Análise experimental de perdas térmicas em um absorvedor fresnel linear, multi-tubos, de cavidade trapezoidal

UNIVERSIDADE FEDERAL DE SANTA CATARINA

PROGRAMA DE PÓS-GRADUAÇÃO EM

ENGENHARIA MECÂNICA

Selen Soares Sousa

ANÁLISE EXPERIMENTAL DE PERDAS

TÉRMICAS EM UM ABSORVEDOR FRESNEL

LINEAR, MULTI-TUBOS, DE CAVIDADE

TRAPEZOIDAL

Florianópolis

2018

Selen Soares Sousa

ANÁLISE EXPERIMENTAL DE PERDAS

TÉRMICAS EM UM ABSORVEDOR FRESNEL

LINEAR, MULTI-TUBOS, DE CAVIDADE

TRAPEZOIDAL

Dissertação submetida ao Programa de Pós-Graduação em Engenharia Mecânica da Universidade Federal de Santa Catarina para a obtenção do Grau de Mestre em Engenharia Mecânica.

Orientador:

Prof. Dr. Julio Cesar Passos

Florianópolis

2018

Ficha de identificação da obra elaborada pelo autor,

através do Programa de Geração Automática da Biblioteca Universitária da UFSC.

Sousa, Selen Soares

ANALISE EXPERIMENTAL DE PERDAS TÉRMICAS EM UM ABSORVEDOR FRESNEL LINEAR, MULTI-TUBOS, DE CAVIDADE TRAPEZOIDAL / Selen Soares Sousa ; orientador, Julio Cesar Passos, 2018.

91 p.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós Graduação em Engenharia Mecânica, Florianópolis, 2018. Inclui referências.

1. Engenharia Mecânica. 2. Energia Solar. 3. CSP. 4. Linear Fresnel. 5. Cavidade trapezoidal. I. Passos, Julio Cesar. II. Universidade Federal de Santa Catarina. Programa de Pós-Graduação em Engenharia Mecânica. III. Título.

Selen Soares Sousa

ANÁLISE EXPERIMENTAL DE PERDAS

TÉRMICAS EM UM ABSORVEDOR FRESNEL

LINEAR, MULTI-TUBOS, DE CAVIDADE

TRAPEZOIDAL

Esta dissertação foi julgada adequada para a obtenção do título de Mestre em Engenharia Mecânica, especialidade Engenharia e Ciências Térmicas e aprovada em sua forma final pelo Programa de Pós-Graduação em Engenharia Mecânica.

Florianópolis, 23 de março de 2018

Prof. Jonny Carlos da Silva, Dr. Eng.

Coordenador do Programa de Pós-Graduação em Engenharia Mecânica

Banca examinadora:

Prof. Dr. Julio Cesar Passos

Orientador / Presidente UFSC

Prof. Edson Bazzo, Dr.

UFSC

Prof. Jorge Luiz Goes Oliveira, PhD.

UFSC

Prof. Samuel Luna de Abreu, Dr.

Este trabalho é dedicado aos meus pais, meus melhores professores e fiéis amigos.

AGRADECIMENTOS

Gostaria de agradecer a todos aqueles que, de alguma forma, contribuíram para a conclusão deste trabalho e fizeram esta caminhada mais agradável.

Ao CNPq (Projeto 406357/2013-7), CAPES, POSMEC/UFSC e LEPTEN/BOILING pelo apoio e infra-estrutura oferecidos.

Aos amigos do LEPTEN e BOILING, Rafael Passarella, Isadora Limas, Mônica Machuca, Alex Cruz, Danielle Lima, Patrícia Bizzotto, Marcel van den Berg, Felipe de Castro, Juliano Oestreich, Felipe Nassif, Indyanara Bianchet, Gregori Rosinski, Ana Roberta, Pedro Alvim, José Lucas Miranda, Gabriela Conte, Victor Longen, Henrique Hipólito, Loic Tachon, entre outros, que fizeram parte do dia-a-dia e juntos dos quais pude aprender bastante. Em especial, aos colegas e amigos Alexandre Bit-tencourt de Sá e Victor Cesar Pigozzo Filho que contribuiram fortemente para a conclusão deste trabalho.

Aos amigos de longa data Marcelo Pereira, Felipe Oliveira, Lucas Brenner e Gabriel Neves. Também aos amigos da “República Patifaria”, “República Taberna” e “Grupo Noiz ki Samba”. Vocês também fazem

parte dessa história.

Aos professores da UFSJ, Túlio Panzera, Antônio Sabariz e José Antônio da Silva que construiram a base do meu conhecimento científico e pelos quais minha gratidão é grande. Aos professores da UFSC Julio Cesar Passos, Edson Bazzo e Álvaro Prata pelas suas contribuições para o trabalho e por servirem como exemplo e inspiração profissional.

Um agradecimento especial à minha irmã Julia Sousa e minha namorada Isabela Coutinho, duas jovens mulheres sonhadoras. Que vocês saibam perseguir os seus sonhos com a garra e determinação que eles merecem.

Finalmente agradeço aos meus pais, meus melhores professores, que moldaram meu caráter, temperamento e maneira de perceber o mundo. É difícil colocar em palavras toda a gratidão de uma vida. Vocês talvez representem algo muito superior a tudo o que almejo um dia ser. A sua simplicidade me mostra sempre o caminho para ser um ser humano melhor e saber levar a vida sem perder o foco no que é realmente mais importante, as pessoas, a família.

"E a coisa mais certa de todas as coisas, não vale um caminho sob o sol"

Caetano Veloso "Eu descobri que quando você realiza um sonho, você descobre também que existem sonhos ainda maiores para serem realizados" Carlos Wizard "É realmente verdade que você só pode ter sucesso melhor e mais rápido se ajudar os outros a prosperarem" Napoleon Hill

RESUMO

O projeto de um coletor Fresnel linear requer a minimização das perdas térmicas no absorvedor. Vários aspectos são considerados, tais como modificações na geometria, seleção dos materiais corretos, pintura seletiva de tubos, entre outros. Neste trabalho, um absorvedor do tipo cavidade trapezoidal, multi-tubos, foi experimentalmente avaliado em um ambiente controlado. As perdas de calor foram avaliadas considerando diferentes temperaturas de trabalho, configurações de pintura na superfície dos tubos, condições convectivas e também a presença de uma janela de vidro na face inferior da cavidade. Além disso, um modelo de perdas térmicas foi utilizado para comparação com os testes experimentais e otimização do absorvedor. Para os testes experimentais, os coeficientes globais de perda de calor, UL, foram plotados em função da diferença de temperatura entre

o elemento absorvedor e o ambiente, ∆T. Os resultados mostraram que os coeficientes globais de perda de calor podem ser minimizados em até 12.2 % se a tinta for aplicada apenas na parte inferior dos tubos. Além disso, a presença da janela de vidro mostrou-se crucial ao minimizar a perda de calor para todas condições experimentadas. O modelo numérico também mostrou que cerca de 81.8 % do calor total é perdido através da janela de vidro, os 18.2 % restantes deixam a cavidade através da carcaça de alumínio. Ainda, foi mostrado que modificando parâmetros como: materiais, geometria e pintura, as perdas térmicas poderiam ser reduzidas em até 38.2 %.

