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

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4 Theoretical Analysis and Modeling In this chapter, detailed thermodynamic and hydrodynamic modeling of various components of the proposed HDH system has been developed. Pertinent theories, several correlations, and closure models adopted from literature will be presented. A mixed micro-macro balance transient simulation model in one spatial dimension for capturing heat and mass transfer phenomena in the HDH plant as a whole has been established. The model is fairly general to be applied as a design and optimization tool for HDH plants with different types of packing and coupled to sensible or latent thermal storage systems. 4.1 System variables The system overall setup and operation processes which have been used for developing the mathematical model are illustrated schematically in figure (4.1). The setup is typically the same as that of figure (3.1) but the main operation parameters of interest for the development of heat and mass balances in the following sections are depicted on figure (4.1) for ease of referencing. As described previously, the setup works on the same principle and contains two main sections; the distillation (HDH) cycle and the solar water heater. The later consists of a solar collector and PCM storage tank. A flat-plate solar collector (FPC) is proposed to provide the thermal power supply to the system. In figure (4.1), it is assumed that part of the outlet brine is blown down to keep the salt concentration within a certain limit identified by the brine recirculation factor (r c ). The other part is blended with the seawater makeup and re-circulated through a heat exchanger (brine heater) downstream of the condenser where the latent heat of condensation is partly recovered by the warm brine blend. The warm brine flow is heated further through the solar water collector and then passed through the external thermal storage and hence the cycle is repeated. The collected solar energy during day time will then be divided between the load and the storage tank. When solar energy is no longer available, the collector flow will be bypassed and the load is handled by discharging the thermal storage until either it is fully discharged (nightly part time operation) or solar energy again is available (24- hour operation). The above description assumes no heat losses during the fluid flows through piping and tube connections. Existence of PCM packing (or any conductive medium) in the evaporator and condenser creates a parallel path for heat and mass transfer between gas and liquid through the packing elements due to partial wetting of the packing surfaces as shown in figure (4.2). Let the subscript “s” identify the solid particles and subscripts “l” and “g” designate the liquid water and humid air (air-water vapor gas mixture) 63
espectively. Because of the partial wetting in the evaporator and condenser, there is heat transfer (q lg ) between water and air, heat transfer (q ls ) between water and PCM beads (or solid phase), and heat transfer (q gs ) between gas and PCM beads. Moreover, there is direct condensation of water vapor on the dry patches of the packing spheres in the condenser. Figure 4.1: Schematic layout of the PCM-Supported HDH desalination unit (AquaTube) and operation cycle 4.2 Mathematical Modeling A single phase model is commonly used for analyzing thermo-fluid flow in packed beds and porous media when fluid is moving relative to a solid matrix. This model assumes local thermal equilibrium between solid and fluid phases, where their temperatures are represented by a unique value. The assumption of local thermal equilibrium breaks down in certain physical situations. For example the temperature at the bounding surface changes significantly with respect to time, and when solid and fluid phases have significantly different heat capacities and thermal conductivities, the local rate of change of temperature for one phase differs significantly from that for the other phase [11]. 64
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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
Page 32 and 33: 2 Literature Survey 2.1 Introductio
Page 34 and 35: There is actually a commercial prod
Page 36 and 37: Q m H c ( T T1) c ( T 2 T ) (2.2)
Page 38 and 39: (solid-liquid) have a storage densi
Page 40 and 41: (iii) a sharp melting temperature.
Page 42 and 43: melt and freeze without segregation
Page 44 and 45: However, the stored heat is less va
Page 46 and 47: 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 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 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
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performance and its threshold value
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It could be interpreted that this p
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Evaporator Condenser Figure 5.8: Av
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within the inaccuracy margins. The
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The last two cases of boundary cond
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natural air flow in the system. In
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6 Model Implementation and Validati
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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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