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Analysis of Heat Transfer in Air Cooled Condensers

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Analysis of Heat Transfer in Air Cooled Condensers Sigríður Bára Ingadóttir FacultyFaculty of of Industrial Industrial Engineering, Engineering, Mechanical Mechanical Engineering Engineering and and ComputerComputer Science Science UniversityUniversity of of Iceland Iceland 20142014 ANALYSIS OF HEAT TRANSFER IN AIR COOLED CONDENSERS Sigríður Bára Ingadóttir 30 ECTS thesis submitted in partial fulfillment of a Magister Scientiarum degree in Mechanical Engineering Advisors Halldór Pálsson, Associate Professor, University of Iceland Óttar Kjartansson, Green Energy Group AS Gestur Bárðarson, Green Energy Group AS Faculty Representative Ármann Gylfason, Associate Professor, Reykjavík University Faculty of Industrial Engineering, Mechanical Engineering and Computer Science School of Engineering and Natural Sciences University of Iceland Reykjavik, May 2014 Analysis of Heat Transfer in Air Cooled Condensers Analysis of Heat Transfer in ACCs 30 ECTS thesis submitted in partial fulfillment of a M.Sc. degree in Mechanical Engi- neering Copyright c 2014 Sigríður Bára Ingadóttir All rights reserved Faculty of Industrial Engineering, Mechanical Engineering and Computer Science School of Engineering and Natural Sciences University of Iceland VRII, Hjardarhagi 2-6 107, Reykjavik, Reykjavik Iceland Telephone: 525 4000 Bibliographic information: Sigríður Bára Ingadóttir, 2014, Analysis of Heat Transfer in Air Cooled Condensers, M.Sc. thesis, Faculty of Industrial Engineering, Mechanical Engineering and Computer Science, University of Iceland. Printing: Háskólaprent, Fálkagata 2, 107 Reykjavík Reykjavik, Iceland, May 2014 Abstract Condensing units at geothermal power plants containing surface condensers and cooling towers utilize great amounts of water. Air cooled condensers (ACCs) are not typically paired with dry or flash steam geothermal power plants, but can be a viable solution to eliminate the extensive water usage and vapor emissions related to water cooled systems. The present thesis investigates two different models that provide tools for calculating the heat transfer coefficient across air cooled tube bundles. An analytical model is created using MATLAB (2013), while ANSYS Fluent (2013a) is used to generate a numerical model. A correlation from literature is used for the heat transfer coefficient calculation in the analytical model and the k − ! shear stress transport (SST) turbulence model is used in ANSYS Fluent (2013a). When compared, the analytical model results in more accuracy than the numerical model. However, both models can be utilized to optimize air cooled condenser design. Útdráttur Kælikerfi í jarðvarmaverum sem notast við varmaskipta ásamt kæliturnum kalla á töluverða vatnsnotkun. Loftkældir eimsvalar eru raunhæf lausn til þess að koma í veg fyrir óþarfa sjónmengun og mikla vatnsnotkun. Vanalega eru loftkældir eimsvalar ekki nýttir við jarðvarmaver og er því brýnt að skoða þá lausn. Í ritgerðinni eru tvö líkön sett fram þar sem hvort þeirra býður upp á möguleika á útreikningum á var- maleiðnistuðli yfir loftkæld rör með kæliplötum. Greiningin er framkvæmd fræðilega í forritinu MATLAB (2013) en einnig er notast við tölulega greiningu í ANSYS Flu- ent (2013a). Þá er notast við jöfnur úr fræðigreinum til að framkvæma útreikninga fræðilega en tölulega er notast við k − ! SST iðustreymislíkanið í ANSYS Fluent (2013a). Þegar líkönin eru borin saman er greinilegt að fræðilega nálgunin er nákvæ- mari, en tölulega nálgunin býður upp á sjónræna túlkun af flæðinu. Hinsvegar geta bæði líkönin verið notuð í bestun á loftkældum eimsvölum. v Contents List of Figures ix List of Tables xi Nomenclature xiii Acknowledgments xvii 1. Introduction 1 2. Background 3 2.1. Condensing Systems . .3 2.1.1. Water Cooling . .3 2.1.2. Air Cooling . .5 2.1.3. Cooling System Summary . .6 2.2. Heat Exchangers . .7 2.2.1. Finned Tube Heat Transfer . .7 2.2.2. Condensation in Inclined Tubes . .8 3. Materials and Methods 11 3.1. ACC Materials . 11 3.2. Analytical Model . 14 3.2.1. Internal Flow . 15 3.2.2. External Flow . 16 3.2.3. Overall Heat Transfer Coefficient . 17 3.3. Numerical Model . 18 3.3.1. Navier-Stokes Equations . 18 3.3.2. Energy Equation . 19 3.3.3. k-! SST Turbulence Model . 19 3.3.4. Cylinder in Crossflow . 21 3.3.5. Tube Bundle in Crossflow . 23 3.3.6. Simulation Setup . 26 4. Results 27 4.1. Analytical Model . 27 vii Contents 4.2. Numerical Model . 28 4.2.1. Cylinder in Crossflow . 28 4.2.2. Tube bundle . 31 4.3. Model Comparison and Discussion . 