A-priori direct numerical simulation assessment of sub-grid scale stress tensor closures for turbulent premixed combustion

Klein, Markus; Kasten, Christian; Gao, Yuan; Chakraborty, Nilanjan

doi:10.1016/j.compfluid.2015.08.003

Cited by 32 publications

(38 citation statements)

References 39 publications

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“…Similar to RANS modelling, the heat release effects also influence the sub-grid stress and sub-grid kinetic energy closures in the context of LES. The filtered momentum conservation equation in the context of LES takes the following form (Klein et al 2015): where denotes the kinematic viscosity, the sub-grid scale (SGS) stress tensor is given by SGS ij = u i u j − ũ iũj , and the isotropic part of the SGS stresses, i.e. the term involving…”

Section: Modelling Implications In the Context Of Large Eddy Simulatimentioning

confidence: 99%

“…Recently, Anderson and Domaradzki (2012) identified the sources of deficiency of the scale similarity models and suggested a new model for momentum transport in the context of LES of incompressible flows, using the assumption of splitting the turbulent kinetic energy spectrum into 3 different ranges denoting small R 3 , intermediate R 2 and large scales R 1 (Anderson and Domaradzki 2012), where R 3 represents the scales unresolved by the mesh, as discussed earlier in the context of sub-grid scalar flux closure. However, the original modelling methodology by Anderson and Domaradzki (2012) has been modified by Klein et al (2015) to make it both Galilei invariant and symmetric. The modified model expression according to Klein et al (2015) takes the following form: Equation 40 will henceforth be denoted as the IET model, i.e.…”

Section: Modelling Implications In the Context Of Large Eddy Simulatimentioning

confidence: 99%

“…However, the original modelling methodology by Anderson and Domaradzki (2012) has been modified by Klein et al (2015) to make it both Galilei invariant and symmetric. The modified model expression according to Klein et al (2015) takes the following form: Equation 40 will henceforth be denoted as the IET model, i.e. inter-scale energy transfer model.…”

Section: Modelling Implications In the Context Of Large Eddy Simulatimentioning

confidence: 99%

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Influence of Thermal Expansion on Fluid Dynamics of Turbulent Premixed Combustion and Its Modelling Implications

Chakraborty

2021

Flow Turbulence Combust

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The purpose of this paper is to demonstrate the effects of thermal expansion, as a result of heat release arising from exothermic chemical reactions, on the underlying turbulent fluid dynamics and its modelling in the case of turbulent premixed combustion. The thermal expansion due to heat release gives rise to predominantly positive values of dilatation rate within turbulent premixed flames, which has been shown to have significant implications on the flow topology distributions, and turbulent kinetic energy and enstrophy evolutions. It has been demonstrated that the magnitude of predominantly positive dilatation rate provides the measure of the strength of thermal expansion. The influence of thermal expansion on fluid turbulence has been shown to strengthen with decreasing values of Karlovitz number and characteristic Lewis number, and with increasing density ratio between unburned and burned gases. This is reflected in the weakening of the contributions of flow topologies, which are obtained only for positive values of dilatation rate, with increasing Karlovitz number. The thermal expansion within premixed turbulent flames not only induces mostly positive dilatation rate but also induces a flame-induced pressure gradient due to flame normal acceleration. The correlation between the pressure and dilatation fluctuations, and the vector product between density and pressure gradients significantly affect the evolutions of turbulent kinetic energy and enstrophy within turbulent premixed flames through pressure-dilatation and baroclinic torque terms, respectively. The relative contributions of pressure-dilatation and baroclinic torque in comparison to the magnitudes of the other terms in the turbulent kinetic energy and enstrophy transport equations, respectively strengthen with decreasing values of Karlovitz and characteristic Lewis numbers. This leads to significant augmentations of turbulent kinetic energy and enstrophy within the flame brush for small values of Karlovitz and characteristic Lewis numbers, but both turbulent kinetic energy and enstrophy decay from the unburned to the burned gas side of the flame brush for large values of Karlovitz and characteristic Lewis numbers. The heat release within premixed flames also induces significant anisotropy of sub-grid stresses and affects their alignments with resolved strain rates. This anisotropy plays a key role in the modelling of sub-grid stresses and the explicit closure of the isotropic part of the sub-grid stress has been demonstrated to improve the performance of sub-grid stress and turbulent kinetic energy closures. Moreover, the usual dynamic modelling techniques, which are used for non-reacting turbulent flows, have been shown to not be suitable for turbulent premixed flames. Furthermore, the velocity increase across the flame due to flame normal acceleration may induce counter-gradient transport for turbulent kinetic energy, reactive scalars, scalar gradients and scalar variances in premixed turbulent flames under some conditions. The propensity of counter-gradient transport increases with decreasing values of root-mean-square turbulent velocity and characteristic Lewis number. It has been found that vorticity aligns predominantly with the intermediate principal strain rate eigendirection but the relative extents of alignment of vorticity with the most extensive and the most compressive principal strain rate eigendirections change in response to the strength of thermal expansion. It has been found that dilatation rate almost equates to the most extensive strain rate for small sub-unity Lewis numbers and for the combination of large Damköhler and small Karlovitz numbers, and under these conditions vorticity shows no alignment with the most extensive principal strain rate eigendirection but an increased collinear alignment with the most compressive principal strain rate eigendirection is obtained. By contrast, for the combination of high Karlovitz number and low Damköhler number in the flames with Lewis number close to unity, vorticity shows an increased collinear alignment with the most extensive principal direction in the reaction zone where the effects of heat release are strong. The strengthening of flame normal acceleration in comparison to turbulent straining with increasing values of density ratio, Damköhler number and decreasing Lewis number makes the reactive scalar gradient align preferentially with the most extensive principal strain rate eigendirection, which is in contrast to preferential collinear alignment of the passive scalar gradient with the most compressive principal strain rate eigendirection. For high Karlovitz number, the reactive scalar gradient alignment starts to resemble the behaviour observed in the case of passive scalar mixing. The influence of thermal expansion on the alignment characteristics of vorticity and reactive scalar gradient with local principal strain rate eigendirections dictates the statistics of vortex-stretching term in the enstrophy transport equation and normal strain rate contributions in the scalar dissipation rate and flame surface density transport equations, respectively. Based on the aforementioned fundamental physical information regarding the thermal expansion effects on fluid turbulence in premixed combustion, it has been argued that turbulence and combustion modelling are closely interlinked in turbulent premixed combustion. Therefore, it might be necessary to alter and adapt both turbulence and combustion modelling strategies while moving from one combustion regime to the other.

