Advanced energy materials

1.2.2 Secondary Tracking Local Movement 1.3.2 Optical Analysis of Residual Aberration 191.4 Optimization of Flux Distribution Pattern 1.5 First Prototype of Non-imaging Focusing 1.5.5 Ha

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ISBN 978-1-118-68629-4

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10 9 8 7 6 5 4 3 2 1

1.2.2 Secondary Tracking (Local Movement

1.3.2 Optical Analysis of Residual Aberration 191.4 Optimization of Flux Distribution Pattern

1.5 First Prototype of Non-imaging Focusing

1.5.5 Hardware and Software Control System 401.5.6 Optical Alignment of Prototype Heliostat 411.5.7 High Temperature Solar Furnace System 461.6 Second Prototype of Non-imaging Focusing

1.6.2 Mechanical Design and Control System

1.6.3 High Temperature Potato Skin

Acknowledgement 65References 65

2 State-of-the-Art of Nanostructures in Solar

Suresh Sagadevan

2.2.1 Importance of Solar Energy 712.2.2 Solar Energy and Its Economy 742.2.3 Technologies Based on Solar Energy 75

2.3 Nanostructures and Different Synthesis Techniques 772.3.1 Classifi cation of Nanomaterials 782.3.2 Synthesis and Processing of Nanomaterials 792.4 Nanomaterials for Solar Cells Applications 812.4.1 CdTe, CdSe and CdS Thin-Film PV Devices 822.4.2 Nanoparticles/Quantum Dot Solar Cells

2.4.3 Iron Disulfi de Pyrite, CuInS2 and Cu2ZnSnS4 842.4.4 Organic Solar Cells and Nanowire Solar Cells 852.4.5 Polycrystalline Thin-Film Solar Cells 862.5 Advanced Nanostructures for Technological

Applications 872.5.1 Nanocones Used as Inexpensive Solar Cells 882.5.2 Core/Shell Nanoparticles towards PV

Applications 1083.3 TiO2Nanomaterials and Nanocomposites for the

Application of DSSC and Heterostructure Devices 1093.3.1 Fabrication of DSSCs with TiO2 Nanorods

for the Application of DSSC and

3.4.1 Fabrication of DSSCs with ZnO Nanotubes

3.4.2 Fabrication of DSSCs with Nanospikes

Decorated ZnO Sheets Based Photoanode 1253.4.3 Fabrication of DSSCs with ZnO Nanorods

(NRs) and Nanoballs (NBs) Nanomaterial

3.4.4 Fabrication of DSSCs with Spindle Shaped

Sn-Doped ZnO Nanostructures Based Photoanode 1323.4.5 Fabrication of DSSCs with Vertically Aligned ZnO Nanorods (NRs) and Graphene Oxide Nanocomposite Based Photoanode 1353.4.6 ZnO Nanocomposite for the Heterostructures Devices 1393.4.7 Fabrication of Heterostructure Device

3.8 Metal Oxide Nanostructures and Nanocomposites

3.8.1 ZnO Flower Nanostructures for Photocatalytic Degradation of Crystal Violet (Cv)Dye 1443.8.2 Advanced ZnO-Graphene Oxide Nanohybrid for the Photocatalytic Degradation of Crystal

3.8.3 Effective Nanocomposite of Polyaniline

(PANI) and ZnO for the Photocatalytic Degradation of Methylene Blue (MB) Dye 1503.8.4 Novel Poly(1-naphthylamine)/Zinc Oxide

Nanocomposite for the Photocatalytic Degradation of Methylene Blue (MB) Dye 1523.8.5 Nanocomposites of Poly(1-naphthylamine)/SiO2 and Poly(1-Naphthylamine)/TiO2 for the Photocatalytic Degradation of Methylene Blue

References 159

4 Superionic Solids in Energy Device Applications 167

Angesh Chandra and Archana Chandra

5 Polymer Nanocomposites: New Advanced Dielectric

Materials for Energy Storage Applications 207

Vijay Kumar Thakur and Michael R Kessler

5.2.1 Dielectric Permittivity, Loss and Breakdown 209

5.6 Conclusion and Future Perspectives 245References 247

6 Solid Electrolytes: Principles and Applications 259

S.W Anwane

6.3 Classifi cation of Solid Electrolytes 2656.4 Criteria for High Ionic Conductivity and Mobility 2666.5 Electrical Characterization of Solid Electrolyte 267

