Fractal modelling of turbulent mixing

The aim of this work is to propose a new model for turbulent flows, called the fractal model (FM), applicable both in a Reynolds averaged Navier–Stokes (RANS) and a large-eddy simulation (LES) formulation, with the ultimate goal of applying it to simulate turbulent combustion irrelevant of its mode (premixed or non-premixed). The model is able to turn itself off in the laminar zones of the flow, and in particular near walls. It is based on the fractal theory. It describes the physics of the smaller spatial scales and therefore represents a small-scales model.

FM describes the physics of the small scales of turbulence based on the phenomenological concept of vortex cascade and on the self-similar behaviour of turbulence in the inertial range. Such a model is used in each cell of a numerical calculation. A characteristic length Δ is associated to each cell, and the local energy u ³ _Δ/Δ is distributed over a certain number of eddies, which depends on the local Reynolds number Re _Δ. Each vortex of the cascade generates N _c vortices; the recursive process of vortex generation terminates at the dissipative scale level, i.e. when the eddy Reynolds number is equal to one. FM is also able to estimate the volume fraction occupied by the dissipative fine structures of turbulence; this quantity is critical in reactive turbulent flows.

The physics of small scales is summarized by a turbulent ‘viscosity’ μ_t, to be added to the molecular one. μ_t is zero where the flow is laminar and, in particular, goes to zero at solid walls. Assuming μ_t to be isotropic, FM is applicable in a RANS formulation (IFM, isotropic fractal model). The model can be extended to the anisotropic case (AFM, anisotropic fractal model) and therefore used to close the transport equations in an LES approach. In the present paper, the model (IFM) is used in a RANS approach and is validated through a test case studied experimentally by Johnson and Bennett, and numerically (with LES) by Akselvoll and Moin. The results obtained are in good agreement both with the experimental and the numerical ones. Other tests are being performed.     

LES/PDF for premixed combustion in the DNS limit

We investigated the behaviour of the composition probability density function (PDF) model equations used in a large-eddy simulation (LES) of turbulent combustion in the direct numerical simulation (DNS) limit; that is, in the limit of the LES resolution length scale Δ (and the numerical mesh spacing h) being small compared to the smallest flow length scale, so that the resolution is sufficient to perform a DNS. The correct behaviour of a PDF model in the DNS limit is that the resolved composition fields satisfy the DNS equations, and there are no residual fluctuations (i.e. the PDF is everywhere a delta function). In the DNS limit, the treatment of molecular diffusion in the PDF equations is crucial, and both the ‘random-walk’ and ‘mean-drift’ models for molecular diffusion are investigated. Two test cases are considered, both of premixed laminar flames (of thickness δ_L). We examine the solutions of the model PDF equations for these test cases as functions of Δ/δ_L and h/δ_L. Each of the two PDF models has advantages and disadvantages. The mean-drift model behaves correctly in the DNS limit, but it is more difficult to implement and computationally more expensive. The random-walk model does not have the correct behaviour in the DNS limit in that it produces non-zero residual fluctuations. However, if the specified mixing rate Ω normalised by the reaction timescale τ_c is sufficiently large (Ωτ_c ? 1), then the residual fluctuations are less than 10% and the observed flame speed and thickness are close to their laminar values. Away from the DNS limit (i.e. h/δ_L ? 1), the observed flame thickness scales with the mesh spacing h, and the flame speed scales with Ωh. For this case it is possible to construct a non-general specification of the mixing rate Ω such that the flame speed matches the laminar flame speed.     

Experimental and numerical study of a conical turbulent partially premixed flame

The structure and dynamics of a turbulent partially premixed methane/air flame in a conical burner were investigated using laser diagnostics and large-eddy simulations (LES). The flame structure inside the cone was characterized in detail using LES based on a two-scalar flamelet model, with the mixture fraction for the mixing field and level-set G-function for the partially premixed flame front propagation. In addition, planar laser induced florescence (PLIF) of CH and chemiluminescence imaging with high speed video were performed through a glass cone. CH and CH₂O PLIF were also used to examine the flame structures above the cone. It is shown that in the entire flame the CH layer remains very thin, whereas the CH₂O layer is rather thick. The flame is stabilized inside the cone a short distance above the nozzle. The stabilization of the flame can be simulated by the triple-flame model but not the flamelet-quenching model. The results show that flame stabilization in the cone is a result of premixed flame front propagation and flow reversal near the wall of the cone which is deemed to be dependent on the cone angle. Flamelet based LES is shown to capture the measured CH structures whereas the predicted CH₂O structure is somewhat thinner than the experiments.     