Palavras-chave: Energia Solar. CSP. Linear Fresnel. Cavidade

EXPERIMENTAL ANALYSIS OF HEAT LOSS FROM

A LFC’S MULTI-TUBE TRAPEZOIDAL CAVITY

ABSTRACT

A proper design of a Linear Fresnel Collector requires minimization of thermal losses in the receiver. Several artifices are used in this attempt, such as geometry modifications, material selection, selective tube paint-ing, among others. In this work, an indoors multi-tube trapezoidal cavity setup was experimentally studied. The heat loss was evaluated consider-ing different workconsider-ing temperatures, paintconsider-ing configurations, convective conditions and also the presence of a glass window placed on the cavity’s aperture. Additionally, a heat loss model was designed as a mean of comparison with the experimental tests and for guidance in the receiver’s optimization. For the experimental tests, the overall heat loss coefficients, UL, were plotted against the temperature difference between the absorber

and environment, ∆T . The numerical results showed that the overall heat loss coefficients can be minimized up to 12.2 % if the ink is applied just on the bottom part of the tubes. Moreover, the window glass application has shown to be crucial upon minimizing the heat loss for all the conditions considered. Finally, for natural convection conditions, about 81.8 % of the total heat loss is lost through the glass window, leaving 18.2 % to be lost through the aluminum walls. Additionally, the mathematical model indicates that the modification of parameters such as: material, cavity geometry and painting, could reduce the overall heat losses up to 38.2 %.

Keywords: Solar energy. CSP. Linear Fresnel. Trapezoidal cavity.

LIST OF FIGURES

Figure 1 – LEPTEN’s linear Fresnel collector . . . 22 Figure 2 – CSP technology main divisions (ENERGY, 2009) . . . 25 Figure 3 – Nova-1 receiver assembly by Novatec Solar [Adapted

from: Selig and Mertins (2010)] . . . 27 Figure 4 – One-dimensional conductive heat transfer representation 29 Figure 5 – Buoyant flow in heated horizontal plates, for the top

and the bottom surfaces (BERGMAN; INCROPERA, 2011) . . . 32 Figure 6 – Representation of the experimental setup (IRILAN,

2017) . . . 35 Figure 7 – Multi-tube trapezoidal cavity absorber module . . . . 36 Figure 8 – Cavity geometry and instrumentation profile showing

the thermocouple locations o the tubes and in the cavity 37 Figure 9 – Wind velocity measurements points in the entrance

section . . . 38 Figure 10 – Spectral reflectivity for stainless steel surface and 2, 3,

4, 5 and 6 layers of SOLKOTE HI/SORB dip coated (SOLEC, 2018) . . . 40 Figure 11 – Spectral absorptivity for stainless steel surface and 2

layers of SOLKOTE HI/SORB spray painting . . . 41 Figure 12 – Temperature behaviour for a given test . . . 43 Figure 13 – Zoom in: temperature profile for a given test obeying

the steady state criteria. Measurements once every 5 seconds . . . 44 Figure 14 – Tube’s temperature under steady state condition . . . 45 Figure 15 – Temperature profile displayed by tubes #1 to #6 . . . 45 Figure 16 – Average temperature displayed by tubes equidistant

from the centre line . . . 46 Figure 17 – Demonstrative of the overall heat loss curve’s behavior 48 Figure 18 – Overall heat loss coefficient comparison between the

three painting configurations for natural convection . 49 Figure 19 – Overall heat loss coefficient comparison between full

and partial painting under 1.9 m/s wind velocity forced convection . . . 50 Figure 20 – Overall heat loss coefficient comparison between

natu-ral and forced convection conditions for fully painted tubes . . . 52

Figure 21 – Natural convection and 1.9 m/s wind velocity forced

convection comparison for partially painted tubes . . . 52

Figure 22 – Overall heat loss coefficient versus wind velocity - a comparison considering fully painted tubes at a ∆T = 180 ◦C . . . . 53

Figure 23 – Overall heat loss coefficient comparison on tests con-sidering different window glass conditions, for fully painted tubes and natural convection . . . 55

Figure 24 – Overall heat loss coefficients considering fully painted tubes, a 2.9 m/s wind velocity - a comparison for glass window conditions . . . 56

Figure 25 – Thermal balance of the linear Fresnel receiver. The indices indicates the heat flow from which surface to which surface, according to Tab. 3 . . . 57

Figure 26 – Thermal resistance model for the LFC receiver . . . . 59

Figure 27 – Representative of considerations regarding the thermal fin model . . . 60

Figure 28 – Comparative between experimental and numerical re-sults for non-painted tubes . . . 64

Figure 29 – Comparative between experimental and numerical re-sults for full painted tubes . . . 65

Figure 30 – Comparative between experimental and numerical re-sults for partially painted tubes . . . 66

Figure 31 – Comparative between experimental and numerical re-sults for full painted tubes, considering εglass ≈ 0.85 and krw = 0.134 . . . 67

Figure 32 – Image of the real experimental setup . . . 77

Figure 33 – Receiver assembly . . . 78

Figure 34 – Electrical resistances . . . 79

LIST OF TABLES

Table 1 – Industrial segment and its respective temperature range for industrial heat [Adapted from: Sharma et al. (2017)] 21 Table 2 – Overall heat loss coefficients for different painting and

convective configurations . . . 56 Table 3 – Overview of subscripts of individual heat transport

mechanisms according to Fig. 25 . . . 58 Table 4 – Heat loss model results for non-painted tubes . . . 62 Table 5 – Heat loss model results for fully painted tubes . . . 62 Table 6 – Heat loss model results for strategically painted tubes . 63

CONTENTS

2.1 CSP and linear Fresnel technology . . . 25 2.1.1 Historical development . . . 26 2.1.2 Solar receiver and absorber . . . 26 2.1.3 Heat Loss on Solar Receivers . . . 27 2.2 Fundamental concepts regarding heat losses on solar receiver 29 2.2.1 Conduction . . . 29 2.2.2 Convection . . . 30 2.2.3 Radiation . . . 33 2.2.4 Composite heat exchange systems . . . 33

3 METHODOLOGY . . . . 35

3.1 Experimental setup . . . 35 3.1.1 Absorber module . . . 36 3.1.2 Instrumentation . . . 36 3.1.3 Power source - Varivolt and electrical resistances . . . 38 3.2 Test configurations . . . 38 3.2.1 Absorber temperature . . . 39 3.2.2 Selective painting and painting configuration . . . 39 3.2.3 Convective conditions . . . 41 3.2.4 Glass window . . . 41 3.3 Overall heat loss coefficient determination . . . 42 3.4 Experimental procedure and temperature behaviour . . . 42

4 EXPERIMENTAL RESULTS AND DISCUSSION . . . 47

4.1 Influence of absorber temperature over heat losses . . . 47 4.2 Influence of selective painting and painting configuration

over heat losses . . . 48 4.3 Influence of convective conditions over heat losses . . . 51 4.4 Influence of the glass window over heat losses . . . 54

5 HEAT LOSS MODEL . . . . 57

5.1 Heat loss model considerations . . . 57 5.2 Mathematical model results . . . 61 5.3 Comparative with experimental tests . . . 63

5.3.1 Possible causes for the discrepancy between tests and model 66 5.4 Using the model for cavity’s improvement . . . 67

6 CONCLUSIONS AND RECOMMENDATIONS . . . . 69

6.1 Considerations regarding the experimental tests . . . 69 6.2 Considerations regarding the mathematical model . . . 70 6.3 Recommendations for future work . . . 70

REFERENCES . . . . 73 Appendix A Images of the experimental setup . . . . 77

A.1 Real experimental setup . . . 77 A.2 Receiver assembly . . . 78 A.3 ht . . . 79

Appendix B Auxiliary tables . . . . 81

B.1 Material properties . . . 81 B.2 Mathematical model heat loss values for ˙qinput = 500 W . 82 Appendix C Experimental uncertainties . . . . 83

C.1 Absorber temperature . . . 83 C.2 Temperature difference . . . 83 C.3 Overall heat loss coefficient . . . 84

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1 INTRODUCTION

The industrial sector consumes a significant portion of the world’s overall energy production varying from country to country depending on industrial activities. Most of this energy is consumed either in electrical or thermal energy forms. While electrical energy is used for air condition-ing and operatcondition-ing motors, thermal energy is used in industrial process heating applications, such as drying, cooking, dehydration, sterilization, pasteurization, etc. (SHARMA et al., 2017). The brazilian industrial sector consumes around 41 % of the country’s overall energy production and a substantial share of this total energy is used for heating process (EIA, 2016; SHARMA et al., 2017). The direct conversion of the solar resource into heat has several advantages, such as not requiring a coupled power cycle for electrical conversion, and good process efficiency. In this context, Concentrating Solar Power (CSP) has been gaining space over other non-clean energy sources.

