A stirred tank is one of the most key process equipment for the synthesis of energy compounds. It is highly required for the flow and heat transfer performance of the stirred tank, due to the harsh synthetic reaction with the exothermic heat. Therefore, the spiral tube is frequently used to enhance the heat transfer in the stirred tank. Different types of blades can also play a decisive role in the flow fields inside the stirred tank. This study aims to explore the flow and heat transfer behavior of the internal spiral tube in the stirred tank with the four-pitched blade-Rushton impeller. The standard k-ε turbulence model and wall functions were also adopted for the numerical simulation. Typical axial and radial flow blades were selected to form the four-pitched blade-Rushton impeller. A systematic investigation was also made to clarify the influence of the rotational speeds on the flow and heat transfer performance of the internally immersed spiral tube inside the stirred tank. The fluid flow and heat transfer were determined using similarity criteria and multiple reference frames. The general applicability of the simulation was obtained for the flow distribution, turbulence kinetic energy pattern, and stirrer power in the stirred tank. The similarity criterion was used to reduce the calculation volume for the high efficiency of the model. The maximum deviation of 3.75% was achieved to simulate the internal immersed spiral tube in the stirred tank, compared with the prototype. The high accuracy was verified for the Froude similarity criterion during the simulation. The rotational speed increased the fluid turbulent kinetic energy, indicating little influence on the formation of the axial circulation. The optimal model achieved a 20% enhancement in the Nusselt number, demonstrating the superior performance of the structural modifications. The higher the rotational speed was, the higher the mixing and diffusion efficiency in the tank were. According to the velocity observation line graph, the axial velocity was symmetrically distributed about the central axis x=0. The radial and tangential velocities were centrally symmetric about x=0. Each velocity component also increased with the increase of rotational speed. The peak axial velocity in the tank increased by approximately 68.93% with the rotational speeds ranging from 30 to 90 r/min. As such, the axial circulation efficiency was improved inside the stirred tank. The maximum scope of peak velocity was 24.3%~33.33% at 15 r/min. At the same time, the extra-tube convection heat transfer coefficient increased by 64.66%, the magnitude of which in the tube basically remained unchanged with the change of rotational speed. There was a constant amplitude of the fluid flow inside the spiral tube, indicating a stable structure. The higher the rotational speed was, the greater the resistance of the paddles was. The power is the 27.09 times at rotational speeds 30 compared to 90 r/min. The power numbers remained consistent across different rotational speeds. The convective heat transfer was fitted to compare for the mixer optimization. Furthermore, the power number exhibited a low sensitivity to the Reynolds number under identical impeller configurations. The maximum deviation of 0.58% was achieved in the combined impeller, indicating the Reynolds number suitable for the power characteristics.

Heat exchangers serve as pivotal components in heat exchange systems. Compared with the straight channels, spiral channels have better performance due to the curvature of the centrifugal force generated by the secondary flow. Consequently, heat exchangers employing spiral channels find widespread application in agricultural engineering, including greenhouse air conditioning, water circulation systems, and agricultural product processing and storage for effective heat management. In this paper, we propose enhancing the heat transfer efficiency of spiral channels by introducing corrugations with longitudinal fins on the outer channel wall. To elucidate the impact of corrugation, we establish three-dimensional models of smooth spiral channels, corrugated spiral channels, and corrugated spiral channels with longitudinal fins. Initially, we investigate the influence of corrugated number on flow and heat transfer performance numerically. Through comparative analysis involving the development and variation of velocity and vorticity fields, average Nusselt number Nu, fanning friction factor f, average Dean number Dn_m, secondary flow intensity Se under different corrugated numbers, and the performance evaluation factor of heat exchanger based on comprehensive (PEC₀), insights are drawn. Subsequently, longitudinal fins are integrated into the corrugated spiral channel, and a numerical study is conducted to assess the effect of varying geometric parameters of the longitudinal fin on the fluid flow and heat transfer performance inside the channel. Analysis of different longitudinal fin widths and heights on velocity and temperature fields, Nu, f, and performance evaluation factor of heat exchanger based on comprehensive (PEC_w) of the channel is performed. The findings indicate that corrugated spiral channels outperform smooth spiral channels in heat transfer and flow performance. With increasing corrugated number n, secondary flow intensity within the corrugated spiral channel intensifies. Notably, at a Reynolds number of 550, a multi-vortex structure emerges in the corrugated spiral channel with a corrugated number of 21. At Reynolds number 750 and corrugated number 21, the Nusselt number of corrugated spiral channel increases by 47.08% compared to the smooth spiral channel. At the same time, the resistance loss in the channel also increases, and the Fanning friction factor of the corrugated spiral channel increases by 59.20%. When the Reynolds number is 750, the PEC₀ of the corrugated spiral channel with 18 corrugations is the highest, which increases by 27.66% compared to the smooth spiral channel. On this basis, longitudinal fins are added to the corrugated spiral channel, and it is observed by numerical simulation that symmetrical longitudinal vortices are induced by the fins. Further, the longitudinal fins induce symmetrical longitudinal vortices, enhancing flow and heat transfer in the channel's middle section. Under the condition of constant fin width and increasing fin height, the comprehensive heat transfer performance of the channel has a maximum value, that is, when fin width w=W/3, fin height h=H/6 and Reynolds number Re=250, the highest PEC_w is 1.157. When the fin height is fixed, increasing the fin width w will also make the PEC_w of the channel first increase and then decrease. The correlation formulas for Nusselt number Nu, Fanning friction factor f and secondary flow intensity Se in corrugated spiral channel are fitted, with deviations within ±14.0%, ±10.2% and ±4.4%, respectively. This provides a certain reference for the application of corrugated spiral channels with longitudinal fins in the thermal design and usage of heat exchangers.