Hybrid Solar Thermoelectric Systems Utilizing
Thermosyphons for Bottoming Cycles
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
by
Nenad Miljkovic
JUL 2 9 2011
BASc, Mechanical Engineering (2009)
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University of Waterloo
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Submitted to the Department of Mechanical Engineering in
Partial Fulfillment of the Requirements for the
Degree of Master of Science in Mechanical Engineering
at the
Massachusetts Institute of Technology
May 2011
@2011 Massachusetts Institute of Technology
All rights reserved
Signature of A uthor: ...................
.................................................................
Department of Mechanical Engineering
May 6, 2011
Certified by: ..........
. .
.................................
Evelyn N. Wang
Assistant Professor of Mechanical Engineering
-
A ccepted by : ..........................
Thesis Supervisor
..........................................
David E. Hardt
Chairman, Department Committee on Graduate Theses
Hybrid Solar Thermoelectric Systems Utilizing
Thermosyphons for Bottoming Cycles
by
Nenad Miljkovic
Submitted to the Department of Mechanical Engineering on May 6 th 2011,
in Partial Fulfillment of the Requirements for the Degree of Master of Science
Abstract
Efficient renewable energy sources are in significant demand to replace diminishing and
environmentally harmful fossil fuels. The combination of commercial and residential buildings
as well as the industrial sector currently consumes 72% of the total energy in the US. The
abundance of solar energy promises efficient methods to meet the current heating and electricity
needs. In most cases, however, current systems are limited to providing either heat or electricity
only.
In this thesis, we present the modeling and optimization of a new hybrid solar thermoelectric
(HSTE) system which uses a thermosyphon to passively and efficiently transfer heat to a
bottoming cycle for various applications including residential hot water heating, solar air
conditioning, chemical drying, and aluminum smelting. The concept utilizes a parabolic trough
mirror to concentrate solar energy onto a selective surface coated thermoelectric to produce
electrical power. Meanwhile, the thermosyphon adjacent to the back side of the thermoelectric is
used to maintain the temperature of the cold junction and carry the remaining thermal energy to a
bottoming cycle. HSTEs are advantageous compared to other approaches such as hybrid
photovoltaics because electrical conversion efficiencies at high temperatures can be comparable
or higher to that at room temperature. The thermoelectric materials bismuth telluride, lead
telluride, and silicon germanium were combined with thermosyphon material-working fluids of
copper-water, stainless steel-mercury, and nickel-liquid potassium for this work. We solved the
energy equation at the evaporator with a thermal resistance model of the system to determine
overall performance. In addition, the HSTE system efficiency, which included the electrical
efficiency of the thermoelectric and the exergetic efficiency of the bottoming cycle waste heat,
was investigated for temperatures of 300 K - 1200 K, solar concentrations of 1 - 100 Suns, and
different thermosyphon and thermoelectric materials with a geometry resembling an evacuated
tube solar collector.
Optimization was performed showing system efficiencies as high as 52.6% can be achieved at
solar concentrations of 100 Suns and bottoming cycle temperatures of 776 K. In addition,
thermosyphons with low wall conductivities (> 1.2 W/mK) and low solar concentrations
(< 4 Suns) have comparable system efficiencies which suggests that lower cost materials,
including glass, can be used. Finally, five bottoming cycle applications with temperatures
ranging from 360 K - 776 K are proposed for potential HSTE integration. This work provides
guidelines for the design, as well as the optimization and selection of thermoelectric and
thermosyphon components for future high performance HSTE systems. Future work will focus
on experimental validation and prototype building of the HSTE system.
Thesis Supervisor: Evelyn N. Wang
Title: Assistant Professor, Mechanical Engineering
Acknowledgements
I would like to graciously thank my advisor, Professor Evelyn Wang, for her care and guidance
over the past two years. I would not have been able to achieve the work in this thesis without her
help and support.
I would also like to express gratitude to my peers in the Device Research Lab for thoughtful
discussions we shared at weekly group meetings. I would like to especially thank Dr. Ryan
Enright, Dr. Shalabh Maroo, Dr. Anand Veeraragavan, Dr. Youngsuk Nam, Andrej Lenert, Ken
McEnaney, Daniel Kraemer, Mandy Muto and Peter Bermel for their insightful advice.
I would also like to thank the US Department of Energy for funding the reported research
through the MIT S3TEC Center and the Natural Sciences and Engineering Research Council of
Canada for additional funding support.
Finally, I would like to thank my girlfriend, Mai Hoang, and my family. Without their
unwavering love and support, I would not be where I am today. Thank you for all the sacrifices
you made so I can achieve this dream of mine.
6
Table of Contents
INTRODUCTION ..........................................................................................................................---..
11
1. 1
M OTIVATION ......................................................................................................................................
11
1.2
BACKGROUND ....................................................................................................................................
12
1.3
THESIS OBJECTIVES AND OUTLINE ..................................................................................................
15
2.
HEAT PIPE AND THERMOSYPHON M ODELING .....................................................................................
17
2.1
M ODEL FORM ULATION ......................................................................................................................
17
2.2
DIMENSIONAL ANALYSIS...................................................................................................................
19
2.3
RESULTS AND D ISCUSSION ................................................................................................................
20
2.4
SCALING .............................................................................................................................................
24
2.5
LOW TEMPERATURE EXPERIMENTAL VALIDATION ...........................................................................
25
2.6
SUM MARY ..........................................................................................................................................
29
1.
3.
HYBRID SOLAR THERMOELECTRIC M ODELING ........................................................................................
30
3.1
M ODEL FORM ULATION ......................................................................................................................
30
3.2
GOVERNING EQUATIONS....................................................................................................................
34
3.3
THERM OSYPHON M ODELING .............................................................................................................
35
3.4
SOLUTION ALGORITHM ......................................................................................................................
41
3.5
RESULTS AND DISCUSSION ................................................................................................................
42
3.6
SUMMARY ..........................................................................................................................................
45
HSTE OPTIMIZATION .......................................................................................................................
46
4.1
OPTIM IZATION EQUATIONS................................................................................................................
46
4.2
RESULTS AND D ISCUSSION ................................................................................................................
47
4.3
SUMMARY ..........................................................................................................................................
54
4.
5.
56
CONCLUSIONS AND ONGOING WORK................................................................................................
5.1
ONGOING W ORK - EXPERIMENTAL DESIGN.....................................................................................
57
5.2
EXPERIM ENTAL PROTOCOL................................................................................................................
59
5.3
FUTURE W ORK ...................................................................................................................................
60
6.
BIBLIOGRAPHY................................................................................................................................62
APPENDIX...........................................................................................................................66........
--...
66
HEAT PIPE CHARACTERIZATION .................................................................................................................
66
H STE MATL AB CODE ..................................................................................................................................
68
EXPERIM ENTAL SECTION CAD DRAW INGS................................................................................................
74
8
List of Figures
FIGURE 1 - 2008 US ENERGY CONSUMPTION FOR (A) RESIDENTIAL AND (B) INDUSTRIAL SECTORS [2] ........................
FIGURE 2 - SOLAR THERMAL SYSTEMS FOR (A) DOMESTIC HOT WATER HEATING [22] AND (B) POWER PRODUCTION
I
[2 3].....................................................................................................................................................................12
FIGURE 3 - (A) HYBRID PHOTOVOLTAIC THERMAL (PVT) SYSTEM [25] AND (B) CROSS-SECTIONAL SCHEMATIC [25].
THE SYSTEM UTILIZES AN ELEVATED TEMPERATURE PV ARRAY TO GENERATE CLEAN ELECTRICAL POWER WHILE
PRODUCING WASTE HEAT BY FLOWING AIR THROUGH THE UPPER AND LOWER CHANNELS. HOWEVER, DUE TO
THE ELEVATED PV ARRAY TEMPERATURES, ELECTRICAL CONVERSION EFFICIENCY DEGRADES DUE TO
13
INCREASED INTERNAL CARRIER RECOMBINATION. ..............................................................................................
FIGURE 4 - HYBRID SOLAR THERMOELECTRIC WATER HEATER [39]. EFFICIENCY DEGRADES DUE TO ELECTRICAL
POWER REQUIREMENTS FOR THE PUMP IN ORDER TO FLOW FLUID (WATER) THROUGH THE COPPER TUBES. ........ 14
FIGURE 5 - SCHEMATIC OF THE HYBRID SOLAR THERMOELECTRIC SYSTEM (HSTE). SOLAR ENERGY IS FOCUSED BY A
PARABOLIC CONCENTRATOR ON THE EVAPORATOR SECTION OF THE EVACUATED TUBE ABSORBER
(THERMOSYPHON), WHICH HEATS THE TE HOT SIDE. THE RESULTING TEMPERATURE DIFFERENCE BETWEEN THE
TE HOT AND COLD SIDES PRODUCES ELECTRICAL POWER WHILE HEAT CARRIED AWAY (WASTE HEAT) BY THE
THERMOSYPHON (ADJACENT TO THE COLD SIDE) IS TRANSFERRED TO THE CONDENSER SECTION FOR THE
15
BOTTO M IN G CY CLE. ............................................................................................................................................
FIGURE 6 - SCHEMATIC OF A HEAT PIPE (A) GEOMETRY OF A HEAT PIPE AND (B) THE ASSOCIATED THERMAL
RESISTANCE NETWORK. THERMOSYPHON GEOMETRY IS IDENTICAL EXCEPT WICK STRUCTURE IS WORKING FLUID
17
FIL M ....................................................................................................................................................................
FIGURE 7 - RESULTS OF DIMENSIONAL ANALYSIS. (A) THREE-DIMENSIONAL PLOT SHOWING NON-DIMENSIONAL HEAT
TRANSFER 1 AS A FUNCTION OF NON-DIMENSIONAL TEMPERATURE H2 AND VAPOR RESISTANCE f14. (B) TWO21
WITH NON-DIM .......................................
DIMENSIONAL PROJECT OF NON-DIMENSIONAL HEAT TRANSFER
FIGURE 8 - NON-DIMENSIONAL HEAT TRANSFER 1 AS A FUNCTION OF NON-DIMENSIONAL TEMPERATURE H2 AND
WICK RESISTANCE H3, FOR A HEAT PIPE OR THERMOSYPHON OF IDENTICAL GEOMETRY AS IN FIGURE 7.
22
PLANE. f5 IS CONSTANT. .......................................................................
CONTOURS ARE SHOWN IN THE H2 -
H1
H3
H1
FIGURE 9 - SENSITIVITY ANALYSIS FOR WALL CONDUCTIVITY OF (A) 400 W/MK, AND (B) 2 W/MK. ......................
23
FIGURE 10 - (A) SCHEMATIC OF EXPERIMENTAL LAYOUT AND (B) EXPERIMENTAL SETUP SHOWING THE ROPE HEATER,
THERMOSYPHON, COOLING SECTION AND CONSTANT TEMPERATURE BATH, THERMOCOUPLE ARRAY (TC) AND
26
DA TA A CQU ISITION SY STEM . ...............................................................................................................................
FIGURE I1 - (A) MEASURED SURFACE TEMPERATURE (B) THERMOSYPHON HEAT TRANSFER AND (C) SYSTEM
EFFICIENCY FOR VARYING CONDENSER TEMPERATURE AND SOLAR CONCENTRATION. AS CONDENSER
TEMPERATURE INCREASES, SURFACE TEMPERATURE INCREASES WHILE THERMOSYPHON HEAT TRANSFER
28
DECREASES DUE TO INCREASED LOSSES. .............................................................................................................
FIGURE 12 - SPECTRALLY AVERAGED EMISSIVITY AS A FUNCTION OF SELECTIVE SURFACE TEMPERATURE (Ts) FOR
FOUR COMMERCIALLY AVAILABLE SURFACE COATINGS [43]. .........................................................................
31
FIGURE 13 - (A) SCHEMATIC CROSS-SECTION OF THE HSTE SYSTEM IN A HORIZONTAL ORIENTATION. SOLAR ENERGY
(QSOLAR) HEATS THE SELECTIVE SURFACE LOCATED ON THE TE HOT SIDE, WHICH CREATES A TEMPERATURE
GRADIENT ACROSS THE TE THAT PRODUCES ELECTRICAL POWER (PTE). THE REMAINING HEAT (QouT) IS
TRANSFERRED AXIALLY BY THE THERMOSYPHON TO A BOTTOMING CYCLE APPLICATION AT TEMPERATURE Tc.
(B) THERMAL RESISTANCE (TR) MODEL OF THE HSTE, WHERE RTE IS THE TE RADIAL TR, R, AND R 6 ARE THE
THERMOSYPHON WALL RADIAL TR, R 2 AND R 3 ARE THE BOILING AND EVAPORATION TRS, RESPECTIVELY, Rs IS
CONDENSATION TR, R 4 IS THE VAPOR TR, R 7 IS THE THERMOSYPHON WALL AXIAL TR, AND R 8 AND R 9 ARE
32
EVAPORATION AND CONDENSATION INTERFACIAL TRS, RESPECTIVELY. ............................................................
F IGURE 14 -...................................................................................................................................................................
33
FIGURE 15 - SCHEMATICS OF THE (A) TE SIDE SHOWING THE FILM EVAPORATION AND POOL BOILING REGION OF THE
EVAPORATOR AND (B) CONDENSER SIDE SHOWING FILM CONDENSATION IN A VERTICAL ORIENTATION. ............ 34
FIGURE 16 - FLOWCHART OF THE ITERATIVE ALGORITHM. [To] IS THE INITIALLY GUESSED TEMPERATURE
DISTRIBUTION, [PO] ARE THE INITIAL CALCULATED FLUID AND THERMOELECTRIC PROPERTIES, I IS THE
ITERATION NUMBER, [TI] IS THE ITH ITERATION TEMPERATURE DISTRIBUTION, AND TcoNTINUUM, QSONIC,
VISCOUS,
42
QENTRAINMENT, QBOILING ARE THE THERMOSYPHON LIMITS. ....................................................................................
FIGURE 17 - (A) THERMOSYPHON HEAT TRANSFER, (B) EMISSIVE LOSSES AND (C) TE POWER OF THE HSTE SYSTEM
FOR VARYING SOLAR CONCENTRATIONS AND CONDENSER TEMPERATURES. AS THE CONDENSER TEMPERATURE
(Tc) INCREASES, EMISSIVE LOSSES (QLoss) INCREASE WHILE TE POWER (PTE) AND THERMOSYPHON WASTE HEAT
DECREASE DUE TO ELEVATED SURFACE TEMPERATURES (Tss). AS SOLAR CONCENTRATION (C) INCREASES,
EMISSIVE LOSSES, TE POWER AND HEAT OUTPUT INCREASE. ..........................................................................