Industrial process heating is demanded for a wide variety of temperature ranges, depending on the industrial process. For a great portion of industrial segments, process heating applications occur at low and medium temperatures. Accordingly to Zauner et al. (2012), medium temperature range between 100 ◦C and 250 ◦C. Table 1 shows some examples of industrial segments and the range of temperature required for process heating.

Table 1 – Industrial segment and its respective temperature range for industrial heat [Adapted from: Sharma et al. (2017)]

.

Industrial Segment Temp. Range [◦C] Food and beverage processing 40-150

Textile 40-180 Pulp and Paper 60-200 Chemical and Pharmaceutical 100-200

Automobile 40-225 Lether, Rubber and Plastic 40-200

On the overall thermal energy demand on industry, around 60 % stays below 250◦C (SHARMA et al., 2017). Additionally, linear Fresnel

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collectors are among the main CSP technologies and are typically used to attain temperatures between 100◦C and 300◦C (ZHU et al., 2014). For these temperatures the linear Fresnel technology with non-evacuated absorber is a good option (MUÑOZ et al., 2011).

1.1 MOTIVATION

A linear Fresnel solar concentrator prototype was developed as part of the Heliotermica project at the LEPTEN laboratory. The project includes the conception and construction of an outdoors functional linear Fresnel workbench designed to operate with direct steam generation at temperatures up to 250◦C. An illustration of the actual LFC setup is shown by Fig. 1.

Figure 1 – LEPTEN’s linear Fresnel collector

Because of its requirements for thermal performance, the absorber is probably the most crucial element on the LFC. A proper evaluation of the thermal mechanisms occurring in the LFC’s absorber includes the incoming radiation heat, coming from the sun and entering the cavity’s aperture and also the heat lost from several mechanisms in the absorber.

Additionally, the heat loss evaluation for the outdoors setup is vulnerable to several environmental parameters such as temperature, solar irradiation, wind velocity, etc. Thus, in order to predict heat losses on the LFC under real conditions, it is recommended to perform the tests in

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a controlled environment. A shorter replication of the actual outdoors absorber was built and simpler tests were performed in a controlled environment (indoors).

1.2 OBJECTIVES 1.2.1 General objectives

This work studies and quantifies the thermal losses occurring on a multi-tube trapezoidal cavity receiver with non-concentrating radiation condition.

1.2.2 Specific objectives

1. To analyze the influence of the working temperature over heat losses;

2. To analyze the influence of the tube’s painting configuration over heat losses;

3. To analyze the influence of the convective conditions over heat losses;

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2 BIBLIOGRAPHICAL REVIEW

2.1 CSP AND LINEAR FRESNEL TECHNOLOGY

The CSP technology consists of devices that make use of mirrors or lens in order to concentrate the solar radiation on a smaller area, in order to achieve higher temperatures and better performance. There are four main CSP technologies: linear Fresnel, parabolic trough, parabolic dish and central receiver (tower). Figure 2 illustrates the mentioned technologies.

Figure 2 – CSP technology main divisions (ENERGY, 2009)

Among them, the LFC’s advantages include easy maintenance, re-duced structural requirements, and also slightly curved mirrors are cheaper to manufacture compared to parabolic through mirrors (MOGHIMI et al., 2015). The LFC has a lower overall optical efficiency when compared with PTC. However, it has a larger versatility in design and relatively

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lower cost (BARLEV et al., 2011; MORIN et al., 2012). 2.1.1 Historical development

Linear Fresnel collectors are a young technology. They were named after the french physicist Augustin-Jean Fresnel (1788 -1827), who among other things developed the Fresnel lens. The first LFC prototype was built in 1964 by the italian researcher Giovanni Francia. Francia designed an equipment to supply 38 kg/h of superheated steam at 450◦C and 100 atm (SILVI, 2005).

During the past decade a number of companies started to develop commercial projects. In the late 1990’s the Australian Solar Heat and Power (SHP - currently named AREVA Solar) and the Belgian Solar-mundo entered the market. In 2006 Novatec Biosol announced the first 1.4 MW linear Fresnel system to feed electricity into the electric grid (HABERLE et al., 2014).

2.1.2 Solar receiver and absorber

The receiver is the part of the collector that converts the concen-trated radiation into usable heat. It is basically composed by an insulated cavity and the absorber. The ideal receiver would be able to transfer a maximum amount of energy to the fluid, losing a minimum amount of heat to the environment.

The absorber is usually a single steel tube or a bundle of steel tubes which are placed inside the receiver’s cavity. The term "absorber" is often used to refer to the whole receiver set. The absorber heat loss is reduced by enclosing the tubes with an insulating cavity with a glass cover facing towards the primary reflectors, and also by using selective painting in the tube’s surface. An effective alternative is the use of a single tube with high absorptivity and low emissivity surface, surrounded by a vacuum holder glass tube. The absorber is probably the most critical components on a CSP project, because it plays a major role in the system’s output usable energy (HABERLE et al., 2014). Figure 3 shows a schematic of the Nova-1 receiver, which corresponds to the first commercial Fresnel power plant to supply energy to the electric grid.

However, thermal efficiency is not the only factor to be taken into account upon deciding for the type of absorber tubes. According to SchottSolar (2016), for parabolic trough and Linear Fresnel, the absorber tubes represent about 39 % of the overall cost of the CSP plant, which is a considerable factor over the absorber type decision.

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Figure 3 – Nova-1 receiver assembly by Novatec Solar [Adapted from: Selig and Mertins (2010)]

2.1.3 Heat Loss on Solar Receivers

Several heat loss mechanisms take place on a receiver and they need to be understood before taking action upon the device’s optimization. An optimum receiver should be able to minimize thermal losses, ensuring process efficiency. Several factors have influence over heat losses and among them are: geometry, materials, surface and painting characteristics, working temperature and atmospheric conditions. The minimization and the understanding of the heat loss mechanisms occurring on LFC receiver has been the object of study for many research.

For instance, Moghimi et al. (2015) applied ANSYS simulations to optimize a trapezoidal cavity receiver. In their work seven geometrical parameters were used as design variables. Used parameters included: cavity shape, coating, insulation thickness, absorber pipe selection, layout and spacing. They concluded that the top insulation thickness and the cavity depth are the most sensitive parameters.

Larsen et al. (2012) conducted experiments using a trapezoidal cavity absorber with a set of pipes for a Linear Fresnel collector. Their measurements revealed a stable thermal gradient in the upper portion of the cavity and a convection zone below it. They concluded that around 91 % of the heat transferred to the atmosphere occurs at the bottom transparent window, for a pipe temperature of 200◦C.

Regarding cavity geometry optimization, Facão and Oliveira (2011) performed CFD simulation using six absorber tubes of 12.7 mm internal diameter (15.87 mm outer diameter) and analyzed two geometri-cal parameters: receiver depth and insulation thickness. They concluded that a cavity with 45 mm depth presents the lowest global heat transfer coefficient. Regarding insulation thickness, 35 mm of rock wool presented

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a good compromise between insulation and shading.

