Range Of Volume Fractions Research Articles

Fluctuations in inertial dense homogeneous suspensions

A theoretical model of liquid and particle random fluctuations is proposed for gravity-driven flows of inertial homogeneous suspensions. It is based on a paradigm assuming that fluctuations of both liquid velocity and particle slip velocity are driven by fluctuations of the phase indicator function. It is shown that this model accurately predicts the energy of the fluctuations of both the fluid and particle phases measured in a homogeneous solid-liquid fluidized bed over a wide range of particle volume fractions, from 10% to 45%

Influence of CuO nanoparticles in enhancing the overall heat transfer around a square cylinder

In this study, steady flow and heat transfer through a copper–water nanofluid around a square cylinder was investigated numerically by using a finite-volume method for Reynolds numbers of 10-40. Furthermore, the range of nanoparticle volume fractions () considered is 0 ≤ ≤ 0.04, with three different nanoparticle diameters dnp = 30, 60 and 90 nm. The variation of the local and the average Nusselt numbers with Reynolds number, and volume fractions are presented for the range of above conditions. The averaged Nusselt number showed clear enhancement comparing with the base fluids. This enhancement is more apparent in flows with higher particle volume concentration, whereas the particle diameter imposes an opposing effect on the heat transfer characteristics.

Direct numerical simulation of mass transfer in bidisperse arrays of spheres

AbstractIn this study, an efficient ghost cell‐based immersed boundary method is used to perform direct numerical simulations of mass‐transfer processes in bidisperse arrays. Stationary spherical particles, with a size ratio of 1.5, are homogeneously distributed in a periodic domain in the spanwise directions. Simulations are performed over a range of solids volume fractions, volume fraction ratios of small‐to‐large particles, and Reynolds numbers. Through our studies, we find that large particles have a negative influence on the overall mass‐transfer performance; however, the performance of individual particle species is independent on the relative volume fraction ratios. We propose two correlations: (a) a refitted Gunn correlation for a better description of the interfacial transfer performance based on individual particle species; (b) a fractional calculation for a simple estimation of the overall performance in bidisperse systems using characteristics of individual particle species. We also investigate how well the overall mass‐transfer coefficient can be predicted by defining an appropriate equivalent diameter.

Magnetic field impact on nanofluid convective flow in a vented trapezoidal cavity using Buongiorno's mathematical model

Numerical study for the effect of an external magnetic field on the mixed convection of Al2O3–water Newtonian nanofluid in a right-angle vented trapezoidal cavity was performed using the finite volume method. The non-homogeneous Buongiorno model is applied for numerical description of the dynamic phenomena inside the cavity. The nanofluid, with low temperature and high concentration, enters the cavity through the upper open border, and is evacuated through opening placed at the right end of the bottom wall. The cavity is heated from the inclined wall, while the remainder walls are adiabatic and impermeable to both the base fluid and nanoparticles. After validation of the model, the analysis was carried out for a wide range of Hartmann number (0 ≼ Ha ≼ 100) and nanoparticles volume fraction (0 ≼ ϕ0 ≼ 0.06). The flow behavior as well as the temperature and nanoparticles distribution shows a particular sensitivity to the variations of both the Hartmann number and the nanofluid concentration. The domination of conduction mechanism at high Hartmann numbers reflects the significant effect of Brownian diffusion which tends to uniform the distribution of nanoparticles in the domain. The average Nusselt number which increases with the nanoparticles addition, depends strongly on the Hartmann number. Finally, a correlation predicting the average Nusselt number within such geometry as a function of the considered parameters is proposed.