44
FIGURE 18 - EFFICIENCY OF THE HSTE SYSTEM FOR VARYING SOLAR CONCENTRATIONS (C) AND BOTTOMING CYCLE
TEMPERATURES (TC). OPTIMAL SYSTEM EFFICIENCIES EXISTS WHICH BALANCE THE THERMAL EFFICIENCY AND
EMISSIVE POWER. INCREASING THE SOLAR CONCENTRATION ALSO INCREASES EFFICIENCY DUE TO A HIGHER
ENERGY INPUT AND THERM AL EFFICIENCY. ........................................................................................................
48
FIGURE 19 - OPTIMIZATION RESULTS FOR A PBTE HSTE AT C= 50 AND TC = 700 K SHOWING A) SYSTEM EFFICIENCY
AND B) TE POWER. AN INCREASE IN TE LEG LENGTH (LTE) DECREASES EFFICIENCY AND INCREASES TE POWER
DUE TO A LARGER TE THERMAL GRADIENT. AS THE TE LEG LENGTH INCREASES, THE MAXIMUM OPERATING
TEMPERATURE (776 K) IS REACHED, AT WHICH POINT THE PERFORMANCE DECREASES TO ZERO (GRAY AREA). IN
ADDITION, FOR SMALL THERMOSYPHON RADII (BOTTOM WHITE AREA), HEAT PIPE LIMITATIONS (E.G., SONIC
LIM IT) PROHIBIT OPERATION . ..............................................................................................................................
50
FIGURE 20 - OPTIMIZATION RESULTS FOR A BI2 TE3 HSTE AT Tc = 470 K AND C= 10 SHOWING A) SYSTEM EFFICIENCY,
B) TE POWER, AND C) WASTE HEAT. AN INCREASE IN TE LEG LENGTH (LTE) RESULTS IN A DECREASE IN
EFFICIENCY AND INCREASE IN TE POWER DUE TO A LARGER TE THERMAL GRADIENT. AS THE TE LEG LENGTH
INCREASES, THE MAXIMUM OPERATING TEMPERATURE IS REACHED, AND THE PERFORMANCE DECREASES TO
ZERO (GRAY AREA). IN ADDITION, FOR SMALL THERMOSYPHON RADII (BOTTOM WHITE AREA), HEAT PIPE
LIMITATIONS (E.G., SONIC LIMIT) PROHIBIT OPERATION. .................................................................................
51
FIGURE 21 - OPTIMIZATION RESULTS FOR A SIGE HSTE AT Tc = 776 K AND C= 50 SHOWING A) HSTE SYSTEM
EFFICIENCY, B) TE POWER AND C) WASTE HEAT. AN INCREASE IN TE LEG LENGTH (LTE) RESULTS IN A DECREASE
IN EFFICIENCY AND INCREASE IN TE POWER DUE TO A LARGER TE THERMAL GRADIENT. FOR SMALL
THERMOSYPHON RADII (BOTTOM WHITE AREA), HEAT PIPE LIMITATIONS (E.G., SONIC LIMIT) PROHIBIT
O PER AT IO N . ........................................................................................................................................................
52
FIGURE 22 - HSTE SYSTEM EFFICIENCY FOR VARYING SOLAR CONCENTRATIONS (C) AND THERMOSYPHON WALL
THERMAL CONDUCTIVITIES (Kw) FOR A BI2TE3 TE AT Tc = 470 K. H* IS THE HSTE EFFICIENCY AT HIGH THERMAL
CONDUCTIVITIES (H* = HHSTE(Kw= 10 W/MK)), WHICH ASYMPTOTES TO A CONSTANT VALUE. FOR SOLAR
CONCENTRATIONS BELOW 4 SUNS, MATERIALS WITH THERMAL CONDUCTIVITIES LARGER THAN 1.2 W/MK HAVE
(QouT)
COMPARABLE SYSTEM EFFICIENCY (H*
~ HHSTE) -----------.
.
-
-....................
..........
..................................
53
FIGURE 23 - (A) SCHEMATIC OF EXPERIMENTAL DESIGN INCLUDING TEST SECTION, HEATER SECTION AND COOLING
SECTION. (B) 3D CAD DRAWING AND (C) AS BUILT ASSEMBLY OF THE MAIN EXPERIMENTAL COMPONENTS. THE
TEST SECTION IS MADE MODULAR FOR EASE OF IMPLEMENTATION OF DIFFERENT THERMOSYPHON MATERIALS
SUCH A S COPPER OR GLA SS. ................................................................................................................................
58
FIGURE 24 - THERMAL RESISTANCES OF THERMOSYPHON CONDENSER AND EVAPORATOR SECTIONS AS A FUNCTION OF
CONDENSER LENGTH. THE TOTAL LENGTH OF THE THERMOSYPHON IS IM, Ro = 0.005M. EVAPORATION AND
CONDENSATION HEAT TRANSFER ARE ASSUMED TO BE EQUAL MAGNITUDE (H 20000W/MK) [40,49]...........61
Chapter 1
1. Introduction
1.1
MOTIVATION
Renewable energy is an area of increasing interest due to the scarcity and growing cost of fossil
fuels and the negative impact of such energy sources on the environment. Building energy in
particular accounts for 39% of the total US energy consumption, nearly equally split between
residential (21%) and commercial (18%) [1]. Of this energy utilization, commercial and
residential buildings consume 32.8% and 45.1% respectively in the form of heat [2]. A further
17.7% and 13% is used for space cooling, which can be offset with heat by utilizing well
established technologies such as solar air conditioning [3-10]. Heat energy also forms a large
fraction of the total energy consumption in the industrial sector as industrial process heat (IPH),
Figure 1. Processes such as boiling, distillation and polymerization that require heat input are
common in chemical industries. This heat is often supplied in the form of hot water or steam and
sometimes involves the direct heating of components in the process.
Figure 1 - 2008 US energy consumption for (a) residential and (b) industrial sectors [2].
Most of the IPH demand today is met by burning fuels such as natural gas, oil, and coal or by
using electric heating [11]. Low temperature IPH used in chemical drying and food processing
requires temperatures ranging from 20 to 2600 C [12-15]. The demand for medium temperature
IPH (200 - 350*C) is more considerable and is used in applications such as high efficiency
industrial solar cooling and milk pasteurization [16, 17]. High temperature IPH used in recycling
of hazardous wastes and processing of metals requires very high temperatures, often greater than
800*C [18, 19].
1.2
BACKGROUND
In order to offset the US energy demand with more renewable energy sources, development of
solar thermal energy conversion systems has been a main topic of investigation. The most
prevalent application for the utilization of solar thermal energy is solar water heating, which is
greatly used in countries such as China and India [20-22] (Figure 2a). These solar heaters supply
large amounts of low quality heat but lack both the electrical production capability and high
temperature operation. In contrast, large scale solar thermal plants produce distributed electrical
power [23, 24] but are limited to providing either heat or electricity (Figure 2b).
Figure 2 - Solar thermal systems for (a) domestic hot water heating [221 and (b) power production [231.
To meet the demand of high quality heat supply with electrical power production, researchers
have extensively studied the concept of hybrid photovoltaic/thermal (PVT) systems which utilize
an elevated temperature photovoltaic (PV) to generate clean electrical power while producing
waste heat by backside cooling [25-30]. However, due to the elevated PV cell temperatures,
electrical conversion efficiency degrades due to increased internal carrier recombination [31, 32].
Glass cover
a)
PVaray
Upper channel
-TMS sheet
Lower channel
b)
Figure 3 - (a) Hybrid photovoltaic thermal (PVT) system [251 and (b) cross-sectional schematic [251. The
system utilizes an elevated temperature PV array to generate clean electrical power while producing waste
heat by flowing air through the upper and lower channels. However, due to the elevated PV array
temperatures, electrical conversion efficiency degrades due to increased internal carrier recombination.
Thermoelectrics (TE), in contrast, promise higher electrical conversion efficiencies at elevated
temperatures because thermal energy is directly converted to electrical energy via the Seebeck
effect. When a temperature difference exists across the TE, power is produced with no moving
parts. Solar TE energy conversion systems [33-38], where solar energy drives the temperature
difference across the TE, have significant potential to produce electrical energy with abundant
waste heat to meet building energy or IPH demands. Rockendorf et al. (1999) and Li et al.
(2010) investigated hybrid solar TE water heaters and numerically determined that low radiative
losses and efficient back side cooling are needed to attain electrical conversion efficiencies up to
30% of the Carnot efficiency. However, Lertsatitthanakorn et al. (2010) experimentally showed
that hybrid solar TE water heaters with backside cooling have efficiencies limited to 0.87% due
to electrical pumping requirements, Figure 4.
Make-up water
Outlet header
bsorber plate
ppA
__J
Inlet header
late
L
t water supply
Plow mecter
TE modules
Note ethermocouples positions
Pump
Figure 4 - Hybrid solar thermoelectric water heater [39]. Efficiency degrades due to electrical power
requirements for the pump in order to flow fluid (water) through the copper tubes.
The results of these studies suggest that the development of more efficient cooling methods for
the TE back side is needed to realize the potential of hybrid TE systems. In addition, parametric
optimizations could extend the utilization of waste heat from hot water systems to a variety of
applications that require a larger range of temperatures.
We investigate a hybrid solar thermoelectric energy conversion system utilizing a solar TE
coupled to a thermosyphon to provide passive and efficient heat transfer to a bottoming cycle.
Figure 5 shows a particular embodiment of this device. A solar parabolic concentrator focuses
light on an evacuated tube absorber, which heats the thermoelectric hot junction located on the
surface of the inner pipe. This heat diffuses radially through the thermoelectric junction to the
thermoelectric cold side, which produces electrical power in the process. If the temperature
difference is not maintained between the hot and cold side, the efficiency of the system suffers.
Therefore a thermosyphon is incorporated adjacent to the cold side to receive heat from the
thermoelectric module in the radial direction and transfer the heat away in the axial direction,
which provides an energy source for co-generation, IPH, or more commonly, hot water heating.
A thermosyphon is utilized as the heat transfer mechanism between the topping and bottoming
cycles to take advantage of its passive nature, high efficiency and reliability as previously shown
in many different applications including preservation of permafrost, deicing roadways, turbine
blade cooling and applications in heat exchangers [40]. Additionally, the utilization of a
thermosyphon does not require any electrical energy input to pump fluid for backside cooling as
required by prior approaches.
+ Condenser Section
Waste Heat
Parabolic
Thermosyphon
Concentrator
---
- --
Selective Absorber
Vacuum
Glass .--
Thermoelectric
Thermosyphon
Solar Energy
LW
Figure 5 - Schematic of the hybrid solar thermoelectric system (HSTE). Solar energy is focused by a
parabolic concentrator on the evaporator section of the evacuated tube absorber (thermosyphon), which
heats the TE hot side. The resulting temperature difference between the TE hot and cold sides produces
electrical power while heat carried away (waste heat) by the thermosyphon (adjacent to the cold side) is
transferred to the condenser section for the bottoming cycle.
1.3
THESIS OBJECTIVES AND OUTLINE
The objective of this thesis is focused on the design and optimization of a hybrid solar
thermoelectric energy conversion system. We aim to increase to operational temperature range of
currently existing renewable hybrid energy conversion systems by using a novel approach of
combining the solid state energy conversion of thermoelectrics with thermosyphons for heat
transfer to secondary (bottoming) applications such as residential heating or higher temperature
IPH. We model the HSTE system for temperatures of 300 K - 1200 K, solar concentrations of
1 - 100 Suns, and different thermosyphon and thermoelectric materials. The model will be used
to i) optimize the HSTE efficiency and radial geometry, ii) investigate the effect of different
thermosyphon wall thermal conductivities for potential material cost reduction, and iii) propose
potential commercial applications for HSTE utilization. This thesis contributes in making solar
thermal power a viable renewable alternative for applications requiring power and low or high
temperature heat. The structure of this thesis is outlined below:
In Chapter 1, the motivation for studying hybrid solar thermoelectrics utilizing thermosyphons
was discussed. Previous approaches were discussed and the most significant contributions were
discussed.
In Chapter 2, we numerically compare the performance of thermosyphons and heat pipes and
show that thermosyphons are advantageous for use in HSTE systems.
In Chapter 3, we develop an energy-based model of the HSTE to investigate the effect of
bottoming cycle temperature, solar concentration, TE and thermosyphon material and geometry
and thermosyphon working fluid.
In Chapter 4, we optimize the model based on HSTE efficiency and radial geometry, and
investigate the effect of different thermosyphon wall thermal conductivities for potential cost
reduction, and propose five potential commercial applications for HSTE utilization.
In Chapter 5, we make concluding remarks and discuss ongoing work that includes the
experimental design of the HSTE test rig.
Chapter 2
Heat Pipe and Thermosyphon Modeling
2.
One of the main bottlenecks in conventional lab scale thermoelectric generators is heat rejection
from the cold side of the thermoelectric module. Currently, traditional fin-fan heat sinks are
used, but are bulky and limited in performance. The incorporation of heat pipes or two-phase
thermosyphons offer one promising solution to efficiently and isothermally transfer heat. A heat
pipe typically utilizes phase-change of a saturated fluid in a closed loop to achieve high heat
transfer, and a wick for liquid return. A two phase thermosyphon has no wick, relying on
gravitational head to drive the liquid [40]. In order to select between heat pipes and
thermosyphons for integration with the HSTEs, a quantitative performance comparison is
required.
2.1
MODEL FORMULATION
We developed a simple analytical system model using a thermal resistance network following
Prasher [41] as shown in Figure 6.
La
Ft
r*
r
ri
R2
R5
R1
R
Vapor Space
Th
Te
a)
QO
Th
qn
Te
b)
ut
Figure 6 - Schematic of a heat pipe (a) Geometry of a heat pipe and (b) the associated thermal resistance
network. Thermosyphon geometry is identical except wick structure is working fluid film.
17
The equivalent thermal resistances are described below:
R 21rLek
((2)
In
=21rLck
R, and R6 represent the thermal resistances of the heat pipe wall, ro, and ri are the outer and inner
radii, respectively, Le and Lc are the evaporator and condenser lengths, respectively, and k is the
heat pipe or thermosyphon material thermal conductivity.
