Design, Test and Mathematical Modeling of Parabolic Trough Solar Collectors

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3 Università Politecnica delle Marche Scuola di Dottorato di Ricerca in Scienze dell Ingegneria Curriculum Energetica Design, Test and Mathematical Modeling of Parabolic Trough Solar Collectors Ph.D. Dissertation of: Marco Sotte Advisor: Prof. Giovanni Latini Curriculum Supervisor: Prof. Massimo Paroncini X edition - new series

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5 Università Politecnica delle Marche Scuola di Dottorato di Ricerca in Scienze dell Ingegneria Curriculum Energetica Design, Test and Mathematical Modeling of Parabolic Trough Solar Collectors Ph.D. Dissertation of: Marco Sotte Advisor: Prof. Giovanni Latini Curriculum Supervisor: Prof. Massimo Paroncini X edition - new series

6 Università Politecnica delle Marche Scuola di Dottorato di Ricerca in Scienze dell Ingegneria Facoltà di Ingegneria Via Brecce Bianche Ancona (AN), Italy

7 to Laura

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9 Acknowledgments I am grateful to Professor Giovanni Latini, who has followed me throughout my entire PhD course. I express my thanks also to Professor Fabio Polonara for his support and to Professor Massimo Paroncini, my PhD curricula supervisor. None of this work would have been possible without the friendship and collaboration of Research Professor Francesco Corvaro, who has also supervised some of the students who worked on PTC.project and PhD Matteo Moglie and Giulio Santori. I am grateful to laboratory technicians Giuliano Giuliani, for his helpful advices, and Gaetano Borrelli and Gabriele Gabrielli for their assistance. The idea from which this work has arisen is an intuition by Daniele Centioni: I am indebted with him for calling me as a consultant in the initial phases of his project, and therefore introducing me to the world of solar thermal power. I also shall acknowledge Piero Dal Sasso and Leonardo Vitaletti: two of the most brilliant engineers I have the pleasure to know, with whom I have worked at the beginning of this project. Italia Futura Foundation also must be thanked, since, through its award "Accade domani 2", has financed most of PTC.project. A number of students dedicated themselves to different aspects of PTC.project: Tommaso Cieri, Michele Biondini, Angela Iezzi, Alessandro Galassi, Federico Lorenzetti, Michele Panni, Luca Paolini, Mattia Pompili, Tommaso Recanatini, Marta Rossi, Nicola Saraceni and Fedele Torelli. I must acknowledge all of them for their effort and their enthusiasm: they have effectively produced many of the results presented in this thesis. Also a particular acknowledge goes to Vitale Melchiorre, who has given an important acceleration to the initial steps of the project and to Gianluca Coccia, whose dedication and critical contribution have made possible to realize the mathematical model and the simulation environment described in this thesis. Not least, perhaps, I should thank my wife Emanuela, for her love and forbearance, and my daughter Laura: her presence is a constant encouragement for me to look forward with confidence and hope. Civitanova Marche, January 2012 Marco Sotte ix

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11 Abstract Solar radiation at its origin is a high-exergy energy source: the Sun has an irradiance of about 63 MW/m 2. But on the Earth s surface solar energy flow dramatically decreases. For this reason, when high temperatures or high-exergy need to be reestablished, concentrated solar systems are adopted. Using the principle of concentration it is possible to transform solar energy into another type of energy (usually thermal) in the focus of solar thermal concentrating systems. Among all possible geometries, parabolic trough collectors are by far the most widespread technology. Applications of PTC can be divided into two main groups, the first one being CSP plants (i.e. plants where the solar source generates thermal energy that is then converted into electric energy) and the second one being IPH (industrial process heat) applications. This second field has a dramatic potential and can be adopted at latitudes like those of central and southern europe. For this reason a research project has been started at Dipartimento di Ingegneria Industriale of Università Politecnica delle Marche (PTC.project) for the study of the application of PTCs to IPH and other heat demands in the temperature range from 80 to 250 C. The lower temperature of the range has been selected so not to compete with commercially available solar thermal technologies, such as FPCs (flat plate collector) or ETCs (evacuated tube collectors). In this thesis the results of this work are exposed. The design and manufacture of two prototypes Univpm.01 and Univpm.02 are described in detail, giving complete information on geometrical characteristics, materials and manufacturing processes. Then the results of preliminary tests on the mentioned prototypes are produced, together with the characteristics of a test bench designed to determine PTCs performances with water and heat transfer oil as working fluids in a temperature range from 10 to 150 C. Then a mathematical model, able to determine the performance of any PTC is described: the model accounts for optical and thermal losses of the collector, and also contains a routine code to calculate the solar position. In the last chapter a simulation environment to run annual analysis on the performance of a PTC applied to a specific process heat demand load is presented and the results obtained with a PTC similar to Univpm.02 on a well determined and realistic heat demand yearly profile are described. xi

12 The energetic results produced suggest that there could be space for this technology in the variety of renewable energies that will be needed to meet many international goals in terms of energy and environments in the nearest future. Also the variety of areas and the wideness of possible applications for PTCs are impressive. But the experience acquired and the results also suggest that investments are needed if an acceleration on the spreading of PTC and other CSP technologies is to be realized. xii

13 Contents 1. Introduction 1 2. Design and manufacture of PTC prototypes Introduction to fiberglass composites and their manufacturing processes Fiber reinforced materials and sandwich composites Fiberglass manufacturing processes PTC prototype Univpm Parabolic support Receiver Manufacture of the fiberglass-eps parabolic support PTC prototype Univpm Parabolic support Receiver Manufacture of the mold of Univpm VARTM procedure for the manufacture of the parabolic support PTC testing First test apparatus and tests on Univpm.01 prototype Hydraulic circuit Movement system Instruments and computational procedure Results and comments Analysis of measurement errors Propagation of uncertainty Uncertainty on efficiency measurements New test circuit Mathematical model of a PTC General description of the model Optical model Concentration ratio Optical efficiency xiii

14 Contents Incident angle modifier Geometrical effects Intercept Factor Thermal model Convection heat exchange between the receiver and the fluid Conduction through the receiver Convection heat exchange between the receiver and the glass Radiation heat exchange between the receiver and the glass Conduction through the glass Convection heat exchange between the glass and surrounding air Radiation heat exchange between the glass and the sky Global efficiency Model implementation Input parameters and variables Resolutive methods Model output Results Annual simulation of performances Simulation scheme Meteorological data Solar radiation database Meteorological variables data Process heat demand daily, weekly and yearly profiles Results of the yearly simulation Final energetic considerations Remarks and conclusions 95 Appendices 96 A. Results of the simulations 97 B. Mathematica code from file posizione_sole.nb 105 C. Mathematica code from file analisi_ottica.nb 109 D. Mathematica code from file analisi_termica.nb 113 xiv

15 List of Figures 2.1. Classification of composite materials, source [1] Scheme of the hand lay-up molding method [2] Scheme of injection molding method [2] Scheme to the vacuum assisted resin transfer molding method [2] D representation of Univpm.01 on its support Support of the receiver of Univpm Support s connection to the structure Reflectance of the MIRO-SUN R weatherproof reflective 90 as a function of the wavelength of the incoming radiation Structure of the mold for the realization of the composite material support of Univpm The mold for Univpm.01 with the EPS stripes and the aluminum tubes positioned on it Parabolic profile equipped with 2 aluminum rectangular crosssection tubes Drawings of Univpm.02 prototype A 3D drawing of Univpm Complete view of the mold [3] Mold cutaway [3] The mold during its realization Detailed views of the central triple-rib The mold completely assembled and with a tensioned wire for setting marks to define rim ends Mold aluminum end-plates [3] Alumimum mating plates to be screwed to the composite structure [3] Frame assemblying procedure [3] Effective surface of the final fiberglass structure [3] Mold with teflon rims [3] Layers manual deposition[3] A detail of the indentation that will host the support of the recover [3] Peel ply and diffusion layer [3] xv

16 List of Figures Enka channel and inlet ports [3] Spiraled tubes and outlets [3] Vacuum bag sealing [3] Hydraulic circuit The hydraulic circuit Components of the movement system RTD inserted at the beginning (end) of the receiver [4] Signals acquiring and data flow scheme [4] Straight-line interpolating experimental points P&I diagram of the test bench Legend of symbols for P& I diagram in Fig A 3D representation of the test bench Area lost due to end-effects [5] Shading by transverse plates [5] Intraarray shading [5] Modeling of potential optical errors in parabolic trough collectors [6] Thermal resistances of the receiver Cross-section of the receiver that shows useful heat fluxes (in red) and heat losses (in orange) Global (in blue), experimental (in green) and optical (in gold) efficiencies as functions of T Experimental data and global efficiency as functions of T and η o Error between experimental and calculated efficiencies as a function of T Probability density function (PDF) of the error normal distribution Scheme of the organization of files and models for annual simulations First possible hydraulic connection scheme Second possible hydraulic connection scheme Average day of the month of November: power hour by hour Average day of the month of November: optical and global efficiency hour by hour Monthly energy totals from the simulation Representation of the summation of energy values throughout the hours of the TMY for the 50 m 2 aperture plane PTC. Highest line represents total energy falling into the aperture plane, middle line is Eprod, while bottom line is Eu xvi

17 List of Figures A.1. Average day of the month of January: power hour by hour A.2. Average day of the month of February: power hour by hour.. 98 A.3. Average day of the month of March: power hour by hour A.4. Average day of the month of April: power hour by hour A.5. Average day of the month of May: power hour by hour A.6. Average day of the month of June: power hour by hour A.7. Average day of the month of July: power hour by hour A.8. Average day of the month of August: power hour by hour A.9. Average day of the month of September: power hour by hour. 102 A.10.Average day of the month of October: power hour by hour A.11.Average day of the month of November: power hour by hour. 103 A.12.Average day of the month of December: power hour by hour xvii

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19 List of Tables 2.1. Characteristics of Univpm.01 concentrator Characteristics of the receiver of Univpm Characteristics of Univpm.02 concentrator Characteristics of the receiver of Univpm Characteristics of the Univpm.02 mold Layering of Univpm.02 composite Calculation system Comparison of collector efficiency equation Parameters for the mathematical model Variables for the mathematical model An example of model output Composition of the typical meteorological year Meteorological data Heat demand profile table An example of model output xix

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21 Chapter 1. Introduction Solar radiation at its origin is a high-exergy energy source: the Sun has an irradiance of about 63 MW/m 2. But on the Earth s surface solar energy flow dramatically decreases down to around 1 kw/m 2 [7]. For this reason, when high temperatures or high-exergy need to be reestablished, CSP systems are adopted. Using the principle of concentration, under proper solar fluxes, it is possible to transform solar energy into another type of energy (usually thermal) in the focus of solar thermal concentrating systems. Among all possible geometries to realize solar concentration (central receiver systems and parabolic dishes or line-focus concentrators, such as parabolictrough collectors and linear Fresnel collectors) parabolic through collectors are by far the most widespread technology. PTCs focus direct solar radiation onto a focal line on the collector axis where a receiver tube is installed; the fluid flowing inside the tube absorbs concentrated solar energy from the tube walls and raises its enthalpy. A solar tracking mechanism ensures that the solar beam falls parallel to the PTC axis. PTC applications can be divided into two main groups: concentrated Solar Power (CSP) plants and applications that require temperatures between 80 and 250 C [8]. The field of CSP is now a well-defined market: several commercial collectors for such applications have been successfully tested under real operating conditions. The second field, that contains mainly industrial process heat (IPH), low-temperature heat demand with high consumption rates (domestic hot water, DHW, space heating and swimming- pool heating) and heat-driven refrigeration and cooling, has been addressed only in the recent past, and the number of commercial proposals is still very limited. For this reason a research project has been started at Dipartimento di Ingegneria Industriale of Università Politecnica delle Marche (PTC.project) for the study of the application of PTCs to IPH, DHW and all other heat demands in the mentioned temperature range. The basic bullets of the projects were defined as studying water and heat transfer oil as working fluids and working in an operative temperature range from 80 to 250 C. The results of the work are the design and manufacture of two prototypes Univpm.01 and Univpm.02 1

22 Chapter 1. Introduction and a test bench to determine PTCs performance with water and heat transfer oil as working fluids in a temperature range up to 150 C. After the realization of the first tests on the prototypes also a mathematical model able to determine the performance of a given PTC has been developed. Finally the model has been applied to a simulated process heat demand profile in a precise geographical location (necessary to define meteorological data). The result of this work is the complete knowledge of the performance characteristics of a particular PTC during an entire year and also the information related to its interaction with a particular heat demand load. 2

23 Chapter 2. Design and manufacture of PTC prototypes Two of the most important factors affecting the efficiency of a PTC are the geometry of the parabolic shape of the modules and the accuracy of the angle of the incident solar beams [9]. These factors depend on the moving system and on the torsional resistance of each line of parabolic mirrors. Since mirrors are generally arranged in lines parallel to each other and each line is rotated in the middle, the weight of the mirrors and of the structure of the PTC line and external forces (mainly wind loads) can generate a high momentum on the line next to the point of junction between the PTC rotation axis and the driving system. In CSP plants the two key issues of accuracy in the shape and torsional resistance of each line are usually solved by two different solutions: a metallic frame, running through each line provides the necessary torsional rigidity to hold each module at the right angle; an accurate parabolic shape is obtained by small (typically 1.5 m 2 ) preshaped glass or metal mirrors anchored to the frame. In the case of a parabolic chord between 4 and 6 m (that is common in CSP applications) this method has several advantages [10]. In such big geometries, in fact, moving parts of the mirrors instead than entire PTC modules is a great simplification. Also the possibility to adjust the position of each reflective surface with respect to the frame, that is necessary to obtain the desired accuracy on a big parabolic arch is a key issue. But this approach is time consuming and expensive: a long assembling work has to be carried out on each PTC line. For smaller values of the chord (0.5 to 2.5 m) it is useful to adopt a structure that realizes both the parabolic shape and the frame, thus having a very accurate parabolic profile and a highly resistant mechanical structure. Other authors have successfully tested the use of reinforced fiberglass to realize the parabola of solar concentrators [11]. Following this line, in the present project, 3

24 Chapter 2. Design and manufacture of PTC prototypes Figure 2.1.: Classification of composite materials, source [1] two PTC prototypes have been realized with a sandwich of fiberglass and extruded polystyrene. The advantages in using a sandwich are well known and fiberglass is a very common element of such composite materials Introduction to fiberglass composites and their manufacturing processes As defined in [1], composite materials are recognized as such if they have two or more constituent materials or phases of significantly different physical properties, and thus the composite properties are quite different from the constituent properties (to distinguish them from other materials like metals, whose components are phases of similar physical properties). Of the phases that make up these materials, one is usually harder and stronger and is called reinforcement material, whereas the other phase is called the matrix Fiber reinforced materials and sandwich composites The properties of composites are determined by those of their constituent, their distribution and interaction. Thus they are usually described in terms of volume fraction of distinct phases, and of the shape, size and distribution of reinforcement material. In particular, the orientation of the reinforcement affects the isotropy of the system. Composites are conveniently classified depending on the geometry of the reinforcement [1]. Fiber reinforced materials are the most widespread kind of composite materials. Fibers usually contribute to the mechanical qualities, while the matrix (usually a thermosetting or thermoplastic polymer) binds the fibers together 4

