thermal-fluid characterization and performance …
TRANSCRIPT
THERMAL-FLUID CHARACTERIZATION AND PERFORMANCE ENHANCEMENT
OF DIRECT ABSORPTION MOLTEN SALT SOLAR RECEIVERS
by
Mélanie Tétreault-Friend
B.Eng., Mechanical Engineering, McGill University (2012)
M.S., Nuclear Science and Engineering, Massachusetts Institute of Technology (2014)
SUBMITTED TO THE
DEPARTMENT OF NUCLEAR SCIENCE AND ENGINEERING
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY IN NUCLEAR SCIENCE AND ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
JUNE 2018
© 2018 Massachusetts Institute of Technology
All rights reserved.
Signature of Author: _________________________
Mélanie Tétreault-Friend
Department of Nuclear Science and Engineering
May 25, 2018
Certified by: ___________________________
Alexander H. Slocum
Walter M. May and A. Hazel May Professor of Mechanical Engineering
Thesis Supervisor
Certified by: ___________________________
Emilio Baglietto
Norman C. Rasmussen Associate Professor of Nuclear Science and Engineering
Thesis Supervisor
Certified by: ___________________________
Gang Chen
Carl Richard Soderberg Professor of Power Engineering
Thesis Reader
Accepted by: ___________________________
Ju Li
Battelle Energy Alliance Professor of Nuclear Science and Engineering
and Professor of Materials Science and Engineering Chair, Department Committee on Graduate Students
3
THERMAL-FLUID CHARACTERIZATION AND PERFORMANCE ENHANCEMENT
OF DIRECT ABSORPTION MOLTEN SALT SOLAR RECEIVERS
by
Mélanie Tétreault-Friend
Submitted to the Department of Nuclear Science and Engineering
on May 25, 2018 in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy in
Nuclear Science and Engineering
Abstract
This thesis presents an in-depth thermal-fluid analysis of direct absorption molten salt solar
receivers. In this receiver concept, an open tank of semi-transparent liquid is directly irradiated
with concentrated sunlight, where it is absorbed volumetrically and produces internal heat
generation. The intensity distribution of the internal heating depends on the optical properties of
the absorber liquid and the dimensions of the receiver. This heating results in a combination of
thermal stratification and radiation-induced natural convection in the receiver, which govern the
general thermal-fluid behavior and performance of the system. Direct absorption requires molten
salts to be contained in open tanks directly exposed to the environment; consequently, the liquid
absorber experiences thermal losses to the environment which reduces absorption efficiency and
produces large temperature gradients immediately below the exposed liquid surface.
The thesis presents an apparatus that allows for the precise measurement of light attenuation in
high temperature, nearly transparent liquids. The apparatus is used to measure and characterize the
absorption properties of the 40 wt. % KNO3:60 wt. % NaNO3 binary nitrate and the
50 wt. % KCl:50 wt. % NaCl binary chloride molten salt mixtures. The analytical model of the
thermal stratification, radiation-induced convection, and radiative cooling effects highlights the
key parameters and conditions for optimizing the thermal-fluid performance of the receiver.
Computational fluid dynamics and heat transfer modeling of the CSPonD Demonstration prototype
of a direct absorption molten salt solar receiver provide further insight into its performance. The
findings from the analytical and computational analyses give motivation to create a new cover
design for open tanks of molten salts consisting of floating hollow fused silica spheres. The cover
concept is demonstrated experimentally and the analysis shows the cover’s ability to reduce
thermal losses by 50%.
Thesis Supervisor: Alexander H. Slocum
Walter M. May and A. Hazel May Professor of Mechanical Engineering
Thesis Supervisor: Emilio Baglietto
Norman C. Rasmussen Associate Professor of Nuclear Science and Engineering
5
In memory of Thomas J. McKrell,
Wherever you may be, I hope you found those mermaids…
R.I.P. 1969 - 2017
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Acknowledgements
Dr. Thomas McKrell started me on my journey at MIT six years ago. He was an advisor, a mentor,
and a friend. He was a gentle force who shared his enthusiasm for science and his love for life
through his mentoring, and taught me to work hard and to appreciate the learning process. His
countless stories and anecdotes reminded me to also pause, reflect on life and science, and share
some good laughs. Tom left us during this journey, but his memory will always inspire me to be a
good scientist, and most importantly, a good person.
My PhD could also not have been possible without the help and support from countless faculty,
colleagues, and friends. First and foremost, I would like to thank my advisor, Prof. Alex Slocum,
for giving me the opportunity to collaborate on this massive project, for sharing his larger-than-
life enthusiasm, and for supporting my creativity. I would also like to thank my committee
members, Prof. Emilio Baglietto and Prof. Gang Chen, for their generous guidance and advice.
This work was supported by the Masdar Institute of Science and Technology, in collaboration with
Prof. Nicolas Calvet’s research group at the Masdar Institute Solar Platform. Special thanks to
Toni, Victor, Thomas, Radia, Benjamin, Peter, Dr. Charles Forsberg, and Miguel, for making
the CSPonD a reality. I would also like to thank Prof. Jacob Karni of the Weizmann Institute for
sharing his expertise in concentrated solar power and thermal energy storage. Thank you also to
Prof. Buongiorno for his continued interest in the CSPonD and for sharing experimental
equipement.
I had the privilege to collaborate with several research groups at MIT during this project. In
particular, NSE’s Green Lab has been my home for the past six years where Carolyn, Guanyu,
Andrew, Bren, Reza, and Matteo became my friends and family at MIT. I would like to thank
Prof. Gang Chen’s Nano group for graciously sharing their research space, and George, Lee, Hadi,
Tom, and Sveta, for sharing their expertise and guidance in solar thermal technology. NSE’s CFD
group provided invaluable computational support to a silly experimentalist. And a special thanks
to all PERGies for sharing your awesome lab environment and your inspiring creativity.
I also had the opportunity to mentor two talented undergraduate students, Shapagat Berdibek and
Luke Gray, who helped build and run extremely hot optical experiments. It was an honor to work
with you and I look forward to mentoring more students like you.
Finally, this work would not be possible without the behind-the-scenes support from family and
loved ones. In addition to my PhD, this project allowed me to find Miguel, the most kind, patient,
and understanding person I know. And of course thank you to my family, my brother, the infamous
trouble-makers Sherlock and Watson, and my courageous mother, for raising two engineers all on
her own.
“It may be the warriors who get the glory, but it’s the engineers who build societies.”
-B’Elanna Torres
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Table of Contents
Abstract ....................................................................................................................................... 3
Acknowledgements ..................................................................................................................... 7
List of Figures ........................................................................................................................... 12
List of Tables ............................................................................................................................ 16
Nomenclature ............................................................................................................................ 17
1. Introduction ........................................................................................................................... 20
1.2. CSPonD Demonstration Project Test Facility ................................................................... 22
1.3. Participating media and natural convection in internally heated fluids ......................... 24
1.4. Molten Salts.................................................................................................................... 28
1.5. Thermal losses in open tanks of molten salt .................................................................. 31
1.6. Objectives ....................................................................................................................... 32
1.6.1. Scope of thesis ........................................................................................................ 33
2. Molten salt optical properties measurements ........................................................................ 35
2.1. Experimental Procedure ................................................................................................. 35
2.1.1. Apparatus description ............................................................................................. 35
2.1.2. Mixture preparation ................................................................................................ 39
2.1.3. Measurement procedure .......................................................................................... 41
2.2.3. Thermal performance evaluation ............................................................................ 41
2.3. Experimental Validation ................................................................................................ 45
2.4. Results ............................................................................................................................ 46
2.5. Discussion ...................................................................................................................... 51
2.5.1. Volumetric absorption ............................................................................................ 51
2.5.2. Effective Emissivity ................................................................................................ 52
2.5.3. Capture Efficiency .................................................................................................. 53
2.6. Conclusions .................................................................................................................... 56
10
3. Theoretical study of direct absorption receivers ................................................................... 57
3.1. Problem formulation ...................................................................................................... 58
3.2. Governing equations ...................................................................................................... 59
3.3. Model validation ............................................................................................................ 64
3.4. Direct absorption receiver optimization ......................................................................... 72
3.5. Conclusions .................................................................................................................... 77
4. CFD and heat transfer model of the Masdar CSPonD Demo prototype ............................... 79
4.1. CSPonD demonstration prototype experiments ............................................................. 80
4.2. Model setup and boundary conditions ........................................................................... 82
4.3. Numerical procedure ...................................................................................................... 86
4.4. Dependence on the grid resolution ................................................................................. 91
4.5. Results for January 23, 2018 experiment ....................................................................... 95
4.5.1. Initial Conditions .................................................................................................... 95
4.5.2. Results: CFD calculated temperature and velocity distributions ............................ 99
4.5.3. Results: Experiment and CFD model temperature profiles comparison .............. 103
4.6. Discussion .................................................................................................................... 107
4.6.1. Solar source intensity ............................................................................................ 107
4.6.2. Salt optical properties ........................................................................................... 109
4.6.3. Demo prototype experimental uncertainty ............................................................ 111
4.7. Conclusions ...................................................................................................................... 112
5. Receiver cover design for enhanced thermal performance ................................................. 113
5.1. Very High Temperature Floating Modular Cover........................................................ 114
5.2. Methodology ................................................................................................................ 118
5.2.1. Laboratory experiments and simulation validation............................................... 119
5.2.2. Large scale molten salt solar pond performance................................................... 129
5.2.3. Solar pond capture efficiency ............................................................................... 139
5.3. Analysis of receiver heat loss mechanisms .................................................................. 140
11
5.3.1. Convection ............................................................................................................ 140
5.3.2. Radiation ............................................................................................................... 142
5.3.3. Evaporation ........................................................................................................... 142
5.3.4. Magnitude Comparison ......................................................................................... 142
5.4. Discussion .................................................................................................................... 145
5.5. Conclusions .................................................................................................................. 149
6. Concluding Remarks ........................................................................................................... 150
6.1. Conclusions .................................................................................................................. 150
6.2. Future Work ................................................................................................................. 153
References ................................................................................................................................... 155
Appendices .................................................................................................................................. 161
A. Effect of temperature on optical properties ........................................................................ 161
B. Uncertainty analysis in optical property measurements ..................................................... 162
C. Reflectance calculation ....................................................................................................... 163
D. Conversion of photon counts to heat flux ratio ................................................................... 165
E. Transmission modeling ....................................................................................................... 167
F. Calculated capture efficiency for 40 mm, 60 mm, and 80 mm spheres.............................. 172
G. Thermophysical properties of SQM Solar Salt ................................................................... 175
H. Divider plate and mixing plate designs ............................................................................... 176
12
List of Figures
Figure 1-1 Cross-section of the general CSPonD molten salt receiver concept during (a) on-sun
operation at the end of the day, and (b) after a prolonged period with continued heat extraction but
without solar heating. .................................................................................................................... 21
Figure 1-2 (a) Photo and (b) simplified diagram of the CSPonD demonstration facility. ............ 23
Figure 1-3 (a) Illustration of the expected thermal behaviour inside the receiver. The internal
heating produces two layers in the receiver: a thermally stratified and stagnant upper layer, and an
unstable bottom mixing layer. The semi-transparent hot salt. (b) Illustration of a re-emitting
participating media........................................................................................................................ 27
Figure 1-4 Ideal Carnot heat engine and associated maximum thermal efficiency based on oK.
Increasing the maximum operating temperature TH using high temperature liquids such as molten
salts allows to increase the maximum possible heat engine efficiency. ....................................... 29
Figure 1-5 Illustration summarizing the four principal thermal-fluid topics investigated in this
thesis. ............................................................................................................................................ 34
Figure 2-1. Simplified diagram of apparatus used to measure the attenuation of light intensity by
liquids. ........................................................................................................................................... 37
Figure 2-2 Picture of the experimental apparatus for measuring the attenuation of light of high
temperature liquids........................................................................................................................ 39
Figure 2-3 40 wt. % KNO3:60 wt. % NaNO3 binary nitrate molten salt mixture at 400 ˚C (a),
decomposed binary nitrate molten salt mixture at 400 ˚C (b), and 50 wt. % KCl:50 wt. % NaCl
binary chloride molten salt mixture at 400 ˚C (c). ........................................................................ 40
Figure 2-4 Diagram illustrating assumptions and boundary conditions for performance evaluation.
....................................................................................................................................................... 44
Figure 2-5 Experimental results for the attenuation coefficient of propylene glycol versus
wavelength. ................................................................................................................................... 45
Figure 2-6 Attenuation Coefficient of 40 wt. % KNO3: 60 wt. % NaNO3 binary nitrate molten salt
(SQM) at 400 ˚C. .......................................................................................................................... 46
Figure 2-7 Attenuation Coefficient of decomposed 40 wt. % KNO3: 60 wt. % NaNO3 binary
nitrate molten salt (SQM) at 400 ˚C. ............................................................................................ 47
Figure 2-8 Attenuation Coefficient of 50 wt. % KCl: 50 wt. % NaCl binary chloride molten salt at
800 ˚C............................................................................................................................................ 47
Figure 2-9 Attenuation Coefficient of binary nitrate and decomposed binary nitrate at 400 ˚C, and
binary chloride at 800 ˚C (log-scale), with corresponding normalized blackbody intensity spectra
Îb,400˚C and Îb,800˚C, and normalized solar spectrum Gs (linear-scale)..................................... 48
Figure 2-10 Solar irradiance distribution at different salt depths for binary nitrate at 400 ˚C. .... 51
Figure 2-11 Solar irradiance distribution at different salt depths for binary chloride at 800 ˚C. . 52
13
Figure 2-12 Effective total emissivity of measured molten salt mixtures for different receiver fluid
depths. ........................................................................................................................................... 53
Figure 2-13 Capture efficiency versus solar concentrations for fluid depths between 0.25 m and 2
m for binary nitrate (a), decomposed binary nitrate (b), and binary chloride (c). ........................ 56
Figure 3-1 (a) Illustration of the heating and flow conditions inside a volumetric receiver. (b)
Illustration of the expected temperature profile resulting from the volumetric (internal) heating and
boundary conditions. ..................................................................................................................... 58
Figure 3-2 Illustration of the modelled region in CFD for validation of the 1D model. Lateral walls
are defined as symmetry planes such that the region is semi-infinite in the xz-plane. ................. 65
Figure 3-3 Illustration of the modelled region in CFD for validation of the 1D model. Lateral walls
are defined as symmetry planes such that the region is semi-infinite in the xz-plane. ................. 66
Figure 3-4 Characteristics temperature difference in the mixing layer T_b versus time as calculated
from the CFD model for three different grid sizes, where ℎ = 1 𝑚 , 𝜅𝑀𝑆 = 2 𝑚−1 , 𝐼𝑜 =37.5 𝑘𝑊/𝑚2, 𝑇𝑜 = 300 ℃, and 𝑅𝑎𝑅𝐵 ≈ 5 𝑥 1010. ..................................................................... 67
Figure 3-5 Axial temperature profile in an internally heated liquid layer calculated with the simple
1D model and the CFD model for ℎ = 1 𝑚, 𝜅𝑀𝑆 = 2 𝑚−1, 𝐼𝑜 = 37.5 𝑘𝑊/𝑚2, 𝑇𝑜 = 300 ℃, and 𝑅𝑎𝑅𝐵 ≈ 5 𝑥 1010........................................................................................................................... 69
Figure 3-6 Temperature distributions (left) and streamlines (right) at a cross-section in an internally
heated liquid layer obtained from CFD model for ℎ = 1 𝑚 , 𝜅𝑀𝑆 = 2 𝑚−1 , 𝐼𝑜 = 37.5 𝑘𝑊/𝑚2 , 𝑇𝑜 = 300 ℃, and 𝑅𝑎𝑅𝐵 ≈ 5 𝑥 1010. . .......................................................................................... 71
Figure 3-7 Variation of the temperature profile with optical thickness calculated using the 1D
model for the case ℎ = 1 𝑚, 𝐼𝑜 = 𝑘𝑊/𝑚2, 𝑇𝑜 = 300 ℃, with absorption coefficient ranging from
𝜅𝑀𝑆 = 1.1 𝑚−1 to 𝜅𝑀𝑆 = 8 𝑚−1 such that the optical thickness 𝜏 = 𝜅𝑀𝑆ℎ varies from 1.1 to 8.
Temperature profiles for heating times of (a) 20 minutes, (b) 40 minutes, and (c) 60 minutes. .. 75
Figure 4-1 (a) Simplified diagram of the CSPonD demonstration facility. (b) CAD model of the
CSPonD demonstration prototype receiver. ................................................................................. 81
Figure 4-2 Diagram of the top view of the thermocouple rod configuration inside the tank. ...... 82
Figure 4-3 Model setup and boundary conditions (plenum not to scale). .................................... 83
Figure 4-4 Distribution of the incident solar irradiation on the final optical element (FOE) for S4,
S6, S8 ordinates discretization. ...................................................................................................... 88
Figure 4-5 Temperature profiles for R1, R3, and R7 line probe locations at 600 seconds for S4, S6,
and S8 ordinates discretization. ..................................................................................................... 90
Figure 4-6 Cross-sectional view of the hexagonal grid of the entire model (a) and of enlarged view
of the refinement region around the MP and DP (b). ................................................................... 92
Figure 4-7 Temperature profiles for R1, R3, and R7 line probe locations at 600 seconds for coarse,
medium, and fine grids. ................................................................................................................ 94
14
Figure 4-8 Average temperature at the salt surface and the mixing plate top surface versus time as
calculated by the CFD model. ....................................................................................................... 95
Figure 4-9 Solar flux bottom output as estimated using ray-tracing [62] and corresponding
polynomial interpolation used as input for the CFD calculations................................................. 96
Figure 4-10 Initial surface irradiation on FOE, salt surface, and MP for spectral band I (solar
spectral band). ............................................................................................................................... 97
Figure 4-11 Initial temperature and velocity distribution for all cases studied. ........................... 98
Figure 4-12 Cross-sectional temperature distribution of all modeled regions after 60 minutes of
solar heating. ................................................................................................................................. 99
Figure 4-13 Temperature distribution of salt cross-section, salt surface, and MP surface after 60
minutes of solar heating. ............................................................................................................. 100
Figure 4-14 Cross-sectional velocity distribution of all modeled regions after 60 minutes of solar
heating. ........................................................................................................................................ 101
Figure 4-15 Cross-sectional velocity distribution of salt region after 60 minutes of solar heating.
..................................................................................................................................................... 102
Figure 4-16 Temperature profiles at location R1 for case 𝜅𝐼,1 = 12.5 𝑚 − 1, 𝜅𝐼𝐼,1 = 3706.9 𝑚 −1 .................................................................................................................................................. 103
Figure 4-17 Temperature profiles at location R1 for case 𝜅𝐼,2 = 5.3 𝑚 − 1,𝜅𝐼𝐼,2 = 135 𝑚 − 1104
Figure 4-18 Temperature profiles at location R1 for case 𝜅𝐼,3 = 2 𝑚 − 1, 𝜅𝐼𝐼,3 = 135 𝑚 − 1 . 105
Figure 4-19 Temperature profiles at location R1 for case 𝜅𝐼,4 = 1 𝑚 − 1, 𝜅𝐼𝐼,4 = 135 𝑚 − 1 . 106
Figure 5-1 Solar pond energy balance and cover concept. ......................................................... 117
Figure 5-2 Validation experiment. Simplified diagram of the experimental setup used for
evaluating the thermal insulation performance of the floating spheres, and 3D representation of the
simulated section. An infrared camera is used to measure the photon flux losses from the surface
of a heated beaker filled with molten salt, with and without floating spheres............................ 120
Figure 5-3 a) Experimental setup for measuring thermal losses from the salt with and without
spheres. b) Image of floating spheres as seen through from the infrared camera position. ........ 121
Figure 5-4 a, Geometry, properties, and boundary conditions of thermal model. b, Sphere
configurations (bottom) for experiment validation. .................................................................... 123
Figure 5-5 Area elements for analytical model thermal conduction resistance evaluation. ....... 126
Figure 5-6 Validation experiment and simulation results. a, Photon flux map to infrared camera
obtained experimentally. Radiosity (b) and temperature distribution (c) at salt and sphere surfaces
calculated numerically. d, Calculated thermal effectiveness of floating spheres versus surface
coverage in laboratory scale experiment and validation simulation. .......................................... 128
Figure 5-7 Geometry, properties, and boundary conditions of thermal model for infinite layer of
hexagonal close-packed (HCP) spheres. ..................................................................................... 130
15
Figure 5-8 Diagram illustrating the simplified analytical model. ............................................... 131
Figure 5-9 Simplified geometry for conduction through layer of spheres. ................................. 133
Figure 5-10 Thermal and transmission performance. a, Thermal effectiveness versus sphere
diameter. b, Transmission efficiency versus sphere diameter. Wall thicknesses in both (a) and (b)
are 1.5 mm for diameters 𝐷𝑜 ≤ 50 𝑚𝑚, and 2.5 mm for diameters 𝐷𝑜 ≥ 60 𝑚𝑚, as specified by
fused silica manufacturer. Transmission calculations and figures were carried out and prepared by
Miguel Diago Martinez. .............................................................................................................. 139
Figure 5-11 Solar pond capture efficiency. Capture efficiency of solar pond with densely packed
HCP cover for 𝐷𝑜 = 20 𝑚𝑚 (a) and 𝐷𝑜 = 100 𝑚𝑚 spheres (b), and with surface temperatures
between 400 °C - 500 °C for 40 wt. % KNO3:60 wt. % NaNO3 binary nitrate molten salt, and
700 °C - 1200 °C for 50 wt. % KCl:50 wt. % NaCl binary chloride molten salt. Dashed lines
represent capture efficiencies without a cover. ........................................................................... 140
Figure 5-12 Capture efficiency comparison between solar central receiver systems and volumetric
receiver for solar concentration C=300 (a) and C=600 (b). Solar central receiver data adapted from
Karni [80]. ................................................................................................................................... 147
Figure A-1 Absorption coefficient of 40 wt. % KNO3: 60 wt. % NaNO3 binary nitrate molten salt
(SQM) at 300 ˚C, 350 ˚C, and 400 ˚C........................................................................................ 161
Figure A-2 Absorption coefficient of decomposed 40 wt. % KNO3: 60 wt. % NaNO3 binary nitrate
molten salt (SQM) at 300 ˚C, 350 ˚C, and 400 ˚C. ..................................................................... 161
Figure E-1 Geometry, properties and boundary conditions of optical model for infinite layer of
hexagonal close-packed (HCP) spheres. ..................................................................................... 167
Figure E-2 Transmission efficiency on binary nitrate molten salt. a, Based on a sphere wall
thickness of 1 mm. b, More generally, as a function of the ratio of the sphere wall thickness to its
diameter....................................................................................................................................... 169
Figure E-3 Transmission efficiency on binary chloride molten salt. a, Based on a sphere wall
thickness of 1 mm. b, More generally, as a function of the ratio of the sphere wall thickness to its
diameter....................................................................................................................................... 170
Figure F-1 Capture efficiency for 40 mm diameter spheres. ...................................................... 172
Figure F-2 Capture efficiency for 60 mm diameter spheres. ...................................................... 173
Figure F-3 Capture efficiency for 80 mm spheres. ..................................................................... 174
Figure H-1 Labelled cross-sectional views of the divider plate (a) and mixing plate (b) designs.
Adapted from Hamer et al. [61]. ................................................................................................. 176
Figure H-2 Equivalent thermal circuit for the axial conduction through the divider plate......... 176
16
List of Tables
Table 2-1 Calculated solar- and re-emission-weighted absorption coefficients and optical
thicknesses based on measured and extrapolated optical properties with L=1 m......................... 48
Table 3-1 Average boundary temperatures calculated for the 1D model and the CFD model for
ℎ = 1 𝑚, 𝜅𝑀𝑆 = 2 𝑚−1, 𝐼𝑜 = 37.5 𝑘𝑊/𝑚2, 𝑇𝑜 = 300 ℃, and 𝑅𝑎𝑅𝐵 ≈ 5 𝑥 1010. ..................... 70
Table 4-1 List of thermal radiative properties and boundary conditions used in the CFD model.85
Table 5-1 Geometrical parameters and calculated properties for experimental validation
simulations .................................................................................................................................. 125
Table 5-2 Molten salt mixture compositions and their corresponding mean densities and
temperature range investigated ................................................................................................... 136
Table 5-3 Estimated heat loss by convection, radiation, and evaporation and comparison of
respective contributions for surfaces at three different temperatures. ........................................ 143
Table 5-4 Error introduced in thermal effectiveness of the cover by neglecting natural convection
as predicted by the analytical model described in Section 5.2.2.1. ............................................ 144
Table 5-5 Error introduced in calculated thermal efficiency of an uncovered receiver by neglecting
natural convection for solar irradiance 𝐺𝑠 ≈ 1𝑘𝑊/𝑚2. ............................................................. 145
Table 5-6 Capture efficiency with covers of 0 mm, 20 mm, and 100 mm diameter spheres at three
operating temperatures and corresponding to the breakeven solar concentration required to achieve
non-negative capture efficiency without a cover ........................................................................ 146
Table H-1 Effective thermophysical properties of divider plate and mixing plate in thermal model.
..................................................................................................................................................... 178
17
Nomenclature
Symbol Description Typical units
𝐴𝑚 Solar-weighted absorption factor -
𝐴𝑟𝑒𝑐 Surface area of the receiver exposed to solar irradiance m2
𝐶 Solar concentration ratio -
𝐶1 First radiation constant, W nm4 m-2
𝐶2
Second radiation constant
nm K
cp Specific heat J kg-1 K-1
𝐷𝑜 Sphere outer diameter mm
𝐹 View factor -
g Gravitational acceleration m s-2
𝐺𝑠 Solar irradiance kW m-2
ℎ𝑐𝑜𝑛𝑣 Convective heat transfer coefficient W m-2 K-1
ℎ𝑛𝑐̅̅ ̅̅ Heat transfer coefficient for natural convection W m-2 K-1
𝐻𝑠𝑖𝑛𝑘 Sink depth mm
𝐻𝑐𝑦𝑙 Cylinder length mm
Δ𝐻𝑣𝑎𝑝 Enthalpy of vaporization J/g
𝐼𝑏𝜆 Spectral blackbody intensity W m-2 μm-1
𝐼𝜆 Spectral intensity W m-2 μm-1
𝑘 Thermal conductivity W m-1 K-1
𝐿 Thickness of equivalent insulation layer mm
𝐿 Actual thickness of fluid layer m
𝐿𝑚 Average mean beam length m
𝐿𝑒,𝑆 Mean beam length through fluid thickness in solar spectrum m
𝐿𝑒,𝐸 Mean beam length through fluid thickness in re-emission spectrum m
𝑙 Characteristic length of receiver for convection m
�̇� Rate of mass transfer kg s-1
𝑛 Refractive index -
𝑁 Number of spheres -
𝑁 Conduction-to- radiation parameter -
𝑁𝑢𝑙̅̅ ̅̅ ̅ Average Nusselt number -
P Pressure Pa
Pr Prandtl number -
𝑞 Heat flux kW m-2
�̇� Rate of heat transfer kW
𝑅 Thermal resistance K W-1
R Reflectance -
𝑅𝑟𝑒𝑐 Receiver solar reflectance -
𝑅𝑎𝑙 Rayleigh number -
�̅� Average path length mm
s Geometric path length
�̇� Volumetric heat generation W m-3
t Wall thickness mm
18
t Time s
𝑇 Temperature °C
�̅�𝑜𝑝 Average operating temperature °C
𝑢𝑖 Velocity component in direction i m s-1
𝒗 velocity m s-1
∆𝑥𝑖 Fluid pathlength m
Greek letters
𝛼 Thermal diffusivity m2 s
β Coefficient of thermal expansion K-1
𝛽𝜆 Spectral attenuation coefficient m-1
𝜖 Emissivity -
𝜖𝑠 Cover thermal effectiveness -
𝜅 Absorption coefficient m-1
𝜅𝑀𝑆 Solar-weighted absorption coefficient m-1
𝜅𝑀𝐸 Re-emission-weighted absorption coefficient m-1
𝜆𝑜 Vacuum wavelength μm
𝜆 =𝜆𝑜
𝑛 Wavelength inside medium
μm
𝜈 Kinematic viscosity m2 s-1
𝜂𝑐 Capture efficiency -
𝜂𝑡ℎ Thermal efficiency -
𝜃 Irradiation half-angle °
𝛿𝑡 Themal boundary layer thickness mm
𝜌 Reflectivity -
𝜌 density kg m3
𝜌∗ Apparent reflectivity -
𝜌∥ Parallel-polarized reflectivity component -
𝜌⊥ Perpendicular-polarized reflectivity component -
𝜎 Stefan-Boltzmann constant W m-2 K-4
𝜎𝑠 Scattering coefficient m-1
𝜏 Optical thickness -
𝜏𝑀𝑆 Solar-weighted optical thickness -
𝜏𝑀𝐸 Re-emission-weighted optical thickness -
τ𝑟𝑒𝑐 Receiver transmittance -
𝜏 Transmissivity -
𝜏∗ Apparent transmissivity -
𝜇 Dynamic viscosity mPa s
𝜑 Surface coverage -
Φ𝑖 Photon flux at pixel 𝑖 m-2 s-1
Subscripts
𝑎𝑏𝑠 Absorption
𝑐𝑜𝑛𝑑 Conduction heat transfer
𝑐𝑜𝑛𝑣 Convective heat transfer
𝑒𝑓𝑓 Effective
𝑒𝑣𝑎𝑝 Evaporative losses
𝑐𝑦𝑙 Cylinder
𝑖 Pixel index
19
𝑙𝑜𝑠𝑠 Thermal loss
𝑚 Mixing layer
𝑝𝑟𝑜𝑗 Projected surface
𝑞 Quiescent
𝑟𝑎𝑑 Radiative heat transfer
𝑟𝑒𝑐 Receiver air-salt interface
𝑟𝑒𝑓 Reference situation with no cover
𝑠 Molten salt surface
𝑠𝑎𝑙𝑡 Salt surface
𝑠𝑎𝑙𝑡 − 𝑠𝑝ℎ𝑒𝑟𝑒 Salt-sphere interface
𝑠𝑝 Sphere
𝑡𝑜𝑡 Total
𝑣 Virtual surface
𝑤 Wall
∞ Environment
Abbreviations
IR Infrared
OD Outside diameter
VHT Very high temperature
20
1. Introduction
Concentrating solar power (CSP) technologies generate solar power by concentrating natural
sunlight from a larger area onto a smaller area using mirrors. This concentrated sunlight can be
converted into heat (solar thermal energy), which in turn can be used to drive a heat engine to
produce power. CSP technologies paired with highly cost-effective thermal energy storage (TES)
have proven to be viable sources of dispatchable renewable power [1]. The most widely
demonstrated technology is the two-tank molten salt system [2,3], but despite its low-cost energy
storage and dispatchability, two-tank molten salt technologies still suffer from major limitations
due to the elevated costs associated with high pumping requirements, heat tracing, long-term
durability, and low capture efficiencies [4].