Additionally, Manikumar and Arasu (2014), performed numerical and experimental studies to analyze heat losses on a trapezoidal cavity absorber with and without plate for a Linear Fresnel collector for natural convection condition. The authors concluded that natural convection plays an important role in the overall heat loss. Their experiments pointed that cavities with plate displayed overall heat loss coefficients 16.5 % lower as compared to cavities without plates.

An experimental study was conducted by Sahoo et al. (2013) to evaluate the effects of parameters such as tube temperature, cavity depth and ideal number of tubes for heat losses optimization on trapezoidal cavity multi-tube absorber. Among the principal results it has been observed that the dominant mode of heat losses from the absorber’s cavity is radiation. Hence using selective coating on the tubes and cavity inside wall, the overall heat losses can be minimized. Although, the heat losses are mainly due to radiation, those by natural convection accounted for 8 - 15 % and are, therefore, significant.

Saxena et al. (2016) numerically analyzed convective and radia-tive heat losses in a trapezoidal receiver. Among the considerations, the absorber element was considered as a flat plate in order to generate an overview independent of the number of tubes. The authors concluded that under steady state conditions radiation is the dominant heat transfer mode.

Finally, Irilan (2017) studied the heat losses in a similar apparatus (same cavity geometry and materials). In his experiments two experimental configurations were compared, considering a glass window in the cavity’s aperture and not considering it. The experimented temperature ranged between 100 - 200 ◦C. Tests were performed considering full painted tubes (same selective ink used) and natural convection. On his results the global heat loss coefficient ranged between 5.19 - 6.34 W/m2K and 7.25 -8.86 W/m2K for tests with and without the glass window, respectively. It was concluded that the glass window reduced the overall heat loss coefficient in between 11 - 17 %.

The results demonstrated by Irilan (2017) were consistent when compared to the literature. However the constructional material and geometry differed from the literature and some difference was expected on the results as well. Therefore, in this work, a proper methodology was applied, a steady state criteria was defined, the overall heat loss coefficient was obtained for partial painted tubes, as described in Chapter 3, and a mathematical model was used for comparison with the experimental tests.

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2.2 FUNDAMENTAL CONCEPTS REGARDING HEAT LOSSES ON SOLAR RECEIVER

Heat transfer (or heat) is the thermal energy in transit due to a temperature difference in space (BERGMAN; INCROPERA, 2011).

The receiver heat loss occurs through conduction, convection and radiation mechanisms along the elements. Those mechanisms com-bined with the cavity geometry and material characteristics determine the device’s heat loss. In this section, some important concepts for the mathematical model conceptualization are presented.

2.2.1 Conduction

The conductive heat transfer mechanism involves molecular ac-tivities which maintain this heat transfer mode. It can be seen as the energy transfer from more energetic particles to less energetic particles due to interaction among these particles. It is possible to quantify the conductive heat transfer using the Fourier equation. Figure 4 illustrates the normal heat flux through a wall, with thermal distribution and the equivalent thermal circuit

Figure 4 – One-dimensional conductive heat transfer representation

For the one-dimensional wall, as shown by Fig. 4, with an imposed temperature gradient dT_dx, the heat flux is represented by the Fourier’s law, in the following equation:

q00x= −k

dT

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where the heat flux q00x is the rate in which heat is being transferred per area perpendicular to the x direction. The parameter k is the thermal conductivity and is intrinsic to the wall’s material.

Considering a wall thickness L, and a temperature difference ∆T, the integration of Eq. 2.1, results in the conductive heat transfer

rate and can be written as: qx=

kA

L ∆T (2.2)

2.2.2 Convection

2.2.2.1 Average and local convective coefficient

A fluid with temperature T∞, velocity V , flows over a surface of area As. The total rate at which heat is being transferred can be obtained by integrating the local heat flux over the whole surface:

q = (Ts− T∞) Z

As

hdA (2.3)

where h is the local heat transfer coefficient. Additionally, an average convective coefficient h can be defined for the whole surface area, as:

h = 1 As

Z

As

hdA (2.4)

Now, the rate at which heat is being transferred by convection can be written as:

q = hAs(Ts− T∞) (2.5)

2.2.2.2 Natural convection

While forced convection is caused by external forces, in natural convection the fluid’s movement is caused by buoyancy forces in the fluid that are caused by the presence of a specific mass gradient which enables a gravitational force difference.

For a laminar flow on the boundary layer region, considering two dimensions and constant fluid properties in which the gravitational force acts on the negative direction of direction y. Also, consider an incompressible flow. The simplified equation which describes the fluid’s

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movement can be obtained from the Newton’s second law of movement and is known as the Navier-Stokes equation, as described in Eq. 2.6:

u∂u ∂x + v ∂u ∂y = gβ(T − T∞) + ν ∂2_u ∂y2 (2.6)

where u and v are the velocity components on x and y directions respec-tively, g is the gravity’s acceleration and ν is the kinematic viscosity of the fluid. On the previous equation, the term associated with the deformation of the material volume accomplished by viscous forces is obtained from the coefficient of volumetric expansion. If the variation of specific mass of the fluid is only a result of temperature variation, then:

β = −1 ρ  ∂ρ ∂T  (2.7) This thermodynamic property of the fluid quantifies the variation of specific mass for a temperature change, at constant pressure. It can be written in the following approximation:

β≈ −1 ρ

ρ∞− ρ

T∞− T

(2.8) For natural convection acting in external flows, the following equations govern most of engineering applications:

N uL = hL k = CRaL n (2.9) RaL= gβ(T − T∞)L3 να (2.10)

Equations 2.9 and 2.10 are known as Nusselt and Rayleigh equa-tions. The first one describes the ratio between convective heat transfer and conductive heat transfer. The second one is simply the product of Grashof, Gr, and Prandtl, P r, numbers, which can be found in Bergman and Incropera (2011).

2.2.2.3 Natural convection on the bottom and top surfaces of a heated plate

For a heated horizontal plate, the flow pattern depends exclusively of the plate’s surface orientation. In the inferior surface of the heated plate, a colder fluid tends to exert an ascendant movement which will be impeded by the plate. The flow is now horizontal before it can ascend beyond the plate’s limits. The fluid is heated but the heat transfer is

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somehow not effective in this process. Figure 5 demonstrates the flow on the inferior surface of a heated plate and the convective heat transfer coefficient can be obtained using Nusselt number correlation described by Eq. 2.11.

Figure 5 – Buoyant flow in heated horizontal plates, for the top and the bottom surfaces (BERGMAN; INCROPERA, 2011)

N uL = 0.27RaL

1

4 _{: (10}5≤ Ra_L≤ 1010_{) (2.11)}

Similarly, on the superior surface of a heated plate, as shown by Fig. 5 above, the flow occurs in portions of the fluid, which descend gaining heat and then ascend again, forming several vortices. This heat transfer process is somehow more effective than the one in the inferior surface. The Nusselt number correlation for the superior surface of a heated plate is described by Eq. 2.12.

N uL = 0.54RaL

1

4 : (104≤ Ra_L≤ 107) (2.12)

2.2.2.4 Natural convection on confined spaces

Considering a horizontal cavity heated by the bottom surface with a Rayleigh number ranging in between 3 · 105 _{and 7 · 10}9_{, the} convective coefficient in the cavity can be obtained from the following correlation proposed by Dropkin and Globe (1959):

N uL= 0.069RaL

1

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2.2.3 Radiation

The emissive power of a matter, E [W/m2], is the rate at which radiation is emitted from a surface per unit area, over all wavelengths and in all directions. It can be written as in Eq. 2.14, where ε is a surface property known as emissivity and σ is the Stephan-Boltzmann constant.

E = εσTs4 (2.14)

In order to evaluate the radiation exchange between surfaces, it is important to introduce the view factor concept. The view factor Fij is defined as the fraction of radiation which leaves surface i and is intercepted by surface j. There are several methods which can be applied to obtain the view factor, as for instance, shown by Bergman and Incropera (2011), Howell et al. (2010).

