A second-order accurate cell-vertex nite volume nite element h ybrid scheme is proposed. A nite volume method is used for the hyperbolic stress equations and a nite element method for the balance equations. The nite volume implementation incorporates the recent a d v ancement on uctuation distribution schemes for advection equations. Accuracy results are presented for a pure convection problem, for which uctuation distribution has been developed, and an Oldroyd-B benchmark problem. When source terms are included consistently, second-order accuracy can be achieved. However, a loss of accuracy is observed for both benchmark problems, when the ow near a boundary is almost parallel to it. Accuracy can be recovered in an elegant manner by taking advantage of the quadratic representations on the parent nite element mesh. Compared to the nite element method, the second-order accurate nite volume implementation is ten times as e cient.
Stability of a second-order finite element/finite volume hybrid scheme is investigated on the basis of flows with increasing Weissenberg number. Finite elements are used to discretise the balances of mass and momentum. For the stress equation a finite volume method is used, based on the recent development with fluctuation distribution schemes for pure convection problems. Examples considered include a start-up channel flow, flow past a cylinder and the non-smooth 4:1 contraction flow for an Oldroyd-B fluid. A considerable gain in efficiency per time step can be obtained compared to an alternative pure finite element implementation. A distribution based on the flux terms is unstable for higher Weissenberg numbers, and this is also true for a distribution based on source terms alone. The instability is identified as being caused by the interaction of the balance equations and stress equation. A combination of distribution schemes based on flux and source terms, however, gives a considerable improvement to the hybrid FE/FV implementation. With respect to limiting Weissenberg number attenuation, the hybrid scheme is more stable than the pure finite element alternative for the smooth flow past a cylinder, but less so for the non-smooth contraction flow. The influence of additional strain-rate stabilisation techniques is also analysed and found to be beneficial.
SynopsisFrom the thermodynamics with internal variables we will derive the temperature equation for viscoelastic fluids. We consider the type of storage of mechanical energy, the dissipation of mechanical energy, the compressibility of the fluid, the nonequilibrium heat capacity and thermal expansion, and deformation induced anisotropy of the heat conduction. The well-known stress differential models that fit into the thermodynamic theory will be treated as an example. Adapting a power-law scaling of the shear moduli on temperature and density, as is usual in rubber elasticity, we will derive an approximation of the temperature equation in measurable quantities. This equation will be compared with experimental results.
SynopsisFiber suspension theory model parameters for use in the simulation of fiber orientation in complex flows are, in general, either calculated from theory or fit to experimentally determined fiber orientation generated in processing flows. Transient stress growth measurements in startup of shear flow and flow reversal in the shear rate range, ␥ =1-10 s −1 , were performed on a commercially available short glass fiber-filled polybutylene terephthalate using a novel "donut-shaped" sample in a cone-and-plate geometry. Predictions using the Folgar-Tucker model for fiber orientation, with a "slip" factor, combined with the Lipscomb model for stress were fit to the transient stresses at the startup of shear flow. Model parameters determined by fitting at ␥ =6 s −1 allowed for reasonable predictions of the transient stresses in flow reversal experiments at all the shear rates tested. Furthermore, fiber orientation model parameters determined by fitting the transient stresses were compared to the experimentally determined evolution of fiber orientation in startup of flow. The results suggested that fitting model predictions to the stress response in well-defined flows could lead to unambiguous model parameters provided the fiber orientation as a function of time or strain at some shear rate was known.
The objective of this review is to elucidate the rheological behavior of glass fiber suspensions whose suspending
mediums are non-Newtonian fluids. In particular, this review focuses on determining the impact of fiber
concentration, aspect ratio, orientation distribution, interaction with the suspending medium, and suspending
medium viscoelasticity on the rheology of glass fiber composite fluids. The presence of glass fiber can induce
a yieldlike behavior, causing shear thinning to occur at reduced shear rates. Glass fiber can impede the elastic
properties of the suspending medium but enhance the first normal stress function. Large stress overshoots in
both the shear and normal stress growth functions are observed that are associated with changes in fiber
orientation. Upon cessation of flow, stress relaxation follows that of the suspending medium but fibers retain
their orientation. The presence of glass fiber can induce extension rate thinning and suppress the strain
thickening behavior of the suspending medium.
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