LES studies of the flow in a swirl gas combustor

Environmental and other practical concerns have led to the development of compact gas turbine combustors burning lean mixtures leading to potentially low CO and NO_x emissions. The compact design requires efficient atomization and mixing together with a compact premixed flame. Associated with these requirements are higher temperatures, increased heat transfer, and thermal load, thus increasing the danger of combustion instabilities (causing performance deterioration and excessive mechanical loads), and possible off-design operation. Numerical simulations of reacting flows are well suited to address these issues. To this end, large eddy simulation (LES) is particularly promising. The philosophy behind LES is to explicitly simulate the large scales of the flow and the thermochemistry, affected by boundary conditions whilst modeling only the small scales, including the interaction between the flow and the combustion processes. Here, we examine the flow and the flame in a model gas turbine combustor (General Electric’s lean premixed dry low NO_x LM6000) to evaluate the potential of LES for design studies of engineering applications and to study the effects of the combustor confinement geometry on the flow and on the flame dynamics. Two LES models, a Monotone Integrated LES model with 1 and 2 step Ahrrenius chemistry, and a fractal flame-wrinkling LES model coupled to a conventional one-equation eddy-viscosity subgrid model, are used. Reasonable agreement is found when comparing predictions with experimental data and with other LES computations of the same case. Furthermore, the combustor confinement geometry is found to strongly affect the vortical flow, and hence also the flame and its dynamics.     

Comparison of a spectral model for premixed turbulent flame propagation to DNS and experiments

A recently developed spectral model for premixed turbulent combustion in the flamelet regime (based on the EDQNM turbulence theory) has been compared with both direct numerical simulations (DNS) and experimental data. The 128³ DNS is performed at a Reynolds number of 223 based on the integral length scale. Good agreement is observed for both single- and two-point quantities (i.e. ratio of the turbulent to laminar burning velocities, scalar autocorrelation, dissipation and scalar-velocity cross correlation spectra) for the two different values of u′/s _L0 considered. The model also predicts the rapid transient behaviour of the flame at early times. An experimental set-up is then described for generating a lean methane-air flame and measuring two-point spatial correlations along the midpoint of the flame brush (i.e. along the C¯=0.5 contour). The experimental measurements in the flamelet regime take the form of a discontinuous or ‘telegraph’ signal. The EDQNM model, in contrast, describes an ‘ensemble’ of flames, and thus is based solely on continuous variables. A theoretical relationship between the correlation obtained from the EDQNM model and the equivalent correlation for a discontinuous (experimental) flame is derived. The relationship is used to enable a meaningful comparison between experimentally observed and model correlations. In general, the agreement is good for the three different cases considered in this study, with most of the error occurring at the lowest Reynolds number (Re _L =22). Furthermore, it is shown that considerably more error would result if no attempt is made to convert the ensemble representation in the model to an equivalent single-flame or ‘telegraph’ signal.     

Vorticity,backscatter and counter-gradient transport predictions using two-level simulation of turbulent flows

The two-level simulation (TLS) method evolves both the large-and the small-scale fields in a two-scale approach and has shown good predictive capabilities in both isotropic and wall-bounded high Reynolds number (Re) turbulent flows in the past. Sensitivity and ability of this modelling approach to predict fundamental features (such as backscatter, counter-gradient turbulent transport, small-scale vorticity, etc.) seen in high Re turbulent flows is assessed here by using two direct numerical simulation (DNS) datasets corresponding to a forced isotropic turbulence at Taylor’s microscale-based Reynolds number Re_λ ≈ 433 and a fully developed turbulent flow in a periodic channel at friction Reynolds number Re_τ ≈ 1000. It is shown that TLS captures the dynamics of local co-/counter-gradient transport and backscatter at the requisite scales of interest. These observations are further confirmed through a posteriori investigation of the flow in a periodic channel at Re_τ = 2000. The results reveal that the TLS method can capture both the large- and the small-scale flow physics in a consistent manner, and at a reduced overall cost when compared to the estimated DNS or wall-resolved LES cost.     

