FEDERAL UNIVERSITY OF SANTA CATARINA GRADUATE PROGRAM IN

Raúl Andrés Puentes Beltrán

STUDY OF RADIATIVE RECUPERATORS APPLIED TO HIGH TEMPERATURE

Florianópolis 2017

Raúl Andrés Puentes Beltrán

ESTUDO DE RECUPERADORES RADIATIVOS EM FORNOS DE ALTA TEMPERATURA

Dissertação submetida ao Programa de Pós-Graduação em Engenharia Mecânica da Universidade Federal de Santa Catarina para a obtenção do título de Mestre em Engenharia Mecânica. Orientador: Prof. Vicente de Paulo Nicolau, Dr.

Florianópolis 2017 Ficha de identificação da obra elaborada pelo autor, através do Programa de Geração Automática da Biblioteca Universitária da UFSC.

Puentes Beltrán , Raúl Andrés Study of radiative recuperators in high temperatures furnaces / Raúl Andrés Puentes Beltrán ; orientador, Vicente de Paulo Nicolau, coorientador, Edson Bazzo, 2017. 117 p.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós Graduação em Engenharia Mecânica, Florianópolis, 2017.

Inclui referências.

1. Engenharia Mecânica. 2. Trocadores de calor. 3. Recuperadores radiativos. 4. Fornos de alta temperatura. 5. Recuperação de calor residual. I. Nicolau, Vicente de Paulo . II. Bazzo, Edson. III. Universidade Federal de Santa Catarina. Programa de Pós-Graduação em Engenharia Mecânica. IV. Título. Raúl Andrés Puentes Beltrán

ESTUDO DE RECUPERADORES RADIATIVOS EM FORNOS DE ALTA TEMPERATURA

Esta Dissertação foi julgada adequada para obtenção do Título de “Mestre em Engenharia Mecânica”, e aprovada em sua forma final pelo Programa de Pós-Graduação em Engenharia Mecânica da Universidade Federal de Santa Catarina.

Florianópolis, 8 de maio de 2017.

Prof. Vicente de Paulo Nicolau, Dr. Orientador Universidade Federal de Santa Catarina

Prof. Jonny Carlos da Silva., Dr. Eng. Coordenador do Curso

Banca Examinadora:

Prof. Vicente de Paulo Nicolau, Dr. – Presidente Universidade Federal de Santa Catarina

Prof. Amir Antônio Martins de Oliveira Jr., Ph.D Universidade Federal de Santa Catarina

Prof. Talita Sauter Possamai, Dra. Universidade Federal de Santa Catarina (Membro externo)

Prof. Alexandre Kupka da Silva, Ph.D. Universidade Federal de Santa Catarina

ABSTRACT

The present dissertation is dedicated to study heat exchangers applied to high temperature furnaces, in order to recover thermal energy from gases. Applications as preheating the air, for the purpose of reduce the fuel consumption and others are emphasized. The classification of these equipments is varied, but the two most important types are the recuperators and regenerators. The particularities of each one them are shown in this work. The study is focused on the radiative recuperators due to its extensive use and simplicity in construction and assembly. Traditionally, LMTD and 휀-NTU methods are used for the calculation and design of heat exchangers. CFD simulation of the and fluid mechanics phenomena are involved, resulting in a numerical solution of temperature distributions and recuperator effectiveness. In addition the influence of parameters such as the flue gases temperature and flow rate, the air flow rate on the effectiveness are studied and some conclusions are presented. Finally, an experimental approach is considered in order to compare the respective results with the simulated one, for a particular type of .

Keywords: Radiative Recuperators, Heat Exchangers, Recovery, High Temperature Furnaces.

RESUMO EXPANDIDO

INTRODUÇÃO O aproveitamento da energia residual nos equipamentos industriais como fornos de grande e médio porte é uma tendência cada vez maior, face ao crescente consumo mundial de energia. Este aproveitamento é feito, principalmente, com o uso de trocadores de calor que recuperam parte da energia proveniente dos gases de exaustão, a qual normalmente é utilizada no pré-aquecimento do ar de combustão ou para outros usos como secagem de produtos e condicionamento de ar. No caso de fornos industriais, os recuperadores e os regeneradores são os equipamentos mais usados. As diferenças entre estes dois tipos de equipamentos são explicadas mais detalhadamente neste trabalho. Os recuperadores radiativos tem especial importância devido a sua simplicidade de instalação e por serem os recuperadores mais usados nestes fornos.

OBJETIVOS O objetivo geral deste trabalho é estudar os principais parâ- metros que influenciam a efetividade térmica nos recuperadores radiativos, utilizando a metodologia de simulação numérica por CFD. Os objetivos específicos estabelecidos neste trabalho são os seguintes: 1. Fazer uma revisão bibliográfica dos recuperadores e regeneradores e um resumo sobre os conceitos fundamentais para o projeto de trocadores de calor; 2. Simular com o software ANSYS CFX as configurações mais importantes de recuperadores radiativos para obter a efetividade e outras variáveis de interesse; 3. Comparar os resultados simulados com os métodos tradicionalmente utilizados no cálculo de trocadores de calor; e 4. Comparar os modelos simulados com medições feitas em um trocador instalado e em funcionamento. MATERIAIS E METODOS A metodologia deste trabalho consiste em construir modelos discretizados de um trocador de tubos concêntricos a contra-corrente, utilizando o software ANSYS CFX, o qual é baseado no método dos volumes finitos. Variáveis como vazão mássica e temperatura são alteradas para o ar e gases de exaustão, de forma a determinar a influência destas na efetividade do trocador. Diferentes configurações geométricas (sem aletas, com aletas, com tubulações internas), também são analisadas. Uma abordagem experimental é feita para comparar os valores simulados com os valores medidos.

RESULTADOS No primeiro caso analisado, a temperatura e a vazão do gases de exaustão foram variadas. A geometria foi fixada e consiste em uma chaminé cilíndrica por onde escoam os gases de exaustão, ao redor da qual escoa o ar para pré-aquecimento, sendo o recuperador isolado na parte exterior. Os resultados obtidos mostram que, à medida que a vazão dos gases de exaustão aumenta, a efetividade do trocador aumenta também. Para o caso de uma temperatura de entrada dos gases de exaustão de 1200 K e uma vazão de 0,0842 kg/s, a efetividade calculada pela simulacão é de 30%. Já para o caso de uma temperatura 530 K e uma vazão de 0,5 kg/s, a efetividade aumentou a um valor de 51%. A efetividade analítica calculada pelo método 휖-NTU para a temperatura de entrada de gases de 1200 K e uma vaão de 0,0842 kg/s é de 1,6% e para uma temperatura e vazão de gases de 530 K e 0,5 kg/s respetivamente, a efetividade pelo método 휖-NTU aumenta para 2,1%. No segundo caso, apenas a vazão de ar mudou. As condições dos gases na entrada foram fixadas em 1200 K e 0,0842 kg/s e a temperatura na entradado ar foi fixada em 298 K. A efetividade foi de 34% para ocasode 0,5 kg/s de vazão de ar e foi de 35% para a vazão de ar de 1 kg/s. As efetividades pelo método 휖-NTU são de 6,0% para uma vazão de 0,5 kg/s e de 15,5% para o caso de uma vazão de 1 kg/s . No terceiro caso, foi mudada a geometria da parede exterior da chaminé e foram adicionadas aletas para aumentar a superfície de troca de calor com o ar. Para umas condições de 0,0842 kg/s e 1200 K de entrada nos gases de exaustão e uma vazão de 0,1 kg/s de ar a 298 K e com a adição de 80 aletas, a efetividade resultou em 42%. A queda de pressão com o aumento de aletas também foi calculado. Para o caso sem aletas a queda de pressão resultou em 10,2 Pa e 128,2 Pa para o caso de 80 aletas. O último caso analisado foi uma geometria tipo gaiola onde escoa o ar por tubulações no interior da chaminé. A efetividade resultou no maior valor dentre todos os casos de 45%. Entretanto a queda de pressão calculada foi de 420 Pa. A análise experimental apresentou um bom resultado comparado com a solução simulada, tendo uma diferença de aproximadamente 11 K nas temperaturas de saída, tanto de ar e de gases. A redução no consumo de combustível foi calculada e apresentou um valor de 38% para um trocador montado num forno de cristais, considerando apenas a perda de energia no forno, não incluindo a perda associada aos gases de exaustão. Aumentando o comprimento do trocador em quatro vezes, ocorre a diminuição do consumo de combustível em 51%, além do que aumenta a efetividade do trocador em 35%.

CONCLUSÕES As efetividades do recuperador são diretamente proporcionais à vazão dos gases de exaustão; quanto maior esta vazão, maior é a efetividade. Os métodos tradicionais de cálculo de trocadores de calor, como o método 휀-NTU, apresentam resultados afastados dos resultados simulados, pelo fato de não ter em conta a radiação dos gases de exaustão. Esta diferença é quase de 90%. Dessa forma, os métodos tradicionais apresentam uma diferença no caso de recuperadores radiativos para temperaturas superiores a 1200 K. Quando a temperatura dos gases diminui e a vazão aumenta, a radiação térmica deixa de ser o mecanismo dominante. Como trabalho futuro propõe-se um parâmetro para classificar os recuperadores baseado no principal mecanismo de trasferência de calor. O uso de superfícies extendidas aumenta a efetividade dos recuperadores, mas também aumenta a queda de pressão no escoamento. Um número ótimo de aletas poderia ser calculado para uma queda de pressão adequada. A redução em consumo de combustivel é considerável; quando o ar é pré-aquecido até ∼600 K a redução pode chegar a 51% das perdas associadas ao forno.

Palavras Chave: Recuperadores Radiativos, Trocadores de Calor, Recuperação de Calor Residual, Fornos de Alta Temperatura. To my mother Deisy, my father Raul, my sister Diana, my aunts Sandra and Stella and all my family. In memory of my always beloved and never forgotten grandmother Carmen Guerrero. ACKNOWLEDGMENTS

I would like to express my very great appreciation to Professor Vicente de Paulo Nicolau for his valuable and constructive suggestions during the planning and development of this research work. His willingness to give his time so generously has been very much appreciated. I would like to express my deep gratitude to Professor Amir Antônio Martins de Oliveira Jr., Professor Alexandre Kupka, and Professor Talita Sauter Possamai, my research examining board, for their enthusiastic encouragement and useful critiques of this research work. Special thanks to Edemar Morsch Filho, Daniel Bonin, Flávia Belló Artuso and Carlos Mahl Spohr, whom work in the group of energy efficiency of LABCET for their professional guidance and constructive recommendations on this project. I wish to thank to the post-graduate program of mechanical engineering of Federal University of Santa Catarina (POSMEC-UFSC), Santa Catarina Gas company (SCGÁS), Smalticeram Unicer do Brasil Ltda. and Cristal Blumenau Ltda. Finally my sincerely gratitude to my parents and friends for their support and encouragement throughout my academic life. “No te des por vencido, ni aún vencido, no te sientas esclavo, ni aún esclavo; trémulo de pavor, piénsate bravo, y arremete feroz, ya mal herido. Ten el tesón del clavo enmohecido, que ya viejo y ruin, vuelve a ser clavo; no la cobarde estupidez del pavo que amaina sus plumas al primer ruido. Procede como Dios que nunca llora, o como Lucifer, que nunca reza; o como el robledal, cuya grandeza necesita del agua y no la implora. ¡Que muerda y vocifere vengadora, ya rodando en el polvo, tu cabeza!” Pedro Bonifacio Palacio (1854-1917) LIST OF FIGURES

Figure 1 – Fuel shares on total primary energy consumption (IEA, 2014)...... 29 Figure 2 – Fixed bed regenerator operation. (Willmott, 2016)...... 34 Figure 3 – Regenerators in glass . (PCO, 2017). . . 35 Figure 4 – Rotating regenerator scheme. Adapted from Reay (1980)...... 35 Figure 5 – Radiative recuperator. (Turner & Doty, 2007). . 36 Figure 6 – Typical convective recuperator. (Kalfrisa, 2016) . 38 Figure 7 – Global energy balances in a heat exchanger. (Bergman et al., 2011)...... 39 Figure 8 – Temperature distributions in heat exchanger. a) Parallel flow. b)Counter flow. (Bergman et al., 2011)...... 40 Figure 9 – Effectiveness in heat exchanger. a) Parallel flow b) Counter flow. Adapted from Bergman et al. (2011). 42 Figure 10 – Configurations of hybrid recuperator-steam Rankine cycle system: a) Series arrangement b) Parallel arrangement. Adapted from Incropera et al. (1985)...... 43 Figure 11 – Outlet air temperature in radiative and convective recuperators, adapted from Prescott & Incropera(1985)...... 45 Figure 12 – Effectiveness in function of NTU and non dimensional number Π, adapated from Sahin (1997)...... 47 Figure 13 – Concentric shell radiation heat exchanger control volumes (Sharma et al., 2012)...... 50 Figure 14 – Variation of effectiveness with a) Mass flow of flue gases for a inlet gases temperature of 1500 K and b) Inlet flue gases temperature with a gases mass flow rate of 1.33 kg/s and mass flow rate of1.25 kg/s. Adapted from Sharma et al. (2012). . . . . 51 Figure 15 – In ceramic houseware industry, the frit is used as a glaze component...... 54 Figure 16 – Frit furnace. a) Side view. b) Front view...... 54 Figure 17 – Main parts of frit furnace...... 55 Figure 18 – Frit formation cooling the melting material. . . . 55 Figure 19 – Packing the frits into big bags ...... 56 Figure 20 – Variation of temperature of flue gases with of air (Temperature of air for dilution = 298 K)...... 58 Figure 21 – General dimensions of recuperator ...... 59 Figure 22 – Thermal resistances in the recuperator...... 59 Figure 23 – y+ parameter and a generic wall function used to solve the boundary layer...... 65 Figure 24 – Emissivity in a mixture with nonradiating gases at 100 kPa. (Bergman et al., 2011) ...... 67 Figure 25 – Emmisivity correction factor in a mixture of water vapor and carbon dioxide. (Bergman et al., 2011) ...... 67 Figure 26 – Mesh independence test applied to flue gases temperature along the stack...... 71 Figure 27 – Meshes used in the simulation (1/4 of the cross section): a) Coarse mesh (289,266 control volumes) b) Intermediate mesh (645,946 control volumes) c) Fine mesh (1,308,986) ...... 72 Figure 28 – Detail of the finned mesh (40 fins)...... 78 Figure 29 – Effectiveness and pressure drop (Case 3: Finned recuperator)...... 79 Figure 30 – Cross section of recuperator with bundle of tubes (Case 4)...... 80 Figure 31 – Furnace for production of crystal products. . . . 83 Figure 32 – Furnace scheme. Adapted from Trombini(2013) . 84 Figure 33 – Recuperator analyzed ...... 85 Figure 35 – Fuel consumption and temperature in a typical furnace operation day...... 85 Figure 34 – The handcrafted process of lead glass production. 86 Figure 36 – Measurements of air mass flow, equal areas method. 87 Figure 37 – Volumetric flow measurement...... 88 Figure 38 – Wall temperatures in the recuperator a) Low consumption b) High consumption ...... 90 Figure 39 – Furnace scheme with recuperator, adapted from Turns(1996) ...... 94 Figure 40 – Radiation interactions on a surface (Siegel & Howell, 2001)...... 106 Figure 41 – Network representation of radiative exchange between surface 푖 and the 푁 remaining surfaces of an enclosure. Adapted from Bergman et al. (2011)...... 108 Figure 42 – Radiation heat transfer in participating media. Adapted from Modest(2003)...... 109 Figure 43 – Mesh-point cluster for the one dimensional steady heat conduction problem. Adapted from Patankar(1980)...... 116 Figure 44 – Mesh-point cluster for the two dimensional situation. Adapted from Patankar(1980). . . . . 117

LIST OF TABLES

Table 1 – Effectiveness of radiative recuperator in a hybrid system recuperator-waste heat ( series arrangement case). Adapted from Incropera et al. (1985)...... 44 Table 2 – Effectiveness of radiative recuperator in a hybrid system recuperator-waste heat boiler ( parallel arrangement case with 푚˙ 푠=0.5 kg/s). Adapted from Incropera et al. (1985)...... 44 Table 3 – Effectiveness of radiative recuperator in a hybrid system recuperator-waste heat boiler ( parallel arrangement case with 푚˙ 푠=0.75 kg/s). Adapted from Incropera et al. (1985)...... 44 Table 4 – Process variables in frit furnace...... 56 Table 5 – Theoretical molar fraction of combustion products. 57 Table 6 – Case 1: Varying the temperature and mass flue gases. 61 Table 7 – Physical properties of domains. Adapted from Bergman et al. (2011)...... 62 Table 8 – Model constants in 푘 − 휔 model (ANSYS, 2009). . 64 Table 9 – Absorption coefficients for the temperatures of flue gases considered in Case 1 ...... 66 Table 10 – Boundary conditions ...... 69 Table 11 – Analytical forced convective heat transfer coefficients (Case 1)...... 73 Table 12 – Mean temperatures in the inlet and outlet sections (T푖푛 air = 298 K, T푟푒푓 =298 K)...... 73 Table 13 – Effectiveness predicted by the 휀-NTU method (T푖푛=298 K)...... 74 Table 14 – Simulated and 휀-NTU effectiveness...... 75 Table 15 – Mean temperatures and Heat rate in the entrance and exit sections (Case 2: gases mass flow = 0.0842 kg/s, T푖푛 gases = 1200 K, T푖푛 air= 298 K). . . . 76 Table 16 – Analytical forced convective heat transfer coefficients (Case 2)...... 76 Table 17 – Analytical effectiveness predicted by the 휀NTU- method (Case 2)...... 77 Table 18 – Simulated and 휀-NTU effectiveness in the recuperator (Case 2)...... 77 Table 19 – Effectiveness extended surfaces...... 79 Table 20 – Effectiveness (Case 4: Bundle of 52 tubes with an external diameter of 1")...... 81 Table 21 – Comparison between differents configuration of recuperators, inlet gases temperature = 1200 K, gases mass flow = 0.0842 kg/s, air mass flow= 0.1 kg/s...... 81 Table 22 – Air velocities (low consumption); Tube radio R = 109.5 mm...... 88 Table 23 – Comparison between variables measured . . . . . 90 Table 24 – Heat wall loss ...... 91 Table 25 – Boundary conditions for the numerical simulation 92 Table 26 – Temperatures at the domains boundaries . . . . . 93 Table 27 – of products at 1153 K...... 95 Table 28 – Fuel efficiency and fuel savings for several recuperator lengths, L=1.39 m, 휂퐹,298퐾 = 0.17 . . 96 Table 29 – Summary of radiation properties of real surfaces. Adapted from Modest(2003)...... 112 Table 30 – Summary of conservation equations. Adapted from Maliska(2004)...... 115 LIST OF SYMBOLS AND ABBREVIATIONS

Roman

푉¯ Mean velocity, m/s. 푚˙ Mass flow, kg/s 푛˙ Molar flow, kmol/s. 퐴 Area, m2. 푎 Absorption coefficient, 1/m 퐶 Heat capacity rate, kg/K s.