In(ri
(3)
r-t
Lekeff
R2 =
In rt
(4)
Rs =
21ckkeff
2 + k'
20 1 _k,\
k
keff = k
2+ L+ 20
er
(1
k )
(5)
-k
R 2 and R5 represent the thermal resistance of the wick structure saturated with liquid, keff is the
effective thermal conductivity of the saturated wick, k, is the working fluid thermal conductivity,
0 and t are the wick porosity and thickness, respectively. The relation used for effective thermal
conductivity keff is for sintered metal powdered wicks [40]. The wick material is assumed to be
the same as the pipe material. For thermosyphons, the wick porosity is assumed to be 1.
T2
pvpvri
R= 8 L2 R
3gL
(6)
R3
represents the thermal resistance associated with the vapor temperature drop along the axial
direction of the heat pipe or thermosyphon, where T is the fluid operating temperature, Py, PV, pv,
and L are the vapor dynamic viscosity, density, pressure and latent heat of vaporization of the
working fluid, respectively, and R is the gas constant per unit mass.
R4 =
(7)
L___i2
7rk(r0z - r 2 )
R4 represents the thermal resistance of the axial heat pipe or thermosyphon wall, where Lo is the
total length. The thermal resistances associated with the vapor liquid interfaces are not included
in this model, since they can be considered to be negligible [41].
DIMENSIONAL ANALYSIS
2.2
In order to study the effects of geometry and different material properties on heat pipe
performance, dimensional analysis was performed on Eqns. 1 to 7, where initially the heat
transfer
Q, is dependent on 16 independent variables:
, k, k 1, 0, t, pv, Pv, PV)
Q = f(ro, ri,Le L , LoT, TfT Tc,
(8)
Through dimensional analysis, five non-dimensional parameters, 1 groups, can be obtained:
H1i = f(M2, M3 ,H4, s)
(9)
where
11
k(r
2
QLo
-
r, 2 )(Th
-
Tc)
is the non-dimensional heat transfer (Q-R4/(Th-Tc)),
(10)
Th -Tf
(11)
is the non-dimensional temperature,
In
(Frt)(r2 -
f13=-
r2)
LoLe
k
(12)
ke! 1
is the non-dimensional wick resistance (R 2/R4), and
H14
2 - r, 2)
RyoTk(r
2
L pp r 4
=
is the non-dimensional vapor resistance (R/R 4)
In (o)
Hs =
(r2 - r2)
(14)
LoLe
The non-dimensional wall resistance, fls, is excluded from the subsequent analysis because it is
a strict ratio of only geometric parameters, i.e., it will remain invariant with geometric scaling of
the heat pipe.
2.3
RESULTS AND DISCUSSION
Figure 7a shows a three-dimensional plot of the non-dimensional heat transfer fl as a function
of the non-dimensional temperature H2 and the vapor resistance f14, with a constant Us. The
non-dimensional temperature H2 ranges from 0 to 1, which implies that the bulk fluid
temperature inside the heat pipe can vary between the condenser temperature and evaporator
temperature. As U2 increases, the working fluid temperature T approaches the condenser
temperature Te, and H, approaches zero. The drop in the working fluid temperature results in a
pressure drop, which in turn increases the vapor thermal resistance, thereby reducing the heat
flux transferred.
6000
5000
4000
3000-
2000
1000
.......
...
0
0
00
0.5
0.5
21
nI(
i
2 1
(a)
1000
900
800
700
600
- 5001
400
300
200
-L-
100
01
0
0.1
0.3
0.2
0.4
0.5
1I4
(b)
Figure 7 - Results of dimensional analysis. (a) Three-dimensional plot showing non-dimensional heat transfer
fl as a function of non-dimensional temperature H2 and vapor resistance 114. (b) Two-dimensional project of
non-dimensional heat transfer Hi with non-dim
Figure 7b, which is the projection of the results of Figure 7a in the 114-HI plane, shows that as
the non-dimensional vapor resistance 114 is gradually increased from zero and approaches 0.01,
the heat transfer abruptly diminishes to zero. The results suggest the order of magnitude
difference required between vapor and axial thermal resistances for proper heat pipe operation.
As 14 <0.01, Jj, no longer is a strong function of H4, which is representative of typical heat pipe
operating conditions. In this case, the vapor thermal resistance becomes negligible when
compared to the other thermal resistances, which agrees well with prior work and can be
excluded from the analysis. This result has important consequences with respect to scaling,
which will be discussed in greater detail in section 2.4.
Figure 8 relates the non-dimensional heat transfer fl, to the non-dimensional temperature 12 and
wick resistance flj, with a constant Us. The results agree with those of Figure 7, where an
increase in
f12
decreases 111. As
113
increases, the wick thermal resistance increases and
heightens the overall thermal resistance of the heat pipe, causing fl, to decrease. The contours
show that in order to maintain H, as a constant, 112 and
which suggests that the same
f,
11
must have inverse relationships,
can be achieved with a high 112 value and a low fJ value, or
vice versa. In order to maintain the same heat transfer, the overall thermal resistance must be
kept constant, so the wick resistance and vapor resistance which are thermal resistances in series
must have inverse relationships.
6000
5000
4000
2000
-3000
0.
1
H13 x 104
1.2
0.6
1.4
1
04
0.82
Figure 8 - Non-dimensional heat transfer ~1ias a function of non-dimensional temperature ]12 and wick
resistance f13, for a heat pipe or thermosyphon of identical geometry as in Figure 7. ]lj contours are shown in
the H2 - 113 plane. 115 is constant.
The dimensionless analysis and results provide insight into the effect of various parameters. But,
to optimize the design for a glass heat pipe or thermosyphon, a sensitivity analysis, where the
change in ]H; with respect to change in the other non-dimensional parameters dll/dfl, where n
denotes the varying non-dimensional parameter, was used to investigate the implications on
performance with different thermal conductivity materials.
100
k=400W/mK
10-
-e- dnI/drl 3
10~ - ---
drI/dnI
(a2
(a)
(b)
Figure 9 - Sensitivity analysis for wall conductivity of (a) 400 W/mK, and (b) 2 W/mK. For k = 400 W/mK, the
change in Hi with respect to the change in the other three non-dimensional groups at low values of 12 is
approximately equal. However, when H2 ranges from approximately 0.2 to 0.4, which is representative of the
typical operating conditions for heat pipes and thermosyphons, dr 1/dH3 is increasingly more sensitive than
dfl/dH4 or dH/dHs. In contrast, k = 2 W/mK, dfl/dfl and dl/drls are approximately equal.
The results in Figure 9a shows that for the case of a copper wall material, where the thermal
conductivity is high, the change in
Jf,
with respect to the change in the other three non-
dimensional groups at low values of H2 is approximately equal. However, when H2 ranges from
approximately 0.2 to 0.4, which is representative of the typical operating conditions for heat
pipes and thermosyphons, dJ11/dfJ3 is increasingly more sensitive than dfjJ/dfl 4 or dHj/ dfJs. In
contrast, for glass heat pipes, where the thermal conductivity is typically 2 W/m- K, as shown in
Figure 9b, d1j/dfJ and dHJ/dfJs are approximately the same. The reason for this difference in
the case of the glass heat pipe is that the wall and wick thermal resistance become major
contributors to the overall thermal resistance of the system and are of the same order, whereas
the vapor resistance is orders of magnitude smaller. In the case of the copper heat pipe, the wick
is the major contributor to the overall thermal resistance, which is an order of magnitude larger
than the wall and vapor resistances.
The sensitivity analysis shows that for high thermal conductivity materials, the wick design is
very important in maximizing heat transfer and becomes the critical bottleneck in heat pipe
performance. A wickless heat pipe, (thermosyphon) would be the best configuration for heat
transfer. However, for low thermal conductivity heat pipes made of materials such as glass;
changing the wall or wick properties will yield an approximately equal change in heat transfer.
Therefore, if glass heat pipes were to be used for HSTEs, it would be ideal to make the heat pipe
wickless and thin walled, to lower the effective thermal resistance. These advantages make the
thermosyphon the better heat transfer device for the HSTE system depicted in Figure 5.
2.4
SCALING
The results of the dimensional analysis show that 17, is a weak function of the
below 0.01. In this case, the non-dimensional vapor resistance
f14
IT4
in regions
can be removed from the
analysis.
QL
k(r
2
- r,2)(Th -_Tc
f( Th -Tf ln(rit)(ro2
T -_T'Loe"
(15)
15
With constant temperature limits of Th, Te, and Tf, the dimensional analysis shows that with
similarity, the remaining ]] groups must remain constant. Therefore, for
geometric
thermosyphon or heat pipe geometries 1 and 2, where 2 is scaled up from 1 by a factor of n:
Q1 L0 j
-
ri 2 )
=__________
k(ro 2 -
_
2
ri2 2 )
Q 2 nL
kn 2 (r
1
2
0 j
- r,12)
(16)
(17)
=2
Q1
Eqn. 17 show that the heat transfer scales proportionally with size, for the case where the ratio of
vapor to the axial thermal resistance is approximately zero. However, this assumption is only
valid for low thermal conductivity wall materials.
2.5
LOW TEMPERATURE EXPERIMENTAL VALIDATION
To verify the accuracy of the thermosyphon model described in the previous sections, a low
temperature experimental study was performed. The goal of this study was not to replicate the
environmental conditions and solar concentration levels that would be typical of a HSTE system,
but to experimentally verify key assumptions and accuracy of the thermosyphon model
developed in chapter 2. Two of these assumptions state that the evaporator and condenser
operate with a uniform spatial temperature distribution at steady operation. Figure 1Oa illustrates
the main components of the experimental setup, including the rope heater, thermosyphon,
cooling section and constant temperature bath, thermocouple array and data acquisition system
while Figure lOb shows the actual experimental setup.
Figure 10 - (a) Schematic of experimental layout and (b) experimental setup showing the rope heater,
thermosyphon, cooling section and constant temperature bath, thermocouple array (TC) and data acquisition
system.
A commercially available solar application copper-water thermosyphon was obtained (WK Solar
Water Heater Co.) and characterized (see appendix) to obtain critical geometric parameters for
the model (Le= 70 cm, Le = 5.1 cm, La = 67 cm, r, = 4 mm, ri = 2.5 mm). The heat supply to the
evaporator side of the thermosyphon was accomplished by using a thin rope heater (HTC-120,
OMEGA) wrapped around the evaporator section. The base of the evaporator was heavily
insulated (9158T23, McMaster) to limit conduction or convection losses to the surroundings. A
custom water jacket cooling section was built using copper due to its high thermal conductivity
(398 W/mK) to ensure isothermal condenser temperatures. The cooling section was also
insulated to minimize heat losses to the environment. Cooling deionized water was supplied from
a temperature controlled bath with 0.05 K resolution (RE-207, Lauda-Brinkmann). The mass
flow rate of the cooling water was measured by a liquid mass flow meter with ±1 CCM accuracy
(L Series Mass Flow Meter, 0-50 CCM Alicat Scientific). Temperature measurements were
obtained using type-K thermocouple probes (5TC-GG-K-36-36, Omega). Three thermocouples
were located on the evaporator section, two on the adiabatic section and three on the condenser
section. Two thermocouples were used in the cooling section to measure the average temperature
of the inlet and outlet water streams. A data acquisition system (USB-TC, Measurement
Computing) was used to record the temperature reading of each thermocouple at a rate of 2
samples per second.
Three different heat transfer rates corresponding to solar concentrations of 1, 2 and 3 were
supplied by the heater in the experimental study. To quantify the effect of condenser cooling
temperature (Tsc), cooling water temperatures were varied in 10 degree increments from 293 K
to 343 K. A higher range of condenser temperatures would have been optimal, but was not
feasible due to the limits of the constant temperature bath; the fluid temperature should not
approach the boiling point of the fluid.
Figure 11 a shows the experimentally measured surface temperature as a function of the
condenser cooling water temperature. The measured temperatures were obtained by averaging of
the three surface temperature measurements. Averaging was appropriate since the spatial
variability of the evaporator and condenser surface temperatures were ± 2.6 K and ± 0.3 K
respectively. Figures 11 b and c depict the experimentally measured thermosyphon heat transfer
and the system thermal efficiency respectively as a function of condenser temperature. The total
uncertainty in the temperature measurements was estimated to be ± 0.5 K. The experiments show
a linear increase in surface temperature with a linear decrease in thermosyphon heat transfer as a
function of condenser temperature, indicating the thermosyphon has a finite conductance and can
be approximated as an effective thermal resistance at low temperature ranges. As the
concentration increases at a fixed condenser temperature, the surface temperature and the
thermosyphon heat transfer increase due to the larger heat flux and temperature drop from the
surface to condenser. As the condenser temperature increases at a constant heat flux, the surface
temperature increases, decreasing thermosyphon heat transfer due to increased heat loss. This
effect is shown in the thermal efficiency, which decreases non-linearly with increasing condenser
temperatures. The numerically predicted results (lines) are shown for the same increments in
solar concentration in Figure 11. To effectively model the experiment, a natural convection heat
transfer coefficient was included to model the heat loss from the evaporator section. The
calculation included variable properties of air with temperature and was added because the
experiments were conducted at temperatures below 360 K, where the effects of natural
convection cannot be neglected when compared to radiative loss.
360
C=1
C=2
C=3
350
340-
330
320
310-
"14
300
300
100
310
320
330
340
Condenser Temperature, Tc [K]
350
-
C= 1
---
C=3
80
-
60
40
20
0'
300
310
320
330
340
Condenser Temperature, Tc [K]
350
310
320
330
340
Condenser Temperature, Te [K]
350
C) 0.12
0.1
0.08
0.06
0.04
0.02
300
Figure 11 - (a) Measured surface temperature (b) thermosyphon heat transfer and (c) system efficiency for
varying condenser temperature and solar concentration. As condenser temperature increases, surface
temperature increases while thermosyphon heat transfer decreases due to increased losses.
Minor discrepancies can be observed between the model and experimental results at elevated
concentration ratios. The experimental surface temperatures were below the model predictions.
This was indicative of the experimental evaporator section having greater losses to the
environment than the model predicts. The higher loss was attributed to under predicting the
natural convection heat loss due to the extra surface area of the evaporator created by the
wrapping of the thin rope heater. However, the model predicts the experimental behavior
reasonably well and shows that for low temperature ranges, the assumptions of spatially uniform
evaporator and condenser temperatures under steady operation are valid and that the
thermosyphon heat transfer behavior can be accurately modeled at low temperatures by the
developed effective resistance model developed in this chapter.
2.6
SUMMARY
In this chapter, we developed a non-dimensional thermal resistance model of heat pipes and
thermosyphons to compare performance and identify which is better for integration with HSTEs.