X-ray radiography of viscous resuspension

We use X-ray imaging to study viscous resuspension. In a Taylor-Couette geometry, we shear an initially settled layer of spherical glass particles immersed in a Newtonian fluid and measure the local volume fraction profiles. In this configuration, the steady-state profiles are simply related to the normal viscosity defined in the framework of the suspension balance model. These experiments allow us to examine this fundamental quantity over a wide range of volume fractions, in particular, in the semidilute regime where experimental data are sorely lacking. Our measurements strongly suggest that the particle stress is quadratic with respect to the volume fraction in the dilute limit. Strikingly, they also reveal a nonlinear dependence on the Shields number, in contrast with previous theoretical and experimental results. This likely points to shear-thinning particle stresses and to a non-Coulomb or velocity-weakening friction between the particles, as also evidenced from shear reversal experiments.

Effects of hydrogen addition on the combustion characteristics of diesel fuel jets under ultra-high injection pressures

Many applications use hydrogen addition and high-pressure fuel injection technology to improve combustion performance. In this study, spray atomization and combustion characteristics of a diesel fuel jet, under the injection pressure of 350 MPa, injecting into a constant volume combustion vessel filled with air-hydrogen mixture at the diesel engine relevant condition are investigated by simulation method. A simplified mechanism of the n-heptane (C7H16) oxidation chemistry mechanism consisting of 26 reactions and 25 species integrated with the Kéromnès-2013 hydrogen combustion mechanism and EDC combustion model are utilized to predict the diesel fuel spray auto-ignition and combustion. The ambient gas is the mixture of air and hydrogen range in volume fraction from 0% to 10%. The ambient temperature and pressure is set to 1000 K and 3.5 MPa, respectively. The results indicate that as the hydrogen volume fraction is 2%, the minimum overall droplet SMD (Sauter Mean Diameter) is approximately 0.95 μm, which is obviously smaller than that of the case with the conventional high injection pressure. In cases that H2 v/v% larger than 4%, the maximum gaseous temperature increased significantly up to 2700 K. There are two peaks in the temperature growth rate curves as the hydrogen fraction of 8% and 10%. The high temperature at the outer edge of the spray is clearly seen due to its high value when the hydrogen fraction is larger than 4%. The hot reaction layer is the main location of CO formation. The H, OH radicals are formed at the edge of the spray where the temperature is high. The hydrogen species obviously promotes the oxidation and combustion of diesel fuel.

Effects of Prandtl Number on Natural Convection in a Cavity Filled with Silver/Water Nanofluid-Saturated Porous Medium and Non-Newtonian Fluid Layers Separated by Sinusoidal Vertical Interface

This study investigates the effect of Prandtl number on the natural heat convection inside a square cavity filled with two layers of Ag/water nanofluid-saturated porous medium and non-Newtonian fluid separated by a sinusoidal vertical interface. The left wall, which is adjacent to the nanofluid porous layer, has a relatively hot temperature, while the right wall is cold. Other walls of the cavity are thermally insulated. All cavity walls are impermeable except for the sinusoidal vertical interface located between the two layers. Galerkin finite element method was used to numerically solve the governing differential equations. The study examined the effects of power-law index (0.6 < n < 1.4), Darcy number (10−5 < Da < 10−1), volume fraction (0 < ∅ < 0.2), and undulation number (1 < N < 4) on the thermal performance of the cavity for Prandtl numbers (Pr) ranging from 0.015 to 13.4 and Rayleigh number (Ra) equal to 105. Results showed that increasing Prandtl and Darcy numbers raised the average Nusselt number. However, increasing the power-law index reduced the average Nusselt number. When the non-Newtonian fluid behaves as a shear-thinning fluid (n = 0.7) and Pr = 13.4, the effect of the undulations number of the sinusoidal vertical interface on average Nu is not evident for a given range of volume fraction.