25 2.1. Introduction to fiberglass composites and their manufacturing processes and protects them against environmental attacks. Among all fiber reinforced materials, fiberglass (also called glass-reinforced plastic) is a fiber reinforced polymer obtained with a plastic matrix and fine fibers of glass. The characteristics of the final material depend upon the characteristics of the glass fiber and the characteristics of the plastic matrix. This last material may be epoxy, a thermosetting plastic or thermoplastic. In the manufacture of the PTC prototypes an epoxy resin has been used, since it reasonably cheap and easy to lay. Regarding the glass fibers, they are available in various forms; a first division is among: woven fabrics, that are continuous bidirectional fiber reinforcements, available in yarns, rovings or tows, in mat form or in a single layer. The important variable in this fabrics is the amount of fibers, their direction and the woven pattern; non woven fabrics, that are discontinuous unidirectional reinforcements in which glass fiber yarns are placed parallel to each other and stitched together with a chemical binder or with polyester fibers. The main advantage of this fabrics if the fact that fibers can be laid at any almost any angle and in the greater strength due to the fact that fibers remain straight (whereas they bend over each other in woven fabrics); chopped mats are non-woven fabrics obtains by laying evenly distributed chopped glass fibers ( mm length) and bounding them together using a chemical binder. The choice between these different possibilities depends on many factors, such as cost evaluation and considerations on the intensity and the directionality of the stresses that the material will have to withstand. The choice does not only regard the fabric: also the direction of the fibers must be defined together with the thickness of the final material. Considerations linked with the particular manufacture process can suggest between one thick fabric or two thinner ones, for instance. Among all composite materials, a particular field is that of sandwich-structured composites, that are fabricated attaching two thin skins to a thick lightweight core (generally being the core a low strength material, and the skins made of stiff materials). The core is often made of open- and closed-cell-structured foams of honeycombs. Also balsa wood is often adopted (especially in naval industry); for the skins, laminates of glass or carbon fiber reinforced thermoplastics or polymers are widely adopted; in some cases also metal sheets are used. For the purpose of building the parabolic structure for the prototypes a sandwich-structured-composite, with fiberglass as skin material has been used. 5

26 Chapter 2. Design and manufacture of PTC prototypes Figure 2.2.: Scheme of the hand lay-up molding method [2] Fiberglass manufacturing processes Generally fiberglass composites manufacturing processes require the use of a mold. Different molding methods can be used to obtain the final fiberglass material in the desired shape. The simplest molding method is open molding, that is used both for small and large fiberglass parts. The mold can be made from wood, metal of plastic; its only requirement is that its surface has the shape that is to be obtained in the final piece. Once the mold has been prepared, fibers are placed again the mold surface together with the resin. A typical molding process involves the following operations: mold waxing: several coats of wax paste are applied on all the parts of the mold that will come into contact with the resin; this is necessary for allowing final mold release; gel coating: a special resin, called "gel-coat" can be applied to the surface before the resin. Being the first layer applied after the wax paste, it becomes the outer layer of the laminate. Its general purpose is to protect the resin from atmospheric agents and from sunlight, but it could also have a pure decorative purpose. hand lay-up is the core process: fiberglass in the chosen form is laid on the mold (or on the gel-coat). Resin and hardener are mixed and applied. In this phase it is important to ensure complete air removal from the laminate, and total impregnation of the fibers; this last requirement can be sometimes hard to obtain in particular geometries. The hand lay-up method, in some cases, can be substituted with a partially automated method, called spray-up method. This method can be adopted only if fiber is in the form of short chopped strips. In this method the fibers and the resin are mixed together and applied simultaneously to the mold via a spray 6

27 2.1. Introduction to fiberglass composites and their manufacturing processes Figure 2.3.: Scheme of injection molding method [2] Figure 2.4.: Scheme to the vacuum assisted resin transfer molding method [2] gun. Due to the reduced length of the fibers, the fiberglass obtained presents reduced mechanical performance. For this reason a combination of hand lay-up and spray-up methods is often adopted. An alternative to open molding is closed molding, that includes a variety of different methods: injection molding, compression molding, resin transfer molding and others. In the case of injection or compression molding, both a male and female mold are required. For this reason these methods are not appropriate for prototyping. Therefore vacuum assisted resin transfer molding is the most common method, because it can be adopted with just a male or a female mold, and it is cost-effective for low to medium volume applications. The mold can be made of aluminum or steel, but plastic or wood are also used for low production volumes. The requirements for the mold are to be hermetic to air and to have discrete mechanical properties to withstand the loads induced by the low pressure on the surfaces. Continuous fiber is usually adopted in resin transfer molding, so that fiber direction in the component can be controlled: resin flows along the path of least resistance, so it is paramount 7

28 Chapter 2. Design and manufacture of PTC prototypes Figure 2.5.: 3D representation of Univpm.01 on its support to control resin ports sizing and placement. The main advantages of VARTM with respect to hand lay-up are the possibility to control the quantity of resin and the speed of the process; on the other hand, VARTM requires experienced personnel and some equipment and accessories that are not necessary in the hand lay-up PTC prototype Univpm.01 Univpm.01 is a small PTC: it presents a focal length of 0.25 m; its concentration ratio can range between 5 and 10, (considering reasonable diameters for the receiver). The main purpose of its realization was to verify its design concept and to acquire experience in the manufacture procedure; since this aspect has given a positive feedback, the prototype has been completed and also used for thermal testing Parabolic support Univpm.01 presents a rim angle equal to π 2. This particular value of the rim angle is suggested by different authors [12]. The main characteristics of the 8

29 2.2. PTC prototype Univpm.01 Figure 2.6.: Support of the receiver of Univpm.01. Figure 2.7.: Support s connection to the structure Table 2.1.: Characteristics of Univpm.01 concentrator Focal distance (F ) Rim angle (φr ) Parabola length (Lc ) Aperture area (Aap ) Total thickness of the sandwich (t) 0.25 π m rad m m2 m parabola are reported in Tab 2.1. Since the aim of the prototype is testing, the supports for the receiver have been designed to allow adjustment on the position of the receiver itself (both in terms of height and angle with respect to the origin of the parabola). This has been done in order to be able to test different receivers on the same parabolic reflector. For the reflective surface, there is a few commercial alternatives. For this particular prototype a special kind of anodized aluminum has been used: it R is known with the commercial name of MIRO-SUN weatherproof reflective 90 [?]. It is basically anodized aluminum with a specially coated surface on one side studied for outdoor solar applications that require high reflectance and resistance to atmospheric agents. Fig Receiver The receiver adopted is an aluminum pipe of circular section; the outer surface is painted with a black high temperature resistant paint. It is contained in a low iron glass envelope (the same glass used for evacuated tube collectors). Three teflon rings hold the glass in place on the aluminum receiver. Small 9

30 Chapter 2. Design and manufacture of PTC prototypes Figure 2.8.: Reflectance of the MIRO-SUN R weatherproof reflective 90 as a function of the wavelength of the incoming radiation Table 2.2.: Characteristics of the receiver of Univpm.01 Inner aluminum diameter (d ri) 25 mm Outer aluminum diameter (d re) 30 mm Inner glass diameter (d vi) 46 mm Outer glass diameter (d ve) 48 mm Receiver length (L r) 2.60 m Receiver external surface (A re) m 2 holes have been drilled in the rings to allow little circulation of air inside the annulus and avoid water condensation on the glass. One particular receiver having characteristic reported in Tab. 2.2 has been analyzed. With such a receiver the concentration ratio is [13]: C = A ap = 1.85 = 7.41 (2.1) A re Manufacture of the fiberglass-eps parabolic support As mentioned, the parabolic support structure has been realized with a composite material of extruded polyester (EPS) core in a fiberglass shell. Mechanical and chemical characteristics of fiberglass are well known. Extruded polyester, instead, is not so common in composite materials, but it has several advantages: it is very economic, it is light (20 kg/m 2 ), and it presents good mechanical properties. It has a high resistance to compression from evenly distributed forces, thus being very suitable to be used in a sandwich structure. It is widely used in buildings for thermal insulation, and therefore it sold in sheets of various 10

31 2.3. PTC prototype Univpm.02 dimension and thickness. Different varieties of polyester are used in construction, but the extruded one presents the best mechanical properties at a low price (0.25 e/m 2 for 40 mm thick sheets). For the design of the parabolic support, a 40 mm thick sheet has been cut in stripes; this allows the adoption of a parabolic shape when all stripes are positioned one close to the other; the empty spaces are filled with epoxy resin. In two symmetrical places, two EPS stripes have been replaced by aluminum tubes having rectangular cross-section. The tubes have been firmly joined to the EPS by four smaller tubes positioned perpendicular to the big ones. The mold for the structure has been realized by joining 9 pieces of light plastic sheets (13 mm in thickness) that had been water-cut on a computer controlled machine to obtain a very accurate profile. A stainless steel sheet (0.8 mm thickness) has been laid on the plastic pieces and hold in place by two transversal wood beams screwed to the plastic parts to create a parabolic profile. After the application of a wax polish on all the necessary surfaces the first and second glass fiber and resin layers have been applied on the stainless steel parabolic surface. Normal mesh glass fiber tissue has been used: this kind of mesh presents mechanical properties that are better defined than those of chopper strand fiberglass, so it is generally preferred for thin layers although it is more expensive. While the compound was still liquid, all the EPS stripes and aluminum frame pieces have been arranged in their place. Then all the remaining surfaces have been covered with two layers of resin and glass fiber; a good penetration of the resin between the EPS pieces has been carefully checked. When the application of the resin was finished the upper surface has been covered with a plastic sheet and three straps have been arranged on it. Both the sheet and the straps have been pulled down by screws on the supports to ensure a perfect adhesion of the new structure to the mold. When dry the structure has been pulled out of the mold and the reflective aluminum foil has been glued to the concave surface of the support to create a parabolic reflective surface. The weight of this structure is approximately 12 kg PTC prototype Univpm.02 As mentioned before, prototype Univpm.01 has been intentionally kept small in size; the reasons of this choice lie in the necessity of ease of manufacture and handling of the parabolic structure and also in the fact that the main purpose of its realization was to test the manufacture process. It has provided a good platform to gather experience on these aspects, but its shortcomings were immediately visible with the first results from the mathematical model and the tests. In no particular order: 11

32 Chapter 2. Design and manufacture of PTC prototypes Figure 2.9.: Structure of the mold for the realization of the composite material support of Univpm.01 Figure 2.10.: The mold for Univpm.01 with the EPS stripes and the aluminum tubes positioned on it 12

33 2.3. PTC prototype Univpm.02 Figure 2.11.: Parabolic profile equipped with 2 aluminum rectangular crosssection tubes attainable temperatures were too low for the intended use ( C); to reach higher temperature concentration ratio can be increased by reducing the diameter of the receiver, but there is a lower limit for this value. If the receiver is too small two problems are encountered: the first one being the reduction of optical efficiency (linked to the necessity of a very accurate tracking system), and the second one lying in the necessity to increase the thickness of the pipe in order to contain its deflection under its own weight and the weight of the liquid contained in it and maintain it on the focal line; obtaining a good focus and keeping it during tracking has proven difficult; the lack of appropriate references on the frame of the concentrator have not allowed to distinguish between geometric errors in the reflecting surface and errors due to misalignment of the receiver; after a short period outdoor water seeped through the fiberglass-resin layer (especially next to the edges, where most irregularities are concentrated); even if water was noticeable to the naked eye, no damages to the structure or to the shape were visible. Anyhow this aspect was a main concern, because freezing of the water could seriously damage the structure, add an unwanted source of optical errors and threaten the structural integrity of the concentrator; 13

34 Chapter 2. Design and manufacture of PTC prototypes Figure 2.12.: Drawings of Univpm.02 prototype For these reasons, gathered all the experience from prototype Univpm.01, a second PTC was designed so to address al the listed problems and adding some useful characteristics: Univpm.02 has to be designed in such a way to allow a modular array deployment; the design, together with the choices in the manufacture process and in materials have to be cost-effective; its entire structure looks less "amateurish" and more like a proper deployable industrial solar collector; this might seem as a foolish aspect, but, indeed, it is an important issue. It does not only involve surface finishes or color, but it includes important design choices, such the solution for the connection to the composite material structure to the metallic frame, or the arrangement to hold in place the support of the receiver. The structural concept for Univpm.02 has been kept the same as Univpm.01 (sandwich composite), as it has proven to be an excellent solution in terms of stiffness, weight and cost. To address the fiberglass manufacturing problems and subsequent shortcomings of Univpm.01, the hand lay-up method that had been used for Univpm.01 has been replaced with a VARTM. In the following paragraphs the details on the design of the parabolic concentrator and of the receiver of Univpm.02 are described. The last two paragraphs are dedicated to the description of the manufacture of the mold and to the VARTM procedure that has been used to realize the sandwich composite structure. Most of what is described in the following paragraphs can be found in [3] in a more extended form Parabolic support Univpm.02 is about twice the size of the previous prototype; its structure has been realized with the same concept of Univpm.01, but a different material 14

35 2.3. PTC prototype Univpm.02 Figure 2.13.: A 3D drawing of Univpm.02 has been used for the matrix: low density polyvinyl chloride (PVC)instead than extruded polystyrene (EPS). PVC is widely used in naval industry as a matrix for sandwiches thanks to its mechanical strength and also to the many different densities, thicknesses and geometries that are commercially available. For instance, for its use as a matrix in sandwiches, it can be found in sheets that are pre-cut in little cubes, held together by a net on one side. This allows it to be put in position also on curved surfaces (like in the present case). Also Univpm.02 has been realized with a gel-coat superficial coating, so that it can withstand atmospheric agents. The main characteristics of Univpm.02 are described in Tab The rim angle has been kept close to the value of π 2 for the same reason above mentioned. The total thickness of the sandwich has been increased (from 4 to 5 cm), and also the total length of the structure has been increased of about 25 % Receiver The present study is referred to the use of one particular receiver having characteristics reported in Tab Except that for dimensions, it is exactly equal to the one adopted on Univpm.01, so no further explanation is necessary. 15

