Farhad A. Jaberi

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 ...

Filtered mass density function for large-eddy simulation of turbulent reacting flows

A methodology termed the ‘filtered mass density function’ (FMDF) is developed and implemented for large-eddy simulation (LES) of variable-density chemically reacting turbulent flows at low Mach numbers. This methodology is based on the extension of the ‘filtered density function’ (FDF) scheme recently proposed by Colucci et al . (1998) for LES of constant-density reacting flows. The FMDF represents the joint probability density function of the subgrid-scale (SGS) scalar quantities and is obtained by solution of its modelled transport equation. In this equation, the effect of chemical reactions appears in a closed form and the influences of SGS mixing and convection are modelled. The stochastic differential equations (SDEs) which yield statistically equivalent results to those of the FMDF transport equation are derived and are solved via a Lagrangian Monte Carlo scheme. The consistency, convergence, and accuracy of the FMDF and the Monte Carlo solution of its equivalent SDEs are assessed. In non-reacting flows, it is shown that the filtered results via the FMDF agree well with those obtained by the ‘conventional’ LES in which the finite difference solution of the transport equations of these filtered quantities is obtained. The advantage of the FMDF is demonstrated in LES of reacting shear flows with non-premixed reactants. The FMDF results are appraised by comparisons with data generated by direct numerical simulation (DNS) and with experimental measurements. In the absence of a closure for the SGS scalar correlations, the results based on the conventional LES are significantly different from those obtained by DNS. The FMDF results show a closer agreement with DNS. These results also agree favourably with laboratory data of exothermic reacting turbulent shear flows, and portray several of the features observed experimentally.

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.

Large scale simulations of two-dimensional nonpremixed methane jet flames

Abstract Direct numerical simulation (DNS) and large eddy simulation (LES) of two-dimensional nonpremixed methane jet flames are conducted to assess the performance of subgrid-scale LES models and reduced kinetics mechanisms in transitional and turbulent flows. The LES is via the recently developed “filtered mass density function” (FMDF) method of Jaberi et al. [1] . The FMDF represents the single-point joint probability density function (PDF) of the mass weighted subgrid-scale scalar quantities, and is obtained by solving its transport equation via a Lagrangian Monte Carlo scheme. In the FMDF transport equation, the effects of chemistry appear in a closed form, allowing reliable LES of turbulent flames with complex chemistry models. The LES/FMDF results are appraised by detailed comparisons with DNS data for various reduced and skeletal mechanisms. It is shown that the filtered values of the major and minor species and the compositional structure of the methane flames are accurately predicted by FMDF for all the tested chemistry models. However, the DNS and LES results as obtained by the reduced mechanisms are found to be substantially different than those calculated by the skeletal mechanism in some flow conditions. This is consistent with our laminar coflow and counterflow jet results, and indicates the importance of kinetics models in the numerical simulation of transitional/turbulent hydrocarbon flames.

Large-Eddy Simulations of Turbulent Flows in an Axisymmetric Dump Combustor

A hybrid Eulerian-Lagrangian, mathematical/computational methodology is developed and evaluated for large-eddy simulations of turbulent combustion in complex geometries. The formulation for turbulence is based on the standard subgrid-scale stress models. The formulation for subgrid-scale combustion is based on the filtered mass density function and its equivalent stochastic Lagrangian equations. An algorithm based on high-order compact differencing on generalized multiblock grids is developed for numerical solution of the coupled Eulerian-Lagrangian equations. The results obtained by large-eddy simulations/filtered mass density function show the computational method to be more efficient than existing methods for similar hybrid systems. The consistency, convergence, and accuracy of the filtered mass density function and its Lagrangian-Monte Carlo solver is established for both reacting and nonreacting flows in a dump combustor. The results show that the finite difference and the Monte Carlo numerical methods employed are both accurate and consistent The results for a reacting premixed dump combustor also agree well with available experimental data. Additionally, the results obtained for other nonreacting turbulent flows are found to be in good agreement with the experimental and high-order numerical data. Filtered mass density function simulations are performed to examine the effects of boundary conditions, subgrid-scale models, as well as physical and geometrical parameters on dump-combustor flows. The results generated for combustors with and without an inlet nozzle are found to be similar as long as appropriate boundary conditions are employed.

Dispersion and polydispersity of droplets in stationary isotropic turbulence

Abstract A detailed parametric study is conducted of dispersion and polydispersity of liquid drops in stationary isotropic turbulence via direct numerical simulation. It is assumed that the flow is very dilute so that the effect of particles on the carrier fluid is negligible (one-way coupling). Both non-evaporating and evaporating drops are simulated; in the latter both constant and variable rates of evaporation are considered. The simulations of non-evaporating drops are used to validate the numerical methodology and to assess the effects of the particle time constant and the drift velocity on the particle velocity autocorrelation, turbulence intensity and diffusivity. The simulated results are also used to appraise the performance of some of the available theoretical models for particle dispersion in stationary isotropic turbulence. The effects of the initial drop time constant, the initial evaporation rate, and the drop Schmidt number on the probability density function (pdf) of the drop size are studied. It is found that, after an initial transient period the pdf of the drop size becomes nearly Gaussian. However, the pdf deviates from Gaussian as the mean drop time constant becomes very small. The extent of this deviation depends on the evaporation rate. The effect of the initial spray size on the pdf is also studied and it is shown that as the spray size increases, the interaction between the spray and large scale turbulence structures influences the pdf. The effect of the initial size distribution on the pdf is also investigated by varying the initial standard deviation. Both Gaussian and double-delta initial drop size pdfs are considered. In the latter it is shown that a transition to Gaussian is possible provided that the initial mean drop time constant is large and/or the initial standard deviation of the drop diameter is small.