Homogenization and localization of imperfectly bonded periodic fiber-reinforced composites

An elasticity-based micromechanics model is derived analytically to investigate the homogenized and localized responses of unidirectional composites with imperfect interfaces. To mimic the perturbation of the inclusion positioning caused by the consolidation process, an arbitrarily parallelogram-shaped repeating unit cell (RUC) is developed with periodic boundary conditions. Different from the finite-element/volume approaches which solve a boundary-value problem in the discretized domain, the present work avoids the complicated mesh discretization and instead adopts the Trefftz concept that employs the complete elastic solutions with unknown coefficients to represent the internal trial displacement/stress fields. The solutions of the unknown coefficients are obtained by applying the flexible separation relations along the fiber/matrix interface that govern the interfacial traction reciprocities and displacement discontinuities, as well as the periodic balanced variational principle at the circumference of microstructures. The homogenization equations are then applied to generate the effective properties of composite materials with different architectures over a wide range of fiber volume fractions. In addition to validating the effective properties and underpinning stress fields against other micromechanical techniques in the literature, new results are generated extensively aiming at demonstrating the effects of the interfacial stiffness, radius of fiber and shape of the unit cell on the homogenized and localized composite responses. The analytical framework developed in this communication also facilitates the identification of the interfacial stiffness that minimizes the difference between the effective moduli and targeted material properties through the incorporation of Particle Swarm Optimization algorithm.

A numerical investigation of the heat transfer characteristics of water-based mango bark nanofluid flowing in a double-pipe heat exchanger

In this study, the heat transfer characteristics of a new class of nanofluids made from mango bark was numerically simulated and studied during turbulent flow through a double pipe heat exchanger. A range of volume fractions was considered for a particle size of 100 nm. A two-phase flow was considered using the mixture model. The mixture model governing equations of continuity, momentum, energy and volume fraction were solved using the finite-volume method. The results showed an increase of the Nusselt number by 68% for a Reynolds number of 5,000 and 45% for a Reynolds number of 13 000, and the heat transfer coefficient of the nanofluid was about twice that of the base fluid. In addition, the Nusselt number decreased by an average value of 0.76 with an increase of volume fraction by 1%. It was also found that there was a range of Reynolds numbers in which the trend of the average heat transfer coefficient of the nanofluid was completely reversed, and several plots showing zones of higher heat transfer which if taken advantage of in design will lead to higher heat transfer while avoiding other zones that have low heat transfer. It is hoped that these results will influence the thermal design of new heat exchangers.

Homogenization and localization of elastic-plastic nanoporous materials with Gurtin-Murdoch interfaces: An assessment of computational approaches

This paper critically examines the predictive capabilities of three computational approaches for the elastic-plastic response of nanoporous materials with energetic surfaces simulated with the Gurtin-Murdoch coherent interface model. These approaches involve the classical composite cylinder assemblage model, and the finite-element and generalized finite-volume homogenization theories. Exact elastic-plastic solution to the composite cylinder assemblage under axisymmetric loading is obtained analytically such that all the governing differential equations are satisfied exactly. Hence it is used as gold standard in assessing the predictive capability of the newly developed generalized finite-volume theory with surface and plasticity effects, as well as a comparable finite-element approach, under axisymmetric loading and porosity volume fractions for which pore interactions are small. The assessment includes homogenized response and local stress and plastic strain fields, as well as solution stability issues for surfaces with negative strain energies that limit the range of pore radii and volume fractions of nanoporous materials that may be analyzed. The effect of surface elasticity is shown to be magnified in the elastic-plastic region. Anomalous homogenized response that results from the use of the elastic Gurtin-Murdoch model which impacts limit surface calculations is highlighted. The generalized finite-volume theory is shown to exhibit larger range of pore radii relative to the finite-element based homogenization wherein stable solutions are obtained under both axisymmetric and asymmetric loading of hexagonal and square arrays of porosities with negative strain energies.

