Krishna M. Pillai

Modeling the Unsaturated Flow in Liquid Composite Molding Processes: A Review and Some Thoughts

The liquid composite molding (LCM) processes for manufacturing polymer composites involve injecting a thermoset resin into a fiber-packed mold cavity. Very often, the fiber preform behind the resin front is partially saturated during the mold-filling process in LCM, giving rise to an unsaturated flow in that region. This paper first discusses the role of dual-scale porous media in inducing unsaturated flow in certain directional (woven, stitched, or braided) mats due to the delayed impregnation of tows. The approach of using a sink term in the mass balance equation is compared with the traditional approach of using unsaturated permeability for modeling unsaturated flow in dual-scale directional mats. Later, the relation of unsaturated flow with the phenomenon of bubble formation and migration is discussed. The lack of connection between the unsaturated flow research on the one hand, and the bubble creation and migration research on the other, is highlighted next. A few suggestions are offered on related topics, including the modeling of bubble motion, and the need for accurate experiments in unsaturated flow.

Governing equations for unsaturated flow through woven fiber mats. Part 1. Isothermal flows

Abstract Correct modeling of resin flow in liquid composite molding (LCM) processes is important for accurate simulation of the mold-filling process. Recent experiments indicate that the physics of resin flow in woven (also stitched or braided) fiber mats is very different from the flow in random fiber mats. The dual length-scale porous media created by the former leads to the formation of a sink term in the equation of continuity; such an equation in combination with the Darcys law successfully replicate the drooping inlet pressure history, and the region of partial saturation behind the flow-front, for the woven mats. In this paper, the mathematically rigorous volume averaging method is adapted to derive the averaged form of mass and momentum balance equations for unsaturated flow in LCM. The two phases used in the volume averaging method are the dense bundle of fibers called tows, and the surrounding gap present in the woven fiber mats. Averaging the mass balance equation yields a macroscopic equation of continuity which is similar to the conventional continuity equation for a single-phase flow except for a negative sink term on the right-hand side of the equation. This sink term is due to the delayed impregnation of fiber tows and is equal to the rate of liquid absorbed per unit volume. Similar averaging of the momentum balance equation is accomplished for the dual-scale porous medium. During the averaging process, the dynamic interaction of the gap flow with the tow walls is lumped together as the drag force. A representation theorem and dimensional analysis are used to replace this drag force with a linear function of an average of the relative velocity of the gap fluid with respect to the tow matrix for both the isotropic and anisotropic media. Averaging of the shear stress term of the Navier–Stokes equation gives rise to a new quantity named the interfacial kinetic effects tensor which includes the effects of liquid absorption by the tows, and the presence of slip velocity on their surface. Though the gradient of the tensor contributes a finite force in the final momentum balance equation, a scaling analysis leads to its rejection in the fibrous dual-scale porous medium if the permeability of flow through the gaps is small. For such a porous medium, the momentum equation reduces to the Darcys law for single-phase flow.

Experimental Investigation of the Effect of Fiber-mat Architecture on the Unsaturated Flow in Liquid Composite Molding

In liquid composite molding technologies such as RTM, this study of the inlet-pressure history for the constant flow-rate 1-D flow experiment reveals that the measured pressure profile, which droop downwards as in earlier studies on the unsaturated flow, is at a variance with the linear pressure profile predicted by the physics used for state-of-the-art LCM mold filling simulations. The droop along with the error in the inlet-pressure predictions increase with an increase in the fibermat compression. The effect of fiber-mat architecture on the droop in the inletpressure profiles is studied and significant droops are observed for various stitched mats as compared to the woven mats. This study repudiates the long-held view that mere presence of cylindrical or elliptical tows in the woven or stitched fiber-mats automatically leads to the unsaturated flow characteristic of dual-scale porous media; rather the presence of continuous uninterrupted macrochannels along the flow direction for preferential channel-flow is found to be necessary for the appearance of a drooping inlet-pressure history characteristic of the unsaturated flow.

A study on moisture absorption and swelling in bio-based jute-epoxy composites

Woven jute fibers, a class of affordable and biodegradable ‘green’ fibers, are being increasingly used as a substitute for the artificial glass and carbon fibers used in polymer composites. However, all natural fiber composites absorb water and swell in a moist environment For the first time, the swelling and weight gain behavior of bio-based composites made from jute fibers and bio-based or ordinary epoxy is presented in this experimental characterization study. Several such composites specimens were made using a low-pressure resin injection process similar to resin transfer molding; the specimens were made according to ASTM D 570 consisted of three compositions: pure resin, pure resin with a single jute fabric layer, and pure resin with two jute fabric layers. The effects of number of layers on moisture absorption, thickness swelling, volume swelling, and density were measured as a function of immersion time. It is observed that the moisture diffusion rate into composites increases with an increase in the jute-fiber-to-epoxy ratio. The type of epoxy used as the matrix appeared to have an influence on the moisture absorption percentages of the composites – the study showed that both water absorption and swellings were higher in the bio-epoxy parts compared to the epoxy parts. The swelling of composites was correlated with an increase in diameters of jute fiber in water and possibilities for the appearance of micro-cracks around fibers in composites were discussed. The data on moisture absorption, thickness swelling, and volume swelling of bio-based composites made from woven jute fibers, and bio-based and ordinary epoxies presented in this article will lead to a better understanding of how these composites react in wet environmental conditions.

Mechanical, physical and tribological characterization of nano-cellulose fibers reinforced bio-epoxy composites: An attempt to fabricate and scale the 'Green' composite.

