Study of the shape optimization of a variable diameter in a ventilation and air-conditioning duct based on the Boltzmann function

Abstract Ventilation and air-conditioning systems feature high-resistance ducts and long, complex pipelines. Consequently, how to structurally optimize the local components to reduce resistance and energy consumption has become an urgent problem to be solved. In this paper, the sedimentation-induced variable shape of a river channel was used to study the resistance reduction of local components, and the relationship between silty sediment and resistance within the channel was discussed. On this basis of this theory, a reduced-scale test bench was constructed, and a Boltzmann curve form was obtained and applied for a variable diameter. Finally, a method for optimizing the resistance reduction of variable diameters suitable for different aspect ratios and area ratios was obtained. Through our research, we found that the local resistance coefficients of the novel variable diameter using a Boltzmann curve connection are significantly smaller than those of the traditional variable diameter. Compared with a traditional straight-line variable diameter, the novel variable diameter weakens the fluid deformation, thereby reducing energy dissipation and resistance, and the resistance reduction rate can reach 28.92%. The resistance reduction rates of variable diameters adopting optimized forms were 14.3%–16.2%, 3.0%–25.17%, 5.81%–28.92%, and 4.99%–7.11% when the area ratios were 1.25, 1.28, 1.56, and 2, respectively.