Loading...
12 results
Search Results
Now showing 1 - 10 of 12
- Viscoelastic flow in a 3D square/square contraction: Visualizations and simulations.Publication . Alves, M. A.; Pinho, Fernando; Oliveira, Paulo J.The inertialess three-dimensional (3D) flow of viscoelastic shear-thinning fluids in a 4:1 sudden square-square contraction was investigated experimentally and numerically and compared with the flow of inelastic fluids. Whereas for a Newtonian fluid the vortex length remains unchanged at low Reynolds numbers, with the non-Newtonian fluid there is a large increase in vortex length with fluid elasticity leading to unstable periodic flow at higher flow rates. In the steady flow regime the vortices are 3D and fluid particles enter the vortex at the middle plane, rotate towards its eye, drift sideways to the corner-plane vortex, rotate to its periphery, and exit to the downstream duct. Such dynamic process is reverse of that observed and predicted with Newtonian fluids. Numerical predictions using a multimode Phan-Thien–Tanner viscoelastic model are found to match the visualizations accurately and in particular are able to replicate the observed flow reversal. The effect of fluid rheology on flow reversal, vortex enhancement, and entry pressure drop is investigated in detail.
- The log-conformation tensor approach in the finite-volume method frameworkPublication . Afonso, A. M.; Oliveira, Paulo J.; Pinho, Fernando; Alves, M. A.The log-conformation formulation, proposed by Fattal and Kupferman [J. Non-Newt. Fluid Mech. 123 (2004) 281], has helped to provide further insights into the High-Weissenberg Number Problem. In this work, we investigate the performance of the log-conformation formulation in the Finite Volume Method (FVM) framework for creeping flows of viscoelastic fluids in steady and unsteady flows around a confined cylinder. The Oldroyd-B and Phan-Thien–Tanner (PTT) constitutive equations were used to assess the effect of different rheological behaviour on the flow patterns and solution stability. The calculation of the polymer stress contribution is carried out with both the standard technique and with the logconformation methodology. For all test cases, up to the critical conditions when both methods converge to a steady solution, the use of the log-conformation technique provides solutions with similar accuracy as the standard approach. In terms of stability the log-conformation formulation is found to be significantly more robust, and solutions could be obtained at higher Deborah number flows.
- Adaptive multiresolution approach for two-dimensional PDE'sPublication . Santos, J. C.; Cruz, P.; Alves, M. A.; Oliveira, Paulo J.; Magalhães, F.D.; Mendes, AdélioA multiresolution adaptive approach for the solution of two-dimensional partial differential equations (PDEs) is presented. This methodology is a multidimensional extension of that presented in a previous work [Comput. Methods Appl. Mech. Engrg. 191 (2002) 3909]. The method proposed is unconditionally stable, by incorporating convection differencing schemes with the TVD property, and the grid is dynamically adapted so that higher spatial resolution is automatically allocated to domain regions where strong gradients are observed. The two desired properties of any PDE solver, stability and accuracy, are therefore retained. Numerical results for four test problems are presented which serve to demonstrate the robustness and cost effectiveness of the method.
- Purely Elastic Flow AsymmetriesPublication . Poole, R. J.; Alves, M. A.; Oliveira, Paulo J.Using a numerical technique we demonstrate that the flow of the simplest differential viscoelastic fluid model (i.e., the upper-convected Maxwell model) goes through a bifurcation to a steady asymmetric state when flowing in a perfectly symmetric ‘‘cross-slot’’ geometry. We show that this asymmetry is purely elastic in nature and that the effect of inertia is a stabilizing one. Our results are in qualitative agreement with very recent experimental visualizations of a similar flow in the microfluidic apparatus of Arratia et al. [Phys. Rev. Lett. 96, 144502 (2006)].
- Enhanced Microfluidic Mixing via a Tricritical Spiral Vortex InstabilityPublication . Haward, Simon J.; Poole, R. J.; Alves, M. A.; Oliveira, Paulo J.; Goldenfeld, Nigel; Shen, Amy Q.Experimental measurements and numerical simulations are made on fluid flow through cross-slot devices with a range of aspect (depth:width) ratios, 0.4 < alpha < 3.87. For low Reynolds numbers Re, the flow is symmetric and a sharp boundary exists between fluid streams entering the cross-slot from opposite directions. Above an alpha-dependent critical value Re_c, the flow undergoes a symmetry-breaking bifurcation (though remains steady and laminar) and a spiral vortex structure develops about the central axis of the outflow channel. An order parameter characterizing the instability grows according to a sixth-order Landau potential, and shows a progression from second order to first order transitions as alpha increases. A tricritical point occurs for alpha ~ 0.55. The spiral vortex acts as a mixing region in the flow field and this phenomenon can be used to drive enhanced mixing in microfluidic devices.
