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η2,Ch (t) = mstore .c.[Tavg (t) − Tini ] = η1,Ch (t) t.m& .c[Tinlet − Tini ] t * The term η2,Ch represents the actual energy change divided by the energy change that would have occurred in the same experiment assuming an ideal plug flow (Yoo and Pak, 1993; Mavros et al, 1994; Hahne and Chen, 1998; Bouhdjar and Harhad; 2002; Shah et al, 2005). 4.2.2 Figures of Merit Further development of charging and discharging efficiencies lead to figures of merit (FOMs) derived from cycles of full, or partial, charging and subsequent discharging (Tran et al, 1989; Wildin, 1990; van Berkel et al, 1999; Bahnfleth and Song, 2005). A TES with a more pronounced temperature gradient and hence better stratification always contains more exergy than a comparative storage with equal energy content but less pronounced stratification (Rosen et al, 2004). Therefore FOMs based on the second law of thermodynamics may be used to give information about the stratification efficiency. The dimensionless MIX-number (Davidson et al, 1994) expresses the degree of mixing that occurs during a charging process based on moment of energy (ME). The moment of energy of a TES is an integration of the sensible energy content along its vertical axis, weighted with the height of its location along the vertical axis. In practice a summation over ith storage segments along the vertical axis is used to calculate ME: N ME =∑yi.Ei i=1 The MIX-number is the difference of moment of energy between a perfectly stratified storage and the experimental storage, divided by the difference of moment of energy between a perfectly stratified storage and a fully mixed storage: MIXDav = ME,str0,h1 − ME,exp ME,str0,h1 −ME,mix0,h1 Both “theoretical” storage temperature profiles, stratified and fully mixed, are calculated assuming full stratification and mixing respectively, from the beginning of the experiment, and including heat losses to the surroundings calculated with the heat loss coefficient that was determined for the experimental storage. The “moment of energy” introduced by Davidson was later adapted and used by Andersen et al (2007). In contrast to the method of Davidson, the theoretical storages in this later method are mixed or stratified at each instant and thus have the same energy content as the experimental storage at any time. MIXAnd = ME,str1a −ME,exp ME,str1a −ME,mix1 The advantage of this latter method is that the determination of the heat loss coefficient of the experimental storage is not necessary. 31PDF Image | EPSRC Thermal Management of Industrial Processes
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