A dynamic similarity model for large eddy simulation of turbulent combustion

A dynamic similarity subgrid-scale (SGS) unmixedness model is presented for large eddy simulation (LES) of turbulent reacting flows. The model is assessed both a priori and a posteriori via data obtained by direct numerical simulations (DNS) of homogeneous compressible turbulent flows involving a single step Arrhenius reaction. The results of a priori analysis indicate that the local values of the SGS unmixedness are accurately predicted by the model. A posteriori results also indicate that the statistics of the resolved temperature and scalars as obtained by LES compare favorably with DNS values.

Temperature fluctuations in particle-laden homogeneous turbulent flows

Abstract The statistical behavior of the fluid and particle temperatures in homogeneous two-phase turbulent flows are investigated via direct numerical simulations. The effects of the flow Reynolds number ( Re λ ) , the Prandtl number ( Pr ) , the particle response time ( τ p ) , the ratio of specific heats ( α ) , and the mass loading ratio ( φ m ) on the fluid and particle temperature statistics are studied. The results show that the particle temperature intensity decreases as the magnitudes of τ p , Pr , α , and Re λ increase. Also, by decreasing the magnitudes of α and⧹or Pr , the difference between the particle velocity and temperature diffusivity coefficients increases. The ratio of particle to fluid temperature intensities and the dissipation rate of the fluid temperature are affected by two-way coupling effects and decrease as the mass loading ratio increases. Additionally, with increased mass loading, the probability density function of the fluid temperature deviate more from the Gaussian distribution.

The effects of heat release on the energy exchange in reacting turbulent shear flow

The energy exchange between the kinetic and internal energies in non-premixed reacting compressible homogeneous turbulent shear flow is studied via data generated by direct numerical simulations (DNS). The chemical reaction is modelled by a one- step exothermic irreversible reaction with Arrhenius-type reaction rate. The results show that the heat release has a damping effect on the turbulent kinetic energy for the cases with variable transport properties. The growth rate of the turbulent kinetic energy is primarily in uenced by the reaction through temperature-induced changes in the solenoidal dissipation and modifications in the explicit dilatational terms (pressure–dilatation and dilatational dissipation). The production term in the scaled kinetic energy equation, which is proportional to the Reynolds shear stress anisotropy, is less affected by the heat release. However, the dilatational part of the production term increases during the time when the reaction is important. Additionally, the pressure–dilatation correlation, unlike the non-reacting case, transfers energy in the reacting cases, on the average, from the internal to the kinetic energy. Consequently, the dilatational part of the kinetic energy is enhanced by the reaction. On the contrary, the solenoidal part of the kinetic energy decreases in the reacting cases mainly due to an enhanced viscous dissipation. Similarly to the non-reacting case, it is found that the direct coupling between the solenoidal and dilatational parts of the kinetic energy is small. The structure of the flow with regard to the normal Reynolds stresses is affected by the heat of reaction. Compared to the non-reacting case, the kinetic energy in the direction of the mean velocity decreases during the time when the reaction is important, while it increases in the direction of the shear. This increase is due to the amplification of the dilatational kinetic energy in the x 2 -direction by the reaction. Moreover, the dilatational effects occur primarily in the direction of the shear. These effects are amplified if the heat release is increased or the reaction occurs at later times. The non-reacting models tested for the explicit dilatational terms are not supported by the DNS data for the reacting cases, although it appears that some of the assumptions employed in these models hold also in the presence of heat of reaction.

Large Eddy Simulation of Scalar Transport in a Turbulent Jet Flow

Large eddy simulation (LES) of turbulent reacting flows has been the subject of widespread investigation (McMurtry et al., 1992: Galperin and Orszag, 1993; Menon et al., 1993; McMurtry et al., 1993; Gao and O’Brien, 1993; Madnia and Givi, 1993; Frankel et al., 1993; Cook and Riley. 1994; Givi, 1994; Fureby and Lofstrom, 1994; Moller et al., 1996: Branley and Jones, 1997; Cook et al., 1997; Jimenez et al., 1997: Mathey and Choilet, 1997; Colucci et al., 1998; DesJardin and Frankel, 1998: Jaberi and James. 1998; Reveillon and Vervisch, 1998; Vervisch and Poinsot, 1988). Amongst these, recently Colucci et al. (1998) developed a methodology, termed the “filtered density function” (FDF). The fundamental property of the FDF is to account for the effects of subgrid scale (SGS) scalar fluctuations in a probabilistic manner. This is similar to probability density function (PDF) methods which have proven to be very useful in Reynolds averaging procedures (Libby and Williams, 1980; Libby and Williams. 1994: O’Brien. 1980; Pope, 1985; Dopazo, 1994). Colucci et al. (1998) developed a transport equation for the FDF in constant density flows in which the effects of unresolved convection and subgrid mixing are modeled similarly to those in “conventional” LES, and Reynolds averaging procedures. This transport equation was solved numerically by a Lagrangian Monte Carlo procedure and the results were compared with those obtained by direct numerical simulation (DNS) and by a conventional finite difference LES in which the effects of SGS scalar fluctuations are ignored (LES-FD).