Estimation of heat transfer coefficient in turbulent regime during agitation by two-blade wide paddle impellers

Significance 

Heat transfer is a fundamental aspect of many industrial processes, including mixing, dissolution, reaction, and evaporation. Efficient heat transfer ensures that the desired temperature conditions are achieved, which is critical for the successful completion of these processes. Accurate estimation of heat transfer coefficients allows for the optimization of process parameters, leading to enhanced process efficiency and productivity. Agitated vessels and heat exchangers are commonly used in industrial settings. The design of these equipment components relies heavily on accurate estimation of heat transfer coefficients. By knowing the heat transfer characteristics, engineers can appropriately size the equipment, determine the necessary heat transfer surface area, and select the appropriate materials. Accurate estimation ensures that the equipment is designed to meet the desired thermal requirements, resulting in reliable and cost-effective systems. Moreover, heat transfer processes often involve the input or removal of thermal energy. Accurate estimation of heat transfer coefficients enables engineers to design systems that minimize energy consumption. By optimizing heat transfer, the energy input can be reduced, leading to energy savings and cost reduction.  Indeed, precise temperature control is crucial for ensuring process safety in many industrial applications. In processes where exothermic reactions occur or where sensitive materials are involved, accurate estimation of heat transfer coefficients helps prevent overheating, thermal runaway, or other undesirable conditions.  Therefore, accurate estimation and optimization of the heat transfer coefficient contribute to overall process cost-effectiveness. However, existing equations to relate the heat transfer coefficient with parameters such as the impeller Reynolds number or Reynolds number based on energy dissipation rate are not applicable to two-blade wide paddle impellers or other impeller designs. Additionally, the equations for other impellers, such as anchor blades and double helical-ribbon blades, are inconsistent when no baffles are used due to the temperature distribution within the vessel.

In a recent study published in the peer-reviewed Journal of Chemical Engineering Research and Design, Dr. Yuya Murakami, and Dr. Atsushi Shono from Tokyo University of Science and Dr. Masao Aida from the Lithium Battery Material Department at Idemitsu Kosan Co., Ltd proposed a new equation to estimate heat transfer coefficients in a turbulent regime during agitation by two-blade wide paddle impellers. The equation takes into account the Nusselt number, Prandtl number, Reynolds number based on energy dissipation rate, ratio of impeller diameter to vessel diameter, and ratio of blade width to vessel diameter. The researchers examined previous correlation equations proposed by Nagata et al. (1971) and Sano et al. (1978). Although Sano et al. extended the equation to include the Reynolds number based on energy dissipation rate, the applicability of both equations to systems with varying quantities of baffles and impellers was limited. Furthermore, correlation equations for anchor blades and double helical-ribbon blades reported by other researchers were inconsistent due to the inhomogeneous temperature distribution in the vessel during agitation, caused by the absence of baffles.

To address these limitations, the research team devised a reliable correlation equation by considering the proposed relationship between heat transfer and momentum transfer by Chilton and Colburn (1934). Building upon this relationship and considering the characteristics of two-blade wide paddles, a new correlation equation was derived, incorporating parameters such as the Nusselt number, Prandtl number, Reynolds number based on the energy dissipation rate, ratio of impeller diameter to vessel diameter, and ratio of blade width to vessel diameter. To account for the differences in exponents related to the impeller diameter in the correlation equation, the representative length proposed by Hiraoka and Ito (1973) was obtained. To validate the proposed correlation equation, experimental data from numerous studies conducted with various impellers, including two-blade wide paddles and conventional impellers, were collected. The Nusselt number, Prandtl number, and Reynolds number were calculated for each case based on the energy dissipation rate. The correlation equations were evaluated using the mean accuracy (MA) and estimated accuracy range (EA). A correlation equation was considered reliable if it satisfied the conditions 0.95 < MA < 1.05 and 0.75 < min(EA),  max(EA) < 1.25. The results demonstrated that the proposed correlation equation accurately estimated the heat transfer coefficients during agitation by two-blade wide paddles and conventional impellers. The equation exhibited excellent agreement with the experimental data, indicating its dependability and applicability to a wide range of impeller configurations.

In conclusion, Tokyo University of Science and Idemitsu Kosan Co., Ltd scientists successfully demonstrated the effectiveness of the proposed correlation equation for estimating heat transfer coefficients in vessels stirred by wide paddles with two blades and conventional impellers. This equation serves as a valuable tool for optimizing the initial cost of processes involving mixing, dissolution, reaction, and evaporation. By enabling accurate estimation of the heat transfer coefficient, it facilitates the design and operation of agitated vessels, leading to improved process efficiency and cost-effectiveness.

Reference

Masao Aida, Yuya Murakami, Atsushi Shono. Estimation of heat transfer coefficient in turbulent regime during agitation by two-blade wide paddle impellers. Chemical Engineering Research and Design, Volume 189,  2023, Pages 46-51.

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