EVAPORADOR PARA TERMOSSIFÃO BIFÁSICO EM CIRCUITO FABRICADO POR DIFUSÃO, VISANDO
APLICAÇÕES VEICULARES
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.
Orientadora:
Profa Márcia B. H. Mantelli, Ph. D Coorientador:
Juan Pablo Florez Mera, Dr. Eng.
Florianópolis 2017
Catalogação na fonte elaborada por Marcelo Cavaglieri CRB 14/1094 Simas, Gabriela Coelho Vieira
Evaporador para termossifão bifásico em circuito fabricado por difusão, visando aplicações veiculares. Gabriela Coelho Vieira Simas. – Florianópolis, 2017.
173f.: il. ; 14,81cm21cm.
Dissertação (Mestrado em Engenharia Mecânica)– Universidade Federal de Santa Catarina, 2017.
Bibliografia: f. 139-142.
1. Controle térmico passivo. 2. Termossifão em circuito. 3.Evaporador assistido por tela. I. Título.
EVAPORADOR PARA TERMOSSIFÃO BIFÁSICO EM CIRCUITO FABRICADO POR DIFUSÃO VISANDO
APLICAÇÕES VEICULARES
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, 13 de dezembro de 2017. __________________________________________
Prof. Jonny Carlos da Silva, Dr. Eng.
Coordenador do Programa de Pós-Graduação em Eng. Mecânica - UFSC
__________________________________________ Profa. Márcia B. H. Mantelli, Ph. D. - Orientadora - UFSC
__________________________________________ Juan Pablo Florez Mera, Dr. Eng. - Coorientador - UFSC Banca examinadora:
__________________________________________ Profa. Márcia B. H. Mantelli, Ph. D. - Presidente - UFSC
_________________________________________ Prof. Cristiano Binder, Dr. Eng. - UFSC __________________________________________
Prof. Fernando H. Milanese, Dr. Eng. - UFSC __________________________________________
Ricardo Gandolfi, Dr. Eng. - EMBRAER __________________________________________
A todos que contribuíram com a realização desde trabalho.
Primeiramente agradeço à Professora Márcia Barbosa Henriques Mantelli, minha orientadora, pela confiança depositada no meu trabalho e pela oportunidade de integrar um excelente grupo de trabalho. Além disso, um grande exemplo de pessoa e de profissional que não mede esforços em contribuir com a sua equipe.
Ao meu coorientador, Juan Pablo Florez Mera, pela intensa dedicação, seriedade e contribuições destinadas a este trabalho.
À UFSC e ao POSMEC pela oportunidade de cursar uma pós-graduação de excelência.
A todos os colegas do laboratório que contribuíram diretamente com o projeto, Leandro da Silva, Charles Nuernberg, GrégoriRosinski, Priscila Gonçalves, Arthur R. Facin, Nelson Y. L. Pabon, Andrés P. Sarmiento, Luis H. R. Cisterna, Antônio Alexandre, LuisBetancur, Cassiano Tecchio, e especialmente aos amigos João Victor Colin Batista e Luiz Domingos que dedicaram boa parte do seu tempo para fornecer ajuda indispensável ao trabalho.
Aos colegas da pós-graduação e do laboratório que colaboraram indiretamente, Pedro Bellani, Felipe de Castro, Guilherme P. Jaenisch, Guilherme Carqueja, Danielle Lima, Thyane Oliveira, Franciene I. P. de Sá e Ana Roberta Gomes.
Às minhas queridas amigas ThayanaSartor, GreiciWeinzierl e Vivian Rogoski pelo apoio, preocupação e pelos momentos de divertimento neste período.
Aos meus pais, Ana e Marco, por sempre me incentivarem a estudar e ir atrás dos meus objetivos. Minha determinação se deve exclusivamente aos exemplos e ensinamentos que me deram ao longo da vida.
Ao meu irmão, Thiago, por estar sempre ao meu lado e pela ajuda ao longo deste trabalho.
Ao meu marido, Gustavo, por acreditar no meu potencial, por me dar suporte, pelos constantes momentos de descontração e pela compreensão nesta trajetória árdua.
Este trabalho apresenta tanto o estudo teórico como o experimental de um termossifão em circuito, projetado para promover controle térmico passivo de componentes eletrônicos em veículos. O foco desse trabalho é desenvolver um evaporador plano que compreende dez placas de cobre empilhadas e soldadas por difusão. Cortes são executados nas placas internas de modo a formar canais internos após a soldagem do empilhamento. Água é empregada como fluido de trabalho. O dispositivo foi testado com duas razões de enchimento. O desempenho de um evaporador assistido por tela, foco desse estudo, é comparado com o de um dispositivo desprovido de tela com a mesma geometria. Testes com fonte de calor concentrada e distribuída sobre a superfície externa do evaporador foram realizados com o intuito de avaliar o espalhamento térmico. O sistema de controle térmico assistido pelo evaporador com tela fornece resfriamento passivo eficiente mesmo para fonte de calor concentrada entregando até 18 W/cm2. Com um sumidouro operando a 20oC, no caso de fonte de calor concentrada- densidade de potência entre 6 e 18 W/cm2- posicionada na extremidade da superfície externa do evaporador, a temperatura máxima na parede do evaporador foi 75,1oC e a resistência térmica 0,122oC/W. No caso da fonte quente centralizada, a temperatura máxima na parede do evaporador foi 44,7oC e a resistência térmica 0,055oC/W. A maioria dos testes realizados com o evaporador desprovido de tela apresentou geyserboiling, fenômeno que foi eliminado ao empregar o evaporador assistido por tela. Efeitos das variações da vazão mássica do banho térmico e das inclinações de até 8,1o no comportamento térmico do protótipo são considerados irrelevantes. O Erro Médio Quadrático entre a resistência térmica obtida pelo modelo matemático proposto e aquela obtida experimentalmente é 6.6% quando a fonte quente é posicionada em uma das extremidades da parede externa do evaporador, enquanto que quando a fonte quente está localizada no centro o erro é de 4.8%. Palavras-chave: Controle térmico passivo. Termossifão em circuito. Evaporador assistido por tela. Fonte de calor concentrada. Espalhamento térmico.
Introdução
Na sociedade moderna, o progresso tecnológico tem permitido cada vez mais a substituição de atividades por equipamentos eletroeletrônicos. Esses equipamentos devem ser eficientes, leves e transportáveis. Nesse sentido, essas tecnologias demandam o desenvolvimento de componentes eletrônicos mais eficientes e miniaturizados. Como pode ser visto em aplicações em telecomunicações, na aeronáutica e em maquinário para indústria, por exemplo, a correta operação desses dispositivos requer um controle rígido de temperatura dos componentes eletrônicos uma vez que estes aquecem durante a operação. Para garantir uma performance desejada, um sistema de controle térmico efetivo é essencial. Assim, a dissipação do calor oriundo de componentes eletrônicos tem sido um problema prático de engenharia a ser explorado. O foco desse trabalho é o desenvolvimento de um equipamento para controle térmico passivo de componentes eletrônicos visando aplicações veiculares. Sistemas efetivos de resfriamento devem garantir que componentes não ultrapassem limites de temperatura específicos. Temperaturas excessivas, além do nível tolerável, podem comprometer a vida útil dos eletrônicos, a sua funcionalidade e o controle do veículo. Sistemas típicos de convecção forçada empregados em sistemas de resfriamento podem gerar barulho excessivo, incrementar peso, ocupar espaço útil e requerer manutenção periódica. Nesse cenário, tubos de calor e termossifões representam uma alternativa a ser considerada com o intuito de solucionar parcial ou totalmente esses problemas. Tubos de calor e termossifões são equipamentos que transportam calor com altas taxas já que eles usam o calor latente de mudança de fase de um fluido de trabalho.
