Volumetric Average Research Articles

Conditional analysis on extreme wall shear stress and heat flux events in compressible turbulent boundary layers

This study presents a comprehensive analysis on the extreme positive and negative events of wall shear stress and heat flux fluctuations in compressible turbulent boundary layers (TBLs) solved by direct numerical simulations. To examine the compressibility effects, we focus on the extreme events in two representative cases, i.e. a supersonic TBL of Mach number $M=2$ and a hypersonic TBL of $M=8$ , by scrutinizing the coherent structures and their correlated dynamics based on conditional analysis. As characterized by the spatial distribution of wall shear stress and heat flux, the extreme events are indicated to be closely related to the structural organization of wall streaks, in addition to the occurrence of the alternating positive and negative structures (APNSs) in the hypersonic TBL. These two types of coherent structures are strikingly different, namely the nature of wall streaks and APNSs are shown to be related to the solenoidal and dilatational fluid motions, respectively. Quantitative analysis using a volumetric conditional average is performed to identify and extract the coherent structures that directly account for the extreme events. It is found that in the supersonic TBL, the essential ingredients of the conditional field are hairpin-like vortices, whose combinations can induce wall streaks, whereas in the hypersonic TBL, the essential ingredients become hairpin-like vortices as well as near-wall APNSs. To quantify the momentum and energy transport mechanisms underlying the extreme events, we proposed a novel decomposition method for extreme skin friction and heat flux, based on the integral identities of conditionally averaged governing equations. Taking advantage of this decomposition method, the dominant transport mechanisms of the hairpin-like vortices and APNSs are revealed. Specifically, the momentum and energy transports undertaken by the hairpin-like vortices are attributed to multiple comparable mechanisms, whereas those by the APNSs are convection dominated. In that, the dominant transport mechanisms in extreme events between the supersonic and hypersonic TBLs are indicated to be totally different.

Dosimetric calibration of GafChromic HD-V2, MD-V3, and EBT3 films for dose ranges up to 100 kGy.

A dosimetric calibration of three types of radiochromic films (GafChromicTM HD-V2, MD-V3, and EBT3) was carried out for absorbed doses (D) ranging up to 100 kGy using a 130 TBq Co60 γ-ray source. The optical densities (ODs) of the irradiated films were acquired with the transmission-mode flatbed film scanner EPSON GT-X980. The calibration data were cross-checked using the 20-MeV proton beam from the azimuthally varying field cyclotron at the Research Center for Nuclear Physics in Osaka University. These experimental results not only present the measurable dose ranges of the films depending on the readout wavelength, but also show consistency with our hypothesis that the OD response curve [log(OD)-log(D) curve] is determined by the volumetric average of the absorption dose and does not strongly depend on the type of radiation for the excitation.

Stochastic Approach to the Solution of Boussinesq-Like Problems in Discrete Media

A vertical surface load acting on a half-space made of discrete and elastic particles is supported by a network of force chains that changes with the specific realization of the packing. These force chains can be transformed into equivalent stress fields, but the obtained values are usually different from those predicted by the unique solution of the corresponding boundary value problem. In this research the relationship between discrete and continuum approaches to Boussinesq-like problems is explored in the light of classical statistical mechanics. In the principal directions of the stress established by the continuum-based approach, the probability distribution functions of the extensive normal and shear stresses of particles are anticipated to be exponential and Laplace distributions, respectively. The extensive stress is the product of the volumetric average of the stress field within a region by the volume of that region. The parameters locating and scaling these probability distribution functions (PDFs) are such that the expected values of the extensive stresses match the solution to the corresponding boundary value problem: zero extensive shear stress and extensive normal stresses equal to the principal ones. The continuum-based approach is still needed to know the expected values, but this research article presents a powerful method for quantifying their expected variability. The theory has been validated through massive numerical simulation with the discrete element method. These results could be of interest in highly fragmented, faulted or heterogeneous media or on small length scales (with particular applications for laboratory testing).