퐶푟 Heat capacity ratio.

퐶푝 Specific heat at constant pressure, kJ/kg K. 퐷 Diameter, m. 퐸 Emissive Power, W/m2. 퐸푐 Eckert number. 푓 Friction factor.

퐹푖푗 View factor from i-surface to j-surface. 퐺 Irradiation, W/m2. ℎ Convective heat transfer coefficient, W/m2 K. ℎ Specific enthalpy, kJ/kg 푖 Radiation intensity, W/m2 µm sr. 퐾 Extinction coefficient, 1/m. 푘 Thermal conductivity, W/m K 퐿 Length, m 푀 Molar mass, kg/kmol. 푀푊 Molecular weight, kmol/kg. 푛 Number of moles, kmol 푁푢 Nusselt number. 푃 푟 Prandtl number. 푞 Heat rate, W 푅 Thermal resistance, K/W. 푟 Radius, m. 푟 Residual 푅′′ Fouling factors, K m2/W. 푅푎 Rayleigh number. 푅푒 Reynolds number. 푆 Source. 푠 Thickness, m. 푆푡 Stanton number. 푇 Temperature, K. 푈 Overall heat transfer coefficient, W/m2 K. 푣 Flow velocity , m/s Greek 훼 Thermal difussivity, m2/s.

훼휆 Absortivity. 훽 Coefficient of compressibility, m2/N. 휒 Molar fraction.

휖휆 Emissivity

휂푓 Single fin efficiency, 휂표 Global surface efficiency,

휂퐹 Fuel efficiency. Γ Generic diffusive term in conservative equations. 휅 Optical thickness. 휇 Dynamic viscosity, Pa s. 휈 Kinematic viscosity, m2/s. 휔 Solid angle, sr. Φ Phase function. 휑 Azimuth angle, rad. 휑 Generic conservative variable. 휌 Density, kg/m3.

휌휆 Reflectivity. 휎 Stefan-Boltzmann constant, W/m2K4.

휎푠 Scattering coefficient, 1/m. 휏 Transmittance. 휃 Zenith angle, rad. 휀 Effectiveness Subscript 0 Position zero. 푏 Blackbody 푐 Cold fluid/. 푑 Downstream/diluted/dry. 푒 Emitted. 푓 Finned. 푔 Incident/Flue gases. ℎ Hot fluid 푖 Inlet/initial. 푚푎푥 Maximum. 푚푖푛 Minimum. 표 Outlet. 푟 Ratio/Radiation. 푠 Shell. 푢 Upstream. 푤 Wall/wet. Abbreviation DNS Direct Numerical Simulation DOE United States Department Of Energy. FDM Finite Differences Method. FEM Finite Elements Method. FS Fuel Savings. FVM Finite Volumes Method. HRSG Heat Recovery Steam Generator . HVAC Heating, Ventilating and . IEA International Energy Agency. LES Large Eddy Simulation. LHV Low Heating Value, kJ/kg. LMTD Log. Mean Temperature Difference. LPG Liquid Petroleum Gas. MTOE Millions of Tons of Oil Equivalent. NTU Number of Transfer Units. RANS Reynolds Averaged Navier Stokes. RTE Radiation Transport Equation. CONTENTS

Page

1 INTRODUCTION...... 29 1.1 Objectives...... 32 2 HEAT EXCHANGER DESIGN THEORY AND LITERATURE REVIEW ...... 33 2.1 Heat exchanger...... 33 2.2 Regenerators ...... 33 2.3 Radiative Recuperator...... 36 2.4 Convective Recuperator ...... 36 2.5 Thermal Analysis...... 38 2.5.1 Logarithmic Mean Temperature Difference Method for Heat Exchangers-LMTD ...... 39 2.5.2 휀 − 푁푈푇 method...... 40 2.6 Literature Review ...... 42 3 METHODOLOGY ...... 53 3.1 Introduction...... 53 3.2 Frit Furnace...... 53 3.2.1 Mass balance and equilibrium composition of products ...... 55 3.3 The radiative recuperator problem...... 58 3.3.1 Cases to analyze...... 61 3.3.2 Physical domains...... 61 3.3.3 Turbulence models...... 62 3.3.3.1 Reynolds Averaged Navier-Stokes (RANS) Equations...... 63 3.3.3.2 푘 − 휔 model and wall function...... 64 3.3.4 Radiative properties of the flue gases ...... 66 3.3.5 Meshing Parameters...... 67 3.3.6 Boundary conditions...... 68 3.3.7 Solving the model ...... 69 3.3.7.1 Residuals...... 70 4 RESULTS...... 71 4.1 Mesh independence test ...... 71 4.2 Case 1: Varying flue gases condition ...... 72 4.2.1 Pure convective effectiveness ...... 74 4.3 Case 2: Varying the mass flow of air ...... 75 4.3.0.1 Effectiveness by 휀-NTU Method ...... 75 4.3.1 Case 3: Finned surfaces in recuperators ...... 77 4.3.1.1 Pressure drop in extended surfaces ...... 78 4.3.2 Case 4: Radiative recuperator with bundle of tubes 80 5 APPLICATION TO AN INDUSTRIAL FURNACE...... 83 5.1 Furnace and process description...... 83 5.2 Measurements...... 86 5.2.1 Volumetric flow measurements...... 86 5.2.2 Mass balance and equilibrium of combustion products ...... 89 5.2.3 Temperature measurements...... 89 5.3 Energy balance...... 90 5.4 Recuperator effectiveness ...... 92 5.5 Numerical simulation...... 92 5.6 Results...... 93 5.7 Savings in fuel consumption...... 93 6 CONCLUDING REMARKS ...... 97

BIBLIOGRAPHY ...... 99

ANNEX A - RADIATIVE HEAT TRANSFER . . . 105

ANNEX B - CFD AND FINITE VOLUMES METHOD113 29

Chapter 1

INTRODUCTION

The advantages of heat recovery in engineering applications can be remarked: 1. Savings in consumption of non-renewable energy sources in order to preserve the environment with the reduction of pollutants emission; 2. Reductions of capital costs in new installations. Figure1 illustrates the mainly primary energy sources consumed in 1973 and 2013. As it can be seen, the energy consumption was duplicated reaching 13,541 MTOE (millions of tons of oil equivalent) in 2013 and the oil, coal and natural gas were over 80% of total primary energy consumption. Additionally, Forman et al. (2016) has shown that around 72% of energy is lost in the process of conversion from these primary sources to their final energy form. Hence, the research in heat recovery applications has increased in importance in the development of more efficient thermal systems.

Figure 1 – Fuel shares on total primary energy consumption (IEA, 2014).

The opportunity of heat recovery in industrial equipment is promising. The industrial sector accounted for 27% of the total global energy use in 2005 (Banerjee et al., 2012) and considering that the major part of industries use furnaces for their process, the 30 Chapter 1. Introduction heat recovery in these equipments represent an important role. DOE(2008) reveals that, in industrial furnaces, the efficiency improvements resulting from waste heat recovery can improve energy efficiency from 10% to as much as 50%. Three essential components are required for waste heat recovery:

• An accessible source of waste heat. • A recovery technology. • The use for the energy recovered.

In the case of furnaces, the waste heat source is found mostly in the flue gases. The equipment to recover the waste heat often are heat exchangers and also the choice of heat recovery technology depends on the temperature source. The waste heat sources can be classified in the following ranges depending on the temperature source (DOE, 2008).

• High Temperature: (> 650∘C). • Medium Temperature:(230-650∘C). • Low Temperature (< 230∘C).

The preheating of combustion air, furnace load preheating, and steam generation for mechanical or electrical work are the most common applications of from high temperature sources. On the other hand, applications like space heating, domestic water heating and organic Rankine cycles make use of low temperature sources. The waste heat recovery projects are frequently affected by the temperature limits and the costof recovery equipment. High temperature means greater investment in equipment. There are several ways to recover heat in furnaces. Khoshmanesh et al. (2007) present three independent solutions to reduce the fuel consumption in industrial glass melting furnaces. The solutions include air preheating, raw material preheating, and improving the insulation of combustion chamber refractory. In the case of air preheating, Turns(1996) shows that the use of recuperators in furnaces with air combustion allows to save 30% in fuel consumption when the combustion air is preheated from 298 K to 600 K. 31

Possamai et al. (2012) report that the percentage of flue gases energy losses is 33% and the percentage of wall energy losses is 30% in frit production furnace, meaning that up to 63% of waste heat can be recovered. In the case of flue gases heat recovery systems, Reay(1980) classifies these heat exchangers in two categories:

• Recuperators. • Regenerators.

The difference between these categories will be explained in the next chapters. The focus of this work is the analysis of the recuperators due to its extended use in medium-size furnaces and also because the steady state operation make easier for an accurate thermal analysis in contrast with the regenerators. The recuperators are classified by two types (Reay, 1980):

• Convective. • Radiative.

This classification depends on the main heat transfer mechanism. The radiation recuperators show an interesting challenge because there are no theoretical correlations to design this kind of heat exchangers, due to the complex phenomena of thermal radiation. In this work, the study is based in the radiation recuperators. The design of more complex and more efficient heat exchangers isa new challenge nowadays. Numerical simulation allows to solve complex problems, like thermal radiation heat transfer, in contrast with the traditional analytical methods. In the present times, CFD tools offer an excellent way to solve engineering problems with less cost, compared with experimental methodologies and permit analyzing different scenarios (different boundary conditions, complex geometries, different materials, etc.) with a better accuracy and faster than experimental models. This kind of approach can help to explore new research fields looking for better materials, new geometries, new working fluids etc; all of this in order to achieve better commercial equipments. This dissertation is divided in five chapters. Chapter 2 shows the fundamentals of heat exchanger design theory and does a literature review of heat exchangers with the basics and heat transfer theory. In addition, this chapter contains a review of typical commercial devices for heat 32 Chapter 1. Introduction recovery. The methodology employed in the simulation of radiative recuperators is shown in Chapter 3. Chapter 4 addresses the results obtained from the simulations. Chapter 5 shows some experimental measurements made in an installed radiative recuperator to compare with the numerical results, and finally Chapter 6 ends this work with concluding remarks.

1.1 OBJECTIVES

The main objective of this work is to study the most important parameters that influence the thermal effectiveness in radiative recuperators using numerical simulation. The specific objectives are:

1. To make a bibliographic compilation of heat exchangers types typically used for the heat recovery in furnaces and review the fundamentals concepts of heat exchangers design; 2. To simulate with a CFD tool the most important configurations of radiation recuperators for obtaining the effectiveness and other variables of interest; 3. To compare the results obtained by CFD with the analytical methods for heat exchangers design; 4. To compare the numerical model with measures acquired in an installed recuperator. 33

Chapter 2

HEAT EXCHANGER DESIGN THEORY AND LITERATURE REVIEW

2.1 HEAT EXCHANGER

Heat exchangers can be defined as any device where two or more fluid streams promote a heat transfer due to a temperature difference between themselves. These devices have been widely used in industry in general, including power generation, chemical process, HVAC etc. Kakaç & Liu(2002) classify heat exchangers based on the following criteria:

• Recuperators and regenerators. • Transfer process: direct contact or indirect contact. • Geometry of construction. • Heat transfer mechanism: single phase or multi-phase. • Flow arrangement: parallel, counter flow, cross flow.

Reay(1980) made an extensive study about the gas-gas heat recovery systems including recuperators and regenerators. The analysis includes: rotating regenerators, static regenerators, plate heat exchangers, run-around coils, convection recuperators, radiation recuperators, recuperative burners, thermosyphon and heat exchangers, multiple tower enthalpy exchangers, and gas-gas heat pumps.

2.2 REGENERATORS

A recuperator is a device where a cold stream “recovers” heat from other hot stream. Normally, a solid wall separates both streams. On the other hand, regenerators make the heat transfer between the hot and cold streams with a high thermal capacity matrix, commonly a ceramic matrix. The matrix stores energy that later is given to the cold stream. The regenerators can be 34 Chapter 2. Heat exchanger design theory and literature review clasiffied as fixed bed regenerators and rotary regenerators. In fixed bed regenerators, the hot fluid passes through the channels of the packing for a portion of time at the end of which, the hot fluid is switched off for allow to the entry of the fresh air to preheat. The operation is alternated between two regenerators. Figure2 shows the operation of a fixed bed regenerator. In this kind of regenerators, the operation is transient. The fixed bed regenerators have an extended use in the glass industry due to its simplicity in maintenance, operation and cost in general (Willmott, 2016). Figure3 shows a scheme of a typical glass melting furnace with fixed bed regenerators in both sides.

Figure 2 – Fixed bed regenerator operation. (Willmott, 2016).

The other type of regenerator is the rotating regenerators or Ljungstrom wheel. This device has been used widely in the world 2.2. Regenerators 35

Figure 3 – Regenerators in glass furnace. (PCO, 2017).

and it was estimated that in Europe there were a 15,000 rotating regenerators installed in 1975 (Reay, 1980). In this case, the two fluid streams (hot flue gases and cold gases to heat) are separated. When the matrix rotates, it absorbs heat from the flue gases and gives this energy to the cold gases. Figure4 shows the operation of rotating regenerators.

Figure 4 – Rotating regenerator scheme. Adapted from Reay(1980). 36 Chapter 2. Heat exchanger design theory and literature review

2.3 RADIATIVE RECUPERATOR

A conventional radiative recuperator mainly consist of two concentric cylinders, the air to be heated normally flowing through the outer annulus, while the flow through the central . The main heat transfer mechanism in this kind of recuperators is the radiation emitted by the high temperature exhaust gases, more significant when compared with convection heat transfer due to gas flow. For its simplicity in assembly and maintenance, itisthe most popular heat recovery device for stacks in glass furnaces. The main limitation in the radiative recuperator is the use of special materials when the temperature is very high. Sunden(2005) made an extensive research about the materials (metals and ceramics) used in the fabrication of high temperature heat exchangers. The use of radiative recuperators is recommended when the flue gases exceed 600∘C. Figure5 shows a longitudinal section of a typical radiative recuperator.

Figure 5 – Radiative recuperator. (Turner & Doty, 2007).

2.4 CONVECTIVE RECUPERATOR

The main heat transfer mechanism in this heat exchanger type is the convection between the air and the hot walls of the tubes. These kind of recuperators consists in a bundle of tubes with 2.4. Convective Recuperator 37

diameters between 1 to 3 inches where the air flows in the interior. The heat transfer area in the tubes is larger due to the number and length of tubes employeed reaching high convective heat transfer. These exchangers can work from low temperatures (<1,000∘C) to high temperatures (>1,000∘C) but their use is recommended for low temperatures and high mass flow of air. The main disadvantage of these devices is the fouling and difficult cleanliness. Prescott & Incropera(1985) discuss the advantages of convective recuperators for Rankine cycle use. That work proposes some arrangements including radiative and convective recuperators exploiting the advantages of each one of them e.g. in the bottom of the stack, where the hotter exhaust gases are presented, the radiative recuperators should be installed; in higher stack positions, the convective recuperators are recommended. The work reveals the increase of global effectiveness of these arrangements compared with the effectiveness of single equipments in the same operation conditions. Narendran et al. (2016) made a CFD simulation of a convective recuperator. In their work, the exhaust mass flow and inlet temperature are 50,000 kg/h and 200∘C. The low temperature in the inlet is offset by the high mass flow. This situation is usually presented in large size furnaces such as steel and aluminum production furnaces. The air velocity in this simulation vary from 15 to 25 m/s, it reveals the important role of high velocities of air to help to increase the convective heat transfer coefficient in these equipments. Figure6 illustrates the configuration of a convective recuperator (Kalfrisa, 2016). The main differences between the radiative and convective recuperators are:

• The main heat transfer mechanism: Radiation from flue gases in the case of radiative recuperators and convection in the air side in the case of convective recuperators.