The wick was determined to be a significant resistance in high thermal conductivity heat pipes,
while the wick and wall resistances were comparable for low thermal conductivities. In both
cases, a wickless design would minimize temperature drop meaning thermosyphons are better
options for integration with HSTEs. A low temperature experimental study was performed to
validate the modeling results, which are in good agreement. In the following chapters, we modify
and couple the thermosyphon model developed in this chapter with the thermoelectric element to
develop a model of the complete HSTE system.
Chapter 3
3. Hybrid Solar Thermoelectric Modeling
In order to accurately model the HSTE, the thermosyphon model (Chapter 2) is incorporated
with the TE. Additionally, the thermosyphon model requires modification to operate in the
temperature regimes dictated by the TE (i.e. the model of chapter two is valid for low
temperature operation, but fails to represent performance at elevated temperatures where liquid
metals are used). The goal of this chapter is to develop the complete system model and analyze
the results in terms of variable input parameters to gain an understanding of the physics behind
the operation of the HSTE.
3.1
MODEL FORMULATION
A cross-sectional schematic with the geometric parameters of the HSTE and the equivalent
thermal resistance model [41, 42] are shown in Figures 13a and b, respectively. A solar parabolic
concentrator (as shown in Figure 5) focuses sunlight (Qsoiar) on a selective surface (SS) with a
low thermal emissivity and high solar absorbtivity. The surface also emits thermal radiation
(Qloss) at a spectrally averaged emissivity (e) due to its elevated temperature (Tss). To accurately
capture the absorptive and emissive properties, NREL data was used for four thermally and
mechanically robust commercially available surface coatings [43]. The emissivity of the
selective surface as a function of temperature is shown in Figure 12. For temperatures exceeding
the maximum tabulated temperature, a sixth order polynomial was used to extrapolate the
properties at the higher temperature. The absorbtivity of the selective surface is shown in
Table 1.
Table 1 - Spectrally averaged absorbtivity [431.
Solar a
Black Chrome
Luz Cermet
UVAC A UVAC B
0.916
0.938
0.954
0.935
0.2751
Black Chrome
0.25
0.25 00 Luz Cermet
0.225 3o UVAC A
AA UVAC B
0.2
0.175
*2
AD
o
0.15
H
0.125
0.1
0.075
A
A
0
A
0
0
0.05
250
350
450
550
650
750
Selective Surface Temperature, T5s [K]
Figure 12 - Spectrally averaged emissivity as a function of selective surface temperature (T,,) for four
commercially available surface coatings [43].
The selective surface is assumed to be isothermal along its length, and the temperature drop from
the SS to the TE hot side is across a thin film (< 500 pm) and therefore can be neglected. We
also assume that in the evacuated concentric tube design there are only radiative losses from the
selective surface.
The net heat absorbed by the SS is conducted through the TE element with a radial conduction
thermal resistance Rte, which leads to a temperature gradient between the TE hot (Tss) and cold
(T,E) side to produce TE power (Pte). The temperature gradient is dependent on the TE leg
geometry, material thermal conductivity (kte), and figure of merit (ZT). Due to the high
sensitivity of these parameters on system performance, temperature dependent properties were
used for the TE thermal conductivity (Figure 14a) and figure of merit (Figure 14b) [44-48].
a)
rte
Le
La
Thermoelectric
4.
ro
I
t
VaporSpace
rI
TS,E
T
S
HIM||
Qos
Qsoiar
>
QoUt
Selective Surface
Iar
Figure 13 - (a) Schematic cross-section of the HSTE system in a horizontal orientation. Solar energy (Qsolar)
heats the selective surface located on the TE hot side, which creates a temperature gradient across the TE
that produces electrical power (Pte). The remaining heat (Q.,) is transferred axially by the thermosyphon to
a bottoming cycle application at temperature Te. (b) Thermal resistance (TR) model of the HSTE, where R,, is
the TE radial TR, R2 and R6 are the thermosyphon wall radial TR, R 2 and R3 are the boiling and evaporation
TRs, respectively, R5 is condensation TR, R 4 is the vapor TR, R 7 is the thermosyphon wall axial TR, and
R 8 and R, are evaporation and condensation interfacial TRs, respectively.
1.2
N
E 3.6
3
~
0
0.8
p2.4
0.6
1.80
1.20.4
E
0.6
1l.2-
0
200
-a-
Bi2Te3 (Poudel et at.,2008; Snyder et at.,2008)
PbTe (Snyder et al. 2008; Morelli et al., 2008)
-A- SiGe (Snyder et at. 2008)
400
600
800
1000
1200
E
E
0.2
0.2
01
200
Bi2Te (Minnich et al 2009; Poudel et at 2008)
PbTe (Minnich et al., 2009: Snyder et at., 2008)
-Ar SiGe (Minnich et al., 2009; Snyder et al. 2008)
'-
400
600
800
Temperature [K]
Temperature [K]
a)
b)
1000
1200
Figure 14 - Thermoelectric (a) thermal conductivity (kte) and (b) figure of merit (ZT) as a function of
temperature for three TE materials used for the model: bismuth telluride (Bi2Te3), lead telluride (PbTe) and
silicon germanium (SiGe) [44-461.
An inclined two-phase thermosyphon in contact with the TE cold side transfers heat (Q,,)
axially to the bottoming cycle application at temperature Tc. The thermosyphon achieves
efficient spreading via a working fluid that undergoes phase-change due to the heat supplied to
the evaporator. The generated vapor axially transports to the condenser section at. As heat is
transferred to the bottoming cycle application, the vapor condenses and returns back to the
evaporator by gravity. The heat transfer processes in the thermosyphon are modeled as thermal
resistances (Figure 13b): R, and R6 are the radial conduction wall resistances of the evaporator
and condenser, respectively; R2 and R3 are the evaporation and boiling resistances, respectively;
R4 is the saturated vapor resistance from the vapor flow pressure drop; R 5 is the condensation
resistance at the condenser; R7 is the axial conduction thermal resistance; R8 and R9 are the
evaporation and condensation liquid-vapor interfacial thermal resistances, respectively. For ideal
thermosyphon operation, the temperature drop from the evaporator (Ts,E) to the bottoming cycle
application (Tc) should be small.
The TEs selected for HSTE analysis are bismuth telluride (Bi2 Te 3), lead telluride (PbTe), and
silicon germanium (SiGe), which have a range of operating temperatures with moderate ZTs
(Figure 14), relatively low cost, and commercial availability [44, 46]. Based on the TE and
bottoming cycle application temperatures (T,), different combinations of thermosyphon wall
materials and working fluids are considered that ensure working fluid compatibility and high
effective thermal conductivity. Conventional water-copper (300 K -550 K), mercury-stainless
steel (550 K - 875 K), and liquid potassium-nickel (885 K - 1273 K) thermosyphons were
investigated for Bi 2 Te3 (300 K - 525 K), PbTe (525 K - 850 K), and SiGe (850 K - 1200 K) TEs,
respectively. The PbTe and SiGe HSTEs are suitable for medium to high temperature IPH
applications, while Bi 2Te 3 HSTEs can be used for low temperature IPH or residential heating.
3.2
GOVERNING EQUATIONS
We solve the energy equation governing the thermoelectric and thermosyphon over a wide range
of input parameters including solar concentration, TE and thermosyphon material and geometry,
thermosyphon working fluid, and bottoming cycle temperature. All transport properties vary
with temperature including the TE thermal conductivity (ke), figure of merit (ZT), thermosyphon
wall thermal conductivity (k,), and fluid properties (k, k,
P,y,
P, P,
Cp,, Cpi, hfg). Figures
15a and b show schematics of the thermosyphon evaporator and condenser, respectively, which
include the energy inputs and outputs in the system.
a)
b)
IILI
-+
OLo
+-
Figure 15 - Schematics of the (a) TE side showing the film evaporation and pool boiling region of the
evaporator and (b) condenser side showing film condensation in a vertical orientation.
34
At the TE side (Figure 15a), the energy gained from the solar heat input (Qsoiar) and lost from
emissive loss (Q0u) is balanced by the generated TE power (Pe) and waste heat (Qou1)
aAcsCG -
-BEAE(Tss4
Solar Heat Input (Q.,,)
-
Too
Radiative Loss (Q,,)
= Pte
+ Qout
TE Power
(18)
Waste Heat
where C is the solar concentration ratio, Asc is the evaporator cross sectional area (2 reLe), AE is
the evaporator surface area (2 7rrteLe), G is the average solar insolation (1000 W/m2 ), a and E are
the selective surface spectrally averaged solar absorbtivity and thermal emissivity, respectively,
'Bis the Stefan-Boltzmann constant, Ts is the selective surface and TE hot side temperature, and
T is the ambient temperature (300 K). The TE power is defined as
Ts - Ts' E
Pte = (Qsolar - Qioss) - rte = (Qsolar - Qioss) '
1 + 2
-- 1
(19)
TSS
where il, is the TE electrical generation efficiency, T,E is the TE cold side temperature, and ZT is
the thermoelectric figure of merit. The TE material properties were averaged over the operating
temperature interval [Tss, Ts,E]. At the thermosyphon condenser side (Figure 15b), the energy
transferred from the evaporator (Qo
0 u) is transferred directly to the bottoming cycle application at
the condenser temperature (T,).
3.3
THERMOSYPHON MODELING
The thermosyphon is modeled using a thermal resistance network, R = AT/Q, where R is the
thermal resistance, A T is the temperature difference across each thermal resistance, and Q is the
heat transfer (Figure 13b). The resistances were determined for low (T < 500 K) and high
(T > 500 K) temperature operating regimes ( - ). At low temperatures, classical Nusselt
condensation/evaporation film theory [40, 49] was used. However, at high temperatures with
liquid metals as the working fluid, high vapor velocities result in large interfacial shear stresses
and additional interfacial heat transfer resistances (R8 and R 9) at the liquid vapor interface.
Therefore, a modified Nusselt analysis with pool boiling and thin film evaporation [40, 50-52]
more effectively captures the phase-change at the evaporator. In all cases, the ratio of condensate
film thickness (6) and tube radius (r) was assumed to be very small (6/r, «1), such that the tube
can be modeled as laminar film condensation on a flat inclined surface.
Table 2 - Thermal Resistances for Low and High Temperature HSTE Models.
Low Temperature Model (T < 500 K)
High Temperature Model (T > 500 K)
(20)
Rte =27Lekte
in
(30)
27(Lekte
(~
In00)
(21)
=
R,
In(r,)
r
Rte
(31)
R 2in
2T(Lekw
1-27nLekw
1
R2 =
2
hE
rje
i
1
- pv)hfgkl
hE = 0.943 pigcosO(pi
Mi(TW,E - Tsat,E)LE
3
]4
(22)
R2 =
(23)
R3 =
[
1
R3 = 0
Tsat,c)
8L0 Ri (TsatE
R4 =
R5
=
(24)
1thfg 2 pvpvrs
8L0 Ryv (TsatE
yTsatC
(34)
T hfg2 Pvpri,
R5 = 2-nic
2hcirirLc
3
0.943 pigcos6(p - p)hfgki 4
L 0 i (Tsat,c - Tw,Lc
(25)
c= 0.943
in(r)
R6 =
(33)b
(2nriL, + rri2)h,,p
2
2hc7riLc
=
(32)a
2hE,f nri(Le - L)
(26)
r
21nLck,
(35)
-pigcosO(pi
-
p)h1,i
1 (Tsat,c - Tw,c)Lc
l
In(
(36)
R6 = 2i
62nLek,
1
0(Le+Lc)+
La
(27)
1(Le+
R
=
Lc)+ La
(37)
2
3
R8 = 0
Re~
= 22-
(28)
M)2PsatE fg
(38)
Tsat,E2
R8 =
R9 = 0
(29)
(M)2Psatchf
Tsatc
a) See text for definition of hEf
b) See text for definition of hEp
(39)
3.3.1
Low Temperature Thermosyphon Model
(Ts,E
< 550 K)
We considered Nusselt film condensation and evaporation for a specified condenser outer wall
temperature (Tc) to obtain the temperature distribution of low temperature thermosyphons, where
the thermal resistances are given by Eqns. 20 - 29. The thermosyphon tube is modeled as
laminar film condensation on a flat inclined surface, where the condensed film returns to the
evaporator by gravity and evaporates completely by the end of the evaporator section (i.e. no
liquid pool exists at the base of the evaporator). The vapor is assumed to be at saturation
conditions, and shear forces are negligible [40] resulting in thermal resistances of evaporation
and condensation heat transfer described by Eqns. 22 and 25, respectively.
To determine the difference in saturation temperature from the evaporator (Tsat,E) to condenser
(Tsatc), the Clapeyron relation is used which accounts for the vapor flow thermal resistance
(Eqn. 24). While previous works have found this resistance to be negligible [41], the moderate
heat fluxes and temperatures in this analysis can make the temperature drops appreciable.
3.3.2
High Temperature Thermosyphon Model
(T,,E
> 550 K)
At higher temperatures, the interfacial shear stresses can create significant error in the predicted
film thickness profile using classical Nusselt theory. Therefore, a separate high temperature
model is used to predict thermosyphon performance using a modified Nusselt model with pool
boiling heat transfer, where the thermal resistances are given by Eqns. 30 - 39. For simplicity,
we also assume that the evaporator and wall temperatures are uniform and use the modified
Nusselt condensation model in the condenser section [50, 51] with the addition of liquid vapor
interfacial resistances (R 8 and R9).
To determine the liquid vapor interfacial resistances (Eqns. 38 and 39), we assume condensation
and evaporation coefficients (a) of 0.1 which is appropriate for large engineering systems which
typically are difficult to maintain in a pure environment [52]. The film evaporation heat transfer
coefficient from the top of the evaporator section to the liquid pool is [51]
kgESatE
3p,
(Tsa t,E
[
-
L [( A(Lt - Ly ) +
P,E)Le - LP)
E)e
Tw,c)Lc 4
gcos19j
p(p1 - pv) hfg
Lo
- A(Lc + La))
-
0SL)
1
4 ki/pi(Tsat,c -
where
SL0
4ki pi(Tsat,E
'
~ w,E)
gcos9pi(pi - pv)hfg
is the film thickness at the end of the adiabatic section, L is the length of the pool
region, Le is the evaporator length, Lc is the condenser length, and Lt is the total length of the
thermosyphon. Eqn. 40 is combined with Eqn. 33 to determine the effective thermal resistance of
the thin film liquid metal evaporation.
