Entropy productions in granular materials

Granular materials display more abundant dissipation phenomena than ordinary materials. In this paper, a brief energy flow path with irreversible processes is illustrated, where the concept of granular temperature T_g, initially proposed for dilute systems, is extended to dense systems in order to quantify disordered force chain configurations. Additionally, we develop the concept of conjugate granular entropy s_g and its production equation. Our analyses find out that the granular entropy significantly undermined the elastic contact between particles, seriously affecting the transport coefficients in granular materials and creating new transport processes.     

Finite deformation thermo-mechanical behavior of thermally induced shape memory polymers

Shape memory polymers (SMPs) are polymers that can demonstrate programmable shape memory effects. Typically, an SMP is pre-deformed from an initial shape to a deformed shape by applying a mechanical load at the temperature T_H>T_g. It will maintain this deformed shape after subsequently lowering the temperature to T_L<T_g and removing the externally mechanical load. The shape memory effect is activated by increasing the temperature to T_D>T_g, where the initial shape is recovered. In this paper, the finite deformation thermo-mechanical behaviors of amorphous SMPs are experimentally investigated. Based on the experimental observations and an understanding of the underlying physical mechanism of the shape memory behavior, a three-dimensional (3D) constitutive model is developed to describe the finite deformation thermo-mechanical response of SMPs. The model in this paper has been implemented into an ABAQUS user material subroutine (UMAT) for finite element analysis, and numerical simulations of the thermo-mechanical experiments verify the efficiency of the model. This model will serve as a modeling tool for the design of more complicated SMP-based structures and devices.     

Scalar Dissipation Rate Transport in the Context of Large Eddy Simulations for Turbulent Premixed Flames with Non-Unity Lewis Number

The effects of global Lewis number Le on the statistical behaviour of the unclosed terms in the transport equation of the Favre-filtered scalar dissipation rate (SDR) Ñ _c have been analysed using a Direct Numerical Simulation (DNS) database of freely propagating statistically planer turbulent premixed flames with Le ranging from 0.34 to 1.2. The DNS data has been explicitly filtered to analyse the statistical behaviour of the unclosed terms in the SDR transport equation arising from turbulent transport T ₁, density variation due to heat release T ₂, scalar-turbulence interaction T ₃, reaction rate gradient T ₄, molecular dissipation (?D ₂) and diffusivity gradients f(D) in the context of Large Eddy Simulations (LES). It Le has significant effects on the magnitudes of T ₁, T ₂, T ₃, T ₄, (?D ₂) and f(D). Moreover, both qualitative and quantitative behaviours of the unclosed terms T ₁, T ₂, T ₃, T ₄, (?D ₂) and f(D) are found to be significantly affected by the LES filter width Δ, which have been explained based on a detailed scaling analysis. Both scaling analysis and DNS data suggest that T ₂, T ₃, T ₄, (?D ₂) and f(D) remain leading order contributors to the SDR \(\tilde {{N}}_{c} \) transport for LES. The scaling estimates of leading order contributors to the SDR \(\tilde {{N}}_{c} \) transport has been utilised to discuss the possibility of extending an existing SDR model for Reynolds Averaged Navier Stokes (RANS) simulation for SDR \(\tilde {{N}}_{c} \) closure in the context of LES of turbulent premixed combustion.     

Statistical Analysis of Cross Scalar Dissipation Rate Transport in Turbulent Partially Premixed Flames: A Direct Numerical Simulation Study