Impact of ionomer film on effective transport properties and performance of cathode catalyst layer of proton-exchange membrane fuel cells

The ionomer films coated over the agglomerate surfaces in the cathode catalyst layer (CL) are an essential component of proton-exchange membrane fuel cells as they provide pathway for protons to move from the membrane to the catalyst sites. Excessive ionomer coating, however, could reduce the space for gaseous oxygen to move and increase the resistances for dissolved oxygen to diffuse. We investigate these using pore-scale modelling and tomography in this paper. Pore-scale models were developed to simulate proton transport and oxygen diffusion in the structure assuming that the proton transport is through the ionomer and gaseous oxygen diffusion is through the secondary pores. The results indicate that the increase of the effective proton conductivity with ionomer content can be fitted to the Bruggeman’s formula. With the ionomer content increasing, the effective gas diffusion coefficient decreases much faster than predicted by the Bruggeman’s formula, which reveals that the interaction between the bulk and Knudsen diffusions at pore scale creates an extra resistance after the volumetric average. We also elucidated the impact of the ionomer films on cell performance and found that the optimal ionomer content is approximately 20% in the model.

Effect of Laser Remelting on Tribological Performance of Ni-Cr-B-Si Coatings Deposited by Laser Metal Deposition

Abstract: Ni-superalloys coatings deposited via laser metal deposition (LMD) have been known to perform well in increasing components lifespan and consequently reducing production and repair costs. Although most of these coatings already present good results in its hardness, and tribological behavior, some can be improved by post-deposition treatments, such as laser remelting. In this ambit, the present paper aims to evaluate the laser remelting posttreatment effects on the Ni-Cr-B-Si coating sliding tribological behavior. For this, two conditions were compared: Ni-Cr-B-Si coating as-deposited and Ni-Cr-B-Si coating as-deposited and remelted. The coating’s occurrence of superficial macro defects, their microhardness, and tribological performance in the pin-on-disk (ASTM G99) test were compared. Friction coefficient (load cell), volumetric loss (optical interferometry), Archard's wear coefficient and worn surfaces (SEM and EDS), were evaluated. Results show that the laser remelting posttreatment was effective in reducing cooling cracks, increasing hardness and reducing friction coefficient oscillation and volumetric loss average.

Approach to Accurate Octane Number Calculation for Gasoline Blending

The octane number of gasoline is one of the most important measures of gasoline quality to predict accurately the octane ratings of blending gasolines. This measured on a scale that ranges from that equivalent to isooctane (octane number of 100) to that of n-heptane (octane number of zero) octane no is effected by the saturates, aromatics, and olefins contents of gasoline. We take it as a standard and measure octane number by comparison with this standard. The accurate octane blending method will optimize the blending of gasoline components, when gasoline components are blended together, we will calculate the octane number of the blend with different octane number of the component or if the four components are of equal octane number. The blend octane number may be greater than, equal to or less than that calculated from the volumetric average of the octane numbers of the blend components, which indicates nonlinear blending. Blending would be linear if octane number of a blend was equal to that predicted by summing the octane numbers of the components in proportion to their concentrations. In practices, the discrepancies between the octane numbers of blends and the linearly predicted values have been correlated by specific empirical equations and these have been used to correct the linear predictions.

Water flow across the interface of contrasting materials: Pressure discontinuity and its implications

