which is developed at the National Institute of Advanced Industrial Science and Technology (AIST) as a prospective standard reference TEM. Comparative measurements at AIST and the German Aerospace Center (DLR) demonstrate the high repeatability and precision of custom‐built TEM characterization facilities at AIST and DLR. Tests at elevated temperatures up to 773 K hot side temperature and 450 K temperature difference reveal excellent accordance of electric measurands with a standard deviation <0.3% for the open‐circuit voltage and <0.85% for electric resistance and maximum power output. Deviations of the heat flow measurement of up to 7.22% arise from individual uncertainties of the used characterization methods and point to the importance of standardization for TEM metrology.

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Using the constant properties model for accurate performance estimation of thermoelectric generator elements

Cited by 35 publications

References 38 publications

Discrepancy between Constant Properties Model and Temperature-Dependent Material Properties for Performance Estimation of Thermoelectric Generators

Discrepancy between Constant Properties Model and Temperature-Dependent Material Properties for Performance Estimation of Thermoelectric Generators

Efficiency Measurement and Modeling of a High‐Performance Mg₂(Si,Sn)‐Based Thermoelectric Generator

Interlaboratory Testing for High‐Temperature Power Generation Characteristics of a Ni‐Based Alloy Thermoelectric Module

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Using the constant properties model for accurate performance estimation of thermoelectric generator elements

Cited by 35 publications

References 38 publications

Discrepancy between Constant Properties Model and Temperature-Dependent Material Properties for Performance Estimation of Thermoelectric Generators

Discrepancy between Constant Properties Model and Temperature-Dependent Material Properties for Performance Estimation of Thermoelectric Generators

Efficiency Measurement and Modeling of a High‐Performance Mg2(Si,Sn)‐Based Thermoelectric Generator

Interlaboratory Testing for High‐Temperature Power Generation Characteristics of a Ni‐Based Alloy Thermoelectric Module

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Efficiency Measurement and Modeling of a High‐Performance Mg₂(Si,Sn)‐Based Thermoelectric Generator