The development of bio-based composites is essential in order to protect the environment while enhancing energy efficiencies. In the present investigation, the plant-derived cellulose nano-fibers (CNFs)/bio-based epoxy composites were manufactured using the Liquid Composite Molding (LCM) process. More specifically, the CNFs with and without chemical modification were utilized in the composites. The curing kinetics of the prepared composites was studied using both the isothermal and dynamic Differential Scanning Calorimetry (DSC) methods. The microstructure as well as the mechanical and tribological properties were investigated on the cured composites in order to understand the structure-property correlations of the composites. The results indicated that the manufactured composites showed improved mechanical and tribological properties when compared to the pure epoxy samples. Furthermore, the chemically modified CNFs reinforced composites outperformed the untreated composites. The surface modification of the fibers improved the curing of the resin by reducing the activation energy, and led to an improvement in the mechanical properties. The CNFs/bio-based epoxy composites form uniform tribo-layer during sliding which minimizes the direct contact between surfaces, thus reducing both the friction and wear of the composites.

Role of Hydraulic and Capillary Radii in Improving the Effectiveness of Capillary Model in Wicking

In this paper the liquid absorption under capillary pressure, or wicking, in cylindrical polymer wicks made of sintered polymer beads is studied experimentally and theoretically. Three different polymer wicks (made from Polycarbonate, Polyethylene and Polypropylene) and three different well-characterized liquids (Hexadecane, Decane and Dodecane) are used in the present experimental study. These experimental results are then compared with the predictions of the capillary model. The capillary and hydraulic radii used in the model are found to behave like two independent wicking parameters and are needed to be measured separately to improve the accuracy of the capillary model in predicting wicking in polymer wicks. Accurate measurement of the capillary radius ensured a good prediction by the capillary model of the final steady-state height in the large-pore wicks.Copyright

A method to estimate the accuracy of 1-D flow based permeability measuring devices

This paper presents a new experimental procedure for calibrating the permeability measuring 1-D flow set-up used routinely by the composites processing community using the liquid composite molding processes such as RTM and VARTM. A reference porous medium consisting of a bank of parallel cylindrical holes is created in an aluminum plate whose theoretical permeability is computed using the Hagen—Poiseuille flow equation and whose numerical permeability is estimated using Fluent©. It is observed that the deviation of the experimentally measured permeability from the theoretical as well as the numerical permeabilities increases with the flow rate for an injection set-up using a gear pump as well as a piston-cylinder pump. The cause of permeability deviation is traced to opening of a small gap above the rigid reference porous medium due to high pressures at higher flow rates. However no such deviation is observed while measuring the permeability of a fiber mat at different flow rates. So the proposed reference porous medium can calibrate a conventional 1-D flow based permeability measuring set-ups at low flow rates; the accuracy thus obtained can be extended to higher flow rates as well if permeability of a fiber mat can be shown to remain constant with the flow rate.

Numerical simulation of LCM mold-filling during the manufacture of natural fiber composites:

In this paper, a finite element/control volume (FE/CV) method based computer code is adapted to simulate the flow of resin-like liquids in swelling jute fabrics during the manufacture of natural-fiber composites using the liquid composite molding (LCM) technique. A novel treatment of the continuity equation using the rigorous volume-averaging method indicates that the despite liquid absorption and fiber swelling, the form of the continuity equation may remain identical to the traditional form seen for non-absorbing carbon or glass fibers. Such a continuity equation in conjunction with the Darcy’s law with a time-varying permeability function is employed to model the resin flow as a fully saturated porous medium flow behind a clearly defined liquid front. Two new methods of estimating the time-varying local permeability and porosity of the wetted fiber mats behind the moving liquid-front are proposed. Later, the two time-dependent permeability models, one based on direct experimental estimation and the other based on indirect estimation using the Kozeny-Carman model, are used to alter permeability in finite elements behind the moving liquid-front during the numerical simulation. Such numerical modeling of the mold-filling process, as applied to the one-dimensional flows with constant flow rate and constant injection-pressure conditions, shows significant improvement over the traditional analytical solution obtained for a constant permeability. A good prediction of the experimentally observed flow-front location and inlet-pressure evolution plots by the two permeability models is observed. Of the two permeability models, the one based on direct estimation of permeability is found to be superior to the one employing the indirect approach. The novel analytical solution developed for the constant flow-rate (one-dimensional flow) case under a time-dependent permeability is shown to perform extremely well while predicting the flow-front location and inlet pressure evolution.

NUMERICAL STUDY OF HEAT TRANSFER DURING UNSATURATED FLOW IN DUAL-SCALE POROUS MEDIA

This numerical study investigates the heat transfer during unsaturated flow in dual-scale fibrous porous media. An iterative, control-volume approach, based on energy balance in a two-layer model, is used for developing discretized equations for average temperatures in the channels and fiber bundles. A significant difference in the channel and bundle temperatures is observed near the flow front. The ratio of the outer- and inner-region pore volumes, the ratio of liquid and fiber heat capacities, and the fiber-bu ndle thermal conductivity are identified as the three important parameters for temperature distribution. The proposed model deviates significantly from the conventional single-scale model.

A numerical study of nonisothermal reactive flow in a dual-scale porous medium under partial saturation

ABSTRACT This numerical study investigates the temperature and cure distribution during the flow of a reactive liquid in dual-scale fibrous porous media under partial saturation. An iterative, control-volume approach, based on energy and cure balances, is used for developing discretized equations in the channels and fiber tows of the two-layer model of a dual-scale porous medium. Significant differences in the average temperatures and cures within the channels and fiber tows are observed. The ratio of the channel and fiber-tow pore volumes, the ratio of liquid and fiber heat capacities, the fiber-bundle thermal conductivity, along with the reaction rate are identified as the important parameters for temperature and cure distributions.