Water flow along or across the interfaces of contrasting materials is ubiquitous in hydrology and how to solve them in macroscopic models derived from volumetric average of the pore-scale processes remains elusive. While the change in the average velocity and pressure at water-sediment interface has been well established for channel flow over porous beds, whether a volumetric average alerts the pressure continuity when water flows across the interface of two porous materials is poorly understood despite its imperative implications in hydrological modelling. The primary purpose of this paper is to provide evidences via pore-scale simulations that volumetrically averaging the pore-scale processes indeed yields a discontinuous pressure when water flows across a material interface. We simulated two columns numerically reconstructed by filling them with stratified media: One is an idealised two-layer system and the other one is a 3D column filled by fine glass beads over coarse glass beads with their pore geometry acquired using x-ray computed tomography. The pore-scale simulation is to mimic the column experiment by driving fluid to flow through the void space under an externally imposed pressure gradient. Once fluid flow reaches steady state, its velocity and pressure in all voxels are sampled and they are then spatially averaged over each section perpendicular to the average flow direction. The results show that the average pressure drops abruptly at the material interface no matter which direction the fluid flows. Compared with the effective permeability estimated from the homogenization methods well established in the literature, the emerged discontinuous pressure at the interface reduces the combined ability of the two strata to conduct water. It is also found that under certain circumstances fluid flow is direction-dependant, moving faster when flowing in the fine-coarse direction than in the coarse-to-fine direction under the same pressure gradient. Although significant efforts are needed to incorporate these findings into practical models, we do elicit the emergence of discontinuous pressure at material interface due to volumetric average as well as its consequent implications in modelling of flow in heterogeneous and stratified media.

Thermomechanical formulation for micromechanical elasto-plasticity in granular materials

The aim of this paper is to answer the question: how to construct a thermodynamically consistent micromechanical model and to analyze the existing micromechanical models from an energy perspective. For this purpose, we extended the framework of thermodynamics to micromechanical models by considering the energy stored and dissipated at the inter-particle contacts. In the suggested framework, the Helmholtz free energy and the dissipation energy at the macro scale are equaled to the volumetric average of the Helmholtz free energy and the dissipation energy at the micro scale. Consequently, the elasto-plastic formulation at inter-particle contacts can be obtained from the expressions of the micro free energy and the micro dissipation potentials. A thermodynamically consistent micromechanical model has been constructed on the basis of the static hypothesis. An isotropic compression and several triaxial tests were simulated with the model to analyze the energy conservation and dissipation under loading. Free energy and dissipation energy were computed at both micro and macro scales, and the orientation of the failure plane was explained by the evolution of the local dissipation energy. The maximum micro dissipation energy agreed with the static hypothesis for which, when one direction reaches the limit state, the rupture at the macro scale is obtained. The model has been implemented into a finite element code, and with this code a biaxial compression test was performed. Strain localization appeared, and the orientations of the shear band displayed by either the accumulated deviatoric plastic shear strain or the dissipative energy were consistent.

Pore-scale simulation of gas diffusion in unsaturated soil aggregates: Accuracy of the dusty-gas model and the impact of saturation

Gas diffusions in soil control all physical and biogeochemical processes in terrestrial ecosystems and correctly describing them is critical to numerical modelling of these processes. The movement of gases in soil needs to overcome the resistances caused by both gas-gas collision and gas-wall collision, and the relative significance of one resistance over another depends on the size and spatial distribution of the pores. Practical models often use the empirical dusty-gas formula to estimate the effective gas diffusion coefficient, assuming that all resistances are addable even after a volumetric average. Since it is impossible to separately measure the two resistances, the accuracy and reliability of this approach remains unknown. We investigate this using pore-scale modelling and tomography. Soil aggregates are acquired using X-ray computed tomography and the size and spatial distribution of their pores are calculated using a morphological model; each pore is associated with a bulk diffusion coefficient and a Knudsen diffusion coefficient, with the latter calculated based on the pore size. We then develop pore-scale models to simulate gas diffusion, and the diffusive flux and gas concentration simulated at pore scale are volumetrically averaged to calculate i) the effective Knudsen diffusion coefficient assuming the bulk diffusion coefficient is infinite, ii) the effective bulk diffusion coefficient assuming the Knudsen diffusion coefficient is infinite, and iii) the overall effective diffusion coefficient considering both the bulk and the Knudsen diffusions. The dusty-gas model estimates the effective diffusion coefficient using the effective bulk and the Knudsen diffusion coefficients, and its accuracy is tested against the effective diffusion coefficient directly calculated from the pore-scale simulations. The results indicate that the dusty-gas model is accurate when the diffusion is dominated by either bulk diffusion or Knudsen diffusion, whereas in the transition regime it systematically overestimates the effective diffusion coefficient. We also investigate the impact of saturation on the effective diffusion coefficients when the aggregates are either hydrophobic or hydrophilic, elucidating the significance of the Knudsen diffusion as the saturation of the aggregates increases.

