Peyman Givi

Filtered density function for large eddy simulation of turbulent reacting flows

A methodology termed the “filtered density function” (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities. A transport equation is derived for the FDF in which the effect of chemical reactions appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The FDF transport equation is solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of the equivalent stochastic differential equations (SDEs) are obtained. These solutions preserve the Ito-Gikhman nature of the SDEs. The consistency of the FDF approach, the convergence of its Monte Carlo solution and the performance of the closures employed in the FDF transport equation are assessed by comparisons with results obtained by direct numerical simulation ...

Model-free simulations of turbulent reactive flows

A critical review of the modern computational methods for solving the transport equations of turbulent reacting single-phase flows is presented. Primary consideration is given to those methods which lead to ‘model-free’ simulations while some attention is devoted to ‘turbulence modeling’. Emphasis is placed upon the role of supercomputers and how their increased computational capacities may be exploited to allow better simulations of the physics of turbulent reactive flows. Comparisons between the commonly employed computational schemes for simulating these flows are given, with the advantages and the limitations associated with each scheme being highlighted. Examples are presented of recent applications of model-free simulations to a variety of unsteady reacting flows, with detailed discussions on the physical phenomena captured by such simulations. Due to the nature of this review, experimental contributions are mentioned only in the context of providing empirical evidence. References are made to other contributions which are not directly related to the computational efforts in order to provide a reasonably comprehensive bibliography for those interested in pursuing various topics in greater detail. Predictions of future accomplishments, as well as some suggestions for future work, are also given.

Velocity filtered density function for large eddy simulation of turbulent flows

A methodology termed the “velocity-scalar filtered density function” (VSFDF) is developed and implemented for large eddy simulation (LES) of turbulent flows. In this methodology, the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function (PDF) of the velocity and scalar fields. An exact transport equation is derived for the VSFDF in which the effects of the SGS convection and chemical reaction are closed. The unclosed terms in this equation are modeled in a fashion similar to that typically used in Reynolds-averaged simulation procedures. A system of stochastic differential equations (SDEs) which yields statistically equivalent results to the modeled VSFDF transport equation is constructed. These SDEs are solved numerically by a Lagrangian Monte Carlo procedure in which the Ito–Gikhman character of the SDEs is preserved. The consistency of the proposed SDEs and the convergence of the Monte Carlo solution are assessed by comparison with results obtained by a finite difference LES procedure in which the corresponding transport equations for the first two SGS moments are solved. The VSFDF results are compared with those obtained by the Smagorinsky model, and all the results are assessed via comparison with data obtained by direct numerical simulation of a temporally developing mixing layer involving transport of a passive scalar. It is shown that the values of both the SGS and the resolved components of all second order moments including the scalar fluxes are predicted well by VSFDF. The sensitivity of the calculations to the model’s (empirical) constants are assessed and it is shown that the magnitudes of these constants are in the same range as those employed in PDF methods.

Filtered Density Function for Subgrid Scale Modeling of Turbulent Combustion

Abstract : This research was concentrated primarily on developments and applications of the filtered density function (FDF) for subgrid scale (SGS) modeling of turbulent reacting flows. During the past three years, this work addressed: (1) development of the joint velocity-scalar filtered mass density function (VSFMDF), (2) development of the joint frequency-velocity-scalar filtered mass density function (FVS-FMDF), and (3) implementation of the scalar filtered mass density function (SFMDF) and VSFMDF for large eddy simulation of complex turbulent flames. This is a final report of our activities sponsored by AFOSR under Grant FA9550-06-1-0015.

Velocity-scalar filtered density function for large eddy simulation of turbulent flows

A methodology termed the “velocity-scalar filtered density function” (VSFDF) is developed and implemented for large eddy simulation (LES) of turbulent flows. In this methodology, the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function (PDF) of the velocity and scalar fields. An exact transport equation is derived for the VSFDF in which the effects of the SGS convection and chemical reaction are closed. The unclosed terms in this equation are modeled in a fashion similar to that typically used in Reynolds-averaged simulation procedures. A system of stochastic differential equations (SDEs) which yields statistically equivalent results to the modeled VSFDF transport equation is constructed. These SDEs are solved numerically by a Lagrangian Monte Carlo procedure in which the Ito–Gikhman character of the SDEs is preserved. The consistency of the proposed SDEs and the convergence of the Monte Carlo solution are assessed by comparison with r...