To incorporate the effect of pool boiling of liquid metals, the heat transfer coefficient is
determined by [53]
hp,E
Cq0r
where P, = PI/Pe, C = 13.7, m
(41)
=
0.22 for Pr < 0.001, and C
=
6.9, m
=
0.12 for Pr > 0.001, q is
the evaporator heat flux, Pc is the critical pressure of the liquid metal, and Pi is the liquid
pressure in contact with the heated surface. This average heat transfer coefficient is used with
Eqn. 33 to determine the effective thermal resistance due to liquid metal pool boiling (R3 ).
For both low and high temperature thermosyphon models, we assume steady operation below
limiting thermosyphon operating conditions. To verify this assumption, the continuum, sonic,
viscous, entrainment, and boiling limits [40, 54] are calculated and compared with the
corresponding operational performance. In addition, non-condensable gases are assumed to be in
negligible amounts as to not affect the heat transfer characteristics. We also verified that the film
condensation is laminar using the condensation Reynolds number (Re6 < 30).
3.3.3
Thermosyphon Heat Transfer Limits
Although thermosyphons are efficient heat transfer devices, they are subject to operating limits
that determine their maximum heat transfer. The limit that has the lowest value at a specific
operating condition causes failure of the thermosyphon [40]. The results were all checked against
the operating limits.
The vapor continuum limit [54], applicable to high temperature liquid metal thermosyphons,
occurs when the heat transfer is not high enough to form continuum flow conditions inside the
thermosyphon. The vapor temperature associated with transition into continuum flow is
2VZrd 2 PKnr1
Tcontinuum =
1.051k
(42)
where d is the effective molecular diameter of the liquid metal atom, P, is the liquid metal vapor
pressure, Kn is the Knudsen number, r, is the thermosyphon inner radius, and k is the Boltzmann
constant. The effective molecular diameters for potassium and mercury are 4.44 A and 3.02 A,
respectively [54, 55]. The vapor flow is considered to be continuum when Kn < 0.01. We
determine the continuum temperature for each simulated result and ensure it is higher than the
evaporator (Tsat,E) and condenser (Tsat,C) saturation temperatures. In all cases, the continuum limit
temperature is well below saturated vapor temperatures in the system.
The sonic limit occurs at the evaporator of the thermosyphon as a result of the pressure driven
liquid metal vapor acceleration towards the evaporator end. The low downstream vapor pressure
of the liquid metal thermosyphon during startup can lead to sonic vapor velocities at the
evaporator exist [40]. The heat transfer corresponding to the sonic limit is
1
1
Qt
Qsonic = 7ri2hr psat,E
= jRTsat,E
r
(43)
where Cp,g and C,g are the heat capacities of the liquid metal vapor at the evaporator conditions,
and R is the working fluid gas constant.
The viscous limit describes the maximum heat transfer that the thermosyphon can experience
before the viscous forces of the vapor flow begin to overcome the inertial forces from the
evaporator to the condenser. This limitation was checked using
nr
4
hfgpsat,EPsat,E
16pLO
s
(44)
where hjg is the latent heat of evaporation of the working fluid, psat,E and Psat,E are the evaporator
vapor density and pressure, respectively, Lo is the effective thermosyphon length, and p is the
evaporator vapor dynamic viscosity.
The entrainment limit occurs when the vapor flow rate is high enough to entrain some of the
back flowing liquid moving down the thermosyphon. This limitation is more predominant in
thermosyphons containing wick structures; however, it was verified for both low and high
temperature thermosyphon models using [40]
Qentrainment =
p
.14
)
1
tanh2 Boihgiri2 (g.(p _ p))
1
1
4
(pv- 4+ p-
1\-2
4
(45)
where Bo is the Bond number, o is the working fluid surface tension, pi and pv are the densities
of the liquid and vapor, respectively. All properties were evaluated at the evaporator saturation
temperature.
The boiling limit describes when the evaporator surface temperature (TwE) exceeds the superheat
corresponding to the critical heat flux (CHF), resulting in catastrophic failure of the
thermosyphon. The boiling limit is determined by [56]
Qboiling =
aog(pi -p)
pt,
( 2 wri Le)0.149pvhfg [YPi2
(46)
where Le is the evaporator length, and ri is the thermosyphon inner radius. Equation 48 is
applicable to liquid metals as a conservative estimate since the experimentally measured CHF for
the boiling of liquid metal is 2 to 4 times higher than that predicted by the equation [56].
3.4
SOLUTION ALGORITHM
The HSTE model was solved iteratively where the solar concentration (C), bottoming cycle
temperature (Tc), TE and thermosyphon geometry and materials and thermosyphon working fluid
are input parameters to obtain the temperature distribution ([T]), thermoelectric power (Pe),
waste heat (Q0 w), emissive loss (Qoss) and system efficiency. To determine the transport
properties ([P]o), a guessed initial temperature distribution ([T]o) is used. Once initial properties
are obtained, the model iterates to determine a new temperature distribution ([T]I) by solving the
energy equation (Eqn. 20) with thermal resistances (Eqns. 22-41). The transport properties ([P]I)
are recalculated with the new temperature distribution and used in the next iteration. The
convergence criterion is defined as when the difference between successive temperatures for
each point is less than 0.01 degrees (|T+j -Til < 0.01). The choice of materials for the
thermosyphon and TE is made based on the calculated temperature distribution in each
successive iteration. Figure 16 shows the flowchart of the iterative algorithm used in the model.
[ T; - Ti-I I-: 0. 01
J1HSTE
Qns 1 Pte
4 P
fOUT
vi7
FAM,
7IIHSTE=
0
Figure 16 - Flowchart of the iterative algorithm. [T.] is the initially guessed temperature distribution, [Po] are
the initial calculated fluid and thermoelectric properties, i is the iteration number, [Ti] is the ith iteration
temperature distribution, and Tc,,,d.um, Qsonc, Qvscous, Qenrainment,
3.5
Qboiling are the thermosyphon limits.
RESULTS AND DISCUSSION
The modeling results were obtained for a particular solar collector resembling the glass tube
evacuated design (Le= 50 cm, Le = 10 cm, La = 200 cm, r, = 2.25 cm, ri = 2 cm, rte = 3 cm,
0= 30*) with black chrome as the selective surface which is stable at high temperatures
(300 K to 800 K). Also, the emissivity is relatively high (0.08 < e < 0.3) compared to the other
selective surfaces, allowing for a conservative estimate of performance. Figure 17a shows the
bottoming cycle heat transfer (Q, 1) as a function of bottoming cycle temperature (Tc) and solar
concentration (C). Three distinct regimes for different TEs exist with Tc. When the TE or
thermosyphon temperatures exceed 550 K, the PbTe TE with the mercury-stainless steel
thermosyphon replaces the Bi 2 Te 3 TE with the water-copper thermosyphon, creating a
discontinuity in the system performance. These discontinuities are larger at higher Cs because a
larger temperature difference exists at higher heat fluxes. A similar shift occurs at T,E> 778 K to
an SiGe TE with the liquid potassium-nickel thermosyphon. As the C increases, the shift occurs
at a lower T, because the thermosyphon temperature drop is greater, leading to a higher cold side
TE temperature. As a result, Bi 2Te 3 HSTE systems at high Cs have a very narrow operation
window (300 K < T, < 340 K).
Figure 17b shows the emissive loss (Qoss) as a function of Te, C, and TE material. As C
increases, the selective surface temperature (Tss) increases, leading to higher emissive loss.
Therefore, the decrease in
Q,,, (Figure
17a) is more pronounced at Te > 500 K due to the fourth
order dependence of emissive losses on temperature. Figure 17c shows the output TE power as a
function of Te, C, and TE material. The TE efficiency is dependent on the temperature difference
(Tss - Tw,E) across the TE module and figure of merit (ZT). As T, increases, P1e decreases due to a
decrease in Q0u. With higher C, however, a higher temperature difference across the TE element
can be attained due to the higher heat flux, leading to a higher power output (Pte).
Inclination angles (0) up to 300 were examined and show a small effect on the performance of
the HSTE system (<2%). Similarly, the thermosyphon adiabatic section length (La) shows
minimal effect (< 0.1%) on performance at low condenser temperatures (T, < 550 K) and solar
concentrations (C < 50), indicating that the saturation temperature drop associated with the vapor
pressure drop in the thermosyphon is negligible in these regimes. However, as discussed in
Section 3.4.2, the saturation temperature drop needs to be considered in liquid metal HSTE
systems due to a significant vapor pressure drop at high solar concentration ratios.
4500
a)
3750
-C=1
PbTe
Bi 2Te 3
c=10
CC=50
C = 100
3000
SiGe
2250
£
PbTe
Bi2Te 3
1500
0
SiGe
7I.. r
0
.
E
I-
----PbTe
Bi2 Te 3
0
300 450 600 750 900 1050 1200
Condenser Temperature, Tc [K]
b) 4500
C =1
C =10
3750
C 50
Sie
C = 100
/
3000
q 2250
SiGe
/
.-
5/
-E 1500
750
PbTe.B.2Te3
V
300
450 600 750 900 1050 1200
Condenser Temperature, Tc [K]
-C
-C
180
150
Bi2 Te 3
120
90
-
=1
= 10
C
= 100
PbTe
Bi2Te 3
60
30
PbTe
Bi2Te 3
-
SiGe
0
300
450 600 750 900 1050 1;200
Condenser Temperature, Tc [K]
Figure 17 - (a) Thermosyphon heat transfer, (b) emissive losses and (c) TE power of the HSTE system for
varying solar concentrations and condenser temperatures. As the condenser temperature (Tc) increases,
emissive losses (Qi,.) increase while TE power (P,)and thermosyphon waste heat (Q,,,)decrease due to
elevated surface temperatures (T,). As solar concentration (C) increases, emissive losses, TE power and heat
output increase.
3.6
SUMMARY
In this chapter, we developed an energy-based model of a new hybrid solar thermoelectric
(HSTE) system which uses a thermosyphon to passively and efficiently transfer heat to a
bottoming cycle. The thermosyphon model in Chapter 2 was modified to better represent
thermosyphons at elevated temperatures. The TE materials bismuth telluride, lead telluride, and
silicon germanium were combined with thermosyphon material-working fluids of copper-water,
stainless steel-mercury, and nickel-liquid potassium for the model simulations. System
performance was investigated for temperatures of 300 K - 1200 K, concentrations 1 - 100 Suns,
and different thermosyphon and thermoelectric materials with a geometry resembling an
evacuated tube solar collector (Le = 50 cm, L, = 10 cm, La = 200 cm, r, = 2.25 cm, ri = 2 cm,
re = 3 cm, 0 = 300). The results show as the condenser temperature (Tc) increases, emissive
losses (Q0 ss) increase while TE power (Pte) and thermosyphon waste heat (Qur) decrease due to
elevated surface temperatures (Tss). Additionally, as solar concentration (C) increases, emissive
losses, TE power and heat output increase due to higher heat input.
Chapter 4
4. HSTE Optimization
To maximize electrical power and waste heat production while minimizing emissive heat loss,
HSTE optimization is required. In order to optimize both power and heat, a combined hybrid
efficiency is developed and optimized over a wide range of variables including: condenser
temperature, solar concentration, thermosyphon and thermoelectric material properties, and
system geometry.
4.1
OPTIMIZATION EQUATIONS
The HSTE is optimized based on a combination of two efficiencies: 1) the electrical efficiency
(lie) defined as the TE efficiency (Eqn. 19) and 2) the thermal efficiency (qe) from waste heat
(Qoss) defined using an exergetic approach with the Carnot efficiency (Eqn. 47) [57].
T7cc
(47)
The defined thermal efficiency serves as an ideal upper limit to the amount of work obtained
from the waste heat if a heat engine is used as the bottoming cycle. The overall system efficiency
(qHSTE)
is therefore defined as the ratio of useful energy extracted, including the thermal (Qow)
and electrical components (Pte), compared to the total energy input. The ideal thermoelectric
efficiency qte is used to determine the TE electrical power output, given by
(T~~~
Pte = 1 te (Qsolar -
-AE(ss 4 ~s
-T
V + ZT -S1i
s,EA(Qsolar -
s,E
Z+
The electrical power from the waste heat (Wg) is given by
T4)1SS
rEAE(ss
-
)
(4
(48)
Wg
=
7c (Qsolar - Pte - UEAEss 4 -
(49)
where q, is the ideal Carnot efficiency (qe = 1-Tc/T.) and T, is the ambient temperature (300 K).
To obtain the overall HSTE system efficiency, the two components of the useful energy output
(Pte, Wcg) are combined and compared to the total energy input
_
1
7 HSTE -
te
+ Weg
(50)
Qsolar
Substituting Eqns. 48 and 49 into 50, we obtain
nte
(Qsoiar -
7EAE(T s 4 -
Tw)
+ ?jc (Qsolar
T1HSTE=
-
oEAE(TSs
4
-
T
)
1
7te
(Qsolar - UEAE(TS
4
-
T 4)
(51)
Qsoar
where C is the solar concentration, Gs is the solar heat flux (1000 W/m 2), AE is the absorber
surface area, and e is the absorber emissivity. By simplifying Eqn. 51, the system efficiency is
expressed as
Useful Energy Out
Incident Solar Energy = (ate +
where Qoss = asAE(Ts
4.2
4
i/
-
ltelc)
QIOsS
CG))
(2c
- Th/) represents the radiative loss term.
RESULTS AND DISCUSSION
Figure 18 shows the HSTE efficiency as a function of bottoming cycle temperature and solar
concentration. Similar to Figure 17, discontinuities due to temperature operation limits of the TE
and thermosyphon exist. To obtain HSTE efficiency for a particular bottoming cycle application,
the. end use temperature at which the thermal energy will be transferred to must be known. For
example, if the HSTE system is to be used for space heating, the temperature is set to the
condenser temperature (Tc), and the system performance can be obtained from Figure 18.
0.5
C1
PbTe
S0.4~
Bi2Te
0.
0
Al
e
\
/
.2 f Bi2Te3
0.11
0
300
C00
-
10
SiGe
PbTe
\
SiGe'
Bi 2Te 3
450 600 750 900 1050 1200
Condenser Temperature, Te [K]
Figure 18 - Efficiency of the HSTE system for varying solar concentrations (C) and bottoming cycle
temperatures (Te). Optimal system efficiencies exists which balance the thermal efficiency and emissive
power. Increasing the solar concentration also increases efficiency due to a higher energy input and thermal
efficiency.