Stratified turbulent Bunsen flames: flame surface analysis and flame surface density modelling

In this paper it is investigated whether the Flame Surface Density (FSD) model, developed for turbulent premixed combustion, is also applicable to stratified flames. Direct Numerical Simulations (DNS) of turbulent stratified Bunsen flames have been carried out, using the Flamelet Generated Manifold (FGM) reduction method for reaction kinetics. Before examining the suitability of the FSD model, flame surfaces are characterized in terms of thickness, curvature and stratification.

All flames are in the Thin Reaction Zones regime, and the maximum equivalence ratio range covers 0.1?φ?1.3. For all flames, local flame thicknesses correspond very well to those observed in stretchless, steady premixed flamelets. Extracted curvature radii and mixing length scales are significantly larger than the flame thickness, implying that the stratified flames all burn in a premixed mode. The remaining challenge is accounting for the large variation in (subfilter) mass burning rate.

In this contribution, the FSD model is proven to be applicable for Large Eddy Simulations (LES) of stratified flames for the equivalence ratio range 0.1?φ?1.3. Subfilter mass burning rate variations are taken into account by a subfilter Probability Density Function (PDF) for the mixture fraction, on which the mass burning rate directly depends. A priori analysis point out that for small stratifications (0.4?φ?1.0), the replacement of the subfilter PDF (obtained from DNS data) by the corresponding Dirac function is appropriate. Integration of the Dirac function with the mass burning rate m=m(φ), can then adequately model the filtered mass burning rate obtained from filtered DNS data. For a larger stratification (0.1?φ?1.3), and filter widths up to ten flame thicknesses, a β-function for the subfilter PDF yields substantially better predictions than a Dirac function. Finally, inclusion of a simple algebraic model for the FSD resulted only in small additional deviations from DNS data, thereby rendering this approach promising for application in LES.     

Assessment of dynamic closure for premixed combustion large eddy simulation

Turbulent piloted Bunsen flames of stoichiometric methane–air mixtures are computed using the large eddy simulation (LES) paradigm involving an algebraic closure for the filtered reaction rate. This closure involves the filtered scalar dissipation rate of a reaction progress variable. The model for this dissipation rate involves a parameter β_c representing the flame front curvature effects induced by turbulence, chemical reactions, molecular dissipation, and their interactions at the sub-grid level, suggesting that this parameter may vary with filter width or be a scale-dependent. Thus, it would be ideal to evaluate this parameter dynamically by LES. A procedure for this evaluation is discussed and assessed using direct numerical simulation (DNS) data and LES calculations. The probability density functions of β_c obtained from the DNS and LES calculations are very similar when the turbulent Reynolds number is sufficiently large and when the filter width normalised by the laminar flame thermal thickness is larger than unity. Results obtained using a constant (static) value for this parameter are also used for comparative evaluation. Detailed discussion presented in this paper suggests that the dynamic procedure works well and physical insights and reasonings are provided to explain the observed behaviour.     

Level set simulations of turbulent thermonuclear deflagration in degenerate carbon and oxygen

We study the dynamics of thermonuclear flames propagating in fuel stirred by stochastic forcing. The fuel consists of carbon and oxygen in a state which is encountered in white dwarfs close to the Chandrasekhar limit. The level set method is applied to represent the flame fronts numerically. The computational domain for the numerical simulations is cubic, and periodic boundary conditions are imposed. The goal is the development of a suitable flame speed model for the small-scale dynamics of turbulent deflagration in thermonuclear supernovae. Because the burning process in a supernova explosion is transient and spatially inhomogeneous, the localized determination of subgrid scale closure parameters is essential. We formulate a semi-localized model based on the dynamical equation for the subgrid scale turbulence energy k _sgs. The turbulent flame speed s _t is of the order √2k _sgs. In particular, the subgrid scale model features a dynamic procedure for the calculation of the turbulent energy transfer from resolved toward subgrid scales, which has been successfully applied to combustion problems in engineering. The options of either including or suppressing inverse energy transfer in the turbulence production term are compared. In combination with the piece-wise parabolic method for the hydrodynamics, our results favour the latter option. Moreover, different choices for the constant of proportionality in the asymptotic flame speed relation, s _t∝√2k _sgs, are investigated.     

