Mixing In Isotropic Turbulence Research Articles

Numerical investigation on mixing performance in rod bundle with spacer grid based on anisotropic turbulent mixing model

The interchannel mixing effect is very important for the thermal-hydraulic performance of fuel assembly subchannels in Pressurized Water Reactor (PWR), especially for that of the fuel assembly with spacer grid. In this study, an anisotropic turbulent mixing model with a turbulent mixing coefficient matrix is developed and embedded in an in-house code to analyze the thermal-hydraulic performance of the fuel assembly. The validation of the present turbulent mixing model has been performed by comparing the numerical results with the experimental results for the outlet temperature distribution of the fuel assembly. Then, the thermal-hydraulic performance of 5 × 5 rod bundle with spacer grid is analyzed by comparing the present turbulent mixing model and the conventional isotropic turbulent mixing model which uses a constant value to consider the average mixing effect. It is found that stronger diversion crossflow, more uniform outlet temperature distribution, higher Critical Heat Flux (CHF) and higher Departure from Nuclear Boiling Ratio (DNBR) of the fuel assembly are achieved when using anisotropic turbulent mixing model. In summary, the anisotropic turbulent mixing model depicts the interchannel mixing characteristics of spacer grid more reasonably.

Joint probability density function models for multiscalar turbulent mixing

Modeling multicomponent turbulent mixing is essential for simulations of turbulent combustion, which is controlled by mixing of fuel, oxidizer, combustion products, and intermediate species. One challenge is to find functions that can reproduce the joint probability density function (PDF) of scalar mixing states using only a small number of parameters. Even for mixing with only two independent scalars, several statistical distributions, including the Dirichlet, Connor–Mosimann (CM), five-parameter bivariate beta (BVB5), and statistically-most-likely distributions, have previously been proposed for this purpose, with minimal physical justification. This work uses the concept of statistical neutrality to relate these distributions to each other, relate the distributions to physical mixing configurations, and develop a systematic approach to model selection. This approach is validated by comparing the ability of these distributions to reproduce the evolution of the scalar PDF from Direct Numerical Simulations of three-component passive scalar mixing in isotropic turbulence with 11 different initial conditions that are representative of a wide range of mixing conditions of interest. The approach correctly identifies whether the Dirichlet, CM, and BVB5 distributions, which are increasingly complex bivariate generalizations of the beta distribution, can accurately model the joint PDFs, but knowledge of the mixing configuration is required to select the appropriate distribution. The statistically-most-likely distribution is generally less accurate than the appropriate bivariate beta distribution but still gives reasonable predictions and does not require knowledge of the mixing configuration, so it is a suitable model when no single mixing configuration can be identified.

Conditionally Statistical Description of Turbulent Scalar Mixing at Subgrid-Scales

Conditionally filtered passive scalar density function (FDF), dissipation (CFD), diffusion (CFDIF) and conditionally filtered velocity (CFV) are studied by using direct numerical simulation (DNS) data of homogeneous isotropic turbulent mixing with an imposed mean scalar gradient. The velocity and scalar fields are statistically stationary and have a Taylor micro-scale Reynolds number of 209. A three-dimensional box filter with a filter width of 21 scalar dissipation scales is employed to obtain filtered variables. The PDFs of conditioning variables, filtered scalar ( $\left \langle \phi \right \rangle _L $ ), and subgrid-scale (SGS) scalar variance ( $\left \langle \phi ^{\prime \prime 2} \right \rangle _L$ ), are shown and are in reasonably good agreement with the experimental results of a one-dimensional filter. Since the three-dimensional filter has been used, the PDF of the filtered scalar exhibits perfect symmetry, and this significantly affects the symmetry of succeeding conditionally filtered statistics on $\left \langle \phi \right \rangle _L$ such as FDF, CFD, and CFDIF. The FDF, CFD, and CFDIF also show visible dependence on $\left \langle \phi ^{\prime \prime 2} \right \rangle _L$ . When $\left \langle \phi ^{\prime \prime 2} \right \rangle _L$ varies from large to small, CFD varies from bell-shaped to U-shaped curves, and CFDIF varies from an inverse-S curve to a linear line; these are in accordance with the evolution of the FDF varying from bimodal to Gaussian. It suggests that the SGS mixing could be compared with global binary mixing in the view of the conditional description and this also suggests that it would reveal the non-equilibrium characteristics of the SGS scalar mixing; this SGS scalar mixing is supposed to be caused by diffusion-layer-like structures. In addition, the CFV remains linear regardless of the value of $\left \langle \phi ^{\prime \prime 2} \right \rangle _L$ . These results numerically confirm two distinct regimes of SGS mixing observed in previous experimental studies and extend the experimental results into isotropic turbulence, which suggests that the characteristics of the SGS scalar are intrinsic behavior of SGS mixing, independent of flow types.

The Batchelor Spectrum for Mixing of Passive Scalars in Isotropic Turbulence

We examine the support for the Batchelor spectrum from well-resolved simulations of high-Schmidt-number mixing in isotropic turbulence, and resolve a conundrum with respect to the numerical value of the prefactor, also known as the Batchelor constant. Our conclusion is that the most probable value of the most compressive principal strain rate is more relevant than its mean, at least asymptotically.