Statistically planar turbulent partially premixed flames for different initial intensities of decaying turbulence have been simulated for global equivalence ratios <????> = 0.7 and <????> = 1.0 using three-dimensional simplified chemistry based Direct Numerical Simulations (DNS). The simulation parameters are chosen such that the combustion situation belongs to the thin reaction zones regime and a random bi-modal distribution of equivalence ratio ?? is introduced in the unburned gas ahead of the flame to account for mixture inhomogeneity. The DNS data has been used to analyse the statistical behaviour of the transport of the cross-scalar dissipation rate based on the fuel mass fraction Y _F and the mixture fraction ?? fluctuations $\,\tilde{\varepsilon}_{Y\xi}={\overline{\rho D\nabla Y_{F}^{\prime\prime}.\nabla \xi^{\prime\prime}} } \big/ {\bar {\rho }}$ (where $\bar{q}$ , $\tilde{q}={\overline{\rho q} } \big/ {\bar {\rho }}$ and $q^{\prime\prime} =q-\tilde {q}$ are Reynolds average, Favre mean and Favre fluctuation of a general quantity q) in the context of Reynolds Averaged Navier?CStokes simulations where ?? is the gas density and D is the gas diffusivity. The statistical behaviours of the unclosed terms in the $\tilde{\varepsilon }_{Y\xi } $ transport equation originating from turbulent transport T ₁, density variation T ₂, scalar?Cturbulence interaction T ₃, chemical reaction rate T ₄ and the molecular dissipation rate D ₂ have been analysed in detail. It has been observed that the contributions of T ₂, T ₃, T ₄ and D ₂ play important roles in the $\tilde{\varepsilon }_{Y\xi } $ transport for the globally stoichiometric cases, but in the globally fuel-lean cases the contributions of T ₂ and T ₄ become relatively weaker in comparison to the contributions of T ₃ and D ₂. The term T ₁ remains small in comparison to the leading order contributions of T ₃ and D ₂ for all cases, but the contribution of T ₁ plays a more important role in the low Damköhler combustion cases. The term T ₂ behaves as a sink term towards the unburned gas side but becomes a source term towards the burned gas side. The scalar?Cturbulence interaction term T ₃ has been found to be generally positive throughout the flame brush, but in globally stoichiometric cases the contribution of T ₃ becomes negative in regions of intense heat release. The combined contribution of (T ₄ ?C D ₂) remains mostly as a sink in all cases studied here. Models are proposed for the unclosed terms of the $\tilde{\varepsilon }_{Y\xi } $ transport equation in the context of Reynolds Averaged Navier?CStokes simulations, which are shown to satisfactorily predict the corresponding quantities extracted from the DNS data for all cases.     

Quantitative In Situ Enhanced Oil Recovery Monitoring Using Nuclear Magnetic Resonance

Quantitative in situ monitoring of oil recovery from sedimentary rock is demonstrated for the first time using advanced two-dimensional (2D) nuclear magnetic resonance (NMR) correlation measurements on a low field spectrometer. The laboratory-scale NMR system was chosen to provide a common physics of measurement with NMR well-logging tools. The NMR protocols are used to monitor recovery of a heavy Middle East crude oil from high permeability sandstone plugs using a brine (water) flood followed by chemical enhanced oil recovery agents: polymer and alkaline?Csurfactant?Cpolymer solutions. 2D correlations between relaxation time (T ₁, T ₂) and apparent self-diffusion coefficient D _app are used to obtain simultaneously a volumetric determination of the oil and aqueous fluid-phase saturations present in the porous material. The T ₁ ? T ₂ and D _app ? T ₂ correlations are bulk measurements of the entire rock core-plug; excellent agreement is shown between the measures of remaining oil (from NMR) and recovered oil (from gravimetric assay of the effluent). Furthermore, we introduce the capability to measure spatially resolved T ₂ distributions on a low field spectrometer using a rapid frequency-encoded y ? T ₂ map. A non-uniform distribution of remaining oil is observed due to viscous instabilities in the flowing liquids; the final oil saturation ranges from ${S_{\rm o}^{\rm{(final)}} \approx 0}$ to 20?% along the direction of flow. These results highlight the quantitative nature of the NMR data obtainable in low field NMR core analysis and also the importance of spatially resolved measurements when studying short core-plugs.     