• Air mass flow: For high mass flow of air is recommended the use of convective recuperators due to the high velocities reached by the air causing high convective heat transfer coefficients.

• Fouling: Due to the amount of air tubes and low diameters used, the fouling is a common problem in convective 38 Chapter 2. Heat exchanger design theory and literature review

Figure 6 – Typical convective recuperator. (Kalfrisa, 2016)

recuperators. In contrast, the radiative recuperators don’t have this problem. • Operation cost and maintenance: The power required to move the air inside the tubes in a convective recuperator is higher compared with the radiative recuperators due to the pressure drop. The assembly and maintenance of convective recuperator are more expensive.

2.5 THERMAL ANALYSIS

Different energy interactions are typically involved in heat exchangers as heat transfer mechanisms - conduction, convection and radiation - are present in heat exchangers. The energy balances and heat transfer relations are the basis for designing heat exchangers of any kind. In an adiabatic heat exchanger with two fluid streams, the energy balance becomes:

푞 =푚 ˙ ℎ(ℎℎ,푖 − ℎℎ,표) (2.1)

푞 =푚 ˙ 푐(ℎ푐,표 − ℎ푐,푖), (2.2) where 푞 is the heat flux exchanged between the hot and cold fluid streams, 푚˙ ℎ and 푚˙ 푐 are the mass flow of hot and cold streams respectively, ℎℎ,푖 and ℎℎ,표 are the specific enthalpy of the hot fluid at the inlet and outlet respectively and in the same manner, ℎ푐,푖 and ℎ푐,표 are the specific enthalpy of the cold fluid at the inlet and 2.5. Thermal Analysis 39 outlet respectively. Equations (2.1) and (2.2) are independent of the heat exchanger type or flow configuration. Figure7 is the scheme of the general energy balance between two streams.

Figure 7 – Global energy balances in a heat exchanger. (Bergman et al., 2011).

2.5.1 Logarithmic Mean Temperature Difference Method for Heat Exchangers-LMTD Other useful equations for heat flux between the two fluid streams that links the geometry and heat exchanger type are the following (Bergman et al., 2011).

푞 = 푈퐴Δ푇푙푚 (2.3) where Δ푇2 − Δ푇1 Δ푇푙푚 = (2.4) 푙푛(Δ푇2/Δ푇1)

The Δ푇푙푚 can be understood as an average temperature difference resulted from the infinitesimal energy balance along the whole heat exchanger length. In the analysis, the overall heat transfer coefficient 푈 is considered constant along all the heat exchanger. Bergman et al. (2011) made the complete deduction of Δ푇푙푚. The values for Δ푇2 and Δ푇1 depend on the flow configuration (parallel or counter-flow array):

Δ푇1 ≡ 푇ℎ,푖 − 푇푐,푖 (2.5) and Δ푇2 ≡ 푇ℎ,표 − 푇푐,표 Parallel flow (2.6)

Δ푇1 ≡ 푇ℎ,푖 − 푇푐,표 (2.7) 40 Chapter 2. Heat exchanger design theory and literature review and Δ푇2 ≡ 푇ℎ,표 − 푇푐,푖 Counter flow (2.8)

Figure 8 – Temperature distributions in heat exchanger. a) Parallel flow. b)Counter flow. (Bergman et al., 2011).

a) b)

Figure8 presents the difference between the profiles if the configuration is counter or parallel flow. In heat exchangers, in general, the overall heat transfer coefficient 푈 and the global surface efficiency 휂표 are defined by, respectively(Bergman et al., 2011):

1 1 1 푅”푓,푐 푅”푓,ℎ 1 = = + + 푅푤 + + 푈푐퐴푐 푈ℎ퐴ℎ (휂표ℎ퐴)푐 (휂표ℎ퐴)푐 (휂표ℎ퐴)ℎ (휂표ℎ퐴)ℎ (2.9) and 퐴푓 휂표 = 1 − (1 − 휂푓 ), (2.10) 퐴 where 푈 is the overall heat transfer coefficient, 휂표 is the global surface efficiency, 휂푓 is the efficiency of a single fin, 퐴푓 is the fin ′′ area, 퐴 is the total area, 푅푓 is the fouling factor, 푅푤 is the wall thermal resistance, ℎ is the convective heat transfer coefficient. This method is useful when all temperatures are known; the goal of this method is calculate the surface area required for heat exchange. These kind of problems are called Heat Exchanger Design problems.

2.5.2 휀 − 푁푈푇 method This method is useful when only the inlet temperatures of both fluids are known. The LMTD method, in this case, requires iterations and the calculations are tedious. The 휀 − 푁푈푇 method 2.5. Thermal Analysis 41 solves this kind of problem in a easier way than LMTD method. The next definitions are required, starting with the maximum heat flux, which is defined by:

푞푚푎푥 = 퐶푚푖푛(푇ℎ,푖 − 푇푐,푖) (2.11)

where 퐶푚푖푛 is smaller value between 퐶푐 and 퐶ℎ, where 퐶푐 and 퐶ℎ are the heat capacity rate (퐶 =푚퐶 ˙ 푝) of the cold and hot fluids, respectively. 퐶푝 is the specific heat at constant pressure and 푚˙ is the mas flow rate. The effectiveness, number of transfer units (NTU) and heat capacity ratio 퐶푟 are, respectively, defined by:

푞 휀 ≡ (2.12) 푞푚푎푥

푈퐴 푁푇 푈 ≡ (2.13) 퐶푚푖푛

퐶푚푖푛 퐶푟 ≡ (2.14) 퐶푚푎푥

The relation between the NTU and effectiveness in a counter flow arrangement heat exchanger is(Bergman et al., 2011):

1 − 푒푥푝[−푁푈푇 (1 − 퐶푟)] 휀 = (2.15) 1 − 퐶푟푒푥푝[−푁푈푇 (1 − 퐶푟)]

The literature in general has a lot of graphs 휀 − 푁푈푇 for different configurations. Figure9 lets to obtain the effectiveness in a heat exchanger in the cases of parallel or counter flow for different heat capacity ratios. With this information is possible to obtain the heat flux between the fluids, and later, by energy balance, the outlet temperatures of the fluids. 42 Chapter 2. Heat exchanger design theory and literature review

Figure 9 – Effectiveness in heat exchanger. a) Parallel flow b) Counter flow. Adapted from Bergman et al. (2011).

a) b)

When the geometry and flow configuration of the heat exchanger are known, the problem is finding the outlet temperature of hot and cold fluids. This kind of problem is called Heat Exchanger Performance problem.

2.6 LITERATURE REVIEW

The researches about recuperators can be classified by: • Researches about the availability of the industrial equipments (furnaces, , etc.) to recover the heat from flue gases. • Simulations with a known conditions to obtain temperature fields from the gases and the air. • Simulations to explore optimal shapes or typologies where the heat recovery from the gases can be maximized. The first work about heat recovery are based in zonal method, whose complete description can be found in Modest (2003). The basis of the method is to divide certain control volumes (with a isothermal surface around the control volume) and apply an initial variables field. By iterations, the variables field is refined in the way to verify that the conservative balances are satisfied. With this method it is possible obtain a temperature distribution in both fluids. 2.6. Literature Review 43

Johnson & Beer(1973) made a complete study of heat transfer in furnaces using the zonal method. The work explains all the development of the method evaluating the radiation heat transfer focused in the combustion flame. The results of the zonal method were compared with experimental measurements resulting a difference of 10%.

Seehausen(1980) proposed a design of radiation recuperators of two concentric tubes, with the inclusion of fins in both sides of the stack. It relates that almost 75 to 95% of heat recover from flue gases is due to thermal radiation.

Incropera et al. (1985) applied the zone method in a concentric shell radiation heat exchanger. In this work, the radiation properties in the flue gases are determined by the weighted sum of gray gases. Energy balances in the control volumes and surface balances are applied in each zone. The waste heat from an aluminum melting furnace is recovered to be used in a Rankine cycle. There were considered two arrangements in the hybrid recuperator-steam Rankine cycle system. (Figure 10 shows the two configurations):

Figure 10 – Configurations of hybrid recuperator-steam Rankine cycle system: a) Series arrangement b) Parallel arrangement. Adapted from Incropera et al. (1985).

The recuperator has a length of 7 m, a diameter of 1.4 m and an annular gap of 0.046 m. The results of effectiveness in the 44 Chapter 2. Heat exchanger design theory and literature review recuperator are summarized in Tables1,2 and3.

Table 1 – Effectiveness of radiative recuperator in a hybrid system recuperator- waste heat boiler ( series arrangement case). Adapted from Incropera et al. (1985).

Inlet flue gases temperature 푇푔,푖 [K]

1000 1100 1200 1300 1400 1500 1600

휀 (푚˙ 푔=3.5 kg/s) 0.164 0.193 0.221 0.249 0.276 0.303 0.327

휀 (푚˙ 푔=2.0 kg/s) 0.239 0.275 0.310 0.343 0.373 0.401 0.425

When the mass flow of the flue gases 푚˙ 푔 rise, the effectiveness 휀 decreases; and it rises with the increment of the temperature of the flue gases.

Table 2 – Effectiveness of radiative recuperator in a hybrid system recuperator- waste heat boiler ( parallel arrangement case with 푚˙ 푠=0.5 kg/s). Adapted from Incropera et al. (1985).

Inlet flue gases temperature 푇푔,푖 [K]

1000 1100 1200 1300 1400 1500 1600

푚˙ 푔,푅 [kg/s] 1.07 1.56 1.88 2.11 2.29 2.42 2.53

휀 0.129 0.165 0.196 0.226 0.255 0.281 0.306

Table 3 – Effectiveness of radiative recuperator in a hybrid system recuperator- waste heat boiler ( parallel arrangement case with 푚˙ 푠=0.75 kg/s). Adapted from Incropera et al. (1985).

Inlet flue gases temperature 푇푔,푖 [K]

1000 1100 1200 1300 1400 1500 1600

푚˙ 푔,푅 [kg/s] N/A 0.41 0.96 1.34 1.62 1.84 2.01

휀 N/A 0.100 0.162 0.200 0.233 0.263 0.290

The parallel arrangement has a lower effectiveness compared 2.6. Literature Review 45 with the series arrangement.

Prescott & Incropera(1985) simulated convective recuperators ( ceramic tube and ceramic plate-fin ) in an aluminum melting furnace applying the 휖 − 푁푇 푈 method. The application of the convective recuperator is for a Rankine cycle. The work reports that the global efficiency in Rankine cycles using convective recuperators is greater than using radiation recuperators. However, problems like leakage and material failure can be present in this kind of recuperators. With ceramic materials, these recuperators raise temperatures to the order of 1700 K. Figure 11 shows the comparison between the outlet air temperature in radiative and convective recuperators varying the inlet flue gases temperature푔,푖 T .

Figure 11 – Outlet air temperature in radiative and convective recuperators, adapted from Prescott & Incropera(1985).

The ceramic convective recuperators have a better performance than the radiative recuperators, obtaining an outlet air difference temperature of nearly ∘400 C in the case of ∘ T푔,푖=1600 C.

Mediokritskii et al. (1997) obtained a set of equations to predict the temperature profiles in air and flue gases in a radiation 46 Chapter 2. Heat exchanger design theory and literature review recuperator. The results of this work are a set of integral-differential equations. The deduction of these equations differs from the zonal method because the energy balances were developed in infinitesimal control volumes, in contrast of discretized zones used on the other works. The calculations show that an increase in the heated surface of the recuperator by a factor of 2.3 increases the temperature of air heating by only 27 to 31%. Sahin(1997) developed an optimization methodology to obtain a better recuperator size in convective recuperators taking into account the viscous dissipation. They obtained relations between geometric parameters and efficiency. The method used was 휖 − 푁푇 푈. In this work, a non dimensional number Π is defined: 퐸푐 Π = 8 , (2.16) 푆푡푅푒 where

푁푢퐷 푆푡 = , (2.17) 푅푒퐷푃 푟 and 푉 2 퐸푐 = (2.18) 퐶푝[푇ℎ(퐿) − 푇푐(0)]

The Eckert number evaluates the strength of the viscous dissipation. The conclusions of this work are the following:

1. Viscous frictional heating reduces the recuperator effectiveness.

2. An optimum size (NTU) is obtained in which the thermal effectiveness becomes a maximum.

Figure 12 shows an 휀-NTU graph varying the adimensional parameter Π. 2.6. Literature Review 47

Figure 12 – Effectiveness in function of NTU and non dimensional number Π, adapated from Sahin(1997).

Kakaç & Liu(2002) made a general study about the pressure drop in heat exchangers considering several experimental correlations based in different geometries and typologies. The correlations depend basically on the flow regime (Reynolds number) and they are limited to some simple geometries.

Yu & Tao(2004) made a experimental work measuring the pressure drop in annular tubes with different quantities of wave fins. They obtain several correlations for friction factor and Nusselt number for different cases. Wang et al. (2008) made numerical simulations to obtain correlations for friction factors and Nusselt numbers in annular tubes.

Karczewski(2006) and Karczewski(2005) propose a general method for calculating a radiation recuperators with simple correlations. The focus of these works are to study ceramic recuperators. The work concludes that high efficiency ceramic recuperators using magnesia materials or casted alumina-mullite-zirconia materials are from 15 to 25% more thermal efficient than of conventional ceramic heat exchangers. 48 Chapter 2. Heat exchanger design theory and literature review

Also concludes that in glass melting furnaces the heat exchangers are capable to provide a reduction of total fuel consumption about 15 to 25%.

Aquaro & Pieve(2007) made an overview of the recent high temperature heat exchangers technology developments, both in the thermal-fluid dynamic innovative solutions and in the materials. The focus is the recuperator use in recuperative cycles, micro turbine systems, indirectly fired cycles and high temperature gas cooled nuclear reactors. A similar work was made by Gil et al. (2015) using the waste heat from exhaust gases to use in a gas power cycle plant.

Mitov(2011) compares the efficiency between radiation and convective recuperators and conclude that, in the same conditions, the radiation recuperators can be more efficient than convective recuperators when the flue gases temperature raises.

Oosterhuis et al. (2012) simulated a finned recuperator. The method used was a CFD simulation. The work related the utility of CFD tool to obtain temperature profiles in this kind of equipment, compared with the traditional methods of heat exchanger design (휖 − 푁푇 푈 and LMTD) because these methods do not take into account the axial conduction and non uniform heat transfer coefficients. The numerical model was compared with a experimental setup and the mean temperature deviation between the numerical and experimental results was ±5 K.

Karamarković et al. (2013) studied a waste heat recovery in a rotary kiln for magnesium production. This work identified the kiln shell losses in 26.35%. In the same way, the exhaust gases losses represents 18.95% of the total input energy. The solution proposed is a annular recuperator around the rotary kiln. The mathematical model developed is based on energy balances in zones, using correlations for the calculus of convection and radiation heat transfer in each zone. The validation of the mathematical model was made with direct measurements of the temperature along the kiln. The recuperator installation decrease fuel consumption in 12%. The difference against other works is the heat recover from kiln walls. 2.6. Literature Review 49

Hatami et al. (2014) mentioned several ways to increase the heat transfer in recuperators for engines. Fins, coated surfaces, displaced insert devices, micro-channels, swirl flow devices, coiled tubes, nanoparticles additives, porous media, baffles and corrugated tubes, vortex generators are some of the techniques.

Kalfrisa(2016) explains the main advantages of the radiative recuperators with bundle of tubes where air flows inside:

• A better distribution of the air, resulting in a homogeneous temperature of the tubes in the cage;

• A higher resistance to corrosion, due to a better choice of the material;

• An easier maintenance, since the exchange element (tubes cage) is independent of the frame;

• Higher working pressures, even up to 2,000 mmH2O.

But the configuration of handle of tubes has the disadvantage of the vitrification where some high temperature particulate matter merge to the external wall of the tubes reducing the heat transfer and also raising the pressure drop in the stack. In the works developed about recuperators, the choice of a turbulence model for the gases and air flows is not be mentioned. Hence, the importance of the choice of the turbulence model and the wall functions will be discussed in this work. Other aspect neglected in other previous works was the choice of the method adopted for the resolution of the radiative transport equation (RTE). These methods depend on the media optical thickness and the composition of hot gases mainly. The composition of the flue gases has direct influence onthe absorption and emission of radiation intensity in participating media. This aspect is neglected in most of previous works. The effect of the temperature and the mass flow of gases were studied independently, but, in some practical cases, the flue gases are diluted by a cold stream of air due to several infiltrations in the furnaces. In these cases, the stream that enters in the stack is composed by flue gases and cold air. The consequence is a growth of mass flow and decrease in temperature. Both effects are analyzed simultaneously in this work. 50 Chapter 2. Heat exchanger design theory and literature review

The main reference to this work was the research developed by Sharma et al. (2012). The model was compared with real measurements and the mean percentage error was 3%. The solution procedure is to guess initial temperatures and solve the energy balance equations by the Newton-Raphson method. By iteration, the final temperatures are obtained with 0.03% of numerical error. The geometry of the recuperator is the same of radiative recuperator studied by Incropera et al. (1985) but considering an exterior layer of insulating material. Figure 13 represents a longitudinal section of the recuperator. The effect of inlet temperature and mass flow of flue gases in the effectiveness of the recuperator are studied in this work and Figure 14 shows the effectiveness in both cases. The behavior is the same with respect of Incropera’s work: the effectiveness rise with an increment of temperature of the flue gases and decrease with the increase of mass flow of the flue gases. The effectiveness considering convective phenomena with and without the inclusion of thermal radiation is discussed in the present work. The pure convective effectiveness is calculated by the method 휀-NTU.

