Jon MackeyMechanical Engineering University of AkronMaterials Science and Engineering Case Western Reserve UniversityFred DynysNASA Glenn Research CenterNASA Cooperative Agreement NNX08AB43ANASAUSRA ID: 880407
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1 Analytic thermoelectric couple modeling:
Analytic thermoelectric couple modeling: variable material properties and transient operation Jon MackeyMechanical Engineering, University of AkronMaterials Science and Engineering, Case Western Reserve UniversityFred DynysNASA Glenn Research CenterNASA Cooperative Agreement: NNX08AB43ANASA/USRA Contract: 04555-004 Thermoelectricity Spacecraft Power GPHS-RTG (Galileo/Ulysses) Study of the coupled transport of electr
2 ical and thermal energy.Solid-state phen
ical and thermal energy.Solid-state phenomenon requires no moving parts or working fluids, and generates no noise, torque, or vibrations.As a result thermoelectric devices are extremely reliable.Power GenerationSpacecraft, automotive, aerospace, gas pipelines, well sites, and offshore platforms.RefrigerationOn chip cooling, electronics, and automotive. High reliability, low conversion efficiency. Bennett et al. AIP
3 Proceedings (2008) 663-671.Radioisotope
Proceedings (2008) 663-671.Radioisotope thermoelectric generators (RTG) have powered 45 spacecraft.Voyager (1977), Ulysses (1990), Cassini (1997), New Horizons Lange et al. Energy Conversion and Management (2008) 391-401. Analytic Couple Modeling1 of 7 Analytic Couple Modeling1 of 7 Thermoelectricity Spacecraft Power GPHS-RTG (Galileo/Ulysses) Study of the coupled transport of electrical and thermal energy.Solid-sta
4 te phenomenon requires no moving parts o
te phenomenon requires no moving parts or working fluids, and generates no noise, torque, or vibrations.As a result thermoelectric devices are extremely reliable.Power GenerationSpacecraft, automotive, aerospace, gas pipelines, well sites, and offshore platforms.RefrigerationOn chip cooling, electronics, and automotive. High reliability, low conversion efficiency.Bennett et al. AIP Proceedings (2008) 663-671.Radiois
5 otope thermoelectric generators (RTG) ha
otope thermoelectric generators (RTG) have powdered 45 spacecraft.Voyager (1977), Ulysses (1990), Cassini (1997), New Horizons Lange et al. Energy Conversion and Management (2008) 391-401. A na ytic Coup l e Mode l in l e c d a result thermoelectric devicesareextremelyreliable. efficiency. 71. Radioisotope thermoelectric generators ioisotope t h ermoe ectric enerato G) have powdered 45 spacecraft. Voya er (19
6 77), Ulysses (1990), Cassini , New Hor
77), Ulysses (1990), Cassini , New Horizons ( 2006 , and Curiosit y ( L an g e et a l . Ener g y Conversion and Mana g ement ( 2008 391 - 4 4 4 4 4 4 4 4 4 4 0 Curiosity y of the coupled transport of c c c c c c c c t t rica and t h erma ener g y. tate p h enomenon requires m m m m m m m m m m m m ovin parts or workin g fluids, d d g enerates no noise, tor q ue, or r r r r r a a a a a a a a ti o n
7 s . New Horizons devices are extreme