36 Chapter 2. Design and manufacture of PTC prototypes Table 2.3.: Characteristics of Univpm.02 concentrator Focal distance (F ) 0.55 m π Rim angle (φ r) rad 2 Chord m Parabola length (L c) m Mirror length m Length of the structure m Aperture area (A ap) m 2 Total thickness of the sandwich (t) m Table 2.4.: Characteristics of the receiver of Univpm.02 Inner aluminum diameter (d ri) 25 mm Outer aluminum diameter (d re) 30 mm Inner glass diameter (d vi) 46 mm Outer glass diameter (d ve) 48 mm Receiver length (L r) 2.60 m Receiver external surface (A re) m Manufacture of the mold of Univpm.02 The mold for Univpm.02 has been designed and assembled firsthand. It takes the mold of Univpm.01 as a reference, but improves on it on several aspects: robustness in general has been improved; structural stiffness has been increased (some transverse deformations of the parabolic ribs have been experienced in the previous mold); all parts have been pre-manufactured with computer-controlled machines, as far as possible; the vertical plastic ribs are holder in 4 different point to ensure that all angles match the desired value of π 2 and to increase their structural stiffness (some transverse deformations of the parabolic ribs had been experienced in the previous mold); all necessary geometric references for the significant points of the chosen parabola have been set on it, as the lack of references has proven to be a significant failure of the first design; a particular procedure has been to draw the holes for the coupling of the sandwich structure to the water-cut aluminum edges can be drilled while it is still on the mold; in this way, since the hold on the end-walls of the mold have been also water-cut a particular precision can be reached in this assembly. 16

37 2.3. PTC prototype Univpm.02 Fig and 2.15 show the assembled, as drawn by CAD software which has been used for its design (Solid Edge), along with a cutaway. The parabolic frame is composed of 13 PVC ribs, 15 mm thick. The more ribs in the structure, the stiffer the mold is, but cost and weight considerations led to this number, which has proven a good compromise. All the ribs present two rectangular cuts on their lower part (Fig. 2.14); this is to provide some room for four longitudinal steel L-profiles, 2 mm thick, as reinforcements for added stiffness. They keep the ribs in place and assure their verticality with respect to the bottom wood sheets. The PVC ribs and L-profiles have been connected via screws. The lower (floor) surfaces of both PVC ribs and L-profiles have been screwed to a wood floor, this being 12 mm thick. Once they were all in place, the upper edges of the ribs laid on a parabolic surface (see Fig. 2.16). Two AISI 304 steel sheets, 0.8 mm thick, have been placed upon this parabolic surface and constitute the area on which the fiberglass layers is to be laid. These two sheets were placed side by side, held in position by two longitudinal aluminum bars that are screwed to the PVC ribs, with a small gap of approximately 2 mm between them. This gap has been set on purpose. The VARTM process, or any other vacuum fiberglass-composite process, requires a tight seal around the vacuum bag. Since two steel sheets have been chosen for the parabolic surface, as no single sheet has been found with the required dimensions, the gap between them had to be carefully sealed for the RTM process to run properly. Therefore, a central 3 ply PVC rib section was arranged, with a lower central rib (3 mm lower than the rest of the ribs). The result is a 15 mm wide and 3 mm deep channel, running the length of the 3 ply assembly visible in Fig Before fixing the two steel sheets on the frame, this channel has been filled with a silicon high-temperature resistant sealant, which subsequently filled the gap between the mounted sheets and provided a tight seal. Two 5 mm aluminum plates are fixed at the mold ends. These plates have some cuts and holes purposely set on them, for use in the subsequent RTM manufacturing process. The end plate parabolas are 50 mm higher than the rib parabolas. On them three slits, 2 mm wide, were used to set the relevant positions for the parabola (vertex and edges, corresponding to π 2 angle) on the steel sheet. This was done by passing a wire between slits on opposite ends, and tensioning it as shown in Fig Marks were then scratched on the sheets along the wire; these marks will be present as little bulges on the parabolic surface of the infused fiberglass frame. The six holes on the end plates, visible in Fig have a different function. They are reference points for the placing of six (twelve, if considering both sides) small brass plates (3 cm sides and 1 cm thickness) that are to be embedded on the side surfaces of the infused concentrator frame. The function of these embedded plates is to provide a mating support for the fiberglass frame end plates supports, which are to be bolted on them. 17

38 Chapter 2. Design and manufacture of PTC prototypes Figure 2.14.: Complete view of the mold [3] s Figure 2.15.: Mold cutaway [3] 18

39 2.3. PTC prototype Univpm.02 Figure 2.16.: The mold during its realization Figure 2.17.: Detailed views of the central triple-rib 19

40 Chapter 2. Design and manufacture of PTC prototypes Figure 2.18.: The mold completely assembled and with a tensioned wire for setting marks to define rim ends Figure 2.19.: Mold aluminum end-plates [3] 20

41 2.3. PTC prototype Univpm.02 Figure 2.20.: Alumimum mating plates to be screwed to the composite structure [3] Table 2.5.: Characteristics of the Univpm.02 mold Length 3100 mm Width 2524 mm Maximum heigth 860 mm Parabolic profile length 3000 mm Parabolic surface 9 m 2 Total weight 250 kg Thus the design of the mating plates for the concentrator fiberglass frame has been carried out as well, being it deeply influenced by the shape, form and function of the mold. This plate is cut from a 5 mm aluminum sheet. The accurate mating of plate and infused fiberglass frame is done by taking as a reference the parabola vertex hole, the corresponding vertex bulges on the infused frame, and the upper side edge of these mating plates, which except in the central portion follows precisely the parabolic curvature. The central part is rounded; it provides hole through mountings for the receiver support and the ground support frame (see Fig. 2.21). In conclusion, the characteristics of the mold realized are reported in Tab The final dimensions and weight of the mold have to be take in account in the case of prototyping, since they can be problematic if operations are carried out in a laboratory environment: such a structure, with its dimensions and its weight is hard to hand lift and is larger than most doors. One last important remark: the fiberglass final frame will have a parabolic surface smaller than 9 m 2, as Teflon rim placed along the borders of the steel surface is needed for sealing the RTM-VIP vacuum bag before the infusion process. The reduced usable surface is nonetheless sufficient for a concentrator frame whose size has been specified in Tab

42 Chapter 2. Design and manufacture of PTC prototypes Figure 2.21.: Frame assemblying procedure [3] Figure 2.22.: Effective surface of the final fiberglass structure [3] 22

43 2.3. PTC prototype Univpm.02 Table 2.6.: Layering of Univpm.02 composite Layer fiber material specific area weight g/m 2 1 gelcoat n.a. 2 mat mat biaxial low density PVC biaxial VARTM procedure for the manufacture of the parabolic support As previously mentioned VARTM has been used to realize the parabolic support of Univpm.02. In this paragraph this procedure is described and some details are given regarding few particular aspects. First of all the layering: the layering of Univpm.02 has been defined based on the knowledge of the layering of Univpm.01 and on general considerations on its structural performance. Some simulations have been carried to verify that the obtained performance would meet the requirements, and they can be found in [5]. But the simulation of structural performances of sandwich composites is a very difficult matter, so results can be used as a reference, but in our case they are not yet accurate enough to be reliable for further decisions on the design. Anyhow, the chosen layering is described in Tab Mat 300 is a chopped mat layer, while biaxial, as suggested by the name, is a non-woven fabric with 0-90 fiber orientation and polyester stitchings. The specific area weight is referred to the fiber and the resin, since the amount of resin to the laminate basically depends on the chosen layering. The fact that the layers on the parabolic surface are more than those on the back depends on two reasons: obviously the parabolic surface requires better mechanical properties, but a second reason lies in the fact that before proceeding with VARTM the first layer is hand-laid. In this way it is easier to close all possible small holes in the surface and to properly seal the vacuum bag. The molding procedure has been realized following precise steps: 1. mold preparation; 2. gelcoating; 3. deposition and lamination of the first layer; 4. deposition of all the following layers; 5. collocation of the peel-ply and of the diffusion layer; 23

44 Chapter 2. Design and manufacture of PTC prototypes Figure 2.23.: Mold with teflon rims [3] 6. positioning of the Enka channels and of the inlet ports; 7. positioning of the vacuum tube and of the outlet ports; 8. sealing of the vacuum bag; 9. vacuum tests on the bag; 10. infusion; 11. extraction of the laminate. Following the above mentioned steps, the mold preparation includes the realization of teflon rims on all the future edges of the laminate; the mold with the rims is shown in Fig As all the rims are in place all the surfaces that will be then laminated must be carefully covered with removal wax paste. Gelcoat is then simply laid down by hand; it is important to depose the right amount of gelcoat: no untreated spots but, in the mean-time no excessive deposits. Then the first layer of MAT is collocated on its position and resin is applied. Once the resin has hardened, all the successive layers can be arranged (see Fig In particular Fig shows a detail of the indentation that has been produced on the sides and that will host the supports of the receiver. When all the structural layers are in place, then some other layers and accessories are added: these layers and objects have non influence in the final laminate, but are necessary for the infusion process (Fig. 2.26, 2.27, 2.28 and 2.29). Peel plies are a tightly woven fabric, often nylon, impregnated with some 24

45 2.3. PTC prototype Univpm.02 Figure 2.24.: Layers manual deposition[3] Figure 2.25.: A detail of the indentation that will host the support of the recover [3] 25

46 Chapter 2. Design and manufacture of PTC prototypes Figure 2.26.: Peel ply and diffusion layer [3] type of release agent. The peel ply sticks to the laminate, but it will pull away without too much difficulty. Diffusion layers are broad woven fabrics that help the resin spread on the upper surfaces; they are placed over the peel plies. Enka-Channel is a 100 mm wide, 4 mm thick, supply channel consisting of a black three-dimensional polyester filament core structure wrapped in a white polyester filter. It facilitates the resin uniform distribution from inlets. A spiraled tube, covered by the peel plies border edges, and outlets are placed on the fiberglass frame outer edges. The polyethylene vacuum bag is fixed on the Teflon borders with a strong sealant (tacky tape). 26

47 2.3. PTC prototype Univpm.02 Figure 2.27.: Enka channel and inlet ports [3] Figure 2.28.: Spiraled tubes and outlets [3] 27

48 Chapter 2. Design and manufacture of PTC prototypes Figure 2.29.: Vacuum bag sealing [3] 28

49 Chapter 3. PTC testing One of the main objectives of PTC project was to perform tests on the prototypes that have been designed and manufactured. The aim of the tests is to acquire information regarding the efficiency of the two prototypes, and also to validate the mathematical model that has been developed. In order to have a reference on how to perform tests, a standard was found that described this particular aspect. In fact, ASHRAE Standard 93/2010 [9] "Methods of Testing to Determine the Thermal Performance of Solar Collectors" has always been kept as a reference in designing the test facilities and in performing tests. Unfortunately some of the requirements of this standard have not been met during the first tests due to limitations in the available instrumentation. Therefore, a new test bench has been designed, and is now being realized to overcome the shortcomings of the initial apparatus. Anyhow, the results produced are valid and have been very useful, especially to correctly set the mathematical model. In the following sections the first experimental apparatus that has been used to perform tests is described in detail and some results of the tests performed with this apparatus are presented (tests of thermal performance of prototype Univpm.01 with water as working fluid in a temperature range from 25 to 75 C). Also a statistical analysis of the errors that affect these efficiency simulations are given. Then the new bench that has been designed to perform tests with water and heat transfer oil as working fluids, in a temperature range from 10 to 150 C is presented. Many of the contents treated in the next paragraphs can also be found in references [4] and [14]. One last remark is important: at the moment when PTC.project test began standard EN "Thermal solar systems and components - Solar Collectors"was not applicable to solar concentrators; in December 2010 an amendment has extended its scope to solar concentrating collectors. A preliminary analysis of this standard suggests that the apparatus that has been designed will also allow to perform tests in compliance of the requirements of this standard, but a detailed study has not been performed yet. This is the reason it will not be referenced in the following chapter. 29

50 Chapter 3. PTC testing 3.1. First test apparatus and tests on Univpm.01 prototype As mentioned, soon after prototype Univpm.01 was completed a set of outdoor tests have been performed in order to characterize this apparatus. ASHRAE Standard [9] has been adopted as reference to perform tests, although not all requirements of the standard have been met. The test system is composed of several parts; all the automation and control is implemented in "Lab- View" [15] environment. Tests have been performed in the period from March to July 2011 in Ancona (Italy - Latitude: Longitude: ) Hydraulic circuit The hydraulic system used for tests is composed of some different elements elements; a schematic representation of the circuit is given in Fig Tests have been performed with demineralized water is the working fluid. The circuit is composed of a pump, that circulates the fluid into the PTC, and a regulation valve that allows the desired flux into the solar system. Since mass flow rates required for the test are very small, for a finer adjustment of the mass flow regulation, and since the pump s nominal rate of flow was larger than the one needed, a second line has been installed parallel to the one of the PTC, thus creating a sort of by-pass for the pump; in this way the flow rate through the pump could be kept close to the pump s design value, while adjusting the one through the PTC. Also, since the flow rate on the parallel line was very large, a certain recirculation of the liquid in the storage tank was obtained. In this way stratification in the tank was avoided. The mass flow rate has been chosen equal to 5.45 l min 1, thus a little larger than the value suggested by ASHRAE Standard (0.02 kg s 1 m 2 ). This choice is due the fact that turbulent flow was desired in the receiver, and since the concentration ratio of the system is small (and therefore the receiver is quite large), adopting a large flow rate favors this condition. No cooling system was present in the circuit; to overcome the absence of this element, a very large storage has been adopted ( 300 l). In this way the temperature rise in the system through each acquisition is so small that it can be neglected. In the most sunny condition it was measured to be less than 0.02 C min 1 Since the length of each acquisition was about 5 minutes, the maximum variation in inlet temperature during a single acquisition was about 0.1 C min 1. The system s maximum operating temperature is about 80 C, mainly due to restrictions on the materials maximum temperature. A scheme of the setup and a photograph of the system are reported in Fig. 3.1 and Fig

51 3.1. First test apparatus and tests on Univpm.01 prototype Figure 3.1.: Hydraulic circuit Figure 3.2.: The hydraulic circuit 31