6.6 Ionic Conductivity and Temperature 2716.7 Concentration-Dependent Conductivity 2746.8 Ionic Conductivity in Composite SE 2756.9 Thermodynamics of Electrochemical System 278

7 Advanced Electronics: Looking beyond Silicon 295

Surender Duhan and Vijay Tomer

7.3 Need for Carbon-Based Electronics Technology 300

7.7.1 Nanotube-Based FET Transistors CNTFET 313

7.7.3 Carbon Nanotube Sensor of Polar Molecules 3157.7.4 Carbon Nanotube Crossbar Arrays for

7.8 Advantages of CNT-Based Devices 317

and Optical Properties of Lead Sulfi de for Energy

Applications 327

Pooja B and G Sharma

8.3.1 Phase Transition and Structural Parameters 3298.3.2 Pressure Dependent Electronic Properties 3338.3.3 Pressure-Dependent Dielectric Constant 340

Acknowledgements 342References 342

9.2.1 Threshold Displacement Energy: Theory

9.2.2 Radiation Defects in GaN: Defects Levels,

Effects on Charge Carriers Concentration, Mobility, Lifetime of Charge Carriers,

9.3 Radiation Effects in Other III-Nitrides 3669.4 Radiation Effects in GaN Schottky Diodes, in

AlGaN/GaN and GaN/InGaN Heterojunctions

9.5 Radiation Effects in GaN-Based Devices 3749.6 Prospects of Radiation Technology for GaN 376

Acknowledgments 380References 380

10 Antiferroelectric Liquid Crystals: Smart Materials

Manoj Bhushan Pandey, Roman Dabrowski and

Ravindra Dhar

10.1.1 Molecular Packing in Liquid Crystalline

Phases 39110.2 Theories of Antiferroelectricity in Liquid Crystals 39810.3 Molecular Structure Design/Synthesis of AFLC

Materials 40210.4 Macroscopic Characterization and Physical

10.4.2 Dielectric Parameters of AFLCs 41010.4.3 Switching and Electro-Optic Parameters 41910.5 Conclusion and Future Scope 425Acknowledgements 426

11 Polyetheretherketone (PEEK) Membrane for Fuel

Tungabidya Maharana, Alekha Kumar Sutar,

Nibedita Nath, Anita Routaray, Yuvraj Singh Negi

and Bikash Mohanty

11.2.2 Why PEEK is Used as Fuel Cell Membrane 445

11.4 Modifi ed PEEK as Fuel Cell Membrane 452 11.4.1 Sulphonated PEEK as Fuel Cell Membrane 45311.5 Evaluation of Cell Performance 459