4.2.1
Effect of Bottoming Cycle Temperature (Tc)
and Concentration (C)
Figure 18 shows that the HSTE efficiency (qHSTE) has optimal values as a function of bottoming
cycle temperature (Tc). The initial increase is due to the increase in thermal efficiency with
increasing temperature. However, as Te continues to increase, the surface temperature (Tss) of the
TE element reaches a point where the emissive losses (Q0 ss) begin to dominate. As a result, with
any additional increase in Te, the efficiency decreases due to the fourth order temperature
dependence of the emissive losses. At constant Te, the system efficiency (iHSTE) increases with
increasing solar concentration (C) due to higher heat transfer (Qwt) through the thermosyphon
and greater thermal efficiency. Concentrations beyond 100 Suns may be more advantageous but
may have economic implications on the construction of the concentrator; and therefore were not
considered here.
4.2.2
Effect of TE Leg Length (Lt,,) and Thermosyphon Size (r,/r,,)
Figure 19a examines the HSTE system efficiency with TE leg length (L,,) and cross-sectional radii ratio (r/r,,) for a
particular solar concentration (C = 50) and bottoming cycle temperature (T, = 700 K) determined from Figure 18. As
L,, increases, the system efficiency decreases due to the additional thermal resistance of the TE leg, leading to an
elevated surface temperature (T,,) and higher emissive loss (Q,0 ss). The TE leg length, however, has different effects
on system performance depending on the bottoming cycle temperature (T,). At high T,, small increases in L,, result
in larger decreases in system efficiency due to the higher emissive losses at increasing temperatures. However,
Figure 19b shows that the TE power increases with increasing TE leg length because collector area
increases and a higher TE temperature gradient exists. Depending on the power needs of the
application, increasing TE leg length may have advantages. For example, if the application has larger
electrical demands, it may be more favorable to sacrifice overall system efficiency for electrical production.
Figure 19 also shows that as the radial ratio of the thermosyphon (r/rte) decreases for a constant
LTE, the system efficiency decreases due to reduced area for heat transfer through the
thermosyphon and the TE power decreases due to reduced selective surface area for solar input.
As the TE leg length increases, the maximum operating temperature (776 K) is reached, and the
performance decreases to zero (gray area). In addition, for small thermosyphon radii (bottom
white area), heat pipe limitations (e.g., sonic limit) prohibit operation. Furthermore, as the
thermosyphon radius becomes less than r0 ~ 2 mm, the model is no longer accurate because the
thermosyphon pipe wall cannot be modeled as a flat plate.
'IHSTE
0.8
> 0.48
0.6
0.39
0.37
0.35
0.45
0.43
0.4
0.2
Qout > Qulmit
0
I0
0
0.005
0.01
0.015
0.02
Lt. [m]
Pte [W]
37
0.8
> 55
46
129
0.6
0.4
0.2
Qout > Qglmit
0 0
0.005
0.01
0.015
0.02
Lt, [M]
Figure 19 - Optimization results for a PbTe HSTE at C= 50 and Te = 700 K showing a) system efficiency and
b) TE power. An increase in TE leg length (Lt) decreases efficiency and increases TE power due to a larger
TE thermal gradient. As the TE leg length increases, the maximum operating temperature (776 K) is reached,
at which point the performance decreases to zero (gray area). In addition, for small thermosyphon radii
(bottom white area), heat pipe limitations (e.g., sonic limit) prohibit operation.
Figures 20 and 21 show the HSTE system performance for two other optimal bottoming cycle
temperatures and solar concentrations (T, = 470 K, C = 10 and Te = 776 K, C = 50) determined
from Figure 18. A gray area is not shown in Figure 21 because the optimum bottoming cycle
temperature is at the low end of the operating temperature range and only exists at Lt, > 0.05.
0.8
7
IHSTE
> 0.331
10.321
0.328
0.324
0.317
<0.314
0.2Qlimit
out
0
0
0.01
0.02
0.03
Lre [m]
b) 1
0.8
Pte [W'
1 >10
8
6
2
0
Qout >Qlmit
0
0.01
0.02
0.03
L. [im)
0.8 -
QoUt [W]
> 1100
880
0.6
880
0.4
140220
0.2
0-
-
Qout > Qulmit
0
0
i
I
0.01
0.02
Lt@ [m]
0.03
Figure 20 - Optimization results for a Bi 2Te3 HSTE at Te = 470 K and C = 10 showing a) system efficiency,
b) TE power, and c) waste heat. An increase in TE leg length (Lt) results in a decrease in efficiency and
increase in TE power due to a larger TE thermal gradient. As the TE leg length increases, the maximum
operating temperature is reached, and the performance decreases to zero (gray area). In addition, for small
thermosyphon radii (bottom white area), heat pipe limitations (e.g., sonic limit) prohibit operation.
a) 1 ,
0.8 -
J7HSTE
>0.33
0.6 -
0.24
0.20
0.15
4 0.10
0.4
0.2
0
0
0.010 0.020 0.030 0.040 0.050
Lt [m]
0.8
Pte [W]
> 20
16
12
0.6
19
5
0.4
0
0 Q
0
2 .0
.0mi
t.
0.01 0.02 0.03 0.04 0.05
Lt [m]
c)
1
0.8
Qo,, [W]
l>2000
1640
I920
0.6
1280
560
< 200
0.4
0.2
0
m
0oUt > Qiim'
-----
0
-17.r ---
r
-----
r"II
0.01 0.02 0.03 0.04 0.05
Lte
[M]
Figure 21 - Optimization results for a SiGe HSTE at Te = 776 K and C =50 showing a) HSTE system
efficiency, b) TE power and c) waste heat. An increase in TE leg length (Le) results in a decrease in efficiency
and increase in TE power due to a larger TE thermal gradient. For small thermosyphon radii (bottom white
area), heat pipe limitations (e.g., sonic limit) prohibit operation.
4.2.3
Effect of Thermosyphon Material
In an effort to broaden thermosyphon material selection, we investigated the effect of
thermosyphon wall thermal conductivity (k,) on performance. Only the low temperature model
was considered due to material compatibility issues for high temperature liquid metals. Figure 22
shows the HSTE system efficiency (QHSTE) as a function of solar concentration (C) and
thermosyphon wall thermal conductivity (k.) for a Bi 2Te 3 TE at T, = 470 K. As k, decreases
from 10 W/mK, the efficiency does not decrease appreciably, which indicates that the radial
conduction resistance of the thermosyphon wall is not dominant. However, as the thermal
conductivity decreases below approximately 1.2 W/mK, system efficiency begins to decrease
more significantly from the efficiency at high k, values (r*). The results indicate that materials
such as glass can be used for thermosyphons in HSTE systems when solar concentrations are
below 4 Suns, which can reduce material costs [58].
0.35
Ttec > 550 K
C=5
0.3
0.25
C=2--i
u
0.2
0.15
0.1
0.05
x 0.951*
0
0
1 2
3
4
5
6
7
8
9 10
kw [W/mK]
Figure 22 - HSTE system efficiency for varying solar concentrations (C) and thermosyphon wall thermal
conductivities (k,) for a Bi 2Te3 TE at Te = 470 K. I* is the HSTE efficiency at high thermal conductivities
(*
=
HSTE (k, = 10 W/mK)), which asymptotes to a constant value. For solar concentrations below 4 Suns,
materials with thermal conductivities larger than 1.2 W/mK have comparable system efficiency (I * ~ '7sTE).
To achieve the optimal HSTE system for a prescribed bottoming cycle using the framework
described above, the following procedure should be followed: 1) an initial geometry should be
specified for which an optimum solar concentration and bottoming cycle temperature can be
determined (e.g., Figure 18). 2) The thermosyphon and TE geometry should be optimized based
on results from step 1 (e.g., Figure 19). 3) A new geometry can then be selected that meets the
power and heat requirements of the particular application. 4) Steps 1 to 3 need to be repeated
until convergence is reached. In practice, system constraints such as the bottoming cycle
temperature and solar concentration are specified, which simplifies the optimization routine to
geometry only. Step 4 was not deeded for this study because the geometry of interest was
specified.
Five applications for HSTE systems are proposed in Table 3 showing applications requiring
relatively high heat output compared to electrical power production, such as residential heating,
solar AC, and industrial process heating, are ideal for HSTE integration. Additionally, HSTEs
show great promise at high temperatures, where previous renewable hybrid technologies (PVT)
were not applicable; for high quality heat applications such as aluminum smelting. The results
also demonstrate the applicability of HSTEs for high temperature applications such as chemical
drying and aluminum smelting, previously not possible with existing PVT systems.
Table 3 - HSTE Potential Applications and Performance (Per Unit Length of Evaporator Section).
HSTE Application
TlHSTE
Tc [K]
C
[%]
Residential Heating
Solar Air Conditioning [4, 6-9]
Low temperature IPH - Chemical Drying [12, 15]
Medium Temperature IPH [16, 17]
High Temperature IPH - Aluminum Smelting [19]
4.3
15.2
25.4
34.4
48.1
52.6
360
400
500
700
776
50
50
100
100
100
Pte
[W/m]
200
100
250
140
60
out
[kW/m]
4
4
7.6
7
7.5
SUMMARY
In this chapter, we developed an HSTE system efficiency that combines electrical (TE) and
thermal (Camot) efficiency. Optimization was performed on the geometry examined in Chapter
3 showing system efficiencies as high as 52.6% can be achieved at solar concentrations of
100 Suns and bottoming cycle temperatures of 776 K. Geometric optimization of the TE leg
length and the radii ratio shows that there is a competing effect between electrical power and
efficiency. This result implies if the application has larger electrical demands, it may be more
favorable to sacrifice overall system efficiency for electrical production. In addition, the effect of
thermosyphons wall conductivity was investigated, showing thermosyphons with low wall
conductivities (> 1.2 W/mK) at low solar concentrations (< 4 Suns) have comparable system
efficiencies which suggests that lower cost materials, including glass, can be used. Finally, five
bottoming cycle applications with temperatures ranging from 360 K - 776 K are proposed for
potential HSTE integration.
Chapter 5
5. Conclusions and Ongoing Work
In this thesis, we numerically investigated a hybrid solar thermoelectric system using a
thermosyphon to efficiently transport heat for a bottoming cycle (HSTE) over a wide range of
temperatures (300 K - 1200 K), solar concentrations (1 - 100 Suns), as well as thermosyphon
and TE materials and geometries. A simplified thermal resistance based model for heat pipes and
thermosyphons was developed (Chapter 2) and used to identify thermosyphons as the better
technology for integration into HSTEs due to smaller temperature drops and higher thermal
efficiencies. In Chapter 3, a separate integrated thermoelectric and thermosyphon energy-based
model was developed to predict the temperature distribution of the HSTE and to determine the
performance of the overall system. The results show that HSTE system efficiency is a strong
function of solar concentration and bottoming cycle temperature due to the coupling between
temperature and thermosyphon performance, TE performance and selective surface properties.
As the bottoming cycle temperature increases, the thermal efficiency increases up to an optimum
critical temperature. Beyond this temperature, the emissive losses dominate, resulting in a
decrease in HSTE efficiency. As solar concentration increases, both thermal and thermoelectric
efficiencies increase due to higher heat fluxes to the HSTE.
Geometric optimization of the HSTE (Chapter 4) also shows at higher TE leg lengths and radii
ratios, higher levels of electrical power and waste heat could be obtained but with decreased
efficiency. A range of optimum efficiencies were determined, the highest of which include:
34.4% (Tc= 500 K, C= 50), 48.1% (Tc= 700 K, C= 100), and 52.6% (Te = 776 K, C= 100). The
results from varying the thermosyphon wall material show when wall thermal conductivities
exceed 1.2 W/mK, system efficiency is approximately constant, indicating glass thermosyphons
could be used at low temperature (T < 550 K) HSTEs to potentially reduce material cost. The
outcomes of this study indicate a major benefit of using the HSTE system where unlike PVT
systems, they can be utilized at high temperatures while maintaining electrical conversion
efficiencies comparable to or greater than room temperature operation. The development of the
HSTE system extends the applicability of hybrid solar thermal to higher temperature processes
such as chemical drying and aluminum smelting, which mainly require mainly high quality heat.
This study serves as a framework for selection and optimization of HSTE system configuration
based on the end use application.
5.1
ONGOING WORK - EXPERIMENTAL DESIGN
In order to verify the results of the HSTE model, an experimental setup was designed and is
currently being built. The experimental was designed to allow for maximum versatility in input
conditions, including temperature, heat flux and material. Figure 23a shows a schematic of the
experimental setup, while Figures 23b and c show a 3D CAD drawing and physical assembly of
the main components, respectively.
A - Experimental System
B- Fill Rig
C- CoolingSection
D- Calorimeter Bar
E- Cartridge Heater Block
"B
:a
(-)2
45
i System
i
Axquisition
E
-Cmputer
c
(a)
3
Section
Condenser
= I
El
71
Adiabatic
Evaporator
Flux Measurement
Thermoelectric
Heater
(b)
(c)
Figure 23 - (a) Schematic of experimental design including test section, heater section and cooling section. (b)
3D CAD drawing and (c) as built assembly of the main experimental components. The test section is made
modular for ease of implementation of different thermosyphon materials such as copper or glass.
A roughing pump (Alcatel 210SDMLAM), capable of achieving pressures as low as 10- torr will
be used to evacuate the system. Heat will be supplied to the evaporator side of the thermosyphon
with a 500 W cartridge heater (SS - 120 V, McMaster) located in a milled copper calorimeter bar
instrumented with multiple thermocouples for measurement of heat flux. A custom water jacket
cooling section was build out of clear polycarbonate sheets due to their low thermal conductivity
(~ 1 W/mK) to limit heat transfer between the cooling water and the environment. Cooling
deionized water is supplied from a temperature controlled bath with 0.05 K resolution (RE-207,
Lauda-Brinkmann). The mass flow rate of the cooling water is measured by a liquid mass flow
meter with ±1 CCM accuracy (L Series Mass Flow Meter, 0-50 CCM, Alicat Scientific).
Temperature measurements are taken using type-K thermocouples (5TC-GG-K-36-36, Omega).
Two thermocouples are placed in the cooling section to measure the average temperature of the
inlet and outlet water streams. Internal pressure of the thermosyphon, and fill stations are
measured with a vacuum pressure transducer (FP2000 Pressure Transducer, Honeywell) and a
separate pressure gauge (MKS 925, MicroPirani Vacuum Transducer), respectively, due to the
isolation between the two during filling. A data acquisition system (cDAQ-9174 CompactDAQ,
National Instruments) is used to record the temperature and pressure readings at all times at a
rate of 4 kHz.
