Experimental and Numerical Analysis of a PCM-Supported ...

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liquid and solid phases, respectively. At steady state conditions, the energy flow from gas to solid phase equilibrates with the energy flow from solid to liquid phase and the local temperatures of all phases remain constant. Any change of the system parameters will break steady state conditions, and the local temperatures will change. The condensation rate depends mainly on the vapor pressure gradient between the bulk gas phase from one side and both the gas-liquid interface and the gas-solid interface from the other side. The vapor pressure is a direct function of the respective local temperatures, assuming saturation conditions in closed loop cycles. However, the sensible energy flow components also affect the film temperature at gas-liquid interface and gas-solid interface, which indirectly affects the condensation rate. On the other hand, condensation contributes a considerable fraction of latent heat to the liquid and solid phases and leads to rising their temperatures, which in turn affects both heat and mass balances. In fact, the microscopic analysis of the condensation process is much more complicated than the described macroscopic analysis, while the later is sufficiently accurate for the present application and range of operation conditions in comparison with the experimental measurements as will be presented later. 4.2.4 Closure relationships Predictive models for packed column performance incorporate macroscopic properties of the entire column based on volume or spatial averaging technique which was developed by Slattery [26], rather than focusing rigorously on underlying local variations of momentum, heat, and mass transfer processes. Hence, closure models have to be provided in the numerical scheme to capture the information that is lost in the averaging process. Careful selection of the appropriate closure relationships from literature is therefore a fundamental factor for achieving high accuracy of the simulation model. Modeling and design of a randomly packed distillation column requires a reliable specification of effective interfacial areas, phase fractions, heat and mass transfer coefficients, and pressure drop. The next sections will be devoted to the adopted modeling procedures and calculations of such critical parameters. 4.2.3.1 Evaporation and condensation rates The evaporation rate, the condensation rates at the gas/liquid interface and the gas/solid interface can be written respectively as a function of the difference between the vapor pressure or vapor concentration at these interfaces and the vapor pressure or vapor concentration at the bulk gas: m evap k g a e c inter ( T ) c (4.36) l 79
m m k a c c ( T ) cond , gl g e inter l k a P P ( T ) cond , gs gs gs v v, inter s (4.37) (4.38) Where P v is the saturation vapor pressure (pa), P v,inter (T s ) is the saturation vapor pressure at the interface as a function of the particle temperature, c is the water vapor concentration (mol/m 3 ), and c inter (T l ) is the interfacial water vapor concentration at the liquid water temperature. As the liquid side heat transfer coefficient is generally much greater than that of the gas side, the temperature difference between the interface and bulk liquid is very slight, the interfacial temperatures are assumed equal to the liquid temperature. The interfacial concentration can be expressed as a function of the interface temperature (T inter ) by combining the Clapeyron equation, which represents the dependence of saturation pressure on saturation temperature, and the ideal gas equation of state: c inter p ref hfg 1 1 ( T inter ) exp (4.39) RTinter R Tinter Tref where the reference pressure p ref =618.9Pa, the universal gas constant R=8.314J/mol/K, latent heat of condensation h fg =45050J/mol, and the reference temperature T ref =273.15K. Thermodynamic relationships are used to evaluate the phases partial pressures and other thermophysical properties of humid air as presented in Appendix D. 4.2.3.2 Void fraction and specific packing area The void fraction is defined as the ratio of the volume of voids to the overall volume of a packing. It is not only strongly dependent on the method by which the container is packed but also on the ratio of the container diameter to the diameter of the packing particle (d bed /d p ). An empirical relationship between the void fraction for randomly packed uniform spheres in a cylindrical bed was derived by Torab and Beasley [27] from real data as follows: 3 5 2 l g 0.4272 4.51610 ( dbed / d p) 7.88110 ( dbed / d p) (4.40) This relation can be used to predict the void fraction as a function of (d bed /d p ) for modeling and optimization of schemes for values of (d bed /d p )28 the void fraction is 0.3625 [27]. The solid fraction in the packed bed can be directly determined: 1 s (4.41) 80
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Technische Universität München In
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It is my pleasure to thank Prof. Th
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Contents List of figures ..........
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5.3 Functional description ........
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List of Figures Figure 1.1: Cost br
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78cm; Top: Evaporator, Bottom: Cond
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xii
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m Mass flow rate; [kg.s -1 ] m eva
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ed c coll cond cw d d e or eff evap
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1 Introduction The first part of th
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summarized in figure (1.2). Thermal
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1.3.2 Selection criteria of desalin
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of energy storage or hybridization
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Desalination development focuses on
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Introduction of the indirect type s
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2 Literature Survey 2.1 Introductio
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There is actually a commercial prod
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Q m H c ( T T1) c ( T 2 T ) (2.2)
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(solid-liquid) have a storage densi
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(iii) a sharp melting temperature.
