Admilson T. Franco

The yielding and the linear-to-nonlinear viscoelastic transition of an elastoviscoplastic material

Elastoviscoplastic materials present a transition from a gel-like to a liquidlike state induced by shearing: While the first is primarily elastic, the second is predominantly viscous. The point that characterizes this transition is usually known as the yield point, which is associated to critical quantities such as yield stress and/or yield strain. Another characteristic of elastoviscoplastic materials is the transition from linear to nonlinear viscoelasticity. In the current work, a commercial hair gel, which is an elastoviscoplastic material, was tested in two rotational rheometers in order to evaluate these two transition points. Stress oscillatory amplitude sweeps at different frequencies were performed and a Fourier-Transform analysis was applied to the results in order to determine the linear viscoelastic limit. The linear viscoelastic limit stresses and strains at different frequencies were then compared to quantities that are usually associated to the yield point: The extrapolated zero-shear-rate ...

Galerkin Solution of Stochastic Reaction-Diffusion Problems

In this paper, the Galerkin method is used to obtain numerical solutions to twodimensional steady-state reaction-diffusion problems. Uncertainties in reaction and diffusion coefficients are modeled using parameterized stochastic processes. A stochastic version of the Lax–Milgram lemma is used in order to guarantee existence and uniqueness of the theoretical solutions. The space of approximate solutions is constructed by tensor product between finite dimensional deterministic functional spaces and spaces generated by chaos polynomials, derived from the Askey–Wiener scheme. Performance of the developed Galerkin scheme is evaluated by comparing first and second order moments and probability histograms obtained from approximate solutions with the corresponding estimates obtained via Monte Carlo simulation. Results for three example problems show very fast convergence of the approximate Galerkin solutions. Results also show that complete probability densities (histograms) of the responses are correctly approximated by the developed Galerkin basis. [DOI: 10.1115/1.4023938]

Numerical Investigation of Natural Convection in Heterogeneous Rectangular Enclosures

The aim of this study is to investigate numerically the steady natural convection resulting from horizontally heating a rectangular enclosure filled with a fluid and containing uniformly distributed, conducting, fixed and disconnected solid blocks (i.e., not touching each other). In particular, the effects of solid volume fraction, solid–fluid thermal conductivity ratio, and total number of blocks on the heat transfer process are determined by solving the mass, momentum, and energy conservation equations using the finite-volume method. The enclosure aspect ratio is varied from 0.25 to 4, the Rayleigh number from 105 to 108, and the Prandtl number is set as unity. Results of the numerical simulations are presented in terms of the surface-averaged Nusselt number, streamfunction, and streamline and isotherm distributions. The interference phenomenon caused by the solid blocks on the natural convection process is considered in detail and used to explain and predict the surprising and complex behavior of surface-averaged Nusselt number.

Numerical Study of the Free Surface Flow in a Centrifugal Gas-Liquid Separator

This work presents a numerical investigation of the free surface flow in a gas-liquid separator with a cylindrical expansion chamber using Computational Fluid Dynamics. The centrifugal flow is set through a tangentially oriented nozzle at the chamber wall and is modeled using an inhomogeneous Eulerian-Eulerian multiphase flow model with the free surface approach to capture the phases interface. Fluid dynamics is examined for a range of fluid viscosities and flow rates for a single-phase liquid flow at the inlet. Liquid-gas bubbly-flow at the inlet is also considered to investigate some aspects of the phases separation inside the cylindrical chamber. Analysis of the flow field reveals that the impact of the fluid at the chamber wall combined with the centrifugal movement push part of the fluid upwards, stabilizing a liquid level above the nozzle. Near the inlet, the flow dynamics is characterized by a strong centrifugal motion, which decreases continuously below the entrance position due to gravity and viscous effects. The liquid level over the chamber wall and the centrifugal intensity increase with the flow rate, but decrease with viscosity. Viscosity also tends to enlarge the liquid layer thickness over the chamber wall and diminish the residence time of the liquid from the inlet down to the chamber’s bottom exit. Investigation of liquid-gas bubbly-flows in this equipment shows that separation occurs mainly near the chamber entrance due to the sudden expansion and the formation of a thin fluid layer over the chamber wall. In a percentage basis, phases tend to be more effectively separated for higher inlet gas volume fractions, lower liquid viscosities and bigger gas bubbles. These conclusions give technically interesting information for dimensioning hydrocyclones for gas-liquid flow separation.Copyright

