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- Design of calibrators for extruded profiles. Part I: modelling the thermal interchangesPublication . Nóbrega, J. M.; Carneiro, Olga; Covas, José A; Pinho, Fernando; Oliveira, Paulo J.The parameters influencing the calibration/cooling stage of profile extrusion are discussed, and a numerical finite-volume method code to model the heat transfer is described and validated. For this purpose, the numerical predictions are compared with the analytical solution of a simple problem, with results available in the literature and with those produced by a commercial software. The routines developed are then used to identify the main process parameters and boundary conditions and to estimate their relative importance. The investigation clearly shows the advantages of using several calibrators separated by annealing zones, relative to a single calibrator of the same total length, and the large impact of the contact resistance between extrudate and cooling unit while showing negligible impact of other boundary conditions. A decrease of the extrudate velocity is seen to be also an effective control parameter, but it decreases the production rates.
- Analytical solution for fully developed channel and Pipe Flow of Phan-Thien/Tanner FluidsPublication . Oliveira, Paulo J.; Pinho, FernandoAnalytical expressions are derived for the velocity vector, the stress components and the viscosity function in fully developed channel and pipe flow of Phan-Thien/ Tanner (PTT) fluids; both the linearized and the exponential forms of the PTT equation are considered. The solution shows that the wall shear stress of a PTT fluid is substantially smaller than the corresponding value for a Newtonian or upperconvected Maxwell fluid, with implications for comparing predicted and measured values in a non-dimensional form.
- Bifurcation phenomena in viscoelastic flows through a symmetric 1: 4 expansionPublication . Rocha, Gerardo N.; Poole, R. J.; Oliveira, Paulo J.In this work we present an investigation of viscoelastic flow in a planar sudden expansion with expansion ratio D/d = 4. We apply the modified FENE–CR constitutive model based on the non-linear finite extensibility dumbbells (FENE) model. The governing equations were solved using a finite volume method with the high-resolution CUBISTA scheme utilised for the discretisation of the convective terms in the stress and momentum equations. Our interest here is to investigate two-dimensional steady-state solutions where, above a critical Reynolds number, stable asymmetric flow states are known to occur.We report a systematic parametric investigation, clarifying the roles of Reynolds number (0.01 < Re < 100),Weissenberg number (0 < We < 100) and the solvent viscosity ratio (0.3 < β < 1). For most simulations the extensibility parameter of the FENE model was kept constant, at a value L2 = 100, but some exploration of its effect in the range 100–500 shows a rather minor influence. The results given comprise flow patterns, streamlines and vortex sizes and intensities, and pressure and velocity distributions along the centreline (i.e. y = 0). For the Newtonian case, in agreement with previous studies, a bifurcation to asymmetric flow was observed for Reynolds numbers greater than about 36. In contrast viscoelasticity was found to stabilise the flow; setting β = 0.5 and We = 2 as typical values, resulted in symmetric flow up to a Reynolds number of about 46. We analyse these two cases in particular detail.
- A method for particle location and field interpolation on complex, three-dimensional computational meshesPublication . Oliveira, Paulo J.; Gosman, A. D.; Issa, R. I.A method for locating particles within arbitrary three-dimensional computational meshes is described. It is based on an iterative procedure which uses transformed coordinates defined by iso-parametric functions. The method also enables one to interpolate field values from the mesh nodes to the particle position. Example applications demonstrate how effective the method is. For very distorted computational cells special practices have to be introduced in order to keep the number of iterations to a minimum.
- Accounting for temperature-dependent properties in viscoelastic duct flowsPublication . Nóbrega, J. M.; Pinho, Fernando; Oliveira, Paulo J.; Carneiro, OlgaA numerical and theoretical study is conducted to evaluate the effect of temperature-dependent properties on the hydrodynamic and thermal characteristics of viscoelastic fluid flow. The rheological constitutive equation of the fluid under consideration follows a common form of the PTT model, which embodies both influences of elasticity and shearthinning in viscosity. A large number of simulations were carried out for a developing channel flow with an imposed constant wall temperature by varying the parameters controlling elasticity (Weissenberg number) and viscous dissipation (Brinkman number). The resulting Nusselt number and friction factor were determined from the numerical results, for both conditions of constant and temperature-dependent properties. The properties that were allowed to vary with temperature were the viscosity, thermal conductivity, specific heat and relaxation time of the PTT model. From the results it was possible to determine how the usual correlations for Nu and Cf have to be modified, following the property-correction method, in order to represent variable-property flow of this viscoelastic fluid. An alternative method to account for variable properties, based on the definition of an equivalent temperature to be used with the constant property Nu and Cf expressions, is also proposed and shown to be less sensitive to the influence of viscous dissipation. The corrections are highly non-linear and strongly depend on eWe2 and Br especially when viscous dissipation is weak.