Esse trabalho apresenta estudos teóricos e experimentais de um evaporador de um termossifão bifásico em circuito, tecnologia sob desenvolvimento no LABTUCAL/LEPTEN. A performance do dispositivo, sujeito à fonte de calor concentrada e distribuída na superfície externa plana desse evaporador, é avaliada. Evaporadores com e sem tela metálica são estudados para a avaliar a influência do meio poroso do evaporador no espalhamento do líquido (bombeamento de líquido contra a gravidade), no caso de fonte de calor concentrada. Condições em diferentes inclinação também foram avaliadas.
Assim, buscando explorar tanto sustentabilidade como a eficiência térmica da tecnologia de tubos de calor como dispositivo de resfriamento para aeronaves, por exemplo, a presente dissertação
apresenta avanços tecnológicos e científicos em sistemas de controle térmico passivo.
A principal motivação desse trabalho é o aumento do uso de dispositivos eletroeletrônicos na nova geração de veículos, demandando tecnologias de controle térmico passivo para dissipação de calor. Dentre essas aplicações, pode-se incluir o resfriamento de lâmpadas de LED em carros modernos e o controle térmico de facilidades eletrônicas (TV’s, videogames, acesso à internet, etc) oferecidas aos passageiros em aeronaves comerciais.
Uma característica importante a ser considerada na seleção da melhor tecnologia para controle térmico é que veículos motorizados podem desenvolver altas velocidades, estando expostos a fluxos externos de ar, o que pode ser utilizado como um sumidouro de calor em potencial. Esse trabalho propõe um termossifão em circuito como um sistema de controle térmico passivo para resfriamento de eletrônicos em veículos motores, especialmente aeronaves.
Objetivo
O principal objetivo deste trabalho é estudar um evaporador plano de um termossifão em circuito, com estrutura capilar e fabricado por difusão, projetado para promover controle térmico passivo de eletrônicos em veículos.
Metodologia
Inicialmente são apresentados os princípios físicos fundamentais da tecnologia de tubos de calor. Em seguida são discutidas as análises de perda de carga e resistência térmica em termossifões, bem como a questão da fonte de calor sendo aplicada de forma concentrada e o conceito de espalhamento térmico. Posteriormente,o processo de soldagem por difusão é descrito. O projeto do termossifão é explicado detalhadamente desde a concepção do evaporador plano. Cobre é empregado na construção do termossifão e água foi escolhida como fluido de trabalho.Tela de fios de cobre é empregada como estrutura capilar em um dos evaporadores construídos. É proposto um modelo teórico baseado no conceito de resistências térmicas capaz de predizer a temperatura em qualquer ponto da parede do evaporador, além de temperaturas intermediárias como na saída do evaporador e na entrada do condensador. Uma bancada de teste e equipamentos de medição são empregados a fim de avaliar a performance térmica do termossifão em circuito assim como validar o modelo teórico proposto. Uma série de testes são executados variando parâmetros como: inclinação do dispositivo, vazão mássica do banho térmico (sumidouro de calor),
Resultados e discussão
O tempo de startup variou de 60 a 200 segundos. Quando o nível do líquido estava mais longe da fonte quente, temperaturas na parede do evaporador subiam em uma taxa mais alta. Isso porque nessas situações o dispositivo depende da condução para transferir calor para o fluido de trabalho, processo com menor capacidade de promover transferência de calor que a mudança de fase, processo verificado quando a parede se encontra molhada. Esse é o mesmo motivo pelo o qual o evaporador assistido por estrutura porosa atingiu menores valores de temperatura na parede: a capilaridade de tela metálica foi capaz de manter a parede do evaporador molhada.
Os testes realizados com evaporador sem estrutura capilar apresentaram a ocorrência de geyser boiling, um fenômeno indesejável do ponto de vista estrutural. Observou-se que a amplitude das oscilações de temperatura reduzem com o aumento do fluxo de calor entregue a superfície do evaporador, enquanto que a frequência aumenta. Menores razões de enchimento implicam a ocorrência do geyser boiling mais cedo.
Os resultados também indicam que geyser boiling ocorre mais frequentemente com razões de enchimento menores.
O emprego de estrutura capilar no evaporador afetou positivamente a performance térmico do termossifão em circuito. A tela metálica além de preencher a parede interna do evaporador com fluido de trabalho por capilaridade, foi capaz de conduzi-lo até a posição onde a fonte quente estava sendo aplicada. Além disso, o formato da tela permite a criação de mais sítios de nucleação favorecendo a criação de bolhas e, consequentemente, o processo de ebulição. Os testes executados com tela apresentaram menores temperaturas na parede do evaporador e menores valores de resistência térmica equivalente, além na eliminação do efeito de geyser boiling.
Redução de aproximadamente 20% na vazão mássica do banho térmico e inclinações de até 8,1º do dispositivo não geraram comportamentos térmicos diferentes do termossifão.
Considerações finais
O sistema de controle térmico assistido pelo evaporador com tela fornece resfriamento passivo eficiente mesmo para fonte de calor concentrada entregando até 18 W/cm2. Com um sumidouro operando a 20oC, no caso de fonte de calor concentrada - densidade de potência entre 6 e 18 W/cm2 - posicionada na extremidade da superfície externa
do evaporador, a temperatura máxima na parede do evaporador foi 75,1oC e a resistência térmica 0,122oC/W. No caso da fonte quente centralizada, a temperatura máxima na parede do evaporador foi 44,7oC e a resistência térmica 0,055oC/W. A maioria dos testes realizados com o evaporador desprovido de tela apresentou geyserboiling, fenômeno que foi eliminado ao empregar o evaporador assistido por tela. Efeitos das variações da vazão mássica do banho térmico e das inclinações de até 8,1o no comportamento térmico do protótipo são considerados irrelevantes. O Erro Médio Quadrático entre a resistência térmica obtida pelo modelo matemático proposto e aquela obtida experimentalmente é 6.6% quando a fonte quente é posicionada em uma das extremidades da parede externa do evaporador, enquanto que quando a fonte quente está localizada no centro o erro é de 4.8%.
Palavras-chave: Controle térmico passivo. Termossifão em circuito. Evaporador assistido por tela. Fonte de calor concentrada. Espalhamento térmico.