Considering two surfaces in an aperture, if surface 1 has higher temperature than surface 2 there will be radiative heat exchange from surface 1 to surface 2. The radiative heat exchange which takes place between those two surfaces is represented by Eq. 2.15

q12= q1= −q2= σ(T14− T24) 1−ε1 ε1A1 + 1 A1F 12 + 1−ε2 ε2A2 (2.15)

2.2.4 Composite heat exchange systems

In composite systems, it is convenient to use an overall heat transfer coefficient, UL, defined by Eq. 2.16:

q = ULA(T1− T2) (2.16)

Finally, the overall heat loss coefficient can be obtained using Eq. 2.17 below:

UL=

q A(T1− T2)

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3 METHODOLOGY

3.1 EXPERIMENTAL SETUP

The experimental setup consisted of a multi-tube trapezoidal cavity absorber module installed on a controlled indoors environment. In this case, no solar radiation is incident over the cavity and the heat losses are evaluated for a non concentrated solar radiation condition. A schematic of the experimental setup is shown in Fig. 6.

Figure 6 – Representation of the experimental setup (IRILAN, 2017)

The setup is consisted of the multi-tube trapezoidal cavity ab-sorber module, a varivolt transformer, T and K type thermocouples, AC watt transducer and an Agilent data acquisition system. Each tube inside the absorber held a cylindrical electrical resistance as heat supply. Also, an axial fan with a 55 W power was used to flow wind longitudinally in the absorber.

The apparatus was designed to operate up to a 350◦C maximum temperature. Therefore, the setup can be used to predict heat losses in the LFC on a non concentrating condition for any medium temperature range. The actual experimental setup is represented in Appendix A.1. The setup’s components are described in the following sections.

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3.1.1 Absorber module

The absorber module has the same geometry as the module used on the LFC constructed by the LEPTEN laboratories (outdoors). The indoors receiver used in this work is 1 m long, and as described by Pigozzo et al. (2018), the actual outdoors receiver is 12 m long. The cavity is built using two folded aluminum sheet of 2 mm thickness. The spacing between the aluminum sheets is filled with rock wool. Six stainless steel tubes, each with an outer diameter of 25.4 mm, were used as the absorber elements and they were fixed at the top of the cavity’s aperture. Figure. 7 illustrates the absorber module. The receiver was kept suspended with a 1.5 m distance between the aperture and surrounding objects.

Figure 7 – Multi-tube trapezoidal cavity absorber module

3.1.2 Instrumentation

3.1.2.1 Data acquisition system

The absorber module was instrumented with K and T type sheath thermocouples. K type thermocouples were attached to the bottom surface of each tube and another one at the top surface of tube 3. Also, T type thermocouples were used to measure the environment air, window glass, rock wool and the aluminum wall temperatures. In total, sixteen temperature points are measured in the experimental setup, plus the room’s temperature. The setup’s instrumentation was implemented in the middle section of the absorber in order to avoid the influence of the extremities. The instrumentation profile is illustrated in the scheme of Fig. 8, where the thermocouples are indicated.

An Agilent, model 34972A, was used as the data acquisition system. The software Benchlink Data Logger Pro was used to interpret the electrical signals produced by thermocouples and watt transducer.

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Figure 8 – Cavity geometry and instrumentation profile showing the thermo-couple locations o the tubes and in the cavity

3.1.2.2 Watt transducer

An "Ohio Semitronics" electrical watt transducer, model No. PC5-119C, input power ranged from 0 to 5 kW, was used to measure the total power dissipated by the electrical resistances. The equipment generates an output signal ranged from 0 to 10 Vcc.

3.1.2.3 Anemometer

A Reed hot wire anemometer, model SD-4214, was used to measure the velocity of the wind incident over the absorber. Once the fan is turned on and positioned longitudinally with the receiver. The wind velocity is considered as an average of the velocities in six different points, adjacent to the setup, all 10 cm distant from the cavity, measured in the entrance section. Figure 9 displays the positions at which the wind velocities are measured.

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Figure 9 – Wind velocity measurements points in the entrance section

3.1.3 Power source - Varivolt and electrical resistances

The used varivolt transformer, model TDGC2-10 10 KVA, is used to control the electrical power supplied to the electrical resistances. The device is inputted for a mono 220 Vac and the output signal ranged between 0 - 250 Vac.

The electrical heaters have a 19 mm outer diameter and could each supply a maximum heat of 500 W with a 96 Ω ±2 % electrical resis-tance. The tubes have an internal diameter of 22.5 mm. For positioning the resistances in the centre of tubes, a metal wire was wrapped around the resistances in the extremities. Figure 35 on Appendix A demonstrates the actual tube - resistance setting.

3.2 TEST CONFIGURATIONS

The heat loss of the trapezoidal cavity absorber was evaluated in a controlled environment. The room’s temperature was controlled by adjusting the room’s air conditioning system to 20◦C. In any case, the room’s temperature was monitored for reference with ∆T . The humidity of the air was not monitored and therefore ignored. There was no atmo-spheric wind incident over the experimental receiver module. The forced convection considered in the tests was an exclusive result of the fan. As described in section 1.2, tests were conducted in order to evaluate the effect of specific constructional, working and atmospheric conditions.

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3.2.1 Absorber temperature

It is known that the increasing temperature difference will also increase thermal losses. However, the behavior of this cavity, in terms of heat losses, for different temperatures, is not known yet.

The main parameter analyzed to make the comparison is the overall heat loss coefficient.

The overall heat loss coefficients, UL, were experimentally evalu-ated around six different absorber temperatures, 100◦C, 125◦C, 150◦C, 175 ◦C, 200 ◦C and 225 ◦C for each test configuration. The absorber temperature was estimated as an average temperature of the six tubes. 3.2.2 Selective painting and painting configuration

Selective coating is used to improve solar radiation absorptivity. Several authors have already studied and demonstrated the thermal efficiency improvements which can be accomplished with the application of selective painting on absorber tubes (SINGH et al., 2010; KHAN, 1999; NEGI et al., 1989).

In this work three painting configuration are considered. Naked tubes (polished stainless steel) were evaluated, and painted tubes were experimented with a full painting. A third configuration consisted of painting only the bottom part of the tubes. The bottom part of tubes is the portion that, on real operation condition, will receive the concentrated radiation. In this work we refer to this configuration as "partial painting".

On real operational conditions, the upper half of the tubes (facing the upper absorver wall) does not receive solar radiation, and since the naked tube’s surface has a lower thermal emissivity than the coating (SOLEC, 2018), there is no need for painting the upper part of the tubes.

The selected tubes are made of polished stainless steel AISI 304, and their surface emissivity is about 0.17. The ink’s manufacturer provides the spectral reflectivity, which depends on the number of painting layers, as shown by Fig. 10.

Considering that the ink doesn’t allow any radiative transmission, then:

τλ= 0 (3.1)

the spectral absorptivity can be obtained from:

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Figure 10 – Spectral reflectivity for stainless steel surface and 2, 3, 4, 5 and 6 layers of SOLKOTE HI/SORB dip coated (SOLEC, 2018)

also, the Kirchhoff’s law displays that:

αλ= ελ (3.3)

The tubes were painted using a paint gun and 2 layers of ink. From the equations above, the graph for spectral absorptivity can be obtained for stainless steel and 2 layers of painting and is demonstrated in Fig. 11.

Solar radiation has most of its energy on the left part of the graphs in Fig. 11 (lower wavelengths) and will, therefore, be absorbed in the correspondent spectral absorptivity. On the other hand, the heat loss occurring in the receiver considers temperatures in the range of 60 - 240◦C and these temperature emissions occur in the right part of the graphs in Fig. 11 (higher wavelengths) and will, therefore, emit and absorb in the correspondent spectral absorptivity.