Liquid-based direct absorption receivers (DAR) eliminate many of the problems associated with
the two-tank design by directly irradiating a semi-transparent, volumetrically absorbing fluid. Heat
is therefore generated directly in the heat transfer fluid, which allows to achieve better temperature
uniformity within the heat transfer fluid, effectively reducing hot spots and thermal stresses.
Furthermore, surface temperatures associated with emissive losses are expected to decrease with
respect to the bulk, which in turn increases the efficiency of the system [5]. In particular, the
Concentrated Solar Power on Demand (CSPonD) concept [6] is a collocated receiver and storage
system which consists of an open tank of volumetrically absorbing, semi-transparent molten salt,
directly irradiated with concentrated sunlight, as illustrated in Fig. 1. In this design, the receiver
and hot and cold storage tanks are all integrated into a single-tank system that does not require
high-pressure, high-flow molten salt pumps, or significant heat tracing, and allows to store heat at
high temperature. The receiver consists in an open tank of molten salt with a divider plate
separating a hot layer of salt (top) from a cold layer of salt (bottom). During on-sun operation, the
21
free surface exposed to the environment is directly irradiated with sunlight as shown in Fig. 1.a. A
small fraction of incoming solar radiation is reflected at the salt surface, while the remaining
unreflected fraction penetrates the surface where it is absorbed volumetrically throughout the semi-
transparent molten salt and by the divider plate and tank walls. Actuators allow control of the
divider plate height, and an annulus between the divider plate and tank walls allows salt to move
from the cold layer to the hot layer and vice versa. During the day, the height of the divider plate
decreases to allow cold salt to flow to the hot salt layer as the hot salt layer charges. Hot salt is
continuously extracted from the top of the tank at relatively constant temperature and pumped to
a heat exchanger to extract heat for power generation. The cold (liquid) molten salt exiting the heat
exchanger is then sent back to the bottom of the tank. During night-time operation (Fig. 1.b), the
tank is closed to minimize thermal losses to the environment, and hot salt continues to be extracted
from the top layer and pumped to a heat exchanger. The divider plate height therefore increases as
the stored excess thermal energy decreases during the discharge phase.
(a) (b)
Figure 1-1 Cross-section of the general CSPonD molten salt receiver concept during (a) on-sun operation at the end
of the day, and (b) after a prolonged period with continued heat extraction but without solar heating.
22
1.2. CSPonD Demonstration Project Test Facility
The present work was carried out in the context of the development and construction of the
CSPonD Demonstration project at the Masdar Institute Solar Platform. A photo and a simplified
diagram of the receiver concept with integrated TES are shown in Fig. 1.2. The 100 kW beam-
down tower facility consists in a field of ground-based heliostats which track and concentrate
sunlight during the day to an array of central reflectors located at the top of a tower as shown in
Fig. 1.2.a. The central reflectors beam the concentrated solar radiation through a final concentrator
(Final Optical Element – FOE) [7] to an open aperture, and directly into an open tank of molten
salt located on a ground structure.
The open tank of molten salt includes a divider plate (DP) which separates the hot layer of liquid
(top) from the cold layer (bottom). A thin mixing plate (MP) positioned approximately 10 cm
above the DP during normal operation can be rapidly actuated to mix the salt in the event of large
temperature gradients resulting from unexpected localized overheating.
24
When the system is off-sun, the tank is closed with an insulating lid to reduce heat losses and to
protect the salt during inclement weather such as desert sand storms. During on-sun operation, the
incident concentrated solar radiation penetrates the salt where it is primarily absorbed
volumetrically. The remaining radiation that is not absorbed by the salt is absorbed by the tank
walls and the MP. The absorbed solar radiation is converted into heat and allows the salt
temperature to increase during the day as it stores excess thermal energy.
Design and construction of the CSPonD demonstration prototype shown in Fig. 2a was recently
completed at the Masdar Institute Solar Platform in Abu Dhabi [8,9]. The prototype has been in
operation since the completion of the construction, and the concept was successfully demonstrated
experimentally by thermally cycling molten salt between 280 °C and 450 °C during daily
charging/discharging cycles. Nevertheless, the molten salt receiver is subjected to volumetric
heating conditions that produce complex thermal and flow behavior within the salt that remain
poorly understood [10] and limits the ability to make accurate thermal-hydraulics predictions. The
desired temperature profile within the hot salt layer could not be predicted and was therefore
maintained using feedback controls for the divider plate motion. Improving our understanding of
complex heating and flow conditions in direct absorption, liquid-based volumetric receivers is
therefore necessary to further improve the design and operation of this technology which remains
in its early stages of development.
1.3. Participating media and natural convection in internally heated fluids
The interaction of a material with thermal radiation depends on its optical properties. For semi-
transparent liquids such as molten salts, thermal radiation emitted within the fluid itself or from an
external source travels an appreciable distance within the fluid between interactions. Such media
25
are known as participating media. Their interaction with thermal radiation is in contrast with
transparent media which involve only surface interactions at the boundaries, known as surface-to-
surface radiation. The radiation transport in participating media is governed by the radiative
transfer equation, given as
𝑑𝐼𝜆
𝑑𝑠= 𝜅𝜆𝐼𝑏𝜆 − 𝛽𝜆𝐼𝜆 +
𝜎𝑠𝜆
4𝜋∫ 𝐼𝜆(�̂�𝑖)Φ𝜆(�̂�𝑖
4𝜋
, �̂�)𝑑Ω𝑖 (1.1)
where 𝜅𝜆 is the spectral absorption coefficient, 𝜎𝑠𝜆 is the spectral scattering coefficient, 𝛽𝜆 = 𝜅𝜆 +
𝜎𝑠𝜆 is the spectral attenuation coefficient and is expressed as the sum of the absorption and
scattering coefficients, 𝛺 is the solid angle, 𝜆 is the wavelength, 𝐼𝑏𝜆 is the spectral blackbody
radiative intensity, 𝐼𝜆 is the radiative intensity, and 𝑠 is the path. For non-scattering liquids (𝜎𝑠𝜆 ≈
0), the radiative transfer equation reduces to
𝑑𝐼𝜆
𝑑𝑠≈ 𝜅𝜆(𝐼𝑏𝜆 − 𝐼𝜆) (1.2)
When an external source of radiation such as the sun is incident upon a participating media’s
boundary, this radiation will penetrate and be absorbed within the volume of the medium, resulting
in volumetric heat generation. This volumetric heat generation is described by the radiative flux
equation, given as
𝛻 ∙ 𝒒𝑹 = ∫ 𝜅𝜆 (4𝜋𝐼𝑏𝜆 − ∫ 𝐼𝜆𝑑𝛺4𝜋
)∞
𝜆=0
𝑑𝜆 (1.3)
26
In the case of a liquid-based, direct absorption receiver, incident solar flux penetrates the liquid
surface where it is absorbed volumetrically by the semi-transparent liquid. The volumetric
absorption generates internal heating that decays with increasing depth from the molten salt’s
irradiated surface. If the incident solar energy is approximately normal to the liquid surface, the
volumetric heat generation �̇� will given as
�̇� ≈ 𝜅𝑀𝑆𝐺𝑠𝑒−𝜅𝑀𝑆𝑧 (1.4)
where 𝜅𝑀𝑆 is the solar weighted absorption coefficient, 𝐺𝑠 is the direct normal solar irradiance, and
𝑧 is the depth from the surface. The amount and distribution of solar energy absorbed directly by
the liquid therefore depends on its absorption properties. The remaining unabsorbed solar energy
that penetrates the salt is absorbed (or reflected) by the tank walls. Due to the combination of
volumetric heating and surface heating, two layers develop within the fluid as shown in Fig. 1.3:
(1) a stagnant, thermally stratified upper layer where the bulk of volumetric heating occurs, and
(2) a colder unstable bottom layer where the fluid is heated from below from the remaining solar
radiation absorbed by the bottom surface, and the competing volumetric heating is weak such that
natural convection develops. The flow inside the receiver resulting from internal heating implies
that the governing equations describing the flow inside the receiver given as
𝜕𝒗
𝜕𝑡+ 𝒗 ∙ 𝛻𝒗 = −
1
𝜌𝛻𝑝 + 𝜈𝛻2𝒗 − 𝐠𝛽𝑇 (1.5)
𝛻 ∙ 𝒗 = 0 (1.6)
are strongly coupled to the radiative transfer equations through the energy equation which depends
on the radiative flux (Eq. 1.3) such that
27
𝜌𝑐𝑝
𝜕𝑇
𝜕𝑡+ 𝜌𝑐𝑝𝒗 ∙ 𝛻𝑇 = 𝛻 ∙ (𝑘𝑐𝛻𝑇) − 𝛻 ∙ 𝒒𝑹 (1.7)
where 𝑡 is time, 𝒗 is the velocity vector with respect to the 3D coordinate system, 𝜌 is density, 𝑝
is the static pressure, 𝜈 is the kinematic viscosity, 𝐠 is the gravitational acceleration vector, 𝛽 is
the thermal expansion coefficient of the fluid, 𝑇 is the temperature, 𝑐𝑝 is the specific heat, and 𝑘𝑐
is the thermal conductivity.
(a)
(b)
Figure 1-3 (a) Illustration of the expected thermal behaviour inside the receiver. The internal heating
produces two layers in the receiver: a thermally stratified and stagnant upper layer, and an unstable
bottom mixing layer. The semi-transparent hot salt. (b) Illustration of a re-emitting participating media.
The occurrence of a natural convection layer penetrating into a stable, stratified fluid is commonly
referred to as penetrative convection [11]. Penetrative convection and internal heat generation are
28
present in a wide variety of geophysical and astrophysical phenomena such as convection resulting
from solar heating in the atmosphere, oceans, lakes and reservoirs [11,12], stellar convection [13],
and volumetrically absorbing solar receivers. Convection generated by internal heating is also an
important heat transfer process in several nuclear reactor applications such as heat generation in
spent nuclear pools and during post-accident heat removal [14–16].
Previous analyses of the thermal-fluid behavior of liquid filled cavities with solar radiation
absorption have typically been limited to 2D numerical studies of isolated cavities [17–19], and in
some cases neglect the effects of convection entirely [20]. In addition, studies of radiation induced
convection are typically concerned with low temperature applications such as absorption in water
bodies, and do not allow for the possibility of internal re-radiation. In particular, Hattori et al. [21]
developed an analytical solution for the nonlinear temperature stratification and its effects on
internal mixing for water bodies subjected to heating by solar radiation. The two-dimensional
analysis was carried out for a simple adiabatic surface boundary condition and was validated
numerically. None of the previous investigations model a solar receiver under real operating
conditions and limited analytical and computational tools exist for making predictions for better
design and optimization. Furthermore, analyses have been limited to low temperature water
applications and do not account for the significant effects of radiative cooling at the surface. The
fundamental numerical and scaling analyses provide insufficient insight into complex behavior of
the system and the design and operation of a receiver.
1.4. Molten Salts
Typical solar collectors absorb incident solar radiation through surface absorbers before
transferring this radiation as thermal energy to a working fluid or storage material. The CSPonD
29
concept uses a volumetrically absorbing high temperature fluid as storage medium and working
fluid as an alternative solar absorption approach which allows incident solar radiation to be directly
absorbed and stored by the working fluid and eliminates the need for intermediate surface
absorbers. This alternative absorption and storage method allows to increase performance and
efficiency [5,20,22]. In addition, the use of a high temperature working fluid allows to increase
operating temperatures (𝑇𝐻), leading to higher heat engine efficiencies, which in turn reduces the
Levelized Cost of Electricity (LCOE). This is clearly seen in Fig. 4, illustrating how the maximum
thermal efficiency of a heat engine 𝜂𝑡ℎ,𝑚𝑎𝑥~1
𝑇𝐻 and can therefore be increased by increasing the
heat engine’s maximum temperature 𝑇𝐻.
Figure 1-4 Ideal Carnot heat engine and associated maximum thermal efficiency based on oK. Increasing the
maximum operating temperature TH using high temperature liquids such as molten salts allows to increase the
maximum possible heat engine efficiency.
Molten salts are excellent candidate high temperature fluids to be used as direct absorbers since
they are semi-transparent liquids which do not necessarily require nanoengineered particle
suspensions to tailor their optical properties [20] for solar absorption. They are generally low cost
and have heat capacities similar to water such that they can store large amounts of thermal energy
at high temperature. In addition, molten salts generally have low vapor pressures and many can
30
safely be used in open baths, in contrast with synthetic oils which are typically too hazardous to
use in open environments. Molten salts are in fact used in an increasing number of energy
applications including Generation IV nuclear reactors [23] and for thermal energy storage (TES)
[4].
The candidate molten salts generally behave as semi-transparent participating media. Radiative
heat transfer is therefore expected to be a dominating mechanism for heat absorption and transport
within the salts and their absorption properties are required to characterize their thermal behavior
as previously discussed. The CSPonD Demo prototype uses a 40 wt. % KNO3:60 wt. % NaNO3
binary nitrate molten salt mixture (solar salt) [9] for which measured absorption properties are
only available for wavelengths from 400 nm to 800 nm [24] for high purity salts that do not
accurately capture the behavior of commercial salts used under real operating conditions. In
contrast with the typically smaller volumetrically absorbing solar receiver designs and the
associated optical property data available [25–27], Slocum et al. [6] have proposed a large scale
commercial CSPonD design 5 m deep × 25 m diameter and consider the use of chloride salts
which commonly operate at 900 ˚C. Ideal solar penetration depths for such volumetrically
absorbing systems should closely match the depth of the absorber liquid, requiring the ability to
measure nearly-transparent high-temperature materials. However, typical methods for measuring
the optical properties of liquids use reflectance techniques [28,29] with small sample thicknesses
(≤ 10 mm). The measurement resolution for these techniques is typically > 100 m-1 which does not
accurately capture the properties of nearly transparent liquids. In addition, these techniques are
often used in conjunction with spectrometers [24,30,31] which do not provide accurate
measurements for high temperature materials at infrared wavelengths. The high operating
temperatures also suggest participating media effects within the salts are non-negligible, further
31
emphasizing the necessity of measuring optical properties over a wider spectral range extending
into the mid-infrared spectrum. It is therefore of great value to characterize the solar absorption,
the internal re-emission, and the radiative losses for these systems at elevated temperatures.
1.5. Thermal losses in open tanks of molten salt
The benefits of operating solar-receivers at higher temperatures are often offset by significant
thermal losses, particularly for relatively low solar concentration ratios 𝐶 [32] in an open-tank
configuration. This can be understood in terms of the receiver thermal efficiency 𝜂𝑡ℎ, defined as
the ratio of collected thermal energy to total incident solar energy [20], which is given by
𝜂𝑡ℎ =�̇�𝑎𝑏𝑠 − �̇�𝑙𝑜𝑠𝑠
𝐶𝐺𝑠𝐴𝑟𝑒𝑐 (1.8)
where �̇�𝑎𝑏𝑠 is the solar power absorbed by the receiver, 𝐶 is the solar concentration ratio, 𝐺𝑠 is
the direct normal irradiance, 𝐴𝑟𝑒𝑐 is the surface area of the receiver exposed to the concentrated
solar irradiation, and �̇�𝑙𝑜𝑠𝑠 is the sum of the convective, conductive, evaporative, and radiative
heat losses to the environment. For a sufficiently deep receiver with highly absorbing containment
walls, most of the non-reflected incident energy is absorbed such that �̇�𝑎𝑏𝑠 ≈ (1 − 𝑅𝑟𝑒𝑐)𝐶𝐺𝑠𝐴𝑟𝑒𝑐,
where 𝑅𝑟𝑒𝑐 is the receiver’s solar reflectance, and the thermal efficiency becomes
𝜂𝑡ℎ ≈ (1 − 𝑅𝑟𝑒𝑐) −�̇�𝑐𝑜𝑛𝑣
𝑙𝑜𝑠𝑠 + �̇�𝑒𝑣𝑎𝑝𝑙𝑜𝑠𝑠 + �̇�𝑟𝑎𝑑
𝑙𝑜𝑠𝑠
𝐶𝐺𝑠𝐴𝑟𝑒𝑐 (1.9)
For moderate to low solar concentration ratios, thermal losses, and in particular radiative losses
�̇�𝑟𝑎𝑑𝑙𝑜𝑠𝑠 at high temperature, will be significant relative to the total incident concentrated solar energy
𝐶𝐺𝑠𝐴𝑟𝑒𝑐, resulting in low thermal efficiencies.
32
In addition to impeding the capture efficiency of a receiver, the large thermal losses at the liquid
surface also lead to very large thermal gradients near the salt surface as illustrated in Fig. 3. The
temperature at the surface will typically be significantly reduced due to radiative cooling, and the
temperature rapidly increases in only a few centimeters immediately below the liquid surface
where the volumetric heating is strongest.
Many methods have been explored to mitigate these losses in a wide variety of solar-thermal
applications [33–39]. In particular, spectrally selective surface absorbers are engineered to
maximize solar absorptivity and minimize thermal radiative losses [40–42]. High temperature
open-top liquid-based receivers such as the CSPonD have large radiative and convective losses
that are much more challenging to manage. Standard methods for reducing losses such as reflective
cavities [33,34] and windows [36,39] cannot readily be implemented in open-tank configurations,
and their effectiveness is limited due to fabrication, cost, and operation constraints especially in a
desert environment [43,44].
1.6. Objectives
In order for liquid-based direct absorption volumetric solar receivers to become competitive CSP
energy technologies, the efficiency and operation must be improved in order to reduce capital and
operation costs. The complex nature of internally heated fluids and the unique open-tank design at
high temperature are major challenges in optimizing the design and operation in volumetrically
absorbing solar receiver. A complete thermal-hydraulics analysis will therefore provide significant
insight into the complex thermal-fluid behavior of the receiver, allowing to identify optimal
operating conditions and to prevent critical system failures due to thermal stresses and thermal
degradation resulting from large temperature non-uniformities.
33
1.6.1. Scope of thesis
Given the importance in solar receiver design and the limited studies available for predicting the
thermal behavior in volumetrically absorbing solar receivers, this thesis focuses on characterizing
and improving the thermal-hydraulic design and operation of a CSPonD receiver. In addition, the
design of a transparent cover created from hollow quartz spheres is presented as a means to reduce
thermal losses. This work was carried out in collaboration with researchers in the Nuclear and
Mechanical Engineering departments at MIT, and with Prof. Nicolas Calvet’s research group at
the Masdar Institute Solar Platform in Abu Dhabi. The broader scope of the project was the
development and construction of the CSPonD Demonstration Project at the Masdar Institute Solar
Platform which was completed and went into operation in June 2017.
The thesis focuses on four main aspects as illustrated in Fig. 1.5: (1) fundamental molten salt
properties, (2) theoretical analysis, (3) computational modeling, and (4) thermal design
improvements. Chapter 2 describes the experimental apparatus developed and used for measuring
the optical properties of nearly-transparent, high temperature liquids, and presents the
measurement results. Chapter 3 outlines the fundamental thermal-fluid scaling parameters in the
receiver and presents theoretical analysis of the optimal operation and design conditions. Chapter
4 presents the computational fluid dynamics (CFD) and heat transfer model of the entire receiver
using the measured optical properties presented in Chapter 2, and compares the results with
experimental results collected at the CSPonD Demonstration Project test facility. Chapter 5 details
the design of a solar-transparent, modular molten salt cover for insulating the open tank receiver
to improve the thermal efficiency and increase the temperature uniformity. Finally, Chapter 6
summarizes the critical take-aways from the presented work and outlines future research paths.
34
Figure 1-5 Illustration summarizing the four principal thermal-fluid topics investigated in this thesis.
35
2. Molten salt optical properties measurements
In this section, we present a simple and accurate apparatus that allows for the precise measurement
of light attenuation in high temperature, nearly transparent liquids, over a broad spectrum
extending from the visible region (400 nm) into mid-infrared (8 µm). The apparatus is used to
measure the attenuation of light in the 40 wt. % KNO3:60 wt. % NaNO3 binary nitrate and the
50 wt. % KCl:50 wt. % NaCl binary chloride molten salt mixtures. The effects of salt
contamination due to thermal decomposition are also evaluated. Sources of contamination in the
CSPonD include thermal decomposition due to unexpected heating conditions and local hot spots,
and sand/dust contamination due to the open receiver design. The implications of the results are
discussed in the context of the CSPonD Demo and for general volumetrically absorbing solar
receiver applications.
2.1. Experimental Procedure
2.1.1. Apparatus description
The attenuation coefficient is a function of temperature and wavelength and is expressed in terms
of absorption and scattering as:
𝛽(𝑇, 𝜆𝑜) = 𝜅(𝑇, 𝜆𝑜) + 𝜎𝑠(𝑇, 𝜆𝑜) (2.1)
where 𝛽(𝑇, 𝜆𝑜) is the attenuation coefficient, 𝜅(𝑇, 𝜆𝑜) is the absorption coefficient, and 𝜎𝑠(𝑇, 𝜆𝑜)
is the scattering coefficient, each evaluated at temperature 𝑇 and (vacuum) wavelength 𝜆𝑜. There
are several ways of measuring the attenuation coefficient. The method selected in this work
evaluates the attenuation coefficient by measuring and comparing the transmission of light through
different material thicknesses and relating them via Beer-Lambert's Law:
36
𝛽(𝑇, 𝜆𝑜) =
−1
∆𝑥𝑗 − ∆𝑥𝑖ln (
𝐼𝑗(𝑇, 𝜆𝑜)
𝐼𝑖(𝑇, 𝜆𝑜))
(2.2)
where 𝐼𝑖(𝑇, 𝜆𝑜) and 𝐼𝑗(𝑇, 𝜆𝑜) are the measured transmitted outgoing intensities measured by the
detector for corresponding path lengths ∆𝑥𝑖 and ∆𝑥𝑗 through the fluid at temperature 𝑇 , for a
constant collimated incoming light source 𝐼𝑜(𝜆𝑜) perpendicularly incident to the cuvette windows.
To carry out the optical measurements, the furnace based apparatus developed by Passerini[24,31]
was modified and adapted to be used in conjunction with a Bruker VERTEX 70 Fourier Transform
Infrared (FTIR) spectrometer with a 150W tungsten lamp externally adapted light source, which
replaces the integrating sphere and spectrometer in the original experimental setup. FTIRs operate
over a much wider spectral range than dispersive infrared spectrometers used in previous studies.
One of the main disadvantages of dispersive methods is that the radiation emitted by the apparatus
at high temperatures inevitably contributes to the overall IR radiation signal for temperatures above
700 °C.
37
Figure 2-1. Simplified diagram of apparatus used to measure the attenuation of light intensity by liquids.
The apparatus consists of a vertically oriented and electrically heated split tube furnace. Two
coaxial quartz cuvettes are positioned inside the furnace. Both cuvettes are closed at the bottom
with fire polished quartz windows. The sample fluid is added to the outer cuvette only and the
inner cuvette is partially immersed in the fluid and has an adjustable vertical position. Attenuation
38
measurements can therefore easily be made for different fluid thicknesses by adjusting the inner
cuvette’s height. Heights of up to 10 cm provide the sensitivity required to measure the nearly
transparent salt’s attenuation coefficient. The double cuvette design is also advantageous because
it minimizes vibrational issues by eliminating the free surface of the fluid from the beam path. A
schematic of the apparatus is shown in Fig. 2.1 and a picture of the apparatus is presented in
Fig. 2.2.
As illustrated in the diagram, the outgoing intensities are measured by the FTIR detector for
different path lengths through the liquid. The selected double cuvette design and method for
calculating attenuation coefficient eliminate the effects of surface reflections at the cuvette
interfaces and any effects from impurities deposited at the bottom of the cuvette. Impurity deposits
correspond to a constant attenuation over all path lengths and do not contribute to the volumetric
attenuation. A radiation shield was required for the much higher temperature chloride in order to
prevent undesirable photons emitted by the hot fluid surface from saturating the detector. The
radiation shield is made of refractory material wrapped in aluminum foil with a small aperture in
the center allowing the light source to pass through. The design can also be extended to
wavelengths between 2.5 µm and 5.0 µm where quartz is only partially transmissive since its
attenuation is constant at all path lengths. For measurements at wavelengths greater than 5.0 µm,
the quartz windows would be replaced with a more optically transmissive window material such
as diamond, zinc selenide, or calcium fluoride. Window material selection will also depend on its
compatibility with the measured fluid.
39
Figure 2-2 Picture of the experimental apparatus for measuring the attenuation of light of high temperature liquids.
2.1.2. Mixture preparation
Refined grade sodium and potassium nitrate salts (>99.5 % purity) were provided by SQM and
pre-mixed to obtain a 40 wt. % KNO3:60 wt. % NaNO3 binary nitrate molten salt mixture. Sodium
and potassium chloride salts (>99.0% purity) were purchased separately from Alfa Aesar
(https://www.alfa.com/en/ product numbers #12314 and #11595) and pre-mixed to obtain a
50 wt. % KCl:50 wt. % NaCl binary chloride molten salt mixture. None of the salts contained anti-
caking agents.
The salts are then dried in an oven at 50 ˚C for at least 1 hour to remove excess moisture before
being loaded in the outer cuvette. A K-type thermocouple positioned at the mid-height of the
40
furnace on the outer wall of the outer cuvette is connected to a temperature controller, which
controls the furnace output and allows the salts to be heated at a slow and steady rate to a set
temperature. Passerini and McKrell[31] characterized the axial variation in temperature along the
outer cuvette and reported a maximum deviation of 10%.
Thermal decomposition of the binary nitrate molten salt mixture was achieved by raising the
temperature of the molten salt to 550 ˚C (open system decomposition temperature[45]) for
45 minutes. Bubbling was observed during decomposition and the salt developed a green tint. The
results for the three salts investigated are shown in Fig. 2.3. in their molten state.
(a) (b) (c)
Figure 2-3 40 wt. % KNO3:60 wt. % NaNO3 binary nitrate molten salt mixture at 400 ˚C (a), decomposed binary
nitrate molten salt mixture at 400 ˚C (b), and 50 wt. % KCl:50 wt. % NaCl binary chloride molten salt mixture at
400 ˚C (c).
41
2.1.3. Measurement procedure
Once the salt mixture has melted, the inner cuvette is moved to its lowest position corresponding
to approximately 1-2 cm of liquid thickness, and a transmission spectrum is acquired at each
vertical position in 5 mm increments up to its highest position. Once the maximum position is
reached, the cuvette is lowered and the measurements are taken again in 5 mm downward
increments to ensure repeatability of the collected data versus depth. In total, measurements were
taken twice for 10 to 20 different path lengths. In addition, the measurements were acquired for
three different salt temperatures for the nitrate mixture: 300 ˚C, 350 ˚C, and 400 ˚C, and at 800 ˚C
for the chloride mixture due to its weak temperature dependence as will be discussed. The
transmission spectrum scanning resolution is 8 cm-1 (< 5 nm resolution over the measured
spectrum). Error bars are only given every 25 nm for clarity. In addition, a moving average filter
with a maximum size of 160 cm-1 (< 20 nm) was used in the visible spectrum to compensate for
the noise in the signal.