This work presents both theoretical and experimental studies of a two-phase loop thermosyphon designed to promote passive thermal management of electronics components in motor vehicles. The major concern of this work is to develop a flat evaporator which comprises ten square stacked copper plates bonded by diffusion. Channels were manufactured in the inner plates so that internal grooves are obtained after the stack is bonded. Water was employed as working fluid. The device was tested with two filling ratios. The performance of a wicked evaporator, major concern of this study, is compared to a wickless device with the same geometry. Tests with concentrated and distributed heat sources over the evaporator external surface were performed in order to evaluate thermal spreading. The thermal control system assisted by the wicked evaporator provides efficient passive cooling even for concentrated heat source delivering up to 18 W/cm2. For a heat sink operating at 20oC, in case of concentrated heat source - power density ranging from 6 to 18 W/cm2 - situated in the edge of the external surface of the evaporator, the maximum wall temperature in the evaporator wall was 75.1oC and thermal resistance 0.122oC/W. Regarding the centralized heat source, maximum wall temperature in the evaporator wall was 44.7oC and thermal resistance 0.055oC/W. The majority of the tests performed with the wickless evaporator presented geyser boiling, phenomenon which has been vanished by employing the wicked evaporator. Effects of variations of the thermal bath mass flow rate and of inclinations up to 8.1o on the thermal behavior of the prototype are considered irrelevant. The Mean Squared Error between the thermal resistance obtained by the mathematical model proposed and that experimentally obtained is 6.6 when the heat source is positioned in one of the edges of the evaporator external surface, while when the heat source in located in the center the error is 4.8%.
Keywords: Passive thermal control. Loop thermosyphon. Wicked evaporator. Concentrated heat source. Thermalspreading.
Figure 1 – Schematics of the operating principle of typical heat pipes
and thermosyphons. ... 36
Figure 2 – Schematics of a loopthermosyphon. ... 37
Figure 3 – Hydraulic head in a loop thermosyphon. ... 43
Figure 4 – Thermal resistance circuit of a typical heat pipe. ... 45
Figure 5 – Frontal and superior views of an isotropic plate with an eccentric heat source laid down. ... 47
Figure 6 – Mechanisms in the material interface during bonding diffusion. a) located plastic deformation, superficial roughness collapse and increase in the real contact area; b) filling of remaining voids by diffusion mechanism in grain contours; c) final bonding by interfacial movement of grain contours. ... 53
Figure 7 – Illustration of the geyser boiling phenomena within a loop-themosyphon. ... 58
Figure 8 – Exploded view of the evaporator. ... 62
Figure 9 – Design of the inner plates... 63
Figure 10 – Wickless and wicked evaporator, respectively, without the closing plate before diffusion bonding and final cutting. ... 64
Figure 11 – Fourth plate design emphasizing margins and its justification. ... 64
Figure 12 – Structural simulation result – equivalent stress distribution. ... 66
Figure 13 – Structural simulation result - total deformation distribution. ... 66
Figure 14 – Fluid dynamic simulation results. ... 68
Figure 15 – Schematics of the condenser operation. ... 69
Figure 16 – Approximation of the geometry for a concentric tubes heat exchanger. ... 69
Figure 17 – Temperature differences. ... 70
Figure 18 – Loop thermosyphon design highlighting the helical condenser. ... 74
Figure 19 – Thermal physical model for the flat evaporator. ... 75
Figure 20 – Mathematical modeling... 76
Figure 21 – Beams as fins. ... 80
Figure 22 – Thermal resistances circuit in the wickless evaporator. ... 82
Figure 24 – Photos of lateral view of the evaporator after diffusion
bonding. ... 88
Figure 25 – Liquid channels of the wicked evaporator without the closing plate before diffusion bonding. ... 88
Figure 26 – Vapor outlet of the wicked evaporator without the closing plate viewed from inside before diffusion bonding... 89
Figure 27 – Vapor outlet of the wicked evaporator viewed from outside after diffusion bonding and final cut (right photo amplified)... 89
Figure 28 – Water-jet cutting machine. ... 90
Figure 29 – Porous wick pieces after cutting. ... 90
Figure 30 – Plates polish. ... 91
Figure 31 – Spot welding machine and spot welding process respectively. ... 91
Figure 32 – Template for spot welding: bottom and top piece respectively. ... 92
Figure 33 – Wicked closing plate... 92
Figure 34 – Final assembly of the wicked evaporator without the closing plate. ... 93
Figure 35 – Three evaporators ready to be bonded by diffusion in the furnace... 94
Figure 36 – Wicked evaporator without the closing plate (before bonding) where dashed lines illustrates cut positions after bonding. .... 94
Figure 37 – Dismantled set: external cylinder in the top and condenser and helix welded in the internal cylinder in the bottom. ... 95
Figure 38 – Thermosyphon assisted by thermocouples. ... 96
Figure 39 – Thermocouples positions. ... 97
Figure 40 – Blocks supporting device illustrating the centered position outside and inside the system respectively. ... 98
Figure 41 – Experimental complete system. ... 98
Figure 42 – Schematics of the tests. ... 101
Figure 43 – Pure conduction of the device –heat source in the center. 103 Figure 44 – Pure conduction of the device –heat source in the edge. . 104
Figure 45 – Thermocouples arrangement selected for analysis. ... 105
Figure 46 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 60% of filling ratio – distributed heat source (T01). ... 107
source concentrated in right top (T02). ... 108 Figure 48 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 60% of filling ratio – heat source concentrated in center (T04). ... 109 Figure 49 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 60% of filling ratio – heat source concentrated in right bottom (T05). ... 110 Figure 50 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 60% of filling ratio – heat source concentrated in right bottom and thermosyphon inclined (T07). ... 111 Figure 51 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 40% of filling ratio – distributed heat source (T11). ... 112 Figure 52 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 40% of filling ratio – heat source concentrated in right top (T12). ... 113 Figure 53 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 40% of filling ratio – heat source concentrated in center (T14). ... 114 Figure 54 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 40% of filling ratio – heat source concentrated in right bottom (T15). ... 115 Figure 55 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 40% of filling ratio – heat source concentrated in right bottom and thermosyphon inclined (T17). ... 116 Figure 56 – Effect of the input power on thermal behavior of the prototype with wicked evaporator and 40% of filling ratio – distributed heat source (T21). ... 117 Figure 57 – Effect of the input power on thermal behavior of the prototype with wicked evaporator and 40% of filling ratio – heat source concentrated in right top (T22). ... 118 Figure 58 – Effect of the input power on thermal behavior of the prototype with wicked evaporator and 40% of filling ratio – heat source concentrated in center (T24)... 119
Figure 59 – Effect of the input power on thermal behavior of the prototype with wicked evaporator and 40% of filling ratio – heat source
concentrated in right bottom (T25). ... 120
Figure 60 – Effect of the input power on thermal behavior of the prototype with wicked evaporator and 40% of filling ratio – heat source concentrated in right bottom and thermosyphon inclined (T27). ... 121
