Large Eddy Simulation Particle Research Articles

Lagrangian tracking of soot particles in LES of gas turbines

Expected stringent legislation on particulate matter (PM) emission by gas turbine combustors is currently motivating considerable efforts to better understand, model and predict soot formation. This complex phenomenon is very difficult to study in detail with experiment, and numerical simulation is an essential complementary tool. Considering that the chemistry of soot particles strongly depends on their size, the numerical prediction of soot formation requires the description of their size distribution. To do so, either Eulerian methods (sectional or moments), or stochastic Lagrangian approaches are reported in the literature. In the present work a far more simple semi-deterministic Lagrangian approach is proposed. Combined to the semi-empirical model of Leung et al. (1991) for soot chemistry, the Lagrangian approach is first validated on a one-dimensional premixed ethylene-air flame. The model is then applied to a gaseous non-premixed ethylene-air burner measured at DLR and computed with Large Eddy Simulation (LES). The gaseous chemistry is described with an Analytically Reduced Chemistry (ARC) to guarantee a good prediction of combustion and gaseous soot precursors. Results are validated against experiment and compared, in terms of accuracy and CPU cost, to an Eulerian semi-empirical model. To the authors knowledge, it is the first time that such Lagrangian particle tracking approach is used for soot. Results obtained in terms of accuracy and computing time are very encouraging.

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

ABSTRACTThe rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.

LARGE EDDY SIMULATION FOR TRANSESTERIFICATION OF WASTE VEGETABLE OIL

The paper provides detailed information involved in the numerical simulation of transesterification of waste vegetable oil (WVO). The main objective of this work is to perform mixing study based on large eddy simulation particle image Velocimetry (LES-PIV) which resolved the turbulent scale. Reynolds stress model (RSM) was subsequently used to validate the result using a multiple reference frame (MRF) approach for the impeller-vessel geometry. Experimental FAME yield and liquid velocities were found to be dependent on stirrer speeds, impeller bottom distance and bulk flow pattern. Thermodynamic properties of the reaction components were incorporated as user defined function (UDF) for the mixing models. FAME yield were predicted in terms of species concentration and compared fairly well with experimental condition for 1 and 2-L STR, where yield from the numerical model varied by about 18 and 23 % for 1 and 2-L STR respectively. The characteristic time scales were used to show the relevant mixing scale to describe the process.

A nonlinear model for the subgrid timescale experienced by heavy particles in large eddy simulation of isotropic turbulence with a stochastic differential equation

The effects of subgrid scale (SGS) motions on the dispersion of heavy particles raise a challenge to the large-eddy method of simulation (LES). As a necessary first step, we propose the use of a stochastic differential equation (SDE) to represent the SGS contributions to the relative dispersions of heavy particles in LES of isotropic turbulence. The main difficulty is in closing the SGS-SDE model whilst accounting for the effects of particle inertia, filter width and gravity. The physics of the interaction between heavy particles and SGS turbulence is explored using the filtered direct numerical simulation method. It is found in the present work that (i) the ratio of the SGS Lagrangian and Eulerian timescales is different from that of the full-scale Lagrangian and Eulerian timescales. The ratios are also dependent on filter widths. (ii) In the absence of gravity, the SGS timescale seen by heavy particles non-monotonically changes with particle Stokes number and has a maximum at particle Stokes number (St = τp/δTE) near 0.5. (iii) In the presence of gravity, a similarity law exists between the SGS Lagrangian correlation function seen by a heavy particle within a time-delay τ and the SGS spatial correlation function with the displacement 〈w〉τ, where 〈w〉 is the average settling velocity of a heavy particle. The joint effects of particle inertia and gravity are accounted for using the elliptic model for pair correlation of SGS velocity seen by heavy particles. The SGS timescale seen by heavy particles is extracted from the elliptic model and used to close the SGS-SDE model. The validations of the model against direct numerical simulation show that the SGS-SDE model can improve the performance of LES on relative dispersions especially when their initial separations are in the inertial subrange. Furthermore, we assess the performance of the SGS-SDE model by comparing the results with the approximate deconvolution method. The results show that the SGS-SDE model is more suitable for particles with small Stokes numbers, StK < 2. The model developed here provides a basis for the development of a more advanced SGS model for particles in non-homogeneous and anisotropic turbulent flows in pipes or channels.