Experimental investigation of porous medium structural effects on a coupled porous media-free zone laminar flow

An experimental research program was conducted to investigate the effects of solid volume fraction, arrangement of rods, and rod shape on slow flow through and over two-dimensional model porous media. The porous media were modeled using in-line and staggered arrays of rods of circular and square cross-sections to cover a range of solid volume fraction of 0.06 to 0.49. Each model was installed into a test section so as to fill three-quarters of the total depth of the flow section; and the flow was driven through the test section by pressure. Using a refractive-index matched viscous fluid, the bulk Reynolds numbers for the respective test conditions were kept considerably lower than unity. Particle image velocimetry measurements were made across the streamwise-transverse plane of the test section. Results indicate that the flow through the free zone increases from 75% to nearly 100% as the solid volume fraction increases from 0.06 to 0.49. While the bulk distribution is independent of the shape of the rods, or the mode of arrangement, at the interface, penetration of the free flow is dependent on the solid volume fraction and arrangement of rods. The interfacial flow is predicted by a new formulation from which a boundary condition is derived which unlike others in the literature, is devoid of jumps at the interface. This work provides detailed experimental data and important predictive tools for validations of theoretical and numerical work.

Study of temperature, apparent spectral emissivity, and soot loading of a single burning coal particle using hyper-spectral imaging technique

A hyper-spectral imaging device that can simultaneously capture three-dimensional data information of spectra, space, and time is employed to experimentally investigate the combustion behavior of a single coal particle. Three types of single pulverized coal particles are injected and burned on a Hencken flat-flame burner, and their flames are captured by a high-speed camera and the hyper-spectral imaging device. The camera observations demonstrate that the three single coal particles undergo particle heat-up, volatile release and combustion, and volatile and char oxidation during the combustion process. Furthermore, the image captured by the hyper-spectral imaging device records the spectral and spatial history of the single burning coal particles throughout the combustion process. Then, the time–space temperature and apparent spectral emissivity of the single burning char particles are calculated from the time–space spectra radiative intensity obtained by the hyper-spectral imaging device. The gray characteristic exhibited by the spectral emissivity of the three single burning char particles in the longer wavelength range demonstrates the feasibility of calculating the temperature using the two-color method. Finally, the soot temperature and volume fraction distribution in the volatile flames are obtained to investigate the formation of soot during the combustion of a single coal particle. The results show that an elongated tail-like soot cloud is formed around the two single bituminous coal particles during the combustion process, but a nearly spherical soot cloud is formed around the single lignite coal particle. Moreover, the range of soot volume fractions in the three envelope volatile flames is comparable to the order of magnitude of the values measured by other researchers.

An experimental investigation for study the rheological behavior of water–carbon nanotube/magnetite nanofluid subjected to a magnetic field

This study aims at experimentally investigating the influence of magnetic field on the rheological behavior of water–carbon nanotube (CNT)/magnetite (Fe3O4) nanofluid. Tetramethylammonium hydroxide (TMAH) and Gum arabic (GA) are respectively used to stabilize the nanofluid. Scanning Electron Microscope (SEM), Dynamic Light Scattering (DLS) and X-ray Diffraction (XRD) methods were used to characterize the prepared nanofluid samples. Experiments were performed to evaluate the viscosity of water–CNT/magnetite nanofluid in the shear rate range of 1–100 s−1, volume fraction range of 0.5-1.5%, and magnetic field strength range of 0–480 mT. It was found that the presence of an external magnetic field causes an increase in the viscosity of the water–CNT/magnetite nanofluid. In addition, the results depicted that the viscosity of the nanofluid augments by boosting the concentration of the nano-materials. Moreover, it was reported that increasing the magnetic field strength to more than 360 mT has a negligible influence on the augmentation of nanofluid viscosity. Furthermore, the non-Newtonian shear thinning behavior was depicted because of the decrease in viscosity with intensifying the shear rates.

Fluid medium effect on stresses in suspensions of high-inertia rod-like particles

The rheology of suspensions of high-inertia (or granular) non-spherical particles characterized by high particle Stokes and Reynolds numbers is rarely investigated. In this study, we investigate the rheology of suspensions of inertial rod-like particles of aspect ratio 4 subjected to shear flow. In particular, the effect of fluid medium (air, water) against dry granular simulations on the developed stresses is assessed. CFD-DEM simulations are performed for a periodic shear box for a range of shear rates and volume fractions of particles. The dependence of rheological properties like shear stress, normal stress difference, pressure and relative viscosity on volume fraction, shear rate, granular temperature and the particle orientation are discussed. These results provide insight into the macroscopic rheology of suspensions of rods and demonstrate that the effect of particle shape and surrounding fluid cannot be completely ignored. Air as a fluid medium shows similar scaling as compared to dry granular simulations, but the stress values are generally lower. We observe drastic change in both scaling and values for water as fluid medium. In all cases, the rods show strong alignment in the direction of shear. This study can be further extended to develop stress closures for use in Eulerian flow models.

