Flow directions in gas assisted injection molding when cavities of square flat plates and pipes are involved 1. Theory of flow model and its criterion

Abstract

In such a complex situation as the cavity of two square plates connected to cavities composed of four pipes with same length and different diameter connected in series and parallel, the resistance of cavity of two square plates should be combined with that of pipes to determine the gas direction in gas assisted injection molding (GAIM). The flow model of Newtonian fluid was previously suggested under the fan-shaped geometry incuding relatively thin cavity of two square plates when$\rho \bar v_r H/\mu \left( {H/R_0 } \right) \ll 1$,$\left( {H/R_0 } \right)^2 1 / \hat \theta ^2 \ll 1$ and (H/R₀)².However, one may frequently encounter the problem of relatively thick fan-shaped cavity between two square plates where (H/R₀)² is around 10^-1 and$\hat \theta ^2$ is the order of one. The rule of thumb containing a first order-approximated flow model by perturbation technique was introduced to show, in qualitative way, whether the resistance of the relatively thick cavity of two square plates may affect the gas direction in GAIM under the fore-said geometry. Subsequently, various simulations were performed under the conditions that all dimensions of cavity of two square plates and pipes were fixed except for the diameters of pipes. The results of simulation were compared with the results of the rule of thumb (RT1) containing the approximated flow model as well as those of another rule of thumb (RT2) without the resistance of the relatively thick cavity of two square plates. The results of simulations were generally consistent with the former in qualitative way to determine gas directions in gas assisted injection molding even though a relatively large value of 0.36 was applied as the value of ε to describe a relatively thick cavity of two square plates. In addition, the situation was treated when cavities of pipes and runners were involved in configuration. The rule of thumb was used for the ratio of initial velocities to be recalculated at the first coming change of diameters when the ratio was close to unity and it was quite consistent to the results of simulation.