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Energies 2022, 15, 1316 simulations by Schwaiger [12] (p. 170). This may be explained by tubes in the bundle increasing the local bubble frequencies at tubes above them by redirecting the bubbles towards them. An increased bubble frequency is related to higher HTCs in the correlation by Mickley and Fairbanks, and a narrower tube spacing has a better chance of individual tubes influencing the local bubble frequency at other tubes than a wider spacing. 18 of 22 Finned tubes with a fin pitch of 9 mm and fin thickness of 2 mm in a transversal arrangement in respect to the sand mass flow show a 3–6 times greater (virtual) HTC • • The use of baffles in between tubes in a transversal arrangement seems to decrease • factor is about 3.5 at 1250 W/m2K (gross) in respect to the plain tube surface. than plain tubes in the same arrangement. At a degree of fluidization of about 4, the than plain tubes in the same arrangement. At a degree of fluidization of about 4, the factor is about 3.5 at 1250 W/m2K (gross) in respect to the plain tube surface. The use of baffles in between tubes in a transversal arrangement seems to decrease the achievable HTC. the achievable HTC. In the intended thermal energy storage application, the fluidized bed would be oper- In the intended thermal energy storage application, the fluidized bed would be ated at significantly higher temperatures (compared to the experiments that were conducted operated at significantly higher temperatures (compared to the experiments that were at about 40 ◦C) and the thermal energy of the exhausted fluidization air would be recuper- conducted at about 40 °C) and the thermal energy of the exhausted fluidization air would ated with the supply air. The net HTC, which only accounts for the heat directly transferred be recuperated with the supply air. The net HTC, which only accounts for the heat directly into the storage material (sand), is then expected to increase and be closer to the gross HTC. transferred into the storage material (sand), is then expected to increase and be closer to The reason for this is that heat losses through fluidization depend on the mass flow of the the gross HTC. The reason for this is that heat losses through fluidization depend on the fluidization gas while the degree of fluidization depends on fluidization gas velocity. Since mass flow of the fluidization gas while the degree of fluidization depends on fluidization gas density decreases with rising temperatures, a lower mass flow is required to achieve gas velocity. Since gas density decreases with rising temperatures, a lower mass flow is the same degree of fluidization: required to achieve the same degree of fluidization: m. (T) 𝑚A𝑇 𝑤 𝑇𝜌(𝑇) . = w (T) ρ(T) m(f ) m (T)= w ((T)0)ρ(T0) 𝑚A𝑇0 𝑤mf𝑇 𝜌(𝑇) where 𝑤 where w is the minimum fluidization velocity gathered from Richardson’s correlation. is the minimum fluidization velocity gathered from Richardson’s correlation. mf FFoorrdrryaiiratambient pressureasflfluiidiizattiiongaassaannddT𝑇==4040C°C, t,htehererlealtaiotinonisishsohwown in iFnigFuigruer2e42. 4. ◦ 0 Figure 24. Required fluidization air mass flow depending on temperature relative to 40 °◦C. Figure 24. Required fluidization air mass flow depending on temperature relative to 40 C. It is clear that the required mass flow decreases very quickly with the rising tem- perature. At 400 ◦C, only about 27% of the original air mass flow at 40 ◦C is required to achieve the same degree of fluidization. In this way, the net HTC approaches the gross HTC with increasing temperatures. When the lost thermal energy caused by the fluidization is recuperated with the supplied air, heat losses can be further decreased and the net HTC moves even closer to the gross HTC. In the experimental work of this paper, the differences in particle convective heat transfer for different geometries and particle flow arrangements at temperatures slightly above ambient temperature (40 ◦C) was determined. In order to estimate the temperature dependence of the HTC, several of the aforementioned correlations were investigated in respect to their sensitivity to temperature changes, namely the ones by Andeen and Glicksman [2], Grewal [4], Molerus [5], Zabrodsky [20], Martin [7], and Gelperin and Einstein [21]. Unfortunately, there are great discrepancies between the predictions, as shown in Figure 25.PDF Image | Heat Transfer between Finned Tubes
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