Proposed stochastic parameterisations of subgrid turbulence in large eddy simulations of turbulent channel flow

Stochastic and deterministic subgrid parameterisations are developed for the large eddy simulation (LES) of a turbulent channel flow with friction-velocity-based Reynolds number of Re_τ = 950 and centreline-based Reynolds number of Re₀ = 20,580. The subgrid model coefficients (eddy viscosities) are determined from the statistics of truncated reference direct numerical simulations (DNSs). The stochastic subgrid model consists of a mean-field shift, a drain eddy viscosity acting on the resolved field and a stochastic backscatter force of variance proportional to the backscatter eddy viscosity. The deterministic variant consists of a net eddy viscosity acting on the resolved field, which represents the net effect of the drain and backscatter. LES adopting the stochastic and deterministic models is shown to reproduce the time-averaged kinetic energy spectra of the DNS within the resolved scales.     

The effect of subgrid-scale models on the entrainment of a passive scalar in a turbulent planar jet

Classical large-eddy simulation (LES) modelling assumes that the passive subgrid-scale (SGS) models do not influence large-scale quantities, even though there is now ample evidence of this in many flows. In this work, direct numerical simulation (DNS) and large-eddy simulations of turbulent planar jets at Reynolds number Re_H = 6000 including a passive scalar with Schmidt number Sc = 0.7 are used to study the effect of several SGS models on the flow integral quantities e.g. velocity and scalar jet spreading rates. The models analysed are theSmagorinsky, dynamic Smagorinsky, shear-improved Smagorinsky and the Vreman. Detailed analysis of the thin layer bounding the turbulent and non-turbulent regions – the so-called turbulent/non-turbulent interface (TNTI) – shows that this region raises new challenges for classical SGS models. The small scales are far from equilibrium and contain a high fraction of the total kinetic energy and scalar variance, but the situation is worse for the scalar than for the velocity field. Both a-priori and a-posteriori (LES) tests show that the dynamic Smagorinsky and shear-improved models give the best results because they are able to accurately capture the correct statistics of the velocity and passive scalar fluctuations near the TNTI. The results also suggest the existence of a critical resolution Δ_x, of the order of the Taylor scale λ, which is needed for the scalar field. Coarser passive scalar LES i.e. Δ_x ≥ λ results in dramatic changes in the integral quantities. This fact is explained by the dynamics of the small scales near the jet interface.     

Flame front analysis of high-pressure turbulent lean premixed methane–air flames

An experimental study on lean turbulent premixed methane–air flames at high pressure is conducted by using a turbulent Bunsen flame configuration. A single equivalence ratio flame at Φ = 0.6 is explored for pressures ranging from atmospheric pressure to 0.9 MPa. LDA measurements of the cold flow indicate that turbulence intensities and the integral length scale are not sensitive to pressure. Due to the decreased kinematic viscosity with increasing pressure, the turbulent Reynolds numbers increase, and isotropic turbulence scaling relations indicate a large decrease of the smallest turbulence scales. Available experimental results and PREMIX code computations indicate a decrease in laminar flame propagation velocities with increasing pressure, essentially between the atmospheric pressure and 0.5 MPa. The u′/S_L ratio increases therefore accordingly. Instantaneous flame images are obtained by Mie scattering tomography. The images and their analysis show that pressure increase generates small scale flame structures. In an attempt to generalize these results, the variance of the flamelet curvatures, the standard deviation of the flamelet orientation angle, and the flamelet crossing lengths have been plotted against which is proportional to the ratio between the integral and Taylor length scales, and which increases with pressure. These three parameters vary linearly with the ratio between large and small turbulence scales and clearly indicate the strong effect of this parameter on premixed turbulent flame dynamics and structure. An obvious consequence is the increase in flame surface density and hence burning rate with pressure, as confirmed by its direct determination from 2D tomographic images.     

