ANALYSIS OF EVAPORATIVE COOLERS AND CONDENSERS by Andre Alexis Dreyer Thesis presented in partial fulfilment of the requirements for the degree of Master of Engineering at the University of Stellenbosch. Thesis Supervisor: Prof. P.J. Erens Department of Mechanical Engineering University of Stellenbosch November 1988 Stellenbosch University http://scholar.sun.ac.za Declaration I, the undersigned, hereby declare that the work contained in this thesis is my own original work and has not previously, in its entirety or in part, been submitted at any university for a degree. (Signature of candidate) ............... day of 1988. j Stellenbosch Unive(r is )it y http://scholar.sun.ac.za ABSTRACT In this report various mathematical models for the thermal evaluation of evaporative coolers and condensers are presented. These models range from the exact model based on the work by Poppe [84P01] to the simplified logarithmic models based on the work of McAdams [54Mcl] and Mizushina et al. [67MI1], [68MI1]. Various computer programs were written to perform rating and selection calculations on cross-flow and counterflow evaporative coolers and condensers. Experimental tests were conducted on a cross-flow evaporative cooler to determine the governing heat and mass transfer coefficients. The experimentally determined coefficients were cqrrelated and these correlations are compared to the existing correlations. The two-phase pressure drop across the tube bundle was also measured and a correlation for two-phase pressure drop across a tube bundle is presented. Stellenbosch University http://scholar.sun.ac.za ( i i ) ACKNOWLEDGEMENTS The work described in this thesis forms part of an on-going research program on wet and dry cooling in the Department of Mechanical Engineering at the University of Stellenbosch. I would like to acknowledge the valued contributions of each of the following persons: Prof. P.J. Erens for his guidance, support and assistance throughout the project; Prof. D.G. Kroger for his suggestions, patience and interest in the project; Mr.· D.C. Uys for the construction of the test section and practical assistance with the experimental work; Miss. E. Lekas for the typing of the thesis. I would also like to thank the National Energy Council for their finanfcial support. Stellenbosch University http://scholar.sun.ac.za ( i i i) CONTENTS Page ABSTRACT ( i) ACKNOWLEDGEMENTS (ii) CONTENTS (iii) NOMENCLATURE (v) 1 - INTRODUCTION 1.1 2 - LITERATURE SURVEY 2.1 3 - MATHEMATICAL MODELLING OF EVAPORATIVE COOLERS AND CONDENSERS 3.1 3.1) Basic theory for evaporative coolers 3.2 3.1.1) Exact analysis (Poppe model) 3.2 3.1.2) Merkel analysis 3.10 3.1.3) Improved Merkel analysis 3.11 3.1.4) Simplified model 3.12 3.2) Basic theory for evaporative condensers 3.15 3.2.1) Exact analysis (Poppe model) 3.15 3.2.2) Merkel analysis 3.18 3.2.3) Improved Merkel analysis 3.19 3.2.4) Simplified model 3.19 4 - HEAT/MASS TRANSFER AND PRESSURE DROP CORRELATIONS 4.1 4.1) Film heat transfer coefficient 4.1 4.2) Mass transfer coefficient 4.9 4.3) Pressure drop correlations 4.21 5 - COMPUTER SIMULATION 5.1 5.1) Determination of coefficients 5.2 5.2) Successive calculation models 5.4 5.2.1) Cross-flow evaporative cooler simulation 5.7 5.2.2) Counterflow evaporative cooler simulation 5.16 5.2.3) Combination cooler 5.17 5.3) Simplified models 5.25 5.4) Natural draft cooling tower 5.26 6 - EXPERIMENTAL DETERMINATION OF THE HEAT AND MASS TRANSFER 6.1 COEFFICIENTS IN A CROSS-FLOW EVAPORATIVE COOLER 6.1) Description of wind-tunnel and apparatus 6.1 6.2) Data logging and energy balance calculations 6.12 6.3) Experimental procedure 6.13 6.4) Observations and results 6.16 6.5) Determination of coefficients