Figure 13 – Concentric shell radiation heat exchanger control volumes (Sharma et al., 2012). 2.6. Literature Review 51

Figure 14 – Variation of effectiveness with a) Mass flow of flue gases for ainlet gases temperature of 1500 K and b) Inlet flue gases temperature with a gases mass flow rate of 1.33 kg/s and mass flow rateof 1.25 kg/s. Adapted from Sharma et al. (2012).

a) b)

53

Chapter 3

METHODOLOGY

3.1 INTRODUCTION

The first approach to save energy from the flue gases inthe furnace is employing a radiative recuperator. This is due to the simple design and low cost. The radiative recuperator studied here is a double concentric shell exchanger where the flue gases flow inside and air flows outside the stack. The objective is to analyze different geometries and different physical conditions to providea better design of these heat exchangers. The methodology used here is the numerical simulation to resolve the equations of energy, momentum, radiative transport equation and turbulence models to find the temperature field. The process begins with an analysisof combustion in the furnace including the dilution process made in the combustion products. This step is important because allows to obtain input variables such as temperature and mass flow of the exhaust gases. The next stage is the meshing of all domains involved in the analysis. After this, the pre-process environment allows to define the boundary conditions, materials and allthe conditions required to solve the problem. The next stage of analysis is solve the equations. When the solution converges, the post-process shows graphically the variation of physical variables like temperatures, pressures, velocities, etc.

3.2 FRIT FURNACE

The analysis of the furnace is important because the energy of combustion products in the flue gases will be exploited in the recuperator and this information is necessary to design the exchanger. The furnace to be studied in this chapter is a furnace for ceramic frit production through combustion with oxygen. A frit is a ceramic composition that has been fused, quenched to form a glass, and granulated. Frits form an important part of the batches used in compounding enamels and glazes; the purpose of this pre-fusion is to render any soluble and/or toxic components insoluble by causing them to combine with silica and other added 54 Chapter 3. Methodology oxides (Dodd, 1994). A typical use of frit is illustrates in the Figure 15.

Figure 15 – In ceramic houseware industry, the frit is used as a glaze component.

Figure 16 – Frit furnace. a) Side view. b) Front view.

a) b)

Figure 16 shows a general view of the frit furnace used in this work; the bright zones correspond to the exit of the melted raw material. Figure 17 shows the main parts of the frit furnace. The furnace has a length of 5,5 m and approximately a width of 2,6 m and a height of 3,1 m. The material feeding is made with a screw conveyor. The melting of material is caused by the flame, product of the combustion of natural gas and oxygen in the main burner. The secondary burner ensures the correct flow of melting material. The furnace bottom is inclined to help with the flow of material. The frit formation is obtained through abrupt cooling of the melting material with water, causing the breaking of the material into little flakes (Figure 18). The packaging of frit is done in big bags, whose capacity is 1000 kg (Figure 19). 3.2. Frit Furnace 55

Figure 17 – Main parts of frit furnace.

Figure 18 – Frit formation cooling the melting material.

In the process of ceramic frit production, an amount of carbon dioxide is produced due to the chemical reaction between the different solids to be merged. Possamai(2014) reports that between 20 to 46 % of the carbon dioxide measured in the flue gases is product of the chemical reaction between the different components for sodium silicate production.

3.2.1 Mass balance and equilibrium composition of products Table9 is a summary of the process variables used in the operation of the furnace. 56 Chapter 3. Methodology

Figure 19 – Packing the frits into big bags

Table 4 – Process variables in frit furnace.

Product Variable

Temp. flue gases [K] 506

Inside temp. furnace [K] 1508

Mass processed [kg] 167.1

3 Volumetric flow 푂2 [Nm /h ] ( main burner) 173.5

3 Volumetric flow 퐶퐻4 [Nm /h ] ( main burner) 79.9

In this analysis, it will be considered that the composition of the fuel is mostly methane. This simplification is done because% 85 of the natural gas composition is methane (SCGÁS, 2016). The flow rate of methane and oxygen in the main burner are 79.9 Nm3/h and 173.5 Nm3/h, respectively. The mass flow of oxygen and methane at 25∘C and 1 atm, are 247.89 kg/h and 57.28 kg/h. The molar flow rates are 7.74 kmol/h and 3.57 kmol/h for oxygen and methane respectively. The combustion reaction expressed per unit of kmol/h of fuel, is:

퐶퐻4 + 2.16푂2 −→ 푎퐶푂2 + 푏퐻2푂 + 푑푂2 + 푒퐶푂 (3.1)

The coefficients a,b,d,e in equilibrium are obtained from GASEQ software, which gives the following: 3.2. Frit Furnace 57

−5 퐶퐻4 +2.16푂2 −→ 0.999퐶푂2 +2퐻2푂+0.1601푂2 +(2.143×10 )퐶푂 (3.2)

The stoichiometric reaction of methane with oxygen is:

퐶퐻4 + 2푂2 −→ 퐶푂2 + 2퐻2푂 (3.3)

The fuel equivalence ratio 휑 is calculated by:

푚˙ 푂 (푠) 2 휑 = 2 = = 0.92 (3.4) 푚˙ 푂2 2.16 So the combustion in this case is fuel lean. Table5 shows the theoretical molar fraction of products in wet and dry basis.

Table 5 – Theoretical molar fraction of combustion products.

Product Wet basis 휒푤 Dry basis 휒푑

CO2 0.31645 0.8619

H2O 0.63291 N/A

O2 0.05064 0.1380

CO 6.78×10−6 1.85×10−5

The combustion products are not the only contribution to flue gases in the stack of the furnace. The dilution with fresh airis important to decrease the temperature of hot gases to preserve the life of the stack. Nowadays, with the advances in materials science, it is possible to build new stacks with ceramic materials and special steel that resist higher temperatures (∼1400 K and more). In the case of the furnace analyzed in this work, the dilution is made to help a later filtration at lower temperature (300 K). The mixture of the two streams determines the temperature and flow mass at the exit the stack. The energy balance between the two streams is:

푁 푀 ∑︁ ∑︁ 푚˙ 푓 푌푖,푓 ℎ푖,푓 +푚 ˙ 푑 푌푖,푑ℎ푖,푑 =푚 ˙ 푓+푑ℎ푓+푑 (3.5) 푖=1 푖=1 58 Chapter 3. Methodology where the subscripts 푑, 푓 are diluted, flue gases, respectively. The dilution air mass flow is a quantity that varies, depending onthe temperature required in the stack. The frit furnace described here uses oxygen for the combustion process, so the use of heated air can be applied to the frit drying process. Figure 20 helps to determine the final temperature of flue gases after dilution and the total mass flow in the stack.

Figure 20 – Variation of temperature of flue gases with dilution of air (Temperature of air for dilution = 298 K).

3.3 THE RADIATIVE RECUPERATOR PROBLEM

The Figure 22 represents a longitudinal section of the recuperator with the respective thermal resistances. These resistances illustrate the heat transfer mechanisms involved in the calculus of the overall heat transfer coefficient 푈. Figure 21 shows the dimensions of the recuperator. 3.3. The radiative recuperator problem 59

Figure 21 – General dimensions of recuperator

Figure 22 – Thermal resistances in the recuperator.

The overall heat transfer coefficient for this heat exchanger is 60 Chapter 3. Methodology defined by:

1 = 푅푐표푛푣,푔푎푠 + 푅푐표푛푑,푠푡푎푐푘 + 푅푐표푛푣,푎푖푟 + 푅푐표푛푑,푒푥푐ℎ. (3.6) 푈퐴

퐷 퐷 1 1 푙푛( 2 ) 1 푙푛( 4 ) = + 퐷1 + + 퐷3 ; (3.7) 푈퐴 휋퐷1퐿ℎ푔 2휋푘푠퐿 휋퐷2퐿ℎ푎 2휋푘푠퐿 where 퐷1,퐷2,퐷3, and 퐷4 are the inner and outer diameters for stack, recuperator and insulating layer respectively (Figure 22); ℎ푔 and ℎ푎 are the convective heat transfer coefficient for flue gas and air respectively; 푘푠 is the thermal conductivity for steel and 퐿 is the recuperator length. The conduction resistances only depend on the thermal conductivity of the solid domain, in this case, steel, and the calculus is direct. On the other hand, the convective resistances require the use of empirical correlations found in the literature. These correlations depend on the flow regime (laminar or turbulent flow), defined by the Reynolds number value Equation (3.8):

휌푉¯ 퐷 푅푒퐷 = , (3.8) 휇 where 휌 is the density, 푉¯ is the mean velocity, 퐷 is the diameter of the tube, and 휇 is the dynamic viscosity. In both cases, the flow is turbulent. Gnielinski(1976) developed an empirical expression for turbulent flow inside tubes, Equation (3.9):

(푓/8)(푅푒퐷 − 1000)푃 푟 푁푢퐷 = (3.9) 1 + 12.7(푓/8)0.5(푃 푟2/3 − 1) where 푓 is a friction factor defined by Equation (3.10). 1 푓 = 2 (3.10) (0.79(푙푛(푅푒퐷) − 1.64))

For air, the turbulent flow in an annular gap is approximated (Equation (3.11)) by Bhatti & Shah(1987 apud Sharma et al., 2012):

(︂ )︂0.45 0.8 0.4 퐷표 푁푢¯ 퐷 = 0.023(푅푒퐷) 푃 푟 (3.11) 퐷푖 3.3. The radiative recuperator problem 61

With this information, the convective heat transfer coefficient is calculated by the definition of the Nusselt number: ℎ퐷 푁푢퐷 = (3.12) 푘 where ℎ is the convective heat transfer coefficient, 퐷 is the diameter of the tube and 푘 is the thermal conductivity of the fluid.

3.3.1 Cases to analyze The cases analyzed in this work are the following:

1. Case 1: Varying the temperature and mass flow of the flue gases; the temperature and mass flow of air are fixed (298K and 0.1 kg/s). The temperatures and mass flows are obtained from Figure 20. Table6 shows the values of temperature and mass flow of gases considered in this case.

Table 6 – Case 1: Varying the temperature and mass flue gases.

Temperature [K] 1200 1000 720 530

Mass flow [kg/s] 0.084 0.125 0.250 0.500

2. Case 2: Varying the mass flow of the air; the temperature and mass flow of flue gases are fixed (1200 K and 0.0842 kg/s) 3. Case 3: Varying the number of fins in the external surface of the stack wall. 4. Case 4: Using a cage-type recuperator.

3.3.2 Physical domains The control volumes to be simulated in the exchanger are the following:

• The flue gases flow. • The stack wall. • The air flow. 62 Chapter 3. Methodology

• The exchanger wall.

The properties of each domain are summarized in Table7.

Table 7 – Physical properties of domains. Adapted from Bergman et al. (2011).

Thermal Specific heat Density 휌 Domain conductivity 퐶 [kJ/kg K] [kg/m3] 푘 [W/m K] 푝 Stack and exchanger 60.5 0.434 7854 wall (steel)

Air 0.0261 1.004 1.185

The flue gases domain consists in a non-reactant mixture of gases product of the combustion in the furnace. The physical properties of a mixture depend of mass fraction of each component. For the flue gases analyzed here, the components are CO2,H2O, O2 and N2.

3.3.3 Turbulence models For the temperature and pressure fields determination in the recuperator is necessary to solve the conservation equations (Table 30). In particular, the equations of momentum conservation can be solved for laminar and turbulent flow indistinctly. However, turbulent flows at realistic Reynolds numbers span a large range of turbulent length and time scales, and would generally involve length scales much smaller than the smallest finite volume mesh, normally used in a numerical analysis (ANSYS, 2009). For the recuperator analyzed here, a turbulent flow for flue gases and for air is considered. Most turbulence models are statistical in contrast with, for example, Large Eddy Simulation Theory (LES). For a complete description of the turbulence models see ANSYS(2009). Spalart (2000) made a comparison between Reynolds Averaged Navier-Stokes equations (RANS), Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) and have shown the advantages of each of them. The turbulence model adopted here is the RANS model due to less computational effort and good accuracy for simple geometries. 3.3. The radiative recuperator problem 63

3.3.3.1 Reynolds Averaged Navier-Stokes (RANS) Equations. The conservation equations can be modified introducing averaged and fluctuating components. For example, a velocity 푉푖 may be divided into an averaged component 푉¯푖 and a time varying component, 푣푖, Equation (3.13).

푉푖 = 푉¯푖 + 푣푖 (3.13) where the averaged component is given by Equation (3.14)

1 ∫︁ 푡+Δ푡 푉푖 = 푉푖푑푡 (3.14) Δ푡 푡 Substituting the averaged quantities into the mass and momentum conservation equations respectively (Table 30). In Equations (3.15) and (3.16), the bar is dropped for averaged quantities, except for products of fluctuating quantities: 휕휌 휕 + (휌푉푗) = 0 (3.15) 휕푡 휕푥푗

휕휌푉푖 휕 휕푝 휕 + (휌푉푖푉푗) = + (휏푖푗 − 휌푣푖푣푗) + 푆푀 (3.16) 휕푡 휕푥푗 휕푥푖 휕푥푗

The additional term 휌푣푖푣푗 in the Equation (3.16) is the Reynolds stress tensor. It reflects the effect of convective transport due to turbulent velocity fluctuations (ANSYS, 2009). A generic variable Φ may be divided into an averaged component Φ and a time varying component 휑; the conservation of variable Φ is modeled by Equation (3.17) (the bar in the averaged terms was eliminated from the following equations):

휕휌Φ 휕 휕푝 (︂ 휕Φ )︂ + (휌푉푗Φ) = Γ − 휌푢푗휑 + 푆푀 (3.17) 휕푡 휕푥푗 휕푥푗 휕푥푗

where 휌푢푗휑 is the Reynolds flux tensor. The additional term (Reynolds flux tensor) in the turbulence equations must tobe solved. In this work, it was used the Reynolds stress models corresponding to 푘 − 휔 scheme. 64 Chapter 3. Methodology

3.3.3.2 푘 − 휔 model and wall function The 푘 − 휔 model is a two-equation turbulence model. This model solves two transport equations, one for turbulent kinetic energy, 푘, and one for turbulent frequency 휔. The Reynolds stress tensor is computed from the eddy-viscosity hypothesis. It assumes that the Reynolds stresses can be related to the mean velocity gradients and eddy (turbulent) viscosity by a gradient diffusion hypothesis, as presented by Equation (3.18):

(︂ )︂ (︂ )︂ 휕푉푖 휕푉푗 2 휕푉푘 −휌푣푖푣푗 = 휇푡 + − 훿푖푗 휌푘 + 휇푡 (3.18) 휕푥푗 휕푥푖 3 휕푥푘 where 휇푡 is the turbulent viscosity. The turbulent kinetic energy 푘 and turbulent frequency 휔 conservative equations are, respectively, represented by Equations (3.19) and (3.20).

[︂(︂ )︂ ]︂ 휕 (휌푘) 휕 휕 휇푡 휕휔 ′ + (휌푉푗휔) = 휇 + + 푃푘 − 훽 휌푘휔 (3.19) 휕푡 휕푥푗 휕푥푗 휎휔 휕푥푗

[︂(︂ )︂ ]︂ 휕 (휌휔) 휕 휕 휇푡 휕푘 휔 2 + (휌푉푗푘) = 휇 + + 훼 푃푘 − 훽휌푘휔 휕푡 휕푥푗 휕푥푗 휎푘 휕푥푗 푘 (3.20) The term 푃푘 is the turbulence production due to viscous forces, which is modeled using Equation (3.21):

(︂ )︂ (︂ )︂ 휕푉푖 휕푉푗 2 휕푉푘 휕푉푘 푃푘 = 휇푡 + − 3휇푡 + 휌푘 (3.21) 휕푥푗 휕푥푖 3 휕푥푘 휕푥푘 The model constants are given in Table8.

Table 8 – Model constants in 푘 − 휔 model (ANSYS, 2009).

′ 훽 훼 훽 휎푘 휎휔

0.09 5/9 0.075 2 2 3.3. The radiative recuperator problem 65

In the problem of the radiative recuperator studied here, the turbulence phenomena near of the stack wall in the air and gases sides is very important. The velocity profile near the wall has influence on the pressure drop, separation and recirculation ofthe flow and on the shear effects. In general, the turbulence models are suited to model the flow outside the boundary layer. To consider the near wall effects, there are two ways to proceed: 1. Make a very fine mesh to solve the boundary layer; 2. Uses semi-empirical equations to approximate the effects in the boundary layer. The first approach requires greater computational effort. The second approach is used in this work and the semi-empirical equations are called Wall functions. An important dimensionless parameter in the use of wall functions is a pseudo-Reynolds number y+. It is defined by the Equation (3.22)(Welty et al., 2008) and shown in Figure 23. √︀ 휏0/휌 푦+ = 푦 (3.22) 휈 where 휏0 is the shear stress in the wall surface, 휌 is the density of the fluid, 휈 is the kinematic viscosity and 푦 is the characteristic length of the flow, in this case is the hydraulic diameter of theflow.

Figure 23 – y+ parameter and a generic wall function used to solve the boundary layer 66 Chapter 3. Methodology

The y+ should typically be < 300 for the wall functions to be valid. On the other hand, if y+ is very small the wall function could be not valid. The 푘 − 휔 model chosen here only requires y+ ≤ 2 with good results and low computational effort, in constrast of 푘 − 휖 model that requires y+ ≤ 0.2 (ANSYS, 2009). This choice guarantees accurate results without excessive refined mesh. ANSYS- CFX for the case of 푘 − 휔 model has the option of automatic wall function.

