“…A radial basis function is a neural network that includes an input layer of all influences, a hidden layer, and an output layer consisting of all responses [ 30 , 31 , 32 ]. The transfer function between the first two layers is a radial basis function, whereas the transfer function between the hidden and output layers is linear.…”
This paper proposed an improved flow-focusing microchannel with a constricted continuous phase inlet to increase microbubble generation frequency and reduce microbubbles’ diameter. The design variables were obtained by Latin hypercube sampling, and the radial basis function (RBF) surrogate model was used to establish the relationship between the objective function (microbubble diameter and generation frequency) and the design variables. Moreover, the optimized design of the nondominated sorting genetic algorithm II (NSGA-II) algorithm was carried out. Finally, the optimization results were verified by numerical simulations and compared with those of traditional microchannels. The results showed that dripping and squeezing regimes existed in the two microchannels. The constricted continuous phase inlet enhanced the flow-focusing effect of the improved microchannel. The diameter of microbubbles obtained from the improved microchannel was reduced from 2.8141 to 1.6949 μm, and the generation frequency was increased from 64.077 to 175.438 kHz at the same capillary numbers (Ca) compared with the traditional microchannel. According to the fitted linear function, it is known that the slope of decreasing microbubble diameter with increasing Ca number and the slope of increasing generation frequency with increasing Ca number are greater in the improved microchannel compared with those in the traditional microchannel.
“…A radial basis function is a neural network that includes an input layer of all influences, a hidden layer, and an output layer consisting of all responses [ 30 , 31 , 32 ]. The transfer function between the first two layers is a radial basis function, whereas the transfer function between the hidden and output layers is linear.…”
This paper proposed an improved flow-focusing microchannel with a constricted continuous phase inlet to increase microbubble generation frequency and reduce microbubbles’ diameter. The design variables were obtained by Latin hypercube sampling, and the radial basis function (RBF) surrogate model was used to establish the relationship between the objective function (microbubble diameter and generation frequency) and the design variables. Moreover, the optimized design of the nondominated sorting genetic algorithm II (NSGA-II) algorithm was carried out. Finally, the optimization results were verified by numerical simulations and compared with those of traditional microchannels. The results showed that dripping and squeezing regimes existed in the two microchannels. The constricted continuous phase inlet enhanced the flow-focusing effect of the improved microchannel. The diameter of microbubbles obtained from the improved microchannel was reduced from 2.8141 to 1.6949 μm, and the generation frequency was increased from 64.077 to 175.438 kHz at the same capillary numbers (Ca) compared with the traditional microchannel. According to the fitted linear function, it is known that the slope of decreasing microbubble diameter with increasing Ca number and the slope of increasing generation frequency with increasing Ca number are greater in the improved microchannel compared with those in the traditional microchannel.
“…There are many mature algorithms for multi-objective optimization, including NSGA-II [33], multi-objective particle swarm optimization (MOPSO) [34], and multi-objective ant colony optimization (MOACO) [32], etc. In the cooling process of sinter, Tian et al [35] have demonstrated the reliability of the NSGA-II, hence the algorithm of NSGA-II is adopted in this work to optimize the objective functions. The Pareto frontier in different iteration numbers is shown in Figure 10. Figure 10. The Pareto frontier with different generations.…”
A vertical layered cooling process is developed to get more uniform cooling and higher heat transfer efficiency when compared with the circular-type and vertical integrated sinter cooling processes in this work, which has been demonstrated by the example. Based on the vertical layered cooling process, the maximum temperature of the cooled sinter and the minimum waste heat recovery is treated as two objective parameters for the multi-objective optimization design. The operating parameters influencing the sinter temperature and waste heat recovery are determined at first. Then, an accurate metamodel is established based on the Latin hypercube sampling technique and radial basis function neural network (RBFNN) approach. Finally, the non-dominated sorting genetic algorithm II (NSGA-II) is employed to iterate the accurate metamodel and acquire the Pareto frontier for acquiring the optimal combinations of the objective parameters. Analysis results are demonstrated to be of great significance for practical engineering applications.
“…In addition, Zhang et al [14,15] also performed exergy transfer analysis in the sinter bed layer of an annular cooler and analyzed the thermal parametric effects on the temperature exergy and pressure exergy in the heat transfer process. Tian et al [16,17] established a simulation model of three-dimensional flow and heat transfer in an annular cooler and optimized the operating parameters of a ring annular cooler by taking the sinter outlet temperature and exergy of SWHR as the objective function. Some other relevant studies were also reported in the literature [18,19].…”
In order to fully understand the energy and exergy transfer processes in sinter vertical coolers, a simulation model of the fluid flow and heat transfer in a vertical cooler was established, and energy and exergy efficiency analyses of the gas–solid heat transfer in a vertical cooler were conducted in detail. Based on the calculation method of the whole working condition, the suitable operational parameters of the vertical cooler were obtained by setting the net exergy efficiency in the vertical cooler as the indicator function. The results show that both the quantity of sinter waste heat recovery (SWHR) and energy efficiency increased as the air flow rate (AFR) increased, and they decreased as the air inlet temperature (AIT) increased. The increase in the sinter inlet temperature (SIT) resulted in an increase in the quantity of SWHR and a decrease in energy efficiency. The air net exergy had the maximum value as the AFR increased, and it only increased monotonically as the SIT and AIT increased. The net exergy efficiency reached the maximum value as the AFR and AIT increased, and the increase in the SIT only resulted in a decrease in the net exergy efficiency. When the sinter annual production of a 360 m2 sintering machine was taken as the processing capacity of the vertical cooler, the suitable operational parameters of the vertical cooler were 190 kg/s for the AFR, and 353 K for the AIT.
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