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The unstrained and strained flamelet closures for filtered reaction rate in large eddy simulation (LES) of premixed flames are studied. The required sub-grid scale (SGS) PDF in these closures is presumed using the Beta function. The relative performances of these closures are assessed by comparing numerical results from large eddy simulations of piloted Bunsen flames of stoichiometric methane-air mixture with experimental measurements. The strained flamelets closure is observed to underestimate the burn rate and thus the reactive scalars mass fractions are under-predicted with an overprediction of fuel mass fraction compared with the unstrained flamelet closure. The physical reasons for this relative behaviour are discussed. The results of unstrained flamelet closure compare well with experimental data. The SGS variance of the progress variable required for the presumed PDF is obtained by solving its transport equation. An order of magnitude analysis of this equation suggests that the commonly used algebraic model obtained by balancing source and sink in this transport equation does not hold. This algebraic model is shown to underestimate the SGS variance substantially and the implications of this variance model for the filtered reaction rate closures are highlighted. Nomenclature AcronymsCDF cumulative distribution function CFL Courant-Friedrichs-Lewy number LES large eddy simulation PDF probability density function RANS Reynolds averaged Navier-Stokes SF strained flamelets SGS sub-grid scale TKE turbulent kinetic energy UF unstrained flamelet Roman c progress variable C p specific heat capacity at constant pressure (kJ kg -1 K -1 ) C 3 , C 4 parameters in Equation (7) D molecular diffusivity (m 2 s −1 )

The turbulent reacting flow in an industrial gas turbine combustor operating at 3 bar is computed using LES paradigm. The subgrid scale (SGS) combustion is modelled using a collection of unstrained premixed flamelets including mixture stratification.The non-premixed combustion mode is also included using a simple closure involving the scalar dissipation rate of the mixture fraction. A close attention is paid to maintain physical consistencies among sub-closure models for combustion and these consistencies are discussed on a physical basis. The importance of non-premixed mode and SGS mixture fraction fluctuations are investigated systematically. The results show that the SGS mixture fraction variance plays an important role and comparisons to measurements improve when contributions from the premixed and non-premixed modes are included. These numerical results and observations are discussed on a physical basis along with potential avenues for further improvements. a Research Associate, il246@cam.ac.uk b Research Associate, zc252@cam.ac.uk c Professor, ns341@cam.ac.uk d Engineer, suresh.sadasivuni@siemens.com 4 combustors. Thus, the ability of reacting flow CFD (Computational Fluid Dynamics) to capture these phenomena is crucial for their use in the design of next-generation combustors [2].Past studies have demonstrated that Large Eddy Simulation (LES) is suitable to capture aerodynamics of swirling flows, and the continuous increase of computing power allows application of LES-based models to practical burners [3][4][5][6][7]. Combustion requires modelling as it is a subgrid phenomenon in LES. Closures developed for the subgrid scale (SGS) reaction rate include: dynamic thickened flame model [8,9], linear eddy model [10], fractal flame-wrinkling model [11], partiallystirred reactor model [12], and Eulerian stochastic fields [13]. Another recently developed flamelet model for LES uses Scalar Dissipation Rate (SDR) closure [14,15], which is shown to be successful in RANS studies of industrial gas turbine combustors [16,17], but this approach has not been tested for LES of reacting flows in these combustors. This provides the motivation for this work.Due to large costs for experiments at realistic operating conditions of gas turbines (i.e. with optical access, high pressure, and preheated air), high quality validation data is rare [18]. One widely studied database is the set of laser-diagnostics obtained for Siemens SGT-100 combustor at 3 bar [19]. Analyses of these measurements and past LES results suggest that the combustion has flamelet-like properties despite the highly turbulent flow [5-7, 20, 21]. Flamelet models assume that the combustion time scale, τ c = s L /δ is shorter than the smallest turbulent scales (this also applies for length scales) implying that the flamelet structure is undisturbed by the turbulence. Thus, the SGS reaction rate can be calculated a priori using laminar flamelets. Hence, this methodology is also known as tabulated chemistry approach.Turbulent eddies can penetrate the flame-front di...