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Figure 11 – Spectral absorptivity for stainless steel surface and 2 layers of SOLKOTE HI/SORB spray painting

3.2.3 Convective conditions

The wind conditions will play a very important role on the heat losses on the outdoors LFC. It is desireble to find out the influence of wind speed over our receiver and how it varies along with temperature. Tests were conducted for natural and forced convection condi-tions, considering 1.9 m/s and 2.9 m/s wind velocities for forced convec-tion. The average wind velocity was estimated as the average flow on six different measuring points on the entering section of the absorber. 3.2.4 Glass window

Finally, the presence of a glass window creates a greenhouse effect by trapping air inside the cavity mouth, hence preventing atmospheric air to reach the tubes. Since the emission from the absorber tubes is in the infrared spectrum, the glass window will block the tubes’ radiation, thus the heat losses are reduced even further. It is desired to evaluate how much heat loss can be prevented by this feature. Tests were performed with and without a glass window on the cavity’s aperture.

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3.3 OVERALL HEAT LOSS COEFFICIENT DETERMINATION To evaluate the heat losses, heat was dissipated by the electrical heaters inside each absorber tube and as the system reached steady state condition, the heat loss from the tubes, Qtubes, equals the rate in which heat is transferred from the absorber to the environment, Qabs. That can be written as:

Qtubes= Qabs (3.4) The absorber heat loss per unit length, Qabs, is assumed as equal to the total power dissipated by the resistances, Wele, when the system achieve the steady state condition, which is written in Eq. 3.5:

Qabs= Wele (3.5)

The average absorber temperature, Tabs, is calculated considering the average of the six tube’s bottom surface temperatures,

Tabs=

T1+ T2+ T3+ T4+ T5+ T6

6 (3.6)

Finally, the overall heat loss coefficient, UL, can be deduced from Eq. 3.7:

Qabs= ULAabs(Tabs− Tenv) (3.7) With exception of the extremities, the absorber is considered to be longitudinally isothermal. Also, the area Aabsof the tubes is considered as if all tubes merged in a single rectangular tube with edges of 25.4 mm and 152.4 mm. The uncertainty in data was based on the standard uncertainties of K and T type thermocouples which are 2.2◦C or 0.75 % for K type and 1◦C or 0.75 % for T type. The uncertainty of the electric power transducer is 0.5 %. The maximum combined uncertainty for the overall heat transfer coefficient is around 2.8 % for the experimental data analyzed.

3.4 EXPERIMENTAL PROCEDURE AND TEMPERATURE BE-HAVIOUR

For the execution of tests, initially, there is no power being dissi-pated by the electrical heaters and the system is in thermal equilibrium with the environment. The power input is then set from zero to a given power, and by doing so, the absorber temperature Tabs rises from Tenv to the equilibrium temperature (steady state). Initially, the temperature

43

goes up rapidly, but will soon decelerate and tend to an asymptote. Even-tually, it will reach an almost steady state condition. In this process, the temperature profile presented by the absorber is similar to the profile presented by Fig. 12. In this figure, the y axis correspond to ∆T and the x axis to the nth _{measurement, which was collected once every minute.}

Figure 12 – Temperature behaviour for a given test

The current methodology assumes steady state condition (steady state criteria) once the tendency of the temperature curve displays a variation lower than 0.5 ◦C within a 10 minute time range. Once the steady state condition is reached, a zoom in the absorber temperature Tabsshows small temperature variations as represented by Fig. 13, below. Those variations occur due to variations in the electrical grid supply, on the room’s temperature and interference such as people walking and causing small forced convection. In Fig. 13, data was collected once every 5 seconds.

Figure 14 displays the temperature for each of the six thermo-couples under steady state condition.

The temperature profile displayed by each of the tubes are observed in Fig. 15. It can be observed that they displayed irregular temperatures which occur mainly due to uncertainties in the electrical resistance values, ±2 % as mentioned before, and uncertainties caused by the thermocouple’s fixation. In a different manner, Fig. 16 displays

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Figure 13 – Zoom in: temperature profile for a given test obeying the steady state criteria. Measurements once every 5 seconds

the average temperature, in pairs, in tubes equidistant from the centre (average of tubes #1 and #6, #2 and #5, #3 and #4). From Fig. 16 it can be seen that the tubes closer to the center display higher temperature values than the tubes on the extremities, which was already expected, since they are surrounded by other tubes (heat sources).

In this work, for all experimental tests which are be described in Chapter 4, data was collected 300 times with intervals of 5 seconds between them, once the system has reached the steady state criteria described before, for every mentioned temperatures and configuration. Each point in graphs, which are displayed in the results, were considered as an average of the 300 measurements.

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Figure 14 – Tube’s temperature under steady state condition

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Figure 16 – Average temperature displayed by tubes equidistant from the centre line

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4 EXPERIMENTAL RESULTS AND DISCUSSION

Prior to the experimentation, the process included the setup’s construction, instrumentation, tube preparation and painting. After the experimentation, the data processing took place. The whole process took about a eight month time period. At the same time, the author participated in the construction of the outdoors experimental setup demonstrated in Fig. 1. In the indoors setup, the experiments were performed combining the test conditions described in Chapter 3 and the results are displayed in the following sections.

As mentioned before, the overall heat loss coefficients were ex-perimentally deduced for absorber temperatures around 100◦C, 125◦C, 150◦C, 175◦C, 200◦C and 225◦C. During the experiments, the room’s temperature remained within the range of 20.4 - 23.9 ◦C. Moreover, a Tabs = 200◦C was chosen as reference temperature as a mean of com-parison between test conditions. Therefore ∆T = 180◦C was chosen to compare results. That temperature difference reference choice can be explained by the fact that this temperature applies to several medium temperature industrial processes, accordingly to Sharma et al. (2017).

The content of this chapter is based on the following articles: Sousa et al. (2017a) and Sousa et al. (2017b).

4.1 INFLUENCE OF ABSORBER TEMPERATURE OVER HEAT LOSSES

For all experimented conditions, the performed tests revealed a pattern in the overall heat loss coefficient for a temperature variation. As expected, the heat loss coefficient increases with the increasing absorber temperature for all experimental conditions. The obtained values of UL were plotted against temperature difference between the absorber and the environment for all test conditions. The curve’s derivative tends to increase along with the temperature for all experimented conditions. That fact can be explained by the fact that radiative heat losses tend to play an increased role on the overall heat losses on higher temperatures. For radiation, the heat loss increases with temperature on the 4th _{power, as} demonstrated in Eq. 2.14. Figure 17 demonstrates the overall heat loss behavior, which represents a tendency for all test conditions.

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Figure 17 – Demonstrative of the overall heat loss curve’s behavior

4.2 INFLUENCE OF SELECTIVE PAINTING AND PAINTING CON-FIGURATION OVER HEAT LOSSES

Tests were performed in order to evaluate the painting configu-ration influence over heat losses and the overall heat loss coefficients. For those tests, three different painting configurations were tested combining with different convective conditions. For each of them, the ULvalues were plotted against temperature difference and a polynomial best-fit curve was created.

It was observed that the unpainted tubes have the smallest UL values due to its lower thermal emissivity. However, the use of unpainted tubes is not of practical interest because under actual operation condition it is desirable for the tubes to be painted, at least on the bottom surface, which is the surface that receives the concentrated solar radiation. Ad-ditionally, the results show that partially painted tubes have a slightly lower UL as compared to fully painted tubes.

