Global linear and nonlinear stability of viscous confined plane wakes with co-flow

The global stability of confined uniform density wakes is studied numerically, using two-dimensional linear global modes and nonlinear direct numerical simulations. The wake inflow velocity is varied between different amounts of co-flow (base bleed). In accordance with previous studies, we find that the frequencies of both the most unstable linear and the saturated nonlinear global mode increase with confinement. For wake Reynolds number Re = 100 we find the confinement to be stabilising, decreasing the growth rate of the linear and the saturation amplitude of the nonlinear modes. The dampening effect is connected to the streamwise development of the base flow, and decreases for more parallel flows at higher Re. The linear analysis reveals that the critical wake velocities are almost identical for unconfined and confined wakes at Re ≈ 400. Further, the results are compared with literature data for an inviscid parallel wake. The confined wake is found to be more stable than its inviscid counterpart, whereas the unconfined wake is more unstable than the inviscid wake. The main reason for both is the base flow development. A detailed comparison of the linear and nonlinear results reveals that the most unstable linear global mode gives in all cases an excellent prediction of the initial nonlinear behaviour and therefore the stability boundary. However, the nonlinear saturated state is different, mainly for higher Re. For Re = 100, the saturated frequency differs less than 5% from the linear frequency, and trends regarding confinement observed in the linear analysis are confirmed.

Heat transfer coefficients from Newtonian and non-Newtonian fluids flowing in laminar regime in a helical coil

This study aimed to carry out experimental work to obtain, for Newtonian and non-Newtonian fluids, heat transfer coefficients, at constant wall temperature as boundary condition, in fully developed laminar flow inside a helical coil. The Newtonian fluids studied were aqueous solutions of glycerol, 25%, 36%, 43%, 59% and 78% (w/w) and the non-Newtonian fluids aqueous solutions of carboxymethylcellulose (CMC), a polymer, with concentrations 0.1%, 0.2%, 0.3%, 0.4% and 0.6% (w/w) and aqueous solutions of xanthan gum (XG), another polymer, with concentrations 0.1% and 0.2% (w/w). According to the rheological study performed, the polymer solutions had shear thinning behavior and different values of elasticity. The helical coil used has internal diameter, curvature ratio, length and pitch, respectively: 0.004575 m, 0.0263, 5.0 m and 11.34 mm. The Nusselt numbers for the CMC solutions are, on average, slightly higher than those for Newtonian fluids, for identical Prandtl and generalized Dean numbers. As outcome, the viscous component of the shear thinning polymer tends to potentiate the mixing effect of the Dean cells. The Nusselt numbers of the XG solutions are significant lower than those of the Newtonian solutions, for identical Prandtl and generalized Dean numbers. Therefore, the elastic component of the polymer tends to diminish the mixing effect of the Dean cells. A global correlation, for Nusselt number as a function of Péclet, generalized Dean and Weissenberg numbers for all Newtonian and non-Newtonian solutions studied, is presented.

FORCED CONVECTION TO LAMINAR FLOW OF LIQUID EGG YOLK IN CIRCULAR AND ANNULAR DUCTS

The steady-state heat transfer in laminar flow of liquid egg yolk - an important pseudoplastic fluid food - in circular and concentric annular ducts was experimentally investigated. The average convection heat transfer coefficients, determined by measuring temperatures before and after heating sections with constant temperatures at the tube wall, were used to obtain simple new empirical expressions to estimate the Nusselt numbers for fully established flows at the thermal entrance of the considered geometries. The comparisons with existing correlations for Newtonian and non-Newtonian fluids resulted in excellent agreement. The main contribution of this work is to supply practical and easily applicable correlations, which are, especially for the case of annulus, rather scarce and extensively required in the design of heat transfer operations dealing with similar shear-thinning products. In addition, the experimental results may support existing theoretical analyses.