11.7 Conclusion and Future Prospects 460Acknowledgement 461References 461

12 Vanadate Phosphors for Energy Effi cient Lighting 465

K N Shinde and Roshani Singh

12.2 Some Well-Known Vanadate Phosphors 466

12.5 Results and Discussion of

M3–3x/2(VO4)2:xEu (0.01 ≤ x ≤ 0.09 for M = Ca

and 0 ≤ x ≤ 0.3 for M = Sr,Ba) Phosphors 470 12.5.1 X-ray Diffraction Pattern of

12.5.2 Surface Morphology of

12.5.3 Photoluminescence Properties of

12.6 Effect of Annealing Temperature on

M3–3x/2(VO4)2:xEu (x = 0.05 for M = Ca, x = 0.1 for

M = Sr and x = 0.3 for M = Ba) Phosphors 484 12.6.1 X-ray Diffraction Pattern of

13 Molecular Computation on Functionalized

Circuits using Os-polypyridyl Complex

13.5 Multiple Redox States and Logic Devices 520

Acknowledgements 523References 525

14 Ionic Liquid Stabilized Metal NPs and Their Role

14.5 Synthesis of Metal Nanoparticles 533

14.7 Stabilization of Metal Nanoparticles in Ionic Liquid 53514.8 Applications of Metal NPs as Potent Catalyst

References 544

15 There’s Plenty of Room in the Field of Zeolite-Y

Enslaved Nanohybrid Materials as Eco-Friendly

Catalysts: Selected Catalytic Reactions 555

C.K Modi and Parthiv M Trivedi

limited and pollute th e environment, leading to climate change on

a global scale In order to avoid an energy crisis, the research efforts

of many scientifi c centers around the globe are being directed towards searching for new solutions and improving those already existing in the energy sector In parallel with the growth rate of renewable energy, essential attention is being paid to the develop-ment of advanced methods and materials for effective utilization of energy resources Technological advantages will help to overcome energy-related diffi culties Among the main criteria for the viability

of new energetic techniques are effi ciency, cost, usability and ronmental infl uence

envi-This book summarizes the current status of know-how in the

fi elds of advanced materials for energy-associated applications, in particular, photovoltaics, effi cient light sources, fuel cells, energy saving technologies, nanostructured materials, etc Tendencies for future development are also discussed A good understanding of the excited state reactivity of photoactive materials would help to prepare new materials and molecules capable of absorbing light over a given wavelength range for use in driving electron trans-fer There has been scientifi cally and technologically well-equipped materials science exploration into the possibility of developing and optimizing charge separation in light-harvesting architectures However, it has yet to bear fruit due to the diffi culty of transport-ing electrons and holes to corresponding electrodes Modeling charge mobility in semiconductors is complicated due to the pres-ence of bulk heterogeneity in the structure The understanding of

the interface between the metal electrode and the active materials, where charge collection takes place, is even more intriguing.

The design and fabrication of molecular-based information cessing devices on conducting substrates have been key areas of research in materials science One particularly attractive applica-tion in this area is the conversion of solar energy into fuel, which

pro-is currently being proposed as a cheaper alternative for energy conversion Energy storage technologies are dealt with in some chapters High energy density capacitors are of particular signifi -cance, for example, in defense-related applications, where tasks in remote areas without traditional energy resources demand novel approaches to energy storage Polymer nanocomposites offer attractive, low-cost potential storage systems for high-energy den-sity capacitors Their tailored characteristics offer unique combina-tions of properties which are expected to play a vital role in the development of new technologies for energy storage applications Other chapters consider the aspects of solar energy Rapid prog-ress in photovoltaic science and technology during the last decades

is a reason that solar cells came out of the laboratories and are ing a part of our everyday life And this is only the beginning of the era of solar energy The number of reports about new approaches

becom-in this fi eld is becom-increasbecom-ing dramatically Among the reported topics are nanostructure compositions, transparent conductors, inclusion

of metal oxide as well as metal-based thin fi lms, light-trapping schemes that enable increased conversation effi ciency, various con-centrators and solar tracking systems, etc Chapters two through ten are devoted to consideration of innovative materials and tech-niques for future nanoscale electronics Two allotropic forms of carbon, carbon nanotubes and graphene, are able to replace con-ducting channels and silicon in elements of integrated circuits, thereby opening a new era of carbon-based electronics which will lead to denser, faster and more power-effi cient circuitry A possible attractive alternative to the semiconductor components in digital processing devices is chip-based molecular logic gates—molecules possessing the property to perform logical operations where a chemical or physical binary input to the molecules causes a binary output Surface-confi ned materials showing switching behavior along with changes in physical properties (i.e., optical, orientation, magnetism) make it possible to create integrated complex circuits for massive networking systems Signifi cant attention is being paid

to the development of fuel cells—devices that convert chemical

the problems related to energy effi cient lighting, In particular, adate phosphors are considered—luminescent materials that have excellent thermal and chemical stability Phosphor layers provide most of the light produced by fl uorescent lamps, and are also used

van-to improve the balance of light produced by metal halide lamps.Also discussed in the book is the role of materials engineering

in providing much needed support in the development of tovoltaic devices with new and fundamental research on novel energy materials with tailor-made photonic properties This book

pho-is written for a large readership, including university students and researchers from diverse backgrounds such as chemistry, materials science, physics, pharmacy, medical science and engineering It can

be used not only as a textbook for both undergraduate and ate students, but also as a review and reference book for researchers

gradu-in materials science, nanotechnology, photovoltaic device ogy and non-conventional energy We hope the chapters herein will provide readers with valuable insight into the state-of-the-art of advanced and functional materials and cutting-edge energy technologies The main credit for this book must go to the authors

technol-of the chapters who have summarized information in the fi eld technol-of advanced energy-related materials

