The flow‐induced and thermally induced residual stresses during injection molding of a thin part with complex geometries are predicted. The injection molding precess was considered to consist of a filling and a post‐filling stage (packing coupled with cooling). Additionally, the analysis were applied to successive stages of the process. The model takes into account the viscoelasticity of the molding polymer, which has been neglected in most previous works, because of the complexity of its inclusion. A unified K‐BKZ viscoelastic constitutive model, capable of modeling both the fluid‐rubbery state and the glass state of amorphous polymers, was employed for simulating this problem. For the flow‐induced residual stress predictions of the filling stage, a quasi‐steady state approximation was employed for each element of the part, for the calculation of stress profile and subsequent stress relaxation after cessation of flowf. Stress calculations were provided for the thermally induced residual stress predictions of the post‐filling stage. These explicit calculations led to the results of pressure and temperature distributions of the part during the post‐filling stage into the viscoelastic constitutive model. Additionally, the pressure and asymmetric temeprature profiles of the post‐filling stage were based on finite element packing analysis coupled with a boundary element cooling analysis of the molding process. Finally, the total residual stress in the part was obtained via superposition of the flow‐induced and thermally induced residual stresses. An example is provided to demonstrate the entire concept. The results indicate that thermally induced residual stress is higher than the flow‐induced residual stress by one to two orders of magnitude.
An airlift reactor with double net draft tubes was developed. A sparger was located between the two draft tubes. The draft tubes had a significant effect on breaking bubbles into smaller ones. The assessment of the reactor performance was based on gas holdup, mixing time, and volumetric mass transfer coefficient. The proposed reactor had higher gas holdup and volumetric mass transfer coefficient, and lower mixing time in comparison with those of the bubble column. Application of the proposed reactor to fermentation of Saccharomyces cerevisiae demonstrated that the cultivation time was significantly shortened.
A novel theory which employs the K-BKZ viscoelastic integral constitutive model was developed in this study for simulating the non-isothermal injection molding filling process and the frozen stresses of a three-dimensional thin part. The simulation of viscoelastic model in such a problem has not yet been discussed in most previous works as a result of the complexity of this problem. A quasi-steady approximation concept was developed in the present investigation for solving the non-isothermal filling process via K-BKZ viscoelastic integral constitutive model. Additionally, the numerical method of flow field was based on the control volume finite element method. The flow field of generalized Newtonian fluid was used as the initial guess of flow kinematics. The quasi-steady state approximation was introduced for each element to calculate the flow kinematics and stress profile from the K-BKZ integral constitutive model. The finite difference method with streamline upwind characteristic was adopted here for calculating the temperature field of process. When the cavity is fully filled, the subsequent non-isothermal stresses would relax after cessation of flow. Thereby, the frozen stresses (or frozen birefringence) could be obtained.
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