Multi-block analysis for the correlation of physico-chemical and rheological data of 42 fruit pulps

The common dimension (ComDim) chemometric method for multi-block analysis and hierarchical cluster analysis (HCA) were used to evaluate the data obtained from the physico-chemical and rheological characterization of 42 commercial fruit pulps. The physico-chemical characteristics and the rheological behavior of the pulps were found to be considerably different. The Herschel-Bulkley equation was fit to the steady-state flow curves of the fruit pulps, and it was found to appropriately describe the materials, which showed a wide range of yield stresses. The soluble solids content and the yield stress were the main factors responsible for the sample discrimination in the multivariate statistical analysis. The ComDim model indicates that these parameters may have a direct correlation. Namely, the soluble solids amount can influence the viscosity, as demonstrated by the similar scores of the samples in both common components, and this corroborated with the HCA analysis. PRACTICAL APPLICATIONS: Fruit pulps can be used as raw materials in the food industry to obtain several products, such as nectars, jellies, ice creams, and juices, which can also be sold directly to consumers. To evaluate the technical and economic feasibility of those industrial processes, it is important to know the physico-chemical properties of the products. Therefore, in this study we attempt to correlate the physical-chemical and rheological data using a new statistical approach.

Numerical Investigation of the Onset of Steady Natural Convection in a Square Cavity Partially Filled With a Single Porous Block

The critical Rayleigh number at the onset of natural convection within a square cavity filled with a centralized porous block was investigated. The porous medium is modeled by using the heterogeneous model and the governing equations are solved for each phase separately. The thermal gradient is applied from the bottom to the top horizontal walls while the vertical walls are kept adiabatic. The amount of solid within the cavity was kept constant by fixing both external and internal porosity in 36% and 40%, respectively. The equations are solved using the Finite Volume Method and the interpolation scheme for the convective terms is the Hybrid Scheme. For the pressure-velocity coupling, the SIMPLEC method is used. The effects on the conductive-convective regime transition, reads critical Rayleigh Number, characterized by the average Nusselt number and the heatlines contour plot, was investigated by varying the Rayleigh number and the porous block permeability. The results show that the so called critical Rayleigh number is affected by the block permeability. As the permeability decreases, the flow tends to recirculate around the block being squeezed against the cavity walls and therefore, more susceptible to viscous effects. A correlation to the critical Rayleigh number is presented as a function of the agglomerate permeability showing that the higher the permeability the lower the amount of energy required to trigger the convection.Copyright

Periodic Horizontal Heating of Enclosed Disconnected Solid Bodies Saturated With a Fluid

In the present study, the ensuing natural convection phenomenon inside a heated enclosure filled with disconnected, discrete solid blocks, and under time-periodic heating in the horizontal direction is investigated numerically. This configuration is akin to several practical engineering applications, such as in the food (baking) industry, metal parts (heat treating) industry, and containerization (storage and transportation) of discrete solid goods. Because of the relative large size of the solid bodies placed inside the enclosure, a porous medium approach is not appropriate in the present case. Hence, the solid and fluid constituents within the enclosure are viewed individually and modeled using continuum balance equations, with suitable compatibility conditions imposed at their interfaces. The periodic heating is simulated by imposing a sinusoidal time-function on the hot wall temperature, while maintaining the cold wall temperature constant. Results are presented in terms of surface-averaged (hot and cold) Nusselt numbers, time-varying energy capacity (equal to the thermal energy stored inside the enclosure), isotherms and streamlines, for Ra varying from 103 to 107, Pr = 1 and 36 uniformly distributed, conducting and disconnected solid square blocks. The results, focusing on the time-periodic regime, indicate the effect of varying Ra on the convection process. As Ra increases, the dynamic capacitor performance of the enclosure tends to be enhanced.© 2014 ASME