2.2.3. Thermal performance evaluation
To understand the thermal behavior of the salt and in particular the radiative heat transfer within
the different media, we consider three factors: the general participating media behavior, the
volumetric absorption, and the effective emissivity. The latter two can be considered together in
the capture efficiency. We first define solar-weighted and re-emission-weighted absorption
coefficients and optical thicknesses for the fluids, given as
𝜅𝑀𝑆 =
∫ 𝐺𝑠𝜅𝜆𝑜𝑑𝜆𝑜
∞
0
∫ 𝐺𝑠𝑑𝜆𝑜∞
0
, (2.3)
42
𝜅𝑀𝐸 =
∫ 𝐼𝑏𝜆𝑜(�̅�𝑜𝑝)𝜅𝜆𝑜
𝑑𝜆𝑜∞
0
∫ 𝐼𝑏𝜆𝑜(�̅�𝑜𝑝)𝑑𝜆𝑜
∞
0
, (2.4)
𝜏𝑀𝑆 = 𝜅𝑀𝑆𝐿𝑒,𝑆 and 𝜏𝑀𝐸 = 𝜅𝑀𝐸𝐿𝑒,𝐸 (2.5)
where 𝐺𝑠 is the spectral solar irradiance[46], 𝜅𝜆𝑜 is the measured spectral absorption coefficient of
the fluid, 𝐿𝑒,𝑆 and 𝐿𝑒,𝐸 are the mean beam lengths through the fluid thickness, and 𝐼𝑏𝜆𝑜(�̅�𝑜𝑝) is the
spectral emissive blackbody intensity inside the fluid at its average operating temperature �̅�𝑜𝑝,
given by Planck’s Law:
𝐼𝑏𝜆(�̅�𝑜𝑝) =
𝐶1
𝜋𝑛2𝜆5[𝑒 𝐶2 (𝑛𝜆�̅�𝑜𝑝)⁄ − 1]
(2.6)
where 𝐶1 and 𝐶2 are the first and second radiation constants, 𝑛 is the index of refraction of the
fluid, and 𝜆 are wavelengths inside the medium, defined as 𝜆 =𝜆𝑜
𝑛. In the optically thick limit
where 𝜏 → ∞, the medium behaves as an opaque body with negligible participating media effects,
and the heat flux at the surface approaches the same value as for a blackbody radiator[47,48]. In
the limit where 𝜏 ≪ 1, the medium is said to be optically thin and its re-emitted radiation travels
long distances without being absorbed by itself. In this work, we assume scattering to be
negligible[26] and take the absorption coefficient to be approximately equal to the measured
attenuation coefficient.
The solar absorption performance can be characterized by evaluating the solar-weighted
absorption factor. The value yields the percentage of incoming solar energy absorbed by the
medium for a given thickness[25] and is defined as:
43
𝐴𝑚 =
(1 − 𝑅) ∫ 𝐺𝑠(1 − 𝑒−𝜅𝜆𝑜𝐿𝑒,𝑆)𝑑𝜆𝑜∞
0
∫ 𝐺𝑠𝑑𝜆𝑜∞
0
(2.7)
where 𝑅 is the reflectance at the surface. The radiative losses to the environment are characterized
by the total emissivity of an isothermal fluid layer of thickness 𝐿𝑒,𝐸 given as
𝜖(𝐿𝑒,𝐸 , �̅�𝑜𝑝) = (
∫ 𝐼𝑏𝜆𝑜(�̅�𝑜𝑝)(1 − 𝑒−𝜅𝜆𝑜𝐿𝑒,𝐸)𝑑𝜆𝑜
∞
0
∫ 𝐼𝑏𝜆𝑜(�̅�𝑜𝑝)𝑑𝜆𝑜
∞
0
) (2.8)
Finally, we evaluate the capture efficiency of the medium as
𝜂𝑐 =
(1 − 𝑅) ∫ 𝐺𝑠(1 − 𝑒−𝜅𝜆𝑜𝐿𝑒,𝑆)𝑑𝜆𝑜∞
0
∫ 𝐺𝑠𝑑𝜆𝑜∞
0
−𝑞𝑠
𝐶 ∫ 𝐺𝑠𝑑𝜆𝑜∞
0
= 𝐴𝑚 −𝑞𝑠
𝐶 ∫ 𝐺𝑠𝑑𝜆𝑜∞
0
(2.9)
where 𝐶 is the solar concentration factor. 𝑞𝑠 is the heat flux at the surface of the isothermal
medium, assuming a vacuum boundary condition at the surface, and is defined as
𝑞𝑠 = 𝜖(𝐿𝑒,𝐸 , �̅�𝑜𝑝)𝑛2𝜎�̅�𝑜𝑝4 (2.10)
where 𝑛 is the refractive index of the medium and 𝜎 is the Stefan-Boltzmann constant.
In this work, we take the average operating temperature as 400 ˚C for the binary nitrate and 800 ˚C
for the binary chloride. From the Kramers-Krönig dispersion relations[47,49–51], the refractive
index has wavelength dependence related to the absorption properties, with only small variations
away from the absorption peaks. The chloride-based salts are therefore not expected to show large
variation in n below 14 µm. Furthermore, experimental evidence from Makino[52] confirms
negligible n-variation in the nitrate salts for wavelengths below 5 µm. Therefore, the refractive
indices are simply taken to be the published values measured at the 589 nm sodium D line, where
44
n=1.41 for eutectic NaNO3-KNO3[53] and n=1.40 for the mass weighted average properties of the
50 wt. % KCl (n=1.417):50 wt. % NaCl (n=1.385)[54,55].
In order to characterize the performance of the salt itself, independently of the containment vessel
wall’s properties, we assume the fluids are contained in infinite slabs with fully reflective bottom
boundary and fully transmissive top boundary, and solar irradiance normal to the surface of the
fluid, as illustrated in Fig. 2.4 The mean beam lengths through the fluid are therefore 𝐿𝑒,𝑆 = 2𝐿
for the solar absorption, where 𝐿 is the actual thickness of the fluid, and 𝐿𝑒,𝐸 = 2𝐿𝑚 for the re-
emission, where 𝐿𝑚 is the average mean beam length given by Modest[47] as 𝐿𝑚 = 1.76𝐿 for an
infinite slab.
Figure 2-4 Diagram illustrating assumptions and boundary conditions for performance evaluation.
45
2.3. Experimental Validation
Using the procedure previously outlined, the spectral attenuation coefficient of propylene glycol
was measured as a reference for validation and the results are presented in Fig. 2.5. The
experimental results are presented with values previously published by Otanicar et al.[30] The
discontinuity at approximately 833 nm corresponds to a switch from a Silicon-Diode detector
(visible) to an Indium Gallium Arsenide detector (near infrared). Experimental repeatability and
deviations in the measurement resulted in much higher uncertainty than the instrumentation
uncertainty. We therefore report the average value of the measurements for each data point with
error bars expressed as the standard deviation of these measurement at each wavelength.
Figure 2-5 Experimental results for the attenuation coefficient of propylene glycol versus wavelength.
The measured results agree well with the published results over the majority of the measured
spectrum, except where the transmission reaches extreme values (≈ 0 % or ≈ 100 %) in the range
46
of thicknesses measured. The uncertainty is largest and diverges most from the published results
between 500 nm and 600 nm where the attenuation is on the order of 1 m-1. Nevertheless,
uncertainty due to repeatability in the measurements remains below 20 % at all reported
wavelengths. The maximum deviation between the measured and published average values is also
at this location, where the two deviate 40 %. Below 425 nm, the intensity of the light source decays
too rapidly to obtain accurate measurements. Above 1400 nm, the attenuation approaches 103 m-1
such that the transmission becomes too small to detect for the sensitivity of the apparatus. Given
these results, the optimal accuracy is achieved for wavelengths above 425 nm and for attenuation
coefficients between 0.5 m-1 to 500 m-1.
2.4. Results
Figure 2-6 Attenuation Coefficient of 40 wt. % KNO3: 60 wt. % NaNO3 binary nitrate molten salt (SQM) at 400
˚C.
47
Figure 2-7 Attenuation Coefficient of decomposed 40 wt. % KNO3: 60 wt. % NaNO3 binary nitrate molten salt
(SQM) at 400 ˚C.
Figure 2-8 Attenuation Coefficient of 50 wt. % KCl: 50 wt. % NaCl binary chloride molten salt at 800 ˚C.
48
Figure 2-9 Attenuation Coefficient of binary nitrate and decomposed binary nitrate at 400 ˚C, and binary chloride
at 800 ˚C (log-scale), with corresponding normalized blackbody intensity spectra Îb,400˚C and Îb,800˚C, and
normalized solar spectrum Gs (linear-scale).
Table 2-1 Calculated solar- and re-emission-weighted absorption coefficients and optical thicknesses
based on measured and extrapolated optical properties with L=1 m.
FLUID 𝜿𝑴𝑺 𝜿𝑴𝑬 𝝉𝑴𝑺 𝝉𝑴𝑬
(𝒎−𝟏) (𝒎−𝟏) (−) (−)
(Na-K)NaNO3
�̅�𝑜𝑝 = 400 ℃ 5.26 >135.00 10.52 >475.20
Decomposed (Na-K)NaNO3
�̅�𝑜𝑝 = 400 ℃ 28.00 >133.60 56.00 >470.27
(Na-K)Cl
�̅�𝑜𝑝 = 800 ℃ 2.51 0.65 5.02 2.29
The measured spectral attenuation coefficient at 400 ˚C for the refined grade
40 wt. % KNO3:60 wt. % NaNO3 binary nitrate molten salt mixture is presented in Fig. 2.6. A
�̂�𝒔
49
short wavelength absorption edge is observed at 500 nm and increases rapidly for decreasing
wavelengths (increasing frequency) below this point. At longer wavelengths, the absorption
decreases slowly until it reaches a minimum of 4.5 m-1 at approximately 1900 nm. Above
1900 nm, an absorption edge corresponding to Reststrahlen bands commences and rapidly
increases up to 160 m-1 at 2500 nm. After this point, the absorption band is expected to continue
increasing, extending beyond the range of accuracy of measurements. The absorption behavior at
both short and long-wavelengths agrees with the Lorentz model for ionic crystals which is valid
for both solids and liquids.[47,56,57] The measured properties had only a very weak dependence
on temperature and are therefore reserved for the supplementary discussion[58]. The short-
wavelength absorption edge shifts very lightly to longer wavelengths for increasing temperature.
A very weak Reststrahlen band shift to shorter wavelengths is also expected but was not observable
over the measured temperature range. Overall, the general behavior can be interpreted from the
solar-weighted and the re-emission-weighted absorption coefficients which were determined to be
κMS = 5.26 m−1 and κME = 135.0 m−1 . For a receiver 1 m deep, and corresponding optical
thicknesses τMS = 10.52 > 1 and τME = 475.20 ≫ 1, the fluid behaves as a participating media
in the solar spectrum, and is optically thick in the re-emission spectrum at 400 ˚C (blackbody
radiator).
The measured spectral attenuation coefficient at 400 ˚C for the decomposed
40 wt. % KNO3:60 wt. % NaNO3 binary nitrate molten salt mixture is presented in Fig. 2.7. The
location of the long-wavelength absorption edge is unchanged, but the overall attenuation in the
NIR and visible spectra increases almost a full order of magnitude. The short-wavelength
absorption edge appears to also commence at 500 nm, but the rapid growth rate with decreasing
wavelength is lessened with respect to the intact mixture. Below 500 nm, the attenuation became
50
too large for the intensity of the light source to obtain an accurate measurement. Nevertheless, the
measured spectrum still captures approximately 84 % of the solar irradiation intensity. In addition,
at this wavelength the attenuation approaches large enough values to be approximated as an opaque
blackbody radiator for large scale volumetric absorbers such as the CSPonD. The effect of
temperature on the measured properties was also negligible in this case[58]. In terms of weighted
properties, κMS = 28.0 m−1 and κME = 133.6 m−1. For a receiver 1 m deep, and corresponding
optical thicknesses τMS = 56.00 ≫ 1 and τME = 470.27 ≫ 1 , the fluid behaves as a surface
absorber in the solar spectrum, and a blackbody radiator in the re-emission spectrum at 400 ˚C.
Lastly, the measured properties for the 50 wt. % KCl:50 wt. % NaCl binary chloride molten salt
mixture at 800 ̊ C are shown in Fig. 2.8. We note here that the large uncertainty in the region below
1,000 nm is due to the combined effects of the highly transparent nature of the mixture and the
reduced measurement sensitivity of the Silicon-Diode detector (visible). The long- and short-
wavelength absorption edges are expected to occur at approximately 200 nm and 20 µm[56,59],
which are beyond the measurement range of this study. The measured properties agree with the
expected behavior, which are indeed fairly uniform over the measured range and no absorption
edges were detected. The properties are again not expected to vary significantly with
temperature[24], in particular because the measured range is far away from the absorption edges
where temperature dependence is most significant. Measurements were not possible beyond
2,500 nm where the fluid is too transparent to be detected by the mid-infrared detector. The solar-
weighted and the re-emission-weighted absorption coefficients which were determined to be
κMS = 2.51 m−1 and κME = 0.65 m−1 , respectively. For the 1 m deep receiver example, the
corresponding optical thicknesses are τMS = 5.02~1 and τME = 2.29~1, indicating the absorbed
51
solar irradiance is volumetrically distributed and the fluid behaves as a participating media in the
re-emission spectrum at 800 ˚C.
2.5. Discussion
2.5.1. Volumetric absorption
The volumetric absorption is visually and intuitively understood by the solar irradiance distribution
at multiple depths in the candidate salts as illustrated in Figs 2.10-2.11 for depths between 0 m and
2 m. The Figures show the absorption distribution for the initial irradiance penetration inside the
fluid without reflection contributions. The binary nitrate has well distributed absorption reaching
> 95 % at 2 m. The binary chloride mixture also displays well distributed absorption, with 83 %
absorbed over a 0.5 m-depth and > 95 % at 2 m. Finally, the decomposed binary nitrate has very
poor volumetric absorption performance and behaves effectively as a surface absorber, with > 95
% absorbed within only 0.25 m. Its graphical representation was therefore omitted here. These
results show that thermal decomposition will have significant detrimental effects on the overall
performance on the salts and should thus be most certainly avoided.
Figure 2-10 Solar irradiance distribution at different salt depths for binary nitrate at 400 ˚C.
52
Figure 2-11 Solar irradiance distribution at different salt depths for binary chloride at 800 ˚C.
2.5.2. Effective Emissivity
The total effective emissivity versus depth is presented in Fig. 2.12 for all three candidate salts.
The total effective emissivity of both the unaffected and decomposed binary nitrates very rapidly
approaches 1 for very thin fluid layers. These results are readily predicted from the re-emission
weighted optical thicknesses τME ≫ 1 indicating the fluids are optically thick in the re-emission
region.
The total effective emissivity of the binary chloride for the range of fluid depths explored is much
lower and requires over 1 m of fluid to reach values greater than 0.9. The results are fortuitous as
they allow to offset the elevated emission losses associated with higher operating temperatures.
Note that for the special case where the bottom boundary in Fig. 2 is a perfect absorber/emitter
53
such that 휀𝜆 = 1, the total effective emissivity becomes unity for all fluids and all temperature for
an isothermal fluid layer.
Figure 2-12 Effective total emissivity of measured molten salt mixtures for different receiver fluid depths.
2.5.3. Capture Efficiency
The capture efficiencies, as defined in section 2.4., are presented in Fig. 2.13 for the candidate salt
mixtures. The dashed line in each figure represents the maximum achievable capture efficiency in
the case where the bottom boundary is “black” over the entire spectrum. This limit is independent
of fluid thickness. Efficiencies are presented versus solar concentrations, with each curve
representing a different total receiver fluid depth. Capture efficiency is independent of the fluid
layer thickness for the decomposed binary nitrate due to the dominating surface absorption and
blackbody radiator behaviors. High capture efficiencies > 90 % are therefore achieved at relatively
low solar concentrations. The binary nitrate requires larger fluid thicknesses to achieve high
efficiency due to the more gradual volumetric absorption. When the fluid is contained in a vessel
54
with highly absorbing walls, capture efficiencies should approximately match those for the
decomposed mixture.
The binary chloride operates at much higher temperatures and the lower total effective emissivity
is not enough to offset the associated large radiative losses for low solar concentrations. For a 2 m
layer of fluid, a solar concentration of 200 suns is required to “break even” (absorption = losses),
and 1000-sun concentration yields an 80 % capture efficiency. Similar to the nitrate salt, the
performance of the chloride would improve with “black” containment vessel walls
56
(c) Binary Chloride
Figure 2-13 Capture efficiency versus solar concentrations for fluid depths between 0.25 m and 2 m for binary
nitrate (a), decomposed binary nitrate (b), and binary chloride (c).
2.6. Conclusions
A method for measuring the attenuation coefficient of nearly transparent high temperature fluids
was developed and implemented. The properties of nitrate and chloride-based salt mixtures were
measured and the effects of thermal decomposition were investigated. A complete characterization
of the thermal radiation performance in the solar and the re-emission spectra was presented and
the behavior of the salts were discussed. The characterization can readily be used as a design tool
for large-scale open receivers. Future work should focus on expanding the optical properties
database of high temperature fluids to better identify optimal heat transfer fluid candidates.
57
3. Theoretical study of direct absorption receivers
Due to the combination of volumetric heating and surface heating inside the receiver, two layers
are expected to develop within the fluid as illustrated in Fig. 3.1: (1) a stagnant, thermally stratified
upper layer where the bulk of volumetric heating occurs, and (2) a colder unstable bottom layer
where the fluid is heated from below from the remaining solar radiation absorbed by the bottom
surface. The presence of non-uniform volumetric heating and surface heating results in penetrative
convection inside the receiver. In addition, radiative cooling at the surface produces a steep
temperature gradient within a thin layer of fluid immediately below the surface. The heating
conditions produce a complex thermal-fluid behavior inside the receiver. It is therefore desirable
to find an expression for the temperature distribution in the receiver versus time to evaluate the
radiative losses at the surface, and optimize the receiver design and operation parameters to
maximize the incoming solar flux while minimizing the peak temperatures. The present section
outlines the governing equations, dimensionless groups, and the development of a simple
expression for the temperature profile in the receiver. The results are compared with CFD
simulations.
58
(a) (b)
Figure 3-1 (a) Illustration of the heating and flow conditions inside a volumetric receiver. (b) Illustration of the
expected temperature profile resulting from the volumetric (internal) heating and boundary conditions.
3.1. Problem formulation
The following analysis is developed for an incompressible fluid that is semi-transparent in the solar
spectrum. Since it was determined in Chapter 2 that the binary nitrate molten salt mixture used in
the CSPonD is highly absorbing in the infrared spectrum and the corresponding optical thickness
is very large (𝜏 ≫ 1), it is assumed in this analysis that the fluid is opaque in the infrared spectrum
and we neglect participating media effects beyond the solar absorption. The coordinate system
used here is shown in Fig 3.1b. Solar radiation is incident at the salt surface where 𝑦 = 0. The
radiative intensity in the fluid layer as a function of depth is given as
𝐼 = 𝐼𝑜𝑒𝜅𝑀𝑆𝑦, 𝑦 ≤ 0 (3.1)
The surface is exposed to the environment where it is assumed thermal losses are dominated by
radiative cooling. The losses at 𝑦 = −ℎ are therefore 𝑞𝑠 = −𝜖𝜎(𝑇𝑦=04 − 𝑇𝑒𝑛𝑣
4 ).
59
The radiation penetrates down to the bottom of the receiver located at depth 𝑦 = −ℎ, where the
remaining thermal radiation unabsorbed by the salt is absorbed by the bottom surface where we
assume the emissivity is equal to unity, i.e. 𝜖𝑦=−ℎ = 1. The heat flux at this boundary is therefore
𝑞𝑤 = 𝐼𝑜𝑒−𝜅𝑀𝑆ℎ.
Initially, the salt is quiescent and at a uniform temperature 𝑇𝑜 . When solar radiation starts heating
the semi-transparent liquid and before natural convection develops, the quiescent temperature
profile 𝑇𝑞(𝑦) is dominated by 1D conduction only. Eventually, the temperature gradient is
sufficient for natural convection to initiate and an unstable mixing layer of thickness ℎ𝑚 develops.
This mixing layer does not disturb the stratified upper layer, which remains stable as it continues
to thermally develop.
3.2. Governing equations
We first define the normalization parameters used in the analysis of the governing equations, given
as
Length: 𝑥𝑖~𝜅𝑀𝑆−1𝑥𝑖
∗
Time: 𝑡 = 𝛼𝜅𝑀𝑆2𝑡∗
Temperature: 𝑇 =𝐼𝑜
𝜌𝑜𝑐𝑝𝛼𝜅𝑀𝑆
𝑇∗
Pressure: 𝑃 =𝑔𝛽𝐼𝑜
𝑐𝑝𝛼𝜅𝑀𝑆2 𝑃∗
Velocity: 𝑢𝑖 = 𝛼𝜅𝑀𝑆𝑢𝑖∗
(3.2)
where 𝜅𝑀𝑆 is the solar-weighted absorption coefficient, 𝑡 is the time, 𝛼 is the thermal diffusivity,
𝑇 is the temperature, 𝜌𝑜 is the density, 𝑐𝑝 is the specific heat, 𝑃 is the pressure, 𝑢𝑖 is the velocity
component in the 𝑥𝑖 direction, 𝛽 is the thermal expansion coefficient, and 𝐼𝑜 is the radiation
60
intensity in 𝑊/𝑚2. Variables with superscripts ‘*’ are the associated dimensionless quantities.
The governing equations in dimensionless form are therefore
𝜕𝒗∗
𝜕𝑡∗+ 𝒗∗ ∙ 𝛻𝒗∗ = −𝑅𝑎𝑃𝑟𝛻𝑝 + 𝑃𝑟𝛻2𝒗∗ + RaPr𝛿𝑖,2𝑇∗ (3.3)
𝛻 ∙ 𝒗∗ = 0 (3.4)
𝜕𝑇∗
𝜕𝑡∗+ 𝒗∗ ∙ 𝛻𝑇∗ = 𝛻2𝑇∗ + �̇�∗ (3.5)
where �̇�∗ is the volumetric heat source given as
�̇�∗ = 𝑒𝑦∗ (3.6)
And the flux Rayleigh number
𝑅𝑎 =𝑔𝛽𝐼𝑜
𝜌𝑜𝑐𝑝𝜈𝛼2𝜅𝑀𝑆4 (3.7)
The boundary conditions are
𝜕𝑇∗
𝜕𝑦∗= −
1
𝑁𝑇∗4
@ 𝑦∗ = 0
(3.8a)
𝜕𝑇∗
𝜕𝑦∗= −𝑒−ℎ∗
@ 𝑦∗ = −ℎ∗
(3.8b)
where 𝑁 is the conduction-to-radiation parameter given as
𝑁 =𝑘𝜅𝑀𝑆
𝜖𝜎(
𝜌𝑜𝑐𝑝𝛼𝜅𝑀𝑆
𝐼𝑜)
3
(3.9)
61
Initially, before heating occurs, the entire liquid layer is at a constant uniform temperature 𝑇𝑜∗ such
that the initial condition is expressed as
𝑇∗(𝑡∗ = 0, 𝑦∗) = 𝑇𝑜∗ (3.10)
In the very early stages before the onset of convection in the bottom layer, the flow is quiescent
and 1D conduction dominates, the energy equation therefore reduces to
𝜕𝑇𝑞∗
𝜕𝑡∗=
𝜕2𝑇𝑞∗
𝜕𝑦∗2 + 𝑒𝑦∗ (3.11)
where 𝑇𝑞∗ is the quiescent dimensionless temperature profile before the onset of natural
convection. The partial differential equation (Eq. 3.11) can be solved with boundary conditions in
Eq. 3.8 and initial condition in Eq. 3.10 to obtain an expression for the temperature distribution
over time
𝑇𝑞∗ = 𝑇𝑞
∗(𝑡∗, 𝑦∗) (3.12)
We now consider the time at which the unstable convective layer has developed. We note that at
the location where 𝑦∗ = 𝑦𝑚𝑎𝑥,1∗ , a local maximum exists and the first spatial derivative is zero such
that 𝜕𝑇∗
𝜕𝑦∗= 0 . The conditions for the fluid layer below 𝑦∗ = 𝑦𝑚𝑎𝑥,1
∗ are identical to the
configuration studied by Hattori et al. [12,21], which investigated the mixing in internally heated
natural convection flow with an insulated upper boundary. The authors found that the optical
thickness of the bottom mixing layer is approximately 𝜏𝑚 ≈ 1, such that ℎ𝑚∗ ≈ 1, meaning ℎ𝑚 ≈
1
𝜅𝑀𝑆
.
62
Following the onset of natural convection in the bottom layer, we assume the mixing is sufficient
to significantly homogenize the temperature distribution. Assuming the thermal boundary layer is
very thin compared to the convective layer thickness (𝛿𝑡∗ ≪ ℎ𝑚
∗ ), we may evaluate the average
bulk fluid temperature 𝑇𝑚∗ in the mixing region 𝑦∗ < ℎ𝑚
∗ as a function of time
𝑇𝑚∗ =
∫ 𝑇𝑞∗(𝑡∗, 𝑦∗)𝑑𝑦∗𝑦𝑐𝑟𝑖𝑡
∗
−ℎ
ℎ𝑚∗
(3.13)
Alternately, noting that 𝑇∗(𝑦∗ < ℎ𝑚∗ , 𝑡∗) = 𝑇𝑚
∗ (𝑡∗) and for the temperature profile to be
continuous, the temperature spatial derivative must be zero at 𝑦∗ = −(ℎ − ℎ𝑚∗ ) such that
𝜕𝑇𝑞∗
𝜕𝑡∗
𝜕𝑇𝑞∗
𝜕𝑡∗|
𝑦∗=−(ℎ−ℎ𝑚∗ )
= 0 (3.14)
We therefore may solve the partial differential equation given by Eq. 3.11 replacing the second
boundary condition in Eq. 3.8 with the condition in Eq. 3.14 and letting 𝑇𝑚∗ (𝑡∗) =
𝑇𝑞∗(𝑦∗ = ℎ𝑚
∗ , 𝑡∗). Eqns 3.1-3.14 can therefore be solved for the temperature profile in the internally
heated liquid layer following the development of the mixing layer.
It is of interest to determine the optimal optical thickness of the receiver that will result in the
highest possible temperature uniformity in the liquid layer (minimize peak temperature). It is
therefore necessary to obtain an expression for the temperature at the bottom boundary to predict
peak temperatures in the system. The temperature difference across the boundary layer 𝛿𝑡 , 𝑇𝑏 =
𝑇𝑦∗=−ℎ∗∗ − 𝑇𝑚
∗ , can be evaluated by considering the Rayleigh-Bénard convection that develops in
the bottom mixing layer. The heat flux at the bottom is given as
63
𝑞𝑤 = 𝐼𝑜𝑒−𝜅𝑀𝑆ℎ (3.15)
In the mixing layer, the classical Rayleigh number is expressed as
𝑅𝑎𝑅𝐵 =𝑔𝛽𝑇𝑏ℎ𝑚
3
𝜈𝛼 (3.16)
and the average Nusselt number can be obtained from Rayleigh-Bénard convection correlations
where it is typically expressed in the form
𝑁𝑢̅̅ ̅̅ℎ𝑚
= 𝐶𝑅𝑎𝑅𝐵𝑛 (3.17)
where 𝐶 and 𝑛 are constants that depend on the geometry and boundary conditions of the system.
For natural convection heat transfer in horizontal layers of fluids heated from below, the classical
asymptotic solution for the Nusselt number for large Rayleigh numbers yields 𝑛 → 1/3 [60], such
that
𝑁𝑢̅̅ ̅̅ℎ𝑚
~𝑅𝑎𝑅𝐵
13⁄ 𝑅𝑎𝑅𝐵 → ∞ (3.18)
We may solve Eqns. 3.14-3.16 for the temperature difference 𝑇𝑏 by noting that
𝑞𝑤 = 𝐼𝑜𝑒−𝜅𝑀𝑆ℎ = 𝑁𝑢̅̅ ̅̅ℎ𝑚
(𝑘
ℎ𝑚) 𝑇𝑏 (3.19)
Solving for 𝑇𝑏, we find
𝑇𝑏 = [ℎ𝑚𝐼𝑜𝑒−𝜅𝑀𝑆ℎ
𝑘𝐶(
𝜈𝛼
𝑔𝛽ℎ𝑚3)
𝑛
]
1𝑛+1
(3.20)
Finally, the bottom surface temperature can be evaluated as
64
𝑇𝑦=−ℎ = 𝑇𝑚 + 𝑇𝑏 = 𝑇𝑚 + [ℎ𝑚𝐼𝑜𝑒−𝜅𝑀𝑆ℎ
𝑘𝐶(
𝜈𝛼
𝑔𝛽ℎ𝑚3)
𝑛
]
1𝑛+1
(3.21)
The thermal boundary layer thickness is therefore given as
𝛿𝑡 ≡𝑇𝑏
𝜕𝑇𝜕𝑦
|𝑦=−ℎ
=𝑘𝑇𝑏
𝑞𝑤=
𝑘
𝐼𝑜𝑒−𝜂ℎ[ℎ𝑚𝐼𝑜𝑒−𝜅𝑀𝑆ℎ
𝑘𝐶(
𝜈𝛼
𝑔𝛽ℎ𝑚3)
𝑛
]
1𝑛+1
(3.22)
3.3. Model validation
The equations developed in Section 3.2. for the simple 1D model can be solved analytically or
numerically. Due to the complexity of the nonlinear surface boundary condition, the partial
differential equation is solved numerically in the present study using Matlab software with a
standard PDE solver. A three-dimensional, unsteady CFD model was developed in parallel in the
commercially available STAR-CCM+ solver, to compare and benchmark the simple 1D model.