A Simple Correlation for Estimating the Viscosity of Pure Ionic Liquids and Their Binary Mixtures

Ionic liquids (ILs) have been of particular interest to researchers in recent years. Viscosity is considered as one of the most important thermophysical properties of ILs. This paper uses a genetic programming approach to propose a simple equation, with only one parameter to adjust, for predicting the viscosity of pure ILs and their binary mixtures as a function of temperature. The adjustable parameter of the equation was calculated for 103 pure ILs. The average absolute relative deviation of 4.60% obtained for 1374 data points confirms the good accuracy of the model. Also, an acceptable average absolute relative deviation of 12.83% at temperatures outside of the temperature range used to develop the model confirms the reliability of the model in the extrapolation of the temperature effect. To predict the viscosity of the binary mixture of ionic liquids by the proposed equation, the volumetric average of the parameter was applied to the proposed equation without introducing any new adjustable parameter. T...

A multi-scale Lattice Boltzmann model for simulating solute transport in 3D X-ray micro-tomography images of aggregated porous materials

The Lattice Boltzmann (LB) model and X-ray computed tomography (CT) have been increasingly used in combination over the past decade to simulate water flow and chemical transport at pore scale in porous materials. Because of its limitation in resolution and the hierarchical structure of most natural soils, the X-ray CT tomography can only identify pores that are greater than its resolution and treats other pores as solid. As a result, the so-called solid phase in X-ray images may in reality be a grey phase, containing substantial connected pores capable of conducing fluids and solute. Although modified LB models have been developed to simulate fluid flow in such media, models for solute transport are relatively limited. In this paper, we propose a LB model for simulating solute transport in binary soil images containing permeable solid phase. The model is based on the single-relaxation time approach and uses a modified partial bounce-back method to describe the resistance caused by the permeable solid phase to chemical transport. We derive the relationship between the diffusion coefficient and the parameter introduced in the partial bounce-back method, and test the model against analytical solution for movement of a pulse of tracer. We also validate it against classical finite volume method for solute diffusion in a simple 2D image, and then apply the model to a soil image acquired using X-ray tomography at resolution of 30μm in attempts to analyse how the ability of the solid phase to diffuse solute at micron-scale affects the behaviour of the solute at macro-scale after a volumetric average. Based on the simulated results, we discuss briefly the danger in interpreting experimental results using the continuum model without fully understanding the pore-scale processes, as well as the potential of using pore-scale modelling and tomography to help improve the continuum models.

Accurate estimation of mixing time in a direct contact boiling heat transfer process using statistical methods

A novel method relying on image analysis and statistics is developed to estimate the mixing time accurately in a direct-contact heat exchanger. The critical point determination of pseudo homogeneous process impact on the accurate estimation of mixing time is investigated by proposed a three-sigma (3σ) method, which satisfies approximately normal distribution and exceeding the range of μ−3σ occurring twice. Quantitative comparisons of the mixing time are conducted with mean value method, slope method and standard deviation method. Results show that correlation degree and correlation coefficient for the mixing time estimated by 3σ method give good agreement with the volumetric heat transfer coefficient average. Additionally, quasi steady state is quantified by time intervals between inhomogeneous time and mixing time. Experiments and simulations confirmed that neglecting critical point could result in significant errors in mixing time estimation. This method is capable of estimating the mixing time obtained by different mixing curves (e.g., slope p) that vary at the beginning of mixing and rapidly become stabilized after fluctuations, which can be an alternative tool for practical engineering applications with good accuracy.