Prediction of insertion torque and stiffness of a dental implant in bovine trabecular bone using explicit micro-finite element analysis

The assessment of dental implant performance is dominated by the concept of mechanical stability. Primary stability is defined as the capacity of a bone-implant structure to bear loads without occurrence of excessive damage and loosening. In order to achieve the highest primary stability, dental implants are inserted into bone using a press-fit procedure. Pre- and postoperative evaluation of primary stability using implantation torque and resonance frequency analysis are valid approaches but do not allow the systematic comparison of different protocols in similar situations. The aim of this research is to develop and validate an explicit, micro-finite element (μFE) methodology to study the effect of different amounts of initial press-fit on implantation torque and initial stiffness of a dental implant. Ten bovine trabecular bone samples were prepared that cover a wide range of bone volume fraction. A dental implant was inserted using two implantation protocols named soft (small initial drilled hole) and dense (increased initial drilled hole). The implantation torque was measured and the stiffness was calculated using an infinitesimal off-axis loading. Finite element simulations of the implant insertion and subsequent loading were performed on micro-computed tomography (μCT) reconstructions of the samples using an explicit solver. Bone was defined as an elasto-plastic material with von Mises yield criteria and hardening. Element deletion was triggered by a threshold in cumulated plastic strains. A sensitivity analysis was performed on friction, hardening and fracture strain to provide a better insight into the effects of these parameters on the results. The implantation torque required for the soft protocol was higher compared to the dense approach in both experiment and simulation due to the higher amount of bone compaction in the first approach. Interestingly, stiffness did not show a significant dependency on the drilling protocol in both experiment and simulation. In conclusion, the explicit microFE methodology developed in this study was able to capture the outcome of two drilling protocols in terms of torque and stiffness and represents a powerful tool to explore the effect of different parameters on primary stability of dental implants.

Stability of the A15 phase in diblock copolymer melts

The self-assembly of block polymers into well-ordered nanostructures underpins their utility across fundamental and applied polymer science, yet only a handful of equilibrium morphologies are known with the simplest AB-type materials. Here, we report the discovery of the A15 sphere phase in single-component diblock copolymer melts comprising poly(dodecyl acrylate)-block-poly(lactide). A systematic exploration of phase space revealed that A15 forms across a substantial range of minority lactide block volume fractions (fL = 0.25 - 0.33) situated between the σ-sphere phase and hexagonally close-packed cylinders. Self-consistent field theory rationalizes the thermodynamic stability of A15 as a consequence of extreme conformational asymmetry. The experimentally observed A15-disorder phase transition is not captured using mean-field approximations but instead arises due to composition fluctuations as evidenced by fully fluctuating field-theoretic simulations. This combination of experiments and field-theoretic simulations provides rational design rules that can be used to generate unique, polymer-based mesophases through self-assembly.

Influences of Temperature, Concentration and Shear Rate on Rheological Behavior of Nanofluid: An Experimental Study with Al2O3-MWCNT/10W40 Hybrid Nano-Lubricant

In this experimental study, the rheological behavior of Al2O3-MWCNT (90%:10%)/10W40 hybrid nano-lubricant has been determined at the temperature range of 5°C to 55°C. Al2O3 nanoparticles (average size of 50 nm) and MWCNTs (inner and outer diameter of 2-6 nm and 5-20 nm, respectively) were dispersed in engine oil (10W40) to prepare 0.05%, 0.1%, 0.25%, 0.5%, 0.75% and 1% solid volume fractions. For each sample, dynamic viscosity was measured at shear rates ranging from 666.5 s-1 to 13330 s-1 with an uncertainty of about 0.6%. The findings insinuated that at the most range of temperature and solid volume fraction the nano-lubricant, as well as the base oil, are non-Newtonian fluids. Thus, by curve fitting the indexes of power law and consistency were calculated. Eventually, the correlations indicated a very well compromise with experimental data.