Figure 18 compares the overall heat loss coefficients for differ-ent painting configurations in natural convection. It can be seen that fully painted tubes displayed a heat loss coefficient ranged between 6.58 - 8.52 W/m2_{K, with an overall heat loss coefficient estimated in} 7.83 W/m2_{K for a 180}◦_{C temperature difference. It can also be observed}

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that partially painted tubes displayed a heat loss coefficient ranged be-tween 6.52 - 8.21 W/m2K, and the UL was estimated in 7.74 W/m2K for a ∆T = 180◦C. Finally, the unpainted tubes displayed a heat loss coefficient ranged between 6.28 - 8.37 W/m2_{K, and the overall heat loss} coefficient was estimated in 7.50 W/m2_{K for a ∆T = 180}◦_{C. The results} indicate a 1.1 % difference between the two painted conditions, and a 4.4 % difference between fully painted tubes and unpainted tubes, both for the reference temperature difference of 180◦C.

Figure 18 – Overall heat loss coefficient comparison between the three painting configurations for natural convection

Similar results are demonstrated for a 1.9 m/s wind velocity forced convection in Fig. 19. This time, fully painted tubes showed an overall heat loss coefficient ranging between 8.25 - 10.20 W/m2_{K, and} the UL of 9.69 W/m2K for ∆T = 180◦C. On the other hand, partially painted tubes displayed a UL ranged between 7.84 - 10,07 W/m2K, with an overall heat loss coefficient of 9.52 W/m2K for the referenced temperature difference. This result represented a 1.7 % difference in heat loss between the two painting conditions.

The difference in heat loss coefficients between those two painting conditions can be attributed to the radiation heat exchange, which takes place between the top surface of the tubes and the cavity. The radiation coming from the top surface of tubes is then conducted by the aluminum

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Figure 19 – Overall heat loss coefficient comparison between full and partial painting under 1.9 m/s wind velocity forced convection

sheets to the outer part of the absorber and then goes to the environment by radiation and convection. Comparing the experimental heat losses for partially painted tubes and fully painted tubes, the difference was in the range of 0.5 – 3.1 % along the whole temperature range. Also, it was observed that this difference tends to increase along with the absorber temperature and wind velocity.

Singh et al. (2010) performed similar heat loss tests considering a multi-tube trapezoidal cavity absorber. In their work, ordinary black painting and selective surface coating were considered and the overall heat loss coefficients were obtained for temperatures ranging between 75 - 175◦C. They also tested using a window glass covering the cavity’s aperture. The heat loss coefficients obtained in their study ranged between 3.83 - 5.55 W/m2_{K for the temperatures mentioned above for full painted} tubes using selective coating under natural convection.

In the present work, if the same test conditions are considered, for Tavg= 175◦C, the overall heat loss coefficient obtained was 7.76 W/m2K, which represents a 39 % increase in heat losses compared to the litera-ture. The reasons for the increased temperature may include our cavity geometry and material.

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4.3 INFLUENCE OF CONVECTIVE CONDITIONS OVER HEAT LOSSES

Tests were also performed in order to evaluate how the increasing wind velocity increases the overall heat loss coefficient. In those, fully painted tubes’ heat loss were evaluated on tests for the six described temperatures, considering a glass window in the cavity’s aperture. The experimented wind velocities were 0 m/s, 1.9 m/s and 2.9 m/s. Addition-ally, tests were also performed for partially painted tubes for the same glass conditions, for 0 m/s and 1.9 m/s. The results of the experiments, described below, showed that the increasing wind speed also increases the overall heat loss coefficients. Moreover, the partial painting also reduced the overall heat loss coefficients for forced convection conditions.

Comparing the overall heat loss coefficients on natural and forced convection conditions, the results demonstrated a considerably increase along with the increasing wind velocity. Figure 20, compares convective conditions for fully painted tubes. The results for the natural convection curve and 1.9 m/s curve were previously described, in Figs. 18 and 19. It can be seen that the value of the overall heat transfer coefficient for a 2.9 m/s wind velocity forced convection ranged between 9.22 -11.50 W/m2_{K, and it corresponds to 10.47 at ∆T = 180}◦_{C. That would} mean a 8 % difference with 1.9 m/s forced convection and a 33 % difference with natural convection condition. The difference in UL between natural convection and 1.9 m/s forced convection is of 23.7 %.

A similar convective comparison, this time for partially painted tubes, is displayed by Fig. 21. As mentioned before, the values of UL for a ∆T = 180 ◦C are 7.74 W/m2_{K and 9.52 W/m}2_{K for natural} convection and 1.9 m/s forced convection, respectively. This represents a 23 % difference between them.

Additionally, Fig. 22 illustrates how the overall heat loss coeffi-cient varies along with the increasing wind speed at a 180◦C temperature difference for fully painted tubes. The tests revealed an almost linear variation of UL along with the wind velocity.

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Figure 20 – Overall heat loss coefficient comparison between natural and forced convection conditions for fully painted tubes

Figure 21 – Natural convection and 1.9 m/s wind velocity forced convection comparison for partially painted tubes

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Figure 22 – Overall heat loss coefficient versus wind velocity - a comparison considering fully painted tubes at a ∆T = 180◦C

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4.4 INFLUENCE OF THE GLASS WINDOW OVER HEAT LOSSES Tests were performed in order to evaluate the influence which a window glass placed in the cavity’s aperture has over heat losses and therefore the overall heat loss coefficient. In those tests, the absorber module’s heat loss was evaluated for four different conditions. Those were the combination of natural convection and forced convection (2.9 m/s wind velocity), also, the tests considered or not the window glass. For each of them, the overall heat loss coefficients, UL, were plotted against temperature difference.

As expected, the heat losses increased along with the absorber’s temperature and also with wind velocity. Figure 23 displays the overall heat loss coefficients for fully painted tubes considering a window glass and also for fully painted tubes without the window glass over natural convective condition. It can be observed that the presence of the window glass contributes to a significant reduction of heat losses, as the curve considering the glass stays below the curves which doesn’t consider the glass, for all experimented temperatures. The overall heat loss coefficient stayed in between 6.58 - 8.52 W/m2_{K for the glass considering condition} and between 8.28 - 10.49 W/m2_{K for non-glass condition. For instance,} at 180◦C temperature difference, the overall heat loss coefficients were 7.83 W/m2_{K and 9.78 W/m}2_{K for the respective test conditions. This} represents a 24.9 % increase on the overall heat loss. Therefore, it can be seen that the presence of that window glass represents a reduction in heat losses on natural convective conditions. That can be explained by the fact that the window glass traps air inside of the cavity, reducing convective losses to environment. Because the glass is opaque to medium temperatures radiative wavelengths, it also retains the tube’s radiation which reach the glass.

The effects of forced convection over the heat loss, comparing those two constructional conditions, are demonstrated by Fig. 24. The overall heat loss coefficients for fully painted tubes with and without a window glass are displayed considering a 2.9 m/s wind velocity. It can be observed that, in this time, the presence of the window glass reduces significantly the heat losses. For instance, the overall heat loss coefficients range in between 9.22 - 11.50 W/m2_{K for tests considering a glass window} and in between 21.00 - 23.80 W/m2_{K for a non-glass condition. At 180}◦_C temperature difference the UL were 10.67 W/m2K and 23.41 W/m2K for the respective tests. As a mean of comparison, these results represented a 119 % difference between test conditions.

Now comparing similar glass conditions represented in Fig. 23 and Fig. 24, it can be seen that the value of ULfor window glass condition

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Figure 23 – Overall heat loss coefficient comparison on tests considering different window glass conditions, for fully painted tubes and natural convection

increased 36.2 % from natural to forced convection condition, while for non window glass condition, the ULincreased 139 %. It can be concluded that the presence of a window glass is crucial upon minimizing heat losses, specially if forced convection is incident over the receiver.