An evaluation of three upwinding approximations for numerical modeling the flow in tubular membrane of Newtonian and non-Newtonian fluids

In this paper, the laminar fluid flow of Newtonian and non-Newtonian of aqueous solutions in a tubular membrane is numerically studied. The mathematical formulation, with associated initial and boundary conditions for cylindrical coordinates, comprises the mass conservation, momentum conservation and mass transfer equations. These equations are discretized by using the finite-difference technique on a staggered grid system. Comparisons of the three upwinding schemes for discretization of the non-linear (convective) terms are presented. The effects of several physical parameters on the concentration profile are investigated. The numerical results compare favorably with experimental data and the analytical solutions. (C) 2011 Elsevier Inc. All rights reserved.

Heat transfer in laminar flow of non-Newtonian fluids in ducts of elliptical section

Laminar forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumption used in this work is a laminar flow of a power flow inside elliptical tube, under a boundary condition of first kind with constant physical properties and negligible axial heat diffusion (high Peclet number). To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm-Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number and the average Nusselt number for various cross-section aspect ratios. (C) 2006 Elsevier. SAS. All rights reserved.

Non-newtonian flow and pressure drop of pineapple juice in a plate heat exchanger

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The carreau-yasuda fluids: a skin friction equation for turbulent flow in pipes and kolmogorov dissipative scales

In this work the turbulent flow of the Non-Newtonian Carreau-Yasuda fluid will be studied. A skin friction equation for the turbulent flow of Carreau-Yasuda fluids will be derived assuming a logarithmic behavior of the turbulent mean velocity for the near wall flow out of the viscous sub layer. An alternative near wall characteristic length scale which takes into account the effects of the relaxation time will be introduced. The characteristic length will be obtained through the analysis of viscous region near the wall. The results compared with experimental data obtained with Tylose (methyl hydroxil cellulose) solutions showing good agreement. The relations between scales integral and dissipative obtained for length, time, velocity, kinetic energy, and vorticity will be derived for this type of fluid. When the power law index approach to unity the relations reduces to Newtonian case.

Control of instabilities in non-Newtonian free surface fluid flows

Free surface flows in inclined channels can develop periodic instabilities that are propagated downstream as shock waves with well-defined wavelengths and amplitudes. Such disturbances are called roll waves and are common in channels, torrential lava, landslides, and avalanches. The prediction and detection of such waves over certain types of structures and environments are useful for the prevention of natural risks. In this work, a mathematical model is established using a theoretical approach based on Cauchy's equations with the Herschel-Bulkley rheological model inserted into the viscous part of the stress tensor. This arrangement can adequately represent the behavior of muddy fluids, such as water-clay mixture. Then, taking into account the shallow water and the Rankine-Hugoniot's (shock wave) conditions, the equation of the roll wave and its properties, profile, and propagation velocity are determined. A linear stability analysis is performed with an emphasis on determining the condition that allows the generation of such instabilities, which depends on the minimum Froude number. A sensitivity analysis on the numerical parameters is performed, and numerical results including the influence of the Froude number, the index flow and dimensionless yield stress on the amplitude, the wavelength of roll waves and the propagation velocity of roll waves are shown. We show that our numerical results were in agreement with Coussot's experimental results (1994).

Percolated non-Newtonian flow for silicone obtained from exfoliated bioinorganic layered double hydroxide intercalated with amino acid

A simple and scalable procedure was used to obtain thin, stable, homogeneous, and easy-to-handle films composed of silicone derived from dimethicones containing dispersed hydrotalcite-type materials previously organo-modified with amino acids. The absence of the typical X-ray pattern of the bioinorganic LDH filler suggested an exfoliation process that was further indirectly evidenced by a drastic change in the rheological behavior, which turned from a quasi-Newtonian behavior for the silicone free of LDH filler to an extensive developed gel-like structure for the nanocomposite derivatives. Visualized by the shear-thinning exponent of the complex viscosity in the low-frequency range, the percolation threshold was evident for filler loading as low as <5 w/W%, suggesting the presence of a largely developed interface between the filler and the polymer. The increase of more than one order of magnitude in viscosity was explained by the rather strong attrition phenomenon between the tethered amino acid anions and the silicone chains. UVB radiation absorption profiles make such bioinorganic polymer nanocomposites potentially applicable in skin protection. Thermo-gravimetric analysis revealed significant improvement in the thermal stability, especially in the final step of the polymer combustion, thus underlining the role of the hybrid material as a thermal retardant agent. (C) 2011 Elsevier B.V. All rights reserved.