Mixing Model Based on Parameterized Scalar Profiles

It is important in engineering to elucidate the mechanism of a chemical reaction in turbulent flow. But there are still few studies on reacting turbulent flow in a liquid phase. In this study, the two-dimensional liquid jet with the second-order reaction (A+B←R) is investigated. The concentrations of the species R and the conserved scalar (which is the concentration of other species independent of the above chemical reaction) are measured simultaneously by the optical fiber probe based on light absorbtion spectroscopic method. The concentrations of species A and B are obtained from the conserved scalar theory. Regarding the velocity field, the streamwise velocity is measured by the hot-film anemometer. The moment closure methods are often used for the prediction of turbulent flow. But it is difficult to apply it to the reacting turbulent flow because of the high non-linearity of the reaction rate terms. It is commonly known that the values of concentrations depend strongly on the mixture fraction (which is a conserved scalar) defined as the normalized concentration of the species which is independent of reaction. Hence, Conditional moment closure (CMC) methods are useful for the prediction of the turbulent flow with chemical reactions. In this study, conditional scalar statistics are investigated by using the conditional moment closure methods and experimental data. It is shown that the conditional averages of concentration of reactant and product species approach the equilibrium limit (which correspond to the limiting case of the fast chemical reaction) in the downstream direction and the value of the conditional scalar (mixture fraction) dissipation decreases and its distribution varies in the downstream direction and comes to show the local minimum value near the point η = ξS (which is the stoichiometric value of the mixture fraction).

We investigate the possibility of determining the local turbulent flame speed by measuring the individual terms in the balance of a mean progress of reaction variable for the case of a low turbulence methane-air Bunsen flame in the thin flame regime. Velocity distributions and flame edge positions were measured by particle image velocimetry techniques at 3 kHz for a flame stabilized by a surrounding pilot of the same stoichiometry, for a turbulent Reynolds number around 66 and Karlovitz numbers of the order of 4. The conservation equation for mean progress variable was analyzed along different streamlines as a balance of terms expressed as velocities, including terms for convection, turbulent diffusion, mean reaction, and turbulent and molecular diffusion. Each term was estimated from local velocities and flame locations using a thin flame approximation, and their uncertainty was evaluated based on propagation of experimentally measured statistical correlations. The largest terms were the convective and reaction terms, as expected, with smaller roles for turbulent and molecular diffusion across the flame brush. Countergradient diffusion and transition to gradient diffusion were observed across the flame brush. Closure of the balance of terms in the conservation equations using independently measured terms was not consistently achieved across the flame brush within the reckoned uncertainties, arriving at a balance within 20–30% of the absolute value. Testable hypotheses are offered for the possible reasons for the mismatch, including the role of spatial filtering and 3D effects on the reaction rate term. Finally, the experiments identify the inaccuracies in measuring a true local turbulent flame speed, and suggest a consistent methodology to reduce errors in such estimations. This is the first time such a detailed experimental closure is attempted for any configuration. The results suggest that the significant improvements in spatial resolution are necessary for a full closure.