Irilan (2017), as mentioned in Chapter 2, studied the heat loss on a similar receiver for conditions with and without a glass placed on the cavity’s aperture. He has found overall heat loss coefficients UL varying

in between 5.2 - 6.3 W/m2K and 7.2 - 9.0 W/m2K for conditions with and without the glass, respectively. The results differ in 35.2 % and 13 %, respectively, with the results presented in this work. The explanations for the difference in results are inconclusive.

The range of overall heat loss coefficient for all cases demon-strated on previous sections are shown in Tab. 2.

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Figure 24 – Overall heat loss coefficients considering fully painted tubes, a 2.9 m/s wind velocity - a comparison for glass window conditions

Table 2 – Overall heat loss coefficients for different painting and convective configurations

.

Overall heat loss coefficient - UL [W/m2K]

No glass Window glass

Full paint. No paint. Full paint. Str. paint. Natural conv. 8.31-10.17 6.53-8.17 6.58-8.52 6.52-8.21

Forc. 1.9 ms-1 8.25-10.20 7.84-10.07

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5 HEAT LOSS MODEL

5.1 HEAT LOSS MODEL CONSIDERATIONS

For a better understanding of the contribution of each heat loss mechanisms, a heat loss model considering heat transfer equations and an equivalent thermal resistance representation was developed. The model is based on the heat transfer thermal analysis described by Heimsath et al. (2014). Whereas in their work a non-evacuated single tube absorber is

modelled for stationary state, the model proposed in this work considers a multi-tube trapezoidal cavity absorber, also for steady state condition. The models proposed by Muñoz et al. (2011), Pino et al. (2013), which studied linear collector performances, were also used as reference for the present model. Figure 25 demonstrates the heat flux which takes place between different receiver components. The indices of heat flow described by Fig. 25 characterize the direction in which heat is being transported. The meanings of the indices are described by Tab. 3

Figure 25 – Thermal balance of the linear Fresnel receiver. The indices indicates the heat flow from which surface to which surface, according to Tab. 3

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Table 3 – Overview of subscripts of individual heat transport mechanisms according to Fig. 25

.

Subscript Surface

1 Inner tube surface 2 Outer tube surface

3 Inner int. aluminum surface 4 Outer int. aluminum surface 5 Inner ext. aluminum surface 6 Outer ext. aluminum surface 7 Inner glass surface

8 Outer glass surface 9 Ground or air

fitted system of equations, following the indices of heat flow according to Fig. 25 and Tab. 3. The equations are as described below:

˙ q1_2_cond= ˙q2_3+ ˙q2_7 (5.1) ˙ q2_3= ˙q2_3_conv+ ˙q2_3_rad (5.2) ˙ q2_7= ˙q2_7_conv+ ˙q2_7_rad (5.3) ˙ q3_9= ˙q2_3 (5.4) ˙ q3_9= ˙q3_6+ ˙qfin (5.5) ˙ q3_6= ˙q6_9 (5.6) ˙ q2_7= ˙q7_8= ˙q8_9 (5.7) ˙ q1_2= ˙q2_9 (5.8)

Generally speaking, the heat loss mechanisms include conduction, convection and radiation among the absorber parts and environment, as

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Figure 26 – Thermal resistance model for the LFC receiver

well as a fin model which was considered for the relatively thick aluminum walls. A thermal resistance model is described by Fig. 26.

The heat exchange between the tubes and inner aluminum wall was modelled considering both convection and radiation. The convection, in this case, was approximated as a conduction through the air. Con-duction also takes place between the two aluminum sheets, through the aluminum walls and rock wool. The heat reaching the outer aluminum wall is dissipated to the environment both by radiation and convection. Convection which drives heat flow from the outer aluminum wall was determined using a model for convection in the upper part of a hot plate, as described by Bergman and Incropera (2011). Also, a model for convection in the bottom part of a hot plate was implemented for outer convection in the window glass. The heat exchange between the tubes and window glass occur both by radiation and convection. The convection between the tubes and glass occur with almost steady air because of the position of the heating source. An approximation for the convection through the air was used in this case. The radiation within the cavity has been implemented by means of the view factor, which was determined by parallel plates and perpendicular plates methods (HOWELL et al., 2010). Also, the radiation between the internal aluminum walls and glass

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( ˙q3_7_rad) is very small because of the aluminum’s reduced emissivity and area. Because of that, this mechanism was approximated as nonexistent.

Finally, because of the high thermal conductivity of the aluminum and relatively high thickness of the sheets, a fin model was implemented in the cavity walls. This model considers two stages, which are a fin exposed to an cavity’s internal environment and a second part conducting heat to the outer aluminum sheet, this time exposed to environmental temperature. The first part of the fin considers the aluminum corner, closer to tube #1, as its base, which for means of simulation is assumed to be at the tubes’ average temperature. The second part of the fin considers the closest corner to the window glass’ edge as its base and goes along the outer aluminum wall. Both fins (left and right of the tubes) are thermally insulated with rock wool in one side and accordingly to the cavity geometry they are 0.36 m long, in total, each. For the calculations, because they are both insulated in one of the sides, the two 2 mm thick fins are considered as one single 4 mm fin, 0.36 m long, in which the central line is assumed adiabatic, as represented in Fig. 27.

Figure 27 – Representative of considerations regarding the thermal fin model

The mathematical model was solved in an iterative process to reach thermal equilibrium in every node along the receiver. It was started by solving a single heat loss mechanism between glass and environment, for example, and then adding the following mechanisms until the tubes’ temperature are found.

The calculation procedure was conducted by using Engineering Equation Solver (64) - Academic, which enabled fast calculation. All graphs, for the experimental tests and mathematical model were plotted using Matlab R2013b. All conduction, convection and radiation thermal resistances used in the mathematical model, described by Fig. 26, were

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obtained by using equations as described in Section 2.2. The resistances are positioned together in a sequence of series and parallel, as shown in Fig. 26 above, in order to correctly represent the heat loss mechanisms. The main input parameter is the inputted heat, Qloss. Other input parameters may include parameters such as emissivity (ε), view factor (Fi,j), area (A), thermal conductivity (k), convective heat transfer coefficient (h), environment (room) temperature(Tenv), among other. The considered material property values can be verifield in Appendix B.1. The output main parameter is the tube’s average temperature Tavg, and from it the overall heat loss coefficient(UL) can be deduced. The choice for the input and output parameters was based on the experimental tests, in which the electrical power (heat loss) is the main input parameter, and from this, an equilibrium temperature will come out in the tubes (output).

Certainly, the input parameters can be modified in order to represent any configuration and real operational condition in the setup. However, differently from the experiments, in which several receiver conditions were experimented, only the painting configuration was varied in the mathematical model. The model considers a glass window in the cavity’s aperture, natural external convection (non wind condition), and the painting configuration considers fully painted, partially painted and non-painted tubes.

Similarities between the numerical model results and experi-mental tests are presented in the following sections. The results of the mathematical model are described in the next section.

5.2 MATHEMATICAL MODEL RESULTS

The numerical analysis results were compared for a range of UL and ∆T comparable to the presented experimental tests. An average tube temperature of Tavg = 200◦C, and therefore a ∆T = 180◦C was used as reference as means of comparison with experimental tests. This temperature difference value, as seen in previous chapter, is produced with an experimental Qloss equals to 502 W, for fully painted tubes and considering a glass window, which is the most appropriate configuration for real LFC tests.

The values for ∆T and overall heat loss coefficients obtained on the numerical simulations are described by Tabs. 4, 5 and 6, respectively.

It can be seen that non painted tubes (lower emissivity) displayed the lowest overall heat loss coefficient, and that fully painted tubes displayed the highest UL. Therefore, the numerical model results agreed to the experimental tests, saying that for real operating conditions, the