Ideal stochastic forcing for the motion of particles in large-eddy simulation extracted from direct numerical simulation of turbulent channel flow

The motion of small particles in turbulent conditions is influenced by the entire range of length- and time-scales of the flow. At high Reynolds numbers this range of scales is too broad for direct numerical simulation (DNS). Such flows can only be approached using large-eddy simulation (LES), which requires the introduction of a sub-filter model for the momentum dynamics. Likewise, for the particle motion the effect of sub-filter scales needs to be reconstructed approximately, as there is no explicit access to turbulent sub-filter scales. To recover the dynamic consequences of the unresolved scales, partial reconstruction through approximate deconvolution of the LES-filter is combined with explicit stochastic forcing in the equations of motion of the particles. We analyze DNS of high-Reynolds turbulent channel flow to a priori extract the ideal forcing that should be added to retain correct statistical properties of the dispersed particle phase in LES. The probability density function of the velocity differences that need to be included in the particle equations and their temporal correlation display a striking and simple structure with little dependence on Reynolds number and particle inertia, provided the differences are normalized by their RMS, and the correlations expressed in wall units. This is key to the development of a general “stand-alone” stochastic forcing for inertial particles in LES.

Turbulence modulation by particles in Large Eddy Simulation of backward-facing step flow

Large Eddy Simulation of backward-facing step flow laden with particles were performed. The number of particles is chosen very large and the volume fraction of particles is high enough for consideration of two-way coupling. This means that the particles are influenced by fluid and vice versa. The inter-particle collisions are neglected. The Euler-Lagrange method is adopted, which means that the fluid is considered to be continuum (Euler approach) and for each individual particle is solved Lagrangian equation of motion. Particles are considered to be spherical. The simulations are performed for different mass fractions of 90 μm glass particles. The results are compared to the single-phase flow in order to investigate the effect of the particles on the turbulence statistics of the carrier phase.

Subgrid scale fluid velocity timescales seen by inertial particles in large-eddy simulation of particle-laden turbulence

Large-eddy simulation (LES) has emerged as a promising tool for simulating turbulent flows in general and, in recent years,has also been applied to the particle-laden turbulence with some success (Kassinos et al., 2007). The motion of inertial particles is much more complicated than fluid elements, and therefore, LES of turbulent flow laden with inertial particles encounters new challenges. In the conventional LES, only large-scale eddies are explicitly resolved and the effects of unresolved, small or subgrid scale (SGS) eddies on the large-scale eddies are modeled. The SGS turbulent flow field is not available. The effects of SGS turbulent velocity field on particle motion have been studied by Wang and Squires (1996), Armenio et al. (1999), Yamamoto et al. (2001), Shotorban and Mashayek (2006a,b), Fede and Simonin (2006), Berrouk et al. (2007), Bini and Jones (2008), and Pozorski and Apte (2009), amongst others. One contemporary method to include the effects of SGS eddies on inertial particle motions is to introduce a stochastic differential equation (SDE), that is, a Langevin stochastic equation to model the SGS fluid velocity seen by inertial particles (Fede et al., 2006; Shotorban and Mashayek, 2006a; Shotorban and Mashayek, 2006b; Berrouk et al., 2007; Bini and Jones, 2008; Pozorski and Apte, 2009).However, the accuracy of such a Langevin equation model depends primarily on the prescription of the SGS fluid velocity autocorrelation time seen by an inertial particle or the inertial particle–SGS eddy interaction timescale (denoted by $\delt T_{Lp}$ and a second model constant in the diffusion term which controls the intensity of the random force received by an inertial particle (denoted by C_0, see Eq. (7)). From the theoretical point of view, dTLp differs significantly from the Lagrangian fluid velocity correlation time (Reeks, 1977; Wang and Stock, 1993), and this carries the essential nonlinearity in the statistical modeling of particle motion. dTLp and C0 may depend on the filter width and particle Stokes number even for a given turbulent flow. In previous studies, dTLp is modeled either by the fluid SGS Lagrangian timescale (Fede et al., 2006; Shotorban and Mashayek, 2006b; Pozorski and Apte, 2009; Bini and Jones, 2008) or by a simple extension of the timescale obtained from the full flow field (Berrouk et al., 2007). In this work, we shall study the subtle and on-monotonic dependence of $\delt T_{Lp}$ on the filter width and particle Stokes number using a flow field obtained from Direct Numerical Simulation (DNS). We then propose an empirical closure model for $\delta T_{Lp}$. Finally, the model is validated against LES of particle-laden turbulence in predicting single-particle statistics such as particle kinetic energy. As a first step, we consider the particle motion under the one-way coupling assumption in isotropic turbulent flow and neglect the gravitational settling effect. The one-way coupling assumption is only valid for low particle mass loading.