5.2
EXPERIMENTAL PROTOCOL
The experiment setup is Figure 23 is designed to accommodate evacuation of the thermosyphon,
degassing of the working fluid (water) and metering and filling of the working fluid while
maintaining a vacuum level below 10-3 torr. To achieve these requirements, the following
experimental procedure was developed
1) Make sure all components are thoroughly cleaned and properly assembled.
2) Fill the freeze pump thaw chamber with DI water, and freeze the water.
3) Close off valves 1, 2, and 3, and open 4 and 5.
4) Pull vacuum down to 10-3 torr (evacuation of thermosyphon chamber).
5) Close off valves 4, and open valve 2.
6) Pull vacuum down to 10-3 torr (evacuation of burette).
7) Close off valves 2 and 5 and open valve 3.
8) Pull vacuum down to 10~3 torr (evacuation of the freeze pump thaw chamber).
9) Close off valve 3, thaw the water, freeze the water, open valve 3.
10) Repeat steps 7 and 8 until sufficient degassing is achieved.
11)
Close valve 3, open valve 1.
12) Heat the FTP chamber until water evaporates and builds pressure to move into the
burette and condense on its sidewalls. Meter out the required amount of liquid.
13) Close valve 1, and open valves 2 and 4 (allow burette liquid to fill the thermosyphon).
14) Close valve 4.
After the procedure is complete, the thermosyphon of the HSTE setup is filled, evacuated and
ready for testing with the thermoelectric module. The constant temperature bath will simulate
different bottoming cycle temperatures, while the cartridge heaters will simulate the solar heat
flux for a range of concentrations.
5.3
FUTURE WORK
The experimental rig will be used to verify the HSTE model; however, other investigations and
experiments are planned for the setup. Experimental investigations of a glass thermosyphon
design and operation has been a recent topic of interest by many companies [58] in an effort to
reduce cost. The current HSTE model investigates the operation of low thermal conductivity
thermosyphons on HSTE performance for low heat flux applications. However, integration of a
glass thermosyphon with a high solar concentration solar collector has not been investigated due
to modeling complexity and presents an interesting research direction for the future. By using
glass, material and processing infrastructure cost decreases significantly over existing metal
technologies, making solar thermal system such as the HSTE more affordable.
A second topic of future investigation is thermosyphon condenser heat transfer enhancement.
Solar thermal systems have the opposite problem encountered in thermal management of solid
state devices such as microprocessors, diodes and transistors [59]. The evaporator area is the
critical bottleneck for design of solid state devices due to the minimal area for heat spreading
[41, 59-61]. Solar thermal systems, however, suffer from the opposite problem, since the
condenser area is minimal when compared to the evaporator (Figure 24).
100
100
Thermosyphons
50
50
20
20
10
10
5
5
2
2
1
1
0.5
0.5
r,=5mm
0.2
h
=
I
20000 W/mK
0.1
0.1
0
0.8
0.6
0.4
0.2
Condenser Length [m]
0.2
1
Figure 24 - Thermal resistances of thermosyphon condenser and evaporator sections as a function of
condenser length. The total length of the thermosyphon is 1m, r, = 0.005m. Evaporation and condensation
heat transfer are assumed to be equal magnitude (h = 20000W/mK) [40, 491.
Efficient condensing surfaces are needed to minimize condensation resistance. Future
investigation into the mechanism of condensation and heat transfer characteristics of different
surfaces and surface modifications such as chemical oxidation [62], ion implantation [63] and
nanostructuring [64, 65] will allow for better understanding and design of enhanced heat transfer
surfaces for HSTE systems.
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Appendix
HEAT PIPE CHARACTERIZATION
Prior to the low temperature experimental validation, four test heat pipes (WK Solar Water
Heater Co.) were opened for characterization of the working fluid. The 'heat pipes' were
determined to be wickless thermosyphons, two of which contained small particles in the working
fluid, while the others contained pure fluid. The fluid-particle combination was determined to be
water-copper with the use of differential scanning calorimetry and X-ray diffraction (Figure A),
respectively. Optical microscopy revealed the size of the particles to be 250pm in diameter.
a)
-
4.5
4.25
*
0X
0
4
-
x
x
3.75
3.5
3.25
3
0.
o 2.75
2.5
* Sample
2.25
2
x
Water
---10 15 20 25 30 35 40 45 50 55 60 65 70
Temperature [*C]
b)
Two - Theta (dog)
Figure A - (a) DSC results for heat pipe fluid sample identifying water as the fluid. (b) XRD results on the
powder material showing copper and copper oxide as the primary components.
66
The experimental setup (Figure 10) described in section 2.5 was used to characterize the heat
transfer performance of both heat pipes (powder and no powder) for variable heat inputs. Overall
thermal resistance was correlated to measured temperature difference (zT) from the evaporator
to the condenser, the smaller the AT, the lower the thermal resistance. In all tests, AT of the
particle heat pipe was smaller than the conventional fluid only heat pipe (Figure B). The effect of
the particles was found to enhance heat transfer in the evaporator section by lowering the time
constant for startup, decreasing evaporation thermal resistance through increased surface area for
thin film evaporation, and lowering condensation heat transfer resistance through the entrainment
of particles with the vapor flow from the evaporator to condenser.
18
16
14
12
0
10
6
4
+ Particle ATHP
U No
2
40
60
80
100
Particle ATHP
120
Heat Input [W]
Figure B - Heat pipe temperature difference between evaporator and condenser for varying heat inputs. The
thermal resistance of the powder heat pipe is lower for all heat inputs indicating performance enhancement
due to the addition of Copper particles.
The heat pipe model developed in section 2.1 does not include the effect of powders. All heat
pipes used in the low temperature verification study of section 2.5 did not contain particles in
order to avoid error between model and experiments.
HSTE MATLAB CODE
%---
Bi2Te3
-----------
---
clc
T C = 300;
C = 1;
k w = 400;
x = 50000;
y = 5;
A = zeros(x, y);
t
=
1;
y=28;
while y<226
%Counter on iteration for TE leg length
W=1;
%Counter on iteration for radius ratio
%TE leg length
while w<250
T c = y+299;
C = 0.l*w;
S=1; %SS material
M=1;
S=1
(%Black Chrome),
%Thermosyphon material.
M=1
S=2
(%Copper),
(Luz Cermet),
M=2
S=3
(Nickel),
M=3
(UVAC A),
(SS
304),
S=4
M=4
(UVAC B)
(Glass)
VARIABLE DEFINITION =============
D_teo=0.06;
D tei=0.045;
D_wo=0.045;
D_wi=0.04;
L e=0.5;
L_C=0.1;
L_a=0.2;
F=0.5;
Theta=0;
%Outer dia. of the TE & outer dia. of the thermosyphon
%Inner diameter of the thermoelectric module
%Outer diameter of the thermosyphon wall
%Inner diameter of the thermosyphon wall
%Length of the thermosyphon evaporator section
%Length of the thermosyphon condenser section
%Length of the thermosyphon adiabatic section
%View factor from the mirror to the collector
%Heat pipe inclination angle
%==========
Sigma=5.67E-8;
g=9.81;
GS=1000;
T_inf=300;
UNIVERSAL CONSTANTS
=====
%Stefan Boltzmann Constant
%Gravitational Constant
%Solar Insolation
%Ambient Temperature
Calculation of thermal resistances - GUESSES
%Thermoelectric material thermal conductivity
R_te=log(D teo/D tei)/(2*pio*Le*kte); %Thermoelectric thermal resistance
%Evaporator Wall thermal resistance
R_we=log(D wo/D wi)/(2*pi(*L_e*k w);
%Condenser Wall thermal resistance
R_wc=log(D wo/Dwi)/(2*pi()*L_c*kw);
%Thin liquid film thermal resistance
R f=0.00449;
%Thermosyphon thermal resistance
R_hp=Rwe+Rwc+2*Rf;
%Total thermal resistance
R_tot=R_hp+Rte;
%Initial
k te=l;
%System Efficiency Calculations
ZT=l;
e=0.05;
a = 0.95;
%Thermoelectric material ZT
%Emissivity of the selective surface
%Selective surface absorbtivity
%Total heat input into the system
Q_in=a*C*GS*pi(*Dteo*Le*F;
%Initial guess for surface temperature
T-sguess=Tc+2;
%Initial guess for TE cold side temperature
T-tecguess=Tc+1;
%Calculation of emissive losses
Q_loss=Sigma*e*pi()*Dteo*L-e*T-sguess^4;
n_te=( (T-sguess-T_tecguess)/Tsguess)*( ((1+ZT)^0.5-1)/((1+ZT)^0.5+T-tecguess/Tsguess)); %TE eff.
n_c=1-(Tinf/Tc);
P te=n te*(Q in-Q loss);
%Carnot Efficiency
%Thermoelectric power
T s=T c+(Q in-P te-Q loss)*R tot; %Calculation of surface temperature
T tec=Tc+(Qin-Pte-Qloss)*R_hp;%Calculation of the TE cold side temperature
%Heat pipe fluid volume
%Condenser inner wall temperature
%Condenser Side saturation temperature
%Evaporator Side saturation temperature
%Heat pipe heat transfer
V t=0.05;
T wc=T c+0.05;
T satC=T c+0.1;
T satE=T satC+0.1;
Q_hp=Q in-Q_loss-Pte;
%
ITERATION
guesses
to a converged solution. The above were initial
%Loops to iterate
%Accuracy of +- 0.5 degrees
while abs(Ttec-Ttecguess)>0.001
%If statement to check which direction to increment the iteration
if Ttec>Ttecguess
T_tecguess=T-tecguess+(T_tec-Ttecguess)/2;
else
T_tecguess=T-tecguess+(T_tec-Ttecguess)/2;
end
%Total heat input
Q_in=a*C*GS*pi()*D teo*L e*F;
%SS emissivity
[a,e] = selectivesurface properties(S,T_sguess);
Q_loss=Sigma*e*pi(*D teo*Le*(T-sguess^4-T-inf^4); %Radiative loss
[ZT,k_te = thermoelectricpropertiesBi2Te3_GOOD(T-sguess,Ttecguess); %TE ZT
%TE thermal resistance
R-te=log(Dteo/D_tei)/(2*pi(*L e*k te);
n_te=((T_sguess-T_tecguess)/Tsguess)*(((l+ZT)A0.5-1)/((l+ZT)^0.5+Ttecguess/Tsguess));
%TE power
P_te=nte*(Qin-Qloss);
%Thermosyphon heat
Q_hp=Qin-Q_loss-Pte;
[R wc, R we]
= wall thermal resistancesV4(D wo,D wi,L c,L e,k w);
transfer
%TS wall resistance
T wc = T c + Qhp*R_wc;
[T_satC,Gamma,Redelta,dLaLc,hc,Repipe]=saturation temperaturecondenserBi2Te3(T c,T
%Condenser saturation temperature
wc,Q_hp,D_wi,L_c,Theta);
T_satE=saturationtemperatureevaporatorBi2Te3(TsatC,Q_hp,Le,L c,La,Dwi);%Evap. Tsat
T_we = thermoelectric-cold-side-temperature(TsatE,Qhp,D_wi,Lc,Theta); %Evap. Twall
if Qhp==o
T tec = T satE;
T_s = Ttec;
nS = 0;
h c = 0;
Re delta = 0;
else
n_s = (Pte+Q_hp*n-c)/(Qin);
T tec = T we + Q-hp*R-we;
T s = T tec+(Q in-Q loss)*R te;
%Thermoelectric cold side temperature
%Selective surface temperature
end
%Loop to iterate surface temperature
%Accuracy of +- 0.5 degrees
while abs(T s-T sguess)>0.001
%If statement to check which increment
if Ts>T-sguess
T_sguess=Tsguess+(T_s-Tsguess)/2;
else
T_sguess=Tsguess+(T_s-Tsguess)/2;
end
%Total heat input
Q_in=a*C*GS*pio)*Dteo*Le*F;
%SS emissivity
[a,e] = selectivesurfaceproperties(S,Tsguess);
Q_loss=Sigma*e*pio)*D teo*Le*(T_sguess^4-T inf^4);%Rad. loss
%TE ZT
[ZT,kte] = thermoelectricproperties_Bi2Te3_GOOD(Tsguess,T_tecguess);
STE thermal resistance
R_te=log(D_teo/D tei)/(2*pio)*L e*kte);
