Scale similarity based models and their application to subgrid scale scalar flux modelling in the context of turbulent premixed flames

The performance of a variety of scale similarity (SS) type models for closure of sub-grid scalar flux in the context of Large Eddy Simulations (LES) of premixed turbulent combustion has been assessed. In addition to the well-known SS models, a more recent development by Anderson and Domaradzki (2012) is included in the analysis and also further model extensions and improvements are discussed. The work is based on a priori analysis of two Direct Numerical Simulation (DNS) databases of freely propagating turbulent premixed flames with a range of different Lewis and turbulent Reynolds numbers. Depending on the balance between the effects of flame normal acceleration due to heat release and the effects of turbulent velocity fluctuations, as well as the filter size, the subgrid-scalar flux exhibits both local gradient and counter-gradient transport which presents a considerable modelling challenge. The assessment is based on a correlation analysis and on the magnitude of the model expressions conditional on the Favre averaged reaction progress variable in comparison to the value obtained from DNS. Despite the fact that most of the models have been developed in the context of momentum transport in non-reactive flows they show either comparable or better performance in comparison to more conventional models used for reactive scalar flux closure. It is found that some models are sensitive to the test filter width and recommendations are provided in this regard. Further it is observed that the use of a Favre test filter substantially increases the correlation strength in direction of mean flame propagation where effects of heat release are most pronounced.     

Improved subgrid scale model for dense turbulent solid-liquid two-phase flows

The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules. Assuming that the solid-phase velocity distributions obey the Maxwell equations, the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow, the solid-particle‘s governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations. Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale (SGS) model, in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor, is proposed to model the two-phase governing equations by applying dimension analyses. Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls, the velocity and pressure fields, and the volumetric concentration are calculated. The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.     

Large eddy simulation in a fully developed turbulent flow in a channel and comparison of subgrid eddy viscosity models

The accuracy and computational efficiency are compared for a number of models of subgrid eddy viscosity (Smagorinsky model, renormalization group model, and dynamic and one-parameter models). Space-filtered Navier-Stokes equations are solved numerically by the control-volume approach on a nonuniform grid with the use of high-resolution schemes in time and space. The numerical data are compared with the results of a physical experiment and direct numerical simulation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 31–42, May–June, 2006.     

On the eddy viscosity model of periodic turbulent shear flows

Physical argument shows that eddy viscosity is essentially different from molecular viscosity. By direct numerical simulation, it was shown that for periodic turbulent flows, there is phase difference between Reynolds stress and rate of strain. This finding posed great challenge to turbulence modeling, because most turbulence modeling, which use the idea of eddy viscosity, do not take this effect into account. The project supported by the National Natural Science Foundation of China (19732005) and Liu Hui Center for Applied Mathematics of Nankai & Tianjin University     

Correlation coefficients of the fluctuating density in turbulent premixed flames

 Two-point density measurements by laser induced Rayleigh scattering are used in this study to fully characterise the scalar field in a Bunsen type turbulent premixed flame. The two points are separated within the flame brush in the axial or radial directions. Correlation coefficients are obtained by comparing the evolution of one-point density fluctuations in time or the two-point density fluctuations in both space and time. Time and length scales of the scalar field, and the mean convection velocity of the turbulent scalar structures are deduced from these correlation coefficients. Time scales are calculated from the auto-correlation coefficients, length scales are determined from the space correlation coefficients and the mean convection velocity of the scalar structures in the axial direction is deduced from the space–time correlation coefficients. The relevance of these results for analysing and modelling the structure of turbulent premixed flames is discussed. Received: 30 April 1996 / Accepted: 2 September 1997     

Dynamics of PIV seeding particles in turbulent premixed flames

Particle image velocimetry (PIV) estimates the fluid velocity field measuring the displacement of small dispersed particles between two successive instants separated by a small time interval. The accuracy of the measurements depends on the ability of the particles to accommodate their velocity to the fluid fluctuations. When the fluid is subjected to extreme accelerations, the small but finite inertia prevents the particles from following the fluid, originating a substantial relative velocity. This effect is shown to be crucial for applications of PIV to turbulent premixed combustion, particularly in the product region at locations just behind the instantaneous flame front. The issuing inaccuracy may easily spoil the estimate of certain statistical observables which are of crucial importance in the theory of turbulent premixed combustion. By exploiting the direct numerical simulation of a model air/methane flame, a suitable criterion for proper particle seeding is validated and compared with the corresponding experiments with a combined PIV/OH-LIF (laser-induced fluorescence) system. The proposed parameter, the flamelet Stokes number, depends on particle properties and thermochemical conditions of the flame and substantially restricts the particle dimensions required for a reliable estimate of the relevant flow statistics.     