On the scalar probability density function transport equation for binary mixing in isotropic turbulence at supercritical pressure

Effects of Soret cross-diffusion, whereby concentration diffusion occurs in the presence of either temperature or pressure gradients, are investigated in the context of the binary isotropic turbulent mixing problem at supercritical pressure with emphasis on results relevant to probability density function (PDF) modeling. Direct numerical simulations (DNS) are conducted for compressible isotropic turbulent binary mixing of heptane with nitrogen at mean pressure and temperature equal to 45 atm and T=700 K, respectively. The formulation is based on a cubic real gas state equation, and includes generalized forms for heat and mass diffusion derived from nonequilibrium thermodynamics and fluctuation theory. Results from two simulations at 1923 resolution are compared. One case is based on the complete diffusion formulation, whereas in the second simulation only “standard” Fickian and Fourier mass and heat flux terms are considered as a basis for comparisons. The evolutions of the two mixing processes are shown to be nearly the same at early times; however, at long times the pressure gradient based Soret diffusion acts as a forcing function resulting in a statistically stationary scalar fluctuation distribution. In this case the scalar variance achieves a stationary value, in contrast to the exponential decay associated with purely Fickian diffusion. The mechanical to scalar time scale ratio, CY=τu/τY, is increased by a factor of approximately 3 by Soret effects during this latter mixing regime. Soret diffusion is shown to substantially alter the forms of the conditional expected diffusion and the conditional expected dissipation at these long times. A commonly used model based on an assumed proportionality between the conditional diffusion and the scalar fluctuation is tested, and is found to perform poorly in the presence of cross diffusion at long mixing times. Several new conditional expectations resulting from cross diffusion are measured. Implications of the results for extension of PDF models to the high pressure regime are discussed.

Analysis and modeling of subgrid scalar mixing using numerical data

Direct numerical simulations (DNS) of passive scalar mixing in isotropic turbulence is used to study, analyze, and, subsequently, model the role of small (subgrid) scales in the mixing process. In particular, we attempt to model the dissipation of the large-scale (supergrid) scalar fluctuations caused by the subgrid scales by decomposing it into two parts: (i) the effect due to the interaction among the subgrid scales, ℰ≫φ; and, (ii) the effect due to interaction between the supergrid and the subgrid scales, ℰ≳<φ. Model comparison with DNS data shows good agreement.

Improved Fokker–Planck model for the joint scalar, scalar gradient PDF

The joint scalar, scalar gradient probability density function (PDF) of an inert nonpremixed scalar diffusing in a one-dimensional system of random-sized lamellas is investigated by numerical simulation. The form of the scalar PDF, at a given RMS value, is nearly identical to that predicted by direct numerical simulation (DNS) of scalar mixing in isotropic turbulence and the mapping closure, and the moments of both the scalar and the scalar gradient suggest that their limiting marginal PDF are Gaussian. The joint scalar, scalar gradient PDF is found to be restricted to a bounded region in the scalar–scalar gradient plane, whose form is independent of the initial mixing ratio. These results are incorporated into the Fokker–Planck (FP) model for the joint scalar, scalar gradient PDF, and the improved model shows good agreement with numerical simulation data. An extension of the FP model that includes random stretching of the scalar gradient in isotropic turbulence is formulated.

Scalar mixing in isotropic turbulence

Eswaran and Pope [Phys. Fluids 31, 506 (1988)] performed direct numerical simulations to study the influence of the initial scalar integral length scale on mixing in stationary, isotropic turbulence. Their data demonstrate that both the decay rate and the shape of the rms versus time curve depend on the initial value of the scalar-to-velocity integral length-scale ratio. The present paper discusses modifications of the high Reynolds number theory of Corrsin [AIChE J. 10, 870 (1964)]. The predictions mirror the behavior found in the moderate Reynolds number simulations.

AN EVALUATION OF MODELS OF MIXING AND CHEMICAL REACTION WITH A TURBULENCE ANALOGY

Five mechanistic models of mixing and chemical reaction having an analogy with isotropic turbulent mixing are evaluated. The turbulence analogies, based on matching variance decay laws of models and turbulence theory, provide a physical basis for the models and a means of estimating their micromixing parameters apriori. Experimental data for single second order liquid phase reactions provide strong support for the analogies. However, it is demonstrated that in spite of their success for single reactions, the models may predict grossly different selectivities in the case of competing reactions in a plug flow reactor. This emphasizes the importance of certain structural features of the models which are independent of the existence of a turbulence analogy, such as: (i) reacting regions which are rich in each of the reactants of a two feedstream reactor, and (ii) unmixed regions in the reaction mixture. The importance of obtaining data for competing reactions in a highly segregated plug flow reactor for the p...

Lagrangian History Direct Interaction Equations for Isotropic Turbulent Mixing under a Second-Order Chemical Reaction

The Lagrangian history direct interaction approximation is applied to isotropic turbulent mixing of a second-order chemical reaction, the resulting closed sets of equations are presented, and an a-bridgement of them is carried out. It is shown that in the limit of a stochastically distributed second-order reaction the equations reduce to those of direct interaction. It is also demonstrated that the approximation preserves an important property of the exact equations; namely, that in the absence of molecular diffusion, the decay of single point statistical functions of the concentration field is independent of the turbulence.

Isotropic turbulent mixing with boundary sources

AbstractA type of turbulent mixing, ubiquitous in occurrence as a limiting case, is defined and given analytical treatment. By combining the Kolmogoroff and Corrsin concepts of inertial subrange with consistent application of the divergence theorem of Gauss, predictions are made for statistical turbulence and mixing parameters in uniformly mixed regions into which fluid streams are introduced of arbitrary number, concentration and speed.

The reactant concentration spectrum in turbulent mixing with a first-order reaction

The power specturm of a passive scalar contaminant undergoing a first-order chemical reaction and isotropic turbulent mixing is deduced for three different spectral ranges: (i) the inertial-convective range; (ii) the viscous-convective and viscous-diffusive ranges for very large Schmidt number; (iii) the inertial-diffusive range for very small Schmidt number. The analysis is restricted to stationary, locally isotropic fields, and to systems so dilute that the heat of reaction has no effect on the reaction rate.