numerical algorithm

The most common method of simulating liquid spray in a gaseous environment is the Eulerian Lagrangian approach where the gas phase is solved by the Euler method and the liquid phase by the Lagrange method. In the dense regime, the effect of the liquid phase on the gas phase and also the effect of the droplets on each other are of great importance. Due to the strong coupling between the gas phase and liquid phase, numerical solution of these equations is one of the main challenges of this approach. In this study, two SIMPLE based algorithms for solving these equations are presented. To do this task, a Lagrangian-Eulerian computer code was developed for the two-phase flow equations. To evaluate the proposed approaches, the diesel fuel spray was solved and by comparing results, the appropriate algorithm was selected. The results showed solving the liquid phase equations at the beginning of the SIMPLE iteration loop and then making two corrections in the appropriate position inside the algorithm, provides a suitable method for solving governing equations of the spray with the assumption of four-way coupling in the Eulerian-Lagrangian approach.

In the current study, semi-crystalline polymers and their properties are introduced, and then a mechanical model is precisely presented in order to predict the behavior of these materials. In this model, a material point of the semi-crystalline polymer is considered as an aggregate of inclusions of two phases, namely, the crystalline and the amorphous phase, with the interface plane of these two phases. Constitutive equations of each phase are demonstrated. A numerical algorithm is presented for solving the constitutive equations of each phase, in stages. Moreover, the general behavior of the material is determined in terms of each phase behavior using volume averaging. Because of the availability of the material parameters for polyethylene, this material has been taken into account. Obtained numerical results are reported and compared to that of previous models. After supporting the validity of the presented model, the effect of some material parameters including crystalline phase damage rate, release parameter, amorphous phase damage rate, saturation damage, rubber shear modulus, and amorphous phase strength on polyethylene behavior has been discussed in details.