Luis Valiño

A field Monte Carlo formulation for calculating the probability density function of a single scalar in a turbulent flow

The probability density function (PDF) formulation of one scalar field undergoing diffusion, turbulent convection and chemical reaction is restated in terms of stochastic fields. These fields are smooth in space as they have a length scale similar to that of the PDF. Their evolution is described by a set of stochastic partial differential equations, which are solved using a finite volume scheme with a stochastic source term. The application of this methodology to a particular flow is shown first for a linear source term, with exact analytical solution for the mean and standard deviation, and then for a nonlinear reaction.

A binomial Langevin model for turbulent mixing

A Langevin model with binomial random diffusion replacing the classical Wiener process is proposed to model the turbulent mixing of a scalar convected by a field of statistically homogeneous turbulence. A Monte Carlo simulation is performed. The results display an excellent agreement with existing data from the numerical experiment of Eswaran and Pope [Phys. Fluids 31, 506 (1988)].

Dynamics of velocity gradient invariants in turbulence: Restricted Euler and linear diffusion models

A complete system of dynamical equations for the invariants of the velocity gradient, the strain rate, and the rate-of-rotation tensors is deduced for an incompressible flow. The equations for the velocity gradient invariants R and Q were first deduced by Cantwell [Phys. Fluids A 4, 782 (1992)] in terms of Hij, the tensor containing the anisotropic part of the pressure Hessian and the viscous diffusion term in the velocity gradient equation. These equations are extended here for the strain rate tensor invariants, RS and QS, and for the rate-of-rotation tensor invariant, QW, using HijS and HijW, the symmetric and the skew-symmetric parts of Hij, respectively. In order to obtain a complete system, an equation for the square of the vortex stretching vector, Vi≡Sijωj, is required. The resulting dynamical system of invariants is closed using a simple model for the velocity gradient evolution: an isotropic approximation for the pressure term and a linear model for the viscous diffusion term. The local topology ...

A binomial sampling model for scalar turbulent mixing

The closure problem generated by the molecular mixing term in the turbulent convection of scalars is studied. The statistical average of this term both in moment formulations and in the probability density function (pdf) approach implicitly encloses the turbulence straining action on scalar gradients leading to a significant enhancement of the molecular dissipative effects. Previous pdf model equations are examined in terms of cumulants evolution and reasons for their failure are diagnosed. A new noninteractive model is proposed, combining a linear mean square estimation (LMSE) deterministic subprocess affecting all the Monte Carlo particles, used to represent the pdf, and a binomial sampling acting on a fraction of them. The scalar lower and/or upper bounds are naturally considered in the formulation. For unbounded scalars, or when the scalar standard deviation is much smaller than the absolute value of the difference between the bounds and the scalar mean, the binomial sampling tends to a Gaussian one. ...

STATISTICAL DESCRIPTION OF THE TURBULENT MIXING OF SCALAR FIELDS

A formulation in terms of probability density function (PDF) transport equations is presented for inert and reactive scalar fields undergoing turbulen mixing. The PDF methodology is related to the classical moment equations. The hierarchy of PDF transport equations resembles the BBGKY equations in statistical mechanics. Closure hypothesis, approximating the molecular mixing term, are described and their predictions for simple systems are compared with direct numerical simulations (DNS). Solution algorithms in terms of Monte Carlo particles are also discussed.

A priori and a posteriori tests of subgrid scale models for scalar transport

A priori tests of subgrid scale (SGS) models for the transport of scalars by turbulence are performed by studying the transfer of scalar fluctuations between resolved and subgrid scales in a temporal mixing layer. They confirm that both forward and backward transfer are present, what can be best represented by mixed models (eddy-diffusivity+scale-similarity). However, a posteriori tests show that eddy-diffusivity models, even if only able to dissipate fluctuations from resolved to subgrid scales, give very similar results to mixed models, provided that an appropriate model is used for SGS stresses.

Monte Carlo implementation and analytic solution of an inert‐scalar turbulent‐mixing test problem using a mapping closure

A simple generalization, using a time‐dependent Gaussian scalar field, of a mapping closure recently proposed by Chen et al. [Phys. Rev. Lett. 63, 2657 (1989)] to model molecular mixing, enhanced by turbulent straining, for a fluctuating scalar field is presented and Monte Carlo implemented. An arbitrary parameter β allows the adjustment of the Gaussian‐scalar dissipation rate; the actual scalar field evolution is, however, independent of β. An analytic solution is obtained for the turbulent mixing of cells with two different values of the scalar content and simple symmetric initial conditions. Numerical results for this problem are produced, combining the Monte Carlo simulation and the analytic solution, in order to show the feasibility of this technique and its accuracy. Future extensions are outlined.

Monte Carlo implementation of a single‐scalar mapping closure for diffusion in the presence of chemical reaction

It is shown how to implement, via a Monte Carlo method, a single‐scalar mapping closure for diffusion when chemical reactions or other processes are present. The mixing term in the one‐point probability density function (pdf) equation of the scalar is closed via a mapping. The chemical term, closed in the pdf formulation, is treated exactly. To isolate each process, a fractional step technique is used. The methodology is the same if more processes are present. As an example, the pdf equation of one scalar reacting with itself in a statistically homogeneous forced turbulent flow is solved. Comparisons with computed direct numerical simulation data are excellent.

MULTISCALAR MAPPING CLOSURE FOR MIXING IN HOMOGENEOUS TURBULENCE

A new methodology to use mapping closures for the mixing of several scalars in homogeneous turbulence is explained. The main idea is the unidimensional mapping for each scalar, with the cross‐dissipation handled by a joint reference field. A restricted and a general closure are described. A Monte Carlo code based on a fractional step technique has been developed. As an example, the segregated double‐delta two‐scalar mixing is analytically and numerically solved and predictions are shown.

Joint Statistics of Scalars and Their Gradients in Nearly Homogeneous Turbulence

The mixing of dynamically passive inert and reactive scalars convected by a solenoidal field of nearly homogeneous turbulence is investigated. The transport equation for the joint probability density function (pdf) of scalars and their gradients is used. Closure approximations are required for those processes describing the turbulent straining of scalar gradients, the cross-dissipation of scalar/scalar-gradient and the scalar-gradient dissipation. Stochastic models in terms of random vectors are proposed and a Monte-Carlo simulation is then conducted. Predictions for a single inert scalar agree rather well with available experimental data. The simulation accurately predicts existing experiments for two moderately fast reacting scalars; large values of the flatness factors of species and species-gradients are strongly suggestive of spatial segregation and small-scale intermittency respectively. A far from gaussian nature of reactive scalars is well documented.