Figure 61 – Overview of the commented results regarding the effect of the input power on thermal behavior of the prototype. First column: wickless evaporator – filling ratio 60%; second column: wickless evaporator – filling ratio 40%; last column: wicked evaporator. ... 122
Figure 62 – Schematics of the lateral view of a wicked evaporator highlighting the wick layer. ... 124
Figure 63 –Temperatures in the evaporator wall for a heat source located in the edge (300 W). ... 125
Figure 64 –Temperatures in the evaporator wall for a heat source located in the center (300 W). ... 126
Figure 65 – Experimental (blue) and analytical (red) temperatures in the evaporator wall for a heat source located in the edge (300 W). ... 128
Figure 66 – Experimental (blue) and analytical (red) temperatures in the evaporator wall for a heat source located in the center (300 W). ... 129
Figure 67 – Temperatures comparison: model vs. experimental. ... 130
Figure 68 – Evaporator external wall temperature distribution according to the theoretical model – heat source in the edge (input power 300W). ... 132
Figure 69 – Evaporator external wall temperature distribution according to the theoretical model – heat source in the center (input power 300W). ... 132
Figure 70 – Evaporator wall maximum temperature... 135
Figure 71 – Thermal resistances. ... 136
Figure 72 – Errors curve - superior limit... 144
Figure 73 – Errors curve - inferior limit. ... 145
Figure 74 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 60% of filling ratio – heat source concentrated in right top and thermosyphon rotated CW-x (T03). ... 147 Figure 75 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 60% of filling ratio – heat
Figure 76 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 60% of filling ratio – heat source concentrated in right bottom and thermosyphon rotated CC-x (T08). ... 148 Figure 77 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 60% of filling ratio – heat source concentrated in right bottom and thermosyphon rotated CC-z – mass flow rate reduced(T09). ... 148 Figure 78 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 40% of filling ratio – heat source concentrated in right top and thermosyphon rotated CW-x (T13). ... 149 Figure 79 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 40% of filling ratio – heat source concentrated in right bottom and thermosyphon rotated CC-z (T16). ... 149 Figure 80 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 40% of filling ratio – heat source concentrated in right bottom and thermosyphon rotated CC-x (T18). ... 150 Figure 81 – Effect of the input power on thermal behavior of the prototype with wickless evaporator and 40% of filling ratio – heat source concentrated in right bottom and thermosyphon rotated CC-z – mass flow rate reduced(T19). ... 150 Figure 82 – Effect of the input power on thermal behavior of the prototype with wicked evaporator and 40% of filling ratio – heat source concentrated in right top and thermosyphon rotated CW-x (T23)... 151 Figure 83 – Effect of the input power on thermal behavior of the prototype with wicked evaporator and 40% of filling ratio – heat source concentrated in right bottom and thermosyphon rotated CC-z (T26).. 151 Figure 84 – Effect of the input power on thermal behavior of the prototype with wicked evaporator and 40% of filling ratio – heat source concentrated in right bottom and thermosyphon rotated CC-x (T28). 152 Figure 85 – Effect of the input power on thermal behavior of the prototype with wicked evaporator and 40% of filling ratio – heat source
concentrated in right bottom and thermosyphon rotated CC-z – mass flow rate reduced (T29). ... 152
Table 1 - Comparative values of the order of magnitude for thermal resistances found in typical heat pipes (Mantelli [4], apud Asselman e Green [10]). ... 46 Table 2 - Polynomial functions employed to estimate saturation pressure and physical properties [1]. ... 83 Table 3 - Experiment conditions for each loop themosyphon prototype (with wicked and wickless evaporator). Input power ranged from 150 to 390W with increments of 30W in each test. ... 100 Table 4 - Relevant experimental results. ... 106 Table 5 - MSE for each theoretical model adopted per power level - heat source in the edge. ... 127 Table 6 - MSE for each theoretical model adopted per power level - heat source in the center. ... 127 Table 7 - Relative errors in evaporator wall temperature prediction - heat source in the edge (300 W)... 128 Table 8 - Relative errors in evaporator wall temperature prediction - heat source in the center (300 W). ... 129 Table 9 - Relative errors and MSE in temperature prediction -
evaporator outlet. ... 130 Table 10 - Relative errors and MSE in temperature prediction -
condenser inlet... 131 Table 11 – Theoretical and experimental evaporator wall temperature and maximum evaporator wall temperature – heat source in the edge. ... 134 Table 12 – Theoretical and experimental evaporator wall temperature and maximum evaporator wall temperature – heat source in the center. ... 134
Acronyms
CC Concentrated heat source in center CC-x Counterclockwise rotation in x-axis CC-z Counterclockwise rotation in z-axis CRB Concentrated heat source in right bottom CRT Concentrated heat source in right top CW-x Clockwise rotation in x-axis
D Distributed heat source
EMBRAER Empresa Brasileira de Aeronáutica EMC Department of Mechanical Engineering LABTUCAL Laboratório de Tubos de Calor
LEPTEN Laboratório de Engenharia de Processos de Conversão e Tecnologia de Energia UFSC Federal University of Santa Catarina Greek alphabet
β, δ, λ Eigenvalues [-]
ΔT Temperature difference [oC]
ΔTml Logarithmic mean temperature difference [
o C]
ΔP Pressure drop [Pa]
ε Porosity [-]
η Efficiency [-]
ηo Efficiency of the set [-]
θ Temperature excess [oC]
μ Dynamic viscosity [Pa.s]
υ Specific volume [m3/kg]
ξ Dummy variable [m-1]
Ω Tube angle with horizontal [o]
ρ Density [kg/m3] σ Surface tension [N/m] ϕ Spreading function [-] Roman alphabet A Area [m2] Ac Cross-sectional area [m 2 ] Cp Specific heat at constant pressure [J/kg.K]
D Diameter [m]
Dh Hydraulic diameter [m]
di Internal cylinder diameter [m]
dw Wire diameter [m]
g Gravity acceleration at sea level [m/s2]
G Mass flux [kg/s.m2]
H Height [m]
h Convective heat transfer coefficient [W/m2.K]
hlv Latent heat of vaporization [J/kg]
k Thermal conductivity [W/m.K]
kws Specific permeability of the wick structure [m
2 ]
L Length [m]
̇ Mass flow rate [kg/s]
N Number of something (quantity) [-]
NM Mesh number [inch
-1 ]
P Pressure [Pa]
p Perimeter [m]
pl Liquid pressure [Pa]
psat Pressure of the saturated pressure [Pa]
q Heat transfer rate [W]
q" Heat transfer flu [W/m2]
r Ratio [m] R Thermal resistance [oC/W] t Thickness [m] T Temperature [oC] Tw Wall temperature [ o C]
Mean source temperature [oC]
T(x,y,z) Local temperature [oC]
u Velocity [m/s]
U Global coefficient of heat transfer [W/m2.K]
x Vapor quality [-]
z Coordinate axis in the direction of the flow [m]
m,n Indices for summation [-]
Xc, Yc Heat source centroid [m]
x,y,z Cartesian coordinates [-]
A0, Am, An, Amn, Bm, Bn, Bmn Fourier coefficients [-] a,b, c, d, e, f, j, s, v, w Linear dimensions [m]
cap Capillary
c Condenser
cc Condenser after conduction cl Condensate line
cw Condenser after water convection conv Convection cond Conduction conde Condensation e Evaporator eff Effective exp Experimental f Fins
Fz Foster and Zuber Gr Groll and Rosler
h Hot fluid hs Heat sink in Inlet Ka Kaminaga Ku Kutateladze l Liquid max Maximum o Cold fluid out Outlet S Spreading s Heat source sat Saturation T Thermosyphon t Total TP Two-phase v Vapor vl Vapor line w Wick 1D One-dimensional Superscripts
1ϕ Single phase flow 2ϕ Biphasic flow
