Modelling of flamelet surface-to-volume ratio in turbulent premixed combustion

Cant, RS; Pope, Stephen B.; Bray, K.N.C.

doi:10.1016/s0082-0784(06)80334-6

Cited by 121 publications

(136 citation statements)

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“…Flame Surface Density (FSD) based reaction rate closure is one of the most popular methods of turbulent premixed combustion modelling in the context of Reynolds Averaged Navier Stokes (RANS) simulations [1][2][3][4][5][6][7][8][9][10][11][12]. In the context of FSD based formulation, the closure of reaction rate translates to the modelling of flame surface area to volume ratio [13].…”

Section: Introductionmentioning

confidence: 99%

“…The fine-grained FSD is defined as [15]: (1) where c * is the value of the reaction progress variable c isosurface that is taken to be the flame surface. Based on the fine-grained definition given by eqn (1) the FSD can be expressed as: (2) where the over-bar indicates a suitable Reynolds averaging operation. According to eqns (1) and (2), Σ is dependent upon the choice of c * .…”

Section: Introductionmentioning

confidence: 99%

“…Thus, it is important to have highfidelity models for FSD transport in the context of RANS simulations. The FSD transport equation has a number of unclosed terms, and previous analyses [1][2][3][4][5][6][7][8][9][10][11][12] indicated that the terms due to fluid-dynamic straining and flame curvature act as leading order contributors to the FSD transport. The current analysis focuses only on the statistical behaviour and modelling of the curvature term in the FSD transport equation in the context of RANS simulations.…”

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confidence: 99%

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Modelling of the Curvature Term in the Flame Surface Density Transport Equation: A Direct Numerical Simulations Based Analysis

Katragadda

Malkeson

Chakraborty

2014

International Journal of Spray and Combustion Dynamics

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A simple chemistry based three-dimensional Direct Numerical Simulations (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different values of Karlovitz number Ka, turbulent Reynolds number Re t , heat release parameter τ and global Lewis number Le has been used for the modelling of the curvature term of the generalised Flame Surface Density (FSD) transport equation in the context of Reynolds Averaged Navier Stokes (RANS) simulations. The curvature term has been split into the contributions arising due to the reaction and normal diffusion components of displacement speed (i.e. T 1 ) and the term arising due to the tangential diffusion component of displacement speed (i.e. T 2 ). Subsequently, the subterms (i.e. T 1 and T 2 ) of the curvature contribution to the FSD transport have been split into the closed (i.e. T 1r and T 2r ) and unclosed (i.e. T 1ur and T 2ur ) components. It has been found that T 2 remains deterministically negative throughout the flame brush. However, the qualitative behaviour of T 1 changes significantly depending upon the values of Ka, Re t and Le. Detailed physical explanations have been provided for the observed behaviours of the components of the curvature term. Moreover, it has been observed that the closed contributions of T 1 and T 2 (i.e. T 1r and T 2r ) remains negligible in comparison to the unclosed contributions (i.e. T 1ur and T 2ur ). Suitable model expressions have been identified for T 1ur and T 2ur in the context of RANS simulations, which are shown to perform satisfactorily in all cases considered in the current analysis, accounting for the variations in Ka, Re t , τ and Le.Keywords: Direct Numerical Simulation, Flame Surface Density, Curvature, Lewis Number, Turbulent Reynolds Number, Reynolds Averaged Navier Stokes Modelling [14] demonstrated that algebraic models may not be adequate for simulating incylinder processes in Spark Ignition (SI) piston engines. Therefore, it may be necessary to consider a modelled FSD transport equation for simulating turbulent premixed flames under some conditions. Moreover, despite ever increasing computational power and capacity, Large Eddy Simulations (LES) are still not routinely used in industrial calculations due to large computational costs associated with it, and, consequently, RANS is still the most commonly used simulation method for industrial engineering problems. The accurate modelling of the chemical reaction rate is a necessity for highfidelity Computational Fluid Dynamics (CFD) simulations, which play important roles in the development of new generation energy-efficient and low-pollution SI engines and Lean Premixed Prevaporaised (LPP) gas turbines. Thus, it is important to have highfidelity models for FSD transport in the context of RANS simulations. The FSD transport equation has a number of unclosed terms, and previous analyses [1][2][3][4][5][6][7][8][9][10][11][12] indicated that the terms due to fluid-dynamic straining and flame curvature act as leading order c...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Modelling of the Curvature Term in the Flame Surface Density Transport Equation: A Direct Numerical Simulations Based Analysis

Katragadda

Malkeson

Chakraborty

2014

International Journal of Spray and Combustion Dynamics

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“…Many models of turbulent pre-mixed combustion are based on flame surface density (FSD), defined as the flame surface area per unit volume. Based on the flame surface density, the reaction rate can be expressed as (13) where S is the flame surface density, S L the laminar flame speed, which could be modified by stretch effects, and is the density of the unburnt mixture. Methods vary depending on the method of determining S, In BML model, an algebraic expression for S is used to obtain the expression for .…”

Section: Pre-mixed Combustion Modelsmentioning

confidence: 99%

“…A conservation equation for flame surface density can be written in the form (14) where n t is the turbulent viscosity, s S is the flame surface turbulent Schmidt number, S 1 ,S 2 are the source terms due to strain rate acting on the surface and induced by the surface, the strain rate due to turbulent motion, respectively and D describes consumption of flame area. These production and destruction terms need to be modelled and several closure terms are proposed by various authors 13,17 . These models have been used for computing flows in IC engines and in closed vessels 14,18 .…”

Section: Pre-mixed Combustion Modelsmentioning

confidence: 99%

Computational Fluid Dynamics in Combustion

Paul¹

2010

DSJ

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Computational fluid dynamics has reached a stage where flow field in practical situation can be predicted to aid the design and to probe into the fundamental flow physics to understand and resolve the issues in fundamental fluid mechanics. The study examines the computation of reacting flows. After exploring the conservation equations for species and energy, the methods of closing the reaction rate terms in turbulent flow have been examined briefly. Two cases of computation, where combustion-flow interaction plays important role, have been discussed to illustrate the computational aspects and the physical insight that can be gained by the reacting flow computation.

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Combustion

Poinsot

Veynante

2017

Encyclopedia of Computational Mechanics Second Edition

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This chapter describes the basic phenomena controlling reacting flows and the corresponding computational methodologies. Combustion regimes (premixed or diffusion flames, laminar or turbulent cases, stable or unstable behavior) are first defined before introducing the basic terminology required to understand numerical techniques for reacting flows. The governing equations for combustion are more complex than those used in classical aerodynamics, and their specificities are discussed before describing numerical methods for laminar flames. Finally, the various methods used for turbulent flames are discussed, focusing on recent techniques such as direct numerical simulations and large eddy simulations.

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Modelling of flamelet surface-to-volume ratio in turbulent premixed combustion

Cited by 121 publications

References 4 publications

Modelling of the Curvature Term in the Flame Surface Density Transport Equation: A Direct Numerical Simulations Based Analysis

Modelling of the Curvature Term in the Flame Surface Density Transport Equation: A Direct Numerical Simulations Based Analysis

Computational Fluid Dynamics in Combustion

Combustion

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