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melt and freeze without segregation
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However, the stored heat is less va
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parameters on the heat transfer and
Page 48 and 49: categories. The first category is b
Page 50 and 51: to 550 kWh/m 3 of distilled water a
Page 52 and 53: The enthalpy and humidity of the sa
Page 54 and 55: Air mass flow rate [kg/h] GOR [-] 1
Page 56 and 57: On the other hand, the efficiency o
Page 58 and 59: 2.8.4.2 Effect of air to water mass
Page 60 and 61: distillate rate. The system was not
Page 62 and 63: were; EnviPac Gr.1, 32 mm, and VFF
Page 64 and 65: Figure 2.15: Height versus air temp
Page 66 and 67: The performance of the condenser is
Page 68 and 69: Klausner and Mei [136] described a
Page 70 and 71: The impact of the collector cost ca
Page 72 and 73: exchanger and energy storage in one
Page 74 and 75: 3 Scope of the Study This chapter p
Page 76 and 77: packing where it gets in direct con
Page 78 and 79: In fact there is a tradeoff between
Page 80 and 81: The energy flow between all and eac
Page 82 and 83: 4 Theoretical Analysis and Modeling
Page 84 and 85: The two-energy equation models whic
Page 86 and 87: solid-liquid phase change inside th
Page 88 and 89: assumed by conduction in both axial
Page 90 and 91: the air pressure drop ∆P per unit
Page 92 and 93: evaporation rate per unit volume of
Page 94 and 95: where β t , β c , ρ ref , c ref
Page 96 and 97: the viscous transport and introduce
Page 100 and 101: 4.2.3.3 Liquid and gas hold-ups Liq
Page 102 and 103: Several models and approaches for m
Page 104 and 105: where G=ρU d /ε g is the pore mas
Page 106 and 107: k k eff s 1 3 2 (4.55) This cor
Page 108 and 109: uncertainties associated with the f
Page 110 and 111: 1 2 (4.62) d1 capp c2 c1 c2 1
Page 112 and 113: [58] evaluated the cooling tower ai
Page 114 and 115: 1 exp NTU 1 C r, cond cond (4
Page 116 and 117: A HE QHE U T HE LM (4.81) Where Q
Page 118 and 119: c M f b (4.86) M b S S f where r
Page 120 and 121: that form the study logical foundat
Page 122 and 123: 5 Experimental Analysis This chapte
Page 124 and 125: 5.2 Measuring Techniques K-type the
Page 126 and 127: The product condensed water was mea
Page 128 and 129: operating limits. In light of the l
Page 130 and 131: In the last two cases, the inlet ho
Page 132 and 133: performance and its threshold value
Page 134 and 135: It could be interpreted that this p
Page 136 and 137: Evaporator Condenser Figure 5.8: Av
Page 138 and 139: within the inaccuracy margins. The
Page 140 and 141: The last two cases of boundary cond
Page 142 and 143: natural air flow in the system. In
Page 144 and 145: 6 Model Implementation and Validati
Page 146 and 147: x t u x u 0 0 , (6.5) and for a s
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Next time step validation were the
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The evaporator and condenser both w
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Figure 6.2: Evolution of inlet and
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Figure 6.4: Evolution of inlet and
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temperature is at its maximum level
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Bottom Top Figure 6.7: Evolution of
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7 Parameters Analysis of the Evapor
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Figure 7.1: Effect of packing size
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e 0.45 kPa under natural convection
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aspect ratio under constant bed vol
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Figure 7.7: Effect of inlet hot wat
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well as the time required to reach
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Figure 7.10: Effect of packing medi
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40°C respectively. This gives flex
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the condensate rate, productivity f
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esult, rather than PCM media which
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Figure 7.18: Effect of PCM thermal
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8 Optimization of HDH plant In this
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The MATLAB model describes how the
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less steep than that of the distill
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8.3.4 Effect of hot water flow rate
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storage materials and thus it can h
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for latent heat storage would be ob
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When T m becomes sufficiently highe
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9 Summary and conclusions 9.1 Summa
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productivities at any cooling water
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[13] Vafai K., Sozen M. An investig
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[48] Crone S., Bergins C., and Stra
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[79] Tiwari G.N. and Yadav Y.P. (78
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[109] Mehling H., Hiebler S. and Zi
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[139] Belessiotis V, Delyannis E (2
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Appendices Appendix A A1. PCM Therm
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A3. Constants and Thermo-physical p
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From the above correlation, the con
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The Ergun analogy factor J h repres
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Equation (C.7) represents an overal
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Appendix D D1. Cooling tower theory
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A m w = the plan or cross sectiona
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