Studies on Effective Elastic Properties of CNT/Nano-Clay Reinforced Polymer Hybrid Composite

This paper presents a computational approach to predict elastic propertiesof hybrid nanocomposite material prepared by adding nano-clayplatelets to conventional CNT-reinforced epoxy system. In comparison to polymers alone/single-fiber reinforced polymers, if an additional fiber is added to the composite structure, it was found a drastic improvement in resultant properties. In this regard, effective elastic moduli of a hybrid nano composite are determined by using finite element (FE) model with square representative volume element (RVE). Continuum mechanics based homogenization of the nano-filler reinforced composite is considered for evaluating the volumetric average of the stresses and the strains under different periodic boundary conditions.A three phase Halpin-Tsai approach is selected to obtain the analytical result based on micromechanical modeling. The effect of the volume fractions of CNTs and nano-clay platelets on the mechanical behavior is studied. Two different RVEs of nano-clay platelets were used to investigate the influence of nano-filler geometry on composite properties. The combination of high aspect ratio of CNTs and larger surface area of clay platelets contribute to the stiffening effect of the hybrid samples. Results of analysis are validated with Halpin-Tsai empirical formulae.

Modelling water intrusion and oxygen diffusion in a reconstructed microporous layer of PEM fuel cells

The hydrophobic microporous layer (MPL) in PEM fuel cell improves water management but reduces oxygen transport. We investigate these conflict impacts using nanotomography and pore-scale modelling. The binary image of a MPL is acquired using FIB/SEM tomography. The water produced at the cathode is assumed to condense in the catalyst layer (CL), and then builds up a pressure before moving into the MPL. Water distribution in the MPL is calculated from its pore geometry, and oxygen transport through it is simulated using pore-scale models considering both bulk and Knudsen diffusions. The simulated oxygen concentration and flux at all voxels are volumetrically averaged to calculate the effective diffusion coefficients. For water flow, we found that when the MPL is too hydrophobic, water is unable to move through it and must find alternative exits. For oxygen diffusion, we found that the interaction of the bulk and Knudsen diffusions at pore scale creates an extra resistance after the volumetric average, and that the conventional dusty model substantially overestimates the effective diffusion coefficient.

Radiation in [formula omitted]-dimensions

In this paper we discuss the radiation equation of state p=ρ/2 in (2+1)-dimensions. In (3+1)-dimensions the equation of state p=ρ/3 may be used to describe either actual electromagnetic radiation (photons) or a gas of massless particles in a thermodynamic equilibrium (for example neutrinos). In this work it is shown that in the framework of (2+1)-dimensional Maxwell electrodynamics the radiation law p=ρ/2 takes place only for plane waves, i.e. for E=B. Instead of the linear Maxwell electrodynamics, to derive the (2+1)-radiation law for more general cases with E≠B, one has to use a conformally invariant electrodynamics, which is a (2+1)-nonlinear electrodynamics with a trace free energy–momentum tensor, and to perform a volumetric spatial average of the corresponding Maxwell stress–energy tensor with its electric and magnetic components at a given instant of time t.

Quantifying the synergy of bubble swarm patterns and heat transfer performance using computational homology

This paper proposes a novel method to quantify the synergy of bubble swarm patterns and heat transfer performance in a direct-contact heat exchanger (DCHE) by using computational homology. Betti numbers are used to estimate the number of bubbles aggregating in flow patterns and to obtain the pseudo-homogeneous time. A simple linear model of a bubble swarm and the heat transfer performance of a DCHE is constructed on the basis of experimental analysis, in which a new index (βt) is defined by the Betti number average as well as the pseudo-homogeneous time. A good fitting curve between βt and the volumetric heat transfer coefficient average is obtained with a correlation coefficient of 0.95. A paradigm is established on the basis of this novel method for the study of flow patterns and heat transfer performance, and it offers an alternative route to explore the relationship of flow patterns and heat transfer in other heat transfer processes such as convection, multiphase flow, and turbulent flow.