52 Chapter 3. PTC testing Movement system The movement system is composed of five elements: - an asynchronous three phase motor, (0.18 kw nominal power) having 4/8 poles (1390/690 rpm); - an inverter that allows motor speed regulation; - three worm drives having gear ratios of 1/60, 1/60 and 1/35; - a final belt drive having a transmission ratio 1/5 that couples the last worm gear to the PTC axis; - a 5000 position per revolution encoder. The system is illustrated in Fig The use of a common industrial asynchronous motor and such a gear reduction system has been adopted because it is a solution that can be easily scaled up. The idea is to rotate an entire line with one motor only, for this reason it is necessary to adopt a solution that can be replicated to produce a high torque value on the final axis. Other solutions, such as stepper motors are easier to adopt for a small system, but become very expensive when a relevant torque has to be produced. Also the non-reversibility of motion in worm drives is an advantage because allows to keep the system in position without powering the motor. The final belt drive allows a fine regulation on the overall gear ratio, and also acts as a clutch and avoids the transmission of too high torques from the PTC to the tracking system. The final speed can be adjusted acting both on the double speed control of the motor and on the inverter: when 8 poles of the motor are powered and a frequency of inverter is set to 23 Hz a final speed of rad s 1 is obtained. When, instead, 4 poles are powered and a frequency of frequency of 40 Hz is set the PTC rotates with an angular speed of rad s 1. These two values of speed correspond to the maximum and minimum tracking speeds for a PTC with its axis laying on the S-N direction. The encoder and the inverter communicate with the PC through apposite electronics; a scheme of all the signals is reported in Fig The desired position is calculated continuously by a routine in the virtual instrument environment in the PC; the output of this routine inputs the motor control routine: it compares the position red on the encoder with the desired one and produces two signals to turn on and off the motor and to set the direction of rotation. Also a soft start is included in the inverter to avoid damages on the motor or on the gears. Computing the solar position has some advantages with respect to systems that decide how to move the PTC based on a feedback signal: there is no disturb due to clouds or sky shading and a high precision can be reached. But there are also some disadvantages: a positioning error in the PTC axis (not pointing north or east) produces errors in the tracking, also small mis- 32

53 3.1. First test apparatus and tests on Univpm.01 prototype Figure 3.3.: Components of the movement system alignments or imperfections in the geometry are not corrected by a feedback signal Instruments and computational procedure The remaining part of the testing loop are the signal acquiring and the calculation systems. Four temperatures, wind speed and two values of DNI are measured. The mass flow rate is acquired only at the beginning of each measuring sequence and manually inserted in the calculation system. Acquired temperatures are: ambient temperature T a, temperature in the tank close to the inlet of the pump, and temperature at inlet T f,in and outlet T f,out of the receiver. The first two temperatures are measured by T-type thermocouples, while temperatures of the fluid entering the receive and exiting it are measured by AA Class RTDs. In this way an accuracy of about 0.8 C is obtained in the range of the measured temperatures (0-100 C). An Agilent 39470A data acquisition unit [16] is used for all acquisitions and for compensation of the thermocouples. The two RTDs for measuring inlet and outlet temperature of the PTC are inserted in the receiver at the beginning and at the end of the ptc, as showed in Fig DNI is measured by two first class [17] normal incidence pyrheliometers mounted on solar trackers [18]. The average of the signals of the two instruments is used in the calculation system. Equations adopted are reported in Tab

54 Chapter 3. PTC testing Table 3.1.: Calculation system Inputs Calculation Outputs T f,in [ C] T = T f,out - T f,in T [ C] T f,out [ C] DNI = ( V P Ea ) V P Eb AccP Ea AccP E /2 DNI[W m 2 ] T amb [ C] DI = DNI cosθ DI[W m 2 ] T tank [ C] Q u = C p,w T F lowrate Q u [W] VPEa,VPEb [V] Q inc = DI S Q inc [W] AccP Ea, AccP eb[v m 2 /W ] T avg = (T f,in +T f,out )/2 T avg [ C] θ [rad] η = Q u/q inc η F lowrate[l s 2 ] Figure 3.4.: RTD inserted at the beginning (end) of the receiver [4] 34

55 3.1. First test apparatus and tests on Univpm.01 prototype Figure 3.5.: Signals acquiring and data flow scheme [4] 35

56 Chapter 3. PTC testing Table 3.2.: Comparison of collector efficiency equation Efficiency equation Reference η = T Murphy and Kenneth (1982) [19] η = T Hurtado and Kast (1984) [20] η = T Kalogirou et al.(1994b) [21] η = T Kalogirou (1996) [22] η = T Valan Arasu and Sornakumar (2006) [23] η = T present work 1.0 Η' s T Figure 3.6.: Straight-line interpolating experimental points Results and comments The efficiency of a collector is generally expressed as a straight line, dependent upon a single variable. The form of the equation is: η = F r η o F ru l C T f,in T amb DI = q + mt (3.1) where T = T f,in T amb (3.2) DI T is a variable used only to express efficiency with a straight line; q and m are generated by a regression on the experimental values. For the meaning of all the other parameters, refer to the next chapter. 36 Interpolating experimentally collected data, the following equation for the

57 3.2. Analysis of measurement errors straight line has been determined: η = T (3.3) Fig. 3.6 represents that equation on the plane combined with experimental points. The comparison with expressions derived from literature, shown in Tab. 3.2, reveals the obtained slope value to be higher. This is justified by the different concentration ratio of the collectors employed during the experimental proofs. For example the adopted collector, shows a concentration ratio C = 7.41; in Valan Arasu and Sornakumar (2006) a concentration ratio C = is declared. Therefore, if this aspect is considered, the mathematical product m C is not very different in among these two cases: Present Collector m C : = 6.41 (3.4) VAS Collector m C : = 7.7 (3.5) 3.2. Analysis of measurement errors As shown in previous sections, the parameters that represent major interest in tests all come from indirect measures; i.e. they are not direct reading of a measurement instrument, but they are obtained combining different direct measurements. Therefore, since the essential focus is not on variables that are directly measured, but is on these variable that come from an indirect measurement procedure, it is essential to analyze the error that affects these measures. To do so, some basic concepts of error propagation theory are necessary, together with the knowledge of the mathematical relations between the variables that are directly measured and those that are calculated Propagation of uncertainty As mentioned, the propagation of uncertainties is the effect of the variables uncertainties on the uncertainty of a function that is calculated from the values of these variables. If the function is a linear combination of the starting variables, then a variance-covariance matrix can be defined and a final expression of uncertainty can be given based on this matrix. But if the combination of the starting variables in the function is non-linear, then a different rule must 37

58 Chapter 3. PTC testing be applied. If measurements uncertainties (δx, δy,..., δu, δv) are linked to the measures (x, y, z,..., u, v), defined function f(x, y,..., u, v) (3.6) the uncertainty on the value of this function will always be less than δf = f x δx + f y δy f u δu + f v δv (3.7) But the above expression can overestimate uncertainty; a correct value ca be obtained, under some hypothesis, with a different expression. The conditions for the second formula to be applied are that errors on the original variables (δx, δy,..., δu, δv) are random and independent of each other. Under these hypothesis measurements on the variables can be considered as ruled by a normal distribution; also, since the combination of two independent normal distributions is also a normal distribution, having standard deviation equal to the square root of the sum of the squares of the initial standard deviations, then the error on f will be equal to: ( f ) 2 ( ) 2 ( ) 2 ( ) 2 f f f δf = x δx + y δy u δu + v δv (3.8) Uncertainty on efficiency measurements When tests are performed the efficiency of the collector is measured as: η = Q u Q i nc = ṁc p(t out T in ) A g DNI cos θ (3.9) where ṁ is the mass flow rate in the receiver; c p is the thermal capacity of the circulating fluid; T out is the temperature of the fluid exiting the collector; T in is the temperature of the fluid entering the collector; A g id the gross aperture area of the collector; DN I is the direct normal incident radiation; cos θ is the cosine of the incidence angle. Therefore, using expression from Eq. 3.10, the uncertainty on efficiency measurements is: 38

59 3.3. New test circuit δ 2 η = ( + ( ) 2 ( cp (T out T in ) A g DNI cos θ δṁ + c p ṁ A g DNI cos θ δt in c p ṁ A g DNI cos θ δt out ) 2 + ) 2 + ( c pṁ(t out T in ) A g DNI 2 cos θ δdni ) 2 (3.10) Using the instrumentation described above, and performing measures with values of the variables similar to those described in section 3.1 are always below 5% New test circuit Since the first test bench has shown many shortcomings, first of all the fact that it is not capable of working with temperatures any higher than 80 C, due to the materials of many of the components, a new test circuit has been designed to be able to test solar thermal apparata with temperatures as high as 150 C. With regards to this new test bench, at the moment, the design process ha been completed. Also the instrumentation (to measure volume flow rate, temperature, pressure and other measurements required by ASHRAE Standard) have been acquired. At the moment the bench is being assembled. No test results are available yet. For this reasons in this section the bench will be only presented and described. Fig. 3.7 shows the P&I diagram of the test bench. Up left is the expansion vessel, that is connected to the main fluid line. The line goes through the pump, and a by-pass line is inserted across the pump. The valve following the pump is to regulate the mass flow rate. Then there is an electric heater: this item has the function of a fine adjustment on the inlet temperature; intact the heat exchanger that is positioned after the PTC will decrease fluid temperature to a value a little lower than the desired inlet temperature, and then, by means of this electric resistance that is in contact with the circulating fluid, fluid will be heated to the desired inlet temperature. Due to the nature of this electric resistance, its time response will be fast enough to provide a constant temperature to the PTC inlet. Gone through the heater, the fluid will cross a filter and then an oscillating piston flow measurement device. Then it will enter the PTC. Two mixing devices will be inserted right before the PTC fluid inlet and after the PTC fluid outlet. These two devices will host the two RTD for temperature measurement across the PTC. Then the fluid will go through a plate heat exchanger and back to the pump inlet. The secondary circuit of the heat exchanger will be cooled by water. The 39

60 Chapter 3. PTC testing final cooling device will be chiller, but a tank will be inserted between the filler circuit and the heat exchanger secondary circuit: the chiller will keep the water inside the tank at a constant temperature. The other water circuit will provide cooling to the heat exchanger. A circulator will pump the water and a threeway valve will regulate the flow so to provide a constant temperature at the outlet of the primary circuit of the heat exchange (that is the fluid going to the pump and then to the PTC ). The circuit will be able to work with both water and heat transfer oil as fluid. Due to the high flammability of heat transfer oil, a safety tank has been inserted in the circuit: this tank is in a position lower than any other object in the circuit and is connected to all the low points of the circuit via some manual valves. In case of danger, by rotating these valves, it will always be possible to evacuate all the oil from the circuit and to store it in the safety tank. The tank is not represented in the P&I diagram, but it is clearly distinguishable in Fig

61 3.3. New test circuit Figure 3.7.: P&I diagram of the test bench 41

62 Chapter 3. PTC testing Figure 3.8.: Legend of symbols for P& I diagram in Fig

63 3.3. New test circuit Figure 3.9.: A 3D representation of the test bench 43

64

65 Chapter 4. Mathematical model of a PTC The theoretical model has been developed in order to characterize the PTC and calculate its efficiency together with all the other working parameters. Even if the performances of a PTC can be easily obtained through tests, and an efficiency curve can be defined, this experimental approach is not completely satisfying if an optimization in the design is to be obtained. In fact, an experimental approach allows the knowledge of the total amount of heat that can be transferred to the fluid under particular working and ambient conditions, but does not allow the prediction of the temperatures of the different parts of the receiver, or the heat losses due to the different heat exchange mechanisms, or the effect of a change in a single ambient conditions, such as air humidity or wind on the efficiency. This aspect is considered very important also because recent scientific literature is rich in experimental activity [19, 20, 21, 23] but poor in terms of mathematical modeling. Different authors, especially in the 1980s, have addressed different aspects of the optical characterization and thermal description of PTCs [24, 25, 26, 27, 28], but very few works have been found that describe a complete modeling of a PTC [29, 30]. In this chapter the model that has been developed is described in detail, together with its application to the specific prototype and its implementation in "Wolfram Mathematica" [31] ambient for technical calculations. A comparison of experimental results and calculated efficiencies is presented at the end of the article; a good fit of predicted values with measured ones is found, thus validating the model and suggesting it is suitable for energy and economic considerations on the application of a PTC field to a particular industrial heat load General description of the model The mathematical model of the PTC accounts for all the optical and thermal effects that produce a loss of radiation or heat. The model implemented is essentially composed of two parts: a model for optical efficiency and a thermal 45

66 Chapter 4. Mathematical model of a PTC model of the receiver. A third section has been inserted at the beginning for the calculation of the solar vector. The first section is not described, since it is just an implementation of Michalsky s algorithm [32] for the calculation of the solar vector; the method allows the calculation of the solar vector for any geographical location with an accuracy of 0.01 deg until year The second section contains the optical analysis: the aim of this section is to define the optical efficiency, that is the ratio between the energy that is absorbed by the receiver and the energy that arrives on the reflective surface. The last section is dedicated to the definition of the thermal efficiency: this efficiency is, again, the ratio between the energy that is transferred to the heat transfer fluid and the total energy that arrives on the receiver. In the following sections the physical model is first described; then all the variables that have been used in the simulations are exposed. Most of what described in the following sections can also be found in [33] Optical model The optical efficiency is defined as the ratio between the energy that is absorbed by the receiver and the energy that hits the aperture surface. Optical efficiency depends on several factors: the optical properties of the used materials, the geometry of the concentrator and of the objects surrounding it and factors depending on the difference between ideal model and real components (imperfections on surfaces, geometrical errors and sun tracking inaccuracy) Concentration ratio The first parameter that is to be considered when calculating optical efficiency is the area concentration ratio 1. This value will be found in the equations for the calculation of the global efficiency of a PTC. It is important to observe that this ratio has an upper limit. If the second law of thermodynamics is applied to radiative hear exchange between the sun and the receiver it is possible to demonstrate that the concentration ratio as an upper value[13]. For a linear concentrator the maximum value is equal to: C max = 1 sin θ s (4.1) where θ s id half of the acceptance angle (semi-acceptance angle). Adopting a few considerations with respect to the radius of the sun and to the distance earth to sun, it is possible to verify that the maximum concentration ratio for 1 also a flux concentration ratio can be defined, but it is uncommon, so the area concentration ratio will be from now on addressed simply as concentration ratio 46

67 4.2. Optical model a linear collector is equal to 212 [13]. This is not very relevant in the case of the developed prototypes (that are well below this value) Optical efficiency Optical efficiency of a parabolic trough concentrator is defined as [34, 35]: where η o = ρ c (τ v α r ) eff γ[(1 A f tan θ) cos θ] (4.2) θ = angle of incidence of the sun s rays on the collector aperture [rad]; it is measured from the normal to the aperture plane; ρ c = average specular reflectance of the reflective surface [dimensionless]; τ v = transmissivity of the glass [dimensionless]; α r = absorbance of the receiver [dimensionless]; γ = instantaneous intercept factor (fraction of rays incident upon the aperture that reach the receiver for a specific value of the incident angle θ) [dimensionless]; A f = geometrical reduction factor [dimensionless]. The subscript eff. signifies the fact that glazing transmittance and absorber s absorbance (τ v and α r ) depend upon the angle of incidence of the sun s rays: this aspect is treated in section The first three terms in the multiplication do not need further explanation. The last two terms, instead, will be described in detail in the following paragraphs. An important observation that arises from Eq. 4.2 is that optical efficiency depends upon the angle of incidence of the sun s rays. This is extremely important because if sets a standpoint that is to be considered when running efficiency simulations Incident angle modifier The optical efficiency as defined in Eq. 4.2 varies with the angle of incidence of the sun s rays on the aperture plane. Several factors besides cos θ contribute to decrease optical efficiency with the increase of θ. Two of them have already been mentioned after the introduction of Eq. 4.2: glazing transmittance and absorber s absorbance decrease with the increase of θ. Also the reflector s longitudinal slope and specularity errors contribute to decrease the value of 1gamma θ with the increase of θ. Another decrease of the intercept factor is produced by the fact that the apparent sun image becomes wider due to longer reflected path length. All the above mentioned aspects are secondary in terms of absolute error of the model, and they are also difficult to be treated in mathematical terms: for these reasons they will be neglected in the mathematical 47