Instability of small-amplitude convective flows in a rotating layer with free boundaries

The stability of steady convective flows in a horizontal layer with free boundaries, heated from below and rotating about a vertical axis, is studied in the Boussinesq approximation (Rayleigh-Bénard convection). The flows considered are convective rolls or square cells that are sums of two perpendicular rolls with equal wave numbers k. It is assumed that the Rayleigh number is almost critical in order for convective flows with a wave number k: R = R _c (k) + ε² to arise, the amplitude of the supercritical states being of the order of ε. It is shown that the flows are always unstable relative to perturbations that are the sum of one long-and two short-wave modes corresponding to linear rolls turned through small angles in opposite directions.     

Wavelet spatial scaling for educing dynamic structures in turbulent open cavity flows

In this work a methodology was developed for the selection of wavelet spatial scales to educe dynamic structures in turbulent cavity flows. The wavelet transform was applied to both the temporal signal and spatial fields to extract structures from the oscillating shear layer. The dominant frequencies were identified from the temporal transform of the shear layer oscillations, and then the corresponding wavelength was obtained using the relation U_cT=λ at each frequency. The wavelet spatial scaling was examined and a one-to-one relationship was established with respect to the wavelength. At each spatial scale, the transformed images of vorticity, velocity, and pressure fluctuations captured the vortical structures. Using this methodology, the dynamic vortical structures were extracted from the turbulent open cavity flows. Energy analysis was performed to examine the contributions of each structure.     

Large-eddy simulation of thermal fatigue in a mixing tee

Temperature fluctuations occur due to thermal mixing of hot and cold streams in the T-junctions of the piping system in nuclear power plants, which may cause thermal fatigue of piping system. In this paper, three-dimensional, unsteady numerical simulations of coolant temperature fluctuations at a mixing T-junction of equal diameter pipes were performed using the large eddy simulation (LES) turbulent model. The experiments used in this paper to benchmark the simulations were performed by Hitachi Ltd. The calculated normalized mean temperatures and fluctuating temperatures are in good agreement with the measurements. The influence of the time-step ranging from 100 Hz to 1000 Hz on the numerical simulation results was explored. The simulation results indicate that all the results with different frequencies agree well with the experimental data. Finally, the attenuation of fluctuation of fluid temperature was also investigated. It is found that, drastic fluctuation occurs within the range of less than L/D = 4.0; the fluctuation of fluid temperature does not always attenuate from the pipe center to the wall due to the continuous generation of vortexes. At the top wall, the position of L/D = 1.5 has a minimum normalized mean temperature and a peak value of root-mean square temperature, whereas at the bottom wall, the position having the same characteristics is L/D = 2.0.     

DEM simulation of particle mixing in a sheared granular flow

Mixing behaviors of particles are simulated in a sheared granular flow using differently colored but otherwise identical glass spheres, with five different bottom wall velocities. By DEM simulation, the solid fractions, velocities, velocity fluctuations and granular temperatures are measured.The mixing layer thicknesses are compared with the calculations from a simple diffusion equation using the data of apparent self-diffusion coefficients obtained from the current simulation measurements. The calculations and simulation results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.     

DEM simulation of particle mixing in a sheared granular flow

Mixing behaviors of particles are simulated in a sheared granular flow using differently colored but otherwise identical glass spheres, with five different bottom wall velocities. By DEM simulation, the solid fractions, velocities, velocity fluctuations and granular temperatures are measured. The mixing layer thicknesses are compared with the calculations from a simple diffusion equation using the data of apparent self-diffusion coefficients obtained from the current simulation measurements. The calculations and simulation results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.     