The modeled region is illustrated in Fig. 3.2. A liquid layer is contained within a rectangular region
of height ℎ and both length and width 𝑊. The height of the modeled region was selected as a
representative height for direct absorption volumetric receiver applications. The lateral boundaries
are defined as symmetry boundaries such that the layer is infinite in the 𝑥𝑧-plane. The width of the
region was selected to be at least large enough to contain three times the largest characteristic
length scale of the flow as shown later in the present section. In the case studied, the largest
characteristic length scale is the flow recirculation and 𝑊 = 2 𝑚.
65
Figure 3-2 Illustration of the modelled region in CFD for validation of the 1D model. Lateral walls are defined as
symmetry planes such that the region is semi-infinite in the xz-plane.
The volumetric heat source is defined in Eq. 3.6 and boundary conditions in Eq. 3.8. The
Boussinesq model was used with a constant density of 1820 𝑘𝑔/𝑚3 and a thermal expansion
coefficient of 3.8124 𝐾−1. The remaining thermophysical properties for commercial solar salt
were obtained from SQM’s product information provided in Appendix H. The natural convection
is expected to be in the transition to turbulent regime with relatively low velocities, and the flow
was therefore modeled with a laminar solver. In addition, a coupled solver was used due to the
strong temperature-flow coupling and the presence of the volumetric source term. An implicit
unsteady solver with 1st-order temporal discretization was selected. A constant time-step of 1 s
with 25 inner iterations provided sufficient temporal resolution and convergence within each time-
step. The coupled solver’s Courant Number was ramped from 1-100 within the initial time-step
and held constant at 100 for the remainder of the simulation.
A grid sensitivity study was carried out to determine the influence of the grid size on the solution.
Three different grid sizes were selected, with the finest grid shown in Fig. 3.3. The base sizes for
66
the three hexahedral meshes were 2.5 cm, 4 cm, and 6 cm. Prism layers were used at the top and
bottom boundaries. The corresponding prism layer mesh thicknesses at the walls were 0.9 mm,
1.3 mm, and 2 mm for the finest, intermediate, and coarsest mesh refinements, respectively.
(a)
(b)
Figure 3-3 Illustration of the modelled region in CFD for validation of the 1D model. Lateral walls are defined as
symmetry planes such that the region is semi-infinite in the xz-plane.
67
We first consider the case where ℎ = 1 𝑚, 𝜅𝑀𝑆 = 2 𝑚−1, 𝐼𝑜 = 37.5 𝑘𝑊𝑚2⁄ , 𝑇𝑜 = 300 ℃. In this
case, the optical thickness of the fluid layer is therefore 𝜏 = ℎ𝜅𝑀𝑆 = 2 and the thickness of the
mixing layer is expected to be ℎ𝑚 = 1𝜅𝑀𝑆
⁄ = 0.5 𝑚 . Fig. 3.4 presents the characteristic
temperature difference 𝑇𝑏 = 𝑇𝑦=−ℎ − 𝑇𝑚 versus time for the three grids studied. There is a rapid
temperature increase in all cases which occurs within the first minute of heating before the onset
of convection where conduction dominates and the bottom layer is still stable. After approximately
1 minute, the layer becomes unstable, plumes develop, and eventually turbulent natural convection
is established after ~200 seconds. The present study will focus on the time after which natural
convection has developed and the bottom layer is well mixed.
Figure 3-4 Characteristics temperature difference in the mixing layer T_b versus time as calculated from the CFD
model for three different grid sizes, where ℎ = 1 𝑚,𝜅𝑀𝑆 = 2 𝑚−1, 𝐼𝑜 = 37.5 𝑘𝑊𝑚2⁄ , 𝑇𝑜 = 300 ℃, and 𝑅𝑎𝑅𝐵 ≈
5 𝑥 1010.
68
The results in Fig. 3.4 show that 𝑇𝑏 oscillates about some constant value in time for a constant heat
flux following the onset of natural convection in the mixing layer, which is expected from the
equations derived in Section 3.2. The constant temperature difference also confirms there is no
change in the natural convection regime for the cases and time studied. The time-averaged
temperature difference 𝑇𝑏 for the coarsest to finest meshes are 22.9 ℃, 21.3 ℃, and 19.6 ℃ ,
respectively. Taking the finest mesh as the reference value, the error reduces monotonically from
16.5 % with the coarsest mesh to 7.6 % with the finest mesh. Using the value 𝑇𝑏 = 19.6 ℃, ℎ𝑚 =
1𝜅𝑀𝑆
⁄ = 0.5 𝑚 , 𝑔 = 9.81 𝑚𝑠2⁄ , 𝛽 = 3.8124 × 10−4 𝐾−1 , 𝜈 = 9.8132 × 10−7 𝑚2
𝑠⁄ , and 𝛼 =
1.886 × 10−7 𝑚2
𝑠⁄ , the Rayleigh number in the mixing layer is estimated to be 𝑅𝑎𝑅𝐵 =
𝑔𝛽𝑇𝑏ℎ𝑚3
𝜈𝛼≈ 5 𝑥 1010. The natural convection is therefore in the transition to turbulent regime. In
addition, the bottom average temperatures after 30 minutes of heating are found to be 341 ℃,
339 ℃, and 338 ℃, for the coarsest to finest grids, which represents a deviation of less than 1 %
in all cases. The finest mesh is therefore considered sufficiently refined for this analysis. To
confirm this conclusion, we evaluate the thickness of the boundary layer assuming 𝑇𝑏 = 19.6 ℃,
which yields 𝛿𝑡 =𝑘𝑇𝑏
𝐼𝑜𝑒−𝜂ℎ ≈ 2 𝑚𝑚. The mesh thickness at the wall for the most refined mesh is
0.9 mm and is therefore sufficiently thin to capture the temperature variation in the boundary layer.
The results for the axial temperature profiles for heating times of 10, 20, and 30 minutes evaluated
with both the simple 1D model and the CFD model are presented in Fig. 3.5, and the corresponding
average boundary temperatures are reported in Table 3.1. In addition, streamlines and temperature
distributions obtained from the CFD model are presented in Fig. 3.6. The bottom boundary
temperature 𝑇𝑦=−ℎ in the 1D model was evaluated using the following Nusselt number correlation
provided by Hollands et al. [60]
69
𝑁𝑢̅̅ ̅̅ℎ𝑚
= 0.0555𝑅𝑎𝑅𝐵
13⁄ (3.23)
Figure 3-5 Axial temperature profile in an internally heated liquid layer calculated with the simple 1D model and
the CFD model for ℎ = 1 𝑚, 𝜅𝑀𝑆 = 2 𝑚−1, 𝐼𝑜 = 37.5 𝑘𝑊𝑚2⁄ , 𝑇𝑜 = 300 ℃, and 𝑅𝑎𝑅𝐵 ≈ 5 𝑥 1010.
Fig. 3.5. shows the excellent agreement between the 1D model and the results obtained from CFD
in the region between −1 𝑚 and ~ − 0.3 𝑚, which includes the mixing layer region. Greater
deviation is present in the 0.3 m-thick layer immediately below the surface. In this region, the 1D
model predicts a sharp temperature peak, whereas the temperatures predicted in this region by the
70
CFD model are more uniform. Nevertheless, the over prediction in the peak temperature in this
region is only 1.8%, 3.4%, and 4.8% at 10, 20, and 30 minutes respectively, with the values
computed from the CFD model taken as reference values. The reason for the deviation in peak
temperature is likely due to the radiative cooling at the surface. The cooler surface disrupts the
stable stratified layer below it, resulting in secondary mixing near the surface, which can clearly
be seen in the streamlines presented in Fig. 3.6. Furthermore, the higher surface temperatures
predicted by the CFD model (Table 3.1.) may also be attributed to the presence of mixing causing
more uniform temperatures in the upper layer. Although the temperatures are more uniform in the
CFD model, the results also indicate surface losses are higher than predicted by the 1D model due
to higher surface temperatures.
Table 3-1 Average boundary temperatures calculated for the 1D model and the CFD model for ℎ = 1 𝑚,
𝜅𝑀𝑆 = 2 𝑚−1, 𝐼𝑜 = 37.5 𝑘𝑊𝑚2⁄ , 𝑇𝑜 = 300 ℃, and 𝑅𝑎𝑅𝐵 ≈ 5 𝑥 1010.
10 min 20 min 30min
Average boundary
temperature (℃)
1D
model CFD
1D
model CFD
1D
model CFD
𝑇𝑦=0 239.15 291.04 231.08 299.00 228.49 306.76
𝑇𝑦=−ℎ 329.07 325.65 335.27 331.68 341.52 337.81
71
10 minutes
20 minutes
30 minutes
Figure 3-6 Temperature distributions (left) and streamlines (right) at a cross-section in an internally heated liquid
layer obtained from CFD model for ℎ = 1 𝑚, 𝜅𝑀𝑆 = 2 𝑚−1, 𝐼𝑜 = 37.5 𝑘𝑊𝑚2⁄ , 𝑇𝑜 = 300 ℃. The mixing layer
ℎ𝑚 = 1𝜅𝑀𝑆
⁄ = 0.5 𝑚 can be seen in the streamlines where the Rayleigh number is 𝑅𝑎𝑅𝐵 ≈ 5 𝑥 1013.
72
The most critical temperature in receiver design and optimization is the bottom boundary
temperature since it is the most likely to be exposed to large solar fluxes and experience significant
temperature peaks and gradients. This temperature therefore limits the maximum amount of solar
irradiation that can be absorbed before reaching critical thermal limits, in particular for liquid
layers with lower optical thicknesses 𝜏 ≲ 1.The temperature calculated at the bottom boundary
𝑇𝑦=−ℎ by the CFD and 1D models have good agreement, as presented in Table 3.1. The calculated
characteristic temperature difference 𝑇𝑏 is 𝑇𝑏,𝐶𝐹𝐷 = 19.6℃ for the CFD model, and 𝑇𝑏,1𝐷 =
23.0℃ for the 1D model. The disagreement of the 1D model with respect to the CFD model in
calculating the characteristic temperature difference is therefore 17 %. The disagreement
suggests limitations in the applicability of the classical Nusselt number correlation provided in
Eq. 3.22 for molten salts and for the configuration studied. Improvements in the computational
modeling approach may also be required. This limitation highlights the need for further
experimental studies of natural convection heat transfer in molten salts to correct and improve the
accuracy of existing heat transfer correlations and validate computational models.
3.4. Direct absorption receiver optimization
Reducing peak temperatures in volumetric receivers allows to increase the maximum energy
deposited in the absorber liquid before exceeding thermal limits. It is therefore of particular interest
to determine the effects of the liquid’s absorption coefficient and the overall optical thickness of
the layer on temperature uniformity. The simple 1D model developed allows to readily explore the
parameter space involved in the internally heated liquid. In particular, Fig. 3.7 shows the variation
of the temperature profile with optical thickness calculated using the 1D model for the case ℎ =
1 𝑚, 𝐼𝑜 = 37.5 𝑘𝑊𝑚2⁄ , 𝑇𝑜 = 300 ℃, and absorption coefficients from 𝜅𝑀𝑆 = 1.1 𝑚−1 to 𝜅𝑀𝑆 =
73
8 𝑚−1 such that the optical thickness 𝜏 = 𝜅𝑀𝑆ℎ varies from 1.1 to 8. Temperature profiles are
shown for 20, 40, and 60 minutes of heating time. The lower limit of the range studied for
absorption coefficient is limited to 𝜅𝑀𝑆 ≈ 1.1 𝑚−1 (𝜏 ≈ 1.1 ) such that ℎ𝑚 ≤ 0.91 𝑚. For optical
thicknesses below this value, the mixing region begins to overlap with the cooled surface layer
and the 1D model is no longer valid.
75
(c) 60 minutes
Figure 3-7 Variation of the temperature profile with optical thickness calculated using the 1D model for the case
h = 1 m , Io = 37.5 kWm2⁄ , To = 300 ℃ , with absorption coefficient ranging from 𝜅𝑀𝑆 = 1.1 m−1 to 𝜅𝑀𝑆 =
8 m−1 such that the optical thickness τ = 𝜅𝑀𝑆h varies from 1.1 to 8. Temperature profiles for heating times of (a)
20 minutes, (b) 40 minutes, and (c) 60 minutes.
It can clearly be seen from the results how the bottom surface temperature increases with
decreasing optical thickness as the radiation increases with respect to volumetric heating.
Conversely, the temperature peak below the surface located at 𝑦𝑚𝑎𝑥,1 increases with increasing
optical thickness as the fluid becomes more opaque and volumetric heating becomes more
localized to the surface. In addition, the temperature gradient within the layer increases more
rapidly with increasing heating time for higher optical thicknesses.
The most notable finding that can be observed from Fig. 3.7 is the optical thickness for which the
highest temperature uniformity (or lowest temperature peak) is achieved. For the heating times
and conditions studied, the ideal optical thickness is found to be in the range 𝜏 = 1.5 − 2. Below
76
this value, the temperature gradient at the bottom boundary becomes more significant due to the
surface absorption and heating. For optical thicknesses above the 𝜏 = 1.5 − 2 range, the
temperature peak near the surface grows too rapidly. It is generally assumed that the ideal optical
thickness for volumetric receivers should be 𝜏 ≈ 1 [44]. Although this assumption may be valid
for very long heating times where the temperature maxima near the surface may grow sufficiently
such that it exceeds the large gradient at the bottom boundary, it cannot be assumed valid at all
time scales. The analysis suggests the optical thickness should be of order 𝜏~ℴ(1) but greater than
1. In addition, the simple 1D model provides a conservative estimate in the maximum allowable
optical thickness. The results from the CFD model demonstrate a non-negligible reduction in the
peak temperature in the upper layer due to the presence of mixing produced by the cooled upper
surface boundary. This mixing allows to further increase the maximum tolerable optical thickness.
For absorption coefficients below the 𝜅𝑀𝑆 ≈ 1.1 𝑚−1 limit investigated, the mixing layer thickness
grows large enough that it overlaps with the thin region 𝑦𝑚𝑎𝑥,1 ≤ 𝑦 ≤ 0 above the first
temperature maximum at 𝑦 = 𝑦𝑚𝑎𝑥,1 such that the model breaks down and is no longer valid.
Thus, for 𝜏 ≲ 1.1, the mixing layer is large enough for stable stratified upper layer to no longer
develops. Nevertheless, it can clearly be seen that smaller values would only further increase the
temperature at the bottom boundary with respect to the bulk. We note however that the calculated
bottom boundary temperatures are first-order estimates. Further study of heat transfer correlations
in molten salts under such natural convection conditions are required to improve the accuracy of
these estimates.
Peak temperatures occurring in the layer can be minimized by adequately partitioning the absorbed
solar energy between the upper layer and the mixing layer. For a specified heating time ∆𝑡, the
ideal partitioning will yield
77
𝑇𝑦=𝑦𝑚𝑎𝑥,1|
𝑡=∆𝑡= 𝑇𝑦=−ℎ|
𝑡=∆𝑡 (3.25)
Eq. 3.25 therefore provides a design condition for direct absorption receivers to minimize peak
temperatures within the liquid absorber. Future work should focus on deriving the full expression
analytically for the 1D model temperature distribution. The expression will allow to derive an
expression for the ideal optical thickness 𝜏 of the receiver as a function of the desired heating time
and the design parameters.
3.5. Conclusions
The present chapter developed a simple expression for the temperature profile in direct absorption
liquid-based receivers based on a two-layer, 1D model of the thermal-fluid behavior. The results
were compared with CFD simulations with good agreement. The 1D model allows to easily
explore the parameter space governing directly absorbing liquid layers and to carry-out
optimization. Using this model, it was shown that the ideal optical thickness should be of order
𝜏~ℴ(1) but greater than 1. The exact value depends on the operating conditions and on the
maximum heating time. Future work should focus on deriving an analytical expression for the
ideal optical thickness as a function of the fluid properties, heating conditions, geometry, and total
heating time. This will allow to develop design rules in terms of the different parameters and to
optimize operating conditions. In addition, experimental studies of natural convection heat transfer
in internal heated layers of molten salts are required to correct and improve the accuracy of existing
heat transfer correlations and validate computational models.
Finally, the analysis also shows how the thickness of the mixing layer is less than the total thickness
of the irradiated liquid layer when the optical thickness 𝜏 > 1 . Under these conditions, the
temperature in the thermally stratified upper layer increases more rapidly than the temperature in
78
the mixed layer below it, which results in less uniform temperatures. The optical thickness is
expected to be 𝜏 > 1 in CSPonD receivers, therefore additional active mixing elements are
required to maintain temperature uniformity. This supports the development of a mixing plate for
CSPonD receivers [61].
79
4. CFD and heat transfer model of the Masdar CSPonD Demo prototype
The demonstration prototype of the CSPonD concept that was built at the Masdar Institute Solar
Platform in Abu Dhabi recently went into operation and successfully demonstrated the concept
experimentally (Section 1.2). The desired temperature profile within the hot salt layer could not
be predicted and was therefore maintained using feedback controls for the divider plate motion.
Accurate modeling is thus necessary to further improve the design and operation of this
technology, which remains in its early stages of development. In addition, an accurate model of
the prototype design would allow to evaluate the thermal losses through the receiver aperture
during on-sun operation, the effects of the time varying-solar flux, and to predict the effective
capture efficiency more accurately to determine the necessary conditions to operate with a net
positive output.
Given the importance in solar receiver design and the limited studies available for predicting the
thermal behavior in volumetrically absorbing solar receivers, three-dimensional CFD modeling of
the CSPonD Demo project receiver is considered particularly advantageous and is presented in
this study. This work provides the first complete CFD model and analysis of a molten salt, direct
absorption volumetric receiver with radiation-induced convection. The predictions are
benchmarked with the experimental results collected at the CSPonD Demonstration project test
facility at the Masdar Institute Solar Platform. The results provide significant insight into the
complex thermal-fluid behavior of the receiver and allow to identify major sources of uncertainty
in receiver operation.
80
4.1. CSPonD demonstration prototype experiments
A simplified diagram of the experimental facility and CAD model of the receiver are presented in
Fig. 4.1. The open tank of molten salt includes a divider plate (DP) which separates the hot layer
of liquid (top) from the cold layer (bottom). A thin mixing plate (MP) positioned approximately
10 cm above the DP during normal operation can be rapidly actuated to mix the salt in the event
of large temperature gradients resulting from unexpected localized overheating. For the validation
of the CFD model, the height of the DP and MP are both maintained constant throughout all
experiments.
(a)
81
(b)
Figure 4-1 (a) Simplified diagram of the CSPonD demonstration facility. (b) CAD model of the CSPonD
demonstration prototype receiver.
The tank is instrumented with 9 multi-junction K-type thermocouple rods 2 meters in length. 6
rods are positioned near the tank wall, and 3 are located 12 cm radially inward, as shown in
Fig. 4.2. The MP and DP are designed with thermocouple rod through tubes to allow the
thermocouple rods to reach the bottom of the tank and remain fixed. Each rod has 13 measurement
points equally spaced along the height of the tank, 15 cm apart. The first measurement point is
located 2 cm from the bottom of the tank and the highest measurement is collected immediately
below the salt surface.
Hsalt ≈ 1.67 m
Dsalt ≈ 1.25 m
82
Figure 4-2 Diagram of the top view of the thermocouple rod configuration inside the tank.
Prior to each experiment, the salt is pre-heated to a relatively uniform temperature with resistance
heaters positioned at the bottom of the tank. To begin the experiment, the lid is removed and the
heaters are turned on. The experiments are carried out until the incident solar radiation is no longer
sufficient to increase the salt temperature, or until the maximum temperature inside the tank
exceeds the thermal limits of the salt (since the DP and MP are not actuated for the validation
experiments).
4.2. Model setup and boundary conditions
A large plenum region filled with air located immediately above the receiver FOE (Fig. 4.3) is
modeled in order to accurately capture the FOE inlet boundary. The length and width were
determined to be large enough such that no significant recirculation developed near the FOE. A
sensitivity analysis on the length and width of the plenum was not necessary since an accurate
solution in this region was not critical for the present study. The height of the plenum corresponds
to the distance between the FOE inlet and the mid-plane of the central reflectors. Ambient air flows
83
through the plenum inlet and above the receiver. An outlet facing opposite the plenum inlet allows
the air to exit the region. The remaining plenum boundaries are modeled as walls with a slip
boundary condition. All boundaries in the plenum excluding the plenum outlet have a constant
average ambient temperature measured at the test facility during the experiment. A constant air
speed defined at the inlet is evaluated taking the average value of the air speed measurements
collected at the test facility throughout the experiment.
The concentrated sunlight beamed down from the central reflectors is approximated as an annular
diffuse, uniform, radiative flux source located at the center of the top boundary of the plenum as
shown in Fig. 4.3. The inner and outer diameters of the source correspond to the inner and outer
diameters of the central reflector mirrors. The intensity of the source versus time of day was
estimated using ray-tracing power predictions scaled with the daily DNI [62].
Figure 4-3 Model setup and boundary conditions (plenum not to scale).
84
Thermal radiation is accounted for in the molten salt and in the air region above the salt surface,
in the FOE, and in the plenum. Spectral radiation is approximated using a two-spectral band model,
Band I (< 2 µm) and Band II (> 2 µm), with average radiative properties calculated in each band
(Appendix A). Thermal radiation is treated as participating media radiation with zero-absorption
in the air regions. The molten salt mixture is treated as an absorbing, non-scattering liquid. Since
the properties of the commercial SQM salt are expected to vary significantly over time and under
various conditions, which will in turn significantly influence the temperature and velocity
distribution in the model predictions, four distinct cases of optical properties summarized in Table
4.1 are investigated in this study and presented in the results. Case 1 uses the properties as reported
by Tétreault-Friend et al. [63]. Case 2 uses the same measured properties with the extrapolation
presented in Chapter 2. The band I absorption coefficient in case 3 was estimated by visually
inspecting the experimental results for the temperature profiles in the CSPonD demo prototype
and estimating the absorption coefficient based on the mixing theory in Chapter 3. Finally, case 4
uses a band I absorption coefficient half the value used in case 3 to determine the effects of a highly
transparent liquid.
A fraction of the radiation emanating from the diffuse flux source first enters the FOE. The
boundaries of the FOE are specularly reflecting and further concentrate the radiation flux source
to the surface of the molten salt. A small fraction of the incident radiation is reflected at the salt
surface; the remainder is transmitted through the surface and is absorbed volumetrically in the salt,
by the mixing plate, and by the tank walls. The remaining fraction of the radiation source that does
not enter the FOE is absorbed by the cold black plenum boundaries. Thermal radiation can in turn
escape the salt surface boundary and be absorbed or reflected by the surrounding structure or
absorbed by the cold black plenum boundaries.
85
Table 4-1 List of thermal radiative properties and boundary conditions used in the CFD model.
Region Property Band I Band II
FOE Reflectivity (𝜌) 0.7 (specular) 0.9 (specular)
Plenum Emissivity (𝜖) 1.0 (diffuse) 1.0 (diffuse)
304L SS tank Emissivity (𝜖) 0.5 (diffuse) 0.85 (diffuse)
Mixing plate Emissivity (𝜖) 0.5 (diffuse) 0.85 (diffuse)
Divider plate Emissivity (𝜖) 0.08 (diffuse) 0.17 (diffuse)
Binary
nitrate
(“solar salt”)
Case 1
Absorption
coefficient
(𝜅, 𝑚−1)
12.5 3706.9
Case 2 5.3 135
Case 3 2 135
Case 4 1 135
The external boundaries of the receiver insulation are assumed to be cold enough such that
convective heat losses dominate and radiation losses are assumed to be negligible. An average heat
transfer coefficient of ℎ∞ = 10 𝑊𝑚2⁄ with the measured ambient temperature 𝑇∞ used for the
ambient conditions.
The divider plate consists of a circular 120 cm-diameter and 22.7 cm-thick evacuated plate with
eight air chambers formed by seven radiation shielding disks, as shown in Fig. I1a. The evacuated
design with radiation shielding allows to further reduce heat transfer the hot layer of salt to the
cold layer. The external walls in contact with the salt are made of 304L stainless steel. Since the
exact temperature distribution inside the divider plate is not required to model and predict the
behavior of the salt in the receiver, the divider plate geometry is simplified to a uniform solid plate
with identical overall dimensions and equivalent thermophysical properties. The details of the
geometry simplification are discussed in Appendix H.
86
The mixing plate consists of two 0.125 in-thick parallel slotted circular sheets made of 304L
stainless steel material connected with tabbed components as shown in Fig. H1.b. The overall
dimensions of the two-sheet mixing plate are 123 cm-diameter and 5 cm-thick. The tabs and slots
form channels such that the salt can flow through the plate’s channels or through the annulus
between the tank walls and the plate when the plate’s motion is actuated. Similarly to the divider
plate, the geometry is simplified to a uniform solid plate with identical overall dimensions and
equivalent thermophysical properties. It is expected that no salt flows through the complex
channels in the mixing plate when the plate is stationary and the fluid above is hotter than the fluid
below. Further details of the geometry simplification of the mixing plate are discussed in
Appendix H.
4.3. Numerical procedure
The penetrative convection within the salt with internal re-radiation requires the ability to model
fluid dynamics within a participating media. The governing equations for the buoyancy-driven
flow in a non-scattering, incompressible fluid with the Boussinesq approximation are therefore
given as
𝜕𝒗
𝜕𝑡+ 𝒗 ∙ 𝛻𝒗 = −
1
𝜌𝛻𝑝 + 𝜈𝛻2𝒗 − 𝐠𝛽𝑇 (4.1)
𝛻 ∙ 𝒗 = 0 (4.2)
𝜌𝑐𝑝
𝜕𝑇
𝜕𝑡+ 𝜌𝑐𝑝𝒗 ∙ 𝛻 = 𝛻 ∙ (𝑘𝑐𝛻𝑇) − 𝛻 ∙ 𝒒𝑹 (4.3)
87
𝛻 ∙ 𝒒𝑹 = ∫ 𝜅𝜆 (4𝜋𝐼𝑏𝜆 − ∫ 𝐼𝜆𝑑𝛺4𝜋
)∞
𝜆=0
𝑑𝜆 (4.4)
𝑑𝐼𝜆
𝑑𝑠= 𝜅𝜆(𝐼𝑏𝜆 − 𝐼𝜆) (4.5)
where 𝑡 is time, 𝒗 is the velocity vector with respect to the 3D coordinate system, 𝜌 is density, 𝑝
is the static pressure, 𝜈 is the kinematic viscosity, 𝐠 is the gravitational acceleration vector, 𝛽 is
the thermal expansion coefficient of the fluid, 𝑇 is the temperature, 𝑐𝑝 is the specific heat, 𝑘𝑐 is
the thermal conductivity, 𝒒𝑹 is the radiative flux vector, 𝜅𝜆 is the spectral absorption coefficient,
𝛺 is the solid angle, 𝜆 is the wavelength, 𝐼𝑏𝜆 is the spectral blackbody radiative intensity, 𝐼𝜆 is the
radiative intensity, and 𝑠 is the path.
The governing equations for three-dimensional, transient, combined convection and radiation are
solved in the STAR-CCM+ commercial software package for its capability to couple the equations
for fluid flow with the radiative transfer equation (RTE). The Boussinesq approximation is applied
for solving the momentum equation. The flow was modeled as laminar in the salt for reasons
outlined in Section 3.3. In addition, since the flow is strongly coupled to the temperature gradients,
a coupled solver is used. The RANS equations in the air region above the receiver were modeled
using the realizable k-ε turbulence model with a coupled solver. A two-layer all Y+ treatment was
used for the walls, with proper care taken for the wall mesh, particularly inside the FOE cavity
where there is significant convection.
