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The physico-chemical processes and individual factors affecting the uniformity of the mix both when the mix components are being mixed in a mixer in a sectional line and when the mix is transported and loaded into a glass-making f...
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The physico-chemical processes and individual factors affecting the uniformity of the mix both when the mix components are being mixed in a mixer in a sectional line and when the mix is transported and loaded into a glass-making furnace are analyzed. The effect of moistening on mix quality in obtaining glass mix and transporting and loading the mix into the furnace by means of mix loaders is determined. The temperature factors ensuring that the mix temperature when the mix is loaded into the furnace is no lower than 35 – 40℃ are determined. The degree to which mix is removed with respect to both quantity and individual components on the loading hopper and regenerators along the glass-making furnace is determined. The direction for further research on optimizing the mix preparation process in order to increase the operational efficiency of a glass-making furnace is proposed on the basis of the results obtained in the present work.
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We study the mixed Hodge theoretic aspects of the B-model side of local mirror symmetry. Our main objectives are to define an analogue of the Yukawa coupling in terms of the variations of the mixed Hodge structures and to study it...
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We study the mixed Hodge theoretic aspects of the B-model side of local mirror symmetry. Our main objectives are to define an analogue of the Yukawa coupling in terms of the variations of the mixed Hodge structures and to study its properties. We also describe a local version of Bershadsky-Cecotti-Ooguri-Vafa's holomorphic anomaly equation.
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A model is developed for describing mixing of several species under high-pressure conditions. The model includes the Peng-Robinson equation of state, a full massdiffusion matrix, a full thermal-diffusion-factor matrix necessary to...
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A model is developed for describing mixing of several species under high-pressure conditions. The model includes the Peng-Robinson equation of state, a full massdiffusion matrix, a full thermal-diffusion-factor matrix necessary to incorporate the Soret and Dufour effects and both thermal conductivity and viscosity computed for the species mixture using mixing rules. Direct numerical simulations (DNSs) are conducted in a temporal mixing layer configuration. The initial mean flow is perturbed using an analytical perturbation which is consistent with the definition of vorticity and is divergence free. Simulations are performed for a set of five species relevant to hydrocarbon combustion and an ensemble of realizations is created to explore the effect of the initial Reynolds number and of the initial pressure. Each simulation reaches a transitional state having turbulent characteristics and most of the data analysis is performed on that state. A mathematical reformulation of the flux terms in the conservation equations allows the definition of effective species-specific Schmidt numbers.Sc/ and of an effective Prandtl number.Pr/ based on effective speciesspecific diffusivities and an effective thermal conductivity, respectively. Because these effective species-specific diffusivities and the effective thermal conductivity are not directly computable from the DNS solution, we develop models for both of these quantities that prove very accurate when compared with the DNS database. For two of the five species, values of the effective species-specific diffusivities are negative at some locations indicating that these species experience spinodal decomposition; we determine the necessary and sufficient condition for spinodal decomposition to occur. We also show that flows displaying spinodal decomposition have enhanced vortical characteristics and trace this aspect to the specific features of high-density-gradient magnitude regions formed in the flows. The largest values of the effective speciesspecific Sc numbers can be well in excess of those known for gases but almost two orders of magnitude smaller than those of liquids at atmospheric pressure. The effective thermal conductivity also exhibits negative values at some locations and the effective Pr displays values that can be as high as those of a liquid refrigerant. Examination of the equivalence ratio indicates that the stoichiometric region is thin and coincides with regions where the mixture effective species-specific Lewis number values are well in excess of unity. Very lean and very rich regions coexist in the vicinity of the stoichiometric region. Analysis of the dissipation indicates that it is dominated by mass diffusion, with viscous dissipation being the smallest among the three dissipation modes. The sum of the heat and species (i.e. scalar) dissipation is functionally modelled using the effective species-specific diffusivities and the effective thermal conductivity. Computations of the modelled sum employing the modelled effective species-specific diffusivities and the modelled effective thermal conductivity shows that it accurately replicates the exact equivalent dissipation.
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The dissipation rate, ε_θ, of a passive scalar (temperature in air) emitted from a concentrated source into a fully developed high-aspect-ratio turbulent channel flow is studied. The goal of the present work is to investigate th...