Modelling alkali metal emissions in large-eddy simulation of a preheated pulverised-coal turbulent jet flame using tabulated chemistry

The numerical modelling of alkali metal reacting dynamics in turbulent pulverised-coal combustion is discussed using tabulated sodium chemistry in large eddy simulation (LES). A lookup table is constructed from a detailed sodium chemistry mechanism including five sodium species, i.e. Na, NaO, NaO₂, NaOH and Na₂O₂H₂, and 24 elementary reactions. This sodium chemistry table contains four coordinates, i.e. the equivalence ratio, the mass fraction of the sodium element, the gas-phase temperature, and a progress variable. The table is first validated against the detailed sodium chemistry mechanism by zero-dimensional simulations. Then, LES of a turbulent pulverised-coal jet flame is performed and major coal-flame parameters compared against experiments. The chemical percolation devolatilisation (CPD) model and the partially stirred reactor (PaSR) model are employed to predict coal pyrolysis and gas-phase combustion, respectively. The response of the five sodium species in the pulverised-coal jet flame is subsequently examined. Finally, a systematic global sensitivity analysis of the sodium lookup table is performed and the accuracy of the proposed tabulated sodium chemistry approach has been calibrated.     

A LES/PDF simulator on block-structured meshes

A block-structured mesh large-eddy simulation (LES)/probability density function (PDF) simulator is developed within the OpenFOAM framework for computational modelling of complex turbulent reacting flows. The LES/PDF solver is a hybrid solution methodology consisting of (i) a finite-volume (FV) method for solving the filtered mass and momentum equations (LES solver), and (ii) a Lagrangian particle-based Monte Carlo algorithm (PDF solver) for solving the modelled transport equation of the filtered joint PDF of compositions. Both the LES and the PDF methods are developed and combined to form a hybrid LES/PDF simulator entirely within the OpenFOAM framework. The in situ adaptive tabulation method [S.B. Pope, Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation, Combust. Theory Model. 1 (1997), pp. 41–63; L. Lu, S.R. Lantz, Z. Ren, and B.S. Pope, Computationally efficient implementation of combustion chemistry in parallel PDF calculations, J. Comput. Phys. 228 (2009), pp. 5490–5525] is incorporated into the new LES/PDF solver for efficient computations of combustion chemistry with detailed reaction kinetics. The method is designed to utilise a block-structured mesh and can readily be extended to unstructured grids. The three-stage velocity interpolation method of Zhang and Haworth [A general mass consistency algorithm for hybrid particle/finite-volume PDF methods, J. Comput. Phys. 194 (2004), pp. 156–193] is adapted to interpolate the LES velocity field onto particle locations accurately and to enforce the consistency between LES and PDF fields at the numerical solution level. The hybrid algorithm is fully parallelised using the conventional domain decomposition approach. A detailed examination of the effects of each stage and the overall performance of the velocity interpolation algorithm is performed. Accurate coupling of the LES and PDF solvers is demonstrated using the one-way coupling methodology. Then the fully two-way coupled LES/PDF solver is successfully applied to simulate the Sandia Flame-D, and a turbulent non-swirling premixed flame and a turbulent swirling stratified flame from the Cambridge turbulent stratified flame series [M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames I: Non-swirling flows, Combust. Flame 159 (2012), pp. 2896–2911; M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames II: Swirling flows, Combust. Flame 159 (2012), pp. 2912–2929]. It is found that the LES/PDF method is very robust and the results are in good agreement with the experimental data for both flames.     