and correlations 6.29 6.6) Discussion of results 6.43 7 - CONCLUSION 7.1 REFERENCES R.1 Stellenbosch University http://scholar.sun.ac.za ( iv) -APPENDICES A - THERMOPHYSICAL PROPERTIES OF FLUIDS A.l B - DEFINITION OF LEWIS NUMBER AND THE LEWIS FACTOR B.l C - DEFINITION OF MASS TRANSFER COEFFICIENTS AND MASS TRANSFER C.l POTENTIALS D - SINGLE PHASE PRESSURE DROP CORRELATIONS ACROSS PLAIN TUBE D.l BUNDLES IN CROSS-FLOW E - DERIVATION OF THE DRAFT EQUATION FOR A NATURAL-DRAFT E.l CROSS-FLOW EVAPORATIVE COOLING TOWER F - SOLUTION OF SIMULTANEOUS DIFFERENTIAL EQUATIONS USING THE F.l 4TH ORDER RUNGE-KUTTA METHOD G - CORRELATIONS FOR CONVECTIVE AND CONDENSATION HEAT TRANSFER G.l COEFFICIENTS ON THE INSIDE OF TUBES H - DETERMINATION OF THE AIR/WATER INTERFACE TEMPERATURE H.l I - CORRECTION OF HEAT TRANSFER COEFFICIENT AT HIGH MASS I.l TRANSFER RATES J - EVALUATION OF CONVENTIONAL COOLING TOWER PACKING IN A J.l COMBINATION EVAPORATIVE COOLER K - RESULTS OF COMPUTER SIMULATIONS K.l L - FORTRAN CODE FOR CROSS-FLOW EVAPORATIVE COOLER SIMULATION L.l PROGRAM Stellenbosch Univ(evrs) ity http://scholar.sun.ac.za NOMENCLATURE A Area, [m2] a Effective suface area of tubes per unit volume, [m2;m3] B Constant defined in section 4.3, [-] b Slope of the air saturation enthalpy curve, [J/kgK] c Concentration, [kg/m3] q 'C2' .. Coefficients, [-] Cp Specific heat at constant pressure, [J/kgK] D Diffus~ity, [m2/s] d Diameter (characteristic length), [m] E Coefficient defined by equation 2.5, [-] EP Dimensionless enthalpy potential defined by equation 4.2.21, [-] F LMTD correction factor or force, [-] or [N] f Friction factor, [-] fa Arrangement factor (Appendix D), [-] fn Correction factor for small number of tube rows (Appendix D), [-] fz Correction factor for non-isothermal flow (Appendix D), [-] fzn Correction factor for non-isothermal flow and small number of tube rows (Appendix D), f-] G Mass velocity, [kg/m2s] g Gravitational acceleration, [m/s2] h Heat transfer coefficient, [W/m2K] ho Mass transfer coefficient based on Tw, [kg/m2s] hoi Mass transfer coefficient based on Ti, [kg/m2s] hoo Overall mass transfer coefficient, [kg/m2s] hop Mass transfer.coefficient based ·on partial pressure driving potential and Tw, [s/m] hopi Mass transfer coefficient based on partial pressure driving potential and Ti, [s/m] i .Enthalpy, [J/kg] Latent heat of evaporation, [J/kg] ~fg Corrected latent heat of evaporation, [J/kg] ~fg ooc, lvo Latent heat of evaporation at [J/kg] Ai "Entalpy potential" defined by equation 4.2.21, [J/kg] Kwb "Wet bulb K" defined by equation 2.1, [-] K Loss coefficient, [-] Kg Coefficient defined by equation C.4, [s/m] k Thermal conductivity, [W/mK] kg Coefficient defined by equation C.S, [s/m] kl Coefficient defined by equation C.6, [m/s] L Length, [m] LMED Log mean enthalpy difference, [J/kg] LMTD Log mean temperature difference, [ C] LVF Liquid void fraction, [-] m Massflow rate, [kg/s] N Constant defined by equation 2.6, [-] n Number [-] NTU Number of transfer units, [-] p Pitch, [m] p Pressure, [N/m2] Ap Pressure drop, [N/m2] Stellenbosch University http://scholar.sun.ac.za (vi) l\p* Pressure drop based on massflow rate of both phases and the properties of one of the phases, [N/m2] q Heat transfer rate, [W] qll Heat flux, [W/m2] R Universal gas constant, [J/kgK] Re* Reynolds number based on the massflow rate of both phases and the properties of one of the phases, [-] RR Ratio defined by equation 4.2.19, [-] Ry Characteristic flow parameter, [m-1] r Ratio defined by equation B.21, [-] T Temperature, [OC] t Thickness, ~m] u Overall heat transfer coefficient, [W/m K] v Velocity, [m/s] w Width, [m] w Humidity ratio, [kg water/kg dry air] X Mole fraction, [-] X Vapour quality, [-] y Ratio defined by equation 4.3.10, [-] z· Height, thickness, [m] a Thermal diffusivity, k/pc~, · [m2/s] r Recirculating water massf ow rate per side per unit length of tube, [kg/ms] fG Ratio defined by equation 4.