Calculation of Flow Distribution

Given An industrial demisting cyclone system consists of three pairs of identical cyclones which share a common hopper, as shown in Fig. 13.B.1. It is estimated that the wall friction factor in the ducting leading up to the cyclone is 0.019 or about 30% greater than that for gas-only. 

Substituting our Moody friction factor into Eq. (13.B.2), we find that n = 7.5. This leads to the flow ratio QbIQf = vb)/ vf) = 1-28. Thus, due to the nonuniform velocity gradient in the inlet ducting, the back cyclones will experience about 30% more vapor flow than the two front cyclones. It is interesting to note that the computed value of the coefficient n, 7.5, is not too different from the Law of the Wall coefficient of 7 often used to describe the velocity profile in fully developed turbulent flow within pipes. 

The plant transient analysis code SPRAT-F, introduced in Sect. 7.9, is used to calculate the flow distribution and the MCST in the three hot channels with respect to the core power and feedwater flow rate. The nodahzation is shown again in Fig. 7.81 [32]. Since the core power and feedwater flow rate are raised very slowly at the power raising phase, the reactor can be practically treated as in a steady state 

Thermal and stability considerations should be done for the hot channels because the hot channels are expected to give the limiting conditions. The ratios of the hot channel flow rate to the average channel flow rate are shown in Figs. 7.85-7.87 [32]. 

The hot-to-average flow rate ratios decrease with the ratio of core power to feed-water flow rate increases because the pressure drop by volume expansion (flow acceleration) increases with the power to flow rate ratio more rapidly in the hot channels than in the average channels. The buoyancy pressure drop has the same tendency in the downward flow channels, which can explain the reason why the hot to average flow rate ratios decrease more significantly for the downward flow conditions compared to the upward flow condition. 

Based on those results, the database of the flow rates in the three hot channels as functions of the core power and feedwater flow rate is prepared. It is used for the thermal and stability considerations introduced next. 

Relative core power (%) Relative core power (%) 

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The method of coordinatewise optimization was proposed for simultaneous choice of flow rates and pressure losses on the closed redundant schemes (Merenkov and Khasilev, 1985 Merenkov et al., 1992 Sumaro-kov, 1976). According to this method motion to the minimum point of the economic functional F(x, Pbr) is performed alternately along the concave (F(x)) and convex (F(Pbr)) directions. The convex problem is solved by the dynamic programming method and the concave one reduces to calculation of flow distribution. The pressure losses in this case are optimized on the tree obtained as a result of assumed flow shutoff at the end points of some branches. The concave problem is solved on the basis of entropy... 

B Flow Distribution in Parallel Demisting Cyclones 317 13.B.1 Calculation of Flow Distribution... 

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