The spectral behavior was modeled using multiband thermal radiation, with spectral bands and
properties as defined in Section 4.2. The intensity of the diffuse radiative source is scaled such that
the concentrated solar flux output from the FOE matches that calculated from ray-tracing of the
FOE. The radiative transfer equation is solved using the Discrete Ordinates Method (DOM) with
88
an S8 discretization, such that the full solid angle is divided into 8 discrete angular intervals. Lower
discretization gave spatial distributions of the solar irradiation on the FOE (Fig. 4.4) that were
inconsistent with those predicted by optics modeling of the CSPonD beam down system [62].
S4 S6 S8
Figure 4-4 Distribution of the incident solar irradiation on the final optical element (FOE) for S4, S6, S8 ordinates
discretization.
Fig. 4.5. shows the temperature profiles calculated in the salt region at the locations of the
prototype thermocouple rod positions R1, R3, and R7 with the top surface of the MP positioned at
1 m after 1200 seconds of solar heating for S4, S6, and S8 ordinates discretization. Overall, the
variation in the temperature profiles for the S6 and S8 discretizations is small. The largest variation
occurs near the mixing plate for the R3 thermocouple rod, where the temperature difference
between S6, and S8 is 4 °C and represents less than 2% uncertainty. Since the variation is small,
the S8 discretization is considered to be sufficiently refined and was therefore selected.
90
(c)
Figure 4-5 Temperature profiles for R1, R3, and R7 line probe locations at 1200 seconds for S4, S6, and S8 ordinates
discretization.
The solid regions include the aluminum FOE, the 304L stainless steel tank, mixing plate and
divider plate, pyrogel insulation and rockwool insulation around the side walls, and promaboard
and foamglass insulation below. Detailed dimensions of each region in the full receiver are
provided in Appendix D. The heat transfer through the solid regions is modeled using a coupled
energy solver. Very thin layers which include the stainless steel tank, FOE, the MP top and bottom
surfaces were modeled using thin shell models.
To initialize the temperature distribution in each region, the temperature in the salt region is first
defined using the temperature measurements collected at the start of each experiment and the test
facility. An initial steady-state calculation is then carried-out while maintaining the salt
temperature constant. The solution to the steady-state calculation is then used as the initial
condition for the subsequent transient calculations.
91
4.4. Dependence on the grid resolution
A grid sensitivity study was carried out to determine the influence of the grid size on the solution.
Three different grid sizes were selected. The base sizes in the salt region for the three hexahedral
meshes were 4.2 cm (fine), 5 cm (medium), and 6 cm (coarse), with the ‘medium’ refinement grid
shown in Fig. 4.6. Prism layers were used on the boundaries, with a 50 % grid refinement region
around the DP and MP as shown in Fig. 4.6b. The corresponding prism layer mesh thicknesses on
the MP and DP walls were 1.5 mm, 1.9 mm, and 2.3 mm for the finest, intermediate, and coarsest
mesh refinements, respectively.
(a)
92
(b)
Figure 4-6 Cross-sectional view of the hexagonal grid of the entire model (a) and of enlarged view of the refinement
region around the MP and DP (b).
Fig. 4.7. shows the temperature profiles calculated in the salt region at the locations of the
prototype thermocouple rod positions R1, R3, and R7 with the top surface of the MP positioned at
1 m after 600 seconds of solar heating. The value for the absorption coefficients used here are
𝜅𝐼 = 2 𝑚−1 and 𝜅𝐼𝐼 = 160 𝑚−1. The three line probes show good agreement within the bulk of
the fluid and at the bottom of the tank. The temperatures deviate more at the salt surface and near
the top surface of the mixing plate. However, this deviation is expected in the presence of natural
convection due to the randomness of plumes rising and unstable recirculation causing larger
oscillations in the temperature near the boundaries.
94
(c)
Figure 4-7 Temperature profiles for R1, R3, and R7 line probe locations at 600 seconds for coarse, medium, and
fine grids.
The oscillatory behavior of the temperature at both the salt surface and MP top surface can clearly
be seen in Fig. 4.8. The salt surface in particular demonstrates significant oscillations. This is due
to the surface being at the interface of the salt and the air which both experience natural convection
with unstable recirculations. The slightly higher disagreement in the initial 100 seconds of the
simulation is likely due to the transition from a conduction dominant heat transfer regime to natural
convection, as discussed in Chapter 4. Overall, Fig. 4.8 shows that the average temperature over
time for the three grids agree well and the sensitivity of the solution on the grid size at the chosen
grid refinements is negligible, particularly for the two finest grids. In addition, the energy balance
for all regions modeled was monitored throughout the simulations and all three grids demonstrated
~99.6 % energy balance. For this reason, the ‘medium’ refinement (base size x = 2.5 cm) was
selected.
95
Figure 4-8 Average temperature at the salt surface and the mixing plate top surface versus time as calculated by the
CFD model.
4.5. Results for January 23, 2018 experiment
4.5.1. Initial Conditions
In this section, results are presented for the experiments carried out with the CSPonD demo
prototype at the Masdar Institute Solar Platform, and the corresponding CFD calculations. In this
experiment, the MP’s top surface is located 1 m from the bottom of the tank, and the salt surface
is located at 1.67 m from the bottom of the tank. The maximum depth through which concentrated
sunlight can penetrate is therefore 0.67 m. The simulations were carried-out for a total time of
120 minutes of real-time heating. The computational runtime for each case studied was
96
approximately 12 days. The solar flux at the FOE outlet to the receiver versus time is shown in
Fig. 4.9. The results calculated using ray-tracing methods were interpolated with a polynomial
function to be used as input for the CFD model. The initial solar irradiation on the FOE internal
boundaries, salt surface, and MP are shown in Fig. 4.10. The variation of intensity at the MP top
surface with varying absorption properties can clearly be seen in the figure. The initial temperature
distribution and velocity distribution for all cases can be seen in Fig. 4.11. Since both the
temperature and velocity distributions are highly uniform throughout the plenum, they have been
cropped to improve visibility of the regions of interest.
Figure 4-9 Solar flux bottom output as estimated using ray-tracing [62] and corresponding polynomial
interpolation used as input for the CFD calculations.
FOE outlet solar irradiation to receiver versus time as estimated using ray-tracing for January 23, 2018 experiment
FO
E o
utle
t so
lar
irra
dia
tio
n (
kW
)
97
𝜅𝐼,
1=
12
.5 𝑚
−1
𝜅𝐼,
2=
5.3
𝑚−
1
𝜅𝐼,
3=
2 𝑚
−1
𝜅𝐼,
4=
1 𝑚
−1
𝜅𝐼𝐼
,1=
37
06
.9 𝑚
−1
𝜅𝐼𝐼
,2=
13
5 𝑚
−1
𝜅𝐼𝐼
,3=
13
5 𝑚
−1
𝜅𝐼𝐼
,4=
13
5 𝑚
−1
Fig
ure
4-1
0 I
nit
ial
surf
ace
irra
dia
tio
n o
n F
OE
, sa
lt s
urf
ace,
and
MP
fo
r sp
ectr
al b
and
I (
sola
r sp
ectr
al b
and
).
99
4.5.2. Results: CFD calculated temperature and velocity distributions
𝜅𝐼,
1=
12
.5 𝑚
−1
𝜅𝐼,
2=
5.3
𝑚−
1
𝜅𝐼,
3=
2 𝑚
−1
𝜅𝐼,
4=
1 𝑚
−1
𝜅𝐼𝐼
,1=
37
06
.9 𝑚
−1
𝜅𝐼𝐼
,2=
13
5 𝑚
−1
𝜅𝐼𝐼
,3=
13
5 𝑚
−1
𝜅𝐼𝐼
,4=
13
5 𝑚
−1
Fig
ure
4-1
2 C
ross
-sec
tio
nal
tem
per
ature
dis
trib
uti
on o
f al
l m
od
eled
reg
ions
afte
r 6
0 m
inute
s o
f so
lar
hea
tin
g.
100
𝜅𝐼,
1=
12
.5 𝑚
−1
𝜅𝐼,
2=
5.3
𝑚−
1
𝜅𝐼,
3=
2 𝑚
−1
𝜅𝐼,
4=
1 𝑚
−1
𝜅𝐼𝐼
,1=
37
06
.9 𝑚
−1
𝜅𝐼𝐼
,2=
13
5 𝑚
−1
𝜅𝐼𝐼
,3=
13
5 𝑚
−1
𝜅𝐼𝐼
,4=
13
5 𝑚
−1
Fig
ure
4-1
3 T
emp
erat
ure
dis
trib
uti
on o
f sa
lt c
ross
-sec
tio
n,
salt
surf
ace,
and
MP
surf
ace
aft
er 6
0 m
inute
s o
f so
lar
hea
tin
g.
101
𝜅𝐼,
1=
12
.5 𝑚
−1
𝜅𝐼,
2=
5.3
𝑚−
1
𝜅𝐼,
3=
2 𝑚
−1
𝜅𝐼,
4=
1 𝑚
−1
𝜅𝐼𝐼
,1=
37
06
.9 𝑚
−1
𝜅𝐼𝐼
,2=
13
5 𝑚
−1
𝜅𝐼𝐼
,3=
13
5 𝑚
−1
𝜅𝐼𝐼
,4=
13
5 𝑚
−1
Fig
ure
4-1
4 C
ross
-sec
tio
nal
vel
oci
ty d
istr
ibuti
on o
f al
l m
od
eled
reg
ions
aft
er 6
0 m
inute
s o
f so
lar
hea
ting.
102
𝜅𝐼,
1=
12
.5 𝑚
−1
𝜅𝐼,
2=
5.3
𝑚−
1
𝜅𝐼,
3=
2 𝑚
−1
𝜅𝐼,
4=
1 𝑚
−1
𝜅𝐼𝐼
,1=
37
06
.9 𝑚
−1
𝜅𝐼𝐼
,2=
13
5 𝑚
−1
𝜅𝐼𝐼
,3=
13
5 𝑚
−1
𝜅𝐼𝐼
,4=
13
5 𝑚
−1
Fig
ure
4-1
5 C
ross
-sec
tio
nal
vel
oci
ty d
istr
ibuti
on o
f sa
lt r
egio
n a
fter
60
min
ute
s o
f so
lar
heat
ing.
103
4.5.3. Results: Experiment and CFD model temperature profiles comparison
Figure 4-16 Temperature profiles at location R1 for case 𝜅𝐼,1 = 12.5 𝑚−1, 𝜅𝐼𝐼,1 = 3706.9 𝑚−1
107
4.6. Discussion
Overall, the results presented in Figs. 4.12-19 show significant disagreement between the CFD
results and the experimental results from the demo prototype at the Masdar Institute Solar
Platform. The results are also highly sensitive to the absorption coefficient, as shown for the four
cases studied. The main sources of uncertainty and disagreement fall within the following three
categories:
1. Uncertainty in solar source intensity
2. Uncertainty in salt optical properties
3. Experimental uncertainty
In the following sections, the results will therefore be discussed in terms of these three key aspects.
4.6.1. Solar source intensity
The total source intensity at the FOE outlet to the receiver has been estimated using ray-tracing
calculations, as noted in Section 4.2, and was not measured. The calculations were carried out
assuming ideal operating conditions and did not account for the uncertainty in heliostat alignment,
degradation of the heliostat reflectivity, and any other sources of uncertainty. The calculated
intensity is therefore an upper limit, and the expected output should be less than the calculated
values presented in Fig. 4.9, which in turn will result in lower temperature increases in the receiver
over time than expected. The temperature gradient in the stratified layer will also grow less rapidly.
However, the deviation in the expected temperature increase over time as calculated by the CFD
model is extremely large (Figs. 4.16-4.19). We may consider a first order analysis of the net energy
increase in the molten salt compared to the calculated source intensity to gain further insight into
the relative magnitude of the uncertainty.
108
We consider the change in temperature between the initial state 𝑡 = 0 and 𝑡 = 120 minutes.
Taking the average temperature of the thermocouple probe readings for line probes R1, R3, and
R7, this yields an estimated average temperature increase of ∆�̅�𝑠𝑎𝑙𝑡 ≈ 12.6 ℃. For an estimated
total mass of salt 𝑚𝑠𝑎𝑙𝑡 = 3150 𝑘𝑔 in the receiver at the time of the experiment, and an average
specific heat 𝑐𝑝,𝑠𝑎𝑙𝑡 ≈ 1500 𝐽
𝑘𝑔℃, the total energy increase of the salt ∆𝐸𝑒𝑥𝑝,𝑡=120 as estimated
from the experiments for the first 120 minutes of heating is therefore
∆𝐸𝑒𝑥𝑝,𝑡=120 = 𝑚𝑠𝑎𝑙𝑡𝑐𝑝,𝑠𝑎𝑙𝑡∆�̅�𝑠𝑎𝑙𝑡 ≈ 3150 𝑘𝑔 × 1500 𝐽
𝑘𝑔℃× 12.6 ℃ = 59,535 𝑘𝐽 (4.6)
Assuming the capture efficiency is approximately 𝜂𝑐 ≈ 60% (Section 2.5.3) for the ranges of
temperatures and solar concentration investigated, and taking the average intensity for the first
120 minutes �̇�𝑠𝑜𝑙𝑎𝑟,𝑎𝑣𝑔 ≈ 51 𝑘𝑊, this yields a theoretically estimated energy absorption in the salt
of
∆𝐸𝑡ℎ𝑒𝑜,𝑡=120 = 𝜂𝑐�̇�𝑠𝑜𝑙𝑎𝑟,𝑎𝑣𝑔∆𝑡 = 0.6 × 51 𝑘𝑊 × 7200 𝑠𝑒𝑐 = 220,320 𝑘𝐽 (4.7)
The experimentally observed change in energy of the salt is therefore 3.7 times smaller than the
expected value. In addition, the capture efficiency used for the theoretical prediction is a
conservatively low value since it was obtained from the results presented in Chapter 2 for an open
surface with a view factor to the environment of 𝐹 = 1. It can therefore be concluded that the
predicted FOE outlet solar flux has been significantly overestimated and introduces a significant
uncertainty the CFD model. Future work should therefore focus on estimating the reduction in
source intensity due to improper heliostat alignment, heliostat and FOE reflectivity degradation,
etc., and measuring the flux output directly. In addition, it would be useful to consider a test
109
apparatus based on the original CSPonD concept where hillside heliostats are used, so potentially
an FOE would not be required.
4.6.2. Salt optical properties
The second large source of uncertainty that can clearly be observed in the results are the salt optical
properties. The range of solar weighted optical thicknesses investigated in the CFD analysis is 𝜏 ≈
0.7 − 8. The experimental results demonstrate relatively good temperature uniformity, suggesting
the mixing is well developed within the layer above the mixing plate. These results suggest that
the molten salt is much more optically transparent in the solar spectrum than predicted by the
optical property measurement results and analysis presented in Chapter 2. Cases 1 and 2 are based
on the measurement results with different extrapolation methods in the absorption bands. It can
clearly be seen in the temperature distributions (Figs. 4.12-4.13) and temperature profiles (Figs.
4.16-4.17) for cases 1 and 2 that the temperature in the stratified upper layer grows very rapidly to
temperatures approaching the thermal limit of the salt compared with the experimental results. The
mixing due to natural convection is also readily observed in the optically thinner cases studied in
the velocity distributions (Figs. 4.14-4.15). There are several sources of uncertainty and error in
the optical property measurements, CSPonD demo prototype experiments, and CFD analysis,
which give rise to the large disagreement between the results.
4.6.2.1. Measurement uncertainty
The measured optical properties of solar salt presented in Chapter 2 have a relatively large
experimental uncertainty in the solar spectrum, particularly at wavelengths near the sun’s peak
intensity. In addition, the extrapolation methods into the absorption bands have a significant effect
on the weighted-average absorption coefficients. These uncertainties are in large part due to the
nature of the experimental technique. The optimal measurement range of the FTIR is in the NIR
110
spectrum where the absorption of the salt falls within a range that is easily measurable. However,
the intensity of the FTIR source is much weaker in the visible and MIR spectra, making
measurements much more challenging, particularly for highly transparent or opaque liquids. To
eliminate any spurious variations in the attenuation during the measurement, the method therefore
requires a combination of near-perfect alignment, a very long column of liquid for highly
transparent media or very thin layers for highly absorbing media. Increasing the length of the liquid
column to increase the path length through which the light source travels further decreases the
accuracy of the optics alignment. Although the transmission method combined with FTIR
spectroscopy allowed to make rapid measurements over a relatively large range of thicknesses and
at high temperature, several limitations in the method introduce uncertainties in the measurements
that potentially limit its applicability in certain applications such as the present study. The method
may therefore be limited to higher wavelengths and a smaller range of measurable absorption
coefficients than previously expected. It may therefore be preferable to use a combination of
different measurement techniques to measure different spectral ranges. For example, the method
proposed by Passerini et al. [31] may be more appropriate in the visible spectrum down to 400 nm.
4.6.2.2. Property modeling in CFD analysis
In addition to the experimental measurement uncertainties, the spectral bands introduce another
source of error in the modeling. In particular, solar salt has a short-wavelength absorption edge
located near the peak intensity of the solar spectrum. The optical properties therefore vary
significantly in the solar spectrum as it shifts from highly absorbing at wavelengths below 450 nm
to highly transparent for wavelengths above this value and into the NIR. For the receiver MP depth
investigated, the heated salt layer is expected to be optically thick in some regions of the solar
spectrum and of order 𝜏~ℴ(1) elsewhere. The weighted-averaging method does not account for
111
this behavior, such that less solar flux appears to reach the MP. More spectral bands would allow
to resolve this limitation, however, would also significantly increase the computational time.
4.6.2.3. Optical properties of salt under receiver conditions
Finally, the solar salt used for the property measurements and prototype experiments is a
commercial grade salt. The impurities present in the salt tend to settle over time, such that the
apparent absorption coefficient may decrease with time. The salt in the demo experiment had gone
several weeks in the receiver, versus at most a few days for the optical property measurements.
This may therefore also explain the lower absorption observed in the receiver prototype. Future
work may potentially focus on characterizing the property variation over time.
4.6.3. Demo prototype experimental uncertainty
Uncertainties also arise from the demo prototype experiments and the temperature measurements
collected which have not been fully characterized. First and foremost, the demo prototype
experiment was only carried-out once and should be repeated at least once to characterize the
repeatability of the experimental results. In addition, the temperature at the MP top surface has not
been measured. This measurement is critical to determine peak temperatures in the receiver. It
would also allow to gain further insight, experimentally validate the mixing theory, and estimate
the effective absorption coefficient in the receiver. In addition, due to salt evaporation over time,
the salt surface height decreases over time and its level can only be estimated by visual inspection.
Furthermore, in the experiment presented, the top-most temperature probe falls approximately
15 cm below the salt surface. It is therefore not possible to determine if there is any thermal
stratification in the top layer, or to estimate the thermal losses to the environment and determine
its effects on the temperature profile immediately below the surface. Finally, the thermocouple
rods create a thermal shortcut which may also affect the temperature distribution and the
112
temperature reading at the locations of the thermocouple probes. Its effects should therefore be
estimated to determine the uncertainty in the measurement.
4.7. Conclusions
This chapter presented the first complete CFD model and analysis of a molten salt, direct
absorption volumetric receiver with radiation induced convection. The model setup and results
were presented and compared with the experimental results obtained at the Masdar Institute Solar
Platform. A large disagreement was observed between the model and experimental results. The
sources of uncertainty in the model input parameters and the validation experiments are
highlighted and discussed. The major sources of uncertainty were determined to be the salt optical
properties, the estimated solar source intensity, and uncertainty in the validation experiments.
Further work should focus on quantifying these uncertainties in order to improve the agreement
between the model and experiments.
113
5. Receiver cover design for enhanced thermal performance
The benefits of converting solar energy at high temperatures in terms of thermal efficiency are
typically offset by high thermal losses, in particular for low solar concentration ratios where the
solar absorption is small relative to thermal losses[32]. Improving efficiency at high temperatures
is a significant challenge in both solar-thermal and solar thermophotovoltaic applications and
many methods have been explored for overcoming this challenge[33–38]. In particular, spectrally
selective surface absorbers for solar-thermal applications are engineered to maximize solar
absorptivity and minimize thermal radiative losses[40,41,64]. Very high temperature (VHT,
> 400 °C) liquid-based receivers such as molten salts and synthetic oils are also inhibited by large
radiative losses, particularly at low solar concentrations. Standard methods for reducing losses in
these receiver designs such as reflective cavities[33,34], windows[36] and radiation shields cannot
readily be implemented, and their effectiveness is limited due to fabrication, cost, and operation
constraints[43,44]. In addition, as seen in Chapter 4, a very large temperature gradient exists near
the salt surface due to the radiative cooling, which further reduces the temperature uniformity
within the liquid absorber.
Here we demonstrate a new modular floating cover for open-tank, VHT volumetric solar-thermal
receivers. The insulating cover consists of an array of densely packed, floating hollow fused silica
spheres. This simple design uses readily available and inexpensive materials and are ideal for
commercial use. Its modular parts are inexpensive, easy to replace during operation, highly solar-
transparent[65] and stable in VHT environments. In addition, the floating parts reduce the liquid
surface area exposed the environment, which decreases the breakdown and oxidation of the fluid
114
and evaporation losses. This in turn decreases damage to structural and optical components due to
reduced vapour exposure. The proposed cover concept could be applied to reduce heat losses and
generate energy savings in a broad range of high temperature open bath applications including
chemical and food processing, and heat treating metals.
5.1. Very High Temperature Floating Modular Cover
Operating VHT fluid volumetric receivers requires significant reduction in thermal losses from the
receiver or very high solar concentrations in order to achieve non-zero system efficiencies[66,67].
This can readily be understood in terms of the receiver thermal efficiency 𝜂𝑡ℎ, defined as the ratio
of collected thermal energy to total incident solar energy[20], which, at steady state, is given by
𝜂𝑡ℎ =�̇�𝑎𝑏𝑠 − �̇�𝑙𝑜𝑠𝑠
𝐶𝐺𝑠𝐴𝑟𝑒𝑐 (5.1)
where �̇�𝑎𝑏𝑠 is the solar power absorbed by the receiver, 𝐶 is the solar concentration ratio, 𝐺𝑠 is
the direct normal irradiance, 𝐴𝑟𝑒𝑐 is the surface area of the receiver exposed to the concentrated
solar irradiation, and �̇�𝑙𝑜𝑠𝑠 is the sum of the convective, evaporative, and radiative heat losses to
the environment. For a sufficiently deep receiver with highly absorbing containment walls, most
of the non-reflected incident energy is absorbed such that �̇�𝑎𝑏𝑠 ≈ τ𝑟𝑒𝑐𝐶𝐺𝑠𝐴𝑟𝑒𝑐 , where
τ𝑟𝑒𝑐 is the receiver’s transmittance to the liquid, and the thermal efficiency becomes
𝜂𝑡ℎ ≈ τ𝑟𝑒𝑐 −�̇�𝑐𝑜𝑛𝑣 + �̇�𝑒𝑣𝑎𝑝 + �̇�𝑟𝑎𝑑
𝐶𝐺𝑠𝐴𝑟𝑒𝑐 (5.2)
For large solar concentrations (𝐶 > 500), thermal losses are typically much smaller than the solar
power input and the efficiency is dominated by the transmission losses 𝜏𝑟𝑒𝑐. However, for lower
concentrations (𝐶 < 100), heat losses become significant with thermal radiation dominating at
115
VHT. It is therefore critical to develop methods for mitigating thermal losses without strongly
increasing reflection losses or degrading the volumetric absorption quality of the receiver.
Fig. 5.1a shows the heat transfer processes involved in a volumetric receiver used with CSP
technology, with and without a cover. For an uncovered receiver at 800 °C, radiative losses from
the surface reach up to 75 kW/m2 for an isothermal fluid contained in a vessel material with high
emissivity. For a nominal solar flux Gs = 1 kW/m2 (≈ 1 sun) and concentration ratio 𝐶 < 100, the
thermal efficiency is limited to less than 25 %, without accounting for transmission reflection
losses. When a solar-transparent window is used to insulate the receiver, vapor condensation on
the internal side of the window and dust impurities on the external side rapidly degrade the optical
transmission. Furthermore, optical quality windows for relatively large receiver apertures (>1 m–
diameter) require expensive manufacturing and maintenance and are highly vulnerable to cracking
and are therefore a challenging option.
Outdoor swimming pool owners are familiar with solar covers which have existed for decades[68–
70]. These inexpensive floating structures are similar to bubble wrap and have the following
characteristics: nearly transparent in the solar spectrum to allow sunlight to be directly absorbed
and converted to heat in the pool, air bubble insulation to minimize convective heat loss, and
surface coverage to prevent water evaporation. Passive heating systems which include covers have
demonstrated the ability to reduce a swimming pool’s annual heating load by 90%[71]. Variations
on the floating pool structure concept have been developed for enhanced steam generation at low
solar concentrations[22,72]. However, their extension to very high temperature (VHT) fluids and
volumetric solar-thermal receiver applications imposes additional engineering constraints and has
not been implemented to this day.
116
The proposed floating hollow fused silica sphere design (Fig. 5.1b) is stable in harsh VHT
environments such as molten salts and is modular to allow easy online maintenance and component
replacement. Similar to the outdoor pool cover, the proposed cover is highly solar-transparent and
introduces minimal reflection losses, it reduces both convective and radiative thermal losses at the
surface, and it minimizes the surface area available for evaporation without trapping vapour. In
addition, the floating spheres allow impurities such as dust and sand to fall through which would
otherwise accumulate on a window’s surface, degrade solar transmission, and potentially burn in
the presence of high solar fluxes. The spheres can readily be used to cover very large surfaces
extending up to 25 m in diameter which cannot be achieved with a single continuous window pane.
(a)
117
(b)
(c)
Figure 5-1 Solar pond energy balance and cover concept. a, Very high temperature solar pond energy balance
with and without solar-transparent window. For an uncovered receiver at 800 °C, radiative losses from the surface
reach up to 75 kW/m2 for an isothermal fluid contained in a vessel material with high emissivity. For a nominal
solar flux Gs = 1 kW/m2 (≈ 1 sun) and concentration ratio 𝐶 < 100, the thermal efficiency is limited to less than
25 %, without accounting for transmission reflection losses. b, Operation of solar pond with solar-transparent
window (left) versus floating spheres (right). Salt vapours and dust from the environment are trapped by the
continuous window pane, reducing solar transmission. Vapours and dust can escape or fall through in the
breathable floating sphere concept. c, Image of a 20 mm-OD fused silica sphere (left) and 20 mm-OD floating
spheres on molten salts (right). A small open port prevents the spheres from pressurizing when subjected to high
temperatures.
118
5.2. Methodology
The purpose of the cover is to enhance the thermal efficiency (Eq. 5.2). We assume at very high
temperatures (≥ 400℃) thermal losses are dominated by thermal radiation such that the thermal
efficiency may be approximated by the capture efficiency[66]
𝜂𝑐 ≈ 𝜏𝑟𝑒𝑐 −�̇�𝑟𝑎𝑑
𝐶𝐺𝑠𝐴𝑟𝑒𝑐 (5.3)
A detailed analysis of the heat loss mechanisms is included in Section 5.3. For fixed solar
concentration and receiver size, the quantity 𝐶𝐺𝑠𝐴𝑟𝑒𝑐 is constant, and we aim to minimize
radiation thermal losses �̇�𝑟𝑎𝑑 while maintaining high transmittance 𝜏𝑟𝑒𝑐 to the liquid. We use
experimental, analytical and numerical tools to demonstrate the floating cover concept and to
determine the achievable enhancement in capture efficiency. We first seek to predict the cover’s
thermal effectiveness defined as
𝜖𝑠 = 1 −�̇�𝑟𝑎𝑑
�̇�𝑟𝑎𝑑𝑟𝑒𝑓
(5.4)
where �̇�𝑟𝑎𝑑𝑟𝑒𝑓
and �̇�𝑟𝑎𝑑 are the thermal radiation losses to the environment from the reference
uncovered liquid and covered liquid, respectively. We evaluate this experimentally and use the
results to validate a numerical thermal model. A simplified analytical thermal model capturing the
effects of the various heat transfer mechanisms is developed in parallel and is used to understand
and discuss the performance of the cover in terms of the physical and geometrical parameters. Ray-
tracing simulations are carried out to evaluate the solar transmission through the cover. Finally,
the overall performance is discussed in terms of the capture efficiency.