Dynamic coefficient evaluation for an algebraic subgrid stress model

Static model coefficients for an algebraic subgrid stress (SGS) model are determined using a dynamic approach, based on results from simulations of isotropic decaying turbulence. The study was motivated by the discrepancies in energy transfer predictions using the previously documented coefficients (Bhushan and Warsi, Int. J. Numer. Meth. Fluids 2005; 49 : 489–519). The discrepancies are identified to be due to inconsistent filter functions used in the analytic estimates and the simulations. The study emphasizes that SGS model development should use filter functions compatible with those inherent in CFD application solvers. The dynamic approach predicts consistent model and transfer coefficients for different grid resolutions and is judged to be a reliable basis for model coefficient adjustments. The predicted Leonard's stress coefficient and associated energy transfer coefficients agree very well with the analytic estimates using a Gaussian/cutoff combination filter. This suggests that the modeling of Leonard's stress term using a truncated Taylor series expansion is robust and may not benefit significantly from dynamic modeling. Validation simulations were performed for turbulent channel flow at Re_τ = 180 and 590. The dynamic approach was found to be reliable only for the lower log‐layer of the Re_τ = 590 case, where the scale invariance condition was satisfied. Nonetheless, in this narrow range, the model and transfer coefficients compare well with the isotropic case. The static coefficient algebraic model with new adjusted coefficients shows improved predictions compared with the previous coefficients, for both isotropic decaying turbulence and channel flow cases. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental criteria for the determination of fractal parameters of premixed turbulent flames

The influence of spatial resolution, digitization noise, the number of records used for averaging, and the method of analysis on the determination of the fractal parameters of a high Damköhler number, methane/air, premixed, turbulent stagnation-point flame are investigated in this paper. The flow exit velocity was 5 m/s and the turbulent Reynolds number was 70 based on a integral scale of 3 mm and a turbulent intensity of 7%. The light source was a copper vapor laser which delivered 20 nsecs, 5 mJ pulses at 4 kHz and the tomographic cross-sections of the flame were recorded by a high speed movie camera. The spatial resolution of the images is 155 × 121 m/pixel with a field of view of 50 × 65 mm. The stepping caliper technique for obtaining the fractal parameters is found to give the clearest indication of the cutoffs and the effects of noise. It is necessary to ensemble average the results from more than 25 statistically independent images to reduce sufficiently the scatter in the fractal parameters. The effects of reduced spatial resolution on fractal plots are estimated by artificial degradation of the resolution of the digitized flame boundaries. The effect of pixel resolution, an apparent increase in flame length below the inner scale rolloff, appears in the fractal plots when the measurent scale is less than approximately twice the pixel resolution. Although a clearer determination of fractal parameters is obtained by local averaging of the flame boundaries which removes digitization noise, at low spatial resolution this technique can reduce the fractal dimension. The degree of fractal isotropy of the flame surface can have a significant effect on the estimation of the flame surface area and hence burning rate from two-dimensional images. To estimate this isotropy a determination of the outer cutoff is required and three-dimensional measurements are probably also necessary.     

Multi-scale analysis of subgrid stress and energy dissipation in turbulent channel flow

In present study, the subgrid scale （SGS） stress and dissipation for multiscale formulation of large eddy simulation are analyzed using the data of turbulent channel flow at Ret = 180 obtained by direct numerical simulation. It is found that the small scale SGS stress is much smaller than the large scale SGS stress for all the stress components. The dominant contributor to large scale SGS stress is the cross stress between small scale and subgrid scale motions, while the cross stress between large scale and subgrid scale motions make major contributions to small scale SGS stress. The energy transfer from resolved large scales to subgrid scales is mainly caused by SGS Reynolds stress, while that between resolved small scales and subgrid scales are mainly due to the cross stress. The multiscale formulation of SGS models are evaluated a priori, and it is found that the small- small model is superior to other variants in terms of SGS dissipation.     