68 Chapter 4. Mathematical model of a PTC model. Anyhow, especially with respect to the comprehension of the standard that will be introduced in the next chapters, it is important to say that there is a way to single-out these effects: it can be done introducing the incidence angle modifier. K(θ) is a coefficient that accounts for these effects and that lowers the value of η θ as follows: η o = (η θ ) n K(θ) (4.3) where (η θ ) n is the value of optical efficiency in the condition of incidence angle equal to zero. The introduction of K(θ) allows to rearrange Eq. 4.2 as follows [25]: η o = [ρ c (τ v α r ) n ]γ[(1 A f tan θ) cos θ][k(θ)] (4.4) In this expression the different contributions to optical efficiency are clearly distinguishable: the first bracketed term represents the properties of the materials; the second term (γ accounts for all optical errors; the third term accounts for geometrical effects and direct effects of the angle of incidence; the last bracketed term is the incidence angle "secondary" effect (secondary intends the fact that the geometrical effects are not included in this term). The sometimes the third term is included within gamma; some authors, instead, consider it inside K(θ) [9] Geometrical effects The geometrical reduction factor accounts for the difference between the aperture area and the effective aperture area; this last area is the area that actually contributes to the reflection. It corresponds to the total aperture area deducted all the areas that do not reflect into the receiver [26]. A f is defined as: where 48 A ap = aperture area [m 2 ]; A i = area lost to end-effects [m 2 ]; A f (A i + A b + A s ) A ap (4.5) A b = area lost to shading by transverse plates [m 2 ];

69 4.2. Optical model Figure 4.1.: Area lost due to end-effects [5] A s = area lost for inter array collector shading (to be considered only if PTCs are deployed in arrays comprising several rows of collectors) [m 2 ]. As in the original reference [26], the approximation has been used instead than the equal sign because overlapping of different effects is not considered. End effects During off-normal operation of a parabolic trough collector sun rays reflected from some areas of the reflective surface near the end of the concentrator do not hit the receiver. This loss effective aperture is generally addressed with the name of end-effect". This effect is generally present on all concentrator because for thermal efficiency and structural modularity it is common to terminate the receiver near the same cross section plane as is the concentrator. Considering Fig. 4.1, the area lost to end-effects is the ruled region (the representation is a plane view of the aperture area): this area can be approximated by the region boded by the end of the collector opposite to the sun and the locus of the points of reflection of the central rays which intercept the focal line at the end of the collector. These rays define a cone with vertex angle 2( π 2 θ) To find the lost area it is therefore necessary to define the intercept between 49

70 Chapter 4. Mathematical model of a PTC the limiting cone and the parabola of the trough, and then the area defined by that curve and the end of the trough projected into the aperture plane. Considering a system of coordinates (x, y, z) having origin at the vertex of the parabola at the end of the collector, the limiting cone is defined by the equation: (z f 2 ) + y 2 = r 2 = x2 tan 2 (4.6) θ The equation of the parabola of the trough can be represented by the cylindrical surface: z = y 2 4f, x > 0 (4.7) Finding the interception between the two equations it is possible to obtain the lost area. Refering to Fig. 4.1, it can be obtained as: So the area of the parabolic sector is: A = f tanθ (4.8) B = f tanθ (4.9) C = d f tanθ (4.10) A ps = 2 (d f tanθ) (4.11) 3 And therefore, by subtracting this area to that of the rectangle and calculating the value of d the lost area will be equal to: Shading by transverse plates ) A i = f w tanθ (1 + w2 48f 2 (4.12) A second cause of reduction of effective aperture area that is as common as end-effects in PTCs is shading by transverse surfaces. This undesired effect is aso called bulkhead blocking" when the shading is caused by such components. The following equations will only consider a shading that extends from rim to rim, but the same procedure found above can be also used for other configurations. Considering Fig. 4.2, the shaded area represents the area lost due to the presence of a transverse opaque surface having geometry as shown in the profile view (the red line represents the focal line). Since: A = h tanθ (4.13) 50

71 4.2. Optical model Figure 4.2.: Shading by transverse plates [5] 51

72 Chapter 4. Mathematical model of a PTC then it will also be: x = (h z)tanθ (4.14) Finding the intercept between Eq and Eq. 4.7, that defines the parabolic surface it is possible to obtain: ( ) f y 2 = 4 (x h tanθ) (4.15) tanθ Eq defines a parabola. Therefore the area lost due to transverse shading will be the area between the parabola and the edge of the surface, that is: A b = 2 w h tanθ (4.16) 3 Intraaray shading In most application PTCs are deployed in arrays comprising several rows. Orientation of the rows is generally on the north-south or east-west direction. The choice of the distance between rows is, therefore, an essential one. If the east-west orientation is chosen, then, depending on the latitude of the place of installation, it is possible to choose the distance based on the solar altitude at winter solstice. In this case, if the distance between arrays is enough to avoid intraarray shading under this condition, then intraarray shading never occurs. But in all other cases this phenomenon will often reduce effective aperture area, and it is, therefore, an important aspect that needs to be considered. In the model presented intraarray shading is modeled as a two-dimensional effect: this produces an overestimate of actual shading. But since in practical applications collector string s length is generally larger than 20 times the collector s width, then the two-dimensional model can be considered accurate enough. More precise algorithms can be found in Ref. [36]. Considering Fig. 4.3 it is possible to observe the geometrical relations between the inclination angle of the collectors and the shaded region. In mathematical terms: Intercept Factor A A S A = w e e = ( ) p sin τ (4.17) w The intercept factor is a complex function; it depends on the geometry of the collector and on random and systematic errors. A complete treatment of this function is given in [35]. Many errors are embedded within this factor; they belong to different sources [25]: 52

73 4.2. Optical model Figure 4.3.: Intraarray shading [5] 1. materials: imperfections in the specularity of the reflective material; 2. manufacture and assembly: local slope errors; profile errors; misalignment of the reflector during assembly; mislocation of the receiver tube; 3. operation; poor tracking and tracking biases after some operation time; increase in profile errors due to wind loads, temperature effects or other operational causes; loss of reflectance due to weathering or dust on the reflecting surface; misalignment of the receiver with respect of the effective focus due to operational causes; Error analysis Ref. [6] gives a way to model all these contributions and define their values in order to obtain a value for the intercept factor. The analysis moves from the definition of the distribution of energy directed toward the receiver and in 53

74 Chapter 4. Mathematical model of a PTC Figure 4.4.: Modeling of potential optical errors in parabolic trough collectors [6] particular from the angular intensity function for the effective sunshade (I eff ), that is expressed as a normal distribution: where I b I eff (ζ) = σ tot,n (2π) 1 2 ζ = angular aperture, rad; I b = beam solar radiation W/m 2 aper; { exp 1 ( ζ µ 2 σ tot ) 2 } (4.18) σ tot,n = reflected energy distribution standard deviation at normal incidence, rad; µ = angular shift of the mean of the distribution, rad; the standard deviation of the energy distribution (σ tot in Eq. 4.18) is obtained by statistical averaging of the distribution of the random errors. Random errors are defined as those errors which are truly random in nature; they give rise to spreading of the reflected energy distribution (see Fig. 4.4). Due to their 54

75 4.2. Optical model nature they are modeled statistically by a total reflected energy distribution standard deviation at the condition of normal incidence: where σ tot = σ 2 sun + 4σ 2 slope + σ2 mirror (4.19) σ sun = standard deviation of the sun s energy distribution at normalincidence, rad; σ slope = standard deviation of the slope error distribution at normalincidence, rad; σ mirror = standard deviation of the mirror specularity error distribution at normal-incidence, rad. Nonrandom errors, instead, are deterministic in nature. They account for the gross error in manufacture ond/or assembly of the concentrator and in operational errors. These errors are analyzed as geometric effects. Due to their nature, each one of these errors is characterized by a single deterministic value. The following bullets indicate the different effects considered and the three physical measures used to characterize these errors are: reflector profile errors: distance between the effective and ideal focus of the reflector measured along the optical axis of the reflector; misalignment of the trough with the sun: distance between the ideal focus of the reflector and the center of the absorber tube; misalignment of the receiver with respect to the effective focus: angle between the central ray from the sun and the normal to reflector s aperture plane β. Regarding the first non-random error, it is represented as receiver mislocation along the y-axis, since it is demonstrated that this is a dominant error direction, and also since this dislocation reduces optical performance more than mislocation along the x-axys [37, 38]. Also, reflector profile errors and receiver mislocation along the y-axis produce about the same error, and one parameter can account for both these effects, namely (d r ) y. Hence, only two independent nonrandom variables are considered and the mean of the reflected energy distribution (µ) is a function of these two variables (namely (d r ) y and β). The decrease in optical efficiency due to errors can be determined by analyzing the effect of these errors on the intercept factor, whose value is influenced by random and nonrandom errors and by the concentrate geometry. The intercept factor at normal-incidence can be written as: γ = f(φ, C, D, σ = σ tot, β, (d r ) y ) (4.20) 55

76 Chapter 4. Mathematical model of a PTC Universal error parameters Random and non-random errors can be combined with the collector geometry (parameters C and D) to obtain parameters universal to all collector geometries. Therefor all errors can be reduced to two universal non-random error parameters and one universal random error parameter: where φ r = rim angle [rad]; = universal nonrandom error parameter due to receiver mis- d = (dr)y D location; γ = f(φσ, β, d ))) (4.21) β = βc= universal nonrandom error parameter due to angular errors [rad]; σ = σc= universal random error parameter [rad]. Once all the errors have been analyzed, considering the energy distribution as it was defined in Eq.??, and the definition of the intercept factor (ratio of the energy absorbed by the receiver with respect to the energy reflected by the reflector) it is possible to derivate the following expression [25]: γ = 1 + cos φ r 2 sin φ r erf φr 0 [ erf ( sin φr (1 + cos φ)(1 2d sin φ) πβ ) (1 + cos φ r ) + 2πσ (1 + cos φ r ) )] ( sin φ r(1 + cos φ)(1 + 2d sin φ) + πβ (1 + cos φ r ) 2πσ (1 + cos φ r ) dφ (1 + cos φ) (4.22) Where the integral variable φ is the angle between the ray reflected from the reflective surface and the plane the comprehends the focal line and the origin of the parabolic surface; therefore φ r will be equal to the value of this angle for the reflected ray closest to the edge of the reflector, that is equal to the rim angle of the PTC Thermal model The aim of the thermal model is to describe all the heat losses on the receiver. It allows to calculate the energy that is transferred to the fluid flowing inside the receiver. Thermal efficiency can be defined as the ratio between this last energy and the heat flux that arrives on the receiver from the concentrator. In order to define a model it is essential do indicate the hypothesis that are 56

77 4.3. Thermal model adopted; in the present case, the model has been developed under the following hypothesis: 1. the phenomenon is studied under steady conditions: this hypothesis is essential. The validity of a model under this assumption depends on many characteristics: in a general way it is possible to say that this assumption is more realistic if the the inertia of the system is small. The main variables that affect the system s inertia are the dimension of the receiver, the quantity of fluid within it and its heat capacity. An indication if the system s inertia can be obtained but determining its time response curve, that has been previously defined. In any case, since measurements on the PTC are to be realized in steady state, this hypothesis is acceptable; 2. The heat exchange phenomenon is mono-dimensional: this means that heat fluxes run only along the radial direction. It also implies that there is no difference among different cross-sections of the receiver; of course, this hypothesis is consistent if temperatures are similar between a section of the receiver close to the fluid inlet and a section section close to the fluid outlet. The validity of this second hypothesis is easy to check by experimentally recording inlet and outlet flow temperatures and then running two simulations at these temperatures. The comparison of the results obtained will give an indication of how this assumption can influence simulations. In any case, as a general reference, Forristall has indicated that this assumption can be accepted for troughs shorter than 100 m [30]. 3. Another simplification regards the dependence of the thermophisical properties of the different materials upon temperature. Thermal conductivity and optical factors (coefficients of transmission, absorption and reflection) of solids has been kept independent of temperature. 4. A last simplification regards the fact that the presence of the supports that hold the receiver, as well as the rings that connect the metal pipe to the glass and both of them to the supports has been neglected, thus considering a receiver having the same cross-section for its entire length. The model consists in a system of energy balance equations on different elements of the receiver. A scheme of the heat fluxes is reported in Fig. 4.6, while Fig. 4.5 shows the thermal resistances. Considering the number of balance equations that will be written, to help the comprehension of this model a scheme of subscripts has been adopted: the first letter indicates the type of heat transfer mode (k for conduction, c for convection and r for radiation); 57

78 Chapter 4. Mathematical model of a PTC Figure 4.5.: Thermal resistances of the receiver Figure 4.6.: Cross-section of the receiver that shows useful heat fluxes (in red) and heat losses (in orange) 58

79 4.3. Thermal model the second letter indicates the element of the system that is losing heat (in accordance with the verse of the vectors in Fig. 4.6); the third letter indicates the element of the system that is acquiring heat (in accordance with the verse of the vectors in Fig. 4.6). In the case of conductive heat transfer the second and third letters in the subscripts are the same, so the third letter is omitted. Considering Fig. 4.6, showing a cross section of the receiver (this term comprehends both the absorber and the glass cover), it is possible to observe that a the radiation reflected from the reflector to the receiver (Q rcr ) hits the glazing before reaching the absorber; therefore it is possible to write: Q rcr = α v Q rcr + τ v Q rcr + ρ v Q rcr (4.23) where: α v is the absorbance of the glass cover; τ v is the transmissivity of the glass cover; ρ v is the reflectivity of the glass cover. In order to increase thermal efficiency of the collector component τ v Q rcr should be as high as possible; also α v Q rcr component is considered, even if it is a very small term. Obviously ρ v Q rcr is not considered, since it does not interest the thermal problem. Therefore solar radiation that crosses the glass envelope reaches the absorber; again, the amount of energy that arrives to the fluid depends upon the three coefficients τ v, α v and ρ v.; the absorber is modeled as an opaque body, therefore τ v = 0, so the amount of heat absorbed by the external surface of the receiver will be equal to τ v α r Q rcr. A fraction of this amount of energy will be conducted trough the receiver (Q kr ) and will be then transferred to the fluid in a convective heat exchange process (Q crf ). All the remaining energy will be lost due to heat exchange between the absorber and the glazing. This amount of heat will be partially lost in a convective mechanism (Q crv ) and partially in a radiative heat exchange (Q rrv ). These two energies will therefore flow in a parallel scheme. The resistances scheme is shown in Fig Based on the scheme developed, the following system of balance equations has been used to describe heat exchange in the elements that compose the receiver: τ v α r Q rcr = Q kr + Q crv + Q rrv Q kr = Q crf = Q f Q crv + Q rrv = Q kv Q kv + α v Q rcr = Q cva + Q rvc (4.24) 59