35 5. Conclusion 37 Bibliography 39 Appendices 42 A. GEA Data 43 B. Fin Efficiency Derivation 45 viii List of Figures 2.1. Water once-through cooling in a surface condenser . .4 2.2. Indirect water recirculating cooling system . .4 2.3. Water recirculating cooling in a direct contact condenser . .5 2.4. A schematic of a dry air cooling system . .5 2.5. A zoomed view of an ACC unit showing the tube bundles (SPX Cool- ing Technologies Inc.) . .6 3.1. A typical A-frame ACC street with two bays . 12 3.2. The fins are designed to have a trapezoidal cross section . 13 3.3. The cross section of the tube bundle shows averaged fin thickness . 13 3.4. The finned tube bundle is designed to have four rows of tubes . 14 3.5. 2D geometry and boundary conditions of cylinder in crossflow . 21 3.6. 2D model mesh refinement is gradual around the cylinder wall . 22 3.7. A section of the tube bundle front is analyzed in the model . 24 3.8. A section of the tube bundle side is analyzed in the model . 24 3.9. The 3D model boundary conditions are similar to the 2D model . 25 3.10. A zoomed view of the 3D mesh shows gradual refinement . 25 4.1. Coefficient of lift plotted agains simulation time . 29 ix LIST OF FIGURES 4.2. Zoomed-in velocity contour of the cylinder in crossflow . 30 4.3. Front side (tube) temperature profile of the tube bundle . 33 4.4. Back side (fin) temperature profile of the tube bundle . 33 4.5. Front side (tube) velocity profile of the tube bundle . 33 4.6. Back side (fin) velocity profile of the tube bundle . 33 4.7. Front side (tube) turbulent intensity profile of the tube bundle . 34 4.8. Back side (fin) turbulent intensity profile of the tube bundle . 34 A.1. Data Sheet provided by GEA (Yazbek, 2013) . 43 A.2. Schematic provided by GEA (Yazbek, 2013) . 44 x List of Tables 2.1. Comparison between condensing systems . .7 3.1. Main specifications for the air cooled condenser design . 11 3.2. ACC Unit Solution from GEA . 12 4.1. Analytical model results are clear . 27 4.2. Number of cells corresponding to various 2D mesh refinements . 28 4.3. Mesh convergence study for the 2D model . 29 4.4. 2D model results are compared to literature . 30 4.5. Number of cells corresponding to various 3D mesh refinements . 31 4.6. Values of y+ for the 3D model . 32 4.7. Mesh convergence study for the 3D model . 32 4.8. Tube bundle model results . 34 4.9. Model results . 35 xi Nomenclature Abbreviations ACC Air Cooled Condenser GEA GEA Power Cooling Inc. GEG Green Energy Group AS P ISO Pressure-Implicit with Splitting of Operators SST Shear Stress Transport Constants g Acceleration due to gravity [m/s2] Greek Letters rel Relative error [%] ηc Cold side fin efficiency ηh Hot side fin efficiency µ Viscosity [kg/ms] ρ Density [kg/m3] Subscripts a Air with properties evaluated at inlet l Liquid phase L Large n Row number S Small s Steam with properties evaluated at inlet xiii Nomenclature v Vapor phase Variables 2 Ac Total cross-sectional area of all steam inlets [m ] 2 Ac Cold side, single tube area [m ] 2 Af Total face area of bundle row 1 [m ] 2 Ah Hot side, single tube area [m ] Cd Coefficient of drag Cl Coefficient of lift Cp Constant pressure specific heat [J/kg K] Df Fin diameter [m] Di Tube inner diameter [m] Do Tube outside diameter [m] G Mass velocity per area [kg/m2s] h Heat transfer coefficient [W/mK] Hf Height of fin [m] hTP Two-phase heat transfer coefficient [W/mK] ifg Enthalpy of vaporization at condenser tube inlet [kJ/kg] 0 ifg Corrected enthalpy of vaporization at condenser tube inlet [kJ/kg] iin Enthalpy of steam at condenser tube inlet [kJ/kg] iout Enthalpy of saturated liquid at condenser tube outlet [kJ/kg] 2 ka Thermal conductivity of air [W/m K] 2 kst Thermal conductivity of steel [W/m K] L Tube length [m] m_ Mass flow rate [kg/s] Nb Total number of bundles in the condenser Nf Total number of fins per meter xiv Nomenclature Nt Total number of tubes in the condenser Ntn Total number of tubes in row n of each bundle Nu Nusselt number q Condenser cooling requirement [kW] qc Condenser cooling capacity [kW] qnet Total heat transfer from tube and fin walls [kW] Re Reynolds number s Average distance between individual fins [m] Sr Strouhal number tm Fin average thickness [m] tb Thickness of fin at base [m] ◦ Tci Temperature of cold fluid at inlet [ C] ◦ Tco Temperature of cold fluid at outlet [ C] ◦ Tg Saturation temperature of liquid film [ C] ◦ Thi Temperature of hot fluid at inlet [ C] ◦ Tho Temperature of hot fluid at outlet [ C] ◦ ∆Tlm Log mean temperature difference [ C] tt Thickness of fin at fin tip [m] ◦ Tw Temperature of the tube wall [ C] V_ Volumetric flow rate [m3/s] xv Acknowledgments This thesis was done under the supervision of Halldór Pálsson, Associate Professor in the Faculty of Industrial Engineering, Mechanical Engineering and Computer Sci- ence in the School of Engineering and Natural Sciences at the University of Iceland. His constant advice, guidance and support kept me afloat throughout my studies.
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