- Numerical simulation of the polymer electrolyte membrane fuel cells with intermediate blocked interdigitated flow fieldsPublication . Bagherighajari, Fatemeh; Ramiar, Abbas; Abdollahzadehsangroudi, Mohammadmahdi; Pascoa, José; Oliveira, Paulo J.The main purpose of this paper is to study fuel cell performance using an interdigitated flow field with intermediate channel blocks on the cathode side. Application of an intermediate block in the middle of the interdigitated flow channel is a very new idea aimed at increasing the performance of polymer membrane fuel cells, which in practice result in novel arrangements of interdigitated flow channels. A middle block is desirable because the change in flow channel is minimal, the cost of fabricating bipolar plates does not increase, and it leads to an increase in the transfer rate of reactants into the gas diffusion layer due to enhanced over-rib flow pattern and direction. In this work, a three-dimensional, isothermal, and two-phase model is used to simulate the performance of such fuel cells. The polarization curves, the distribution of reactants on the cathode side, the distribution of liquid water, and the induced transverse flow were analyzed for three type of interdigitated flow fields along with parallel flow fields at reference conditions. The results showed that interdigitated flow fields with middle blocks lead to an increase in reactant transfer to the catalyst layer, an increase in reaction rate, and better removal of the resulting liquid water within the fuel cell. In the reference condition, in terms of maximum power density, the type I interdigitated flow field (without intermediate block) increased the net power by 8.2% compared to the parallel flow field, and the type II and III interdigitated flow fields also increased the power by 12.58% and 9.03%, respectively. At high current density, the type II interdigital flow field had the best performance in terms of enhancing the transfer of reactants to the catalyst layer and the expulsion of liquid water from that layer.
- Numerical and analytical modeling of unsteady viscoelastic flows: the start-up and pulsating test case problemsPublication . Duarte, A. S. R.; Miranda, Amílcar I. P.; Oliveira, Paulo J.In this paper two test cases adequate for the assessment of viscoelastic flow codes under unsteady flow conditions are investigated. For one of them an analytical solution is also derived. First, the start-up of planar Poiseuille flow between two parallel plates was tackled. For upper-convected Maxwell and Oldroyd-B models there exist analytical solutions making it possible to evaluate exactly the discretization errors of the transient numerical method. Good agreement was found between the present numerical results and those analytical solutions, especially for “shock” propagation. For the UCM fluid, small numerical oscillations were observed at points where the time derivative of velocity was discontinuous, but for the Oldroyd-B fluid a smooth development of the transient evolution was obtained. Results with the PTT model without solvent viscosity and the FENE fluids were also obtained and, as expected, the behaviour was similar to that found for the UCM and Oldroyd-B fluids, respectively. Then, a pulsating flowproblemwas studied. In this test case the flow is generated by a periodic ressure gradient superimposed on a constant Poiseuille flow. The analytical solution for pulsatile Oldroyd-B flow in a channel was derived as part of the work and, again, difficulties in obtaining accurate numerical solutions with the UCM model were encountered, being necessary to employ extremely refined meshes. For the Oldroyd-B fluid no difficulties were found and the accuracy tended to improve with larger solvent viscosity parameter.
- Plane contraction flows of upper convected Maxwell and phan-ThienTanner fluids as predicted by a finite-volume methodPublication . Oliveira, Paulo J.; Pinho, FernandoA finite-volume (FV) procedure is applied to the prediction of two-dimensional (2-D) laminar flow through a 4 : 1 planar contraction of upper convected Maxwell (UCM) and simplified Phan-Thien±Tanner (SPTT) fluids. The method incorporates general coordinates, indirect addressing for easy mapping of complex domains, and is based on the collocated mesh arrangement. Calculations with the UCM model at a Reynolds number of 0.01 were carried out with three consecutively refined meshes which enabled the estimation of the accuracy of the predictions of the main vortex characteristics through Richardson's extrapolation. Converged solutions with the first-order upwind differencing scheme for the convective terms were obtained up to at least De à 8 in the finest mesh, but were limited to De 1, De 3 and De 5 for the fine, medium and coarse meshes, respectively, when using the second-order linear upwind scheme. The predicted flow patterns for increasing Deborah numbers with the UCM model resemble the well known lip vortex enhancement mechanism reported in the literature for constant-viscosity fluids in axisymmetric contractions and shear-thinning fluids in planar contraction, but very fine meshes were required in order to capture the described vortex activity. Predictions with the SPTT model also compared well with the behaviour reported in the literature.
- A general correlation for the local loss coefficient in newtonian axisymmetric sudden expansionsPublication . Oliveira, Paulo J.; Pinho, Fernando; Schulte, A.Results from numerical simulations and guidance from an approximated corrected-theory, developed by Oliveira and Pinho (1997), have been used to arrive at a correlation expressing the irreversible loss coefficient for laminar Newtonian flow in axisymmetric sudden expansions. The correlation is valid for the ranges 1.5 < D2/D1 < 4 and 0.5 < Re < 200 with errors of less than 5%, except for 25 < Re < 100 where the error could be as much as 7%. The recirculation bubble length is also presented for the same range of conditions and the pressure recovery coefficient was calculated for Reynolds numbers above 15.
- 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.