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Section: Modelling Implications In the Context Of Large Eddy Simulatimentioning

confidence: 99%

Section: Modelling Implications In the Context Of Large Eddy Simulatimentioning

confidence: 99%

Section: Modelling Implications In the Context Of Large Eddy Simulatimentioning

confidence: 99%

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Influence of Thermal Expansion on Fluid Dynamics of Turbulent Premixed Combustion and Its Modelling Implications

Chakraborty

2021

Flow Turbulence Combust

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“…21 Another DNS database (flames C and E) was created by Chakraborty et al 22,23 by simulating combustion in small-scale intense turbulence (the thin-reaction-zone regime 1 of premixed burning) and was also analyzed in a number of recent papers cited elsewhere. 24 Because the DNS data were already discussed in detail in the literature, we will restrict ourselves to a very brief summary of the simulations.…”

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confidence: 99%

A transport equation for reaction rate in turbulent flows

et al. 2016

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New transport equations for chemical reaction rate and its mean value in turbulent flows have been derived and analyzed. Local perturbations of the reaction zone by turbulent eddies are shown to play a pivotal role even for weakly turbulent flows. The mean-reaction-rate transport equation is shown to involve two unclosed dominant terms and a joint closure relation for the sum of these two terms is developed. Obtained analytical results and, in particular, the closure relation are supported by processing two widely recognized sets of data obtained from earlier direct numerical simulations of statistically planar 1D premixed flames associated with both weak large-scale and intense small-scale turbulence.

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“…One DNS database (flames H, M, and L) was created by Nishiki et al [ 29 , 30 ] by simulating weakly turbulent combustion in the flamelet regime and was analyzed in a number of recent papers [ 13 – 16 , 27 , 31 – 38 ]. Another DNS database (flames B, C, D, and E) was created by Chakraborty et al [ 39 , 40 ] by simulating combustion in small-scale intense turbulence (the thin-reaction-zone regime [ 1 ] of premixed burning) and was also analyzed in a number of recent papers cited elsewhere [ 15 , 16 , 27 , 41 ]. Because the DNS attributes were already discussed in detail in the literature, we will restrict ourselves to a very brief summary of the simulations.…”

Section: Dns Attributesmentioning

confidence: 99%

A DNS Study of Closure Relations for Convection Flux Term in Transport Equation for Mean Reaction Rate in Turbulent Flow

Lipatnikov

Sabelnikov

Chakraborty

et al. 2017

Flow Turbulence Combust

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The present work aims at modeling the entire convection flux in the transport equation for a mean reaction rate in a turbulent flow, which (equation) was recently put forward by the present authors. In order to model the flux, several simple closure relations are developed by introducing flow velocity conditioned to reaction zone and interpolating this velocity between two limit expressions suggested for the leading and trailing edges of the mean flame brush. Subsequently, the proposed simple closure relations for are assessed by processing two sets of data obtained in earlier 3D Direct Numerical Simulation (DNS) studies of adiabatic, statistically planar, turbulent, premixed, single-step-chemistry flames characterized by unity Lewis number. One dataset consists of three cases characterized by different density ratios and is associated with the flamelet regime of premixed turbulent combustion. Another dataset consists of four cases characterized by different low Damköhler and large Karlovitz numbers. Accordingly, this dataset is associated with the thin reaction zone regime of premixed turbulent combustion. Under conditions of the former DNS, difference in the entire, , and mean, , convection fluxes is well pronounced, with the turbulent flux, , showing countergradient behavior in a large part of the mean flame brush. Accordingly, the gradient diffusion closure of the turbulent flux is not valid under such conditions, but some proposed simple closure relations allow us to predict the entire flux reasonably well. Under conditions of the latter DNS, the difference in the entire and mean convection fluxes is less pronounced, with the aforementioned simple closure relations still resulting in sufficiently good agreement with the DNS data.

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A-priori direct numerical simulation assessment of sub-grid scale stress tensor closures for turbulent premixed combustion

Cited by 32 publications

References 39 publications

Influence of Thermal Expansion on Fluid Dynamics of Turbulent Premixed Combustion and Its Modelling Implications

Influence of Thermal Expansion on Fluid Dynamics of Turbulent Premixed Combustion and Its Modelling Implications

A transport equation for reaction rate in turbulent flows

A DNS Study of Closure Relations for Convection Flux Term in Transport Equation for Mean Reaction Rate in Turbulent Flow

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