n_te=((Tsguess-T_tecguess)/Tsguess)*(((l+ZT)^0.5-1)/((l+ZT)^0.5+T-tecguess/Tsguess));
%Carnot Efficiency
n c=l-(T inf/T c);
%Thermoelectric power
P_te=nte*(Q_in-Qloss);
Q hp=Qin-Qloss-Pte;
%Thermosyphon heat transfer
[R wc, R we] = wall thermal resistancesV4(D wo,D wi,L c,L e,k w); STS wall TR
T_wc = Tc + Q-hp*R-wc;
[T_satC,Gamma,Redelta,dLaLc,hc,Repipe]=saturationtemperature condenserBi2Te3(T_c,T-wc,Q_hp,
%Condenser saturation temperature
D wi,L c,Theta);
T_satE=saturation temperatureevaporatorBi2Te3(T_satC,Qhp,L_e,L_c,La,Dwi);
T_we = thermoelectriccold sidetemperature(T_satE,Qhp,D_wi,Lc,Theta);
if Qhp==0
T tec = T satE;
T s = T tec;
n s = 0;
h c = 0;
Re delta = 0;
else
n_s = (Pte+Qhp*nc)/(Qin);
T_tec = Twe + Q_hp*R-we;
T_s = T_tec+(Qin-Qloss)*Rte;
%TE cold side temperature
%SS temperature
end
T_sat=(TsatE+-T_satC)/2;
%Saturation temperature
T_film = Tsat;
%Film temperature
V t = total fluid volume(Tfilm,Tsat,Le,La,Lc,Qin,Dwi); %Total volume
end
end
if (T_s>525) ||
(T-tec>500)
%If statement to control max temp. of the TE
n s = 0;
P te = 0;
Q-hp = 0;
h c = 0;
Repipe = 0;
end
A(t,l)
= T C;
A(t,2)
A(t,3)
A(t,4)
=
A(t,5)
= real(h c);
=
C;
real(Q_hp);
real(Repipe);
t=t+l
w=w+1
end
y=y+l
end
name3 = num2str(C);
%Converting the numerical value to a string for naming
name4 = num2str(Tc); %Converting the numerical value to a string for naming
string=['Repipe_1COMPILED RESULTS C' name3 'T c' name4 '.xls'];
xlswrite(string,A,'RESULTS');
Bi2Te3
function (a,e] = selectivesurfaceproperties(S,T_sguess)
%If statements to control which surface absorbtivity to report based on selective surface
material
if S==1
a=o.916;
elseif S==2
a=0.938;
elseif S==3
a=0.954;
elseif S==4
a=0.935;
elseif S==5
a=0.78;
else
a=0;
end
%Black Chrome absorbtivity
%Luz Cermet absorbtivity
%UVAC A absorbtivity
%UVAC B absorbtivity
%Matte Copper absorbtivity
%If
the material
%If statements to control which surface
if S==1
%Black Chrome
specified doesn't make
the absorbtivity
emissivity to report based on selective
e =(0.000370756573851)*(Tsguess)+(-0.0294499121865);
elseif S==2
sense,
is
0
surface material
%Black Chrome
%Luz Cermet
e = (0.000244977195297)*(Tsguess)+(-0.01631980331);
%Luz Cermet
elseif S==3 %UVAC A
e = (0.000235350947221)*(Tsguess)+(-0.0222601285472); %UVAC A
elseif S==4 %UVAC A
e = (0.000228258883363)*(Tsguess)+(-0.00203624283375); %UVAC B
elseif S==5
%Matte Copper
e = 0.22;
else
%Unknown Material
= 1.00;
end
Copper
loss term will be unusually
%Matte
- emissivity of I so the heat
large
function [ZT,kte]
clc
= thermoelectricpropertiesBi2Te3(T_sguess,Ttecguess)
%Creating variables read in from the input file
%Average TE temperature
T_avg=(Tsguess+T_tecguess)/2;
ZT = (7.30213424572E-16)*(Tavg)^6+(-8.10744406282E 13)*(T-avg)^5+(2.02282766099E10)*(Tavg)^4+(0.000000064274892335)*(T avg)^3+(0.0000564794376396)*(T avg)^2+(0.0185079361451)*(Tavg)+(-1.43467199937);
k_te = (1.47346849132E-15)*(Tavg)^6+(-2.72551625379E-12)*(Tavg)^5+(1.35978302175E09)*(T_avg)^4+(0.000000316348272135)*(Tavg)^3+(0.000473687506427)*(Tavg)^2+(0.138800778626)*(Tavg)+(-11.9920635856);
function [T_satC,Gamma,Redelta,dLaLc,hc,Repipe) =
saturationtemperaturecondenserBi2Te3(Tc,Twc,Q-hp,Dwi,Lc,Theta)
%Universal Constants
g=9.81;
T_satCguess = T wc + 15;
T_film = (T_satCguess + T-wc)/2;
%Using curve
fits
to get properties
as a function of T sat and T film
u vi = real((1.87495975484E-20)*(T film)^6+(-2.97467001087E-17)*(T film)^5+(1.21967979264E14)*(T film)^4+(3.7053350255E-12)*(T film)^3+(-4.27472054352E09)*(T film)^2+(0.00000121041162089)*(T film)+(-0.000108649900403));
p_li = real((-2.7972369118E-13)*(Tfilm)^6+(4.34835809239E-10)*(T_film)^5+(0.000000173163807888)*(T film)^4+(-0.0000548266717527)*(T film)^3+(0.0583648692187)*(T film)^2+(%Liquid Density
15.3786834405)*(Tfilm)+(2386.52021075));
h-fgi = real((-1.06388077522E-09)*(T-satCguess)^6+(0.00000169858874328)*(TsatCguess)A5+(0.000714769544192)*(TsatCguess)^4+(0.214959081371)*(TsatCguess)^ 3+(258.723262327)*(T satCguess)^2+(-
%Latent heat of vaporization
75814.2921272)*(T satCguess)+(10135356.8597));
k li = real((2.18292141071E-16)*(T film)^6+(-4.0593408048E-13)*(T film)^5+(2.07115013809E10)*(T film)^4+(0.0000000476296098352)*(T film)^3+(0.0000848400723136)*(T film)^2+(0.0305967221022)*(T film)+(-3.06828231166)); %Liquid conductivity
u li = real((-2.83321833095E-18)*(T film)^6+(5.3801747354E-15)*(T film)^ 5+(-2.69609559702E12)*(Tfilm)^4+(-9.14409736254E-10)*(T_film)^3+(0.00000134796515303)*(Tfilm)^2+(%Liquid Dynamic Viscosity
0.000465113955315)*(T film)+(0.0546328677998));
T satC = T wc +
((3/4)*Qhp*((4*uli)/(pIli^2*k-li^3*g*cos(Theta)*hfgi*(pi()^4)*(Dwi^4)*(L_c^3)))^(1/4))^(4/3);
h_c = (4/3)*((pli^2*k-li^3*g*hfgi)/(4*uli*(TsatC-Twc)*L_c))^(1/4);
dLaLc = ((4*k li*u li*(T satC-T wc)*(L c))/(g*(pli^2)*h fgi))^(1/4);
Gamma = (g*(p_li^2)*(dLaLc^3))/(3*uli);
Re-delta = (4*Gamma)/u li;
Repipe = (4*(Q hp/hfgi))/(piO*Dwi*u_vi);
%Transition Reynolds number
if Re-delta > 30
Redelta = ((3.7*kli*Lc*(TsatC-Twc))/(u li*h fgi*(u_li^2/(pli^2*g))^(1/3))+4.8)^(0.82);
h_c = (Redelta*uli*h fgi)/(4*L c*(T satC-T wc));
T satC = T wc + (Q-hp/(h-c*pio*L_c*Dwi));
Repipe =
(4*(Q hp/hfgi))/(pio*D
wi*u vi);
end
while abs(TsatCguess-T-satC)>0.001
%Accuracy of +
%If statement
if T satC>T satCguess
T satCguess=TsatCguess+(TsatC-TsatCguess)/2;
else
T_satCguess=TsatCguess+(TsatC-TsatCguess)/2;
end
T film = (TsatCguess + Tc)/2;
0.1 degrees
u_vi = real((1.87495975484E-20)*(Tfilm)^ 6+(-2.97467001087E17)*(Tfilm)^5+(1.21967979264E-14)*(Tfilm)^ 4+(3.7053350255E-12)*(Tfilm)^3+(-4.27472054352E09)*(Tfilm)^2+(0.00000121041162089)*(Tfilm)+(-0.000108649900403));
p_li
= real((-2.7972369118E-13)*(Tfilm)6+(4.34835809239E-10)*(Tfilm)^ 5+(0.000000173163807888)*(Tfilm)^4+(-0.0000548266717527)*(Tfilm)^3+(0.0583648692187)*(Tfilm)^2+(15.3786834405)*(Tfilm)+(2386.52021075));
%Liquid Density
h_fgi = real((-1.06388077522E09)*(T-satCguess)^6+(0.00000169858874328)*(T
satCguess)^5+(-0.000714769544192)*(T-satCguess)^4+(0.214959081371)*(TsatCguess)^3+(258.723262327)*(TsatCguess)^2+(75814.2921272)*(T satCguess)+(10135356.8597));
%Latent heat of vaporization
k_li = real((2.18292141071E-16)*(Tfilm)^6+(-4.0593408048E13)*(Tfilm)^5+(2.07115013809E-10)*(Tfilm)4+(0.0000000476296098352)*(T film)^3+(0.0000848400723136)*(Tfilm)^2+(0.0305967221022)*(Tfilm)+(-3.06828231166)); %Liquid conductivity
u_li = real((-2.83321833095E-18)*(T_film) ^6+ (5.3801747354E-15)*(Tfilm)^5+(2.69609559702E-12)*(Tfilm)^ 4+(-9.14409736254E-10)*(Tfilm)^ 3+(0.00000134796515303)*(T film)^2+(0.000465113955315)*(Tfilm)+(0.0546328677998));
-Liquid Dynamic Viscosity
d_LaLc = ((4*k-li*u-li*(T-satCguess-T_wc)*(L-c))/(g*(p li^2)*h-fgi))^(1/4);
Gamma = (g*(pli^2)*(dLaLc^3))/(3*uli);
Redelta = (4*Gamma)/uli;
if Re delta < 30
T satC = T
wc
+
((3/4)*Qhp*((4*uhli)/(p_li^2*kli^3*g*cos(Theta)*h fgi*(pi(^4)*(D wi^4)*(L-c^3)))^(1/4))^(4/3);
h_c = (4/3)*((p li^2*k li^3*g*h-fgi)/(4*uli*(TsatC-Twc)*L c))^(1/4);
Repipe = (4*(Qhp/h fgi))/(pi() *D wi*uvi);
else
Redelta = ((3.7*kli*L_c*(TsatCT-wc))/(u-li*h_fgi*(u- li^2/
(p_li^
2*g))^ (1/3))+4 .8)^ (0.82);
h_c = (Redelta*u_li*h fgi)/(4*L_c*(TsatC-Twc));
T_satC = T_wc + (Q-hp/(hc*pio*L_c*D_wi));
Repipe = (4*(Qhp/hfgi))/(pi()*D-wi*uvi);
end
end
function T satE = saturation temperature_evaporatorBi2Te3(TsatC,Qhp,Le,L_c,L_a,Dwi)
clc
%Universal Constants
g=9.81;
%Gravitational constant
R=461.5;
%Water vapor gas constant
T_satEguess = TsatC + 20;
T_film = (TsatEguess + TsatC)/2;
%Using curve fits to get properties as a function of T sat
and T film
P = real(1000000*((4.3744037702E-16)*(Tfilm)^6+(9.69210557312E-14)*(Tfilm)^5+(-4.06519438079E11)*(T film)^ 4+(-
0.0000000970934845583)*(Tfilm)^3+(0.0000219974465825)*(Tfilm)^2+(0.00767630729786)*(Tfilm)+(1.87955921995)));
IPressure
p_vi = real(0.578419628557+0.000651616774107*exp(0.0194286357277*T film));
p_vi = real((2.72020154394E-13)*(Tfilm)^ 6+(-4.33952642858E10)*(Tfilm)^5+(0.000000181459954338)*(Tfilm)^4+(0.0000543146547257)*(Tfilm)^3+(0.065111547115)*(Tfilm)^2+(18.4573484974)*(Tfilm)+(-1756.57071271));
pli = real((-2.7972369118E-13)*(Tfilm)^6+(4.34835809239E-10)*(T film)^ 5+(0.000000173163807888)*(Tfilm)^4+(-0.0000548266717527)*(T film)^3+(0.0583648692187)*(T film)^2+(15.3786834405)*(Tfilm)+(2386.52021075));
%Liquid Density
hfgi =
real((-1.06388077522E-09)*(T
satEguess)^6+(0.00000169858874328)*(TsatEguess)^5+(-
0.000714769544192)*(TsatEguess)^4+(0.214959081371)*(T satEguess)^3+(258.723262327)*(TsatEguess)^2+(75814.2921272)*(TsatEguess)+(10135356.8597));
%Latent heat of vaporization
k_li = real((2.18292141071E-16)*(T film)^ 6+(-4.0593408048E-13)*(T film)^5+(2.07115013809E10)*(T film)^4+(0.0000000476296098352)*(Tfilm)^3+(0.0000848400723136)*(Tfilm)^2+(0.0305967221022)*(Tfilm)+(-3.06828231166)); %Liquid conductivity
u li = real((-2.83321833095E-18)*(Tfilm)^6+(5.3801747354E-15)*(T film)^5+(-2.69609559702E12)*(Tfilm)^4+(-9.14409736254E-10)*(T film)^ 3+(0.00000134796515303)*(T film)^2+(0.000465113955315)*(Tfilm)+(0.0546328677998));
%Liquid Dynamic Viscosity
u_vi = real((1.87495975484E-20)*(T film)^ 6+(-2.97467001087E-17)*(T
film)^5+(1.21967979264E-
14)*(Tfilm)^4+(3.7053350255E-12)*(Tfilm)^3+(-4.27472054352E09)*(Tfilm)^2+(0.00000121041162089)*(Tfilm)+(-0.000108649900403));
T satE = T satC +
(Q-hp)*((8*R*uvi*Tfilm^2)/(pi()*h fgi^2*pvi*P))*(((Le+L-c)/2+La)/(D-wi/2) 4);
while abs(real(TsatEguess-TsatE))>0.001
if real(TsatE)>real(T-satEguess)
%Accuracy of +- 0.5 degrees
%If statement to check direction
T_satEguess=TsatEguess+(TsatE-T_satEguess)/2;
else
T_satEguess=TsatEguess+(TsatE-T_satEguess)/2;
end
T film =
(TsatEguess + TsatC)/2;
P = real(1000000*((4.3744037702E-16)*(T film)^6+(9.69210557312E-14)*(T film)'5+(4.06519438079E-11)*(T film)^4+(0.0000000970934845583)*(T film)^3+(0.0000219974465825)*(T film)^2+(0.00767630729786)*(T film)+(1.87955921995)));
%Pressure
p_vi = real(0.578419628557+0.000651616774107*exp(O.0194286357277*Tfilm));
h fgi = real((-1.06388077522E09)*(TsatEguess)^6+(0.00000169858874328)*(T_satEguess)^5+(-0.000714769544192)*(T_satEguess)^4+(0.214959081371) * (T_satEguess) ^3+ (258. 723262327) * (T satEguess) ^2+ (75814.2921272)*(T_satEguess)+(10135356.8597));
%Latent heat of vaporization
u-vi = real((1.87495975484E-20)*(T film)^6+(-2.97467001087E17)*(T film)^5+(1.21967979264E-14)*(T film)^4+(3.7053350255E-12)*(T film)^3+(-4.27472054352E09)*(T film)^2+(0.00000121041162089)*(T film)+(-0.000108649900403));
T satE = T satC +
(Q-hp)*((8*R*uvi*Tfilm^2)/(pi()*h_fgiA2*pvi*P))*(((L e+L c)/2+L a)/(D wi/2)^4);
end
T satE = real(T satC +
(Q_hp)*((8*R*u vi*T film^2)/(pi()*hfgi^2*pvi*P))*(((Le+Lc)/2+L-a)/(D-wi/2)^4));
= wall thermal resistancesV4(D wo,D wi,L c,L e,k w)
%Evaporator Wall thermal resistance
R_wc=log(Dwo/Dwi)/(2*pi()*L_c*kw);
%Condenser Wall thermal resistance
End
function
[R wc,
R we]
R_we=log(D wo/D-wi)/(2*pio)*Le*kw);
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