Particle resolved direct numerical simulation of a liquid–solid fluidized bed: Comparison with experimental data

Particle-resolved direct numerical simulations of a 3-D liquid–solid fluidized bed experimentally investigated by Aguilar-Corona (2008) have been performed at different fluidization velocities (corresponding to a range of bed solid volume fraction between 0.1 and 0.4), using Implicit Tensorial Penalty Method. Particle Reynolds number and Stokes number are O(100) and O(10), respectively. In this paper, we compare the statistical quantities computed from numerical results with the experimental data obtained with 3-D trajectography and High Frequency PIV. Fluidization law predicted by the numerical simulations is in very good agreement with the experimental curve and the main features of trajectories and Lagrangian velocity signal of the particles are well reproduced by the simulations. The evolution of particle and flow velocity variances as a function of bed solid volume fraction is also well captured by the simulations. In particular, the numerical simulations predict the right level of anisotropy of the dispersed phase fluctuations and its independence of bed solid volume fraction. They also confirm the high value of the ratio between the fluid and the particle phase fluctuating kinetic energy. A quick analysis suggests that the fluid velocity fluctuations are mainly driven by fluid–particle wake interactions (pseudo-turbulence) whereas the particle velocity fluctuations derive essentially from the large scale flow motion (recirculation). Lagrangian autocorrelation function of particle fluctuating velocity exhibits large-scale oscillations, which are not observed in the corresponding experimental curves, a difference probably due to a statistical averaging effect. Evolution as a function of the bed solid volume fraction and the collision frequency based upon transverse component of particle kinetic energy correctly matches the experimental trend and is well fitted by a theoretical expression derived from Kinetic Theory of Granular Flows.     

APPLICATION OF A MODIFIED k–ε MODEL TO THE PREDICTION OF AERODYNAMIC CHARACTERISTICS OF RECTANGULAR CROSS-SECTION CYLINDERS

Aerodynamic characteristics of rectangular cylinders of infinite length and various breadth-to-depth ratios ranging from B/D=0·6 to 8·0 were investigated numerically by a two-layerk –ε model with a modified k -production term. Although the numerical method is two-dimensional (2-D), a physically reasonable smooth, periodic vortex shedding was obtained, even in the range of high Reynolds number. This kind of behaviour cannot normally be simulated by ordinary 2-D analyses which do not incorporate a turbulence model. Various typical aerodynamic features were successfully obtained, particularly including the discontinuity in Strouhal number at the critical section of B/D=2·8 and 6·0. Also, drag coefficients and distributions of mean surface pressure were in good agreement with results of experiments and 3-D analyses for the range of B/D ratios. However, as regards the prediction of pressure and force fluctuations, since the currently available Reynolds-Averaged Navier–Stokes models are able to analyse only periodic components and not stochastic components, the total fluctuations in surface pressure and aerodynamic lift force were considerably underestimated in some cases, compared with those measured in experiments and calculated from 3-D analyses.     

A critical re-appraisal of the jet-thrust technique for normal stresses,with particular reference to axial velocity and stress rearrangement at the exit plane

It is shown that the thrust, T, exerted by a jet on the tube from which it flows, and the corresponding die-swell ratio, D, are closely related and dependent on the axial velocity and stress profiles at the exit plane. Velocity-profile data, calculated by Tanner using a finite element method, have been used to demonstrate that for a Newtonian liquid the reduction in measured thrust from the expected value arises from a re-arranged, non-parabolic axial velocity profile and the related re-arranged non-zero axial stress profile at the exit plane. The axial stress re-arrangement is the major effect.Using the correction-curve thus derived to determine the normal stresses, ν₁ + $\text{1}\text{2}$ν₂ aqueous and non-aqueous polymer solutions gives values that are higher than the “correct” results by a significant, substantial amount. The difference is not due to neglect of the second normal stress difference, ν₂, nor to the neglect of the wall pressure at the exit plane, which is shown experimentally to be very small. It is suggested that the difference, which is a function only of the shear stress (or rate of shear) at the wall, may arise from a difference in the stress profile associated with the velocity re-arrangement at the exit between Newtonian liquids and elasticoviscous liquids for which the extensional viscosity may be high.     