s . New Horizons devices are extremel y reliable. P e r G e n e r a acecraft, automotive, a erospace, as pipe l ines, we ll s ites, and offshore platforms. R R R R R R R R R R R efri eratio On c h ip coo l in , e l ectronics, and au t o m o g h reliability, low conversion e e e e e e e e e e e e e e e f f f f f f f f f f f f f f f f f f f f f f f f i i i i i i i i i i i i c c c c c c c c c c c c i i i i
8 i i i i i i i i e e e e e e e e e e e e
i i i i i i i i e e e e e e e e e e e e n n n n n n n n n n n n c c c c c c c c c c c c y y y y y y y y y y y y . . . . Voyager al BennettetalAIPProceedings (2008) (2008)663 - Photos nasa.gov Analytic Couple Modeling1 of 7 Thermoelectricity Spacecraft Power GPHS-RTG (Galileo/Ulysses) Study of the coupled transport of electrical and thermal energy.Solid-state phenomenon requires no moving parts or working flu
9 ids, and generates no noise, torque, or
ids, and generates no noise, torque, or vibrations.As a result thermoelectric devices are extremely reliable.Power GenerationSpacecraft, automotive, aerospace, gas pipelines, well sites, and offshore platforms.RefrigerationOn chip cooling, electronics, and automotive. High reliability, low conversion efficiency.Bennett et al. AIP Proceedings (2008) 663-671.Radioisotope thermoelectric generators (RTG) have powdered 4
10 5 spacecraft.Voyager (1977), Ulysses (19
5 spacecraft.Voyager (1977), Ulysses (1990), Cassini (1997), New Horizons Lange et al. Energy Conversion and Management (2008) 391-401. A na ytic Coup l e Mode l in wer lysses) tudy of the co u e l and t h Sol i d tate p h e n o movin g parts a n d g enerates n vi a ti o n s . a esul evices a r Po w e r G e n e r a pacecra erospac e ites, and R efri eratio On c h ip c au t o m o g h reliabilit y efficienc
11 Bennett et al. AIP Proceedings s (2008)
Bennett et al. AIP Proceedings s (2008) (2008)663 671. 671 enerators acecraft. s (1990), o rizons Lange et al. Energy Conversion and Management 2008 391 - 4 0 led transport of e e e e e e e e e e e e rma ener g y . o menon requires r workin g fluids, o o o o o o o o o o o o noise, torque, or R adioisotope t h ermoe RTG) have p owdered 45 Voya er (1977), Ulys s s s s e e e e e Cassini , New H H H H H
12 H H o ( 2006), and Curiosity ( ( ( ( (
H H o ( 2006), and Curiosity ( ( ( ( ( ( Global TE l t t t t t t t t t t t t t t t t t t t t t t t t h h h h h h h h h h h h e e e e r r r r m m m m o o o o e e e e l l l l l l l l l l l l e e e e c c c c t t t t t t t t t t r r r r i i i i i i i i i i i i c c c c r r r r r r r r r e e extreme l y re l ia . i , automotive, e e e e e e e e e e e , g as pipe l ines, we ll ffshore latforms. l , e l ectronics
13 , and v v v v v v v v v v v v e . low
, and v v v v v v v v v v v v e . low conversion B B B B B B B B e e e e e e e e n n n n n n n n n n n n n n n n e e e e e e e e t t t t t t t t t t t t t t t t e t a l . A I P P r o c e e d i n g s s g e g y g 2 of 7 Irreversible Thermodynamics Thermocouple Ohms Law Fouriers Law 1931 Lars Onsager discussed coupled irreversible processes to unify thermoelectric phenomena into a single stud
14 y.Study results in two transport laws fo
y.Study results in two transport laws for a thermoelectric conductor. Analytic Couple Modeling Analytic Couple Modeling Classic Model Classic Parameters Electrical-System- ܼ൫ܺ ͳൠẠClassic Solution Geometric- Materials- Analytic Couple Modeling Classic Model Classic Parameters Electrical-System- ܼ൫ܺ ͳൠẠClassic Solution Geometric- Materials- Four Assumptions Analyti