Reaction zone structures and mixing characteristics of partially premixed swirling CH4/air flames in a gas turbine model combustor

The mixing, reaction progress, and flame front structures of partially premixed flames have been investigated in a gas turbine model combustor using different laser techniques comprising laser Doppler velocimetry for the characterization of the flow field, Raman scattering for simultaneous multi-species and temperature measurements, and planar laser-induced fluorescence of CH for the visualization of the reaction zones. Swirling CH₄/air flames with Re numbers between 7500 and 60,000 have been studied to identify the influence of the turbulent flow field on the thermochemical state of the flames and the structures of the CH layers. Turbulence intensities and length scales, as well as the classification of these flames in regime diagrams of turbulent combustion, are addressed. The results indicate that the flames exhibit more characteristics of a diffusion flame (with connected flame zones) than of a uniformly premixed flame.     

Large eddy simulations of turbulent flames using the filtered density function model

Large eddy simulations (LES) of the Sandia/Sydney swirl burners (SM1 and SMA1) and the Sandia/Darmstadt piloted jet diffusion flame (Flame D) are performed. These flames are part of the database of turbulent reacting flows widely considered as benchmark test cases for validating turbulent-combustion models. In the simulations presented in this paper, the subgrid scale (SGS) closure model adopted for turbulence-chemistry interactions is based on the transport filtered density function (FDF) model. In the FDF model, the transport equation for the joint probability density function (PDF) of scalars is solved. The main advantage of this model is that the filtered reaction rates can be exactly computed. However, the density field, computed directly from the FDF solver and needed in the hydrodynamic equations, is noisy and causes numerical instability. Two numerical approaches that yield a smooth density field are examined. The two methods are based on transport equations for specific sensible enthalpy (h_s) and RT, where R is the gas constant and T is the temperature. Consistency of the two methods is assessed in a bluff-body configuration using Reynolds averaged Navier-Stokes (RANS) methodology in conjunction with the transported PDF method. It is observed that the h_s method is superior to the RT method. Both methods are used in LES of the SM1 burner. In the near-field region, the h_s method produces better predictions of temperature. However, in the far-field region, both methods show deviation from data. Simulations of the SMA1 burner and Flame D are also presented using the h_s method. Some deficiencies are seen in the predictions of the SMA1 burner that may be related to the simple chemical kinetics model and mixing model used in the simulations. Simulations of Flame D show good agreement with data. These results indicate that, while further improvements to the methodology are needed, the LES/FDF method has the potential to accurately predict complex turbulent flames.     

Finite element-based large eddy simulation using a combination of the variational multiscale method and the dynamic Smagorinsky model

A finite element-based large eddy simulation (LES) is proposed using a combination of the residual-based variational multiscale (RBVMS) approach and the dynamic Smagorinsky eddy-viscosity model. In this combined model, the cross-stress terms are modelled using the RBVMS approach while the eddy-viscosity model is used to represent the Reynolds stresses. The eddy-viscosity is computed dynamically in a local fashion for which a localized version of the variational Germano identity is developed. To improve the robustness of the local dynamic procedure, two types of averaging schemes are considered. The first type employs spatial averaging over homogeneous direction(s) which is only applicable to turbulent flows with statistical homogeneity in at least one direction. The second type is based on Lagrangian averaging over fluid pathtubes, which is applicable to inhomogeneous turbulent flows. The predictions from the combined model are compared to the direct numerical simulation or experimental data and also to the predictions from the RBVMS model. This is done for two cases: turbulent flow in a channel (Re_τ = 590) and flow over a cylinder (Re_D = 3, 900). For the turbulent channel flow, predictions are similar between the RBVMS model and the combined model. For flow over a cylinder, the combined model provides better predictions, specifically for fluctuations in the streamwise velocity and lift.     

Generalised scale-by-scale energy-budget equations and large-eddy simulations of anisotropic scalar turbulence at various Schmidt numbers