EditorsAshutosh Tiwari, Docent, PhD Sergiy Valyukh, Docent, PhD

Ashutosh Tiwari and Sergiy Valyukh (eds.) Advanced Energy Materials, (1–68)

2014 © Scrivener Publishing LLC

Abstract

Overcoming astigmatism has always been a great challenge in designing

a heliostat capable of focusing the sunlight on a small receiver throughout the year In this chapter, a non-imaging focusing heliostat with dynamic adjustment of facet mirrors in a group manner is presented for optimizing the astigmatic correction in a wide range of incident angles Non-imaging

focusing heliostat that consists of m × n facet mirrors can carry out uous astigmatic correction during sun-tracking with the use of only (m + n

contin-– 2) controllers A further simplifi ed astigmatic correction of non-imaging focusing heliostat is also discussed which reduces the number of control-

lers from (m + n – 2) to only two A detailed optical analysis is carried out

and the simulated result has shown that the two-controller system can perform comparably well in astigmatic correction with a much simpler and more cost effective design The new heliostat is not only designed to serve the purpose of concentrating sunlight to several hundreds of suns, but also to signifi cantly reduce the variation of solar fl ux distribution with incident angle

Keywords: Non-imaging focusing heliostat, new heliostat, optical sis, solar fl ux

off-axis focusing techniques The most popular devices for on-axis focusing include parabolic dish, parabolic trough, spherical bowl (or so-called Fixed Mirror Distributed Focus), Fresnel lens, etc [1, 2] The off-axis focusing device involves the use of heliostat to focus sunlight onto a fi xed receiver in the systems such as the cen-tral power tower, the solar furnace, etc [2–7] The on-axis focusing devices are usually used for distributed and smaller scale power generation (in the range from several kW to tens of kW) compared

to that of off-axis focusing devices in the application of a central receiver system For the central power tower, the concave mirrors used for the heliostat encounter a serious deterioration in focused image due to the off-axis aberration

Off-axis aberration or astigmatism is a key factor in limiting the solar concentration ratio, especially for the central tower system that consists of a stationary receiver located in a fi eld of focusing heliostats [8] Full correction of the astigmatism requires a continu-ous adjustment in the local curvature of the refl ector in both space and time Although this method has been implemented in extremely large telescopes, it is obviously impractical for solar energy applica-tion because it would impose a very expensive and complicated con-

trol system with a total of 2 × m × n motors to orient each facet to its own unique direction for the heliostat composed of m × n facets As

a result, a new non-imaging focusing heliostat, that employs a clever approach to maneuver the facets in group manner for astigmatic cor-rection has been proposed Many research works on non-imaging

focusing heliostat have been carried out by Chen et al [9–15], Chong

et al [16–22] and Lim et al [23] to establish the principle and

technol-ogy of the new heliostat Overall, there are two major advancements achieved in the new heliostat compared to the conventional helio-stat that has remained unchanged for many decades [24] One is the

fi rst mathematical derivation of the new spinning-elevation tracking formula to replace the commonly used azimuth-elevation tracking Even the principle of spinning-elevation or target-aligned tracking

method was fi rst discussed by Ries et al [25] and Zaibel et al [26], but

they did not propose any method of implementation in their papers such as derivation of new sun-tracking formula or construction of

a prototype to implement the new tracking method The second advancement is the correction of the fi rst order astigmatism with the innovative line movements of the facets instead of trivial individual movements that would lead to complex and expensive mechanics

ter mirror is fi xed at the center with slave mirrors surrounding it, they share the same frame but the slave mirrors have two extra moving freedoms about their pivot points To focus all the mirror images into one fi xed target, each slave mirror is angularly moved about its pivot point to refl ect sunrays onto the same target as the master mirror The result at the target is the superposition of indi-vidual mirror images As the sunlight is not coherent, the result

is the algebra sum of the energy of the beams without a specifi c optical image

1.2.1 Primary Tracking (Global Movement for Heliostat

Frame)

