CFD Modeling of the Closed Injection Wet-Out Process For Pultrusion

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INTRODUCTION Over the past decade, the global pultrusion industry has increasingly adopted closed injection wet-out for profile processing. This trend has been driven by awareness of worker safety and mandates by regulatory agencies to reduce volatile organic compounds (VOC s) and by the availability of new resin technology. Polyurethane (PU) resins, in particular, have become an accepted alternate technology which contain no VOC s, especially for applications requiring high strength and durability combined with the potential for high pultrusion line speeds (Ref. 1-3 and references therein). However, the relatively fast reactivity of PU resins requires processing via closed injection wetout. The complex profile geometries and reinforcement schedules used in stateof-the-art profiles make efficient wetout challenging in a constrained state within an injection box. This challenge is even greater for PU resins, considering their inherently fast reactivity. Hence, a more thorough understanding of wet-out dynamics in injection processing for pultrusion is needed to expand acceptance of this process for PU resins and accelerate its implementation. This report describes a mathematical model for closed injection wet-out in the pultrusion process. The model predicts the impact of injection box geometry, process conditions, resin viscosity, reinforcement fraction and permeability on flow patterns, pressure profiles and final part density. EXPERIMENTAL CFD simulations were carried on an injection box for a die profile dimension of 5.21cm x 0.648 cm (2.05 x 0.255 ). The line speeds were varied between 0.6 and 1.5 m/min (24 to 60 inch/min) with injection box lengths from 30.5 to 53.3 cm (12 to 21 ). Resin viscosity was varied between 600 and 2400 cP. Experimental pultrusion runs were made to verify the CFD results. RIMLine ® SK 97007 polyol and Suprasec ® 9700 isocyanate and experimental variants were combined as the polyurethane matrix. Profiles were pultruded with 120 rovings for a total glass content of 77 wt% (60 vol %). A two-component metering unit (Electric Willie from GS Manufacturing) with gear pump flow control was used to ensure delivery of the polyurethane resin at constant pressure. Injection boxes were fabricated using aluminum with HDPE guide plates having small holes to prevent resin leakage. Digital pressure transducers or pressure gauges were placed at ~2.5 cm (1 ) and ~10 cm (4 ) from the die face as well as the injection port. The typical injection box setup is shown in Figure 1. MATHEMATICAL MODEL Due to difficulty in modeling macroscopic transport of resin and reinforcement based on microscopic variation of velocity between fibers, the resin and reinforcement are better treated as a moving porous fiber medium. The moving porous model used is both a generalization of the Navier-Stokes equations and Darcy s law used for flows in porous media. The balance equations for mass and momentum for steady incompressible flow are u 0 2 u u p u S u, p, , , and S are the superficial velocity, pressure, density, viscosity and momentum sources, respectively.
The momentum sources, S, defining the moving porous medium are S u U K K, and U are the permeability tensor, porosity and velocity of the fiber bundle. The geometry of the injection box is shown in Figure 2. This approach is similar to the model demonstrated by Jeswani et al. [Ref. 4] The approach is a phenomenological one with the main assumption being that the surface tension effects are not important or are captured in the permeability tensor. The reinforcements are initially dry and the resin must penetrate the fiber bundles. Capillary forces of attraction and repulsion act at the flow front. These forces, which depend on the surface tension of the resin and on its ability to adhere to the surface of the fibers, have an effect of increasing or decreasing the effective pressure at the resin front. However, they are assumed to be sufficiently small to be neglected by the model. This assumption can be checked with micro-scale modeling of air-resin interface flow in fiber bundles. A further assumption in the model is that degree of conversion and hence build-up of viscosity is small and, hence, can be ignored in the injection box region. It is also assumed that there is no shear rate dependence of viscosity. These complexities can be added to the model without great difficulty. Porosity and Fiber Volume Fraction The porosity of the fiber bundle varies with axial distance in the model 1 Vf ( z) hence, the stream wise and transverse permeability throughout the injection is not constant. An example of porosity variation throughout the injection box is shown in Figure 3. Permeability Model The Gebart permeability model [Ref. 5] with a hexagonal fiber arrangement was chosen to model the permeability in both the axial and transverse fiber directions. The model is particularly suited to pultrusion processes as the fibers are unidirectional. In the axial direction, the permeability is defined by K z 2D 2 3 f 2 c (1 ) where Df is the effective fiber diameter and c a model constant. The permeability in the transverse direction is K K x y C D V 1 2 f f ,max 1 4 (1 ) where Vf,max is the maximum volume fraction of fibers and C1 a model constant. Profiles of stream wise and transverse permeability are shown in Figure 4. Boundary Conditions Where the fiber reinforcement enters the injection box, the pressure is set to atmospheric pressure and a positive pressure is set at the injection port. At the exit of the computational domain, a small distance into the die, the axial velocity is set to the porosity times the pull speed. 5 2
Page 1: CFD Modeling of the Closed Injectio
Page 5 and 6: CONCLUSIONS A mathematical model of
Page 7 and 8: Figure 3: Porosity variation of the
Page 9: Figure 7: Influence of viscosity, g

CFD Modeling of the Closed Injection Wet-Out Process For Pultrusion

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