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The dissipation rate, ε_θ, of a passive scalar (temperature in air) emitted from a concentrated source into a fully developed high-aspect-ratio turbulent channel flow is studied. The goal of the present work is to investigate the return to isotropy of the scalar field when the scalar is injected in a highly anisotropic manner into an inhomogeneous turbulent flow at small scales. Both experiments and direct numerical simulations (DNS) were used to study the downstream evolution of ε_θ for scalar fields generated by line sources located at the channel centreline (y_s/h = 1.0) and near the wall (y_s/h = 0.17). The temperature fluctuations and temperature derivatives were measured by means of a pair of parallel cold-wire thermometers in a flow at Re_τ = 520. The DNS were performed at Re_τ = 190 using a spectral method to solve the continuity and Navier-Stokes equations, and a flux integral method (Germaine, Mydlarski & Cortelezzi, J. Comput. Phys., vol. 174, 2001, pp. 614-648) for the advection-diffusion equation. The statistics of the scalar field computed from both experimental and numerical data were found to be in good agreement, with certain discrepancies that were attributable to the difference in the Reynolds numbers of the two flows. A return to isotropy of the small scales was never perfectly observed in any region of the channel for the downstream distances studied herein. However, a continuous decay of the small-scale anisotropy was observed for the scalar field generated by the centreline line source in both the experiments and DNS. The scalar mixing was found to be more rapid in the near-wall region, where the experimental results exhibited low levels of small-scale anisotropy. However, the DNS, which were performed at lower Re_τ, showed that persistent anisotropy can also exist near the wall, independently of the downstream location. The role of the mean velocity gradient in the production of ε_θ (and therefore anisotropy) in the near-wall region was highlighted.
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An elegant model for passive scalar mixing and decay was given by Kraichnan (Phys. Fluids, vol. 11, 1968, pp. 945-953) assuming the velocity to be delta correlated in time. For realistic random flows this assumption becomes invali...
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An elegant model for passive scalar mixing and decay was given by Kraichnan (Phys. Fluids, vol. 11, 1968, pp. 945-953) assuming the velocity to be delta correlated in time. For realistic random flows this assumption becomes invalid. We generalize the Kraichnan model to include the effects of a finite correlation time, tau, using renewing flows. The generalized evolution equation for the three-dimensional (3-D) passive scalar spectrum ((M) over capk,t) or its correlation function M(r, t), gives the Kraichnan equation when tau -> 0, and extends it to the next order in tau. It involves third-and fourth-order derivatives of M or (M) over cap (in the high k limit). For small-tau (or small Kubo number), it can be recast using the Landau-Lifshitz approach to one with at most second derivatives of (M) over cap. We present both a scaling solution to this equation neglecting diffusion and a more exact solution including diffusive effects. To leading order in tau, we first show that the steady state 1-D passive scalar spectrum, preserves the Batchelor (J. Fluid Mech., vol. 5, 1959, pp. 113-133) form, E-theta(k) proportional to k(-1), in the viscous-convective limit, independent of tau. This result can also be obtained in a general manner using Lagrangian methods. Interestingly, in the absence of sources, when passive scalar fluctuations decay, we show that the spectrum in the Batchelor regime at late times is of the form E-theta(k) proportional to k(1/2) and also independent of tau. More generally, finite tau does not qualitatively change the shape of the spectrum during decay. The decay rate is however reduced for finite tau. We also present results from high resolution (1024(3)) direct numerical simulations of passive scalar mixing and decay. We find reasonable agreement with predictions of the Batchelor spectrum during steady state. The scalar spectrum during decay is however dependent on initial conditions. It agrees qualitatively with analytic predictions when power is dominantly in wavenumbers corresponding to the Batchelor regime, but is shallower when box-scale fluctuations dominate during decay.
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We upscale reactive mixing using effective dispersion coefficients to capture the combined effect of pore-scale heterogeneity and molecular diffusion on the evolution of the mixing interface between two initially segregated dissol...
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We upscale reactive mixing using effective dispersion coefficients to capture the combined effect of pore-scale heterogeneity and molecular diffusion on the evolution of the mixing interface between two initially segregated dissolved species. Effective dispersion coefficients are defined in terms of the average spatial variance of the solute distribution evolving from a pointlike injection, that is, the transport Green function. We numerically investigate the temporal behavior of the longitudinal effective dispersion coefficients for two porous media of different pore-scale heterogeneity as measured by the statistics of the flow speed, and different Peclet numbers. We find that the effective dispersion coefficients evolve with time, or equivalently travel distance. As the solute samples the pore-scale flow heterogeneity due to advection and transverse diffusion, the effective dispersion coefficients evolve from the value of molecular diffusion to the corresponding hydrodynamic dispersion coefficients. Thus, at times smaller than the diffusion time over a characteristic pore length, the effective dispersion coefficients can be significantly smaller than the hydrodynamic dispersion coefficients. This difference can explain frequently observed mismatches between pore-scale reactive mixing data, and predictions using Darcy scale transport descriptions based on hydrodynamic dispersion coefficients that are constant in time. This suggests that the notion of incomplete mixing on the support scale can be quantified in terms of effective pore-scale dispersion coefficients. We use effective dispersion in order to approximate the transport Green function in terms of a Gaussian-shaped distribution that is characterized by the effective variance. This is approximation is termed dispersive lamella. Based on this representation, we study reactive mixing between two initially segregated solutes. The dispersive lamella approach accurately predicts the evolution of the product mass of an instantaneous bimolecular reaction obtained from direct numerical simulations. This demonstrates that effective dispersion is an accurate measure for width of the mixing interface between the two reacting species. These results shed some new light on pore-scale mixing, the notion of incomplete mixing, and its prediction and upscaling in terms of an effective mixing model.