Preliminary Numerical Study of Natural Convection in a Heterogeneous Horizontal Layer Heated From Below

In the present preliminary study the natural convection in a horizontal fluid layer heated isothermally from below and cooled from above, and having disconnected and conducting square solid blocks uniformly distributed in a square array within it, is numerically investigated. Nondimensional steady balance equations are presented, for a Newtonian fluid, with fluid and solid properties being considered constant and uniform. Among the nondimensional parameters ruling the phenomenon, the layer Rayleigh number is set as 105 and 106, the aspect ratio of the layer varies from 1 to 8, and the fluid Prandtl number and the solid-to-fluid thermal conductivity ratio are set as unity. The focus is on the effect of increasing the number of blocks in the layer, the blocks having progressively smaller size as to maintain the solid volume-fraction inside the layer constant and equal to 26% — this is equivalent to dispersing a fixed amount of solid material in smaller and large number of solid blocks within the layer. In general, the increase in the layer aspect ratio, with all other parameters kept constant, affects the results more as Ra increases — as expected because large Ra yields stronger convection effects. The increase in the number of blocks per unit of square cell in the layer affects the flow as to hinder convection; i.e., the finer the dispersion of solid material within the layer is (as the number of blocks increases) the weaker the resulting flow.Copyright

Berkovsky-Polevikov Correlations for Natural Convection in a Nonhomogeneous Enclosure Filled With a Fluid and Disconnected-Conducting Solid Particles

This study investigates the suitability of the known Berkovsky-Polevikov correlations, used for predicting the wall-averaged Nusselt number, Nuav, of “wide” enclosures heated from the side and filled with a fluid undergoing natural convection, to predict the heat transfer coefficient inside a nonhomogeneous enclosure heated from the side, filled with uniformly distributed, disconnected and conducting solid objects also saturated with a fluid undergoing natural convection. Hence, defining γ = RaHPr/(0.2+Pr), a correlation in the form of Nuav = AγB is investigated for curve fitting numerical simulation results. The numerical results are obtained by simulating the heat transfer process of the two distinct constituents, namely the fluid and the solid, within the enclosure using the finite-volume method with appropriate conservation equations and compatibility conditions at their interfaces. The right wall of the enclosure is maintained at temperature lower than that of the left wall, with the horizontal top and bottom surfaces of the enclosure assumed to be adiabatic. Results for 1, 4, 9, 16, and 36, evenly distributed square solid blocks are presented. Appropriate numerical values for coefficients A and B are determined and presented for the utilization of the corresponding Berkovsky-Polevikov correlations. Good correlation is obtained when the Rayleigh number is high (≥107), as to yield distinct boundary layers inside the enclosure.Copyright

The Effects of Solid Thermal Conductivity and Volume-Fraction in the Natural Convection Inside a Heterogeneous Enclosure

In this study, the natural convection inside a fluid filled enclosure containing several solid obstructions and heated from the side is simulated numerically as to determine the effects of the solid thermal conductivity and volume-fraction. The solid obstructions are conducting, disconnected square blocks, uniformly distributed inside the enclosure. The mathematical model follows a continuum approach, with balance equations of mass, momentum and energy presented for each one of the constituents (i.e., fluid and solid) inside the enclosure. The equations are then solved numerically via the finite-volume method. The effects of varying the solid-fluid thermal conductivity ratio (K), the fluid volume-fraction or porosity (φ), the number of solid blocks (N) and the heating strength (represented by the Rayleigh number, Ra) on the natural convection process inside the enclosure are investigated parametrically. The Nusselt number based on the surface-averaged heat transfer coefficient along the heated wall is chosen to characterize the convection strength inside the enclosure. The results indicate a competing effect caused by the proximity of the solid blocks to the heated and cooled walls of the enclosures, vis-a-vis hindering the boundary layer growth, hence reducing the heat transfer effectiveness, and at the same time enhancing the heat transfer when K is large. An analytical estimate of the minimum number of blocks beyond which the convection hindrance becomes predominant is presented and validated by the numerical results.Copyright