Time-resolved measurements of hydroxyl in stable and extinguishing partially premixed turbulent opposed-jet flames

Quantitative hydroxyl time-series measurements from a set of stable and extinguishing turbulent opposed-flow partially premixed CH₄/air flames are used to investigate the effect of Reynolds number and fuel-side equivalence ratio on the structure of turbulent partially premixed flames. The hydroxyl (OH) integral time scale, computed from the autocorrelation function, is used to characterize OH fluctuations and is found to reach a minimum at the axial location of peak OH. Analyses of the duration of and period between bursts in the OH time series are used to examine the dynamics of flame-front motion. In general, with increasing Reynolds number (Re), the distribution in OH burst times shifts towards smaller time scales. A hydroxyl intermittency parameter is also defined from the bursts to quantify the presence or absence of OH. For flames with the same fuel-side equivalence ratio, the hydroxyl intermittency at peak OH remains almost constant when going from stable to extinguishing flames. However, histograms portray an increase in burst separation times for flames displaying occasional extinction events. Hydroxyl time series for a partially premixed flame at a fuel-side equivalence ratio of 2.0 and Re = 6650 are synthesized by using mixture-fraction simulations based on calculated state relationships for OH versus mixture fraction (f). The laminar-flamelet model is employed to explore relations between OH and f so as to predict trends in mixture-fraction time scales.“Time-Series Measurements in Turbulent Opposed-Jet Flames" is submitted for consideration as a full length article to Flow Turbulence and Combustion.     

基于涡粘性模型的翼型湍流流场熵产率计算

利用有限体积法实现了基于非正交同位网格的SIMPLE算法。基于熵分析方法,采用涡粘性模型求解湍流熵产方程,系统研究了湍流模型对二维翼型绕流流场熵产率的影响。通过计算NACA0012翼型在来流雷诺数为2.88×10⁶时,0°攻角~16.5°攻角范围内的翼型表面压力系数分布和升阻力特性,验证了算法及程序的正确性。结果表明,选择不同湍流模型时,翼型流场熵产的计算结果存在差异,湍流耗散是引起流场熵产的主要原因;翼型流场的熵产主要发生在翼型前缘区、壁面边界层和翼型尾流区域,流场熵产率与翼型阻力系数线性相关;当产生分离涡时,粘性耗散引起的熵产下降。     

Large eddy simulation of turbulent premixed piloted flame using artificial thickened flame model coupled with tabulated chemistry

A sub-grid scale (SGS) combustion model, which combines the artificial thickened flame (ATF) model with the flamelet generated manifold (FGM) tabulation method, is proposed. Based on the analysis of laminar flame structures, two self-contained flame sensors are used to track the diffusion and reaction processes with different spatial scales in the flame front, respectively. The dynamic formulation for the proposed SGS combustion model is also performed. Large eddy simulations (LESs) of Bunsen flame F3 are used to evaluate the different SGS combustion models. The results show that the proposed SGS model has the ability in predicting the distributions of temperature and velocity reasonably, while the predictions for the distributions of some species need further improvement. The snapshots of instantaneous normalized progress variables reveal that the flame is more remarkably and severely wrinkled at the flame tip for flame F3. More satisfactory results obtained by the dynamic model indicate that it can preserve the premixed flame propagation characteristics better.     

Large eddy simulation of turbulent channel flow using an algebraic model

In this paper an algebraic model from the constitutive equations of the subgrid stresses has been developed. This model has an additional term in comparison with the mixed model, which represents the backscatter of energy explicitly. The proposed model thus provides independent modelling of the different energy transfer mechanisms, thereby capturing the effect of subgrid scales more accurately. The model is also found to depict the flow anisotropy better than the linear and mixed models. The energy transfer capability of the model is analysed for the isotropic decay and the forced isotropic turbulence. The turbulent plane channel flow simulation is performed over three Reynolds numbers, Re_τ=180, 395 and 590, and the results are compared with that of the dynamic model, Smagorinsky model, and the DNS data. Both the algebraic and dynamic models are in good agreement with the DNS data for the mean flow quantities. However, the algebraic model is found to be more accurate for the turbulence intensities and the higher‐order statistics. The capability of the algebraic model to represent backscatter is also demonstrated. Copyright © 2005 John Wiley & Sons, Ltd.     

Large eddy simulation of turbulent premixed and stratified combustion using flame surface density model coupled with tabulation method

Large eddy simulations (LESs) are performed to investigate the Cambridge premixed and stratified flames, SwB1 and SwB5, respectively. The flame surface density (FSD) model incorporated with two different wrinkling factor models, i.e., the Muppala and Charlette2 wrinkling factor models, is used to describe combustion/turbulence interaction, and the flamelet generated manifolds (FGM) method is employed to determine major scalars. This coupled sub-grid scale (SGS) combustion model is named as the FSD-FGM model. The FGM method can provide the detailed species in the flame which cannot be obtained from the origin FSD model. The LES results show that the FSD-FGM model has the ability of describing flame propagation, especially for stratified flames. The Charlette2 wrinkling factor model performs better than the Muppala wrinkling factor model in predicting the flame surface area change by the turbulence. The combustion characteristics are analyzed in detail by the flame index and probability distributions of the equivalence ratio and the orientation angle, which confirms that for the investigated stratified flame, the dominant combustion modes in the upstream and downstream regions are the premixed mode and the back-supported mode, respectively.     

