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In most PCM systems, the density of the liquid is 3–5% lower than the density of the corresponding solid. In thermochemical storage, gas (CO2, O2) or H2O-vapour are formed, again with a correspond- ing pressure increase in the encapsulation. This pressure increase can be significantly higher than in PCMs, and only special mea- sures such as a pressure relief valve on the encapsulation will be able to cope with the ΔP. For PCM or TCS encapsulation, mostly tubular containment will be applied. A spherical encapsulation, applied by e.g. vapour de- position or electrolysis is also possible, but with additional problems of very high pressure build-up on the capsule [51]. For PCM encapsulations, the pressure to be considered can be calculated as e.g. for a capsule of volume V, filled for ~95% with molten PCM. After cooling and solidification, the filling volume will reduce (through contraction) by e.g. 3.1% for Sb2O3 and 4.4% for KNO3 respectively. The tube is then closed by welding a lid onto the cyl- inder with material-appropriate welding rods, or by a ceramic lid in the event of using ceramic tubes. The enclosed air will expand upon heating and re-melting of the PCM. Since the starting pressure is 1 bar, the internal pressure upon melting will increase (reducing free volume and increasing tem- perature) to P2. For Sb2O3 P =[0.05+(1−0.05)×%]V ×(273.15+750)P ≈5.6P 2 0.05V (273.15+20) 1 1 For KNO3 P2 =0.05+0.95×0.044×(273.15+400)P1 ≈4.2P1 0.05 (273.15 + 20) The internal pressure on the encapsulation will hence increase to approximately 5.3 bar for Sb2O3 and 4.2 bar for KNO3. These values are slightly pessimistic since the expansion of the capsule should be taken into account (V increases as T increases). In TCS-systems, such pressure increases are not expected, since a tubular encapsu- lation will be vented to the atmosphere at 1 bar during the endothermic reaction, whilst pressures will be set at 1–3 bar during the exothermic reverse reaction. The mechanical analysis of E-PCMs is hence also valid for the reversible reaction TCS case. In the event of a complete encapsulation such as in coated PCM spheres [51], no air buffer is present, and the capsule material will need to fully withstand the expansion of the phase change. 5.1.2. Designoftheencapsulation Calculations should focus upon normal design parameters for straight pipes under internal pressure, to determine: • minimum required wall thickness • comparison with Young’s modulus (limit of plastic deforma- tion) [51] • pressure to rupture [185] These calculations are available on Internet calculators, provid- ed by ASME and engineering companies. 5.1.2.1. Wall thickness. When the wall thickness to withstand an in- ternal pressure is used as a design parameter, it requires that the relief-valve setting may not be higher than the design pressure. For piping, the chosen design pressure and temperature are the maximum intended operating pressure and the coincident tem- perature combination. This results in the maximum wall thickness. The allowable stresses for possible capsule materials will be given in Section 5.2. The formula for the minimum required wall thickness tm is given in Eq. 14. For straight metal pipes under internal pressure, this formula is valid for D0/t ratios larger than 6. The factor Y in this formula varies with material and temperature. It is used to take the redistribution of circumferential stress into account: this redistri- bution occurs under steady-state creep at high temperatures and permits a slightly lesser thickness at this range. tm = PD0 +C (14) 2(SE + PY ) where tm = minimum required wall thickness, m; P = design pressure, Pa; D0 = outside diameter of pipe, m; C = sum of allowances for erosion, corrosion and any thread or groove depth, m; SE = allowable stress, Pa; S = basic allowable stress for materials, excluding casting, joints, or structural-grade quality factors, Pa; E = quality factor as the product of several parameters. Typical quality factors are: casting quality factor E0, joint quality factor Ej, and structural-grade quality factor Es. Y = coefficient: 0.4 for ductile nonferrous materials, 0 for brittle materials such as cast iron. 5.1.2.2. Pressure to deformation and to burst (rupture). The Barlow formula [183] for the pressure to deformation or to burst is given in Eq. 15: P = 2Stw (15) D0φ with: P = pressure, Pa; S = material strength, Pa, where the time-dependent creep strength at temperature is commonly used tw = wall thickness, m; D0 = outside pipe diameter, m; φ = safety factor: calculations commonly use 1 as safety factor 5.1.2.3. Young’smodulus. Young’smodulus(tensilemodulusorelastic modulus) characterizes the material and is the stiffness of an elastic material. The definition of Young’s modulus is the ratio between the stress along an axis, and the strain along that axis in the range of stress in which Hooke’s law is valid. The strain is defined as the ratio of deformation over the initial length. Eq. 16 shows the def- inition of Young’s modulus. E= tensilestress =σ=F A0 = FL0 (16) extensional strain ε ΔL L0 A0ΔL When a material has high Young’s modulus, it is rigid. It is im- portant to not confuse rigidity with strength, stiffness, hardness or toughness. The difference between rigidity and stiffness is that ri- gidity characterizes the material (intensive property), the stiffness looks to products and construction (extensive property). The hard- ness of a material is the relative resistance of its surface to the penetration of a harder body. Toughness is the amount of energy that can be absorbed by the material before fracturing when sub- jected to strain. Young’s modulus indicates e.g. how much a sample extends under tension or shortens under compression. Young’s modulus is directly applicable to uni-axial stresses, these are tensile H. Zhang et al./Progress in Energy and Combustion Science 53 (2016) 1–40 27PDF Image | Thermal energy storage: Recent developments
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