80 Chapter 4. Mathematical model of a PTC The system to be solved is a fourth order system of algebraic equations with four unknown quantities, that are: T ri, T re, T vi and T ve, i.e. the superficial internal and external temperatures of the absorber and of the glass. The nonlinearity of the system is due to radiative heat exchanges; if radiation heat transfer coefficients are employed, the system becomes linear, and its solution is immediate. Even if the error produced by this approximation is very small, the nonlinear system has been kept. Heat fluxes involved in the energy balance system are discussed in the following sections Convection heat exchange between the receiver and the fluid Convection heat transfer between the receiver inside surface and the fluid can be expressed with Newton s law [39]: and Q crf = h crf A ri (T ri T f ) (4.25) where h crf = Nu rf λ f d ri (4.26) h cry is the heat transfer coefficient between the receiver and the fluid, W m 2 C 1 ; A ri = π d ri L is the internal surface of the receiver ( l being the length of the receiver expressed in m), m 2 ; T ri is the inner temperature of the receiver, C; t f is the average temperature of the fluid, C; Nu rf is the Nusselt number regarding heat exchange in the internal surface of the receiver; d ri is the inner diameter of the receiver, m; λ f is the thermal conductivity of the fluid W m 1 C 1 ; Being in steady conditions, the heat capacity of the fluid is not necessary. The evaluation of Nusselt number depends on the type of flow. In case of laminar flow (Re f < 2300), Nu rf is independent of Reynold and Prandtl numbers [39] and is considered equal to Nu rf = For transitional and turbulent cases (Re f > 2300), Gnielinski s correlation [40] can be used. 60

81 4.3. Thermal model Conduction through the receiver Conduction heat transfer through the receiver Q kr can be written according to Fourier s law applied in the case of concentric cylinders [41]: where Q kr = (T re T ri ) R kr (4.27) where R kr = ln dre d ri 2πλ r L (4.28) T re is the outer temperature of the receiver, C; T ri is the inner temperature of the receiver, C; d re is the outer diameter of the receiver, m; d ri is the inner diameter of the receiver, m; λ r is the thermal conductivity of the receiver W m 1 C 1 ; As pointed out at the beginning of the chapter, λ r is considered independent of temperature Convection heat exchange between the receiver and the glass Convection heat transfer between the receiver and the glass depends on the evacuation of the pipe. If the pipe is evacuated, heat transfer occurs by freemolecular convection [42]. Otherwise, there will be free convection [43]. In all the tests performed no vacuum was created in the annulus, but this is due to technological reasons: creating a vacuum and providing a proper sealing so that pressure inside the annulus is constant is not an easy task. Also, since no commercially available evacuated absorbers have been found for the desired diameter, tests have been performed only with glazed pipes. But since as the upper limit of the selected temperature range is approached thermal losses become problematic, the model has been built with the possibility of simulating evacuated absorbers. Evacuated absorber: free molecular convection heat exchange When the annulus is evacuated (p < 1 torr, free molecule convection heat transfer occurs, and heat exchange can be modeled as [30]: Q crv = h crv A re (T re T vi ) (4.29) 61

82 Chapter 4. Mathematical model of a PTC with h crv = d re 2 ln d vi dre λ std ( ) (4.30) d + bk vi d re + 1 where b = (2 a)(9γ 5) 2a(γ + 1) (4.31) k = [( T re+t vi ) ] pδ 2 (4.32) h crv is the heat transfer coefficient inside the evacuated annulus, W m 2 C 1 ; λ std is the heat transfer coefficient of the gas in the annulus at standard conditions, W m 1 C 1 ; k is the mean free path of the molecules of the trapped gas, cm; b is the coefficient of interaction of the trapped gas; a accommodation coefficient of the trapped gas; γ ratio of specific heats for the annulus gas; p annulus gas pressure, mmhg; δ molecular diameter of annulus gas, cm; Atmospheric receiver: convection heat transfer In the case of non-evacuated receiver, then convective heat exchange in the annulus will occur by standard natural convection: with Q crv = 2πλ eff L ln dvi d re (T re T vi ) (4.33) λ eff = λ a ( P r a P r a ) 1 4 (Fcil Ra a ) 1 4 (4.34) F cil = ( d vi d re 2 [ln dvi d re ] 4 ) 3 ( d 3 5 vi + d 3 5 re ) 5 (4.35) 62 where λ eff is effective heat transfer coefficient, W m 1 C 1 ; L is the length of the receiver, m; λ a is the convective heat transfer coefficient of air evaluated at its average temperature (T vi + T re )/2, W m 1 C 1 ;

83 4.3. Thermal model P r a is the Prandtl number of air evaluated at its average temperature; Ra a is the Rayleigh number for air evaluated at its mean temperature and with characteristic length equal to (d vi + d re )/2; F cil is the geometrical factor for concentric cylinders. It is important to remind that in case λ eff λ eff = λ a. < λ a, then it will be imposed Radiation heat exchange between the receiver and the glass Radiation heat transfer between the receiver and the glass can be expressed as follows [39]: where Q rrv = πd relσ(t 4 re T 4 vi ) 1 ɛ r + 1 ɛv ɛ v ( dre d vi ) (4.36) σ is the Stefan-Boltzmann constant W m 2 K 4 ; ɛ r is the receiver emissivity; ɛ v is the glass emissivity. It is here reminded that emissivities have been considered independent of temperature Conduction through the glass Conduction heat transfer through the glass has been treated in the same way of conduction through the absorber [41]: where Q kv = (T ve T vi ) R kv (4.37) where R kv = ln dve d vi 2πλ v L (4.38) T ve is the outer temperature of the glass, C; T vi is the inner temperature of the glass, C; d ve is the outer diameter of the glass, m; d vi is the inner diameter of the glass, m; 63

84 Chapter 4. Mathematical model of a PTC λ v is the thermal conductivity of the glass, W m 1 C 1 ; As pointed out at the beginning of the chapter, λ v is considered independent of temperature Convection heat exchange between the glass and surrounding air Convection heat transfer between the glass and the ambient can be written as follows: Q cva = h cva A ve (T ve T a ) (4.39) with where h cva = Nu vaλ a d ve (4.40) h cva is the convection heat transfer coefficient between the glass and ambient air, W m 2 C 1 ; A ve = πd ve L is equal to th e total external surface of the glass, m 2 ; T ve is the outer temperature of the glass, C; T a is the ambient temperature of air, C; Nu va is the Nusselt number regarding heat exchange between the glass and ambient air; λ a is the conductive heat transfer coefficient of air evaluated at air film temperature equal to (T ve + T a )/2, W m 1 C 1 ; d ve is the external diameter of the glass, m. The Nusselt number depends on the wind velocity: in absence of wind, convection heat exchange will occur by natural convection, while in presence of wind, forced convection will take place. In absence of wind Nusselt number is evaluated with the formula proposed by Churchill and Chu for isothermal cylinders [44]: where 64 { } 0.387Ra a Nu va = 0.6[ ( ) 9 ] (4.41) P r a Ra a is the Rayleigh number of ambient air evaluated at air film temperature (T ve + T a )/2 and with characteristic length d ve ; P r a is the Prandtl number of external air evaluated at air film temperature (as above).

85 4.4. Global efficiency In case of presence of wind, then forced convection will occur; in this case the following relation by Churchill and Bernstein will be adopted[45]: Nu va = Ra 1 2 a P r 1 3 a [ ( ) 2 P r a 3 ] 1 4 [ 1 + ( Rea ) 5 ] (4.42) Symbols in equation 4.41 are the same as in equation Radiation heat exchange between the glass and the sky Radiation heat transfer from the glass to the sky can be written as [39]: Q rvc = ɛ v πd ve Lσ(T 4 ve T 4 c ) (4.43) where T c is the sky temperature [K]. This temperature can be correlated to ambient temperature T a and dew point ambient temperature T dp [46]: and ɛ c = T c = ɛ 1 4 c T a (4.44) ( Tdp 100 ) ( Tdp 100 ) 2 (4.45) where ɛ c is the sky emissivity. All the emissivities are independent of temperature Global efficiency Once the theoretical model has been completed and the values of all the parameters have been defined it is possible to solve the system of balance equations; if the optical efficiency if also known, a complete knowledge of the PTC is obtained. The optical model defines all the optical losses and also allows to know how much solar radiation reaches the absorber. The thermal model defines all the temperatures and all the heat fluxes. But in order to compare results from the theoretical model with experimental ones it is necessary to express these results in a different way in order to obtain an efficiency equation in the form [13]: [ η = F r η o U ] l(t f,in T a ) (4.46) C DI where η: global efficiency; F r : heat removal factor; 65

86 Chapter 4. Mathematical model of a PTC U l : collector overall heat loss coefficient, W m 2 C 1 ; T f,in : fluid inlet temperature, C; T a : ambient temperature, C; C: concentration ratio; DI: direct irradiance, W m 2. It is clearly evident that this expression contains two new coefficients: U l and F r. U l is a single factor that resumes in one number all the heat losses; it can be seen as a heat transfer coefficient. The heat removal factor, instead, is defined as the ratio of the actual energy gain and the useful gain if all the receiver s surfaces were at the fluid inlet temperature [13]. In other words, it is the ratio of the actual heat transfer to the maximum possible heat transfer. This concept is derived from the treatment of flat-plate collectors, but since the receiver of a PTC is similar to a single tube of a collector, this concept is commonly adopted in thermal modeling of PTCs too. In order to explain how these two values are reached it is necessary to refer to the equations introduced at the beginning of the description of the thermal model (eq. 4.24) and rewrite them as follows: Q lost = Q crv + Q rrv = Q kv = Q cva + Q rvc α v Q rcr = U l A re (T re T a ) (4.47) U l is a total heat losses coefficient (W m 2 C 1 ) that accounts for all heat losses in the receiver. But proceeding on it is also possible to define a second coefficient that has about the same meaning, that is calculated adding all the thermal resistances between the external surface of the receiver and the fluid: U 0 = [ 1 + d re + d re ln d ] 1 re (4.48) U l h crf d ri 2λ r d ri Therefore the heat transferred to the fluid Q f will be equal to: Q f = τ v α r Q rcr U l A re (T re T a ) (4.49) Expressing the same quantity as a function of average fluid temperature (T f ): Q f = U la re (T re T f ) + dre 2λ r ln dre d re h crf d ri d ri (4.50) Combining the previous two equations it is possible to eliminate T re and obtain: Q f = F [ τ v α r Q rcr U l A re (T f T a ) ] (4.51) 66

87 4.5. Model implementation where F, is efficiency factor of the collector, to be expressed as: F = Now it is possible to write: 1 U l 1 U l + dre h crf d ri + dre 2λ r ln dre d ri = U 0 U l (4.52) Q f = F [ τ v α r Q rcr U l A re (T f T a ) ] (4.53) and therefore to define the above mentioned thermal heat removal factor: F r = ṁc [ ] p 1 e AreU l F ṁcp (4.54) A re U l where ṁ = fluid mass flow [kg s 1 ]; c p = specific heat at constant pressure [J kg 1 C 1 ]; F = collector efficiency factor [dimensionless]; it is the ratio of the actual useful energy gain to the one that would result if the collector absorbing surface had been at the local fluid temperature [13]. Notice that the term α v Q rcr must be subtracted from the numerator in order to respect the energy balance system (see Eq.??) Model implementation The mathematical model has been implemented in an integrated environment for technical computing [31], thus automating all the calculations; the model includes in a single file the routines for the calculation of the solar vector, the optical and thermal models and the importing operations of all experimental data. The output of each elaboration is a complete description of the steady state of the concentrator for a given setup and for the specific working conditions. Also a graphic part is included to visually show the correspondence of experimental data with computed ones Input parameters and variables To explain the solving method for the model, two different types of input values must be distinguished in the model: input parameters and input variables. The first ones represent PTC characteristics (geometrical, optical and thermal) that do not change with time; in other words, they have a single constant value. All the parameters adopted in the model are reported in Tab

88 Chapter 4. Mathematical model of a PTC Table 4.1.: Parameters for the mathematical model. Parameters Values Source of the data A ap 1.85 m 2 prototype A re 0.25 m 2 prototype d re 30 mm prototype d ri 25 mm prototype d ve 48 mm prototype d vi 46 mm prototype d 0.26 prototype f 0.25 m prototype h 0.25 m prototype L 2.6 m prototype L c 2.10 m prototype Z 48 mm prototype α r 0.95 [39] α v 0.02 [30] β 0.10 [25] ɛ r 0.95 [39] ɛ v 0.86 [30] λ r 237 W m 1 C 1 [39] λ v 1.40 W m 1 C 1 [39] ρ c 0.94 [?] σ 0.10 [25] τ v 0.93 [39] π φ r rad prototype 2 ζ r 1.50 µm [39] 68

89 4.5. Model implementation Table 4.2.: Variables for the mathematical model. Variables Values latitude longitude date and time local date and time orientation NS or EW air pressure in the glass boolean T f,in T f,out w f T a w a C C ms 1 C ms 1 RH % DNI W m 2 In order to be able to perform a simulation, some variables need to be entered. These are physical quantities whose value can change during the functioning, so they need to be measured. When comparing calculated data with experimental ones, these variables come from the results of the experimental procedure, and are imported in the model. Tab. 4.2 reports all the variables that are introduced in each run of the model Resolutive methods As stated before, the system composed of the four energy balance equations is a fourth order nonlinear algebraic system. If all the coefficients are known and independent of the variables, its solution process is straightforward. But in the present case some of the coefficients that influence convective heat exchange between the receiver and the glass (Q crv and Q cva ) depend on the temperatures of the glass and of the receiver: ( Q crv = f T m = T ) vi + T re 2 ( Q cva = f T film = T ) ve + T a 2 (4.55) (4.56) T vi, T ve and T re, that are the temperatures of the internal side of the glass, external side of the glass and external side of the receiver, are unknown; they can be calculated only when the system of heat balance equations is solved. This problem has been solved adopting a "While" function; since the only known temperatures are T f and T a, the starting temperatures have been chosen as: T in,film = T in,m = T f + T a 2 (4.57) 69