3.3.4 Radiative properties of the flue gases The radiation properties of a mixture of flue gases can be calculated by a simplified method (Siegel & Howell, 2001) where the emissivity of the flue gases is expressed by Equation (3.23):

휖푔 = 휖푤 + 휖푐 − Δ휖 (3.23) where 휖푤 and 휖푐 are the emissivity of the water vapor and carbon dioxide, respectively, and Δ휖 is a correction factor. At industrial furnaces and combustion chambers, it is only heteropolar gases that absorb and emit significantly, such as2 CO ,H2O, CO, SO2, NO, CH4. On the other hand, gases with symmetric diatomic molecules, such as N2,O2 and H2 are transparent to infrared radiation and do not emit significantly (Siegel & Howell, 2001). Then, only the emission of water vapor and carbon dioxide will be considered. In furnaces and combustion chambers, the scattering phenomena is small and can be neglected (Siegel & Howell, 2001). Figures (24) and (25) show the emmisivity of the water vapor and carbon dioxide, and the mixture correction factor Δ휖, respectively. The emmissivity depends of the partial pressure and the characteristic length, in this case is 0.6D where D is the diameter of the stack. Table9 shows the absorption coefficients for the temperatures of flue gases considered for the case 1.

Table 9 – Absorption coefficients for the temperatures of flue gases considered in Case 1

Temp.Inlet gases [K] 1200 1000 720 530

휖푔 0.28 0.23 0.21 0.17

−1 푎휆 [m ] 0.80 0.64 0.57 0.45 3.3. The radiative recuperator problem 67

Figure 24 – Emissivity in a mixture with nonradiating gases at 100 kPa. (Bergman et al., 2011)

(a) Water vapor (b) Carbon dioxide

Figure 25 – Emmisivity correction factor in a mixture of water vapor and carbon dioxide. (Bergman et al., 2011)

3.3.5 Meshing Parameters

The first step in any numerical simulation is the discretization of the domains. The discretization is necessary to obtain an approximated solution of the conservation equations . The domain meshing has been made through the software ANSYS 68 Chapter 3. Methodology

ICEM CFD. A low mesh quality causes problems in the solution convergence. The quality criteria that must be evaluated are the aspect ratio and the distortion angle of the elements. The aspect ratio is the ratio between the length and the width of the elements. ANSYS(2013) recommend that the aspect ratio must be less than 100, values greater than 100 can show problems in the solution. The distortion angle refers to the ortogonality between element faces. In general, the model simulated here has angles between 80∘ and 90∘ in 95% of the elements. Most of elements have a structured grid and have a regular connectivity between their elements. The elements have a hexaedron-shape and have a quality between 75% and 100%, being 100% the highest quality mesh.

3.3.6 Boundary conditions For all cases the analysis has a steady-state approach, so there are not time dependency. The boundary conditions and all physical conditions are set up in ANSYS CFX-PRE environment. Table 10 summarizes the boundary conditions adopted in the two cases. Other conditions are the domain interface conditions. These conditions let the solver link the information between domains (solid or fluid). These conditions have a default option that all fluxes (energy, mass, momentum etc.) are conserved. Additionally, the non-slip condition is considered in the fluid domain, remaining at the same velocity of the wall. The velocity field at the inlets (flue gases and air)is constant and the flow is not fully developed, due to the short length of the recuperator. The minimum length for case of turbulent fully developed flow is given by the Equation (3.24) (Bergman et al., 2011): (︂ 퐿 )︂ 10 ≤ ≤ 60 (3.24) 퐷 푡푢푟푏 The same approximation is valid for the thermally fully developed condition. The flow of energy in each inlet or outlet boundary is calculated by Equation (3.25):

푁 ∑︁ 퐸 = 휌푖푣푖퐴푖퐶푝,푖(푇푖 − 푇푟푒푓 ), (3.25) 푖=1 where the flow of energy is weighted by the density, velocity, area, specific heat and temperature, respectively, of the element iinthe 3.3. The radiative recuperator problem 69

Table 10 – Boundary conditions

Case 1 (T푎푖푟= 298 K; 푚˙ 푎푖푟=0.1 kg/s)

Temp. gases (inlet) [K] 1200 1000 720 530

푚˙ 푔푎푠푒푠 [kg/s] 0.0842 0.125 0.250 0.500

Case 2 (T푔푎푠푒푠= 1200 K; 푚˙ 푔푎푠푒푠=0.0842 kg/s)

Temp. air (inlet)[K] 298

푚˙ 푎푖푟 [kg/s] 0.10 0.30 0.50 0.75 1.00

Flue gases outlet P푟푒푙= 0 Pa

Air outlet P푟푒푙= 0 Pa

Insulation Adiabatic (0 W)

boundary section. The mean temperature is calculated by Equation (3.26):

∑︀푁 휌푖푣푖퐴푖퐶푝,푖(푇푖 − 푇푟푒푓 ) 푇¯ 푖=1 = ∑︀푁 (3.26) 푖=1 휌푖푣푖퐴푖퐶푝,푖

3.3.7 Solving the model The next step in the simulation is to set up solver parameters. The solver environment used here is ANSYS CFX-SOLVER, which is a coupled-solver, e.g. the software solves the whole linear equations system. The coupled solvers normally require more computational effort because they need to store ofall coefficients in the matrix, even if most of those coefficients were zeros. But this inconvenient is compensated by the simplicity, robustness and generality of this solution. On the other hand, the segregated-solver employs a solution strategy where the momentum equations are first solved, using a guessed pressure field, andan equation for a pressure correction is obtained. Because of the iterative nature of the linear system, a large number of iterations are typically required in addition to the need for judiciously selecting relaxation parameters for the variables (ANSYS, 2013). 70 Chapter 3. Methodology

3.3.7.1 Residuals The residual is a measure of the imbalance of each conservative control volume equation (Sharcnet, 2016). It is the most important of convergence as ot is related to the quality of the numerical solution. The linear system of equations (discretized conservative equations) to be solved can be expressed by Equation (3.27): [퐴][휑] = [푏] (3.27) Such system can be solved iteratively, starting with an approximate solution in the iteration 푛, 휑푛.This can be improved ′ by a correction, 휑 , to yield a better solution (Equation (3.28)) :

′ 휑푛+1 = 휑푛 + 휑 ; (3.28)

′ where 휑 is obtained by the solution of the Equation (3.29):

′ 퐴휑 = 푟푛; (3.29) and the residual, 푟푛, is defined by Equation (3.30):

푟푛 = 푏 − 퐴휑푛 (3.30) When the minimum residual is reached, the solution of the problem is considered satisfactory. The residual chosen for this problem is RMS 1×10−6. This residual guarantees that the temperature and the heat flux at the boundaries (outlets and inlets) reach the steady state. The number of iterations necessary to attain the chosen residual in the present case is about 250 to 300. 71

Chapter 4

RESULTS

4.1 MESH INDEPENDENCE TEST

The selection of the mesh size for any numerical simulation is a important choice because a very refined mesh implies greater computational effort and higher costs. However, a very coarse mesh gives less accurate results. The adequate mesh size is chosen by the mesh independence test. This test consists in the simulation of several cases using different meshes, passing from a coarse mesh to a refined mesh. The test is to get the case where the results don’t change greatly if this mesh is compared with the next refined mesh. If this condition is satisfied, the numerical modelis independent of the size mesh chosen. The test made consists in the simulation of three different mesh with the following sizes: coarse mesh with 289,266 control volumes; medium mesh with 645,496 control volumes for the gases domain; and finally fine mesh with 1,308,986 control volumes. The variable to compare the mesh is the temperature of flue gases along the stack length. Figure 26 presents the three temperature profiles for each mesh size. The difference between the outlet temperature in the medium mesh with the fine mesh is about 3 K, so the mesh chosen is the medium mesh. Figure 27 shows the different meshes used in the test.

Figure 26 – Mesh independence test applied to flue gases temperature along the stack. 72 Chapter 4. Results

Figure 27 – Meshes used in the simulation (1/4 of the cross section): a) Coarse mesh (289,266 control volumes) b) Intermediate mesh (645,946 control volumes) c) Fine mesh (1,308,986)

4.2 CASE 1: VARYING FLUE GASES CONDITION

The temperature of flue gases and air as well as mean velocity of flow in each situation are presented in Table 11. Other parameters and properties involved in the heat transfer are also presented. Flow velocities are not so high, resulting in reduced convection coefficients values, at the same level of natural convection. In all cases, the convective heat transfer coefficients are lower than the expected compared with the values of the literature. Bergman et al. (2011) reports a typical heat transfer coefficients of 25 to 250 W/m2 K. The velocity used in this case is the typical used in flue gases as the oven operates with a very low pressure. 4.2. Case 1: Varying flue gases condition 73

Table 11 – Analytical forced convective heat transfer coefficients (Case 1).

2 푇푖푛 (K) 푣 [m/s] Re퐷 Pr Nu퐷 h [W/m K] C푝 [kJ/kg.K]

Flue gases

1200 0.90 1.41×104 1.02 42.3 1.17 1.400

1000 1.07 1.75×104 0.91 47.6 1.51 1.277

720 1.60 3.21×104 0.83 71.6 2.53 1.150

530 2.40 5.89×104 0.75 111.9 4.35 1.081

Internal air

298 2.11 5.5×103 0.70 20.8 5.69 1.004

The temperatures obtained in the outlet section for flue gases and air are in Table 12, according to the inlet temperature of gases. The flue gases are admitted with decreasing temperatures and increasing mass flow rate as a consequence of an air dilution. Hence, the heat rate exchanged is reduced with an increase of effectiveness. Despite of higher effectivenesses, the dilution offlue gases is recommended only when a higher air volume is necessary, with a lower temperature.

Table 12 – Mean temperatures in the inlet and outlet sections (T푖푛 air = 298 K, T푟푒푓 =298 K).

T gases 푚˙ gases T gases T air Heat rate 푖푛 표푢푡 표푢푡 휀 [K] [kg/s] [K] [K] [kW]

1200 0.0842 971 567 27.0 0.30

1000 0.125 849 540 24.1 0.36

720 0.250 658 475 17.8 0.42

530 0.500 509 410 11.3 0.51 74 Chapter 4. Results

The maximum heat exchanged by the gases is, by definition, 푄푚푎푥 = 퐶푚푖푛(푇푖,푔 − 푇푖,푎), and, in this case, 퐶푚푖푛 is constant. So with the decrease of the gases temperature at the inlet, the difference (푇푖,푔 − 푇푖,푎) falls, making that the effectiveness raises (Equation 2.12). The other effect is the increase of the heat exchanged bythe gases due to the raise of the inlet temperature and the reduce of mass flow. The heat rate exchanged by the flue gases is inversely proportional to the effectiveness of the recuperator.

4.2.1 Pure convective effectiveness

The results of the 휀-NTU effectiveness of the recuperator are shown in Table 13.

Table 13 – Effectiveness predicted by the 휀-NTU method (T푖푛=298 K).

T푖푛 T표푢푡 Heat T표푢푡 UA gases gases Cr NUT rate 휀 air[K] [W/K] [K] [K] [W]

1200 1183 314 0.85 1.701 0.018 1605 0.0178

1000 989 314 0.59 1.833 0.020 1632 0.0181

720 713 316 0.35 2.054 0.023 1831 0.0203

530 526 317 0.17 2.219 0.026 1975 0.0219

Table 14 shows a comparison between the simulated and the 휀- NTU effectiveness. According to Sharma et al. (2012), the difference between the effectiveness considering the radiation is approximately 70%. 4.3. Case 2: Varying the mass flow of air 75

Table 14 – Simulated and 휀-NTU effectiveness.

T푖푛 gases Simulated Simulated 휀-NTU [K] effectiveness without radiation Method

1200 0.30 0.070 0.0168

1000 0.36 0.107 0.0181

720 0.42 0.117 0.0203

530 0.51 0.153 0.0219

4.3 CASE 2: VARYING THE MASS FLOW OF AIR

Similarly to Table 12, Table 15 shows the outlet temperatures of the two flows and other additional parameters needed to calculate the heat transfer involved. The air flow is greater than the used in the previous simulation, resulting in higher convective heat transfer coefficient The results reveal that the effectiveness of the recuperator increase with the raise of air mass flow, obtaining values of 35% in the best of the cases, but the increment of the air temperature is low, only reaches 335 K.

4.3.0.1 Effectiveness by 휀-NTU Method The results obtained from 휀-NTU method for Case 2 are in table in Tables 16 and 17. As in the previous analysis, the NTU parameter and the effectiveness remain in a very low level. In the present situation, as the air flow increases from 0.10 kg/s to 1.0 kg/s the NTU parameter increases to 0.170 and a better effectiveness is attained, but still remaining very low. The numerical simulation results are compared with these one from 휀-NTU in Table 18. The radiation heat transfer also plays an important role as the respective effectiveness is quite superior to the other results. The results presented show the inadequacy of the 휀-NUT method to the analyzed configuration, relative to a very low NUT value, corresponding to an exchanger with a short 76 Chapter 4. Results

Table 15 – Mean temperatures and Heat rate in the entrance and exit sections (Case 2: gases mass flow = 0.0842 kg/s, T푖푛 gases = 1200 K, T푖푛 air= 298 K).

푚˙ air T T air Heat rate 표푢푡 표푢푡 휀 [kg/s] gases[K] [K] [kW]

0.10 971 567 27.0 0.30

0.30 908 412 34.4 0.32

0.50 895 369 35.9 0.34

0.75 891 346 36.4 0.34

1.00 888 335 36.7 0.35

length or low exchange area. The simulated results evidence that the raise of the effectiveness due to the increase of air mass flow.

Table 16 – Analytical forced convective heat transfer coefficients (Case 2).

2 푣 [m/s] Re퐷 Pr Nu퐷 h [W/m K]

Flue gases (푇푖푛= 1200 K)

0.75 11,749 1.02 36.4 1.01

Internal air (푇푖푛= 298 K)

2.11 5.54×103 0.70 15.8 5.69

4.55 1.75×104 0.70 41.3 14.82

7.10 2.96×104 0.70 62.5 22.45

10.31 4.48×104 0.70 86.5 31.05

13.2 5.85×104 0.70 106.7 38.30 4.3. Case 2: Varying the mass flow of air 77

Table 17 – Analytical effectiveness predicted by the 휀NTU- method (Case 2).

T T Heat 푚˙ air 표푢푡 표푢푡 UA gases air Cr NUT rate 휀 [kg/s] [W/K] [K] [K] [kW]

0.10 1182 318 0.84 2.38 0.024 2.08 0.023

0.30 1161 343 0.393 5.26 0.045 4.58 0.043

0.50 1145 361 0.236 7.43 0.063 6.4 0.060

0.75 1085 432 0.157 16.3 0.138 13.5 0.127

1.00 1060 462 0.118 20.1 0.170 16.5 0.155

Table 18 – Simulated and 휀-NTU effectiveness in the recuperator (Case 2).

Simulated 푚˙ 푎푖푟 Simulated NTU effectiveness [kg/s] effectiveness effectiveness without radiation

0.10 0.30 0.070 0.0178

0.30 0.32 0.074 0.043

0.50 0.34 0.079 0.060

0.75 0.34 0.082 0.127

1.00 0.35 0.083 0.155

4.3.1 Case 3: Finned surfaces in recuperators Using finned surfaces in a double pipe heat exchangers appear to be an effective way to increase the heat transfer between thetwo fluids. Due to their simplicity in design and low cost compared with 78 Chapter 4. Results other techniques, the fins are the most common way to increase the heat transfer area. In the case simulated here, mass flow and temperature parameters are fixed. For this condition, the amount of fins varies from 0 to 80. Only the air side surface of stack wouldbe able to be finned. In the flue gases side, fins can promote deposition of solid material from the furnace atmosphere. Due to the symmetry, only a 1/20 section of the whole recuperator was simulated. This is done for reducing the amount of elements and simulation time. Figure 28 shows the mesh refine used in the air domain for the case of 40 fins. The temperature and mass flow of flue gases are1200 K and 0.0842 kg/s respectively. For the air, the temperature and mass flow are 298 K and 0.1 kg/s. Table 19 shows the results of the simulation for the cases of 0, 20, 40, and 80 fins. The results show the increment of the effectiveness with the pressure drop and area reduction.

Figure 28 – Detail of the finned mesh (40 fins).

4.3.1.1 Pressure drop in extended surfaces The pressure drop in heat exchangers is necessary to determine the power required to move the fluids and consequently the operation cost of the exchanger. The methodology includes the solution of the discrete momentum conservation equations in the air domain in order to obtain a relation between the number of fins and pressure drop. The effectiveness increase with the number of the fins or the heat transfer area the pressure drop increases too, as a consequence of the cross section reduction when the fins are 4.3. Case 2: Varying the mass flow of air 79

Table 19 – Effectiveness extended surfaces

푇 Pressure Area 표푢푡 푇 air Number gases 표푢푡 휀 drop reduction [K] of fins [K] [Pa] [%]

0 971 567 0.30 10.2 0

20 947 596 0.33 30.2 4

40 909 641 0.38 65.3 8

80 878 677 0.42 128.2 16

implemented. An excessive pressure drop implies a greater electric power consumption and higher operation costs. Figure 29 shows the pressure drop and the effectiveness varying the number of fins. As expected, an increase of pressure drop and effectiveness with the fins number can be seen. There is not a ideal number of fins, but a number of 20 fins canbe considered; beyond this point the growth of the pressure drip is more important. An excessive pressure drop implies a greater electric power consumption and a higher operations costs, without an significant gain in effectiveness.