- Visualizations of Boger fluid flows in a 4:1 square/square contractionPublication . Alves, M. A.; Pinho, Fernando; Oliveira, Paulo J.Visualizations of the 3-D flow in a 4:1 square/square sudden contraction for two viscoelastic Boger fluids and two Newtonian fluids were carried out at low Reynolds numbers. In these creeping flow conditions, the vortex length remained unchanged for Newtonian fluids, whereas a nonmonotonic variation with flow rate was observed for the Boger fluids. Initially, the corner vortex slightly increased with flow rate to a local peak at a Deborah number of De=6, before decreasing significantly to a minimum at De=15 (De is based on downstream characteristics). Finally, for Deborah numbers = 20 there was intense vortex enhancement until a periodic flow was established at higher flow rates (De=45/ 52). The strong elastic vortex enhancement was preceded by the appearance of diverging streamlines on the approach flow and, for the Boger fluid with higher polymer concentration, vortex enhancement took place through a lip vortex mechanism.
- Plane sudden expansion flows of viscoelastic liquidsPublication . Poole, R. J.; Alves, M. A.; Oliveira, Paulo J.; Pinho, FernandoWe report a systematic numerical investigation of the creeping flow of three different viscoelastic models, the UCM, Oldroyd-B and the linear form of the PTT model, through a 1:3 planar sudden expansion. Although the effect of elasticity is to reduce both the length and intensity of the recirculation region downstream of the expansion, we show that this reduction is much lower than previous studies have suggested and that, at high Deborah number, a significant region of recirculation still exists for all of the models studied.
- Lid-driven cavity flow of viscoelastic liquidsPublication . Sousa, R. G.; Poole, R. J.; Afonso, A. M.; Pinho, F. T.; Oliveira, P. J.; Morozov, A.; Alves, M. A.The lid-driven cavity flow is a well-known benchmark problem for the validation of new numerical meth- ods and techniques. In experimental and numerical studies with viscoelastic fluids in such lid-driven flows, purely-elastic instabilities have been shown to appear even at very low Reynolds numbers. A finite-volume viscoelastic code, using the log-conformation formulation, is used in this work to probe the effect of viscoelasticity on the appearance of such instabilities in two-dimensional lid-driven cavities for a wide range of aspect ratios (0.125 ≤ = height/length ≤4.0), at different Deborah numbers under creeping-flow conditions and to understand the effects of regularization of the lid velocity. The effect of the viscoelasticity on the steady-state results and on the critical conditions for the onset of the elastic instabilities are described and compared to experimental results.
- On the effect of contraction ratio in viscoelastic flow through abrupt contractionsPublication . Alves, M. A.; Oliveira, Paulo J.; Pinho, FernandoA numerical study of the creeping flow of a PTT fluid through planar sudden contractions was carried out to quantify the effect of contraction ratio upon the flow characteristics (streamlines and size and intensity of recirculation vortices). The relevant governing equations were solved with a finite volume method embodying a new high-resolution scheme (Alves et al. [Int. J. Numer. Meth. Fluids 41 (2003) 47]) for the discretisation of convection terms, which is here explained and shown to yield improved accuracy and robustness. The results of the simulations, in terms of streamline patterns, give further evidence for a lip-vortex enhancement mechanism and are in remarkable agreement with flow visualization photographs from the literature. In addition, the results show that the variation of flow features in the vicinity of the re-entrant corner, such as lip vortex size and streamlines, are dominated by downstream quantities and scale with the common definition for the Deborah number in this flow, while flow characteristics in the salient corner region scale with that Deborah number divided by the contraction ratio.
- On extensibility effects in the cross-slot flow bifurcationPublication . Rocha, Gerardo N.; Poole, R. J.; Alves, M. A.; Oliveira, Paulo J.The flow of finite-extensibility models in a two-dimensional planar cross-slot geometry is studied numerically, using a finite-volume method, with a view to quantifying the influences of the level of extensibility, concentration parameter, and sharpness of corners, on the occurrence of the bifurcated flow pattern that is known to exist above a critical Deborah number. The work reported here extends previous studies, in which the viscoelastic flow of upper-convected Maxwell (UCM) and Oldroyd-B fluids (i.e. infinitely extensionable models) in a cross-slot geometry was shown to go through a supercritical instability at a critical value of the Deborah number, by providing further numerical data with controlled accuracy.We map the effects of the L2 parameter in two different closures of the finite extendable non-linear elastic (FENE) model (the FENE-CR and FENE-P models), for a channel-intersecting geometry having sharp, “slightly” and “markedly” rounded corners. The results show the phenomenon to be largely controlled by the extensional properties of the constitutive model, with the critical Deborah number for bifurcation tending to be reduced as extensibility increases. In contrast, rounding of the corners exhibits only a marginal influence on the triggering mechanism leading to the pitchfork bifurcation, which seems essentially to be restricted to the central region in the vicinity of the stagnation point.