Analysis on influence of rotor lead and eccentricity on mixing flow field and efficiency of dough mixer

The chaotic food mixer with an eccentric spiral rotor is a new type of food processing device, in which the food fluids with long molecular chains can not be damaged by high shear stresses, such as traditional twin screw extruders. In fact, the previous researches had demonstrated that the food melt with high viscosity flowing in the food mixer has the nature of chaotic mixing. However, as a dynamic system of flow, the traditional Euler methods is difficult to distinguish the chaotic manifolds, which is a barrier for better understanding the mixing mechanism in the internal mixer. From a new viewpoint of 3D Lagrangian, the objective of our study is to explore the chaotic mixing mechanism in this new kind of food mixer under the disturbance of eccentric spiral rotor, to visually locate the poor and well mixing regions in the mixer and optimize the key geometric parameters of the eccentric spiral rotors. Firstly, a numerical simulation of the three-dimensional flow field in the food mixer is carried out using the mesh superposition technique (MST) and CFD code of Polyflow without considering the re-meshing for the periodical geometric changes. The Carreau-Yasuda constitutive model was used to describe the rheological behavior of the food material. Based on the transient velocity distributions, the finite time Lyapunov exponent (FTLE), Lagrangian coherent structure (LCS) and Poincaré section were calculated to analyze the fluid transport and mixing in the new chaotic food mixer with helical eccentric rotors. The LCS from the ridges of FTLE as a boundary was adopted to reveal the chaotic and regular zones in the mixer. And the particle tracking was used to illustrate the different fluid motions in the flow dynamic system based on the fourth-order Runge-Kutta scheme. Then the effects of rotor eccentric ratio on the chaos scale and particles motions in the regular of the mixer were studied, respectively. Moreover, based on the quantitative mixing measures, such as mixing shear rate, logarithmic of stretching, instantaneous mixing efficiency and average time mixing efficiency, the rotor lead and eccentricity rate were optimized to increase the mixing inefficiency of the chaotic food mixer. The results show that the hyperbolic LCSs divide into two regions with different particle motion characteristics for the food mixer, such as the inner rotary zone and the outer spiral zone. With the increase of rotor eccentric ratio, the strength of chaotic mixing in the outer spiral zone increases and that in the inner rotary zone decreases. When the rotor has little eccentric ratio, the mixing mainly depends on the fluid transport in the inner rotary zone. Then the axial velocity of fluid decreases significantly, but the mixing at radial direction of the inner rotary zone increases. Through optimization of the eccentricity and the lead distance of the eccentric rotor, it can be found that the mixer has relatively higher overall mixing efficiency with the lead of 120 mm and the eccentricity of 0.67, following is the lead of 60 mm and the eccentricity of 0.97, and the mixer has relatively poorer overall mixing efficiency with the lead of 60 mm and the eccentricity of 0.33. This paper has shown that the Lagrangian fresh perspective is more feasible than traditional Euler method in numerically investigate the evolution of two-dimensional mixing performance within a novel mixer. FTLE and LCS are useful tools for analyzing chaotic mixing flow in the mixer. This method provides new research ideas and theoretical basis for the design and optimization of food and other mixed equipment, which provides a better understanding the mixing mechanisms in a flow dynamic system.