Trapping and escape of dislocations in micro-crystals with external and internal barriers

We perform three-dimensional dislocation dynamics simulations of solid and annular pillars, having both free-surface boundary conditions, or strong barriers at the outer and/or inner surfaces. Both pillar geometries are observed to exhibit a size effect where smaller pillars are stronger. The scaling observed is consistent with the weakest-link activation mechanism and depends on the solid pillar diameter, or the annular pillar effective diameter, D_eff = D − D_i, where D and D_i are the external and internal diameters of the pillar, respectively. An external strong barrier is observed to dramatically increase the dislocation density by an order of magnitude due to trapping dislocations at the surface. In addition, a considerable increase in the flow strength, by up to 60%, is observed compared to simulations having free-surface boundary conditions. As the applied load increases, weak spots form on the surface of the pillar by dislocations breaking through the surface when the RSS is greater than the barrier strength. The hardening rate is also observed to increase with increasing barrier strength. With cross-slip, we observe dislocations moving to other glide planes, and sometimes double-cross-slipping, producing a thickening of the slip traces at the surface. Finally the results are in qualitative agreement with recent compression experimental results of coated and centrally-filled micropillars.     

An improved anisotropy-resolving subgrid-scale model for flows in laminar–turbulent transition region

Some types of mixed subgrid-scale (SGS) models combining an isotropic eddy-viscosity model and a scale-similarity model can be used to effectively improve the accuracy of large eddy simulation (LES) in predicting wall turbulence. Abe (2013) has recently proposed a stabilized mixed model that maintains its computational stability through a unique procedure that prevents the energy transfer between the grid-scale (GS) and SGS components induced by the scale-similarity term. At the same time, since this model can successfully predict the anisotropy of the SGS stress, the predictive performance, particularly at coarse grid resolutions, is remarkably improved in comparison with other mixed models. However, since the stabilized anisotropy-resolving SGS model includes a transport equation of the SGS turbulence energy, k_SGS, containing a production term proportional to the square root of k_SGS, its applicability to flows with both laminar and turbulent regions is not so high. This is because such a production term causes k_SGS to self-reproduce. Consequently, the laminar–turbulent transition region predicted by this model depends on the inflow or initial condition of k_SGS. To resolve these issues, in the present study, the mixed-timescale (MTS) SGS model proposed by Inagaki et al. (2005) is introduced into the stabilized mixed model as the isotropic eddy-viscosity part and the production term in the k_SGS transport equation. In the MTS model, the SGS turbulence energy, k_es, estimated by filtering the instantaneous flow field is used. Since the k_es approaches zero by itself in the laminar flow region, the self-reproduction property brought about by using the conventional k_SGS transport equation model is eliminated in this modified model. Therefore, this modification is expected to enhance the applicability of the model to flows with both laminar and turbulent regions. The model performance is tested in plane channel flows with different Reynolds numbers and in a backward-facing step flow. The results demonstrate that the proposed model successfully predicts a parabolic velocity profile under laminar flow conditions and reduces the dependence on the grid resolution to the same degree as the unmodified model by Abe (2013) for turbulent flow conditions. Moreover, it is shown that the present model is effective at transitional Reynolds numbers. Furthermore, the present model successfully provides accurate results for the backward-facing step flow with various grid resolutions. Thus, the proposed model is considered to be a refined anisotropy-resolving SGS model applicable to laminar, transitional, and turbulent flows.     

Modeling of vibration-dissociation oxygen kinetics at temperatures of 4,000-11,000 K

The time profiles of vibrational molecular oxygen temperature T _v measured earlier in experiments behind a strong shock wave were used for testing the theoretical and empirical models of thermal nonequilibrium dissociation of molecules. To do this, dissociating gas flows behind the strong shock wave front were calculated with account for these models. If the initial gas temperature behind the wave front T ₀ < 6.5×10³ K, the models well describe changing the temperature with time. However, for T ₀ > 7×10³ K neither of the models tested describes the measured temperature profiles satisfactorily. Using the empirical model proposed in the present study made it possible to satisfactorily describe the vibrational temperature evolution observed in experiments at temperatures up to 11×10³ K.     