15 c Couple Modeling Classic Model Classic
c Couple Modeling Classic Model Classic Parameters Electrical-System- ܼ൫ܺ ͳൠẠClassic Solution Geometric- Materials- Analytic Couple Modeling Classic Model Classic Parameters Electrical-System- ܼ൫ܺ ͳൠẠClassic Solution Geometric- Materials- Analytic Couple Modeling Classic Model Classic Parameters Electrical-System- ܼ൫ܺ ͳൠẠClassic Solution G
16 eometric- Materials- Analytic Couple Mod
eometric- Materials- Analytic Couple Modeling Classic Model Classic Parameters Electrical-System- ܼ൫ܺ ͳൠẠClassic Solution Geometric- Materials- Analytic Couple Modeling Classic Model Classic Parameters Electrical-System- ܼ൫ܺ ͳൠẠClassic Solution Geometric- Materials- Analytic Couple Modeling Classic Model Classic Parameters Electrical-System- ܼ൫ܺ ͳൠá
17 º Classic Solution Geometric- Ma
º Classic Solution Geometric- Materials- Analytic Couple Modeling Classic Model Classic Parameters Electrical-System- ܼ൫ܺ ͳൠẠClassic Solution Geometric- Materials- Analytic Couple Modeling Classic Model Classic Parameters Electrical-System- Geometric- ܼ൫ܺ ͳൠẠClassic Solution Materials- Analytic Couple Modeling Classic Model Classic Parameters Electrical-Sys
18 tem- Geometric- ܼ൫ܺ ͳൠáº
tem- Geometric- ܼ൫ܺ ͳൠẠClassic Solution Materials- o ytic Coup l e Mode l in a r a m e t e r s Solu ti Mackey et al. Applied Energy (2014) 374-381. Solution Parameters ÝÝÝܼ൫ܺ Analytic Couple Modeling Variable Properties Model Asymptotic Expansion Material Properties by Asymptotic Expansion- Variable Seebeck οܶܶ οܶܶ οܵοܶ οܵοܶ ෤൫ߩοܶܶ Analytic Couple Modeling V
19 ariable Properties Model Asymptotic Expa
ariable Properties Model Asymptotic Expansion Material Properties by Asymptotic Expansion- Variable Seebeck οܶܶ οܶܶ οܵοܶ οܵοܶ ෤൫ߩοܶܶ Analytic Couple Modeling οܶܶ οܶܶ ෤൫ߩοܶܶ Variable Properties Model Asymptotic Expansion Material Properties by Asymptotic Expansion- Variable Seebeck οܵοܶ οܵοܶ 4 ytic Coup l e Mode l in Variable Properties aterial Pro p erties b y As y m
20 p t Asymptotic Expansion Method Tx Lead
p t Asymptotic Expansion Method Tx Leading order temperature solutionFirst order temperature correctionCombined temperature solution Material Properties οܶܶ ෤൫ߩοܶܶ οܶܶ 0 Analytic Couple Modeling οܶܶ οܶܶ ෤൫ߩοܶܶ Variable Model Asymptotic Expansion Material Properties by Asymptotic Expansion- Variable Solution οܶܶ ෤൫ߩοܶܶ οܵοܶ οܵοܶ 7 Analytic Couple Modeling Materi
21 al Properties by Asymptotic Expansion a
al Properties by Asymptotic Expansion a Solu ti S Conversion Efficiency 6.00% Asymptotic Expansion TS Conversion Efficiency 6.30% Variable Seebeck a n n n n n n n n n n n s s TS Conversion Efficiency 6.15% οܶܶ Analytic Couple Modeling οܶܶ οܶܶ ෤൫ߩοܶܶ Variable Model Asymptotic Expansion Material Properties by Asymptotic Expansion- Variable Solution οܶܶ ෤൫ߩοܶܶ οܵοܶ οܵοܶ 7 Analyti
22 c Couple Modeling Material Properties by
c Couple Modeling Material Properties by Asymptotic Expansion a Solu ti k Conversion Efficiency 5.84% Asymptotic Expansion Tk Conversion Efficiency 6.69% 4 4 4 4 4 4 4 4 4 4 4 4 o o o o o o o o o o o f f f f f f f f f f f f 7 7 7 7 7 7 7 7 7 7 7 7 e e e e e e e e e l l l l l l l l l l l l l l l l l l l l l i i i i i i i i i i i i n n n n n n n n n n n g g g g g g g g g g g Variable Thermal a n n n n n n n n n n n s