90 Chapter 4. Mathematical model of a PTC 0.75 Η T Figure 4.7.: Global (in blue), experimental (in green) and optical (in gold) efficiencies as functions of T where T f is the average temperature between T f,in and T f,out. The routine ends when the difference in T m and T film between one iteration of the while cycle and the following is less than C. Due to the nature of the system, its solution includes complex and negative values of temperatures. These values are neglected to keep only the consistent solution Model output When the energy balance system is solved, all temperatures and heat fluxes are known. At this time, it is possible to know every unknown quantity of the model. Output values can be shown in different ways, like tables or graphics. Tab. 4.3 shows a typical model output; notice that there are both input variables (date and time, orientation, DNI,...) and output values (Q loss, Q f, efficiencies,...) Results Fig. 4.7 and Fig. 4.8 show the main results of the mathematical model. The results shown refer to working and ambient condition equal to those of some experimental acquisitions. Running the model with these inpus has allowed 70

91 4.6. Results Η Η o T Figure 4.8.: Experimental data and global efficiency as functions of T and η o a comparison of calculated data with measured ones. In Fig. 4.7 calculated optical and global efficiency and experimental global efficiency are represented as functions of T. The graph includes optical efficiency because it is different between different measures, so it is essential to know its value for each point, to be able to compare global efficiencies. The independent variable on x-axis is defined as follows: T = (T f,in T a ) (4.58) DI In this way global efficiency is a linear function of the term T if the optical efficiency is constant (see Eq. 4.46). It is evident that optical efficiency is always higher than global efficiency. The importance of optical efficiency is very clear from the graph; it has to be pointed out that some end-effects, that are very relevant for a single PTC module, become less important when a line is considered. But the optical losses remain the biggest contribution to overall losses. Of course the difference between fluid mean temperature and ambient temperature influences efficiency, and this is obvious. But what is interesting is the importance of wind speed; the speed of wind contributes to enhance the heat loss process on the receiver. Measurements at the same working conditions but with different wind speed can differ up to some percent points of efficiency. Also errors in the measurement 71

92 Chapter 4. Mathematical model of a PTC of this variable can strongly influence the overall difference between calculated and measured data. Direction of wind should play a role, but this variable is not considered from the model. In order to visualize the global efficiency as a function of η o and T, Fig. 4.8 shows this two-variables function (a plane in the space) and the values of some measured experimental efficiencies. Notice that F r and U l are different for every measurement, so the represented plane is calculated for the mean value of these parameters. For the range of working conditions that have been tested, the efficiency of the PTC is between 72% and 57%. The fact that optical efficiency differs between different measurements makes it hard to draw comparisons between different temperatures, but a clear trend of reduction of efficiency with the increase of temperatures is visible. To end the analysis of the results, a work on errors has been performed and reported in a graphic form in Fig. 4.9 and Fig In Fig. 4.9, the percent error between experimental and calculated data is plotted against T. A weak tendency of the error to increase with T can be noticed, even if the two measures with the highest errors should be analyzed in detail, since the error seems to be too high with respect to the other points. In any way, even considering these two values, the overall average absolute percent error is 3.82% and the maximum overall percent error is 14%. The distribution of the probability density function of the error shows that the model tend to overestimate efficiency, even if this consideration should be studied more deeply, because this trend may be caused by errors in measurements rather than by some erroneous parameter in the model. Only a more extensive database of experimental values could help solving this ambiguity. 72

93 4.6. Results Error T 5 Figure 4.9.: Error between experimental and calculated efficiencies as a function of T 0.10 PDF x Figure 4.10.: Probability density function (PDF) of the error normal distribution 73

94 Chapter 4. Mathematical model of a PTC Table 4.3.: An example of model output. Date and time Orient. DNI T Tf Ta wf wa Qloss Qf ηo ηth η ηs 06/05/11 13:05 NS 918,74 0,01 30,41 21,25 0,09 0,00 27,33 942,22 0,64 0,97 0,62 0,63 06/05/11 13:17 NS 915,97 0,02 36,09 20,80 0,09 0,11 45,20 922,97 0,64 0,95 0,61 0,63 06/05/11 13:43 NS 918,59 0,03 45,01 20,96 0,09 0,00 51,78 929,78 0,64 0,95 0,61 0,61 06/05/11 13:52 NS 920,58 0,03 48,10 21,51 0,09 0,00 56,42 933,16 0,65 0,94 0,61 0,62 06/05/11 14:20 NS 927,74 0,05 62,80 22,01 0,09 0,77 132,56 889,91 0,66 0,87 0,57 0,53 06/05/11 14:44 NS 929,45 0,05 67,57 22,29 0,09 0,25 123,42 929,45 0,67 0,88 0,59 0,54 06/05/11 14:59 NS 924,82 0,05 71,23 22,82 0,09 0,34 138,04 929,79 0,67 0,87 0,58 0,51 06/05/11 15:13 NS 923,15 0,06 75,86 22,70 0,09 0,64 166,78 919,19 0,68 0,85 0,57 0,51 18/05/11 14:00 NS 887,64 0,02 37,27 22,22 0,09 0,88 62,76 946,88 0,67 0,94 0,63 0,62 18/05/11 14:16 NS 885,10 0,02 44,65 22,50 0,09 0,35 70,48 949,31 0,67 0,93 0,62 0,61 15/06/11 14:38 EO 857,88 0,05 68,01 26,25 0,09 0,18 109,78 890,89 0,68 0,89 0,60 0,64 15/06/11 15:06 EO 855,31 0,02 41,79 26,65 0,09 0,72 57,73 838,86 0,64 0,94 0,60 0,65 15/06/11 15:12 EO 851,03 0,02 44,03 26,36 0,09 0,74 64,25 805,03 0,63 0,93 0,58 0,64 16/06/11 13:00 EO 872,28 0,03 56,78 29,30 0,09 0,67 93, ,33 0,74 0,92 0,68 0,67 16/06/11 13:06 EO 874,06 0,03 59,19 29,42 0,09 0,42 93, ,41 0,74 0,92 0,68 0,67 16/06/11 13:13 EO 873,47 0,03 62,09 29,36 0,09 0,29 95, ,52 0,74 0,92 0,68 0,66 16/06/11 13:31 EO 871,12 0,01 38,77 29,84 0,09 0,16 35, ,33 0,73 0,97 0,71 0,68 16/06/11 13:41 EO 870,35 0,01 44,50 29,89 0,09 0,44 55, ,92 0,73 0,95 0,69 0,69 16/06/11 13:53 EO 870,06 0,02 51,12 30,11 0,09 0,00 47, ,09 0,72 0,96 0,69 0,67 74

95 Chapter 5. Annual simulation of performances As mentioned in the introduction, the original and main purpose of PTC.project was to acquire knowledge and develop experience regarding the application of PTCs in industrial environments to provide process heat. Therefore, once the model had been experimentally validated, the next step was to use it to simulate the behavior of a PTC field coupled with an industrial process load. Regarding performances of the PTC, the model developed has proven flexible and easy to handle for the purpose. But many information are needed in order to run a complete annual simulation. The following sections describe the meteorological data that have been used for the simulation, the process heat load that has been defined and the simulation scheme that has been used to process all these data and obtain the desired results Simulation scheme The simulation of the performances of a PTC throughout a one-year period is simply a succession of instantaneous simulations, since a steady mathematical model has been employed. This means that transient working periods are neglected. The error produced by this simplification depends on the time rate of change of the variables that influence simulations, mainly heat load characteristics and meteorological data. If variations in the values assumed by these parameters over the different simulation periods are small and slow with respect to the period chosen, then the results of the simulations will be reliable. If, instead, they increase or decrease in an intense way and fast, then it will be hard to obtain valid results from a succession of steady simulations. In the present case the time steps have been considered equal to 1 hour; this time is correct with respect to the load, that is basically constant in the chosen heat demand curve. Some doubts can be expressed with respect to meteorological data variations, but since the available database also worked with time steps of the unity of hour, then this arbitrary choice has been considered acceptable. Therefore a one-year simulation is simply the sequence of

96 Chapter 5. Annual simulation of performances one-hour steady state simulations, each one representing one hour of a typical year. Two softwares have been used to perform these simulations: Wolfram Mathematica, version 8.0 [31] has been used to write the mathematical model and to automate all the routines. Microsoft Excel has been adopted to define all the lists and tables that are the inputs for each simulation and also to visualize the final outputs. The simulation scheme is shown in Fig. 5.1; it is organized so to be read from left to right. Each one of the three blocks in the middle represent a Mathematica file (called notebook, having.nb file extension) that solves mathematical equations and executes some routines. The list on the left represents all the variables and parameters contained in a file named proprietà.xls that is the input for each simulation. The list on the right, instead, represents a second file, named risultati_simulazioni.xls that contains all the results that are saved by the different.nb files after each run. Following the scheme presented in the mathematical model, variables and properties inputs are divided in two different categories: 76 "fixed inputs" category comprehends all those parameters that are always the same when running an annual simulation. It is indeed divided into some sub-categories of homogeneous parameters. They are colored green in the scheme. geographical coordinates: latitude and longitude of the installation are necessary in order to calculate the sun s position in a cartesian system of coordinates having origin in the location of the installation; PTC geometry: all the geometrical parameters regarding the collector are defined in proprietà.xls; material s properties: optical and thermal properties of materials are required. The properties that do not depend upon temperature (therefore assume just a simple scalar value), or those whose dependency upon temperature is neglected, are simply listed in the properties file; fluid s properties: fluid properties strongly depend upon temperature. For these properties, the scheme in Fig. 5.1 is actually a simplification. In fact, in a manner similar to that explained in the presentation of the mathematical model, the proprietà.xls files defines some experimental values of the parameter at some different temperatures. Proprietà.xls file is called by a dedicated.nb file (not indicated in the scheme) that performs all the regressions on the experimental values in order to obtain the equations that express the

97 5.1. Simulation scheme Figure 5.1.: Scheme of the organization of files and models for annual simulations 77

98 Chapter 5. Annual simulation of performances mentioned parameter as a function of temperature and saves them in a temporary file (that is neither a.xls or a.nb, but is simply a.txt organized in a Mathematica pre-defined form). If fluid properties are not changed between two simulations there is no need to re-run the regression.nb file. Since the model allows calculation both with water (in liquid phase) and with heat transfer oil, the properties of both fluids are inserted in the proprietà.xls file. "variable" represents all the values that are a necessary input for each steady-state simulation (8760 single values). It contains, for instance, the date and time for which the steady-state simulation is being ran, or the wind velocity of that specific moment, and so on. It is important to point out that fluid mass flow rate and fluid inlet temperature belong to this category: this means that inlet fluid temperature and fluid mass flow rate can be different in different moments of the day, or of the week, thus allowing to simulate a real thermal heat load profile. The fact that inlet fluid temperature has been considered instead that delivery temperature depends upon the fact that in this way the mathematical model required much less elaboration time. For the designed fluid connection scheme this does not represent a problem, but it could be a shortcoming for different hydraulic connection designs. However, this aspect can be easily modified if necessary. Diagram in Fig. 5.1 also indicates the different.nb files and the variables that are called by these notebooks. At the top of each notebook is also an arrow: due to the way this simulation scheme has been built, some input variables (all belonging to the category of fixed variables) are defined inside the.nb files; the arrow describes these values. Notebooks and the values reported in the top part of the arrow are described below: 78 "posizione sole" is the first routine that must be ran: it calculates the sun s position. Its inputs and outputs are: input year, month, day and hour, in a a matrix form to identify all the moments for which the solar position is to be calculated (8760 rows in a yearly simulation); input latitude and longitude (scalar values that are the same for all time steps); output θ, a vector that contains a value of the angle of incidence for each moment of the input year, month, day and hour In addition to the date and time matrix and to the geographic reference extracted from proprietà.xls, "posizione sole" embeds and orientation variable the is set to a specific value in the declaration area of the file. It is a

99 5.1. Simulation scheme boolean variable: its 0 value sets the PTC axis on the east-west direction, while its 1 value sets it on the south-north direction. "efficienza ottica" is the second routine file: it acquires the incidence angle vector and the optical properties of the solid materials as well as the variable that define the geometry of the PTC. Its inputs and outputs are: input θ (the output of "posizione sole" file); input geometry, that defines all the required geometrical variables of the PTC; output η o, again, a vector in which each element is a value of optical efficiency corresponding to the linked value of incidence angle, and, therefore to a precise date and time for a given location. This notebook also embeds a specific variable called "concentratore"; since two different prototypes have been manufactured, is was interesting to easily perform comparisons. Therefore a decision was taken to insert two different geometries in the proprietà.xls file. In the simulations carried within PTC.project, these two geometers correspond to those of prototypes Univpm.01 and Univpm.02. By setting this variable to two different values it is possible to choose on which PTC the simulation is to be based. "efficienza termica" is the third routine file. It calculates all heat transfers that occur in the receiver at the specific working conditions, and, therefore, concludes the simulation process. Moreover this file includes all the routines to couple the above mentioned values with those coming from the other simulations to obtain the values of total collector efficiency and the outlet temperature. It is important to point out that these calculations are made considering the instantaneous mass flow rate and inlet temperature. All the outputs of this file are finally saved in an output file in.xls format. Summarizing what just stated, inputs and outputs of this file are: input θ: this file is the output of the first simulation file "posizione sole". Since instantaneous solar radiation is entered in the form of DNI (direct normal incidence) this angle is necessary to calculate the amount of energy really falling onto the aperture plane; input η o, the output of the previous file "optical efficiency" that is necessary to calculate total efficiency; input DNI, ambient temperature, relative humidity and wind speed; all these data are necessary to run the thermal efficiency simulation file; 79

100 Chapter 5. Annual simulation of performances input geometry, material properties and fluid properties: all of them necessary to calculate thermal losses; input fluid mass flow rate and inlet temperature, in the form of a 8765 rows matrix; output final table: the solution of the last module prints put all the information that is requested. Most important outputs are fluid outlet temperature and global efficiency. But also the temperature of each surface, or any single heat flux can be printed. The thermal efficiency file embeds a few variables, in particular variable "fluido" is used to choose between water and heat transfer oil as working fluid (with the same concept previously explained for the variable " concentratore") and also "evacuated receiver" allows to state wether the receiver is atmospheric or evacuated Meteorological data 80 Due to the recent widespreading of photovoltaic fields in Italy, and thanks to european programs also, different accurate and reliable databases are now available for radiation data with regard to italian or european territory References [47] and [48] are two of the most widespread. Also ISO standards exists. But the two electronic online databases have been created for Photovoltaic industry, while standards have been developed mainly for building applications. Data for building calculations do not need to be particularly precise, while, for what regards photovoltaics, the main issue is that data are expressed as total energy per month or average day of the month. This makes these sources of data useless for the purposes of PTC.project. Therefore, if a large amount of hourly DNI data is not available for a specify location (and this is generally the case for DNI), it is necessary to build customized databases that refer to extraterrestrial solar radiation and combine it with meteorological data and, using a clouding model, calculate global radiation and direct normal incidence from extraterrestrial radiation. This, again, moves the issue to finding cloud coverage data for a sufficiently large number of years in order to define a typical year starting from an adequate statistic database. Since, instead, other meteorological data (like ambient temperature, wind speed and relative humidity) are generally available for most location and with good historical coverage, they can be obtained just querying existing databases.