·3.14, [-] 0 Film thickness, [m] oc Concentration boundary layer thickness, [m] om Momentum boundary layer thickness, [m] 6t Thermal boundary layer thickness, [m] E: Heat exchanger effectiveness [-] r Parameter defined by equations 4.3.2_and 4.3.12, [-] 7] Parameter defined by equation 6.17, [-] 8 Angle, [ ] Dynamic viscosity, J.L [kg~ms] Kinematic viscosity, [m /s] II p Density, [kg/m3] !/) Parameter defined by equations 4.3.18 and 4.3.22, [-] Parameter defined by equation 4.3.6, [-] 1/J Xtt Martinelli parameter defined by equation 4.3.21, [-] Dimensionless Groups Le Lewis number, a/D, Sc/Pr Nu Nusselt number, hd/k Pr Prandtl number, CpJ.L/k Re Reynolds number, pvd/J.L Sc Schmidt number,v/D Abbreviations BTF Back-To-Front BTT Bottom-To-Top FTB Front-To-Back TTB Top-To-Bottom Stellenbosch Un(vivieirs)i ty http://scholar.sun.ac.za Subscripts a Air atm Atmospheric as Saturated air asi Air saturated at air/water interface temperature asp Air saturated at process fluid temperature asw Air saturated at bulk recirculating water temperature c Convective or convection or condensate ct Cooling tower crit Critical d Diagonal or downstream db Dry bulb de Drift eliminator e Equivalant or effective eb Equivalent (tube-) bundle ec Equivalent constriction ff Film cooler fr Frontal g Gas go Gas only he · Heat exchanger hor Horizontal i Inlet or inside or interface il In-line 1 Longitudinal or liquid lo Liquid only lsl Laminar sublayer m Mean or moist max Maximum min Minimum a Outlet or outside obl Oblique p Process fluid (water) r Refrigerant rows Rows rest Restrictions st Staggered t Tube or transverse tp Two phase thea Theoretical v Vapour ver Vertical w Recirculating (spray) water wb Wet bulb Free stream ~ Stellenbosch University http://scholar.sun.ac.za 1.1 CHAPTER 1 INTRODUCTION The phenomenon of cooling by evaporation is well-known and it has found many applications. ancient Egyptians used porous clay containers to· Th~ keep water cool thousands of year ago. Today evaporative cooling is used extensively in industry, ranging from the cooling of power generating plants to the cooling of condensers in air conditioning systems. In evaporative cooling, the medium which is being cooled can theoretically reach the air wet bulb temperature whereas the minimum temperature which can be reached in dry cooling would be the air dry bulb temperature. The use of evaporative cooling can lead to major cost ·savings and improvements in thermal efficiency because of the lower temperatures which can be ·. reached. In a conventional direct contact cooling tower (see figure 1.1) the water to be cooled flows through the cooling tower where it is cooled by counterflow or cross-flow airstream. The cooled water is then passed through a heat exchanger or a condenser to cool a process fluid or condense a vapour. This requires two separate units, i.e. the cooling tower and the heat exchanger or condenser. An evaporative cooler or condenser combines the heat exchanger or condenser and the cooling tower in one unit with the evaporative cooler or condenser tubes replacing the packing of the cooling tower. Figure 1.2 shows a schematic layout of a counterflow cooler. ev~porative The operation of an evaporative cooler or condenser can be described as follows: Recirculating water is sprayed onto a bank of horizontal tubes containing a hot process fluid or a vapour which is to be condensed while air is drawn across the wet tube bank. The recirculating water is heated