119
5.2.1. Laboratory experiments and simulation validation
5.2.1.1. Laboratory experiments
The insulating performance of the floating spheres concept was first demonstrated experimentally
in a laboratory environment. An 80 mm-diameter beaker was filled with a
40 wt. % KNO3:60 wt. % NaNO3 binary nitrate molten salt mixture (solar salt) and was heated in
a tube furnace such that the salt remained molten and the surface was maintained at 400 °C. The
photon flux emanating from the surface of the salt was captured using an IRC800 Series infrared
(IR) camera with a 1.0 µm – 5.3 µm spectral response range and an integration time of 0.01 s. At
400 °C, approximately 41 % of the emitted blackbody radiation falls within the cameras response
range. Two different sizes of hollow fused silica spheres (20 mm-OD, 1.5 mm wall thickness and
70 mm-OD, 2 mm wall thickness) were then deposited one by one onto the surface of the salt such
that they were heated from below by the salts and not from the side by the furnace to replicate
solar pond conditions. The spheres included an open port to prevent pressurization when exposed
to high temperatures. An image was captured with the IR camera once the surface temperature
reached equilibrium. A simplified diagram of the experimental setup is shown in Fig. 5.2., and a
picture of the setup and spheres floating on the salt surface are presented in Fig. 5.3. The cover
effectiveness for each sphere configuration was then calculated as
𝜖𝑠 = 1 −∑ Φ𝑖𝑎𝑙𝑙 𝑝𝑖𝑥𝑒𝑙𝑠
∑ Φ𝑖,𝑒𝑓𝑎𝑙𝑙 𝑝𝑖𝑥𝑒𝑙𝑠 (5.5)
where Φ𝑖,𝑟𝑒𝑓 and Φ𝑖 are the photon fluxes at pixel 𝑖 for the reference image without spheres and
the image with spheres, respectively.
120
Figure 5-2 Validation experiment. Simplified diagram of the experimental setup used for evaluating the thermal
insulation performance of the floating spheres, and 3D representation of the simulated section. An infrared
camera is used to measure the photon flux losses from the surface of a heated beaker filled with molten salt, with
and without floating spheres.
(a)
121
(b)
Figure 5-3 a) Experimental setup for measuring thermal losses from the salt with and without spheres. b) Image of
floating spheres as seen through from the infrared camera position.
Images were converted to an intensity distribution (Appendix D) as they were retrieved from the
camera using an in-house calibration procedure[73], and cropped following the edge of the molten
salt beaker. Artefacts such as “dead pixels” were treated using a 2D median filter, replacing each
pixel by the median intensity of the surrounding pixels enclosed in a 7-pixel wide square.
5.2.1.2. Thermal modelling simulations
Steady-state simulations were developed and carried-out in STAR-CCM+ and were validated with
the experimental results. Combined heat transfer including both thermal radiation and conduction
were included inside the system. The surrounding air is modeled as a stagnant (no convection)
such that the results are expected to be a lower limit on the performance. The geometry and
boundary conditions are shown in Figure 5.4. Only radiation thermal losses through the open top
surface are accounted for. Both sphere sizes used in the experiments were modelled. For the
122
smaller, 20 mm-OD spheres, three different configurations were randomly generated to determine
the effects of uncertainty in sphere position and the results were averaged. The standard deviation
in the simulations results from the three randomly generated configurations was 44 % for the single
sphere, and less than 10 % for all other cases. The approximate depth to which the spheres sink,
𝐻𝑠𝑖𝑛𝑘, was calculated from a simple buoyancy balance as an initial estimate. The effectiveness of
the spheres was then calculated as
𝜖𝑠 = 1 −�̇�𝑙𝑜𝑠𝑠
𝑟𝑎𝑑
�̇�𝑙𝑜𝑠𝑠,𝑟𝑒𝑓𝑟𝑎𝑑
(5.6)
where �̇�𝑙𝑜𝑠𝑠𝑟𝑎𝑑 and �̇�𝑙𝑜𝑠𝑠,𝑟𝑒𝑓
𝑟𝑑 are the radiation thermal losses escaping the system through the open
top surface for the covered liquid and reference uncovered liquid systems, respectively.
(a)
123
(b)
Figure 5-4 a, Geometry, properties, and boundary conditions of thermal model. b, Sphere configurations (bottom)
for experiment validation.
The salt is modeled as an opaque medium with spectrally averaged emissivity 𝜖𝑠𝑎𝑙𝑡 = 0.89[63].
Solar salt is expected to be optically thick at these temperatures[63] and the surface can be
approximated as a black-body emitter. Fused silica has a long-wavelength absorption band which
begins around 2.5 µm. As temperature increases, the Planck emission spectrum peak moves from
longer to shorter wavelengths, moving out of the absorption band and into the semi-transparent
region. Fused silica therefore behaves as a participating media and its average optical properties
vary with temperature. Nevertheless, the thermal radiation is treated as diffuse, gray, surface-to-
surface radiation throughout the system. “Apparent” optical properties capturing the radiation
properties of semi-transparent fused silica were evaluated to model the spherical shells with finite
wall thickness as single surfaces for the radiative heat transfer component. The spectral emissivity
𝜖𝜆 , apparent reflectivity 𝜌𝜆∗ , and apparent transmissivity 𝜏𝜆
∗ of the single surface are given by
McMahon[74]:
𝜖𝜆 =[1 − 𝜌𝜆][1 − 𝜏𝜆]
1 − 𝜌𝜆𝜏𝜆
(5.7)
124
𝜌𝜆∗ = 𝜌𝜆 {1 +
𝜏𝜆2[1 − 𝜌𝜆]2
1 − 𝜌𝜆2𝜏𝜆
2 } (5.8)
𝜏𝜆∗ = 𝜏𝜆
[1 − 𝜌𝜆]2
1 − 𝜌𝜆2𝜏𝜆
2 (5.9)
which together satisfy Kirchhoff’s law 𝜖𝜆 + 𝜌𝜆∗ + 𝜏𝜆
∗ = 1. The spectral hemispherically averaged
true transmissivity 𝜏𝜆 is obtained by evaluating the following expression
𝜏𝜆 = 𝑒−4𝜋𝜅�̅�
𝜆 (5.10)
where �̅� is the average path length through the thickness of the fused silica walls. For this study,
we take this to be the minimum possible path length, �̅� = 𝑡 (wall thickness), which yields the
highest possible transmission for thermal radiation and provides a lower limit on the performance.
The spectral, hemispherical, true reflectivity 𝜌𝜆 is given by Dunkle[75]
𝜌∥ = 1 −8𝑛
𝑛2 + 𝜅2{1 −
𝑛
𝑛2 + 𝜅2ln[(𝑛 + 1)2 + 𝜅2] +
𝑛2 − 𝜅2
𝜅(𝑛2 + 𝜅2)tan−1
𝜅
𝑛 + 1} (5.11)
𝜌⊥ = 1 − 8𝑛 [1 − 𝑛 ln(𝑛 + 1)2 + 𝜅2
𝑛2 + 𝜅2+
𝑛2 − 𝜅2
𝜅tan−1
𝜅
𝑛(𝑛 + 1) + 𝜅2] (5.12)
𝜌𝜆 =1
2(𝜌∥ + 𝜌⊥) (5.13)
where 𝑛 = 𝑛(𝜆) is the refractive index and 𝜅 = 𝜅(𝜆) is the extinction index. We assume smooth
and flat surfaces due to large sphere radii[76]. For gray thermal radiation, emission-spectrum
weighted averaged quantities are evaluated as
125
𝜖𝑠𝑝(�̅�𝑜𝑝 = 400 ℃) =∫ 𝐼𝑏𝜆(�̅�𝑜𝑝)𝜖𝜆𝑑𝜆
∞
0
∫ 𝐼𝑏𝜆(�̅�𝑜𝑝)𝑑𝜆∞
0
(5.14)
𝜌𝑠𝑝(�̅�𝑜𝑝 = 400 ℃) =∫ 𝐼𝑏𝜆(�̅�𝑜𝑝)𝜌𝜆
∗𝑑𝜆∞
0
∫ 𝐼𝑏𝜆(�̅�𝑜𝑝)𝑑𝜆∞
0
(5.15)
𝜏𝑠𝑝(�̅�𝑜𝑝 = 400 ℃) =∫ 𝐼𝑏𝜆(�̅�𝑜𝑝)𝜏𝜆
∗𝑑𝜆∞
0
∫ 𝐼𝑏𝜆(�̅�𝑜𝑝)𝑑𝜆∞
0
(5.16)
where 𝐼𝑏𝜆(�̅�𝑜𝑝) is the spectral blackbody intensity at the operating temperature �̅�𝑜𝑝 = 400 ℃.
Using spectral values for 𝑛 and 𝜅 from Palik[65], the calculated properties for the experimental
validation simulations are reported in Table 5.1.
Table 5-1 Geometrical parameters and calculated properties for
experimental validation simulations
𝑫𝒐 (mm) 20 70
𝒕 (mm) 1.5 2.0
𝑯𝒔𝒊𝒏𝒌 (mm) 11 22
𝝐𝒔𝒑𝒉𝒆𝒓𝒆 0.7651 0.7740
𝝆𝒔𝒑𝒉𝒆𝒓𝒆 0.1628 0.1621
𝝉𝒔𝒑𝒉𝒆𝒓𝒆 0.0721 0.0640
𝝐𝒔𝒂𝒍𝒕−𝒔𝒑𝒉𝒆𝒓𝒆 0.8432 0.8432
𝝆𝒔𝒂𝒍𝒕−𝒔𝒑𝒉𝒆𝒓𝒆 0.1568 0.1568
𝝉𝒔𝒂𝒍𝒕−𝒔𝒑𝒉𝒆𝒓𝒆 0 0
126
The validated thermal model is then extended to evaluate the performance of the modular cover
on very large surfaces. Large surfaces are approximated as infinite in the plane of the liquid’s
surface with hexagonal close-packed spheres (91 % surface coverage). To reduce computational
time, a single lattice is modeled with symmetric boundaries as shown in Figure 5.5. The
simulations were carried out for sphere outer diameters 20-100 mm. The sphere wall thickness was
constrained to the minimum possible manufacturable thickness, as specified by the fused silica
sphere manufacturer’s specifications.
Figure 5-5 Area elements for analytical model thermal conduction
resistance evaluation.
5.2.1.3. Experiment and simulation results comparison
Fig 5.6 presents a qualitative side-by-side comparison of the experimental and simulation results
for representative sample runs of the 20 mm spheres. The infrared images captured experimentally
(Fig. 5.6a) correspond to the photon flux (# 𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛𝑠
𝑚2 𝑠) from the salt and spheres to the infrared
camera. The radiosity (total thermal radiation emitted, reflected, and transmitted from the salt and
spheres) and the temperature distribution both obtained from the simulations are shown in
127
Fig. 5.6b and Fig. 5.6c respectively. The dark blue regions in each map correspond to the location
of spheres, and clearly demonstrate their insulating effect such that for the same salt surface
temperature, the radiation emitted at the location of the spheres is visibly reduced with respect to
the uncovered salt.
The effectiveness of the cover for both the experiments and simulations are compared
quantitatively (Eq. 5.4). The effectiveness versus surface coverage 𝜑 for the configuration in Fig.
5.2 is shown in Fig. 5.6d, where the surface coverage is simply expressed as
𝜑 =𝑁𝐴𝑠𝑝
𝑝𝑟𝑜𝑗
𝐴𝑠𝑎𝑙𝑡 (5.17)
𝑁 is the number of spheres on the salt surface, 𝐴𝑠𝑝𝑝𝑟𝑜𝑗
= 𝜋𝐷𝑜2/4 is the projected area of each
sphere, and 𝐴𝑠𝑎𝑙𝑡 is the total surface area of the salt. Overall, there is good agreement between the
experiments and simulations, with a slight over prediction of the effectiveness in the simulations.
The effectiveness reached approximately 8 % thermal loss reduction for the maximum surface
coverage tested with the 20 mm spheres, however, the larger 70 mm spheres reached 32 %
reduction in the small-scale experiments and simulations.
128
(a)
(b)
(c)
(d)
Figure 5-6 Validation experiment and simulation results. a, Photon flux map to infrared camera obtained
experimentally. Radiosity (b) and temperature distribution (c) at salt and sphere surfaces calculated numerically. d,
Calculated thermal effectiveness of floating spheres versus surface coverage in laboratory scale experiment and
validation simulation.
129
5.2.2. Large scale molten salt solar pond performance
The validated thermal model simulations were extended to evaluate the performance of the
modular cover under large scale solar pond conditions. In addition, a simple analytical model
capturing the effects of the various heat transfer mechanisms was developed to gain insight into
the thermal performance of the cover in terms of the physical and geometrical parameters. In
addition, ray-tracing simulations carried out in Lambda Research TracePro 7.5.7 were performed
in parallel by Miguel Diago Martinez at the Masdar Institute of Science and Technology to
evaluate the solar transmission through the spheres to the surface. Further details on the solar-
transmission ray-tracing modelling can be found in Appendix E.
5.2.2.1. Analytical thermal model derivation
A simplified analytical thermal model capturing the effects of the various heat transfer mechanisms
in a cover of an infinite layer of hexagonal close-packed (HCP) spheres, as shown in Figure 5.7,
can be used to understand and discuss the performance of the cover in terms of the physical and
geometrical parameters.
130
Figure 5-7 Geometry, properties, and boundary conditions of thermal model for infinite layer of hexagonal close-
packed (HCP) spheres.
We define a virtual surface 𝑣 located immediately above the layer of spheres as shown in
Figure 5.8. The total heat flux 𝑞𝑙𝑜𝑠𝑠𝑡ℎ𝑒𝑟𝑚𝑎𝑙 leaving the salt surface flows through two layers before
reaching the ambient environment: from the salt surface to the virtual surface 𝑞𝑠−𝑣𝑡ℎ𝑒𝑚𝑎𝑙, and from
the virtual surface to the ambient 𝑞𝑣−∞𝑡ℎ𝑒𝑟𝑚𝑎𝑙
𝑞𝑙𝑜𝑠𝑠𝑡ℎ𝑒𝑟𝑚𝑎𝑙 = 𝑞𝑠−𝑣
𝑡ℎ𝑒𝑟𝑚𝑎𝑙 = 𝑞𝑣−∞𝑡ℎ𝑒𝑟𝑚𝑎𝑙 (5.18)
131
Figure 5-8 Diagram illustrating the simplified analytical model.
The heat flux through the layer of spheres may be decomposed into radiative and conduction
components in a decoupled parallel approach as illustrated in the equivalent circuit in Figure 5.8,
such that
𝑞𝑠−𝑣𝑡ℎ𝑒𝑟𝑚𝑎𝑙 = 𝑞𝑠−𝑣
𝑐𝑜𝑛𝑑 + 𝑞𝑠−𝑣𝑟𝑎𝑑 + 𝑞𝑠−∞
𝑟𝑎𝑑,𝑡𝑟 (5.19)
where 𝑞𝑠−𝑣𝑐𝑜𝑛𝑑 and 𝑞𝑠−𝑣
𝑟𝑎𝑑 are the conduction and radiation heat flux components through the sphere
layer, respectively, and 𝑞𝑠−∞𝑟𝑎𝑑,𝑡𝑟
is the radiative heat flux transmitted directly through the layer to
the ambient. Similarly, the heat flux from the virtual surface to the ambient is decomposed into
radiative and convective component as
𝑞𝑣−∞𝑡ℎ𝑒𝑟𝑚𝑎𝑙 = 𝑞𝑣−∞
𝑐𝑜𝑛𝑣 + 𝑞𝑣−∞𝑟𝑎𝑑 + 𝑞𝑠−∞
𝑟𝑎𝑑,𝑡𝑟 (5.20)
where again 𝑞𝑣−∞𝑐𝑜𝑛𝑣 and 𝑞𝑣−∞
𝑟𝑎𝑑 are the conduction and radiation heat flux components through the
sphere layer, respectively, and 𝑞𝑠−∞𝑟𝑎𝑑,𝑡𝑟
is the radiative heat flux transmitted directly through the
layer to the ambient. We begin our analysis with the heat flow through the layer of spheres. The
132
conduction and radiation transport are coupled by the temperature gradient through the layer. For
a densely packed array of spheres, the view factor from the salt to the infinite layer of spheres will
approach unity. We therefore approximate the layer as a single infinite parallel plane above the
salt surface at the location of the virtual surface. The plane is taken to be a semi-transparent
window with emissivity 𝜖𝑣, reflectivity 𝜌𝑣, and transmissivity 𝜏𝑣, and view factor 𝐹𝑠−𝑣 ≈ 1. The
radiative heat flux can simply by expressed
𝑞𝑠−𝑣𝑟𝑎𝑑 =
𝜎(𝑇𝑠4 − 𝑇𝑣
4)
1 − 𝜖𝑠
𝜖𝑠+
1𝐹𝑠−𝑣
+1 − 𝜖𝑣
𝜖𝑣
=𝜎(𝑇𝑠
4 − 𝑇𝑣4)
1𝜖𝑠
+1𝜖𝑣
− 1 (5.21)
where 𝑇𝑠 is the temperature of the salt surface and 𝑇𝑣 is the temperature of the virtual surface. The
transmitted component through the layer is simply given as
𝑞𝑠−∞𝑟𝑎𝑑,𝑡𝑟 = 𝜏𝑣𝜖𝑠𝜎(𝑇𝑠
4 − 𝑇∞4 ) (5.22)
We now consider the conduction heat transfer component through the layer
�̇�𝑠−𝑣𝑐𝑜𝑛𝑑 =
𝑇𝑠 − 𝑇𝑣
𝑅𝑠−𝑣𝑐𝑜𝑛𝑑 (5.23)
where 𝑅𝑠−𝑣𝑐𝑜𝑛𝑑 is the thermal conduction resistance of the layer. As a first approximation, we
simplify the geometry from spheres to open top and bottom cylinders as shown in Figure 5.9.
133
Figure 5-9 Simplified geometry for conduction through layer of spheres.
In the simplified system, we assume 𝐷𝑜,𝑐𝑦𝑙 = 𝐷𝑜,𝑠𝑝 , 𝐻𝑐𝑦𝑙 = 𝐷𝑜,𝑠𝑝 , 𝑡𝑐𝑦𝑙 = 𝑡𝑠𝑝 , and 𝐻𝑠𝑖𝑛𝑘,𝑐𝑦𝑙 =
𝐻𝑠𝑖𝑛𝑘,𝑠𝑝. The thermal conduction resistance may readily be evaluated for the new configuration by
analyzing a parallel circuit through the air layer and cylinder walls
1
𝑅𝑠−𝑣𝑐𝑜𝑛𝑑 =
1
𝑅𝑎𝑖𝑟𝑐𝑜𝑛𝑑 +
1
𝑅𝑐𝑦𝑙𝑐𝑜𝑛𝑑 (5.24)
𝑅𝑎𝑖𝑟𝑐𝑜𝑛𝑑 =
𝐿
𝑘𝑎𝑖𝑟𝐴𝑎𝑖𝑟
𝑅𝑐𝑦𝑙𝑐𝑜𝑛𝑑 =
𝐿
𝑘𝑠𝑝𝐴𝑐𝑦𝑙𝑝𝑟𝑜𝑗
(5.25)
We take the thickness of the insulation layer between the salt and virtual surface to be 𝐿 = 𝐻𝑐𝑦𝑙 −
𝐻𝑠𝑖𝑛𝑘,𝑐𝑦𝑙. We find the heat flux from conduction to be
134
𝑞𝑠−𝑣𝑐𝑜𝑛𝑑 =
�̇�𝑠−𝑣𝑐𝑜𝑛𝑑
𝐴𝑡𝑜𝑡=
𝑇𝑠 − 𝑇𝑣
𝐴𝑡𝑜𝑡(
1
𝑅𝑎𝑖𝑟𝑐𝑜𝑛𝑑 +
1
𝑅𝑐𝑦𝑙𝑐𝑜𝑛𝑑) =
𝑇𝑠 − 𝑇𝑣
𝐿(
𝑘𝑎𝑖𝑟𝐴𝑎𝑖𝑟
𝐴𝑡𝑜𝑡+
𝑘𝑐𝑦𝑙𝐴𝑐𝑦𝑙𝑝𝑟𝑜𝑗
𝐴𝑡𝑜𝑡)
=𝑇𝑠 − 𝑇𝑣
𝐿[(1 − 𝜙𝑐𝑦𝑙)𝑘𝑎𝑖𝑟 + 𝜙𝑐𝑦𝑙𝑘𝑐𝑦𝑙] =
𝑇𝑠 − 𝑇𝑣
𝐿𝑘𝑒𝑓𝑓
(5.26)
Where 𝑘𝑎𝑖𝑟 and 𝑘𝑐𝑦𝑙 are the thermal conductivities of air and the cylinder (sphere) material (fused
silica), respectively, 𝑘𝑒𝑓𝑓 is the effective thermal conductivity of the layer, 𝐴𝑡𝑜𝑡 is the total surface
area of the symmetric cell projected onto the plane of the virtual surface, expressed as the sum of
the projected areas of the air and cylinders such that 𝐴𝑡𝑜𝑡 = 𝐴𝑎𝑖𝑟 + 𝐴𝑐𝑦𝑙𝑝𝑟𝑜𝑗
, and 𝜙𝑐𝑦𝑙 =𝐴𝑐𝑦𝑙
𝑝𝑟𝑜𝑗
𝐴𝑡𝑜𝑡.
We evaluate 𝜙𝑐𝑦𝑙 taking the symmetric cell shown in Figure 5.5 with two quarter cylinders:
𝜙𝑐𝑦𝑙 =𝐴𝑐𝑦𝑙
𝑝𝑟𝑜𝑗
𝐴𝑡𝑜𝑡=
2 ×14 𝜋(𝑅𝑜,𝑐𝑦𝑙
2 −𝑅𝑖,𝑐𝑦𝑙2 )
𝑅𝑜,𝑐𝑦𝑙 × √3𝑅𝑜,𝑐𝑦𝑙
=𝜋
2√3(1 −
𝑅𝑖,𝑐𝑦𝑙2
𝑅𝑜,𝑐𝑦𝑙2 )
=𝜋
2√3[1 − (1 −
𝑡𝑐𝑦𝑙
𝑅𝑜,𝑐𝑦𝑙)
2
]
(5.27)
The effective thermal conductivity of the layer is thus given by
𝑘𝑒𝑓𝑓 = (1 − 𝜙𝑐𝑦𝑙)𝑘𝑎𝑖𝑟 + 𝜙𝑐𝑦𝑙𝑘𝑐𝑦𝑙 =𝜋(𝑘𝑐𝑦𝑙 − 𝑘𝑎𝑖𝑟)
2√3[1 − (1 −
𝑡𝑐𝑦𝑙
𝑅𝑜,𝑐𝑦𝑙)
2
] + 𝑘𝑎𝑖𝑟 (5.28)
Equations 5.27 and 5.28 may be substituted into Eq. 5.26 to solve for the conductive heat flux
through the layer of spheres 𝑞𝑠−𝑣𝑐𝑜𝑛𝑑. Finally, the total flux through the layer is given as
𝑞𝑠−𝑣𝑡ℎ𝑒𝑟𝑚𝑎𝑙 =
𝑇𝑠 − 𝑇𝑣
𝐿𝑘𝑒𝑓𝑓 +
𝜎(𝑇𝑠4 − 𝑇𝑣
4)
1𝜖𝑠
+1𝜖𝑣
− 1+ 𝜏𝑣𝜖𝑠𝜎(𝑇𝑠
4 − 𝑇∞4 ) (5.29)
135
We now consider the second layer, from the virtual surface to the ambient environment. We take
the ambient to be a perfect absorber and the view factor from the virtual surface to the ambient
environment to be 𝐹𝑣−∞ = 1 . The thermal radiation emitted to the environment is therefore
expressed as
𝑞𝑣−∞𝑟𝑎𝑑 = 𝜖𝑣𝜎(𝑇𝑣
4 − 𝑇∞4 ) (5.30)
where 𝑇∞ is the temperature of the surrounding ambient environment. The transmitted thermal
radiation is identical to the transmitted component through the layer of spheres and is given in Eq.
5.22. Finally, the convective heat flux is expressed as
𝑞𝑣−∞𝑐𝑜𝑛𝑣 = ℎ𝑐𝑜𝑛𝑣(𝑇𝑣 − 𝑇∞) (5.31)
Where ℎ𝑐𝑜𝑛𝑣 is the convective heat transfer coefficient. In this study, we assume thermal radiation
to dominate the thermal losses to the environment as in the computational model and let ℎ𝑐𝑜𝑛𝑣 ≈
0. For a more rigorous analysis, we may obtain the heat transfer coefficient from standard Nusselt
number correlations for heated horizontal plates facing upwards. Finally, the total heat flux from
the virtual surface to the environment is given by
𝑞𝑣−∞𝑡ℎ𝑒𝑟𝑚𝑎𝑙 = ℎ𝑐𝑜𝑛𝑣(𝑇𝑣 − 𝑇∞) + 𝜖𝑣𝜎(𝑇𝑣
4 − 𝑇∞4 ) + 𝜏𝑣𝜖𝑠𝜎(𝑇𝑠
4 − 𝑇∞4 ) (5.32)
Eqns. 5.29 and 5.32 may be substituted into Eq. 5.18 and solved numerically for the thermal losses
𝑞𝑙𝑜𝑠𝑠𝑡ℎ𝑒𝑟𝑚𝑎𝑙 from the salt and the intermediate virtual surface temperature 𝑇𝑣.
5.2.2.2. Solar-transmission ray-tracing and thermal modelling results
Large solar pond molten salt surfaces were approximated as an infinite plane and the liquid was
assumed to be densely covered with floating spheres in hexagonal closed-packed (HCP)
136
arrangement which provides 91 % surface coverage. The simulations and modelling were carried
out for sphere outer diameters from 20 to 100 mm. The sphere wall thickness was constrained to
the minimum possible manufacturable thickness, as specified by the fused silica sphere
manufacturer’s specifications. The analysis was carried out for two different molten salt mixtures
operating within different temperature ranges to characterize the effects of temperature and fluid
density (sphere buoyancy). Mixture composition, temperatures, and densities are summarized in
Table 5.2.
Table 5-2 Molten salt mixture compositions and their corresponding mean densities and temperature
range investigated
Molten salt mixture
composition
Performance analysis
temperature range
Density at mean
temperature
40 wt. % KNO3:60 wt. % NaNO3
binary nitrate (solar salt) 400 °C - 500 °C 1,800 kg/m3
50 wt. % KCl:50 wt. % NaCl
binary chloride 700 °C - 1,200 °C 1,442 kg/m3
The simulation and analytical model results for the thermal effectiveness versus sphere outer
diameter for the HCP cover on very large surfaces are shown in Fig. 5.10a. The effects of
temperature, wall thickness, and sphere diameter are clearly captured. The minimum effectiveness
evaluated by the simulations is 21 % for the smallest spheres (20 mm) at 1200 °C, and reaches a
maximum of 51 % with the largest spheres (100 mm) at 400 °C. The performance of the spheres
increases with increasing sphere diameter until some saturating limit 𝐷𝑜 ≳ 100 𝑚𝑚 , where
radiation dominates, as also predicted by the model. Larger spheres correspond to a thicker
insulation layer which increases the thermal conduction resistance. The insulation performance
drops slightly where the thickness changes from 𝑡 = 1.5 𝑚𝑚 for 𝐷𝑜 ≤ 50 𝑚𝑚 to 𝑡 = 2.5 𝑚𝑚 for
𝐷𝑜 ≥ 60 𝑚𝑚 (as specified by the sphere manufacturer). The thicker walls have lower apparent
137
transmissivities and are expected to increase radiation shielding. However, they also reduce the
thermal conduction resistance as well as the buoyancy of the spheres, which in turn decreases the
thickness of the insulation layer due to greater sinkage. Finally, as temperature increases, the
corresponding Planck emission spectrum of the salts shifts to shorter wavelengths where fused
silica is increasingly transparent and less effective at shielding thermal radiation. In addition, the
higher temperature, lower density chloride salts reduce the spheres’ buoyancy. Overall, the
simulation results capture the same general trends predicted by the analytical model. The deviation
at smaller sphere diameters is largely due to an over prediction in the conduction thermal
resistance. Greater agreement is expected to be achieved with a more accurate equivalent geometry
approximation in the conduction model and will better predict the relative magnitudes between
conduction and radiation effects.
The transmission efficiency of the cover depends on the outer diameter and wall thickness of the
spheres, the angular distribution of the incident irradiation, and on the buoyancy of the spheres.
The dependence of the transmission efficiency versus sphere outer diameter for 1.5 and 2.5 mm-
thick spheres floating on nitrate and chloride molten salt mixtures is shown in Fig. 5.10b. Two
limiting uniform angular distributions are shown: one with half-angle θ = 0.27° corresponding to
natural solar irradiation[77], and a second with half-angle 40° corresponding to the approximate
angular output from a representative optical concentrator. Overall, the transmission efficiency
remains above 92 % over the range studied. The cover transmission efficiency initially increases
with increasing diameter, followed by a gradual decay beyond 30 mm. Performance is higher in
all cases for incident radiation with a smaller angular distribution. The buoyancy of the spheres is
smaller on the less dense chloride molten salt mixture and the transmission increases as the spheres
138
sink deeper with respect to the nitrate molten salt mixture. Further details are provided in
Appendix E.
(a)
(b)
139
Figure 5-10 Thermal and transmission performance. a, Thermal effectiveness versus sphere diameter. b,
Transmission efficiency versus sphere diameter. Wall thicknesses in both (a) and (b) are 1.5 mm for diameters
𝐷𝑜 ≤ 50 𝑚𝑚, and 2.5 mm for diameters 𝐷𝑜 ≥ 60 𝑚𝑚, as specified by fused silica manufacturer. Transmission
calculations and figures were carried out and prepared by Miguel Diago Martinez.