The purpose of primary tracking is to target the solar image of the master mirror into a stationary receiver Then, this image acts as a reference for secondary tracking where all the slave mirror images will be projected on it In Figure 1.1(a), we defi neON

as the tor normal to the refl ector surface; OS

vec-as the vector that points to the sun; OS

as the vector that points to a fi xed target Figure 1.1(b) shows the rotation of the plane of refl ection, that plane which con-tains the three vectors (OS

, ON

and OT

), during primary tracking

In Figure 1.1(b), the vector OS

points to the new position of the sun and the vector ON′ is the refl ector normal of the new orientation

so that the sunlight is still refl ected towards the target The ing movement can be studied by two independent components (Figure 1.2):

track-a Spinning movement:

The heliostat has to rotate about the TT′ axis so that the plane of refl ection can follow the rotation of the vector OS

Therefore, as the sun moves through the sky from the morning to solar noon, the plane will rotate starting from horizontal and turning to vertical

T

(a)

N' θ S'

as the normal vector of the heliostat surface; OS

is the vector that points to the sun; OT

is the vector that points to a fi xed target (b) The plane that contains the three vectors is rotated about the vector OT

during primary tracking The new vectors OS′ and ON′ shown in the fi gure indicate the new position of the sun and the heliostat frame so that the sunlight is still refl ected towards the target.

The heliostat has two tracking axes that are perpendicular to each other, as does the conventional mount The fi rst rotational axis is pointing toward the target and it is indicated by TT’ axis; the second axis is the elevation axis (attached parallel to the refl ector) and it is shown as FF’ axis

between OS~ and OT~ As a result, the sunlight will

be refl ected onto the target This angular movement depends on the incidence angle of the sun relative to the heliostat surface normal and it is denoted as θ

The formulas for ρ and θ can be derived by transformation study of two different coordinate systems: one attached to the center of the earth and the other attached to the local heliostat

In Figure 1.3(a), by defi ning a coordinate system with the gin, C, set at the center of the earth, the CM axis is a line from the origin to the intersection point between the equator and the merid-ian of the observer at Q The CE (east) axis in the equatorial plane

ori-is perpendicular to the CM axori-is The third orthogonal axori-is, CP, ori-is the rotation axis of the earth Vector CS~ pointing to the sun can be

described in terms of its direction cosines, S m , S e and S p to the CM,

CE, and CP axes, respectively Given the direction cosines of CS~ in terms of declination angle (δ) and hour angle (ω), we have a set of coordinates in matrix form

cos coscos sinsin

Sm Se Sp

of mirrors arranged in the horizontal direction The third nal axis, OT axis, is a line pointing out from the origin towards the target direction Similar to the case of CS~ , vector OS~ pointing to the

Solar noon meridian Sun

Observer meridian

β θ θ

Ht

HrH

N

O

T Target Sun

system attached to heliostat reference frame.

Given the direction cosines of OS~ in terms of the angles β and ρ,

we have a set of coordinates in matrix form

cos coscos sinsin

f r t

H H H

The new set of coordinates, H, can be interrelated to the

earth-frame-based coordinates, S, by three successive rotation

point-which are facing angle f and target angle l, it is necessary to have two transformations The facing angle, f, is the rotation angle about

the Zenith made by the spinning axis (OT) when it rotates from the direction pointing towards north to the direction pointing towards

a fi xed target (assuming that the fi xed target and central point of

the master mirror are at the same horizontal level) Hence, f=0° if the heliostat is placed due south of the target; f=90° if the heliostat

is located due west of the target The transformation matrix for the

angle f about the Zenith is

transformation through the angle l about the OU axis is required;

l=0° means the central point of master mirror is at the same

hori-zontal level as the target; l=10° means the OT axis is at the position 10° clockwise from horizontal line, i.e., the target is below the helio-

stat The transformation matrix is then

1.2.2 Secondary Tracking (Local Movement for Slave

Mirrors)