Figure 29 – Effectiveness and pressure drop (Case 3: Finned recuperator). 80 Chapter 4. Results

4.3.2 Case 4: Radiative recuperator with bundle of tubes

In this section, a special recuperator configuration is simulated. In this typology, the air flows in a circular arrangement of tubes. This bundle of tubes lies inside the flue gases stack. This kind of heat exchanger is used in high temperature applications like glass furnaces. For this case, the number of tubes where air is flowing are 52 with a external diameter of 1". Figure 30 shows the configuration analyzed in this case. The stack length is the sameof the other cases. The boundary conditions and the results of the simulation are shown in Table 20.

Figure 30 – Cross section of recuperator with bundle of tubes (Case 4).

Table 21 shows a comparison between different configuration with the same boundary conditions. The bundle of tubes shows the best effectiveness of the three configurations analyzed butthe pressure drop is the greatest too. Other aspects must to be considered in the selection of the configuration of the recuperators, mainly, the aspects related to furnace operations and process aspects. For example, in the case of glass furnaces, the flue gases have particulated matter product of the fusion reaction of glass. Due to the temperature, this matter can be merged to the solid walls of the stack, causing the blocking of the flue gases with consequence to the process too. Thus, an excessive number of fins or tubes inside of the stack could be undesirable. 4.3. Case 2: Varying the mass flow of air 81

Table 20 – Effectiveness (Case 4: Bundle of 52 tubes with an external diameter of 1").

Inlet gases temperature [K] 1200

Outlet gases temperature [K] 856

Outlet air temperature [K] 703

Gases mass flow [kg/s] 0.0842

Air mass flow [kg/s] 0.1

Gases heat capacity rate [W/K] 118

Air heat capacity rate [W/K] 100

Effectiveness 휀 0.45

Table 21 – Comparison between differents configuration of recuperators, inlet gases temperature = 1200 K, gases mass flow = 0.0842 kg/s, air mass flow = 0.1 kg/s.

Configuration 휀 Pressure drop [Pa]

Without fin 0.30 10.2

20 fins 0.33 128.2

bundle of 52 tubes 0.45 420.0

83

Chapter 5

APPLICATION TO AN INDUSTRIAL FURNACE

In this chapter the numerical method applied before in the analysis of radiative recuperators is compared to measured values obtained from an installed unit.

5.1 FURNACE AND PROCESS DESCRIPTION

The furnace analyzed in this chapter is different with respect of the furnace of Chapter 3. In this case, the furnace produces crystal glass products. Figure 31 shows a general view of the furnace and Figure 32 shows the main parts of the furnace.

Figure 31 – Furnace for production of crystal products.

In this furnace, the objective of the recuperator is recover part of the energy in the flue gases to preheat the air used in the combustion process. The “crystal" or “lead glass" is variety of glass in which lead replaces the calcium content of a typical potash glass. Lead glass contains typically 18–40 weight % of lead dioxide, while modern lead crystal, historically also known as flint glass due to the original silica source, contains a minimum of 24%. A complete 84 Chapter 5. Application to an industrial furnace

Figure 32 – Furnace scheme. Adapted from Trombini(2013)

description of the lead glass is found in Montgomery(1946). A historic background of the lead glasses is related in Kurkjian & Prindle(2005). Figure 33 shows the recuperator analyzed in this chapter. A handcrafted process is used to make the crystal products where the operator “blow" the molten glass and generates several kinds of articles. Figure 34 shows the blowing and sizing process The furnace has different fuel consumption along the day, a high fuel consumption time is required to melt and mix the raw materials that begins at 2:00 pm, the furnace is heating which its temperature rises to 1400 ∘C. At 2:00 am, the fuel consumption decrease to the low fuel consumption value, in this case, 7.8 kg/h. In the low fuel consumption stage, the operators process the melted glass and, in several steps, shape lead glass products with the required dimensions . Due to internal stress caused by contraction or dilation of the glass products, it is necessary to make a heat treatment known as annealing. The annealing is made in a special furnace. Later, the products are polished and smoothed eliminating any sharp edge. Finally the products are packed in boxes to the distribution. Figure 35 shows the consumption and temperature in the furnace. 5.1. Furnace and process description 85

Figure 33 – Recuperator analyzed

(a) General view (b) Dimensions

Figure 35 – Fuel consumption and temperature in a typical furnace operation day. 86 Chapter 5. Application to an industrial furnace

Figure 34 – The handcrafted process of lead glass production.

(a) Blowing (b) Sizing products

5.2 MEASUREMENTS

The measurements of temperature, mass flow for air and fuel, and the flue gases composition was made for the low consumption stage due to the availability and accessibility of the furnace.

5.2.1 Volumetric flow measurements The fuel consumption was measured with a rotameter. The rotameter installed in the furnace was calibrated to measure liquid petroleum gas (LPG) but the fuel used in this case is natural gas. The correction factor for the rotameter (Stoyanov & Beyazov, 2005) is shown in the Equation (5.1).

√︂휌푐푎푙 푉˙푟푒푎푙 = 푉˙푚 , (5.1) 휌 where 푉˙푚 is the direct measure from the rotameter, 휌푐푎푙 is the density of the calibration fluid, in this case is LPG (2.23 kg/Nm ) and 휌 is the density of the fluid which is measured at temperature and pressure of the environment, for this case the density of the natural gas is 0.786 kg/m3. The volumetric flow of fuel in the 5.2. Measurements 87 furnace is 10.2 m3/h. The mass flow is 7.8 kg/h. For the measure of volumetric flow of air, it was employed a Pitot tube joined toa micro-manometer for the measure of dynamic pressure of the air. The velocity is obtained by the Equation (5.2)(Delmée, 2003). √︃ 2Δ푃푑푖푛 푉 = (5.2) 휌

The calculus of the volumetric flow of the air is related tothe measure of the velocity by Equation (5.3).

∫︁ 푁 1 ∑︁ 퐴푖 푉˙ = 푣푑퐴 ≃ 푣푖 (5.3) 퐴 퐴 퐴 푖=1 The velocities are measured in several points along the cross section in the duct, in this case it is a circular duct. There are different methods to divide the whole area of the cross section considered (Nicolau & Güths, 2001). In this work the method used is the equal areas and the volumetric flow is calculated averaging all velocities directly. The diameter of the duct is divided in six parts. Table 22 summarizes the measurements obtained. Figure 36 shows the division of areas in the tube and Figure 37 shows the procedure and the Lambrecht brand micro-manometer used in the measurement. The mean velocity is 8.0 m/s, the volumetric flow is 0.075 m3/s, and the mass flow is 0.084 kg/s.

Figure 36 – Measurements of air mass flow, equal areas method. 88 Chapter 5. Application to an industrial furnace

Figure 37 – Volumetric flow measurement.

(a) Inserting the Pitot tube in the duct (b) Micro-manometer

Table 22 – Air velocities (low consumption); Tube radio R = 109.5 mm.

r/R Data 1 [Pa] Data 2 [Pa] Data 3 [Pa] Avg.[Pa] Vel.[m/s]

0.9129 18.0 16.0 18.0 17.3 5.54

0.7071 24.0 25.0 24.0 24.3 6.56

0.4082 32.0 28.0 30.0 30 7.29

0.4082 45.0 50.0 51.0 48.7 9.28

0.7071 50.0 56.0 58.0 54.7 9.84

0.9129 52.0 54.0 56.0 54 9.78

Mean 8.00 5.2. Measurements 89

5.2.2 Mass balance and equilibrium of combustion products For make a comparison between the flue gases analysis and the theoretical combustion reaction is necessary to calculate the stoichiometric coefficients for the reactants and the products. With the measurements of fuel and air mass flow it is possible calculate, for the case of low consumption, it by:

푚˙ 푎푖푟 302.4 kg/h = = 10.51 kmol/h (5.4) 푀푎푖푟 28 kg/kmol and 푚˙ 퐶퐻 7.8 kg/h 4 = = 0.486 kmol/h (5.5) 푀퐶퐻4 16.04 kg/kmol The reaction is given by:

0.486퐶퐻4 + 10.5(0.21푂2 + 0.79푁2) −→ 푎퐶푂2 + 푏퐻2푂 + 푑푂2 + 푒푁2 (5.6) The coefficients of the products were calculated in GASEQ software. the results are:

0.486퐶퐻4 + 10.5(0.21푂2 + 0.79푁2) −→ 0.486퐶푂2 + 0.972퐻2푂+

1.23푂2 + 8.3푁2 (5.7)

The stoichiometric reaction for this case is:

0.486퐶퐻4 + 4.62(0.21푂2 + 0.79푁2) −→ 0.486퐶푂2 + 0.972퐻2푂

+ 3.65푁2 (5.8) the equivalence ratio 휑 in this case is 0.44. It reveals that the combustion reaction in this case is poor in fuel content.

5.2.3 Temperature measurements The estimation of the temperatures was made with a thermocouple K type. Trombini(2013) made several measurements in a lead glass furnace with similar operation conditions. Table 23 compares both measurements. In the external wall of the recuperator was measured the temperatures in four points for the cases of low and high consumption. 90 Chapter 5. Application to an industrial furnace

Table 23 – Comparison between variables measured

Variable This work Trombini(2013)

Air mass flow [kg/s] 0.084 0.134

Fuel mass flow [kg/s] 0.00216 0.00395

Inlet air Temp.[K] 310 303

Outlet air Temp.[K] 470 553

Inlet gases Temp.[K] 1153 1317

Outlet gases Temp.[K] 788 767

Figure 38 – Wall temperatures in the recuperator a) Low consumption b) High consumption

a) b)

5.3 ENERGY BALANCE

The energy balance is required to compare the measurements and later compare with the numerical simulation. In this case, the energy balance must to take account the heat losses in the wall of the recuperator (In the analysis of Chapter 4, the recuperator was 5.3. Energy balance 91

considered adiabatic in the walls). The calculus of the heat losses in the walls can be estimated by a thermal resistances (Equation (5.9)). With the average of the wall temperatures (Figure 38) and the environment temperature, 푇∞, of 303 K is possible to calculate the convective thermal resistance. In the other hand, the conductive thermal resistance due to the insulating layer is calculated with the conductivity and the layer thickness.

푇푠 − 푇∞ 푞푤푎푙푙 = , (5.9) (︂ 푙푛(︀ 푟2 )︀)︂ (︁ )︁ 푟1 + 1 2휋푘푖퐿 2휋푟2퐿ℎ

Table 24 – Heat wall loss

T T r2 r1 L k h 푠 ∞ 푖 q [W] [K] [K] [m] [m] [m] [W/mK] [W/m2K] 푤푎푙푙 423 303 0.47 0.37 1.39 0.038 5 158

where 푇푠 is the average temperature of the recuperator wall, 푟2 and 푟1 are the external and internal radii of the insulating layer, 퐿 is the recuperator length, 푘푖 is the thermal conductivity of the insulating layer and ℎ is the natural convective heat transfer coefficient between the external surface and the environment, and q푤푎푙푙 is the heat losses by the wall. The energy balance has the following form:

푚˙푔퐶¯푝,푔(푇푖푛,푔 − 푇표푢푡,푔) =푚 ˙푎퐶¯푝,푎(푇표푢푡,푎 − 푇푖푛,푎) + 푞푤푎푙푙 (5.10)

Equation (5.10) did not be satisfied with the values measured (Table 23) by the reason of the poor accuracy in the measure of the outlet temperature of the flue gases. This fact have two causes:

• Hard access to the measure place. • Flue gases dilution with fresh air causing a local temperature decrease in the measure point.

The first point is due to the ancient furnace technology without enough instrumentation for the monitoring of the flue gases temperature. The second point is inherent to the technology and it is very difficult to guarantee a total tightness in the stack. 92 Chapter 5. Application to an industrial furnace

For adjust the outlet flue gases temperature, it is necessary apply Equation (5.10) to obtain a new temperature, the result for the outlet flue gases temperature is approximately 1025 K.

5.4 RECUPERATOR EFFECTIVENESS

With the measures of temperature at inlets and outlets of air and flue gases it is possible to calculate the effectiveness 휀 in the recuperator. The effectiveness is related by Equation (5.11):

퐶ℎ(푇ℎ,푖 − 푇ℎ,표) (0.108kJ/K)(1153K − 1025K) 휀 = = = 0.195 퐶푚푖푛(푇ℎ,푖 − 푇푐,푖) (0.084kJ/K)(1153K − 310K) (5.11)

5.5 NUMERICAL SIMULATION

With the aim of compare and verify the measurements that were made in the furnace, the recuperator was simulated by CFD methodology. The recuperator has a parallel flow configuration and it has a concentric tube typology. In the same way of Chapter 3, the physical domains were discretized with the same methodology of mesh quality and mesh independence test. The resume of the boundary conditions for this simulation is in Table 25. The boundary conditions are taken from the direct measurements made in the furnace.

Table 25 – Boundary conditions for the numerical simulation

Domain Boundary Definition.

Air Inlet 푚˙ = 0.084 kg/s; T = 310 K

Air Outlet P=0 Pa

Flue Gases Inlet 푚˙ = 0.0869 kg/s; T = 1153 K

Flue Gases Outlet P = 0 Pa

Recuperator wall Wall 푞푤푎푙푙 = 158 W 5.6. Results 93

5.6 RESULTS

After the simulation of physical domains of the recuperator, it is possible compare the results with measurements. Table 26 shows the comparison between these two approaches:

Table 26 – Temperatures at the domains boundaries

Boundary Measured Simulated.

Air inlet 310 K 310 K

Air outlet 467 K 478 K

Flue gases inlet 1153 K 1153 K

Flue Gases outlet 1036 K1 1012 K

The difference in temperature results between the measured and simulated values is 11 K in the case of outlet air and and 24 K in the case of outlet flue gases. The heat losses in the whole furnace are greater than it was considered here due to simplification of the recuperator wall has a mean temperature of 423 K . The lack of knowledge of the inside recuperator could be a source of error in the results, e.g, the content of dust and rust decreases the performance of the recuperator. There are differences between the real and simulated geometries so the results can differ in some way. The other error presents in the solution is the inherent error induced by the numerical method employed.

5.7 SAVINGS IN FUEL CONSUMPTION

The preheating process of the combustion air is important because it helps to save fuel consumption. The methodology is adapted from Turns(1996) but only the furnace is considered in the analysis. The main loss is represented by the energy associated to the flue gases. Figure 39 shows a furnace scheme with recuperator used to preheat the air for combustion.

1 This temperature was modified according to the explanation of the section Energy balance. 94 Chapter 5. Application to an industrial furnace

Figure 39 – Furnace scheme with recuperator, adapted from Turns(1996)

Equation (5.12) shows energy balance applied to the control volume (dashed line):

푄˙ = 푄˙ 푙표푎푑 + 푄˙ 푙표푠푠푒푠 =푚 ˙ 퐹 ℎ퐹 +푚 ˙ 퐴ℎ퐴 − (푚 ˙ 퐴 +푚 ˙ 퐹 )ℎ푝푟표푑 (5.12) where ℎ푝푟표푑 is the enthalpy of the flue gases. The subscripts 퐹 and 퐴 relate to fuel and air respectively. The 푄˙ 푙표푎푑 in this case is the amount of energy required to melt the raw material and 푄˙ 푙표푠푠푒푠 represents the heat lost by the walls to the environment. Due to the furnace operation, in the half of time the energy is used in the melting and the other half of time the energy is used to keep the furnace at operation temperature, only supplying the heat losses, so the losses must be considered in the fuel efficiency. The fuel efficiency 휂퐹 expresses the amount of heat from the fuel that is consumed by the load when the material raw is melted and the heat supply required to keep the furnace at the operation temperature (푄˙ 푙표푠푠푒푠) (Equation 5.13):

푄˙ 푚˙ 퐹 ℎ퐹 +푚 ˙ 퐴ℎ퐴 − (푚 ˙ 퐴 +푚 ˙ 퐹 )ℎ푝푟표푑 휂퐹 = = (5.13) 푚˙ 퐹 퐿퐻푉 푚˙ 퐹 퐿퐻푉 For this case the mass flow of air and fuel are respectively 0.084 kg/s and 0.00216 kg/s. The efficiency was calculated varying the inlet 5.7. Savings in fuel consumption 95 temperature of the combustion air considering the heat recovery from the flue gases due to the installation of the recuperator. The outlet flue gases temperature is considered equal to all cases and has a value of 1153 K corresponding to the measurement made in the furnace. The LHV and ℎ퐹 have the constant values of 50,016 kJ/kg and 4,664 kJ/kg respectively. For the calculus of ℎ푝푟표푑, the flue gases composition was obtained for the theoretical combustion, Equation (5.7). Table 28 resumes the ℎ푝푟표푑 calculus.

Table 27 – Enthalpy of products at 1153 K.

Chemical ℎ¯ Δℎ¯ 휒 (ℎ¯ +Δℎ¯ ) 휒푖(MW푖) 휒 0,푓 푖 푖 0,푓 푖 species 푖 [kJ/kmol] [kJ/kmol] [kJ/kmol] [kmol/kg]

CO2 0.044 -393,546 38,911 -15,603 1.936

H2O 0.088 -241,845 30,191 -18,625 1.584

O2 0.112 0 26,232 2,937 3.584

N2 0.756 0 24,770 18,726 21.1168

TOTAL -12,565 28.272

The molar enthalpy of flue gases ℎ푝푟표푑 is 12,565.65 kJ/kmol and specific enthalpy is 444.44 kJ/kg.

