Study On SPH-based Constraint Revolving Moving Boundary Problem And Its Application In Extrusion

The constraint moving boundary problem is a kind of time-varying boundary problem imposed by external forces, such as, agitation, forced conveying, wave making etc. in the production and living. Numerical simulation in the field of polymer processing single-screw extruder and twin screw-extruder is a typical constraint moving boundary problem. When using traditional numerical techniques such as the finite volume method and finite element method, mesh distortion frequently encountered, and the calculation process is difficult to track, however, to understand the mechanism in the screw process is very important for design and optimization of the screw. In recent years, numerical methods are being developed from the continuum model to discrete particle model. The meshless particle method, based on the point approximation instead of relying on the grid, is better for calculating the moving boundary, large deformation, and the free surface, which bring opportunity to the simulation of the complex process. Typical meshless particle method is the smoothed particle hydrodynamics (SPH), which has a good self-adaptability than the traditional numerical methods in dealing with the discontinuity problem, and has been widely applied to the wave mechanics, fluid-solid interaction, high-speed collisions, etc.In the beginning, the standard SPH method and its improved form——incompressible SPH (ISPH) method are analyzed. Three type of boundary treatment are investigated. One constraint moving boundary problem in screw extrusion has been investigated, and the program is written in FORTRAN. The dummy particles are used to treat the moving boundary. The moving boundary problem is separately simulated by ISPH and the moving least squares (MLS) corrected standard SPH. Furthermore, a partially filled forced revolving moving boundary with free surface flow model is constructed and simulated by two SPH methods. A set of organic glass constraint revolving moving boundary fluid experimental device is designed and manufactured; finally, a two-dimensional non-Newtonian flow model for cross-section of the groove is simulated. Furthermore, a single screw extruder three-dimensional flow is calculated using this algorithm. It laid the foundation for SPH to compute more complex single screw, twin screw extrusion process. The main innovations are as follows:(1) On the boundary treatment: Three different wall boundary conditions treatments——repulsive boundary, mirror boundary, and static boundary are implemented to simulate lid-driven cavity flow with both SPH algorithms. The results show that simulations are more accurate with the static particles boundary. The repulsive boundary is fitter for the standard SPH than for ISPH.(2) On the filled constraint moving boundary problem:One constraint moving boundary problem in screw extrusion has been investigated, and the dummy particles are used to treat the moving boundary. Then the model is separately computed by ISPH and the MLS corrected standard SPH. Through comparing the results separately produced by the moving boundary model, the fixed boundary model and the commercial software FLUENT, it has been shown that the boundary treatment method is simple and effective. One correcting scheme is suggested:in every time step, only the fluid particles’ density is evolved, every20time steps, all particles’ density is corrected by MLS. The results show that the correction approach can smooth the pressure oscillation in the high pressure gradient zone, guarantee the stability of the calculation without reducing the efficiency.(3) On the partially filled constraint moving boundary problem:A set of constraint revolving moving boundary organic glass fluid experimental device is manufactured. It helps to observe and record the experimental process, the experimental results can be used to test the calculation accuracy of the SPH method. One static boundary particles with doubled wall particles scheme is proposed. If using ISPH algorithm, this scheme can avoid the escape of particles from the boundary when the free surface flow model revolving at a high speed in gravitational field. The results calculated by ISPH at three different angular velocities of the0.5rad/s,1.5rad/s, and2.5rad/s are compared with corresponding experimental results. It is found that, at low speeds, the free surface present a horizontal plane, but, at higher speeds (ω≥1.5rad/s), the free surface show to be a curve under the shear from the groove and barrel, both of them are consistent with the experimental results. With the increase of the speed, the effect of centrifugal force will gradually be revealed, but, when at a low speed (ω≤1.5rad/s), the effect of centrifugal force can be negligible.(4) On the tentative application of SPH in moldling the screw extruding:A two-dimensional non-Newtonian flow model for cross-section of the groove is calculated. The results shows that the vortex center gradually migrate to the bottom of the groove with the shear thickening. In the calculating of non-Newtonian flow, the mirror boundary is the better choice. A single screw extruder three-dimensional flow is calculated using ISPH algorithm. Two types of inflow and outflow boundary implementation schemes including periodic boundary and pressure boundary are elaborated. The results show that:the periodic boundary is more feasible than pressure boundary. Circumfluence form in the cross-section of the groove; shear stress gradient is more concentrated in the top left angle and right angle; the flow along the spiral groove is stable, with the increase of the reverse pressure gradient, the yield decrease linearly.