Adimensional numbers F Friction factor Nu Nusselt number Pr Prandtl number Re Reynolds number
1 INTRODUCTION ... 31 1.1CONTEXT ... 31 1.2MOTIVATION... 32 1.3OBJECTIVES... 32 1.3.1 Global objective ... 32 1.3.2 Specific objectives ... 32 1.4STRUCTUREOFTHEDISSERTATION ... 33 2 LITERATURE REVIEW ... 35 2.1THEORETICALFOUNDATION ... 35 2.1.1 Heat transfer limitations ... 37 2.1.1.1 Capillary limit ... 37 2.1.1.2 Sonic limit ... 38 2.1.1.3 Entrainment limit ... 38 2.1.1.4 Boiling limit ... 38 2.1.1.5 Viscous limit ... 39 2.1.1.6 Dry-out limit ... 39 2.2PRESSUREDROPANDTHERMALANALYSIS ... 39 2.2.1 Pressure drop analysis ... 39 2.2.2 Thermal resistance approach ... 44 2.2.2.1 Thermal spreading resistance ... 46 2.2.3 Correlations for boiling and condensation heat transfer
coefficients ... 50 2.2.3.1 Kutateladze boiling correlation ... 51 2.2.3.2 Foster and Zuber boiling correlation ... 51 2.2.3.3 Groll and Rosler condensation correlation ... 51 2.2.3.4 Kaminaga condensation correlation ... 52 2.3DIFFUSIONBONDING ... 52 2.4THERMOSYPHONASATHERMALCONTROLSOLUTION .. 53 2.5GEYSERBOILINGPHENOMENON ... 57 3 PROTOTYPE DESIGN ... 61 3.1EVAPORATORCONCEPTION ... 61 3.2NUMERICALSIMULATIONS... 64 3.2.1 Structural simulations ... 65 3.2.2 Fluid dynamics simulations ... 67
3.3CONDENSERDESIGN ... 68 4 EVAPORATOR MODELING ... 75 4.1THERMALMODEL... 76 4.2PRESSUREDROPMODELING... 83 5 EXPERIMENTAL SETUP AND PROCEDURE ... 87 5.1EXPERIMENTALSETUP ... 87 5.1.1 Evaporator ... 87 5.1.2 Condenser and final assembly... 95 5.1.3 System description ... 96 5.2EXPERIMENTALPROCEDURE ... 98 5.3EXPERIMENTALUNCERTAINTIES ... 101 6 RESULTS AND DISCUSSION ... 103 6.1EXPERIMENTALRESULTS ... 103 6.1.1 Wickless evaporator – filling ratio 60% ... 107 6.1.2 Wickless evaporator – filling ratio 40% ... 112 6.1.3 Wicked evaporator – filling ratio 40% ... 116 6.1.4 Discussion ... 122 6.2EXPERIMENTALANDNUMERICALRESULTSANALYSIS 124 7 CONCLUSION... 137 REFERENCES ... 139 APPENDIX A – EXPERIMENTAL UNCERTAINTIES ... 143 APPENDIX B – RESULTS OF REMAINING TESTS ... 147 APPENDIX C – MAPLE MODEL ... 153
1INTRODUCTION
1.1 CONTEXT
In modern society, technological progress has allowed, increasingly, the replacement of human work by electro/electronic devices, both for simple domestic tasks and for complex industrial processes. These devices must be efficient, lightweight and transportable. In this sense, necessarily, these technologies demand the development of more efficient, miniaturized electronic components. As it can be seen in applications in telecommunication, aeronautic and industrial machinery, for example, the correct operation of these devices requires a tight temperature control of the electronic components. Actually, during operation, electronic components warm up due to the Joule effect. To ensure a desirable performance, a thermal control system highly effective is essential. Therefore, the heat dissipation of the electro/electronic components has been a practical engineering problem to be explored.
The gist of this work is the development of a passive thermal management device for electronic components of motor vehicle applications. Effective cooling systems must ensure that components do not surpass specific limits of temperature. Excessive temperatures, above the tolerable level, may compromise the electronics useful life, functionality and therefore the vehicle control.
Heat dissipation is usually made by either natural or forced convection. Natural convection presents an inherently high thermal resistance between the heat source and the heat sink. Forced convention by means of fans or air conditioning systems, although effective, feature as an energetically inefficient solution, once part of the energy provided to drive the motor vehicle is extracted to this aim. Besides that, typical systems of forced convection may generate excessively noise, add extra mass, take useful space and require periodical maintenance. In this scenario, heat pipes and thermosyphons represent an alternative to be considered in order to settle partially or totally these problems. Heat pipes and thermosyphons are passive apparatus which transport heat at high rates, as they use the phase change latent heat of a working fluid. The literature shows that these passive technologies are being considered for aeronautical and aerospace vehicle use.
This work presents both theoretical and experimental studies of an evaporator of a two-phase loop thermosyphon technology under development in LABTUCAL/LEPTEN. The performance of the device,
subjected to concentrated and distributed heat sources over the external flat surface of this evaporator, is evaluated. Wicked and non-wicked evaporators are studied in order to evaluate the influence of the porous media within the evaporator in liquid spreading (liquid pumping against gravity), in case of concentrated heat source. Different inclination conditions were also evaluated.
Hence, aiming to explore both the sustainability and thermal efficiency of heat pipes technology as cooling devices for airplanes, for instance, the current dissertation presents technological and scientific advances in passive thermal control systems.
1.2 MOTIVATION
The major motivation of this work is the increasing use of electro/electronics devices in new generation vehicles, demanding for efficient thermal control technologies for passive heat dissipation. Among these applications, one can include the cooling of LED lights in modern cars and the thermal control of electronic amenities (TVs, games, internet access, etc) provided by commercial airplanes to costumers. One important characteristic to be considered in the selection of the best thermal control technology is that motorized vehicles can develop large speeds, being exposed to external air streams, that can be used as potential heat sinks. This work proposes a loop thermosyphon passive thermal control system for electronic cooling of motor vehicles, especially for airplanes.
1.3 OBJECTIVES 1.3.1 Global objective
This work proposes the study of a flat wicked evaporator of a loop thermosyphon, bonded by diffusion, designed to promote passive thermal control of electronic devices in motor vehicles.
1.3.2 Specific objectives
In order to reach this main objective, the following specific objectives must be attained:
Literature review showing the “state of the art” of devices assisted by heat pipe technology, applied to motor vehicles;
To design a loop thermosyphon prototype for electronics cooling aiming vehicular applications;
To develop a theoretical model to evaluate the thermal and hydraulic behavior of the device, to be validated as a designing tool;
To manufacture prototype of the thermosyphon evaporator; To assemble and to instrument a test bench, which includes a complete thermosyphon, for testing its evaporator;
To test two configurations of the thermosyphon evaporator: wicked (metal screens) and wickless, under different operation conditions;
To treat the data and compare with theoretical model results; To evaluate the thermal performance of the thermosyphon. 1.4 STRUCTURE OF THE DISSERTATION
The present dissertation is divided into seven chapters. Apart from Chapter 1 (Introduction), the content of the chapters is described as follows:
Chapter 2: Literature review. Chapter 2 is dedicated to explain the operating principle of heat pipes and thermosyphons and to present the current status of this technology applied to electronic cooling systems. Also, a review of available pressure drop and thermal models is shown. Literature well known heat transfer coefficient correlations are presented. Geyser boiling, a frequent phenomenon verified in loop thermosyphons, is also described. The diffusion bonding manufacturing process is also a subject of this chapter.