The Fuel savings 퐹 푆 is defined by Equation (5.14).

푚˙ 퐹,298퐾 − 푚˙ 퐹 휂퐹,298퐾 퐹 푆 = = 1 − (5.14) 푚˙ 퐹,298퐾 휂퐹

where 푚˙ 퐹,298퐾 and 푚˙ 퐹,298퐾 are the fuel consumption and fuel efficiency without preheating, respectively. Several simulations were made to calculate the outlet air temperature for various recuperator lengths. 96 Chapter 5. Application to an industrial furnace

Table 28 – Fuel efficiency and fuel savings for several recuperator lengths, L=1.39 m, 휂퐹,298퐾 = 0.17

Recuperator Temp. out. Temp. out. 휂 FS 휀 Length air [K] gases [K] 퐹 0.5L 461 1048 0.27 0.34 0.18

L 478 1036 0.28 0.38 0.20

2L 529 1001 0.31 0.44 0.26

4L 605 949 0.35 0.51 0.35

∞ 798 815 0.47 0.63 0.58

The results show that an increase in the length of the recuperator also increases the pre-heating temperature of air. The maximum fuel saving is 63% in the case of infinite length. Also the effectiveness of the recuperator rises with the increase in lengthto a value of 58%. In other words, the recuperator exploited almost a half of the heat from the flue gases, for example, in the case oftwo times the initial length. For the same length,(2L), the saving of fuel is almost 51%. The fuel efficiency without pre-heating 휂퐹,298퐾 for a equivalence ratio of 0.9 and a flue gases temperature of 1700 Kis 27% and, for the same conditions (휑=0.9, T푔=1700 K) the air pre-heating at 600 K resulted in a fuel efficiency and the fuel savings of 39% and 30% respectively. Comparing these results with those obtained in this work (FS=50%, 휑=0.44, T푔=1153 K) for the same pre-heated air of 600 K, it is notorious the influence of the equivalence ratio and the temperature of flue gases in the fuel savings. With low equivalence ratio and flue gases temperature, the fuel saving is bigger. In this analysis, only the furnace is considered. However, it must be remembered that an important component of the losses in a such equipment is represented by the energy conveyed by the flue gases to the environment. 97

Chapter 6

CONCLUDING REMARKS

This work developed a study of waste heat recovery in high temperature furnaces focused in the flue gases energy. Some recovery devices were studied, where the most important are the recuperators and regenerators in the case of recover the flue gases. The energy balance is verified calculating the energy in the inlet and outlet boundaries in the air and flue gases domains. Later, the effectiveness was calculated. In the Case 1, where the inlet flue gases temperature varied, the results are compared with the work of Sharma et al. (2012). It relates a effectiveness of 23% for a temperature of 1200 K. In this work, the effectiveness for the same temperature was 30%. These results were obtained considering the thermal radiation heat transfer due to the flue gases. The outlet heated air temperature is 567 K for the same inlet gases temperature. The effectiveness estimates by the 휀- NTU method diverges of the effectiveness generated by simulation due to the small contribution of convection in heat transfer between the flue gases and the stack wall. The error induced is almost of 90%, and the short heat transfer area, giving a very low NUT number, resulting in a inadequate use of such method to the equipment considered. The effectiveness increases when the gases mass flow increases despite of fall of temperature. This behavior is observed when the radiation phenomena is included, when the radiation is neglected and when the analytical pure convection approach is used. In the Case 2, the air mass flow was varied fixing the flue gases temperature and the mass flow. The effectiveness in this case increase when the air velocity increase too. The range of effectiveness calculated by simulation in this case varies from 30% to 35%. Only 5% of gain when the air mass flow varies from 0.1 to 1.0 kg/s reveals that the mass flow of air does not influence significantly in contrast with the gases mass flow. Considering the effect of the dilution of flue gases, the gases temperature decreases and the mass flow increases. The Cases 1and 2 show that the effectiveness is more sensitive to the gases massflow than the flue gases temperature. The Case 3 study the effect of incorporate fins in the external surface of the flue gases stack, in order to increase the 98 Chapter 6. Concluding Remarks heat transfer area keeping the length and diameters of stack fixed. In this work, was studied only one geometry, that consist in rectangular cross section fin. One finned surface involve greater costs in power, maintenance etc. One important issue considered in this case is the air pressure drop between the inlet and outlet boundaries. The amount of fins increases the recuperator effectiveness. However, the pressure drop rise too. It implies that the power required to move the air will be greater. An experimental approach was made to compare the numerical simulations with real measurements of temperatures in a lead glass production furnace. The difference between the measurements and the simulations is 24 K in the flue gases and 11 K in the air. The possible causes at the flue gases could be due to the inaccurate measurements in the outlet of flue gases. The savings in fuel consumption were estimated for several recuperator lengths and the maximum fuel saving achieved was 63% (regarding only the furnace wall losses) when the recuperator heat transfer area tends to infinity and the recuperator reaches a thermal equilibrium. Some of the activities recommended to give continuity to this work are listed as follows:

1. To develop new correlations and equations in the design and analysis of heat exchangers when the thermal radiation phenomena is included; 2. To simulate other more complex heat exchangers used in energy recovery, such as regenerators and convective recuperators, in order to compare the effectiveness in each one and determine what device is better for certain conditions and applications; 3. To establish a parameter like a dimensionless number that let to determine if the main heat transfer involved is the thermal radiation or the convection; 4. To explore more shapes and optimize the finned surfaces to increase the performance in the heat exchangers; 5. To propose new typologies in heat exchangers to increase the effectiveness and explore new materials in its construction; and 6. To analyze the effect of heat recovery in the draft from the furnace under normal operation. 99

BIBLIOGRAPHY

ANSYS, I. ANSYS CFX-Solver Theory Guide. [S.l.: s.n.], 2009. 724–746 p.

ANSYS, I. ANSYS® Academic Research. [s.n.], 2013. 724–746 p. ISBN Release 12.1. Available at: .

AQUARO, D.; PIEVE, M. High temperature heat exchangers for power plants: Performance of advanced metallic recuperators. Applied Thermal Engineering, v. 27, n. 2-3, p. 389–400, 2007. ISSN 13594311.

BANERJEE, R.; CONG, Y.; GIELEN, D.; JANNUZZI, G.; MARÉCHAL, F. Energy End-Use: Industry. Global Energy Assessment, p. 513–573, 2012. ISSN 0002-7294.

BERGMAN, T. L.; LAVIGNE, A. S.; INCROPERA, F. P.; DEWITT, D. P. Fundamentals of Heat and Mass Transfer. [S.l.: s.n.], 2011. 1076 p. ISSN 13594311. ISBN 9780470501979.

BHATTI, M.; SHAH, R. Turbulent and transition flow con- vective heat transfer in ducts. 1987.

DELMÉE, G. Manual de medição de vazão. 3. ed. Edgard Blucher, 2003. 346 p. ISBN 85-212-0321-7. Available at: .

DODD, A. Dictionary of ceramics. Third edit. [S.l.]: The Institute of Materials, 1994. 399 p. ISBN 0-901 716-56-1.

DOE. Waste Heat Recovery: Technology and Opportunities in U.S. Industry. 2008.

FORMAN, C.; MURITALA, I. K.; PARDEMANN, R.; MEYER, B. Estimating the global waste heat potential. Renewable and Sustainable Energy Reviews, Elsevier, v. 57, p. 1568–1579, 2016. ISSN 18790690. Available at: . 100 Bibliography

GIL, S.; GÓRAL, J.; HORňAK, P.; OCHMAN, J.; WIŚNIEWSKI, T. Pressurized Recuperator For Heat Recovery In Industrial High Temperature Processes. Archives of Metallurgy and Materials, v. 60, n. 3, 2015. ISSN 2300-1909. Available at: . GNIELINSKI, V. New equations for heat and mass transfer in turbulent pipe and channel flow. International Chemical Engineering, v. 16, p. 359–368, 1976. HATAMI, M.; GANJI, D. D.; GORJI-BANDPY, M. A review of different heat exchangers designs for increasing the diesel exhaust waste heat recovery. Renewable and Sustainable Energy Reviews, Elsevier, v. 37, p. 168–181, 2014. ISSN 13640321. Available at: . IEA. Energy Statistics. Statistics, 2014. Available at: . INCROPERA, F. P.; PRESCOTT, P. J.; VOELKEL, D. D. Hybrid systems for furnace waste heat recovery: I. Use of a radiation recuperator with a Rankine cycle. Journal of Heat Recovery Systems, v. 5, n. 4, p. 321–330, 1985. ISSN 01987593. JOHNSON, T. R.; BEER, J. M. Radiative heat transfer in furnaces: Further development of the zone method of analysis. Symposium (International) on Combustion, v. 14, n. 1, p. 639–649, 1973. ISSN 00820784. KAKAÇ, S.; LIU, H. Heat exchangers selection, rating and thermal design. 2002. 87–88 p. Available at: . KALFRISA. Radiation Recuperators. 2016. Available at: .

KARAMARKOVIĆ, V.; MARAŠEVIĆ, M.; KARAMARKOVIĆ, R.; KARAMARKOVIĆ, M. Recuperator for waste heat recovery from rotary kilns. Applied Thermal Engineering, v. 54, n. 2, p. 470–480, 2013. ISSN 13594311. KARCZEWSKI, K. Universal Method of Calculation of Radiation Recuperators with microfinned surface. Metallurgy and foundry engineering, v. 31, n. 2, p. 185–200, 2005. Bibliography 101

KARCZEWSKI, K. High efficiency ceramic recuperators to glass furnaces. Metallurgy and foundry engineering, v. 32, n. 1, p. 49–65, 2006. KHOSHMANESH, K.; KOUZANI, A. Z.; NAHAVANDI, S.; ABBASSI, A. Reduction of fuel consumption in an industrial glass melting furnace. IEEE Region 10 Annual International Conference, Proceedings/TENCON, n. 5, p. 5–8, 2007. KURKJIAN, C. R.; PRINDLE, W. R. Perspectives on the History of Glass Composition. Journal of the American Ceramic Society, v. 81, n. 4, p. 795–813, 2005. ISSN 00027820. Available at: . MALISKA, C. R. Transferência de calor e mecânica dos fluidos computacional. Livros Tecnicos e Cientificos, 2004. ISBN 9788521613961. Available at: . MEDIOKRITSKII, E.; GAPONOV, V.; LOGINOV, V. Study of heat transfer in recuperators by computer models. Journal of Engineering Physics and Thermophysics, v. 70, n. 1, p. 117–122, 1997. MITOV, I. Comparative Analysis of the Energy Efficiency of Metal Recuperators With a Different Design. Journal of the University of Chemical Technology and Metallurgy, v. 46, n. 4, p. 427–432, 2011. ISSN 13117629. MODEST, M. Radiative Heat Transfer. [S.l.: s.n.], 2003. 1689–1699 p. ISSN 1098-6596. ISBN 9788578110796. MONTGOMERY, R. J. The composition of lead glasses. Journal of the American Ceramic Society, v. 1946, n. 8, p. 404–410, 1946. NARENDRAN, V.; SIVAMANI, S.; HARIRAM, V.; GNANAPRAKASH, M.; Mohammed Raffiq, A.; Sathish Kumar, D. Theoretical and Numerical Analysis of Convective Recuperator for an Oil Fired Water Tube Boiler to Improve the Boiler Performance. Indian Journal of Science and Technology, v. 9, n. 42, 2016. ISSN 0974-5645. Available at: . NICOLAU, V. P.; GÜTHS, S. Medição de velocidade de escoamentos com o tubo de Pitot. Florianopolis, Brazil: [s.n.], 2001. 12 p. Available at: . 102 Bibliography

OOSTERHUIS, J. P.; BÜHLER, S.; WILCOX, D.; MEER, T. H. van der. CFD as a Design Tool for a Concentric Heat Exchanger. 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, n. July, p. 110–115, 2012.

PATANKAR, S. V. Numerical heat transfer and fluid flow. [S.l.]: Taylor & Francis, 1980. 196 p. ISBN 978-0891165224.

PCO, Z. Glass Furnace Regenerators. 2017. Available at: .

POSSAMAI, T. S. Análise Térmica e modelagem numérica de um forno de fusão de material vítreo a gás natural. 186 p. Phd Thesis (PhD Thesis) — Universidade Federal de Santa Catarina, 2014.

POSSAMAI, T. S.; OBA, R.; NICOLAU, V. P. Numerical and experimental thermal analysis of an industrial kiln used for frit production. Applied Thermal Engineering, Elsevier Ltd, v. 48, p. 414–425, 2012. ISSN 13594311. Available at: .

PRESCOTT, P. J.; INCROPERA, F. P. Hybrid systems for furnace waste heat recovery: II convection recuperators and a Rankine cycle. v. 5, n. 4, p. 331–339, 1985.

REAY, D. A. A review of gas-gas heat recovery systems. Heat Recovery Systems, v. 1, p. 3 to 41, 1980.

SAHIN, A. Z. Thermodynamic design optimization of heat recuperator. International Communications in Heat and Mass Transfer, v. 24, n. 7, p. 1029–1038, 1997. ISSN 00222860.

SCGÁS. Companhia de gás de Santa Catarina. 2016. Available at: .

SEEHAUSEN, J. W. United States Patent 1191 f. 1980.

SHARCNET. https://www.sharcnet.ca/Software/Ansys/16.2.3/en- us/help/cfx_thry/i1312256.html. 2016.

SHARMA, H.; KUMAR, A.; VARUN. Performance analysis of metallic concentric tube recuperator in parallel flow arrangement. International Journal of Heat and Mass Transfer, v. 55, n. 25-26, p. 7760–7771, 2012. ISSN 00179310. Bibliography 103

SIEGEL, R.; HOWELL, J. Thermal Radiation Heat Transfer, Fourth Edition. Taylor & Francis, 2001. (Thermal Radiation Heat Transfer). ISBN 9781560328391. Available at: . SPALART, P. R. Strategies for turbulence modelling and simulations. v. 21, p. 252–263, 2000. STOYANOV, B.; BEYAZOV, J. Determination of the Flow Rate of Different Fluids by a Rotameter*. Problems of Engineering Cybernetics and Robotics, 55, n. 010057, p. 71–78, 2005. Available at: . SUNDEN, B. High temperature heat exchangers (HTHE). Enhanced, Compact and Ultra-Compact Heat Exchangers: Science, Engineering and Technology, n. September, p. 226– 238, 2005. Available at: . TROMBINI, A. Master Dissertation, Avaliação térmica de um forno industrial de fusão de vidros. Florianopolis, Brazil: [s.n.], 2013. 138 p. TRUELOVE, J. S. Three-Dimensional radiation in absorbing- emitting-scattering media using the Discrete ordinates approximation. Journal of Quantitative Spectroscopy and Radiative Transfer, v. 39, n. I, p. 27–31, 1988. TURNER, W.; DOTY, S. Energy Management Handbook. [S.l.: s.n.], 2007. 274–295 p. ISBN 0881735426. TURNS, S. R. An introduction to combustion: concepts and applications. McGraw-Hill, 1996. (McGraw-Hill series in mechanical engineering). ISBN 9780079118127. Available at: . WANG, Q. W.; LIN, M.; ZENG, M.; TIAN, L. Computational analysis of heat transfer and pressure drop performance for internally finned tubes with three different longitudinal wavy fins. Heat and Mass Transfer/Waerme- und Stoffuebertragung, v. 45, n. 2, p. 147–156, 2008. ISSN 09477411. WELTY, J. R.; WICKS, C. E.; WILSON, R. E.; RORRER, G. L. Fundamentals of Momentum, Heat, and Mass Transfer. 5. ed. 104 Bibliography

[S.l.]: John Wiley & Sons, 2008. 729 p. ISSN 00179310. ISBN 9780470128688. WILLMOTT, A. J. Regenerative heat exchangers. 2016. Available at: . YU, B.; TAO, W. Q. Pressure drop and heat transfer characteristics of turbulent flow in annular tubes with internal wave-like longitudinal fins. Heat and Mass Transfer/Waerme- und Stoffuebertragung, v. 40, n. 8, p. 643–651, 2004. ISSN 09477411. 105

ANNEX A - RADIATIVE HEAT TRANSFER

The last methods described are the most widely used in the analysis of heat exchanger for general purposes. In these models, the main heat transfer mechanism is convection. In the overall heat transfer coefficient, there is no radiation thermal resistance defined. In the case of high temperature gases (e.g. exhaust gases), the heat flux due to radiation is more important than convection mode. For this reason, the radiation heat transfer mode must be understood. Some important concepts are defined below.

Radiation spectral intensity 푖휆(휆, 휃, 휑), is defined as the differential energy flow 푑푞 per unit of solid angle 푑휔 in a certain wavelength 푑휆 in a direction of angle 휃 and 휑 per unit of area 푑퐴 (Bergman et al., 2011).

푑푞 푖휆(휆, 휃, 휑) ≡ (A.1) 푑퐴 cos 휃푑휔푑휆 When the radiation is emitted by the surface, the spectral emissive power 퐸휆 and total emissive power 퐸 are defined respectively, by Equations (A.2) and (A.3), using the emitted spectral intensity 푖휆,푒.