The vertical extent of exchange between surface flow and sediment pore water is a key control on ecological functioning in fluvial systems. Across the diverse disciplines engaged in hyporheic-zone research, however, this exchange depth is characterized using different criteria and definitions. From a hydrodynamic and transport perspective, this raises the question of how far interface-driven scalar transport mechanisms penetrate into a porous sediment bed beneath turbulent open-channel flow.Using pore-resolved Direct Numerical Simulation (DNS), we investigate scalar transport near the sediment--water interface within the framework of effective diffusivity. The porous medium is represented by a random sphere packing overlain by a turbulent open-channel flow characterized by a friction Reynolds number of Reτ = 180 and a permeability Reynolds number of ReK = 1.8. Scalar transport is modeled by solving the advection-diffusion equation for a passive scalar at Schmidt number Sc = 1, subject to a prescribed vertical concentration gradient driving bed-normal transport.To obtain statistically representative descriptions of the strongly three-dimensional flow and transport fields, double averaging, in time and over horizontal planes, is employed. Within this framework, the effective diffusivity model relates the plane-averaged scalar concentration to the vertical scalar flux, enabling a quantitative decomposition into turbulent transport, dispersive transport, and molecular diffusion. Revisiting the theory of horizontal averaging, we discuss the implications of different formulations of effective diffusivity and show that seemingly minor differences become significant in regions of rapidly varying porosity, such as the sediment--water interface.In a systematic pre-study, we assess the influence of grid resolution, sampling duration, and sediment-bed depth on the resulting transport statistics. Based on this analysis, simulations are conducted at a constant flow-depth-to-sphere-diameter ratio of hf / D = 3, combined with three sediment-bed depths corresponding to hb / D ∈ [2, 5, 9]. To isolate interface-induced transport processes, simulations with overlying turbulent flow are compared to reference cases of scalar transport in the porous medium without free flow.This comparison enables a clear distinction between transport mechanisms intrinsic to the porous medium and those induced by the sediment--water interface. The effective diffusivity associated with interface-driven transport decays exponentially with increasing depth below the sediment surface. Turbulent scalar transport is confined to the uppermost sediment layer, penetrating only to depths of approximately z / D ≅ 1 - 2. In contrast, dispersive transport induced by pressure fluctuations at the sediment crest dominates scalar exchange within the sediment bed. Beyond z / D ≅ 5, dispersive transport becomes negligible and scalar transport is governed predominantly by molecular diffusion, indicating the onset of a Darcy-type transport regime. Within the effective diffusivity framework, cases with hb / D = 5 and 9 show indistinguishable behavior, whereas the shallow bed case hb / D = 2 exhibits a pronounced attenuation of dispersive transport.These results provide a quantitative, transport-based definition of the effective depth of interface-driven hyporheic exchange. The exponential decay of effective diffusivity, isolated from background porous-medium transport, offers a promising basis for improving reduced-order models of scalar transport in the hyporheic zone.

Conditional moment closure method with tabulated chemistry in adiabatic turbulent nonpremixed jet flames

The mapping closure of Chen et al. [Phys. Rev. Lett., 63, 1989] is a transported probability density function (PDF) method that has proven very efficient for modelling of turbulent mixing in homogeneous turbulence. By utilizing a Gaussian reference field, the solution to the mapping function (in homogeneous turbulence) can be found analytically for a range of initial conditions common for turbulent combustion applications, e.g. for binary or trinary mixing. The purpose of this paper is to investigate the possibility of making this solution a presumed mapping function (PMF) for inhomogeneous flows. The PMF in turn will imply a presumed mixture fraction PDF that can be used for a wide range of models in turbulent combustion, e.g. flamelet models, the conditional moment closure (CMC) or large eddy simulations. The true novelty of the paper, though, is in the derivation of highly efficient, closed algebraic expressions for several existing models of conditional statistics, e.g. for the conditional scalar dissipation/diffusion rate or the conditional mean velocity. The closed form expressions nearly eliminates the overhead computational cost that usually is associated with nonlinear models for conditional statistics. In this respect it is argued that the PMF is particularly well suited for CMC that relies heavily on manipulations of the PDF for consistency. The accuracy of the PMF approach is shown with comparison to DNS of a single scalar mixing layer to be better than for the β-PDF. Not only in the shape of the PDF itself, but also for all conditional statistics models computed from the PDF.

view Abstract Citations (65) References (15) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Comments on the diffusion model of turbulent mixing. Cloutman, L. D. ; Eoll, J. G. Abstract Several recent investigations of post-main-sequence stellar evolution have used a diffusion model of turbulent mixing, and each author has used a different variation. We justify the diffusion model in the framework of a statistical theory of turbulence and show that the difference between the two diffusion equations that have been proposed is related to an ambiguity in the definition of a Lagrangian hydrodynamical calculation by finite differences in the presence of turbulence. We present difference equations for solving the diffusion equation which theory and experience indicate are free of numerical difficulties. Publication: The Astrophysical Journal Pub Date: June 1976 DOI: 10.1086/154411 Bibcode: 1976ApJ...206..548C Keywords: Finite Difference Theory; Stellar Evolution; Stellar Models; Turbulence Models; Turbulent Diffusion; Turbulent Mixing; Convective Flow; Error Analysis; Main Sequence Stars; Mass Distribution; Transport Theory; Astrophysics full text sources ADS |