Reinforcing Efficiency of Micro and Macro Continuous Polypropylene Fibers in Cementitious Composites

The effect of the microstructure of hydrophilic polypropylene (PP) fibers in the distribution of cracking associated with the strengthening and toughening mechanism of cement-based composites under tensile loading was studied. Using a filament winding system, continuous cement-based PP fiber composites were manufactured. The automated manufacturing system allows alignment of the fiber yarns in the longitudinal direction at various fiber contents. Composites with surface-modified hydrophilic macro-synthetic continuous polypropylene fibers and monofilament yarns with different diameters and surface structures were used. Samples were characterized using the tensile first cracking strength, post-crack stiffness, ultimate strength, and strain capacity. A range of volume fractions of 1–4% by volume of fibers was used, resulting in tensile first cracking strength in the range of 1–7 MPa, an ultimate strength of up to 22 MPa, and a strain capacity of 6%. The reinforcing efficiency based on crack spacing and width was documented as a function of the applied strain using digital image correlation (DIC). Quantitative analysis of crack width and spacing showed the sequential formation and gradual intermittent opening of several active and passive cracks as the key parameters in the toughening mechanism. Results are correlated with the tensile response and stiffness degradation. The mechanical properties, as well as crack spacing and composite stiffness, were significantly affected by the microstructure and dosage of continuous fibers.

Co-Nonsolvency Response of a Polymer Brush: A Molecular Dynamics Study

Using molecular dynamics simulations, we study the response of a polymer brush exposed to co-nonsolvent (CNS), which acts as a preferential solvent for the polymer. We investigate a broad range of attractions between CNS and monomers and of grafting densities over the full range of cosolvent volume fractions. We compare our simulation results with the recently proposed adsorption–attraction model for co-nonsolvency in polymer brushes. The brush layer collapses with increasing CNS concentration into a more compact layer and followed by a reswelling toward sufficiently high CNS concentrations. As the strength of attraction of CNS toward the brush increases, the collapse transition becomes discontinuous. Increasing the grafting density leads to higher sensitivity with respect to CNS but also to a weaker collapse behavior as predicted from the analytical model. In the narrow collapse region, two states of the brush layer coexist, as can be expected from the type-II phase-transition behavior. The coexistence states are identified by analyzing the density profiles. Here, a dense layer is formed at the substrate, which is covered by a swollen layer. Both collapse and coexistence behaviors are even more pronounced in polydisperse brushes, indicating the robust nature of the co-nonsolvency effect in polymer brushes.

A variational method for determining the hydrodynamic parameters of simplified fluidized bed equations

One of the most important parameters in the fluidization process is to determine the minimum fluidization velocity. For this purpose, the conservation equation of momentum in the vertical transport of fluids and solids were used. In this study, the pressure drop term was replaced with Ergun’s equation and the drag force was considered a linear function. The drag coefficient was extremized using the calculus of variations and the relationship between fluidization velocity and voidage was determined. Two test cases with their experimental data were used for validating the presented drag model. Drag functions obtained in previous studies did not match with the empirical data in the bed volume fraction range of 0.45–0.59. The present study reveals that the reason for this difference lies in the use of the Darcy pressure-drop and neglecting the importance of the linear velocity term in the drag model. For vessels of small diameter, the wall effect becomes important. The frictional pressure drop proposed by Ergun is appropriate because this correlation consists of a viscous term. Also, it is expected that by increasing the beds’ voidage, the energy drop decreases. Contrary to Darcy’s model, presented drag model predicts this behavior perfectly.