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We derive a growth-rate model for the Richtmyer–Meshkov mixing layer, given arbitrary but known initial conditions. The initial growth rate is determined by the net mass flux through the centre plane of the perturbed interface im...
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We derive a growth-rate model for the Richtmyer–Meshkov mixing layer, given arbitrary but known initial conditions. The initial growth rate is determined by the net mass flux through the centre plane of the perturbed interface immediately after shock passage. The net mass flux is determined by the correlation between the post-shock density and streamwise velocity. The post-shock density field is computed from the known initial perturbations and the shock jump conditions. The streamwise velocity is computed via Biot–Savart integration of the vorticity field. The vorticity deposited by the shock is obtained from the baroclinic torque with an impulsive acceleration. Using the initial growth rate and characteristic perturbation wavelength as scaling factors, the model collapses the growth-rate curves and, in most cases, predicts the peak growth rate over a range of Mach numbers (1.1≤Mi≤1.9), Atwood numbers (?0.73≤A≤?0.35 and 0.22≤A≤0.73), adiabatic indices (1.40/1.67≤γ1/γ2≤1.67/1.09) and narrow-band perturbation spectra. The mixing layer at late times exhibits a power-law growth with an average exponent of θ=0.24.
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The diffusive layering (DL) form of double-diffusive convection cools the Atlantic Water (AW) as it circulates around the Arctic Ocean. Large DL steps, with heights of homogeneous layers often greater than 10 m, have been found ab...
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The diffusive layering (DL) form of double-diffusive convection cools the Atlantic Water (AW) as it circulates around the Arctic Ocean. Large DL steps, with heights of homogeneous layers often greater than 10 m, have been found above the AW core in the Eurasian Basin (EB) of the eastern Arctic. Within these DL staircases, heat and salt fluxes are determined by the mechanisms for vertical transport through the high-gradient regions (HGRs) between the homogeneous layers. These HGRs can be thick (up to 5 m and more) and are frequently complex, being composed of multiple small steps or continuous stratification. Microstructure data collected in the EB in 2007 and 2008 are used to estimate heat fluxes through large steps in three ways: using the measured dissipation rate in the large homogeneous layers; utilizing empirical flux laws based on the density ratio and temperature step across HGRs after scaling to account for the presence of multiple small DL interfaces within each HGR; and averaging estimates of heat fluxes computed separately for individual small interfaces (as laminar conductive fluxes), small convective layers (via dissipation rates within small DL layers), and turbulent patches (using dissipation rate and buoyancy) within each HGR. Diapycnal heat fluxes through HGRs evaluated by each method agree with each other and range from 2 to 8 W m(-2), with an average flux of 3-4 W m(-2). These large fluxes confirm a critical role for the DL instability in cooling and thickening the AW layer as it circulates around the eastern Arctic Ocean.
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We present a global, multi-scale model of fluid mixing in laminar flows, which describes the evolution of the spatial distribution of coarse-grain concentration and interfacial area in a mixture of two fluids with identical viscos...
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We present a global, multi-scale model of fluid mixing in laminar flows, which describes the evolution of the spatial distribution of coarse-grain concentration and interfacial area in a mixture of two fluids with identical viscosity with no interfacial tension. This results in a efficient computational tool for mixing analysis, able to evaluate mixing dynamics and identify mixing problems such as dead zones (islands), applicable to realistic mixing devices. The flow domain is divided into cells, and large-scale variations in composition are tracked by following the cell-average concentrations of one fluid, using the mapping method developed previously, Composition fluctuations smaller than the cell size are represented by cell values of the area tensor which quantifies the amount, shape, and orientation of the interfacial area within each cell. The method is validated by comparison with an explicit interface tracking calculation. We show examples for 2D, time-periodic flows in a lid-driven rectangular cavity. The highly non-uniform time evolution of the spatial distribution of interfacial area can be determined with very low computational effort. Cell-to-cell differences in interfacial area of three orders of magnitude or more are found. It is well known that, for globally chaotic flows, the microstructural pattern becomes self-similar, and interfacial area increases exponentially with time. This behavior is also captured well by the extended mapping method. The present calculations are 2D, but the method can readily be applied in 3D problems.
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A mixed graph is a graph with edges and arcs, which can be considered as a hybrid of an undirected graph and a directed graph. In this paper we define the mixed adjacency matrix and the mixed energy of a mixed graph. The mixed adj...
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A mixed graph is a graph with edges and arcs, which can be considered as a hybrid of an undirected graph and a directed graph. In this paper we define the mixed adjacency matrix and the mixed energy of a mixed graph. The mixed adjacency matrix generalizes both the adjacency matrix of an undirected graph and the skew-adjacency matrix of a digraph. Then we compute the characteristic polynomial of the mixed adjacency matrix of a mixed graph and deduce some basic results from it. Furthermore, we give bounds to the mixed energy of a general mixed graph, and we compute the mixed energy of some special mixed graphs. At the end of the paper, we introduce mixed unitary Cayley graphs and compute their spectra. (C) 2016 Elsevier Inc. All rights reserved.
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