The new tracking mode encourages the arrangement of the slave mirrors to be grouped into rows and columns, as under this mode, the mirrors in the same row or column will have the same move-ment Figure 1.4 shows the side view of a 25-mirror heliostat with

P representing the heliostat frame and the central row (row 3) taining the master mirror The elevation axis FF′ is out of the page and the spinning axis, OT, points towards the target The slave mir-

con-rors of rows 1, 2, 4 and 5 are attached to the heliostat frame in such

a way that they can turn about their own pivot point P1, P2, P4 and

P5, respectively To superpose 4 rows of solar images onto the tral image, each row of slave mirrors has to be rotated through an angle, σ,

cen-cos1

arctan

x x

H

q s

mir-Figure 1.4 The side view of a 25-mirror heliostat with P representing the heliostat frame and the central row (row 3) containing the master mirror The slave mirrors

of row 1, 2, 4 and 5 are attached to the heliostat frame in such a way that they can turn about their own pivot point P1, P2, P4 and P5, respectively

for rows above the master mirror and negative for rows below the master mirror) is the perpendicular distance between the center of the heliostat and the central line of the row where the slave mirror concerned is located

Referring to Figure 1.5, to superpose 4 columns of slave images onto the central master image, each column has to be moved through an angle,

1arctan

y

H L

per-1.3 Residual Aberration

In the above section, we described a variable focusing method via secondary tracking to correct the off-axis aberration A natural

question then is by how much can we eliminate the aberrant effect This is important, as any residual aberration left will affect the size

of the focused image We have employed a computational method

to conduct a lengthy study on this problem It has shown that although the above method can indeed eliminate most of the aber-ration, some residual aberrant effect still exists, particularly when the distance between the heliostat and target is relatively short The detailed study will be discussed in the following section But it is necessary to point out here that the residual aberration is reason-ably small and can be neglected in most applications In the case of our fi rst generation prototype, which will be discussed in the next

onto the central master image, each column has to be moved through an angle γ.

section, for H x =1 m, if the target is 20 m away from the heliostat, the residual aberration on the target is 1.25 cm, if the distance is 5 m, it

is 5 cm The larger the ratio of L to H x, the smaller the effect will be This is so because Eq 1.4 and Eq 1.5 will make a more effective cor-rection to the residual aberration at a longer distance Of course, at

a longer distance, the precision of the control and resolution of the correction movement of the slave mirrors have to be higher Our theoretical study has been well proven by the observation using the prototype heliostat

In addition to the residual aberration, the focusing area of the heliostat is also limited by the image of the solar disc Since the sun presents as a fi nite object which has an angular diam-eter 9.4 mrad at the earth, the minimum spot diameter of a per-fectly focused solar image is approximated to the focal length

of the refl ector multiplied by 9.4 mrad [2] If a fl at circular ror refl ects solar radiation to a target, the solar image at the tar-get will have a diameter of the mirror itself plus the diameter of the solar disc image provided that the cosine effect is ignored For instance, the image of a fl at mirror with a diameter of 40

mir-cm refl ected to a target 20 m away has a size of 59 mir-cm diameter Nevertheless, the size of the image can be made smaller when the mirror is concave The minimum spot size of the concave mirror

is essentially limited by two main factors: astigmatism and the image of the solar disc For each perfectly focused slave mirror image, the minimum spot size of the solar disc image increases with the target distance Due to this fact, it is easy to understand that there will be a discriminating target distance where the spot size of the solar disc image starts to surpass the mirror size In the case of our heliostat, it is convenient to use square mirror For the use of 40 cm × 40 cm element mirrors, the discriminating distance at which the concentration equal to the number of mir-rors is 42 m

1.3.1 Methodology

To analyze the residual aberration of NIFH, coordinate tions and ray tracing techniques are applied in the numerical simu-lation In principle, the new heliostat has to perform two functions simultaneously during the operation so that it can track the sun and focus the sunlight concurrently

transforma-movement are again rewritten as follows:

tan

q dq

f

(1.17)