Summary form only given. Turbulent mixing displays experimentally universal growth rates, but simulations in most cases disagree with experiments by a factor of 2 or more. We report on a new class of simulations based on (a) an improved front tracking algorithm and (b) inclusion of real fluid effects which agree with experiment. Here the real fluid effects are surface tension for immiscible fluids and mass diffusion for miscible fluids. We document significant dependence of the mixing rate on both physical scale breaking effects (surface tension, mass diffusion and compressibility) and on numerical artifacts such as numerical mass diffusion (for untracked simulations). We conclude that modeling of turbulent mixing is sensitive to details of transport, surface tension, and to their numerical analogues. We also consider the problem of closure for the averaged equations. The numerical data base resulting from experimentally validated simulations is an invaluable resource in providing a rational and systematic way to evaluate proposed closures. We compare some leading closure models and find an approximate agreement, but in some cases, regions of disagreement

A numerical investigation of boundary layer mass transfer flow through an inclined plate with the effect of chemical reaction and thermal diffusion is presented in this study. The governing partial differential equations (PDE) are transformed to a system of dimensionless non-similar coupled PDEs. The transformed, non-similar conservations equations (momentum balance equation, energy balance equation and concentration balance equation) are then solved using a numerical approach known as explicit finite difference method (EFDM). Basically EFDM introduced for the unsteadiness in the momentum, temperature, and concentration fluid fields is based on the time dependent fluid velocity, temperature and concentration of the boundary surface. During the course of discussion, it is found that the various parameters related to the problem influence the calculated resultant expressions. The computed numerical solution results for the velocity, temperature, and concentration distribution with the effect of various important dimensionless parameters (Grashof number, Modified Grashof number, Prandtl number, Schmidt number, Soret number, Dufour number, chemical reaction parameter and inclination parameter) entering into the problems are critically analyzed and discussed graphically. It can be seen that two physical phenomena chemical reaction and thermal diffusion can greatly effect on the boundary layer fluid flows through an inclined plate.

Conditional moment closure for turbulent combustion

Analysis of a model for precipitation and dissolution coupled with a Darcy flux

A simple model for turbulent gas mixing in CFB reactors

The effects of turbulence on molten pool transport during melting and solidification processes in continuous conduction mode laser welding of copper–nickel dissimilar couple

Conditional moment closure (CMC) predictions for a turbulent piloted jet diffusion flame of methanol in air at velocities of 66.2 and 90.3 m s−1 are presented. Predictions are compared with the experimental joint Raman-Rayleigh-LIF results of Masri et al and laminar flamelet calculations. Three comprehensive chemical mechanisms (SKELETAL, GRI-Mech and SUBGRI) are used to represent the chemistry of the methanol flame. The SKELETAL mechanism shows the best agreement among the various mechanisms employed. It is found that the SUBGRI mechanism reduces computational cost in terms of memory and CPU time without compromising results where the focus is on the main reactive chemistry. The k-ε-g turbulence model underpredicts the rate of mixing and the predicted flames are somewhat longer than that reported by experiment. In general, the CMC predictions for conditional mean temperature and species mass fractions are very good and show qualitative agreement with experiment. At downstream locations, the overall trends of predicted temperature and species concentration levels are similar to the upstream ones with the latter showing better agreement with the conditional measured levels. CMC predictions show the same order of agreement at higher velocities. It is believed that the discrepancies on the fuel-rich side may be due to lack of consideration of the conditional fluctuations. The absence of a radially dependent CMC formulation, excluding differential diffusion effects and the inadequacy of the chemical mechanism may also account, partly, for the degree of discrepancy in the predictions.

The governing equations describing methane oxidation in a reverse flow reactor are given by a set of convective-diffusion equations with a nonlinear reaction term, where temperature and methane conversion are dependent variables. In this study, the process is assumed to be a one-dimensional pseudohomogeneous model and takes place with a certain reaction rate in which thewhole process ofthereactor is still workable. Thus, the reaction rate can proceed at a fixed temperature. Under these conditions, we can restrict ourselves to solving the equations for the conversion only. From the available data, it turns out that the ratio of the diffusion term to the reaction term is small. Hence, this ratio is considered as a small parameter in our model and this leads to a singular perturbation problem. Numerical difficulties will be found in the vicinity of a small parameter in front of a higher order term. Here, we present an analytical solutionby means of matched asymptotic expansions. The result shows that, up to and including the first order of approximation, the solution is in agreement with the exact and numerical solutions of the boundary value problem.

A study on nonnegativity preservation in finite element approximation of Nagumo-type nonlinear differential equations