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

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c M f b (4.86) M b S S f where r c is the salt concentration ratio, S b , and S f are the corresponding salt concentrations for rejected brine and feed seawater respectively. The amount of rejected and recirculated brine M r can be determined respectively as: M d M b (4.87) r 1 c M r M M (4.88) hw f The cumulated GOR and daily fresh water production will be used for investigating the performance and transient behavior of the PCM-supported HDH system under varying weather conditions of El-Arish city on the Mediterranean Sea north of Egypt. 4.6 Representation of the MEHH and MECD phenomena The section begins by listing some fundamental points towards laying out the approach to the representation of MEHH by the mathematical mode. The representation approach should answer a key question, which is deemed to be important to an understanding of the connections between the mathematical formulations presented in the previous sections and the coupled multi-physics of dual phase change phenomena involved on both micro and macro scale levels. The intention is to provide a logical conceptual foundation for the subsequent numerical analysis. This foundation will adopt a clear separation between three levels of parameters, which can be identified as “constants”, “state variables”, and “dependent or solution parameters”. This separation offers an easy and straightforward implementation of mathematical formulations at hand. 4.6.1 Fundamental points 1. The first level (or constants) is defined as those parameters, which can be derived directly from the boundary and geometrical conditions (i.e. the independent parameters) and remain constant at their average values along the packing height. For example: The void and solid fractions (equations 4.40, and 4.41), the specific surface area (equation 4.45), the packing permeability (equation 4.21), as well as the effective thermal properties of the solid phase (equations 4.55 to 4.57) can be derived directly from the geometry of the column and packing size. 99
Given the liquid and gas mass flow rates, then the liquid and gas hold up (equations 4.42 to 4.44), average pore velocities (equation 4.17 and equation 4.18 for liquid and gas respectively), relative permeabilities (equations 4.24 to 4.29), as well as the effective thermal properties of the liquid and gas phases (equations 4.56 to 4.57), and pressure drop (equations 4.10 and B1 to B8 in appendix B) can be calculated. Given the characteristics of packing materials (together with the liquid and gas mass flow rates), the interfacial areas between each pair of solid and fluid phases (equations 4.46 to 4.47), effective heat and mass transfer coefficients (equations 4.48 to 4.54 followed by equation 4.9) can be estimated. It has to be pointed out that the parameters mentioned above remain constant as long as the boundary and geometric conditions don’t change. Once one or more of these conditions is changed, values of these parameters will be updated accordingly in the model, Although the saturation permeabilities are only needed for calculations of the pressure drop when the packing size is too small (very dense porous media) or for derivation of the gas flow velocity when operating the system under natural convection, they are always calculated by the model. When operating the system under forced convection, which is the operation mode adopted in the present study, the approach of Stichlmair et al. [29], as described in Appendix (B), is followed. 2. The second level (or state variables) is commonly well known as the thermophysical properties of the involved phases, which are appreciatively affected by or have mutual dependencies on the solution parameters. For instance: The density of the gas phase depends on its temperature and humidity content as described by equation (4.19). The heat capacity of the PCM as described by the apparent heat capacity formulation in equation (4.63) and equations (4.65) to (4.68) depends on its temperature. Other state variables for the gas and liquid phases are estimated at the respective average temperatures in the bed. 3. The third level stands for those parameters, which are derived from the solution of the one dimensional energy and mass balance equations and vary both in space and time (i.e. 4.7 to 4.8 for the external PCM thermal, 4.11 to 4.14 for the evaporator, and 4.32 to 4.35 for the condenser). 4.6.2 Capturing the MEHH and MECD phenomena What immediately follow are the fundamental ideas and calculations strategy on how to evaluate the solution parameters to capture the MEHH and MECD phenomena 100
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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
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categories. The first category is b
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to 550 kWh/m 3 of distilled water a
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The enthalpy and humidity of the sa
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Air mass flow rate [kg/h] GOR [-] 1
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On the other hand, the efficiency o
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2.8.4.2 Effect of air to water mass
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distillate rate. The system was not
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were; EnviPac Gr.1, 32 mm, and VFF
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Figure 2.15: Height versus air temp
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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 98 and 99: liquid and solid phases, respective
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 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
Page 148 and 149: Next time step validation were the
Page 150 and 151: The evaporator and condenser both w
Page 152 and 153: Figure 6.2: Evolution of inlet and
Page 154 and 155: Figure 6.4: Evolution of inlet and
Page 156 and 157: temperature is at its maximum level
Page 158 and 159: Bottom Top Figure 6.7: Evolution of
Page 160 and 161: 7 Parameters Analysis of the Evapor
Page 162 and 163: Figure 7.1: Effect of packing size
Page 164 and 165: e 0.45 kPa under natural convection
Page 166 and 167: 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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