5.2.3. Solar pond capture efficiency
The capture efficiency versus solar concentration at temperatures within the operating range of
40 wt. % KNO3:60 wt. % NaNO3 binary nitrate molten salt and 50 wt. % KCl:50 wt. % NaCl
binary chloride molten salt mixtures for 𝐷𝑜 = 20 𝑚𝑚 and 𝐷𝑜 = 100 𝑚𝑚 spheres are presented in
Fig. 5.11. The dashed lines correspond to capture efficiencies without a cover as reference. There
is a clear increase in capture efficiency for both the 20 mm and 100 mm spheres. The gains in
capture efficiency with respect to the uncovered salt increase both with increasing temperature and
increasing sphere diameter. At the temperatures within the operating range of the nitrate mixture
(solar salt) the cover’s effectiveness is limited to larger spheres and lower solar concentrations
(C < 200). For the higher temperature chloride mixture and larger 100 mm spheres, significant
gains are expected for solar concentrations up to C = 1000.
(a)
140
(b)
Figure 5-11 Solar pond capture efficiency. Capture efficiency of solar pond with densely packed HCP cover for
𝐷𝑜 = 20 𝑚𝑚 (a) and 𝐷𝑜 = 100 𝑚𝑚 spheres (b), and with surface temperatures between 400 °C - 500 °C for
40 wt. % KNO3:60 wt. % NaNO3 binary nitrate molten salt, and 700 °C - 1200 °C for 50 wt. % KCl:50 wt. % NaCl
binary chloride molten salt. Dashed lines represent capture efficiencies without a cover.
5.3. Analysis of receiver heat loss mechanisms
The analysis of the cover’s performance was carried out assuming radiative heat losses are
dominant for the range of operating temperatures considered and all other heat loss mechanisms
are negligible. The following section discussed the accuracy of this assumption based on a first
order analysis of the relative contributions of convection, radiation, and evaporation.
5.3.1. Convection
We first consider heat removed by convection above the surface. We assume the surface of the salt
is shielded from air flow from the surrounding environment as in the CSPonD design[6,9] such
that convection losses are due to natural convection. Assuming the surface of the salt and salt-
141
spheres can be treated as heated horizontal plate facing up and that natural convection is turbulent,
the Nusselt number is given by
𝑁𝑢̅̅ ̅̅𝑙 = 0.14𝑅𝑎𝑙
1/3; 2 × 107 < 𝑅𝑎𝑙 < 3 × 1010 (5.33)
Where the Rayleigh number 𝑅𝑎𝑙 is given as
𝑅𝑎𝑙 =𝛽∆𝑇𝑔𝑙3
𝜈2𝑃𝑟 (5.34)
where 𝛽 is the coefficient of thermal expansion, ∆𝑇 = 𝑇𝑠 − 𝑇𝑒 is the difference in temperature
between the receiver surface temperature 𝑇𝑠 and the environment temperature 𝑇𝑒 , 𝑔 is the
gravitational acceleration, 𝑙 is the characteristic length of the receiver, 𝑃𝑟 is the Prandtl number,
and 𝜈 is the kinematic viscosity. The heat transfer coefficient for natural convection ℎ̅𝑛𝑐 is then
given by
ℎ̅𝑛𝑐 =𝑘𝑁𝑢̅̅ ̅̅
𝑙
𝑙=
𝑘
𝑙0.14 [
𝛽∆𝑇𝑔𝑙3
𝜈2𝑃𝑟]
1/3
= 0.14𝑘 [𝛽∆𝑇𝑔
𝜈2𝑃𝑟]
1/3
(5.35)
where ℎ̅𝑛𝑐~∆𝑇1/3 and does not depend on the characteristic length 𝑙. The heat loss by natural
convection 𝑞𝑛𝑐𝑙𝑜𝑠𝑠 is therefore expressed as
𝑞𝑛𝑐𝑙𝑜𝑠𝑠 = ℎ̅𝑛𝑐∆𝑇 = 0.14𝑘 [
𝛽∆𝑇𝑔
𝜈2𝑃𝑟]
1/3
∆𝑇 (5.36)
142
5.3.2. Radiation
The rate of heat loss by thermal radiation is given by
𝑞𝑟𝑎𝑑𝑙𝑜𝑠𝑠 = 𝜖𝜎(𝑇𝑠
4 − 𝑇𝑒4) (5.37)
5.3.3. Evaporation
The vapor pressures of molten salts are typically quite low, ℴ(0.001 bar) for chloride salts at
900 °C, and the mass losses and corresponding energy losses by evaporation are therefore expected
to small. The fuming rate of chloride salt is given as 200 g/m2/hour of exposed surface area of
chloride salt at 870 °C[78]. Vaporization data for molten salts versus temperature is limited and
we therefore use the available enthalpy of vaporization of sodium chloride at 800 °C (melting
point) to estimate the thermal losses by evaporation, given as ∆𝐻𝑁𝑎𝐶𝑙,800℃𝑣𝑎𝑝 = 45.3 𝑘𝑐𝑎𝑙/𝑚𝑜𝑙[79].
∆𝐻𝑣𝑎𝑝,𝑁𝑎𝐶𝑙 = 45.3𝑘𝑐𝑎𝑙
𝑚𝑜𝑙×
4184 𝐽
1 𝑘𝑐𝑎𝑙×
1
58.44𝑔
𝑚𝑜𝑙
= 3243 𝐽/𝑔
�̇�𝑒𝑣𝑎𝑝𝑙𝑜𝑠𝑠 = 200
𝑔
𝑚2ℎ𝑜𝑢𝑟×
1 ℎ𝑜𝑢𝑟
3600 𝑠= 0.056
𝑔
𝑚2𝑠
𝑞𝑒𝑣𝑎𝑝𝑙𝑜𝑠𝑠 = �̇�𝑒𝑣𝑎𝑝
𝑙𝑜𝑠𝑠 ∆𝐻𝑣𝑎𝑝,𝑁𝑎𝐶𝑙 = 0.056𝑔
𝑚2𝑠× 3243
𝐽
𝑔= 180
𝑊
𝑚2= 0.18
𝑘𝑊
𝑚2
These thermal losses correspond to less than 20 % of a natural, unconcentrated solar irradiance
𝐺𝑠 ≈ 1𝑘𝑊
𝑚2.
5.3.4. Magnitude Comparison
The estimated heat losses by convection and radiation are reported in Table 5.3 for surface
temperatures 𝑇𝑠 = 400 °C, 800 °C, and 1200 °C, which correspond to the lowest, intermediate,
143
and highest temperatures investigated in this study, respectively. The estimated evaporation losses
at 800 °C are also presented for comparison. The Rayleigh numbers calculated for a characteristic
length 𝑙 = 1 𝑚 with thermophysical properties of air at the average temperature 𝑇𝑠+𝑇𝑒
2 with 𝑇𝑒 =
25 ℃, are also presented in Table 5.3 and are shown to be within the range of applicability of
Eq. 5.35. Radiation losses are the largest heat losses over the entire temperature range studied.
Convection losses are relatively significant at 400 °C and represent 25.7% of the total losses at
that temperature. However, this contribution rapidly drops to less than 10% at 800 °C. Evaporation
losses are less than 1 % of the total heat losses at 800 °C and are therefore assumed to be negligible
over the entire temperature range studied.
Table 5-3 Estimated heat loss by convection, radiation, and evaporation and comparison of respective
contributions for surfaces at three different temperatures.
𝑻𝒔 (°𝑪) 𝑹𝒂𝒍=𝟏 𝒎
× 10−8
�̅�𝒏𝒄
(𝐖
𝐦𝟐𝐊)
𝒒𝒆𝒗𝒂𝒑𝒍𝒐𝒔𝒔
(𝐤𝐖
𝐦𝟐, % 𝒕𝒐𝒕𝒂𝒍)
𝒒𝒏𝒄𝒍𝒐𝒔𝒔
(𝐤𝐖
𝐦𝟐, % 𝒕𝒐𝒕𝒂𝒍)
𝒒𝒓𝒂𝒅𝒍𝒐𝒔𝒔
(𝐤𝐖
𝐦𝟐, % 𝒕𝒐𝒕𝒂𝒍)
𝒒𝒕𝒐𝒕𝒂𝒍𝒍𝒐𝒔𝒔
(𝐤𝐖
𝐦𝟐)
400 °C 39.4 9.17 - 3.4
(25.7 %)
10.0
(74.3 %) 13
800 °C 18.1 9.25 0.18
(0.25 %)
7.2
(9.8 %)
66.0
(89.9 %) 73.38
1200 °C 9.3 9.06 - 11.0
(4.3 %)
240.0
(95.7 %) 250
The thermal effectiveness 𝜖𝑠 of the cover is expressed as
𝜖𝑠 = 1 −�̇�𝑐𝑜𝑣𝑒𝑟
𝑙𝑜𝑠𝑠
�̇�𝑛𝑜 𝑐𝑜𝑣𝑒𝑟𝑙𝑜𝑠𝑠
(5.38)
The error introduced by neglecting natural convection in the thermal effectiveness was estimated
using the analytical model described in Section 5.2.2.1. The effectiveness calculated with and
144
without convection for the salt covered with 100 mm-diameter floating spheres, with salt surface
temperatures 𝑇𝑠 = 400 °C, 800 °C, and 1200 °C, and approximate heat transfer coefficient ℎ̅𝑛𝑐 =
10 W
m2K are reported in Table 5.4. The estimated error from neglecting convection is largest at the
lowest temperature (400 °C) but remains less than 10%. This implies that the cover influences
radiation heat losses most significantly. In all cases, the effectiveness of the cover has been under-
estimated by neglecting the effects of convection.
Table 5-4 Error introduced in thermal effectiveness of the cover by neglecting natural
convection as predicted by the analytical model described in Section 5.2.2.1.
𝑻𝒔 (°𝐂) 𝝐𝒔
with convection
𝝐𝒔 without convection
% error in 𝝐𝒔
without convection
400 56 % 51 % -8.9 %
800 44 % 42 % -4.5%
1200 36 % 34 % -5.6 %
The contribution of natural convection losses to the total heat losses, and the corresponding error
introduced by neglecting natural convection is most significant at 𝑇𝑠 = 400 °C, the lowest
temperature investigated. Table 5.5 reports the calculated thermal efficiency of an uncovered
surface at 𝑇𝑠 = 400 °C, for solar irradiance 𝐺𝑠 ≈ 1𝑘𝑊
𝑚2, incident on the liquid surface at half-angle
𝜃 = 0.27°, and solar concentrations C = 50, 100, and 200. It can be seen that the thermal efficiency
is only over-predicted by 8 % for C = 50, and the error falls below 1 % for solar concentrations
above 200. The errors reported in Table 5.5 will further decrease for increasing temperature. We
conclude that for the specific combinations of receiver temperature and solar concentrations
145
relevant to this study, the main quantities of interest, i.e. the thermal effectiveness and thermal
efficiency, are estimated with less than 10 % error by accounting for radiation losses only.
Table 5-5 Error introduced in calculated thermal efficiency of an uncovered receiver by
neglecting natural convection for solar irradiance 𝐺𝑠 ≈ 1 𝑘𝑊 𝑚2⁄ .
Solar
Concentration
𝜼𝒄 @ 𝟒𝟎𝟎 °𝐂 with convection
𝜼𝒄 @ 𝟒𝟎𝟎 °𝐂
without convection
% error in
𝜼𝒄 @ 𝟒𝟎𝟎 °𝐂
without convection
50 0.71 0.77 +8 %
100 0.84 0.87 +4 %
200 0.91 0.92 +1 %
5.4. Discussion
The new cover has been proposed to reduce both convective and radiative thermal losses at the
surface, and minimize the surface area available for evaporation without trapping vapour, while
maintaining high solar-transparency and introducing minimal reflection losses. Overall, the
spheres behave as excellent insulators with minor transmission losses. The larger diameter spheres
demonstrate the best performance due to their larger thermal conduction resistance, while
providing radiation shielding and maintaining high solar transparency under typical incident solar
irradiation angular distributions. For the uncovered salt, the breakeven solar concentrations
required to achieve non-negative capture efficiencies are C = 11 at 400 °C, C = 76 at 800 °C, and
C = 271 at 1200 °C, as shown in Table 5.3. For the same given temperatures and solar
concentrations and using densely packed floating spheres, the capture efficiency increases from
𝜂𝑐 = 0 % to 𝜂𝑐 = 21%, 𝜂𝑐 = 20 %, and 𝜂𝑐 = 18 % with 20 mm spheres, respectively, and 𝜂𝑐 =
46 %, 𝜂𝑐 = 41%, and 𝜂𝑐 = 34 % for the 100 mm spheres, respectively. These gains in capture
efficiencies are significant in terms of both experimental and commercial CSP applications. The
146
cover enables smaller facilities that do not have the solar concentration capabilities required to
offset large thermal losses to carry out system level design of VHT receivers. In addition, despite
reaching high solar flux concentrations, larger facilities will still benefit from the reduction in
thermal losses at lower fluxes by extending operation during hours of lower solar irradiance such
as early morning, evening, and under hazy conditions. For salt bath applications that do not require
solar transparency, the floating fused silica spheres still provide excellent insulation benefits over
other standard methods and materials. In particular, the modularity facilitates maintenance and
allows to vary the covered surface area insulated to accommodate a variety of application sizes,
and the breathability minimizes vapour condensation on the cover. In addition, fused silica has a
lower thermal conductivity and density than materials such as stainless steels and ceramics, which
yield higher thermal losses and reduce buoyancy, and the transparency maintains visibility during
manufacturing processes.
Table 5-6 Capture efficiency with covers of 0 mm, 20 mm, and 100 mm diameter spheres at three operating
temperatures and corresponding to the breakeven solar concentration required to achieve non-negative
capture efficiency without a cover
Receiver
temperature
(°C)
Breakeven solar
concentration
(-)
Capture efficiency
No cover 20 mm-sphere
cover
100 mm-sphere
cover
400 11 0 % 21 % 46 %
800 76 0 % 20 % 41 %
1200 271 0 % 18 % 34 %
Fig. 5.12 compares the capture efficiency versus temperature of a CSPonD-type volumetric
receiver with and without the best performing sphere cover (100 mm spheres) with the capture
efficiency of typical solar central receivers [80] for solar concentration ratios 𝐶 = 300 and 𝐶 =
147
600. The efficiencies in both receiver designs were evaluated assuming radiation losses dominate
and neglecting convection and evaporation.
(a)
(b)
Figure 5-12 Capture efficiency comparison between solar central receiver systems and volumetric receiver for solar
concentration C=300 (a) and C=600 (b). Solar central receiver data adapted from Karni [80].
Temperature (°C)
Temperature (°C)
148
The volumetric receiver design achieves higher efficiencies with and without the cover than the
central receiver for temperatures above 600 °C. The temperatures for the central receiver designs
correspond to the heat engine upper temperature TH. Since the central receiver uses indirect
absorption, this results in lower efficiencies, even with respect to the uncovered volumetric
receiver. The covered receiver shows significant increase in efficiency, particularly for
temperature above 600 °C.
The maximum possible number of spheres 𝑁 required to completely cover a molten salt pond or
bath of diameter 𝐷𝑠𝑎𝑙𝑡 with HCP arranged spheres (91 % surface coverage) of diameter 𝐷𝑜 is given
as
𝑁 ≈ 0.91 (𝐷𝑠𝑎𝑙𝑡
𝐷𝑜 )
2
(5.39)
Thus, for a 1 m-diameter solar pond and 100 mm-diameter spheres, only 91 spheres are required
to achieve maximum salt surface coverage. This surface coverage can be further increased to
approach 100 % using smaller spheres to fill the interstitial voids, which in turn will further
enhance thermal insulation. Using custom-made 100 mm spheres at approximately $100/sphere
would cost US$9,100 to cover the salt surface. The cost of replacing a single broken sphere would
then only be $100 and would not require operation downtime. On the other hand, a single
continuous fused silica window would cost approximately $250,000 and would cost the same
amount to replace when broken, in addition to operation downtime. Furthermore, using the cost of
custom-made spheres is a highly conservative estimate and large-scale manufacturing methods
could be expected to significantly reduce costs. Custom-made fabrication could be replaced by
large scale methods such as automated light-bulb manufacturing techniques, where a standard
149
Corning ribbon machine[81] may could probably be updated to operate with spherical moulds and
at higher temperature to accommodate fused silica fabrication. Other shapes such as cylinders with
pinched ends should be considered in order to further reduce costs. In addition, methods for
vacuum sealing the open port of the spheres, long-term thermal stability, material compatibility,
and transparency reduction over time should all be investigated.
5.5. Conclusions
Overall, we have demonstrated a simple and elegant floating structure that can be used to insulate
and significantly increase the capture efficiency of very high temperature solar ponds facilitating
their use even at moderate solar concentrations. We believe this transparent, insulating cover
represents a significant breakthrough in solar pond technology as it will allow to reach much higher
temperatures than could previously be achieved, and will extend the hours of operation in
commercial power plants. The proposed cover concept could also be applied to a wide range of
high temperature open bath applications to generate energy savings. Examples include molten salt
bath furnaces for heat treating metals and curing plastics and rubbers, fryers for food processing,
and oil baths for chemical processing applications.
150
6. Concluding Remarks
6.1. Conclusions
An in-depth analysis of the thermal-fluid design and operation of direct absorption, liquid-based
receivers has been presented, with specific application to the CSPonD receiver concept. In this
receiver concept, an open tank of semi-transparent liquid is directly irradiated with concentrated
sunlight. The liquid is therefore subjected to volumetric heating and heating from the absorbing
boundaries. The respective intensities of the volumetric heating and boundary heating depend on
the optical properties of the absorber liquid and the dimensions of the receiver. Penetrative
convection develops in the receiver as a consequence of the internal heating, which in turn governs
the overall thermal behavior of the absorber liquid in the receiver. The optical properties and the
dimensions of the receiver can be selected to maximize the temperature uniformity to increase the
maximum allowable solar flux absorbed by the liquid before exceeding thermal limits in the
system. In addition, in order to increase the heat engine efficiency of the overall system, the
receiver is designed to operate at temperatures exceeding 400 °C. In particular, molten salts are
ideal candidate liquids with semi-transparent optical properties that can reach these elevated
temperatures. However, the high temperatures also imply the open tank experiences large thermal
losses to the environment, which limits the overall efficiency and produces large temperature
gradients immediately below the exposed liquid surface. Given these receiver conditions, the
thermal-fluid analysis presented in this work therefore focused on characterizing molten salt
optical properties, developing a theoretical analysis of the convection in the receiver, developing
a computational model of the CSPonD Demo prototype receiver to gain further insight into the
151
design, and proposing design improvements to reduce the thermal losses and large temperature
gradients in the absorber liquid.
In the first part, a simple and accurate apparatus that allows for the precise measurement of light
attenuation in high temperature, nearly transparent liquids, over a broad spectrum extending from
the visible region (400 nm) into mid-infrared (8000 nm) was developed. Measuring the optical
properties of high temperature fluids is challenging since they also emit significantly in the spectral
ranges relevant to solar-thermal and nuclear applications. To circumvent this problem, the method
consisted of a transmission technique paired with FTIR spectroscopy, which allowed to rapidly
measure the transmission of light through a relatively large range of liquid thicknesses up to 10 cm.
The FTIR allowed to filter between the transmitted light source and the thermal emissions from
the measured liquid. The apparatus was then used to measure the attenuation of light in the
40 wt. % KNO3:60 wt. % NaNO3 binary nitrate and the 50 wt. % KCl:50 wt. % NaCl binary
chloride molten salt mixtures. The effects of salt contamination due to thermal decomposition were
also evaluated. Sources of thermal decomposition include unexpected heating conditions and local
hot spots, and sand/dust contamination due to the open receiver design. The method presented
some limitations in the solar spectrum where the measurement resolution decays. These limitations
are inherent to the transmission technique and the FTIR performance at short wavelengths.
Measuring the optical properties of the candidate binary nitrate molten salt used in the CSPonD
Demo prototype allowed to estimate its optical thickness in the solar and thermal spectra, which
in turn allowed to predict the general thermal behavior in terms of direct solar absorption. A simple
expression was then developed for the temperature profile in direct absorption liquid-based
receivers based on a two-layer, 1D model of the thermal-fluid behavior. The results were compared
with CFD simulations with good agreement. The 1D model allows to easily explore the parameter
152
space governing directly absorbing liquid layers and to carry out optimization. Using this model,
it was shown that that the ideal optical thickness of a receiver should be 𝜏~ℴ(1), but must be great
than unity. The exact ideal conditions depend on the operating conditions and on the maximum
heating time.
With the knowledge gained from the molten salt properties and the theoretical analysis, a complete
CFD model of a molten salt, direct absorption volumetric receiver with radiation-induced
convection was developed. The model setup and results were presented and compared with the
experimental results obtained with the CSPonD Demo prototype at the Masdar Institute Solar
Platform. A large disagreement was observed between the model and experimental results, which
highlighted major sources of uncertainty in the demo prototype experiments, model input
parameters, and modeling methods. In particular, the total energy absorbed by the salt was
estimated to be 3.7 times less than the calculated predictions. The computational model therefore
provides an upper limit on expected peak temperatures in the salt and the thermal efficiency of the
receiver. The major sources of uncertainty were determined to be the salt optical properties, the
estimated solar source intensity, and the general uncertainty in the validation experiments.
Finally, in order to address the thermal losses from the open tank of molten salt, a cover consisting
of floating hollow fused silica spheres was proposed. The floating spheres are stable in harsh very
high temperature environments such as molten salts and are modular to allow easy online
maintenance and component replacement. The proposed cover is highly solar-transparent and
introduces minimal reflection losses, it reduces both convective and radiative thermal losses at the
surface, and it minimizes the surface area available for evaporation without trapping vapor. In
addition, the floating spheres allow impurities such as dust and sand to fall through which would
otherwise accumulate on a window’s surface, degrade solar transmission, and potentially burn in
153
the presence of high solar fluxes. The spheres can readily be used to cover very large surfaces
extending up to 25 m in diameter, which cannot be achieved with a single continuous window
pane. Demonstration experiments and computational analysis demonstrated that the cover can
reduce radiative losses by 50 % while only reducing the transmission to the salt by less than 5 %
with respect to the uncovered salt. The transparent, insulating cover represents a significant
breakthrough in solar pond technology as it will allow to reach much higher temperatures than
could previously be achieved, and will extend the hours of operation in commercial power plants.
6.2. Future Work
The next step in the thermal-fluid analysis of the receiver will be to determine how much the
thermal analysis and proposed design improvements can help reduce the levelized cost of
electricity (LCOE) of large scale direct absorption molten salt solar receivers. The most notable
contribution to further reducing current LCOE predictions for the CSPonD concept will be the
energy savings provided by the floating modular cover. Future research is necessary to evaluate
the performance of the cover under actual receiver conditions, to determine any unknown effects
due to long-term salt exposure, to characterize the compatibility with other molten salt candidates,
and to further optimize the shapes.
In terms of future technical research, the spectral range of the optical property measurements
should be extended to shorter wavelengths and the accuracy should be improved in the solar
spectrum. This may potentially involve significant improvements to the overall optics of the
design, or different measurement techniques for the solar and MIR spectra. A different
measurement technique that would also allow for reflection measurements would enable the ability
to evaluate the index of refraction of the liquid. Other candidate molten salt mixtures for nuclear
154
and solar-thermal energy applications should be measured, and samples collected from the
CSPonD Demo receiver should be characterized.
Theoretical studies should focus on deriving a complete analytical expression of the temperature
distribution based on the equations derived in the present study. This would allow in turn to obtain
an expression for the ideal optical thickness as a function of solar heating intensity, heating time,
receiver depth, and any other parameter of interest. The modeling approach can also be extended
to nuclear applications with internal heat generation in molten salt. In addition, the theoretical and
computational analysis in Chapter 3 highlighted the need for further experimental studies of natural
convection heat transfer in molten salts to correct and improve the accuracy of existing heat
transfer correlations. Furthermore, if molten salts that are semi-transparent in the NIR and MIR
such as chloride-based salts are considered potential candidates for large-scale receivers, the
theoretical analysis should be modified to account for the effects of the semi-transparency in the
re-emission spectrum.
Finally, in order to continue the CFD modeling efforts and fully validate the model, in depth
analysis of the sources of uncertainty in the demo experiments will be necessary in order to
improve the agreement. Reducing the computational time would further facilitate the modeling
and would enable the possibility of modeling the motion of the DP and MP. In addition, it would
be useful to consider a test apparatus based on the original CSPonD concept where hillside
heliostats are used, so potentially an FOE would not be required.
155
References
[1] US DOE Office of Energy Efficiency & Renewable Energy, “Concentrating Solar Power”
2017. https://www.energy.gov/eere/solar/concentrating-solar-power.
[2] Baum VA, Aparasi RR, Garf BA. High-power solar installations. Sol Energy 1957;1:6–12.
doi:10.1016/0038-092X(57)90049-X.
[3] Ho CK, Iverson BD. Review of high-temperature central receiver designs for concentrating
solar power. Renew Sustain Energy Rev 2014;29:835–46. doi:10.1016/j.rser.2013.08.099.
[4] Reilly HE, Kolb GJ. An evaluation of molten-salt power towers including results of the
solar two project. Sandia National Labs., Albuquerque, NM (US); Sandia National Labs.,
Livermore, CA (US); 2001.
[5] Khullar V, Tyagi H, Hordy N, Otanicar TP, Hewakuruppu Y, Modi P, et al. Harvesting
solar thermal energy through nanofluid-based volumetric absorption systems. Int J Heat
Mass Transf 2014;77:377–84. doi:10.1016/j.ijheatmasstransfer.2014.05.023.
[6] Slocum AH, Codd DS, Buongiorno J, Forsberg C, Mckrell T, Nave J, et al. Concentrated
solar power on demand. Sol Energy 2011;85:1519–29. doi:10.1016/j.solener.2011.04.010.
[7] Lahlou R, Armstrong P, Grange B, Almheiri S, Calvet N, Slocum A, et al. Thermal
modeling of a secondary concentrator integrated with an open direct-absorption molten-salt
volumetric receiver in a beam-down tower system. AIP Conf. Proc., vol. 1734, AIP
Publishing; 2016, p. 20012.
[8] Gil A, Grange B, Perez VG, Tetreault-Friend M, Codd DS, Calvet N, et al. CSPonD
demonstrative project: Start-up process of a 25 kW prototype. AIP Conf. Proc., vol. 1850,
AIP Publishing; 2017, p. 110003. doi:10.1063/1.4984477.
[9] Gil A, Codd DS, Zhou L, Trumper D, Calvet N, Slocum AH. Concentrated solar power on
demand demonstration: Construction and operation of a 25 kW prototype. AIP Conf Proc
2016;1734. doi:10.1063/1.4949115.
[10] Goluskin D, Spiegel EA. Convection driven by internal heating. Phys Lett Sect A Gen At
Solid State Phys 2012;377:83–92. doi:10.1016/j.physleta.2012.10.037.
[11] Veronis G. PENETRATIVE CONVECTION G. Veronis Woods Hole Oceanographic
Institution Received January 27, 1962; revised August 23, 1962 1962.
[12] Farrow DE, Patterson JC. On the stability of the near shore waters of a lake when subject to
solar heating. Int J Heat Mass Transf 1993;36:89–100. doi:10.1016/0017-9310(93)80069-
7.
156
[13] Spiegel EA. Convection in stars 1971;46:801–12.
[14] Baker L, Faw RE, Kulacki FA. Postaccident Heat Removal-Part I: Heat Transfer Within an
Internally Heated, Nonboiling liquid layer. Nucl Sci Eng 1976;230:222–30.
[15] Faw RE, Baker L. Postaccident Heat Removal-Part II : Heat Transfer from an Internally
Heated Liquid to a Melting Solid. Nucl Sci Eng 1976;238:231–8.
[16] Tasaka Y, Takeda Y. Effects of heat source distribution on natural convection induced by
internal heating. Int J Heat Mass Transf 2005;48:1164–74.
[17] Hattori T, Patterson JC, Lei C. Scaling and direct stability analyses of natural convection
induced by absorption of solar radiation in a parallelepiped cavity. Int J Therm Sci
2015;88:19–32. doi:10.1016/j.ijthermalsci.2014.09.005.
[18] Amber I, O’Donovan TS. Heat transfer in a molten salt filled enclosure absorbing
concentrated solar radiation. Int J Heat Mass Transf 2017;113:444–55.
doi:10.1016/j.ijheatmasstransfer.2017.04.028.
[19] Amber I, O’Donovan TS. Natural convection induced by the absorption of solar radiation:
A review. Renew Sustain Energy Rev 2018;82:3526–45. doi:10.1016/j.rser.2017.10.106.