101 5.2. Meteorological data Solar radiation database In the case of the present study, as mentioned, no solar radiation data was available in a form adequate to the needs of the simulator. For this reason a collaboration has been asked to ENEA (Agenzia nazionale per le nuove tecnologie, l energia e lo sviluppo sostenibile) in order to create a typical year of solar radiation data. The result of this collaboration has been the acquisition of a database of solar radiation data based on extraterrestrial solar radiation and satellite images for the definition of a clouding index. The following explanation is based on a technical communication that ENEA has provided together with the database [49]. Typical Meteorological Year The basic meteorological unit for simulations is the Typical Meteorological Year (TMY), also called Test Reference Year (TRY). It is a collection of 8760 hourly values of all the meteorological variables that are relevant for a specific application, that is statistically representative (generally considered over a database of at least 10 years) of the yearly profile of these variables. In order to build such a collection the work must start from a validated database of the mentioned variables. The typical year is built by selection 12 months among all the ones in the database. Taking the first month as example, all the series representing the month of january are compared and one of them is chosen as the most representative. The choice is based on statistical criteria. Then the TMY is built by appending one after the other the 12 typical months. If correct statistical criteria are applied in choosing the typical months: the average monthly values of all the variables of the chosen months will be similar to the overall average of the same variables over all the occurrences of that month in the original database; the hourly sequences of the selected variables in the different days of the TMY will reproduce the real profiles. It is important to point out the fact that pure averaging processes are not to be applied when treating meteorological and climatological aspects of a precise location, because averaging, due to its intrinsic nature, trends to flatten all the variable and to build homogeneous profile over different days. Once the rough typical year has been defined it is necessary to correct some values and validate them: in fact, when two months that belong to different years are appended one after the other, it is necessary to link 81

102 Chapter 5. Annual simulation of performances Table 5.1.: Composition of the typical meteorological year month year January 2006 February 2006 March 2007 April 2006 May 2008 June 2006 July 2006 August 2010 September 2007 October 2009 November 2010 December 2008 them up in a proper way, avoiding unrealistic jumps in the variables. This is not a problem for solar data (the presence of a night between the day that ends a month and the following day that begins the next month allows to connect every two days without jumps) but it could be unrealistic to join two days with a 5 C temperature jump in between. Simple interpolation techniques allow the elimination of this jumps. For the present application, monthly series of hourly radiation data used to compose the typical meteorological year have been chosen out of a five-year long temporal series, going from january 2006 to december Table?? reports the chosen months. 82 SOLARMET physical model for determinating total and direct solar radiation by meteosat satellite images As mentioned, since an experimental database of DNI and GHI solar radiation data is not available for most locations in Italy, a physical model has been used to calculate DNI and GHI solar radiation data and, therefore, build the database from which the TMY regarding solar radiation is then extracted. The model used (SOLARMET, see ref. [50]) provides solar radiation (total and direct) reaching the ground for any specific location in the italian territory based on satellite images. A radiative transfer model (SBDART) developed at University of California is used to determine atmosphere transmissivity, ground reflection coefficient, and other essential parameters. The satellite maps, instead, are provided from the European Organization odor the Exploitation of Meteorological Satellites (EUMETSAT [51]); they are recorded every quarter of hour and have a

103 5.2. Meteorological data spatial resolution of a pixel for about 1 km 2. For each geographical position one image in clear sky conditions is selected: this image is chosen as a reference; by comparing each recorded image with the reference one, a cloud index K c is defined. To take in account the fact that atmosphere is crossed with different incidence angles at different times of the day and different moments of the year, also a second factor is considered: the clear-sky transmittance (K T c ). For each image the total clearness index is calculated as: K T = K T c K c (5.1) Then, unsing this index, global ground radiation is calculated from extraatmospheric radiation: GHI = EHI K T (5.2) A further step is necessary to produce DNI from GHI. Boland and Ridley correlation is used for this purpose [52]: 1 k = 1 + e α+β K T (5.3) Parameters α and β are assumed with the values suggested by Boland and Ridley, equal to -5 an 8.6 respectively Meteorological variables data Once the reference year had been defined, the remaining meteorological data were obtained for the actual months that compose the test reference year. Out of four different databases only one contained data for all the necessary months. Data are therefore obtained from the online database [53]. Unlikely there is no independent control on the adopted data. Imported data is a simple matrix for each month containing hourly values of ambient temperature, wind speed and relative humidity; since hourly data can be visualized only one day at the time on this website, a routine has been developed that calls the correct url and imports one month at each run. Imported data have been then automatically controlled and validated in order to obtain a database in the desired form; an extract of the database is reported in Tab.?? 83

104 Chapter 5. Annual simulation of performances Table 5.2.: Meteorological data Day-Month Year Hour DNI T a. RH v w W m 2 C % ms : : : : : : : : : : : : : : : : : :

105 5.3. Process heat demand daily, weekly and yearly profiles 5.3. Process heat demand daily, weekly and yearly profiles The construction of a process heat demand curve is a very important process. In fact, different choices in the definition of this curve can lead to very different results in terms of useful energy delivered from the PTC field. To perform simulations that have some sort of general validity, the heat demand curve has been built from real heat profile demands, after an astraction process. The industrial process that has been considered as a reference is a midlow temperature one; a fixed delivery temperature has been chosen, equal to 150 C. The second important variable considered is the required mass flow rate. With regard to this aspect, it is important to define a connection diagram of the PTC with the existing thermal power plant. Different choices on this aspect produce different mass flow rates through the PTC field. Since PTC installation on production plants are likely to be positioned on roofs of manufacture dedicated buildings, then the amount of surface that can be dedicated to the PTC field is limited. For the kind of process that is likely to be interested in such an installation, it is unlikely to have a situation where the PTC field can be dimensioned so to satisfy the entire process heat demand. Therefore the existing thermal power plant must be kept in service (also because, in any case, it would be necessary in absence of the solar source). Then the most cost-effective solution is to install the PTC field in such a way that, when in service, it simply reduces the energy to be delivered from the existing generators by pre-heating part of the heat transfer fluid that is coming back from the process. Such a scheme is shown in Fig. 5.2 and 5.3. The choice between introducing a heat exchanger between the process circuit and the PTC field circuit of using a three way valve will depend on specific factors related to the installation. A positive aspect of both these solutions lies in the less tight requirements on delivery temperature with respect to other possible connection schemes: if the fraction of power produced by the PTC field is limited, then an increase or a decrease in the temperature the fluid is reintroduced in the main circuit will be automatically corrected by the boiler. Therefore final delivery temperature to the process will not be influenced by this error. With both schemes shown, the mass flow rate that circulates within the PTC receivers can be chosen independent of the process mass flow rate. 85

106 Chapter 5. Annual simulation of performances Figure 5.2.: First possible hydraulic connection scheme Figure 5.3.: Second possible hydraulic connection scheme 86

107 5.4. Results of the yearly simulation But other constraints must be considered: a first constraint is linked to the necessity to avoid dangerous high temperatures on the receiver (too high temperatures will only produce a lower PTC thermal efficiency). A second constraint, linked to the first one, lies in the necessity to reach a turbulent flow inside the receiver: in fact if laminar flow develops in the receiver, the fluid will not be able to carry away enough energy from the receiver, and, therefore, high temperatures will be reached on it, thus going back the the problem above mentioned. For the simulations that will be shown a mass flow rate equal to 500 lh 1 has been adopted. Now that the process variables (i.e. delivery temperature and mass flow rate across the PTC are defined) it is possible to calculate how much energy a PTC field could theoretically send to the process. But there is a final aspect that needs to be considered: there will be times when the PTC could produce heat, but the process will not require any. Therefore, since no thermal storage has been considered, the amount of primary energy saving will not only depend upon producible energy, but it will also be a function of the profile of the process heat demand. It has already been stated that if a design concept is chosen so that the maximum amount of power producible from the PTC field is less than the amount of power required by the process, when the process is active, all the power produced by the solar field will be useful energy. But in this way, there will be moments when the PTC field could produce heat, but it will not because no heat is requested by the process at that moment. To consider this aspect working shifts need to be introduced. In the present simulation the process has been considered as a two-shift process, therefore it works 16 hours per day, starting at 5 am, and ending at 9 pm. One shift has been considered during the day of saturday (5 am to 1 pm), while no heat demand has been assumed on sundays. A singleshift process on working days (mon-fri) would be very disadvantageous for such an application, since would lead to an absence in process heat demand for many sunny hours. No plant stops have been considered, but the program has been built so that it is possible to introduce some empty weeks in the year. The heat demand profile input for the simulator is, therefore, a long table like the one in Tab Results of the yearly simulation Finally, after the simulation has run, a complete definition of total power hitting the aperture plane of the PTC field, producible power and useful 87

108 Chapter 5. Annual simulation of performances Table 5.3.: Heat demand profile table week day hour T in ṁ. process C lh 1 on/off=0/ : : : : : : : : : : : : : : : : : :

109 5.4. Results of the yearly simulation Figure 5.4.: Average day of the month of November: power hour by hour power is available for each of the 8760 hours that compose the TMY. Also every other entity that regards the PTC is defined. Results are produced in the form of a 8760 rows table. An extract of this report is presented in Tab All graphs are referred to a simulation based on the use of an array of about 10 modules of prototype Univpm.02, and, therefore, to a value of aperture plane surface equal to 50 m 2. Results in this form are difficult to interpret and to handle. For this reason some graphical outputs are also presented. The first graphical results, illustrated in Fig. A.12 shows the power that reaches the aperture plane, the producible power and the useful power for the average day of the month of November. Fig. 5.5 reports the average values of optical and global efficiency for the average day of the same month. Analogous graphs are presented for all the months of the TMY in Appendix A. Fig. 5.6 reports the monthly totals of the energy reaching the aperture plane, producible energy and useful energy delivered to the process. In the graph it is clearly visible that a two weeks stop has been considered for the month of august; in fact, in that month, the amount of useful energy is much smaller than the amount of useful energy that is calculated or the month of june, even if the total producible energy values are about the same between june and august. Also the stop in April is visible. The one in december, instead, is almost unappreciable. 89

110 Chapter 5. Annual simulation of performances Figure 5.5.: Average day of the month of November: optical and global efficiency hour by hour Figure 5.6.: Monthly energy totals from the simulation 90

111 5.5. Final energetic considerations Figure 5.7.: Representation of the summation of energy values throughout the hours of the TMY for the 50 m 2 aperture plane PTC. Highest line represents total energy falling into the aperture plane, middle line is Eprod, while bottom line is Eu 5.5. Final energetic considerations The main result of the simulation is obtained by the summation of all the useful energies produced. Fig. 5.7 represents the summation of the energy collected hour by hour on the 50m 2 PTC. The upper line represents the amount of energy that reaches the aperture plane (DNI only), the middle line represent all the energy that the PTC could possibly collect with the indicated working conditions ( 150 of inlet temperature and 500 lh 1 of mass flow rate) and the bottom line represents the amount of useful energy sent to the process. Once a total amount of useful energy has been calculated, the following step is to introduce a thermal heat generation efficiency in order to obtain a final value of saved primary energy. A reasonable value for heat generation efficiency in natural gas burners with mid-low temperatures is If this value is then divided for the surface of the PTC that has been considered in the simulation (50m 2 ), then the specific primary energy saving per unit area of PTC is obtained. Therefore: P ES = 8760 i=1 P u,i = η hg Au = (5.4) 91

112 Chapter 5. Annual simulation of performances This is, finally, the value of primary energy that is possible to save over a period of one year per unit aperture area of the PTC (expressed in Jm 2 year 1). It is important to observe that if a different (and more favorable) time profile of heat demand load was applied (keeping the same values for mass flow rate and delivery temperature) than the above calculated value could have reached numbers little over the unity. Higher values can be obtained with lower working temperatures. 92

113 5.5. Final energetic considerations Table 5.4.: An example of model output. week day hour θ DNI Ta Tf,in T wa wf Qprod Qu ηo ηt η W m 2 C C W 1 m 2 ms 1 ms 1 W W : n.a : n.a : n.a : n.a : n.a : n.a : : : : : : : n.a : n.a : n.a : n.a : n.a : n.a

114

115 Chapter 6. Remarks and conclusions The present thesis is mainly a description of the activities carried within PTC.project research. Since the project is still running, some results are temporary or need further investigation and study. But many of the original intents have already been met: two prototypes of PTC have been built and they are described in detail in the presents work; also the ideal intent of developing a solution that integrates the structural requirements and the geometrical needs has been accomplished with the use of a sandwich composite material. Under a technological point of view the approach has proven effective. The solution has another important characteristic: it is adequate for low production quantities, since initial investment costs are moderate; a test bench has been realized and experimental efficiency has been measured on prototype Univpm.01 with water as working fluid; a new test bench has been designed, the instrumentation for this bench has been acquired and its manufacture has started: this new bench will be suitable to execute test in compliance with ASHRAE 93/2010 Standard (and probably also with EN standard); a mathematical model has been developed to calculate PTC efficiency under different ambient and working conditions; the model has been validated via a comparison of predictions with experimental results; also a simulation environment has been developed to simulate the operation of a PTC field under realistic working conditions for any given time period; it includes the interaction between a PTC field and a process heat demand yearly profile. The system has also been applied to a realistic yearly heat demand profile coupled with meteorological data for a given location and the obtained results have been shown and discussed. 95

116 Chapter 6. Remarks and conclusions In the present work no economic considerations have been drawn, except for very general observations. But the analysis of the energetic results gives complete information in order to treat this aspect. From the results that have been shown it is possible to say that PTC is a mature technology that will play an important role in the near future. It is likely to imagine a spreading of PTCs in relation with process heat demand and solar heating/cooling in the near future: this developments will be drawn by technological advances on some components (mainly on the receiver and on the reflective surfaces) and by a reduction of costs on some other parts(tracking systems). As obvious, this process can experiment intense acceleration whereas State regulations will incentive this technology. 96

117 Appendix A. Results of the simulations In the following pages the results of the simulations are reported. All graphs refer to a PTC having characteristics indicated in Chapter 5. Each graph represents one month of the TMY with three values, that are the average of the values assumed from the corresponding variables on all days of the month. Variables represent: Pu_ave, violet: the useful power produced from the PTC field; Pprod_ave, violet + green: the amount of power that could be produced by the PTC; Pdir_ave, violet + green + orange: the DNI flux hitting the surface of the PTC. 97

118 Appendix A. Results of the simulations Figure A.1.: Average day of the month of January: power hour by hour Figure A.2.: Average day of the month of February: power hour by hour 98

119 Figure A.3.: Average day of the month of March: power hour by hour Figure A.4.: Average day of the month of April: power hour by hour 99

120 Appendix A. Results of the simulations Figure A.5.: Average day of the month of May: power hour by hour Figure A.6.: Average day of the month of June: power hour by hour 100

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