Note: Eq 1.14 is obtained from the third row of Eq 1.8; Eqs 1.15(a) and 1.15(b) are derived from second row of Eq 1.8; and Eq 1.17 is derived from the fi rst row of Eq 1.8

In the above formula, L is the horizontal distance from the

inter-section point between the spinning-axis and the elevation-axis

to the target point (or target distance), H z is the offset distance of the refl ector from the plane that contains the elevation-axis (it is

normally identical for all the mirrors), θ is the incident angle of the sunlight relative to the heliostat frame provided that δθ = 0° (Note: the incident angle throughout this paper is referred to as θ),

δθ is the correction angle to θ due to the offset of the refl ector from

the plane that contains the elevation-axis Figure 1.6 depicts how

the two orientation angles of the spinning shaft, i.e., l and f, are

defi ned for a NIFH

Secondly, for the purpose of sunlight focusing, the heliostat has

to perform local movement with the use of local driving devices (or controllers) by driving the mirrors in a group manner in order

Fixed target

Heliostat reflector

focusing heliostat to be orientated relative to the local c oordinate system where

f is the facing angle of the heliostat ( f =0° when the heliostat is due south of the

target and it is positive if the spinning-axis is rotated about the zenith-axis in a clockwise direction) and l is the target angle of the heliostat (l =0° if the heliostat

is the same level height as the target and it is positive if the spinning-axis is rotated in a clockwise direction).

1tan

y z

is located, and H y is the perpendicular distance between the center

of the heliostat and the central line of the column where the mirror concerned is located

For the second generation of heliostat, simplifi cation of the matic correction can be accomplished owing to the tilted angles

astig-σ and γ which are linearly proportional to the values H x and H y respectively, provided that the distance L is reasonably large com- pared to H x and H y Note that, for L >> H x and L >> H y, Eqs 1.18 and 1.19 can be simplifi ed where the function of “tan–1” can be removed

and H x in the denominator can be substituted by a constant value,

of the mirror’s tilted angles for the second generation heliostat are

1, 2, 3, 4, etc This relationship is very important, particularly when

we would like to design the driving mechanism for astigmatic rection of the heliostat with a huge number of mirrors because the local movement for all the facet mirrors can be simply grouped into three clusters, namely upper row, lower row and column Rows

cor-or columns in each cluster can be linked together through a ear torque transmission system such as gearbox or mechanical cam with the ratio 1, 2, 3, 4, etc

lin-For the third generation of heliostat, Eqs 1.20–1.22 can in fact be

fur-ther simplifi ed where both the denominators L + Hx° cos(2dq) sin(q +

dq ) – H z cos(q – dq) and L – Hx° cos(2dq) sin(q + dq) – H z cos(q – dq) in Eqs 1.20 and 1.21, respectively, can be approximated to L only given that L >> H x and L >> H y Hence, the new formulas of the tilted angles for the local movement in the third generation heliostat are as simple

Presetting or canting facet mirrors at any selected incident angle

is the process of adjusting the tilted angles of all the facet mirrors

so that the mirror images are superposed at one point as to achieve zero residual aberration at that particular incident angle Since the residual aberration increases with the incident angle, the purpose

of presetting the tilted angles of facet mirrors is to shift the mum point of the residual aberration in order to effectively reduce the overall aberration over a specifi c range of incident angles Operational incident angle, θop (or theta-op), is defi ned as the cor-responding incident angle in which the presetting work is carried out for all the facet mirrors to completely eliminate the residual aberration Even though it is a very labor intensive work because

mini-of different facet mirrors canted at different angles, the presetting work only needs to be carried out during the installation of all facet mirrors to the heliostat frame To introduce preset angles for each facet mirror, the additional tilted angles Δσ and Δγ in the function

of operational incident angle are added to the tilted angles σ and γ

to form (σ +Δσ) and (γ +Δγ), respectively

Coordinate transformations have been used to model the global

and local movements of the refl ective point on the i,j-mirror face, where i,j means that the mirror is located at i-th row and j-th

sur-column in the heliostat To ease the mathematical representation of coordinate transformations, we can make the translation a linear