Structures and stabilization of low calorific value gas turbulent partially premixed flames in a conical burner

Experiments are carried out on partially premixed turbulent flames stabilized in a conical burner. The investigated gaseous fuels are methane, methane diluted with nitrogen, and mixtures of CH₄, CO, CO₂, H₂ and N₂, simulating typical products from gasification of biomass, and co-firing of gasification gas with methane. The fuel and air are partially premixed in concentric tubes. Flame stabilization behavior is investigated and significantly different stabilization characteristics are observed in flames with and without the cone. Planar laser induced fluorescence (LIF) imaging of a fuel-tracer species, acetone, and OH radicals is carried out to characterize the flame structures. Large eddy simulations of the conical flames are carried out to gain further understanding of the flame/flow interaction in the cone. The data show that the flames with the cone are more stable than those without the cone. Without the cone (i.e. jet burner) the critical jet velocities for blowoff and liftoff of biomass derived gases are higher than that for methane/nitrogen mixture with the same heating values, indicating the enhanced flame stabilization by hydrogen in the mixture. With the cone the stability of flames is not sensitive to the compositions of the fuels, owing to the different flame stabilization mechanism in the conical flames than that in the jet flames. From the PLIF images it is shown that in the conical burner, the flame is stabilized by the cone at nearly the same position for different fuels. From large eddy simulations, the flames are shown to be controlled by the recirculation flows inside cone, which depends on the cone angle, but less sensitive to the fuel compositions and flow speed. The flames tend to be hold in the recirculation zones even at very high flow speed. Flame blowoff occurs when significant local extinction in the main body of the flame appears at high turbulence intensities.     

Collaborative testing of eddy structure identification methods in free turbulent shear flows

 The thrust of this paper is to validate, test and compare several Coherent Structure eduction methods utilizing the same data base. The flow chosen was that of an experimental study of a plane, incompressible, fully developed turbulent two-stream mixing layer. The mixing layer was chosen as the data base because it has been studied extensively from a coherent structures point of view. In addition, its characteristics (similarity, convection velocities, etc.) are well documented. There are also no wall effects so that comparisons between techniques are simplified. The data was collected from hot wire rakes with good spatial resolution thus allowing the contributors to apply and test different structure eduction techniques. The techniques chosen for discussion and used here have found wide utilization over the past decade, and all hold forth the promise of extensive application in the future. These include: Conditional Sampling (Vorticity-based and other methods); Wavelets; Pattern Recognition Analysis; Proper Orthogonal Decomposition; Stochastic Estimation; Topological Concept-based methods; Full Field Methods (e.g., pseudo flow visualization). All are illustrated by application to the mixing layer data base, and comparisons made between the results. This common study has shown that direct comparisons between results of several methods are now possible. Good quantitive and qualitative agreement between the different methods have been observed as well as some differences noted. As an example, the size of the averaged structures computed from the various methods compare to within 6 percent. Received: 15 December 1994/Accepted: 18 December 1997     

An efficient very large eddy simulation model for simulation of turbulent flow

Among the various hybrid methodologies, Speziale's very large eddy simulation (VLES) is one that was proposed very early. It is a unified simulation approach that can change seamlessly from Reynolds Averaged Navier–Stokes (RANS) to direct numerical simulation (DNS) depending on the numerical resolution. The present study proposes a new improved variant of the original VLES model. The advantages are achieved in two ways: (i) RANS simulation can be recovered near the wall which is similar to the detached eddy simulation concept; (ii) a LES subgrid scale model can be reached by the introduction of a third length scale, that is, the integral turbulence length scale. Thus, the new model can provide a proper LES mode between the RANS and DNS limits. This new methodology is implemented in the standard k ? ? model. Applications are conducted for the turbulent channel flow at Reynolds number of Re_τ = 395, periodic hill flow at Re = 10,595, and turbulent flow past a square cylinder at Re = 22,000. In comparison with the available experimental data, DNS or LES, the new VLES model produces better predictions than the original VLES model. Furthermore, it is demonstrated that the new method is quite efficient in resolving the large flow structures and can give satisfactory predictions on a coarse mesh. Copyright © 2012 John Wiley & Sons, Ltd.