휋 ∫︁ 2휋 ∫︁ 2 퐸휆 = 푖휆,푒(휆, 휃, 휑) cos 휃 sin 휃푑휃푑휑 (A.2) 0 0 ∫︁ ∞ 퐸 = 퐸휆(휆, 푇 )푑휆 (A.3) 0 On the other hand, when radiation strikes the surface, the spectral irradiation 퐺휆 and total irradiation 퐺 are defined respectively by Equations (A.4) and (A.5)

휋 ∫︁ 2휋 ∫︁ 2 퐺휆 = 푖휆,푔(휆, 휃, 휑) cos 휃 sin 휃푑휃푑휑 (A.4) 0 0 106 Annex A - Radiative Heat Transfer

∫︁ ∞ 퐺 = 퐺휆푑휆 (A.5) 0 Figure 40 shows the radiation interactions with a surface.

Figure 40 – Radiation interactions on a surface (Siegel & Howell, 2001).

One surface is diffuse when the radiation intensity from emission is independent of direction. Also, a surface is gray for radiation when the radiation properties are independent of wavelength. When the surface is diffuse and gray, the emissive power and the irradiation have the following expressions.

퐸 = 휋푖푒 (A.6)

퐺 = 휋푖푔 (A.7) As the perfect absorber and emitter, the blackbody serves as a standard against which the radiative properties of actual surfaces may be compared. The emissive power of a blackbody is well known and it is expressed by the Stefan-Boltzmann law:

4 퐸푏 = 휎푇 , (A.8) where 휎 is the Stefan-Boltzmann constant with the value of 5.67푋10−8 W/m2K4. The emitted blackbody radiation intensity 107

is: 4 퐸푏 휎푇 푖푏 = = (A.9) 휋 휋 The interactions between the radiation intensity and the surfaces can be explained defining some properties (emissivity, absortivity and reflectivity). The complete deductions of the radiation properties are found in Siegel & Howell(2001) and Modest(2003). Table 29 is a summary of useful expressions.

RADIATION EXCHANGE BETWEEN SURFACES

With the knowledge of the surface radiation properties (emissivity, absortivity and reflectivity etc.), it is possible to calculate the net heat flux between surfaces. The net flux from surface 푖 to other surfaces is related by the following expression:

푁 퐸푏푖 − 퐽푖 ∑︁ 퐽푖 − 퐽푗 푞푖 = = (A.10) − 휖 / 휖 퐴 퐴 퐹 −1 (1 푖) ( 푖 푖) 푗=1 ( 푖 푖푗)

where the variable 퐽푖 is the radiosity of 푖푡ℎ − 푠푢푟푓푎푐푒 defined as:

퐽푖 ≡ 퐸푖 + 휌푖퐺푖 (A.11) The common way to solve the equations to find the net flux is making the analogy with a electrical circuit. This approach is called radiation network approach; a more detailed deduction of all relations is shown by Bergman et al. (2011). Figure 41 shows the radiation network for surface 푖 to 푁 surfaces. Knowing the radiosities (nodes) it is possible obtain the net flux on the surface.

PARTICIPATING MEDIA IN RADIATION

Heat transfer by radiation between two or more surfaces can be influenced by a physical media (e.g. the gases flowing between two solid surfaces). This physical media is called participating media for radiation. A participating media can absorb, emit and scatter radiation. Figure 42 illustrates the radiation phenomena in a participating media. In radiation recuperators, the flue gases are participating media due to the high temperatures reached by these gases (≈ 1000∘C). These gases emit radiation to the inner stack wall and heat it and the wall transfers heat by convection to the air that 108 Annex A - Radiative Heat Transfer

Figure 41 – Network representation of radiative exchange between surface 푖 and the 푁 remaining surfaces of an enclosure. Adapted from Bergman et al. (2011).

flow outside the stack wall. Thus, the radiation heat transfer isnot only between solid surfaces, the participating media has the most important role in the global heat transfer in these equipments. One important radiation property in radiation heat transfer in gases is the extinction coefficient 퐾휆. Relates the the incident intensity 푖휆,0(푠) with a reduced intensity 푖휆,푆(푠) in a thickness S along, for example, the s-direction. The extinction coefficient is composed of two parts, the absorption coefficient 푎휆(휆, 푇, 푃 ) and the scattering coefficient 휎푠휆(휆, 푇, 푃 ) (Siegel & Howell, 2001).

퐾휆(휆, 푇, 푃 ) = 훼휆(휆, 푇, 푃 ) + 휎푠휆(휆, 푇, 푃 ) (A.12)

The relationship between the incident intensity 푖휆,0(푠) and the reduced intensity 푖휆,푆(푠) in the s-direction along a thickness S, is expressed by Bouguer’s law.

[︃ ∫︁ 푆 ]︃ * * 푖휆,푆(⃗푠) = 푖휆,0(⃗푠) exp − 퐾휆(푠 )푑푠 (A.13) 0 109

Figure 42 – Radiation heat transfer in participating media. Adapted from Modest(2003).

The optical thickness, 휅휆, is defined as:

∫︁ 푆 * * 휅휆 ≡ 퐾휆(푠 )푑푠 (A.14) 0 The optical thickness is a measure of the ability of a path length to attenuate radiation of given wavelength. If 휅휆 ≫ 1, the medium is optically thick, that is, the mean penetration distance is quite small compared to dimension of the medium. On the other hand, if 휅휆 ≪ 1 the medium optically thin and the mean penetration distance is much larger than the medium dimension. In other words, a large optical thickness means large attenuation of incident radiation intensity. For a uniform temperature and pressure, 퐾휆 is independent of 푇 and 푃 .

휅휆(푆) = 퐾휆푆 (A.15) The radiation transport equation (RTE) is complex and the general deduction is found in Siegel & Howell(2001):

4휋 푑푖휆 휎푠휆 ∫︁ = −푎휆푖휆(푆)+푎휆푖휆푏(푆)−휎푠휆푖휆(푆)+ 푖휆(푆, 휔푖)Φ(휆, 휔, 휔푖)푑휔푖 푑푆 4휋 휔푖=0 (A.16) 110 Annex A - Radiative Heat Transfer

where Φ(휆, 휔, 휔푖) is a phase function that guide the scattering radiation fraction. The third and fourth terms on the right side of equation (2.30) are neglected because the scattering phenomena in gases in furnaces and combustion chambers is small (휎푠휆 = 0) (Siegel & Howell, 2001). The simplified form of Equation (A.16) is:

푑푖휆 = −푎휆푖휆(푠) + 푎휆푖휆푏(푠) (A.17) 푑푠 The first term of the right side of Equation (2.31) is theloss by absorption of participating media and the second term is the gain by emission of the participating media. Integrating Equation (A.17) from 푠 = 0 to 푠 = 푆 yields:

[−푎휆푆] [−푎휆푆] 푖휆(휆, 푆) = 푖휆(휆, 0)푒 + 푖휆,푏[1 − 푒 ] (A.18)

[−푎 (휆)푆] The term 푒 휆 is the transmittance 휏휆(푠). In virtue of Kirchhoff’s Law:

훼휆 = 1 − 휏휆 = 휀휆 (A.19)

There are several methods to resolve the RTE. A complete description of these methods are found in Siegel & Howell(2001) and Modest(2003). The main methods used to solve the RTE are: Rosseland Model, Monte Carlo Method, P-N methods,and Discrete Ordinates method. The choice of the solution method is mainly related by the optical thickness of the participating media; in very thin media the radiation intensity does not change by absorption, emission or scattering; in thicker media, the absorption and emission have a important role; and in the case of very thick media, the scattering is present too but this is not the case in virue of the simplification explained in Equation (A.17) (Siegel & Howell, 2001). Other aspect in the choice of the solution is the accuracy in the results given by the method. Bigger accuracy implies more computational effort and higher costs. Due to dependency of radiation properties with wavelength 휆 is necessary to define a spectral model to calculate these properties. The accuracy of the radiation models adopted depends on the properties calculation. The spectral models to consider here are:

1. Gray: The emmittance is independent of wavelength 휆. 111

2. Multiband: The emmitance is calculated in several wavelength bands. 3. Weighted Sum of Gray Gases: The emittance of a mixture of N gases can be expressed by:

푁 ∑︁ −휅푘푆 휖(푇, 푆) = 훼(푇, 푆) ≃ 푎푘(푇 )(1 − 푒 , ) (A.20) 푘=0 where the coefficients 푎푘 and 휅푘 are found in Modest(2003). Considering these aspects, the method used to solve the RTE in this work is the Discrete Ordinates Method due to his versatility in all optical thickness range and have a better accuracy compared with the P-N methods (Truelove, 1988), the other methods like Rosseland method are recommended for optically thick media. 112 Annex A - Radiative Heat Transfer

Table 29 – Summary of radiation properties of real surfaces. Adapted from Modest(2003).

Property Expression Comments Emissivity Outgoing

푖휆,푒(휆,휃,휑,푇 ) intensity Spectral directional 휀휆,휃(휆, 휃, 휑, 푇 ) ≡ 푖휆,푏(휆,푇 ) and directions.

푖푒(휃,휑,푇 ) Spectral Total directional 휀휃(휃, 휑, 푇 ) ≡ 푖푏(푇 ) average. Average ∫︀ ∞ over all 휀휆(휆,푇 )퐸푏(휆,푇 )푑휆 Total hemispherical 휀(푇 ) ≡ 0 directions 퐸푏(푇 ) and spectrum. Absorptivity Incoming

푖휆,푖,푎푏푠(휆,휃,휑,푇 ) intensity Spectral directional 훼휆,휃(휆, 휃, 휑, 푇 ) ≡ 푖휆,푖(휆,휃,휑,푇 ) and directions.

퐺휆,푎푏푠(휆,푇 ) Directional Total spectral 훼휆(휆, 푇 ) ≡ 퐺휆(휆,푇 ) average. Average ∫︀ ∞ over all 훼휆(휆,푇 )퐺휆(휆,푇 )푑휆 0 Total hemispherical 훼(푇 ) ≡ 퐺(푇 ) directions and spectrum. Reflectivity Reflected

푖휆,푖,푟푒푓 (휆,휃,휑) intensity Spectral directional 휌휆,휃(휆, 휃, 휑) ≡ 푖휆,푖(휆,휃,휑) and directions.

푖휆,푖,푟푒푓 (휃,휑,푇 ) Spectral Total directional 휌휃(휃, 휑, 푇 ) ≡ 푖휆,푖(휆,휃,휑) average. Average ∫︀ ∞ over all 휌휆(휆,푇 )퐺(휆,푇 )푑휆 0 Total hemispherical 휌(푇 ) ≡ ∫︀ ∞ directions 퐺휆(휆,푇 )푑휆 0 and spectrum. 113

ANNEX B - CFD AND FINITE VOLUMES METHOD

The method in this work to study the radiative recuperators is the FVM. For this, it is important to understand the basis of the method using in the commercial softwares like CFX, Fluent etc. There are two ways to solve problems in heat transfer and fluid flow: the experimental investigation and the theoretical calculation (Patankar, 1980). The experimental investigation brings the most reliable information with the aid of direct measurements of temperature, flow etc. With the direct measurements, it is possible to extrapolate the information to a greater scale when necessary. In the case of theoretical calculation, the physical model is replaced for a mathematical model. In the process, some accuracy can be lost due to some simplifying hypotheses when the mathematical model is made. But this model has the following advantages:

1. Low Cost; 2. Speed; 3. Ability to simulate realistic and ideal conditions;

The mandatory item to consider is the cost. Normally, the fabrication of real model is very expensive and is limited by only one geometry. The theoretical model would be an interesting solution. The basis of any numerical method is simplifying the partial differential equations that govern physical phenomena like conservation of mass, energy, momentum etc. into algebraic equations that are easier to solve than partial differential equations. Maliska(2004) explains that the traditional numerical methods for solve engineering problems can be classified by:

1. Finite Differences Method (FDM); 2. Finite Volumes Method (FVM); 114 Annex B - CFD and Finite Volume Method

3. Finite Elements Method (FEM);

The Finite Differences Method (FDM) is the simplest method in the numerical methods. It employs truncated Taylor series for approximate the derivatives in the differential equations to solve. This method change differential equations into algebraic equations making easy the solution of conservative equations. Its popularity is growing in academic circles due to fast implementation and flexibility. The FDM shows some problems in complex geometries causing a inaccurate solution in the whole control volume. The Finite Elements Method (FEM) was popular in structural problems solution of elasticity problems. The FEM method had some problems in fluid mechanics due to instability in advection-dominant problems. For this limitation, the Finite Volumes Method (FVM) has been widespread for being more accurate than the other numerical methods, basically due to the effectiveness of solutions in irregular geometries. Other important aspect of FVM is the physical interpretation of its equations compared with simplified numerical equations, due to the nature of the method where the properties (e.g. energy, mass, momentum) balances are satisfied in the global control volume. TheFEM method doesn’t have this property. The majority of commercial software for CFD use the FVM.

CONSERVATION EQUATIONS

Conservation equations are necessary to solve the flow problem (velocity and pressure) and the energy problem (temperature) of the fluids in the heat exchanger. The conservation equations have the following Cartesian generic form:

휕(휌휑) 휕 휕 (︂ 휕휑 )︂ + (휌푢푗휑) = Γ + 푆, for j=1,2,3 (B.21) 휕푡 휕푥푗 휕푥푗 휕푥푗 where the first term of the left side of equation (2.35) is a transient term or variation of generic variable 휑 respect of time, 휌 is the density and 푆 is a generic source term and 푗 is one of Cartesian directions.

The second term is the advection of variable 휑, this is the transport of variable of 휑 due to velocity 푢푗. The fist term of the right side is the diffusion of variable 휑 and the last term is the 115

source term or generation of variable 휑. Table 30 shows a summary of conservation equations used.

Table 30 – Summary of conservation equations. Adapted from Maliska(2004).

Equation 휑 Γ 푆

Global mass 1 0 0

휕 (︁ 휕푢 2 )︁ 퐵푥 + 휇 − 휇∇ · 푉⃗ + x-Momentum 푢 휇 휕푥 휕푥 3 휕 (︀ 휕푣 )︀ 휕 (︀ 휕푤 )︀ 휕푃 휕푦 휇 휕푥 + 휕푧 휇 휕푥 − 휕푥

휕 (︁ 휕푣 2 )︁ 퐵푦 + 휇 − 휇∇ · 푉⃗ + y-Momentum 푣 휇 휕푦 휕푦 3 휕 (︁ 휕푢 )︁ 휕 (︀ 휕푤 )︀ 휕푃 휕푥 휇 휕푦 + 휕푧 휇 휕푥 − 휕푦

휕 (︁ 휕푤 2 )︁ 퐵푧 + 휇 − 휇∇ · 푉⃗ + z-Momentum 푤 휇 휕푧 휕푧 3 휕 (︀ 휕푢 )︀ 휕 (︀ 휕푣 )︀ 휕푃 휕푥 휇 휕푧 + 휕푧 휇 휕푧 − 휕푧

푘 1 퐷푃 휇 Energy 푇 퐶 + Φ 푝 퐶푝 퐷푡 퐶푝

i-Specie conservation 퐶푖 휌D 0

FUNDAMENTALS OF DISCRETIZATION

The discretization is a fundamental process in any numerical simulation and consists in divide the physical domain into little “discrete" elements, in the case of CFD problems are the control volumes, and approximating the partial differential conservation equations into linear algebraic equations set. Patankar(1980) clearly illustrates the way to discretization. For example, the steady one-dimensional heat conduction governed by

푑 (︂ 푑푇 )︂ 푘 + 푆 = 0, (B.22) 푑푥 푑푥 where 푘 is the thermal conductivity, 푇 is the temperature and 푆 is the rate of heat generation per unit volume. For one dimension, one point of the mesh adopted is illustrated in the Figure 43. 116 Annex B - CFD and Finite Volume Method

Figure 43 – Mesh-point cluster for the one dimensional steady heat conduction problem. Adapted from Patankar(1980).

The integration of Equation (B.22) is: (︂ 푑푇 )︂ (︂ 푑푇 )︂ ∫︁ 푤 푘 − 푘 + 푆푑푥 = 0 (B.23) 푑푥 푒 푑푥 푤 푒 Then, the first order derivatives in Equation (B.23) can be approximated by a linear function. In the Figure 43 the “control volume" boundaries are the dotted lines e and w. Equation (B.23) results in:

푘푒(푇퐸 − 푇푃 ) 푘푤(푇푃 − 푇푊 ) − + 푆¯Δ푥 = 0, (B.24) (훿푥)푒 (훿푥)푤 where 푆¯ is the average of source term 푆, Equation (B.24) can be expressed by: 푎푃 푇푃 = 푎퐸푇퐸 + 푎푊 푇푊 + 푏, (B.25) where 푘푒 푎퐸 = (B.26) (훿)푒

푘푤 푎푊 = (B.27) (훿)푤

푎푃 = 푎퐸 + 푎푊 (B.28) 117 and 푏 = 푆¯Δ푥 (B.29) for all N-volumes there are N-equations and it is possible solve the linear equation set. If the mesh have 1,000 control volumes, the size of the equation set is 1000 x 1000 and so on. A excessive amount of control volumes (mesh refinement) requires greater computational effort, and few points in the mesh give less accurate results. Inthis example, the solution of the equation set gives the temperature in all points in the domain. The method is general and can be generalized to two and three dimensions. Figure 44 shows a two dimensional mesh point.

Figure 44 – Mesh-point cluster for the two dimensional situation. Adapted from Patankar(1980).

More details of discretization, mesh and solution of conservation equations can be found in Patankar(1980) and Maliska(2004).