23 s Tk Conversion Efficiency 6.15% οܶܶ
s Tk Conversion Efficiency 6.15% οܶܶ Analytic Couple Modeling οܶܶ οܶܶ ෤൫ߩοܶܶ Variable Model Asymptotic Expansion Material Properties by Asymptotic Expansion- Variable Solution οܶܶ ෤൫ߩοܶܶ οܵοܶ οܵοܶ 7 Analytic Couple Modeling Material Properties by Asymptotic Expansion a Solu ti Conversion Efficiency 6.20% Asymptotic Expansion T Conversion Efficiency 6.10% 4 4 4 4 4 4 4 4 4 4 4
24 4 o o o o o o o o o o o f f f f f f f f
4 o o o o o o o o o o o f f f f f f f f f f f f 7 7 7 7 7 7 7 7 7 7 7 7 e e e e e e e e e l l l l l l l l l l l l l l l l l l l l l i i i i i i i i i i i i n n n n n n n n n n n g g g g g g g g g g g Variable Resistivity a n n n n n n n n n n n s s T Conversion Efficiency 6.15% ෤൫ߩοܶܶ Variable Property Model Summary MaterialProperty Temperature ConversionEfficiencySensitivity Absolute Seebeck Coefficient El
25 ectrical Resistivity ܵÝÝÝÝ ÝÝ ÝÝ Ý
ectrical Resistivity ܵÝÝÝÝ ÝÝ ÝÝ ÝÝ Analytic Couple Modeling Tk Conversion Efficiency 6.69% TS Conversion Efficiency 6.30% T Conversion Efficiency 6.10% Analytic Couple Modeling Transient Model Greens Function Solution Electrical-System- Transient Parameters ܽÝÝܽÝÝ Ü½ÝÝܽÝÝ Thermal diffusivity factor-Inductance factor- Analytic Couple Modeling Transient Model Greens Function Solution Electrical
26 -System- Transient Parameters ܽÝÝܽ
-System- Transient Parameters ܽÝÝܽÝÝ Ü½ÝÝܽÝÝ Thermal diffusivity factor-Inductance factor- Analytic Couple Modeling Transient Model Greens Function Solution Electrical-System- Transient Parameters ܽÝÝܽÝÝ Ü½ÝÝܽÝÝ Thermal diffusivity factor-Inductance factor- 6 o ytic Coup l e Mode l in a n s i e nt M odel Gr c ti o u ti e e stem factor hermal diffusivit y Thermal Greens Function Eigenf
27 unctionexpansion- Temperature- Eigenvalu
unctionexpansion- Temperature- Eigenvalue- Analytic Couple Modeling Transient Model Greens Function Solution Electrical-System- 7 Analytic Couple Modeling a n s i e nt M odel Greens Function Solution T h e e System Transient Parameters ܽÝÝܽÝÝ Ü½ÝÝܽÝÝ Thermal diffusivity factor-Inductance factor- t t t t t t t t t t t e m Periodic On/Off Operation Design Guideline àµÍ³àµ Analytic Couple Modeling Tra
28 nsient Model Greens Function Solution E
nsient Model Greens Function Solution Electrical-System- L+4E* Q:T;T; L:TF; Q:T;L):B 7 Analytic Couple Modeling a n s i e nt M odel Gr c ti o u ti e e stem Transient Parameters =RC=RC =RC=RC Thermal diffusivity factor-Inductance factor- Sinusoidal Operation Power Output Amplitude Acknowledgements Tom Sabo, Ray Babuder, Ben KowalskiNASA Glenn Research Center/ Case Western Reserve UniversityDr. Sabah Bux, Dr. Jean
29 -Pierre NASA Cooperative Agreement: NASA
-Pierre NASA Cooperative Agreement: NASA/USRA Contract:Asymptotic expansions are an effective means of understanding thermocouple behavior.Conversion efficiency is most sensitive to thermal conductivity temperature Thermal diffusivity factorGoverns transient operation of a thermocouple, with an ideal value of unity.Inductance factor Governs the balance between thermal and electrical inductance. Analytic Couple Model