Providing flow parameters for approximate die design models and the improvement and verification of those models using cfd analysis

The role of a coating die is to distribute a uniform, two dimensional liquid film over a solid surface, often formed as an intermediate step in the manufacturing process of polymeric sheet products. The goal of coating die design is to deliver, with a single die, the largest range of fluid rheologies and flow conditions to within specified uniformity limits. Demanding applications require the film thickness nonuniformity to be as little as one percent across the entire coating surface for acceptable quality of the final product, necessitating optimized design as well as precision manufacturing. There are two principal techniques used for the prediction of optimal die geometry and the analysis of flow uniformity at the slot exit, which includes full numerical computation and theoretical approximate models. Three dimensional computational solutions are numerically intensive, often requiring long computational times to accurately simulate a single die flow condition, and for this reason it is difficult to optimize coating die design solely through the use of full numerical computation. In the alternative approximate modeling approach, the complete set of three dimensional equations governing flow are averaged across the cavity cross section. As a result, the details of the flow and pressure fields at each node point specified within the cavity geometry is exchanged for average flow properties. The advantage of these simplified approximate models is that they are much easier to solve, allowing for many flow conditions and geometric parameters to be tested quickly; however, quantifiable error is incurred due to the approximations of the complete three dimensional set of governing momentum equations. Much of the initial work on theoretical single cavity die design and the approximate modeling approach focused on the viscous dominated analysis of both the cavity and slot regions for a generalized Newtonian fluid obeying a power law dependence of viscosity on shear rate. Since this initial work, the viscous dominated model has been generalized to include the inertial and gravitational effects within the cavity as well as expanded to incorporate more complex geometries for which the cavity cross sectional area, slot lengths, and slot heights may vary widthwise along the die. For the solution of the single cavity approximate die design model, additional parameters, known as the kinetic and viscous shape factors, are necessary inputs; these parameters incorporate the specific cross sectional shape of the cavity domain into the pressure drop flow relationship. In more complex but often superior designs, a secondary cavity and slot are added to improve flow distribution, where the function of the inner cavity and slot are identical to those respective of the single cavity coating die design, however significant flow occurs in the cross section of the outer cavity between the exit of the inner slot and entrance to the outer slot. Despite the complication of this flow in the outer cavity cross section, much of the initial work on theoretical dual cavity die design directly applied the established governing equations of flow in the inner cavity, represented in the approximate models, to both the inner and outer cavities. Ruschak and Weinstein (1997a) obtain a different outer cavity equation for the analysis of dual cavity coating dies, utilizing a perturbation technique to derive a flow equation which accounts for the three dimensional nature of the outer cavity flow and considers the nonlinearities occurring due to inertia or generalized Newtonian rheology. Here, a similar, yet generalized, shape factor for the outer cavity arises which is defined to be consistent with the usual definition for the inner cavity for purely viscous, Newtonian flow. The focus of this research is to utilize Computational Fluid Dynamics as idealized experimental data, which is to be used for the improvement and verification of the theoretical outer cavity approximate die design model. Additionally, this research provides the first numerical computations of the outer cavity shape factor, incorporating shear thinning fluids as well as fluid inertia. Here, a two dimensional validation of the fundamental assumptions utilized in the derivation of the outer cavity approximate model is performed, while an attempted three dimensional validation of the predicted flow per unit cavity width exiting the outer slot provides confidence in the validity of the approximate modeling approach. A final, practical demonstration of the solution of the outer cavity approximate model provides valuable information for the investigation into the the optimum design of the outer cavity cross section. Ultimately, this research provides a firmer foundation for the design of the outer cavity in a dual cavity coating die, while further demonstrating the utility and importance of the theoretical approximate die design modeling approach