Chapter 3: Prototype design. This chapter describes all the design stages necessary for the prototype fabrication, including the evaporator conception. Numerical simulations are performed for both structural and fluid dynamic designing aspects. The condenser sizing is also a topic of this chapter.
Chapter 4: Theoretical analysis and modeling. A simple theoretical model is proposed and detailed in this chapter, able to predict the temperature in the external surface of the evaporator wall, which depends on the heat sink temperature.
Chapter 5: Experimental setup and procedure. This chapter details the equipment fabrication process. The test bench constructed is also described. Test procedure and test planning close Chapter 5.
Chapter 6: Results and discussion. Chapter 6 encompasses the results and its analysis. Thermal performances of the thermosyphon in different operation conditions are compared among them and evaluated. Finally, results obtained by the theoretical model proposed are compared with experimental data in order to check the validity of the model.
Chapter 7: Conclusions. The main conclusion remarks are point out as well as suggestion for future works.
2 LITERATURE REVIEW
This work comprises a study of a thermosyphon, namely, a traditionally wickless gravity-assisted heat pipe. In this sense, a general overview of this heat pipe technology is performed.
Heat pipes and its variations, are one of the most efficient technologies known to promote and improve heat transfer. According to Faghri [1], the advantage of using a heat pipe over other conventional methods is that large quantities of heat can be transported through a small cross-sectional area over a considerable distance with no additional power input to the system. Furthermore, this research affirms that these devices are simple to design and manufacture, present small end-to-end temperature drops, and possess the ability to control and transport high heat rates at various temperature levels.
2.1THEORETICAL FOUNDATION
Heap pipes and thermosyphons are heat transfer devices which present very high global thermal conductance and therefore, low thermal resistance. They operate in a two-phase closed loop of a working fluid. Using the vaporization and condensation latent heats to promote heat transfer, even when subjected to small thermal gradients. Grover [2], apud Faghri [3], states: "With certain limitations on the manner of use, a heat pipe may be regarded as a synergistic engineering structure which is equivalent to material having a thermal conductivity greatly exceeding that of any known metal". Basically, heat pipes or thermosyphons are formed by a metallic container which is carefully sealed, evacuated and filled with a predetermined amount of working fluid, which is saturated state.
Usually, the equipment consists in three main parts: evaporator, adiabatic and condenser sections. In the evaporator section, heat is provided to the container by an external source, promoting the vaporization of part of the working fluid. The generated steam flows towards the condenser due to slight pressure gradients passing through the adiabatic section. In the condenser, the cold region, heat is rejected to the sink stimulating the condensation of the steam. The gravity effect is responsible for the return of the condensate to the evaporator in thermosyphons whereas in heat pipes this task is performed by capillary pumping through a wick structure, closing the cycle. In order to allow the gravity action in thermosyphons, the evaporator must be always situated below the condenser, while heat pipes offer the versatility to be
used in gravity-free environments. Therefore, the latent heat of vaporization is continuously transported from the evaporator to the condenser sections as long as there is a sufficient pressure to drive the condensate back to the evaporator. Figure 1 shows the operating principle of heat pipes and thermosyphons.
Figure 1 – Schematics of the operating principle of typical heat pipes and thermosyphons.
(a) Heat pip (b) Thermosyphon Source – Adapted from Tecchio [33].
These devices may have multiple heat sources or sinks, with or without adiabatic sections, depending on the specific application. Besides that, they can present several geometries and arrangements according to Mantelli [4]. Trying to achieve a configuration using as less useful space as possible and to transfer large amounts of heat, the apparatus employed in this work is a two-phase loop thermosyphon, demonstrated in Figure 2. The main characteristic of the loop-thermosyphon is the fact that the flows of the working fluid are separated by two sets of tubes within which only vapor or liquid is conducted, avoiding the drag verified in the countercurrent flow of traditional thermosyphons. Additionally, loop thermosyphons offer a high geometry flexibility including the format of evaporator and condenser as well as the number of evaporators or condensers, which can be different for each other.
Figure 2 – Schematics of a loopthermosyphon.
2.1.1Heat transfer limitations
Although heat pipes and thermosyphons have the ability to transfer large quantities of heat, this heat transport rate is subject to a number of restraints as a result of pre-determined operation conditions. According to Faghri [1], some physical phenomena that might limit heat transport in heat pipes or thermosyphons are due to capillary, sonic, entrainment and boiling effects. Mantelli [4] also mentions viscous and dry-out limit. All of these constraints must be evaluated and the lowest limit among them defines the maximum heat transport limitation of a device at a given operation condition.
2.1.1.1Capillary limit
The capillary or hydrodynamic limit is related to the ability of a particular capillary structure to promote the flow of the working fluid. Generally, the capillary limit is the most critical in the operation of low-temperature heat pipes, in accordance with Faghri [1]. It occurs when the sum of the liquid and vapor pressure drops surpass the maximum capillary pressure that the porous media can maintain. If the power input
given to the device exceed the capillary limit, the evaporator section will suffer a dry-out causing an abrupt increase in its wall temperature.
This work comprises a study of a loop thermosyphon, where, usually, there is no capillary structure. Nevertheless, it will be evaluated the influence of a capillary structure in the evaporator section.
2.1.1.2Sonic limit
For certain work parameters of some heat pipes or thermosyphons, the vapor velocity can reach sonic levels in start-up or in steady-state conditions. According to Mantelli [4], when the sonic speed is reached, the vapor, usually located in thermosyphon core, experiences a shock wave and the vapor is considered blocked. In this situation, even if more vapor is generated in the evaporator, the vapor flow does not progress. Thence, increases in the evaporator input power lead to an increase in the evaporator section temperature.
Faghri [1] affirms that the sonic limit is usually associated with liquid-metal heat pipes due to high vapor velocities and low densities. Since this study involves water as working fluid and the velocities verified are so much lower than sonic levels, sonic limit is not a restriction.
2.1.1.3 Entrainment limit
Throughout the operation of typical heat pipes and thermosyphons, vapor and liquid move in opposite directions and, as the vapor has much higher velocity than the liquid, a shear force is verified at the liquid-vapor interface. Mantelli [4] explains that depending on the intensity of this force, the return of the liquid can be impaired and the liquid is accumulated in the condenser, which stay flooded, reaching the entrainment limit.
As loop thermosyphons do not experience vapor and liquid flowing in different directions at the same pipeline, entrainment limit is not assessed here.
2.1.1.4 Boiling limit
Boiling limit is attained in the transition between nucleate pool boiling to vapor film boiling, when the critical heat flux is applied. This condition allows the generation of vapor bubbles which coalesce into one vapor film, thermally insulating the case wall, as the vapor has a
low thermal conductivity. As a consequence, the wall temperature keeps increasing and no more heat is transferred.
2.1.1.5 Viscous limit
For thermosyphons working at low temperatures, the vapor pressure difference between the evaporator and the condenser can be very small. However, this pressure difference must be higher than the viscous forces observed in the working fluid to promote the vapor movement. According to Mantelli [4], this limit may happen during start-up and the best way to face it is to increase the heat flux, which will rise the vapor temperature until the pressure gradient along the tube exceeds the viscous forces.