Upscaling of Forchheimer flows

In this work we propose upscaling method for nonlinear Forchheimer flow in heterogeneous porous media. The generalized Forchheimer law is considered for incompressible and slightly-compressible single-phase flows. We use recently developed analytical results (Aulisa et al., 2009) [1] and formulate the resulting system in terms of a degenerate nonlinear flow equation for the pressure with the nonlinearity depending on the pressure gradient. The coarse scale parameters for the steady state problem are determined so that the volumetric average of velocity of the flow in the domain on fine scale and on coarse scale are close. A flow-based coarsening approach is used, where the equivalent permeability tensor is first evaluated following streamline methods for linear cases, and modified in order to take into account the nonlinear effects. Compared to previous works (Garibotti and Peszynska, 2009) [2], (Durlofsky and Karimi-Fard) [3], this approach can be combined with rigorous mathematical upscaling theory for monotone operators, (Efendiev et al., 2004) [4], using our recent theoretical results (Aulisa et al., 2009) [1]. The developed upscaling algorithm for nonlinear steady state problems is effectively used for variety of heterogeneities in the domain of computation. Direct numerical computations for average velocity and productivity index justify the usage of the coarse scale parameters obtained for the special steady state case in the fully transient problem. For nonlinear case analytical upscaling formulas in stratified domain are obtained. Numerical results were compared to these analytical formulas and proved to be highly accurate.

Theory for flow resistance caused by submerged roughness elements

Herein, a phenomenological theory that unifies the flow resistance caused by a variety of submerged bluff bodies, including cylindrical vegetation, two-dimensional dunes and the roughness elements studied in Schlichting's 1936 experiments, is presented. For the different flow obstructions, scaling relations that relate the equivalent roughness length to the obstructions’ spatial dimensions are derived, by adopting the concepts of the turbulent energy cascade and the momentum thickness in the wake of a bluff body. In the derivation, it is hypothesized that the equivalent roughness height represents the volumetric average of the prevailing turbulence length scale that is present in wakes of the roughness elements. A comparison with experimental literature data indicates that the derived scaling relations capture the dominant dependencies of the equivalent roughness length. These expressions have important engineering applications in large-scale flows where employment of more detailed flow-modelling techniques is not feasible.

Research on identification of nonlinear damping based on time frequency analysis

According to the relationship between damping, strain and time, the piecewise linear wavelet transform and the piecewise linear short time Fourier transform methods are put forward to identify the nonlinear damping of alloy material. The overall nonlinear property of damping is derived from the piecewise local linearisation. The satisfied results obtained from simulations demonstrate that the methods presented are effective. Usually, damping measured in the non-uniform stress field is only a volumetric average. To overcome this deficiency, a trapezoid specimen with quasi-uniform stress field is developed on the basis of the traditional damping experimental equipment. The damping measurement experiment is carried out. The measurement signal is analysed by the two methods presented. The relation curve of damping versus strain has shown that the damping capacity of the alloy Al–33Zn–6Si increases with the increasing strain. The relationship between damping and strain appears obviously nonlinear.

Effective non-local reaction kinetics for transport in physically and chemically heterogeneous media

The correct characterization of the effective reactive transport dynamics is an important issue for modeling reactive transport on the Darcy scale, specifically in situations in which reactions are localized, that is when different reactions occur in different portions of the porous medium. Under such conditions the conventional approach of homogenizing only the porous medium chemistry is not appropriate. We consider here reactive transport in a porous medium that is characterized by mass transfer between a mobile and a distribution of immobile regions. Chemical and physical heterogeneities are reflected by distributions of kinetic reaction rate constants and residence times in the immobile zones. We derive an effective reactive transport equation for the mobile solute that is characterized by non-local physical mass transfer and reaction terms. Specifically, chemical heterogeneity is upscaled in terms of a reactive memory function that integrates both chemical and physical heterogeneity. Mass transfer limitations due to physical heterogeneity yield effective kinetic rate coefficients that can be much smaller than the volumetric average of the local scale coefficients. These results help to explain and quantify the often reported discrepancy between observed field reaction rate constants and the ones obtained under well mixed laboratory conditions. Furthermore, these results indicate that transport under physical and chemical heterogeneity cannot be upscaled separately.