Numerical simulation of non-circular jets

Abstract Results are presented of numerical simulations of spatially developing, three-dimensional jets issued from circular and non-circular nozzles of identical equivalent diameters. Elliptic, rectangular and triangular jets are considered with aspect-ratios of 1:1 and 2:1. Flow visualization results show that large scale coherent structures are formed in both cornered and non-cornered jets. The axis-switching phenomenon is captured in all non-unity aspect-ratio jets and also in the equilateral triangular jet. The square jet does not show axis-switching; however, the rotation of its axes by 45 ° is shown to play a significant role in its entrainment characteristics. All the non-circular configurations are shown to provide more efficient mixers than does the circular jet; the isosceles triangular jet is the most efficient one. It is demonstrated that the near field entrainment and mixing is characterized by the mean secondary flow induced by the stream-wise vortices. The transport of a passive Shvab-Zeldovich scalar variable is used to determine the limiting rate of mean reactant conversion in a chemical reaction of the type Fuel + Air → Products. The results show that the largest product formation occurs in the isosceles triangular jet and the lowest occurs in the circular jet. It is also shown that the 2:1 triangular jet has the shortest scalar core whereas the rectangular jet has the longest core.

Velocity-scalar filtered mass density function for large eddy simulation of turbulent reacting flows

A methodology termed the “velocity-scalar filtered mass density function” (VSFMDF) is developed and implemented for large eddy simulation (LES) of variable-density turbulent reacting flows. This methodology is based on the extension of the previously developed “velocity-scalar filtered density function” method for constant-density flows. In the VSFMDF, the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function of the velocity and scalar fields. An exact transport equation is derived for the VSFMDF in which the effects of SGS convection and chemical reaction are in closed forms. The unclosed terms in this equation are modeled in a fashion similar to that in Reynolds-averaged simulation procedures. A set of stochastic differential equations (SDEs) are considered which yield statistically equivalent results to the modeled VSFMDF transport equation. The SDEs are solved numerically by a Lagrangian Monte Carlo procedure in which the Ito-Gikhma...

Non-Gaussian scalar statistics in homogeneous turbulence

Results are presented of numerical simulations of passive scalar mixing in homogeneous, incompressible turbulent flows. These results are generated via the Linear Eddy Model (LEM) and Direct Numerical Simulation (DNS) of turbulent flows under a variety of different conditions. The nature of mixing and its response to the turbulence field is examined and the single-point probability density function (p.d.f.) of the scalar amplitude and the p.d.f.s of the scalar spatial-derivatives are constructed. It is shown that both Gaussian and exponential scalar p.d.f.s emerge depending on the parameters of the simulations and the initial conditions of the scalar field. Aided by the analyses of data, several reasons are identified for the non-Gaussian behaviour of the scalar amplitude. In particular, two mechanisms are identified for causing exponential p.d.f.s: (i) a non-uniform action of advection on the large and the small scalar scales, (ii) the nonlinear interaction of the scalar and the velocity fluctuations at small scales. In the absence of a constant non-zero mean scalar gradient, the behaviour of the scalar p.d.f. is very sensitive to the initial conditions. In the presence of this gradient, an exponential p.d.f. is not sustained regardless of initial conditions. The numerical results pertaining to the small-scale intermittency (non-Gaussian scalar derivatives) are in accord with laboratory experimental results. The statistics of the scalar derivatives and those of the velocity-scalar fluctuations are also in accord with laboratory measured results.

Frequency-velocity-scalar filtered mass density function for large eddy simulation of turbulent flows

A methodology termed “frequency-velocity-scalar filtered mass density function” (FVS-FMDF) is developed for large eddy simulation (LES) of turbulent flows. The FVS-FMDF takes account of unresolved subgrid scales (SGSs) by considering the joint probability density function (PDF) of the frequency, the velocity, and the scalar fields. An exact transport equation is derived for the FVS-FMDF in which the effects of convection and chemical reaction are in closed forms. The unclosed terms in this equation are modeled in a fashion similar to PDF methods in Reynolds-averaged Navier–Stokes simulations. The FVS-FMDF transport is modeled via a set of stochastic differential equations (SDEs). The numerical solution procedure is based on a hybrid finite-difference (FD)/Monte Carlo (MC) method in which the LES filtered transport equations are solved by the FD, and the set of SDEs is solved by a Lagrangian MC procedure. LES of a temporally developing mixing layer is conducted via the FVS-FMDF, and the results are compare...

An Irregularly Portioned Lagrangian Monte Carlo Method for Turbulent Flow Simulation

A novel computational methodology, termed “Irregularly Portioned Lagrangian Monte Carlo” (IPLMC) is developed for large eddy simulation (LES) of turbulent flows. This methodology is intended for use in the filtered density function (FDF) formulation and is particularly suitable for simulation of chemically reacting flows on massively parallel platforms. The IPLMC facilitates efficient simulations, and thus allows reliable prediction of complex turbulent flames. Sample results are presented of LES of both premixed and non-premixed flames via this method, and the results are assessed via comparison with laboratory data.