2.1.1.6 Dry-out limit
There are different means to reach dry-out in a thermosyphon. Dry-out may happen when the radial heat flux or the total volume of working fluid is very small, so that the rate of vapor generated is not enough to assured a continuous circulation of vapor and liquid, causing cold and hot spots respectively. This restriction also can occur associated with the entrainment limit, when the liquid film cannot reach the pool forming dry regions in the internal thermosyphon wall.
2.2 PRESSURE DROP AND THERMAL ANALYSIS
Typically, heat pipe theory consists of fundamental analyses related to hydrodynamic and heat transfer processes. Axial liquid pressure drop in the wick structure, maximum capillary pumping head and vapor flow in the vapor channel are issues taken into the hydrodynamic analysis. In parallel, heat transfer theory is used to model the transfer of heat into and out of the heat pipe.
2.2.1Pressure drop analysis
The flow of working fluid inside a loop thermosyphon generates a pressure drop. According to Milanez and Mantelli [5], the larger the heat transfer rate through the loop thermosyphon, the larger are the working fluid mass flow rate, velocity, and pressure drop.
In order to estimate the pressure drop in the proposed device, a literature review was done to assess the available models. The model recommended by Milanez and Mantelli [5] is based on the literature
correlations, for viscous fluid flows. In this model, the total pressure drop ΔPt is the summation of the pressure drops due to fluid flow in
evaporator ΔPe, vapor line ΔPvl, condenser ΔPc, and condensate return
line ΔPcl:
∆ = ∆ + ∆ + ∆ + ∆ (1)
Assuming that the vapor line is well insulated, no condensation occurs and the vapor flows in single phase. Besides, if the hypothesis of thermosyphon operating at the limit is admitted, the condensate return line is expected to be completely filled with liquid and the flow in the condensate return line is also single phase, this time, liquid. The single-phase flow pressure drop can be obtained from classical fluid flow textbooks, such as Fox et al. [6], as:
∆ =
2 (2)
where F is the friction factor, L is the sum of the vapor line total length of the circuit, including the equivalent length of the bends and other accessories, ρ is the density of the fluid, u is the velocity of the flow and Dh is the inner diameter of the pipe.
The friction factor is given by:
=64, < 2,300 ( ) (3)
=0.316. , > 2,300 ( ) (4)
For this application the Reynolds Number is established as:
= (5)
where velocity of flow u is obtained from continuity equation:
andDh is the hydraulic diameter defined as:
=4 (7)
whereA is the cross sectional area and p is the wetted perimeter. Finally, mass flow rate is calculated by:
̇ =
ℎ (8)
Then, rearranging the equations mentioned for laminar flow and circular pipes, one gets:
∆ =128 ̇ (9)
In this sense, ΔPvl and ΔPcl can be calculated by the Eq. 9. While
vapor and condensate lines can be characterized by single phase flow, components ΔPe and ΔPc tend to be more complex due to the two-phase
nature of the flow.
One should note that density is in the denominator of the last equation, and since the density of the liquid is so much higher than the density of the vapor, and therefore, the order of magnitude of pressure drop caused by the vapor is quite larger than by the liquid inthe evaporator. Suggested by Singh et al. [7], this simplification implies neglecting the pressure drop generated by the liquid, admitting the pressure drop due to the vapor the total pressure drop verified. However, this simplification is not suitable for the condenser because its geometry generates more losses and, consequently, it could lead to inaccurate values. Therefore, the pressure drop in the two-phase flow verified in the condenser is estimated by the homogeneous model reported by Milanez and Mantelli [5]. In the homogeneous model for two-phase flow pressure drop, the two phases flow at the same velocity and it is assumed that the flow is one-dimensional. Calculations manage the two phases as a hypothetical fluid comprising homogeneous properties. According to Milanez and Mantelli [5], apud Collier and Thome [8], the pressure gradient in the flow direction for an incompressible flow is calculated as:
− =2 1 + + sin Ω ( + )+ (10) where = ̇ (11) = ̇ ̇ (12) = 0.079 ̅ . (13)
The literature presents several models for the equivalent viscosity. In this work, the Cicchitti model is used:
̅ = + (1 − ) (14)
The vapor quality variation is assumed to be linear because the heat flux, and consequently the condensation rate, is uniform along the condenser length in each power level. Therefore, the vapor quality, x, is 1 at the condenser inlet and 0 at the outlet. Vapor quality is defined as:
= 1 − (15)
Finally, the condenser pressure drop is calculated as:
∆ = (16)
whereLc is the total condenser length, including the equivalent lengths of
accessories and bends.
Nevertheless, the total pressure drop due to the working fluid flow must be compensated by a hydraulic head between evaporator and condenser. Milanez and Mantelli [5] explain that H is the vertical distance between evaporator liquid pool surface and condenser bottom. When the thermosyphon attains its heat transfer limit due to pressure drop, H=Hmax, it means that any further increase in the heat transfer rate
this case, the thermal resistance of the system rises by the fact that only the portion of the condenser that is filled by vapor is effective for heat transfer.
Figure 3 – Hydraulic head in a loop thermosyphon.
(a) (b) (c)
(a) above the pressure drop limit (Hmax>H); (b) pressure drop limit (Hmax=H); (c) beyond the pressure drop limit (H>Hmax).
Finally, the total pressure drop of the working fluid flow is related to the hydraulic head H through the following expression:
∆ = ( − ) (17)
whereg is gravity acceleration at sea level, 9.81 m/s2. To find the maximum distance admissible Hmax, just make both equations equal.
Additionally, if the device comprises a porous media, its capillarity must overcome the pressure drop due to flow through the media. Assuming the porous media as a wick, the pressure drop due to liquid flow through the wick thickness ΔPl,w can be determined by
Darcy’s law, as suggested by Singh et al.[7] andpresented as follows:
∆ , = ℎ
1
(18)
wherekwsis the specific permeability of the wick and describes its ability
to transport liquid under an applied pressure gradient. In case of wick, Mantelli [4] suggests that:
=
122(1 − ) (19)
andε, the porosity of the wick, is: = 1 − 1.05
4 (20)
whereNM is the mesh number and dw the wire diameter of the wick.
A pressure gradient can describe the ability of the wick to transport liquid and so, can be estimated by the following equation, as recommended by Mantelli [4]:
∆ = 2 (21)
wherereffis the effective ratio of the pore, which vary for each type of
media porous. Mantelli [4], apudChi [9], suggests that the effective ratio for wicks made by round wires can be obtained by:
= 1
2 (22)
2.2.2Thermal resistance approach
The analogy between thermal and electrical circuits is largely used in steady-state problems in order to determine the global thermal resistance of heat pipes and thermosyphons. The global thermal resistance is the inverse of the global thermal conductance. Namely, this property allows for the measurement of the device capability to transfer heat. In this sense, it is desirable to minimize the global thermal resistance of a thermal control system.
The global thermal resistance of a heat pipe or thermosyphon is defined by the ratio between the temperature difference of the evaporator and condenser and the power input transferred, which is:
The thermal resistance model offers the possibility to associate different phenomena such as heat conduction in the wall and wick, evaporation and condensation at the liquid-vapor interface, forced convection in the vapor channel and also heat spreading. Each phenomenon has its respective resistance and an equivalent thermal circuit can be built associating them.