Figure 1.7 The optical confi guration of the non-imaging focusing heliostat with

two-controller system for astigmatic correction showing the global movement (spinning angle, ρ, and elevation angle, θ ) as well as local movement (tilted

angles of each mirror attached to the heliostat) The relationship between the tilted angle,σ (or γ), and the distance, H x (or H y), is also shown.

transformation by increasing the dimensionality of the space For

example, the coordinate (H x , H y , H z)i,j is equivalent to (H x , H y , H z, 1)

i,j, which is also treated as a vector in matrix form By omitting the lengthy derivation, here we present the fi nal result in the matrix form as follows:

H H H

H H H

H H T

0 0 1

x y z

H H T

Pij = [ρ][θ – δθ] [g + Δg][s + sΔ] (1.28)

and provided that

1

x y z ij

N N N

In the ray tracing technique, the initial coordinate of the central

point of i,j-mirror (H x , H y , H z)ij in the heliostat is fi rst transformed

to the new position with coordinate (H′ x , H′ y , H′ z)ij due to the global and local movements The sunray incident onto the central point

of i,j-mirror will then be traced from the new coordinate, (H′ x , H′ y,

H′z)ij, to the target plane and the intersection point is determined

as (T x , T y , L) ij For the heliostat with m rows and n columns of facet mirrors, the above methodology is repeated from i = 0 and j = 0 to

i = m and j = n, respectively, in order to compute the position of

mirror image (T x , T y)ij and then to plot the solar images distribution

on the target plane For simulating the solar images distribution in

the case of fi rst generation heliostat in which (m + n – 2) controllers

are needed, Eqs 1.18 and 1.19 are applied in the methodology On the other hand, for the case of second generation heliostat in which only three controllers are required, Eqs 1.20–1.22 are used in the simulation Finally, for the case of newly proposed third generation heliostat that requires two controllers for astigmatic correction, Eqs 1.23 and 1.24 are employed

1.3.2 Optical Analysis of Residual Aberration

In this analysis, the optical characteristics of NIFH are studied based

on the specifi cation and design parameters as listed in Table 1.1 For the optical modeling, let us consider the architectural design of the new heliostat with 81 pieces of square fl at mirrors arranged into 9 rows and 9 columns where the pivot point of the mirror is located

at the center of that mirror Furthermore, the distance between the central points of two adjacent mirrors is constant throughout the heliostat, which is 40.5 cm, so that the refl ector width of heliostat,

D, is 3.64 m In this study, we only deal with the residual

aberra-tion resulted from the fi rst order astigmatic correcaberra-tion via the local movement and isolate it from the astigmatism of individual curved mirror because the latter aberration effect is very much dependent

on the geometry and size of the mirror that is not the main eration here

consid-At fi rst, the study will focus on the comparison of residual aberration for the three astigmatic correction methods, which

involves two, three and (m + n – 2) controllers The following

parameters are chosen as the case study for a solar furnace tem that only involves a single heliostat to ease the comparison: latitude (Φ) 3.08° North, longitude 101.7° East, target angle (l) 0°,

sys-facing angle (f) 180° and target distance (L) that is also defi ned

as focal distance of the heliostat (f) 18.34 m The annual variation

of incident angles with local time from 8 am to 7 pm ranges from 31.7° (happened on 21st December, 1 pm) to 56.6° (happened on 21st Jun, 7 p.m.) To quantify the residual aberration, the aberrant spread is defi ned as the distance between the central points of the two most distant mirror images as indicated in Figure 1.8(a)

To optimize the aberrant spread over the year, in our case study, the operational incident angle is chosen as 44.17° so that the aber-rant spreads at the two extreme incident angles of 31.7° and 56.6°

Table 1.1 Specifi cations and design parameters for the optical analysis of non-imaging focusing heliostat

Perpendicular distance between mirrors

and the plane that contains the elevation

axis

18.85 cm

Spacing between two adjacent mirrors 0.5 cm