Proper orthogonal decomposition of wall-pressure fluctuations under the constrained wake of a square cylinder

The proper orthogonal decomposition (POD) analysis of the wall-pressure fluctuations below the constrained wake of a two-dimensional square cylinder in proximity to a plane wall was made on two systems, i.e., G/D = 0.25 and 0.5, which corresponds to the wakes with and without suppression of the vortex shedding, respectively. Here, G is the gap distance and D is the width of the square cylinder. Synchronized measurements of wall-pressure fluctuations were made using a microphone array. For the system G/D = 0.5, the first two energetic modes contribute 34.7% and 23.4% to the total fluctuation energy, respectively; however, the fluctuation energy corresponding to the third mode are relatively small and less than 10%. This sharp variation in eigenvalue is due to the presence and dominance of the Karman-like vortex shedding. However, for the system G/D = 0.25, the considerable reduction in the eigenvalues of the first several modes is due to the suppression of the Karman-like vortex shedding. The spatial wavy pattern of the first several energetic eigenmodes was shown to be a good reflection of convective vortices superimposed in the wakes. The spectra of the POD coefficients determined the frequency of the dominant structures. Based on the coherence of the POD coefficients, an effective method of determining the number of POD modes for reconstruction of the low-order wall-pressure field was proposed. Accordingly, the low-order wall-pressure fluctuations in the systems G/D = 0.5 and 0.25 were reconstructed by using the first four and five POD modes, respectively. The coherence and cross-correlation analysis of the reconstructed wall-pressure fluctuations, which excluded the influence of the small-scale structures and background ‘noise’, gave an insight view of the footprints of the dominant flow structures, which otherwise could not be effectively captured by using the original wall-pressure fluctuations.     

Numerical study of oscillating boundary layer flow over a flat plate using k–kL–ω turbulence model

Oscillating boundary layer flow over an infinite flat plate at rest was simulated using the k–k_L–ω turbulence model for a Reynolds number range of 32 ⩽ Re_δ ⩽ 10,000 ranging from fully laminar flow to fully turbulent flow. The k–k_L–ω model was validated by comparing the predictions with LES results and experimental results for intermittently turbulent and fully turbulent flow regimes. The good agreement obtained between the k–k_L–ω model prediction with the experimental and LES results indicate that the k–k_L–ω model is able to accurately simulate transient intermittently turbulent flow and as well as accurately predict the onset of turbulence for such oscillatory flows.     

Numerical investigations of drop solidification on a cold plate in the presence of volume change

We present a front-tracking/finite difference method for simulation of drop solidification on a cold plate. The problem includes temporal evolution of three interfaces, i.e. solid–liquid, solid–gas, and liquid–gas, that are explicitly tracked under the assumption of axisymmetry. Method validation is carried out by comparing computational results with exact solutions for a two-dimensional Stefan problem, and with related experiments. We then use the method to investigate a drop solidifying on a cold plate in which there exists volume change due to density difference between the solid and liquid phases. Numerical results show that the shape of the solidified drop is profoundly different from the initial liquid one due to the effects of volume change and the tri-junction in terms of growth angles ϕ_gr on the solidification process. A decrease in the density ratio of solid to liquid ρ_sl or an increase in the growth angle results in an increase in the height of the solidified drop. The solidification process is also affected by the Stefan number St, the Bond number Bo, the Prandtl number Pr, the Weber number We, the ratios of the thermal properties of the solid to liquid phases k_sl and C_psl. Increasing St, Bo, Pr, We, or k_sl decreases the solidified drop height and the time to complete solidification. Moreover, the solidification growth rate is strongly affected by St, k_sl and C_psl. An increase in any of these parameters hastens the growth rate of the solidification interface. Contrarily, increasing ρ_sl decreases the growth rate. However, other parameters such as ϕ_gr, Bo, Pr and We have minor effects on the solidification growth rate.