A necessary condition for the accurate prediction of turbulent flows using large-eddy simulation (LES) is the correct representation of energy transfer between the different scales of turbulence in the LES. For scalar turbulence, transfer of energy between turbulent length scales is described by a transport equation for the second moment of the scalar increment. For homogeneous isotropic turbulence, the underlying equation is the well-known Yaglom equation. In the present work, we study the turbulent mixing of a passive scalar with an imposed mean gradient by homogeneous isotropic turbulence. Both direct numerical simulations (DNS) and LES are performed for this configuration at various Schmidt numbers, ranging from 0.11 to 5.56. As the assumptions made in the derivation of the Yaglom equation are violated for the case considered here, a generalised Yaglom equation accounting for anisotropic effects, induced by the mean gradient, is derived in this work. This equation can be interpreted as a scale-by-scale energy-budget equation, as it relates at a certain scale r terms representing the production, turbulent transport, diffusive transport and dissipation of scalar energy. The equation is evaluated for the conducted DNS, followed by a discussion of physical effects present at different scales for various Schmidt numbers. For an analysis of the energy transfer in LES, a generalised Yaglom equation for the second moment of the filtered scalar increment is derived. In this equation, new terms appear due to the interaction between resolved and unresolved scales. In an a-priori test, this filtered energy-budget equation is evaluated by means of explicitly filtered DNS data. In addition, LES calculations of the same configuration are performed, and the energy budget as well as the different terms are thereby analysed in an a-posteriori test. It is shown that LES using an eddy viscosity model is able to fulfil the generalised filtered Yaglom equation for the present configuration. Further, the dependence of the terms appearing in the filtered energy-budget equation on varying Schmidt numbers is discussed.     

Stabilization mechanism of turbulent premixed flames in strongly swirled flows

The stabilization of turbulent premixed flames in strongly swirled flows undergoing vortex breakdown is studied in the case of the ALSTOM En-Vironmental (EV) double cone burner using a simple one-dimensional boundary layer type model and computational fluid dynamics, mainly at the level of large-eddy simulation. The analysis shows that, due to flame curvature effects, the flame speed on the combustor axis is 2 D _t/R _F lower than the turbulent burning rate, where D _t is a characteristic turbulent diffusion coefficient and R _F the flame radius of curvature. Flame propagation with negative speed observed in the experiments, i.e. the flame completely embedded in the central recirculation zone on the symmetry axis, is explained with the one-dimensional model as caused by the factor 2 D _t/R _F being larger than the characteristic turbulent burning rate. A peculiar sudden displacement of the flame anchoring location deep into the burner, which takes place experimentally at a critical value of the equivalence ratio, cannot however be explained with the present one-dimensional approach due to the modelling assumptions. The mathematical analysis is supported in this case with large-eddy simulation which can accurately reproduce the flame behaviour across the full operating range. It is finally shown that steady RANS methods cannot cope with the problem due to their inability to correctly predict the velocity flowfield in this burner.     

Zonal PANS: evaluation of different treatments of the RANS–LES interface

The partially Reynolds-averaged Navier–Stokes (PANS) model can be used to simulate turbulent flows either as RANS, large eddy simulation (LES) or DNS. Its main parameter is f_k whose physical meaning is the ratio of the modelled to the total turbulent kinetic energy. In RANS f_k = 1, in DNS f_k = 0 and in LES f_k takes values between 0 and 1. Three different ways of prescribing f_k are evaluated for decaying grid turbulence and fully developed channel flow: f_k = 0.4, f_k = k^3/2 _tot/? and, from its definition, f_k = k/k_tot where k_tot is the sum of the modelled, k, and resolved, k_res, turbulent kinetic energy. It is found that the f_k = 0.4 gives the best results. In Girimaji and Wallin, a method was proposed to include the effect of the gradient of f_k. This approach is used at RANS– LES interface in the present study. Four different interface models are evaluated in fully developed channel flow and embedded LES of channel flow: in both cases, PANS is used as a zonal model with f_k = 1 in the unsteady RANS (URANS) region and f_k = 0.4 in the LES region. In fully developed channel flow, the RANS– LES interface is parallel to the wall (horizontal) and in embedded LES, it is parallel to the inlet (vertical). The importance of the location of the horizontal interface in fully developed channel flow is also investigated. It is found that the location – and the choice of the treatment at the interface – may be critical at low Reynolds number or if the interface is placed too close to the wall. The reason is that the modelled turbulent shear stress at the interface is large and hence the relative strength of the resolved turbulence is small. In RANS, the turbulent viscosity – and consequently also the modelled Reynolds shear stress – is only weakly dependent on Reynolds number. It is found in the present work that it also applies in the URANS region.