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.

A numerical investigation is conducted to shed light on the reasons leading to different flame configurations in gas turbine (GT) combustion chambers of aeronautical interest. Large eddy simulations (LES) with a flamelet-based combustion closure are employed for this purpose to simulate the DLR-AT big optical single sector (BOSS) rig fitted with a Rolls-Royce developmental lean burn injector. The reacting flow field downstream this injector is sensitive to the intricate turbulent–combustion interaction and exhibits two different configurations: (i) a penetrating central jet leading to an M-shape lifted flame; or (ii) a diverging jet leading to a V-shaped flame. The LES results are validated using available BOSS rig measurements, and comparisons show the numerical approach used is consistent and works well. The turbulent–combustion interaction model terms and parameters are then varied systematically to assess the flame behavior. The influences observed are discussed from physical and modeling perspectives to develop physical understanding on the flame behavior in practical combustors for both scientific and design purposes.

A laboratory gas turbine model combustor with dual-swirler configuration is investigated using Large Eddy Simulation (LES) with a flamelet subgrid combustion model. Two partially premixed methane/air flames with different equivalence ratio and thermal power are simulated: one stably burning with an elongated V-shape and another undergoing pronounced thermoacoustic oscillations exhibiting a flat shape. Additionally, both flames feature a hydrodynamic instability in the form of a precessing vortex core (PVC). Detailed comparisons between experimental and LES results show that the different flow and reaction zone structures in these two flames are reproduced well. The various flow dynamics resulting from the PVC and thermoacoustic oscillations are also captured accurately in the simulation. Further analyses on the lifted swirl flame stabilisation using phase averaged statistics at the PVC frequencies reveal that the PVC-induced stagnation points provide an anchoring mechanism for both the stable and unstable flames, although in the latter case large self-excited pressure oscillations are present. It is found that the PVC is significantly influenced by these oscillations, being axially stretched and compressed at high and low pressures, respectively. However, the formation of flame leading edge due to the PVC is robust during these unstable processes and the azimuthal movement of the leading point is found to be strongly correlated with the rotation of the PVC in both flames, further confirming the vital role of the PVC in the stabilisation process of these lifted swirl flames.

Multi-regime turbulent combustion modelling remains challenging and is explored with occurrence of local extinction in this study. A partially premixed model based on unstrained premixed flamelets is used in this work to investigate a piloted jet flame configuration with inhomogeneous inlets. Three di↵erent cases are simulated, which di↵er in the bulk mean velocity that amounts respectively to about 50%, 70% and 90% of the blow o↵ velocity measured experimentally.As the jet velocity approaches the blow o↵ limit, local extinctions start to occur along the flame surface and thus these flames are challenging from a modelling prospective. Two di↵erent numerical approaches, involving scaled and unscaled progress variable respectively, are compared to elucidate their abilities and limitations to predict local extinctions and to deal with the three-stream problem at the pilot/coflow interface. The key modelling details for such predictions are indicated and discussed. LES results are systematically compared to two sets of

Understanding the nature of the unsteady flow at the combustor exit is required to accurately simulate time dependent phenomena in the turbine entry, such as indirect noise generation. Using Large Eddy Simulations of the combustion process in a realistic geometry, we analyse the flow at its exit. Two realistic, near-ground certification operating conditions are considered. Different mechanisms for large-scale flow and thermal structure generation are described, which are ejected into the turbine. Modal decomposition methods are used to extract the spatial and temporal scales at the turbine entry. We find that, depending on the operating condition, the entropy waves convect as elongated streaks in the core of the combustor annulus or the proximity of the walls. The dominant unsteady character of the fluctuations exhibits different spectral properties, i.e. low-frequency in the core and high-frequency towards walls. At the combustor exit, the vortical field is dominated by the swirl in the air inlet, which is found to have little influence on the entropy perturbations. Further, the importance of considering the interaction of multiple fuel injectors and combustion zones in an annular combustor is investigated. It is shown that pulsating circumferential vorticity modes can occur in multi-sector annular combustors but these, however, do not affect the entropy wave distribution.