[20] Lenert A, Wang EN. Optimization of nanofluid volumetric receivers for solar thermal
energy conversion. Sol Energy 2012;86:253–65. doi:10.1016/j.solener.2011.09.029.
[21] Hattori T, Patterson JC, Lei C. Mixing in internally heated natural convection flow and
scaling for a quasi-steady boundary layer. J Fluid Mech 2015;763:352–68.
doi:10.1017/jfm.2014.680.
[22] Ni G, Li G, Boriskina S V., Li H, Yang W, Zhang T, et al. Steam generation under one sun
enabled by a floating structure with thermal concentration. Nat Energy 2016;1:16126.
doi:10.1038/nenergy.2016.126.
[23] Sabharwall P, Ebner M, Sohal M, Sharpe P. Molten Salts for High Temperature Reactors:
University of Wisconsin Molten Salt Corrosion and Flow Loop Experiments--Issues
Identified and Path Forward. Idaho National Laboratory (INL); 2010.
[24] Passerini S. Optical and Chemical Properties of Molten Salt Mixtures for Use in High
Temperature Power Systems. Massachusetts Institute of Technology, 2010.
[25] Drotning WD. Optical properties of solar-absorbing oxide particles suspended in a molten
salt heat transfer fluid. Sol Energy 1978;20:313–9. doi:10.1016/0038-092X(78)90123-8.
[26] Webb BW, Viskanta R. Analysis of Heat Transfer and Solar Radiation Absorption in an
Irradiated Thin, Falling Molten Salt Film. J Sol Energy Eng 1985;107:113.
doi:10.1115/1.3267663.
157
[27] Viskanta R, Anderson EE. Heat transfer in semitransparent solids. Adv Heat Transf
1975;11:317–441.
[28] Myers PD, Yogi Goswami D, Stefanakos E. Molten Salt Spectroscopy for Quantification
of Radiative Absorption in Novel Metal Chloride-Enhanced Thermal Storage Media. J Sol
Energy Eng 2015;137:41002. doi:10.1115/1.4029934.
[29] Makino T, Maeda T, Edamura M, Yasuo T, Yoshida A. Thermal radiation properties of
molten salts (properties of alkali metal chlorides and conductive-radiative transfer in the
salts). Heat Transf Japanese Res 1991;20:711–21.
[30] Otanicar TP, Phelan PE, Golden JS. Optical properties of liquids for direct absorption solar
thermal energy systems. Sol Energy 2009;83:969–77. doi:10.1016/j.solener.2008.12.009.
[31] Passerini S, McKrell T. A Facile Apparatus for the High Temperature Measurement of Light
Attenuation in Nearly Transparent Liquids/Molten Salts. J Nanofluids 2012;1:78–84.
doi:10.1166/jon.2012.1010.
[32] Weinstein LA, Loomis J, Bhatia B, Bierman DM, Wang EN, Chen G. Concentrating Solar
Power. Chem Rev 2015;115:12797–838. doi:10.1021/acs.chemrev.5b00397.
[33] Weinstein L, Kraemer D, McEnaney K, Chen G. Optical cavity for improved performance
of solar receivers in solar-thermal systems. Sol Energy 2014;108:69–79.
doi:10.1016/j.solener.2014.06.023.
[34] Reynolds DJ, Jance MJ, Behnia M, Morrison GL. An experimental and computational study
of the heat loss characteristics of a trapezoidal cavity absorber. Sol Energy 2004;76:229–
34. doi:10.1016/j.solener.2003.01.001.
[35] Rowe DM. A high performance thermoelectric solar powered generator. Appl Energy
1981;8:269–73. doi:10.1016/0306-2619(81)90023-4.
[36] Cui F, He Y, Cheng Z, Li Y. Study on combined heat loss of a dish receiver with quartz
glass cover. Appl Energy 2013;112:690–6. doi:10.1016/j.apenergy.2013.01.007.
[37] Arpin KA, Losego MD, Cloud AN, Ning H, Mallek J, Sergeant NP, et al. Three-dimensional
self-assembled photonic crystals with high temperature stability for thermal emission
modification. Nat Commun 2013;4:2630. doi:10.1038/ncomms3630.
[38] Selvakumar N, Barshilia HC. Review of physical vapor deposited (PVD) spectrally
selective coatings for mid- and high-temperature solar thermal applications. Sol Energy
Mater Sol Cells 2012;98:1–23. doi:10.1016/j.solmat.2011.10.028.
[39] Singh PL, Sarviya RM, Bhagoria JL. Thermal performance of linear Fresnel reflecting solar
concentrator with trapezoidal cavity absorbers. Appl Energy 2010;87:541–50.
doi:10.1016/j.apenergy.2009.08.019.
158
[40] Bogaerts WF, Lampert CM. Materials for photothermal solar energy conversion. J Mater
Sci 1983;18:2847–75. doi:10.1007/BF00700767.
[41] Atkinson C, Sansom CL, Almond HJ, Shaw CP. Coatings for concentrating solar systems
– A review. Renew Sustain Energy Rev 2015;45:113–22. doi:10.1016/j.rser.2015.01.015.
[42] Kennedy CE. Review of mid-to high-temperature solar selective absorber materials.
National Renewable Energy Lab., Golden, CO.(US); 2002.
[43] Epstein M, Segal A, Yogev A. A molten salt system with a ground base-integrated solar
receiver storage tank. J Phys IV Fr 1999;9. doi:10.1051/jp4:1999315.
[44] Codd DS. Concentrated Solar Power on Demand. Massachusetts Institute of Technology,
2011.
[45] Alqaydi MS, Delclos T, Almheiri S, McKrell T, Calvet N. Effect of sand and moisture on
molten salt properties for open direct absorption solar receiver/storage system. AIP Conf.
Proc., vol. 1734, 2016. doi:10.1063/1.4949100.
[46] ASTM Standard G173-03, Standard Tables for Reference Solar Spectral Irradiances: Direct
Normal and Hemispherical on 37˚ Tilted Surface. 2003.
[47] Modest MF. Radiative Heat Transfer. Third. Oxford: Academic Press; 2013.
[48] Howell JR, Menguc MP, Siegel R. Thermal radiation heat transfer. CRC press; 2010.
[49] Hutchings DC, Sheik-Bahae M, Hagan DJ, Van Stryland EW. Kramers-Kronig relations in
nonlinear optics. Opt Quantum Electron 1992;24:1–30. doi:10.1007/BF01234275.
[50] Kramers HA. La diffusion de la lumiere par les atomes. Atti Congr Int Fis Como
1927;2:545.
[51] Kronig R. On the theory of dispersion of x-rays. J Opt Soc Am 1926;12:547–57.
[52] Makino T, Maeda T, Edamura M. Thermal radiation properties of molten salts (properties
of alkali metal nitrates) 1991:700–10.
[53] Jindal H, Harrington G. Refractometry in fused alkali nitrates and thiocyanates. J Phys
Chem 1967;71.6:1688–94.
[54] Bloom H, Rhodes DC. Molten Salt Mixtures. Part 2. The Refractive Index Of Molten
Nitrate Mixtures And Their Molar Refractivities. J Phys Chem 1956;60:791–3.
doi:10.1021/j150540a022.
[55] Janz GJ. Molten Salts Handbook. New York: Academic Press; 1967.
159
[56] Smakula A. Synthetic Crystals and Polarizing Materials. Opt Acta (Lond) 1962;9:205–22.
doi:10.1080/713826427.
[57] Lorentz HA. The radiation of light. Collect. Pap., Springer; 1935, p. 17–27.
[58] Supplementary information n.d.
[59] Touloukian YS, Dewitt DP. Thermal radiative properties, nonmetallic solids,
thermophysica1 properties of matter 8, IFI 1972.
[60] Hollands KGT, Raithby GD, Konicek L. Correlation equations for free convection heat
transfer in horizontal layers of air and water. Int J Heat Mass Transf 1975;18:879–84.
doi:10.1016/0017-9310(75)90179-9.
[61] Hamer TT, Zhou L, Trumper D, Slocum AH, Calvet N. Implementation of Thermal-
Insulating and-Mixing Elements in a Concentrated Solar Power on Demand System. AIP
Conf Proceeding - SolarPACES 2017 Conf 2018;0.
[62] Grange B, Kumar V, Gil A, Armstrong PR, Codd DS, Slocum A, et al. Preliminary optical,
thermal and structural design of a 100 kWth CSPonD beam-down on-sun demonstration
plant. Energy Procedia 2015;75:2163–8.
[63] Tetreault-Friend M, Gray LA, Berdibek S, McKrell T, Slocum AH. Optical properties of
high temperature molten salt mixtures for volumetrically absorbing solar thermal receiver
applications. Sol Energy 2017;153:238–48. doi:10.1016/j.solener.2017.05.054.
[64] Kennedy CE. Review of Mid- to High- Temperature Solar Selective Absorber Materials.
2002.
[65] Palik ED. Handbook of Optical Constants of Solids. Elsevier; 1997.
[66] Fletcher EA, Moen RL. Hydrogen and Oxygen from Water. Science (80- ) 1977;197:1050–
6. doi:10.1126/science.197.4308.1050.
[67] Fletcher EA. Solarthermal Processing : A Review. J Sol Energy Eng 2001;123:63–74.
doi:10.1115/1.1349552.
[68] Francey JLA, Golding P, Clarke R. Low-cost solar heating of community pools using pool
covers. Sol Energy 1980;25:407–16. doi:10.1016/0038-092X(80)90447-8.
[69] Francey JLA, Golding P. The optical characteristics of swimming pool covers used for
direct solar heating. Sol Energy 1981;26:259–63. doi:10.1016/0038-092X(81)90211-5.
[70] Czarnecki JT. A method of heating swimming pools by solar energy. Sol Energy 1963;7:3–
7. doi:10.1016/0038-092X(63)90129-4.
160
[71] Katsaprakakis D Al. Comparison of swimming pools alternative passive and active heating
systems based on renewable energy sources in Southern Europe. Energy 2015;81:738–53.
doi:10.1016/j.energy.2015.01.019.
[72] Ghasemi H, Ni G, Marconnet AM, Loomis J, Yerci S, Miljkovic N, et al. Solar steam
generation by heat localization. Nat Commun 2014;5:4449. doi:10.1038/ncomms5449.
[73] Bucci M, Richenderfer A, Su GY, McKrell T, Buongiorno J. A mechanistic IR calibration
technique for boiling heat transfer investigations. Int J Multiph Flow 2016;83:115–27.
doi:10.1016/j.ijmultiphaseflow.2016.03.007.
[74] McMahon HO. Thermal Radiation from Partially Transparent Reflecting Bodies. J Opt Soc
Am 1950;40:376. doi:10.1364/JOSA.40.000376.
[75] Dunkle R V. “Thermal radiation characteristics of surfaces” in Theory and Fundamental
Research in Heat Transfer. New York: ed. J. A. Clark, Pergamon Press; 1963.
[76] Boriskina S V, Weinstein LA, Tong JK, Hsu W-C, Chen G. Hybrid Optical–Thermal
Antennas for Enhanced Light Focusing and Local Temperature Control. ACS Photonics
2016;3:1714–22. doi:10.1021/acsphotonics.6b00374.
[77] Duffie JA, Beckman WA. Solar Engineering of Thermal Processes. Wiley; 2013.
[78] ASM. ASM Handbook. Heat Treating, 10th ed. vol. 4. 10th ed. 1991.
[79] Blander M. Molten salt chemistry. New York: Interscience Publishers; 1964.
[80] Karni J. Solar-thermal power generation. Annu Rev Heat Transf 2012;15:37–92.
[81] Cable M. Mechanization of glass manufacture. J Am Ceram Soc 1999;82:1093–112.
[82] ASTM E490-00a(2014), Standard Solar Constant and Zero Air Mass Solar Spectral
Irradiance Tables, ASTM International, West Conshohocken, PA, 2014, www.astm.org n.d.
161
Appendices
A. Effect of temperature on optical properties
Figure A-1 Absorption coefficient of 40 wt. % KNO3: 60 wt. % NaNO3 binary nitrate molten salt (SQM) at
300 ˚C, 350 ˚C, and 400 ˚C.
Figure A-2 Absorption coefficient of decomposed 40 wt. % KNO3: 60 wt. % NaNO3 binary nitrate molten salt
(SQM) at 300 ˚C, 350 ˚C, and 400 ˚C.
162
The absorption coefficient versus wavelength for the SQM binary nitrate salt and the decomposed
binary nitrate at 300 ˚C, 350 ˚C, and 400 ˚C are given in Figures S1 & S2, respectively. Although
it appears there could be a dependence on temperature for wavelengths less than 1500 nm, error
bars overlap significantly and there is no clear trend.
B. Uncertainty analysis in optical property measurements
𝛽 =
−1
∆𝑥𝑗𝑖ln (
𝐼𝑗
𝐼𝑖) =
−1
∆𝑥𝑗𝑖[ln(𝐼𝑗) − ln(𝐼𝑖)] B.1
𝛿𝛽 = √(𝜕𝛽
𝜕(∆𝑥𝑗𝑖)𝛿(∆𝑥𝑗𝑖))
2
+ (𝜕𝛽
𝜕𝐼𝑗𝛿𝐼𝑗)
2
+ (𝜕𝛽
𝜕𝐼𝑖𝛿𝐼𝑖)
2
B.2
𝜕𝛽
𝜕𝐼𝑗=
−1
𝐼𝑗∆𝑥𝑗𝑖 B.3
𝜕𝛽
𝜕𝐼𝑖=
1
𝐼𝑖∆𝑥𝑗𝑖 B.4
𝜕𝛽
𝜕(∆𝑥𝑗𝑖)=
1
(∆𝑥𝑗𝑖)2 ln (
𝐼𝑗
𝐼𝑖) B.5
𝛿𝛽 = √(1
(∆𝑥𝑗𝑖)2 ln (
𝐼𝑗
𝐼𝑖) 𝛿(∆𝑥𝑗𝑖))
2
+ (−1
𝐼𝑗∆𝑥𝑗𝑖𝛿𝐼𝑗)
2
+ (1
𝐼𝑖∆𝑥𝑗𝑖𝛿𝐼𝑖)
2
B.6
𝛿𝐼𝑗 = 𝛿𝐼𝑗 = 0.1% B.7
163
𝛿(∆𝑥𝑗𝑖) = 0.5 𝑚𝑚 B.8
𝛿𝛽 ≅ √(𝛿(∆𝑥𝑗𝑖)
(∆𝑥𝑗𝑖)2 ln (
𝐼𝑗
𝐼𝑖))
2
=𝛿(∆𝑥𝑗𝑖)
∆𝑥𝑗𝑖𝛽 B.9
Uncertainty dominated by the path length measurement uncertainty. The maximum uncertainty
calculated from the experimental data, given that the smallest path length ∆𝑥𝑗𝑖 = 10 𝑚𝑚 , is
therefore
𝛿𝛽
𝛽=
𝛿(∆𝑥𝑗𝑖)
∆𝑥𝑗𝑖≤ 5% B.10
Note that although intensity measurements were taken at 5 mm increments, the minimum path
length difference was taken such that
∆𝑥𝑗𝑖 = ∆𝑥𝑗 − ∆𝑥𝑖 = 10 𝑚𝑚, 15 𝑚𝑚, 20 𝑚𝑚, … B.11
C. Reflectance calculation
The normal reflectance 𝑅𝑛𝑜𝑟𝑚 is given as
𝑅𝑛𝑜𝑟𝑚 =
1
2[(
𝑛1 cos 𝜃2 − 𝑛2 cos 𝜃1
𝑛1 cos 𝜃2 + 𝑛2 cos 𝜃1)
2
+ (𝑛1 cos 𝜃1 − 𝑛2 cos 𝜃2
𝑛1 cos 𝜃1 + 𝑛2 cos 𝜃2)
2
] = (𝑛 − 1
𝑛 + 1)
2
C.1
where 𝑛1 and 𝑛2 are the refractive indices in the liquid and air, respectively. Taking 𝜃1 = 𝜃2 ≈ 0,
and letting 𝑛1 = 𝑛 and 𝑛2 = 1, yields
164
𝑅𝑛𝑜𝑟𝑚 = (
𝑛 − 1
𝑛 + 1)
2
C.2
The diffuse, hemispherical reflectance 𝑅𝑑𝑖𝑓𝑓 is given as
𝑅𝑑𝑖𝑓𝑓 = 1 −
1
2(𝜖∥ + 𝜖⊥) C.3
𝜖∥ =
8
𝑛2 + 𝑘2(1 −
𝑛
𝑛2 + 𝑘2ln[(𝑛 + 1)2 + 𝑘2] +
(𝑛2 − 𝑘2)
𝑘(𝑛2 + 𝑘2)tan−1
𝑘
𝑛 + 1) C.4
𝜖⊥ = 8𝑛 (1 − 𝑛 ln
(𝑛 + 1)2+𝑘2
𝑛2 + 𝑘2+
(𝑛2 − 𝑘2)
𝑘tan−𝑎
𝑘
𝑛(𝑛 + 1) + 𝑘2) C.5
where 𝑘 is the absorptive index in the complex index of refraction, with 𝑛 ≫ 𝑘 in semi-transparent
liquids. Taking the limit as 𝑘 → 0, we obtain after applying L’Hôpital’s rule and some math,
lim𝑘→0
𝜖∥ =8
𝑛(1 −
2
𝑛ln(𝑛 + 1) +
1
𝑛 + 1) C.6
lim𝑘→0
𝜖⊥ = 8𝑛 (1 − 2𝑛 ln𝑛 + 1
𝑛+
𝑛
𝑛 + 1)
C.7
and
lim𝑘→0
𝑅𝑑𝑖𝑓𝑓 = 1 −4
𝑛(1 −
2
𝑛ln(𝑛 + 1) +
1
𝑛 + 1) − 4𝑛 (1 − 2𝑛 ln
𝑛 + 1
𝑛+
𝑛
𝑛 + 1) C.8
165
D. Conversion of photon counts to heat flux ratio
The effectiveness of the cover is calculated as in Equation (1), where Φ𝑖 is the photon count at
pixel 𝑖.
𝜖𝑠 = 1 −∑ Φ𝑖𝑎𝑙𝑙 𝑝𝑖𝑥𝑒𝑙𝑠
∑ Φ𝑖,𝑟𝑒𝑓𝑎𝑙𝑙 𝑝𝑖𝑥𝑒𝑙𝑠 (D.1)
The spectral response range of the IR camera is [𝜆𝑎, 𝜆𝑏]. Therefore, the ratio of photon counts can
be expanded as shown in Equation (2), where 𝑓(𝜆𝑇) = ∫ 𝐸𝜆𝑏𝜆
0𝑑𝜆, 𝐴 is the pixel area, and 𝜎 is the
Stefan-Boltzmann constant.
∑ Φ𝑖𝑖
∑ Φ𝑖,𝑟𝑒𝑓𝑖=
∑ [𝑓(𝜆𝑏𝑇𝑖) − 𝑓(𝜆𝑎𝑇𝑖)]𝐴𝜎𝑇𝑖4
𝑖
∑ [𝑓(𝜆𝑏𝑇𝑖,𝑟𝑒𝑓) − 𝑓(𝜆𝑎𝑇𝑖,𝑟𝑒𝑓)]𝐴𝜎𝑇𝑖,𝑟𝑒𝑓4
𝑖
=∑ [𝑓(𝜆𝑏𝑇𝑖) − 𝑓(𝜆𝑎𝑇𝑖)]𝑇𝑖
4𝑖
∑ [𝑓(𝜆𝑏𝑇𝑖,𝑟𝑒𝑓) − 𝑓(𝜆𝑎𝑇𝑖,𝑟𝑒𝑓)]𝑇𝑖,𝑟𝑒𝑓4
𝑖
(D.2)
The ratio of radiative heat flux emitted from the experiment can be put as in Equation (3).
�̇�
�̇�𝑟𝑒𝑓
=∑ 𝐴𝜎𝑇𝑖
4𝑖
∑ 𝐴𝜎𝑇𝑖,𝑟𝑒𝑓4
𝑖
=∑ 𝑇𝑖
4𝑖
∑ 𝑇𝑖,𝑟𝑒𝑓4
𝑖
(D.3)
Considering that in each observation the temperature of the surface is homogeneous, Equations (2)
and (3) can be approximated as:
∑ Φ𝑖𝑖
∑ Φ𝑖,𝑟𝑒𝑓𝑖≈
[𝑓(𝜆𝑏𝑇𝑖) − 𝑓(𝜆𝑎𝑇𝑖)]𝑇4
[𝑓(𝜆𝑏𝑇𝑖,𝑟𝑒𝑓) − 𝑓(𝜆𝑎𝑇𝑖,𝑟𝑒𝑓)]𝑇𝑟𝑒𝑓4
(D.4)
166
�̇�
�̇�𝑟𝑒𝑓
≈𝑇4
𝑇𝑟𝑒𝑓4 (D.5)
The relative error of approximating the radiative heat flux ratio via the ratio of photon counts is
obtained by dividing Equation (4) by Equation (5).
∑ Φ𝑖𝑖
∑ Φ𝑖,𝑟𝑒𝑓𝑖
�̇�
�̇�𝑟𝑒𝑓
=𝑓(𝜆𝑏𝑇) − 𝑓(𝜆𝑎𝑇)
𝑓(𝜆𝑏𝑇𝑟𝑒𝑓) − 𝑓(𝜆𝑎𝑇𝑟𝑒𝑓) (D.6)
Fixing 𝑇𝑟𝑒𝑓 = 400°𝐶, it is possible to evaluate the relative error of the approximation given in
Equation (6) at different representative temperatures 𝑇 of the experiment. The spectral response
range of the camera is [𝜆𝑎, 𝜆𝑏] = [1.0 𝜇𝑚, 5.3 𝜇𝑚] . The relative error made using this
approximation grows as the difference in temperature with respect to the reference increases (Δ𝑇),
being below 15% for differences as large as 50 K.
167
E. Transmission modeling
Ray-tracing simulations in Lambda Research TracePro 7.5.7 are used to estimate the transmission
efficiency of concentrated solar radiation across an infinite sphere array as illustrated in
Supplementary Figure 7.
Figure E-1 Geometry, properties and boundary conditions of optical
model for infinite layer of hexagonal close-packed (HCP) spheres.
The infinite array is modeled using the symmetry characteristics of the hexagonal close-packed
arrangement, as shown in Supplementary Figure 6. The body of the spheres is modeled as a region
with spectral refraction index n and absorption coefficient 𝜅 for fused silica as provided by
Palik[65]. According to their buoyancy on molten salts, the spheres are partially immersed in a
volume with the refraction index of either nitrate (n = 1.41) of chloride (n = 1.40) molten salts[63].
Rays are generated from a plane above the sphere array and follow the solar spectral wavelength
168
distribution[82]. The intensity is constant and uniform over the entire plane source and at all angles
within the cone defined by the specified half-angle 𝜃 (c.f., Supplementary Figure 7). The power
refracted into the molten salts is measured as the power incident on the lower face of the molten
salts volume. The inputs to each simulation are the irradiation half-angle (𝜃), the diameter of the
spheres (𝐷), and their thickness (𝑡). Using 106 rays in each simulation, the relative standard
deviation on the transmission efficiency is measured below 0.3 % on the simulation results. The
geometry of the system allows to report the cover transmission efficiency as a function only of the
t/D ratio and θ. Supplementary Figures 8 and 9 show the transmission efficiency though modular
fused silica covers which rest on either nitrate or chloride molten salts.
169
(a)
(b)
Figure E-2 Transmission efficiency on binary nitrate molten salt. a, Based on a sphere wall thickness of 1
mm. b, More generally, as a function of the ratio of the sphere wall thickness to its diameter.
170
(a)
(b)
Figure E-3 Transmission efficiency on binary chloride molten salt. a, Based on a sphere wall thickness of 1 mm.
b, More generally, as a function of the ratio of the sphere wall thickness to its diameter.
In all cases, transmission efficiency decreases as the angular spread of the irradiation increases.
For each irradiation angular distribution, transmission efficiency has two local maxima. As the
spread of the irradiation increases, the first local maximum is found at increasingly lower t/D
171
values, whereas the second local maximum is found at larger t/D values. Additionally, the distance
between the maxima increases and the second maximum becomes dominant. For nitrate molten
salts, the absolute transmission efficiency maximum for each irradiation angular distribution
occurs always at high t/D values, near the sinking point of the spheres. For chloride molten salts,
the largest transmission efficiency is exceptionally found at low t/D values for a small range of
irradiation half-angles, and otherwise at high t/D values.
172
F. Calculated capture efficiency for 40 mm, 60 mm, and 80 mm spheres
Figure F-1 Capture efficiency for 40 mm diameter spheres.
176
H. Divider plate and mixing plate designs
(a)
(b)
Figure H-1 Labelled cross-sectional views of the divider plate (a) and mixing plate (b) designs. Adapted from
Hamer et al. [61].
Assuming heat transfer is approximately 1-dimensional in the axial direction along the tank, the
thermal circuit for the axial conduction through the divider plate is given in Fig. H.1.
Figure H-2 Equivalent thermal circuit for the axial conduction through the divider plate.
177
Where 𝑅𝑡ℎ,𝑡𝑜𝑡𝑐𝑜𝑛𝑑 is the total thermal conduction resistance through the divider plate, expressed as
𝑅𝐷𝑃,𝑡𝑜𝑡𝑐𝑜𝑛𝑑 = 𝑅𝑆𝑆−𝑡𝑜𝑝
𝑐𝑜𝑛𝑑 + 𝑅𝑎𝑖𝑟 𝑔𝑎𝑝,1𝑐𝑜𝑛𝑑 + 𝑅𝑠ℎ𝑖𝑒𝑙𝑑 1
𝑐𝑜𝑛𝑑 + ⋯ (H.1)
We can evaluate equivalent thermal conduction properties by defining an effective thermal
conductivity 𝑘𝐷𝑃,𝑒𝑓𝑓 such that
𝑅𝐷𝑃,𝑡𝑜𝑡𝑐𝑜𝑛𝑑 =
𝑡𝐷𝑃,𝑡𝑜𝑡
𝑘𝐷𝑃,𝑒𝑓𝑓𝐴
(H.2)
where 𝐴 = 𝐴𝑆𝑆−𝑡𝑜𝑝 = 𝐴𝑎𝑖𝑟 = 𝐴𝑠ℎ𝑖𝑒𝑙𝑑 = 𝜋𝑅𝐷𝑃2 . The effective thermal conductivity can be
calculated by equating Eqns. H.1 and H.2 and solving for 𝑘𝐷𝑃,𝑒𝑓𝑓.
The total thermal radiation from the top surface to the bottom surface of the divider plate is given
as
�̇�𝐷𝑃𝑟𝑎𝑑 = [
𝜖𝑠ℎ𝑖𝑒𝑙𝑑
(𝑛 + 1)(2 − 𝜖𝑠ℎ𝑖𝑒𝑙𝑑)] 𝜎𝐴(𝑇𝐷𝑃,𝑡𝑜𝑝
4 − 𝑇𝐷𝑃,𝑏𝑜𝑡4 )
(H.3)
where 𝑛 = 7 is the total number of shields. We can therefore model only the radiation exchange
between the top and bottom surfaces using an effective emissivity
�̇�𝐷𝑃𝑟𝑎𝑑 = [
𝜖𝑠ℎ𝑖𝑒𝑙𝑑
(𝑛 + 1)(2 − 𝜖𝑠ℎ𝑖𝑒𝑙𝑑)] 𝜎𝐴(𝑇𝐷𝑃,𝑡𝑜𝑝
4 − 𝑇𝐷𝑃,𝑏𝑜𝑡4 )
= [𝜖𝐷𝑃,𝑒𝑓𝑓
2 − 𝜖𝐷𝑃,𝑒𝑓𝑓] 𝜎𝐴(𝑇𝐷𝑃,𝑡𝑜𝑝
4 − 𝑇𝐷𝑃,𝑏𝑜𝑡4 )
(H.4)
assuming all surfaces have the same emissivity. Solving for the effective emissivity yields
178
𝜖𝐷𝑃,𝑒𝑓𝑓 =2𝜖𝑠ℎ𝑖𝑒𝑙𝑑
𝜖𝑠ℎ𝑖𝑒𝑙𝑑 + (𝑛 + 1)(2 − 𝜖𝑠ℎ𝑖𝑒𝑙𝑑)
(H.5)
Effective density and specific heat are simply calculated taking mass averages of each material in
the divider plate. A summary of the properties of the divider plate are given in Table H.1.
Table H-1 Effective thermophysical properties of divider plate and mixing plate in
thermal model.
Property Divider Plate Mixing Plate
𝒌𝒆𝒇𝒇 (𝑾
𝒎𝟐𝑲) 0.03 0.593
𝝆𝒆𝒇𝒇 (𝒌𝒈
𝒎𝟑) 2738 2609
𝑪𝒑,𝒆𝒇𝒇 (𝒌𝑱
𝒌𝒈 − 𝑲) 0.5 1.12