Figure 4 shows the thermal resistance circuit of a typical heat pipe, where the porous media covers the internal wall of the pipe. The first resistance encountered by the heat flow is an external resistance, usually related to convection, radiation or a contact resistance between the heat source and the external wall of the evaporator (R1). Following, there is the resistance of heat conduction in the wall of the heat pipe. In this stage, the heat flow has two different paths to follow, radial conduction (towards to the working fluid through the wall – R2) and axial conduction (along the adiabatic region – R3). Following the radial direction, the heat flow faces the contact thermal resistance between the internal wall of the evaporator and the porous media (R4). Once the porous media is reached, the heat flow has two options to proceed over again: radial conduction (towards to the working fluid through the porous media – R5) and axial conduction (along the porous media – R6). Achieving the inner area of the evaporator, the heat flow faces the boiling thermal resistance (R7). In the vapor channel, there is the axial resistance through the adiabatic section until the condenser is reached (R8). The resistances found in the condenser are similar to those of the evaporator.
Some issues such as geometry, thermal conductivity of the case and heat pipe installation are determinants to evaluate the relevance of each resistance in the equivalent resistance circuit. The order of magnitude of some resistances were investigated by researchers and the result is presented in Table 1.
Table 1 - Comparative values of the order of magnitude for thermal resistances found in typical heat pipes (Mantelli [4], apudAsselman e
Green [10]).
Thermalresistance Order of magnitude (oC/W)
R6 10 4 R3 10 2 R5,R10 101 R2,R12 10-1 R7,R9 10-5 R8 10 -8
Evaluating data from Table 1 it can be inferred that some resistances have values considerably larger than the others. When they act in parallel, these resistances could be removed from the circuit without a significant loss in the accuracy of the equivalent thermal resistance. Considering the schematic shown in Figure 4, the resistances in parallel, R4 e R7 could be removed creating a circuit compounded only by resistances in series. A similar analysis of circuit of thermal resistances can be applied to different types of heat pipes and thermosyphons based on this typical one.
2.2.2.1Thermal spreading resistance
Many typical applications in engineering systems presents concentrated heat sources instead of a regular distribution of heat dissipation in its external surface. This feature requires an analysis on how thermal spreading resistance works. A general solution based on separation of variables method for thermal spreading resistances of eccentric heat sources on a rectangular flux channel is presented by Muzychkaet al. [11]. The solution may be applied to isotropic or compound material as well as to single or multi-source systems, using superposition methods. In addition, the solution can be either employed in cases involving single or multiple heat sources.
The general solution will depend on several dimensionless geometric and thermal parameters. Generally, the total resistance is given by:
= + (24)
whereRs is the spreading resistance and R1D is the one dimensional
resistance of the system calculated by:
= + 1
ℎ (25)
whereAc=ab, and h is a convective heat transfer coefficient (see
Figure 5).
Figure 5 – Frontal and superior views of an isotropic plate with an eccentric heat source laid down.
Source – Adapted from Muzyshkaet al.[11].
= − (26)
where is the mean source temperature and Te is the temperature of the
fluid located after the wall. Consider an isotropic plate with single heat source as shown in
Figure 5. The temperature distribution is obtained by the solutions of the Laplace’s equation:
= + + = 0 (27)
which is subject to a uniform flux distribution within the heat source area, As=cd, given by:
∂T
∂z = −
q/
k (28)
The remaining area is thermally insulated, or: ∂T
∂z = 0 (29)
The bottom surface is submitted to the following convective (mixed) boundary condition:
= −ℎ[ ( , , ) − ] (30)
The edges of the plate are considered insulated:
,
= 0 (31)
,
Muzychkaet al. [11] applied the method of separation of variables to solve the Eq. 20, subjected to the boundary conditions given by Eqs. 21 to 25 and the solution, for θ(x,y,z)=T(x,y,z)-Te, is:
( , , )
= +
+ cos( ) [ cosh( ) + sinh ( )]
+ cos( ) [ cosh( ) + sinh ( )]
+ cos( )cos ( ) [ cosh( )
+ sinh ( )] (33)
The eigenvalues are, where m and n are real numbers varying from 1 to ∞:
= (34)
= (35)
= + (36)
Fourier coefficients are defined as follows:
=2 ( ) − ( ) ( ) (37) =2 ( ) − ( ) ( ) (38) =16 ( ) cos( ) , ( , ) (39)
= − ( ) = 1,2,3 (40) where,
( ) = sinh( ) + ℎ cosh ( ) cosh( ) + ℎ sinh ( )
(41)
and is replaced by λ, δ or β, accordingly.
Finally, the last two coefficients, considering uniform input heat flux over the heating area, are determined by:
= +1
ℎ (42)
= − (43)
2.2.3 Correlations for boiling and condensation heat transfer coefficients
In order to determine the equivalent thermal resistance of the system, the calculation of both boiling and condensation coefficients are necessary. A large amount of studies in literature developed correlations to determine condensation and boiling coefficients. Besides that, there are specific correlations for each type of condensation (film, drop, etc) and each type of boiling (pool, confined, etc) depending on the physical phenomenon involved.
In the present work, nucleate pool boiling is considered in the evaporator. As boiling is a very complex phenomenon, different correlations can give divergent results for the same situation because they regard to different physical aspects involved in the boiling process. In this sense, two boiling correlations are used in this work, aiming to compare with experimental results. Regarding condensation, two different correlations for film condensation were employed. Thence, the most appropriate correlation will be evaluated in order to analyse the validity of the model suggested.
2.2.3.1 Kutateladze boiling correlation
The Kutateladze correlation (1952) considers bubble size in nucleated boiling phenomenon. In accordance with Michels [12], apudKutateladze [13], this researcher proposed the following correlation: ℎ = 0.0007 ( − ) . . ℎ . . (44)
2.2.3.2 Foster and Zuber boiling correlation
Foster and Zuber correlation (1955) depends on thermophysical properties of fluids on the superheating of the heated surface (to onset the bubble nucleation) and saturation pressure difference. According to Carey [14], apudFoster and Zuber [15], it is given by:
ℎ = 0.00122 . . . . . ℎ . . [ − ( )] . ∆ . (45) where, ∆ = ( ) −
2.2.3.3 Groll and Rosler condensation correlation
Groll and Rosler [16] developed a correlation based on physical properties of working fluid, power input and geometric aspects, specifically for two-phase thermosyphons. Groll and Rosler correlation (1992) is represented by the following expression according to Angelo [17]: ℎ = ( ) ⁄ ⁄ 0.235 ⁄ (46)
2.2.3.4 Kaminaga condensation correlation
Kaminagaet al. [18] developed a correlation for two-phase thermosyphons based one experimental analysis. According to Angelo [17], the correlation was conceived by linear regression of data obtained under forced convection conditions, being given as:
ℎ = (47)
where,
= 25 . . (48)
= 4
ℎ (49)
The above correlations will be used in this work to determine thermal resistances for the electrical circuit analogy model, as it will be presented later.
2.3 DIFFUSION BONDING
A brief explanation about diffusion bonding is pertinent once this process is employed in the evaporator fabrication. Diffusion bonding is a technique in which the joining process happens in the solid state. Therefore, there is no melted zone near the connection interface, which prevent or minimize the degradation of functional microstructures and avoid macroscopic plastic deformation of the structure [19]. Figure 6 shows the present mechanisms in the material interface during bonding diffusion.
