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Influence of Thermal Expansion on Fluid Dynamics of Turbulent

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Influence of Thermal Expansion on Fluid Dynamics of Turbulent Flow, Turbulence and Combustion (2021) 106:753–848 https://doi.org/10.1007/s10494-020-00237-8 Infuence of Thermal Expansion on Fluid Dynamics of Turbulent Premixed Combustion and Its Modelling Implications Nilanjan Chakraborty1 Received: 8 September 2020 / Accepted: 11 December 2020 / Published online: 5 March 2021 © The Author(s) 2021 Abstract The purpose of this paper is to demonstrate the efects of thermal expansion, as a result of heat release arising from exothermic chemical reactions, on the underlying turbulent fuid dynamics and its modelling in the case of turbulent premixed combustion. The ther- mal expansion due to heat release gives rise to predominantly positive values of dilatation rate within turbulent premixed fames, which has been shown to have signifcant implica- tions on the fow topology distributions, and turbulent kinetic energy and enstrophy evo- lutions. It has been demonstrated that the magnitude of predominantly positive dilatation rate provides the measure of the strength of thermal expansion. The infuence of thermal expansion on fuid turbulence has been shown to strengthen with decreasing values of Kar- lovitz number and characteristic Lewis number, and with increasing density ratio between unburned and burned gases. This is refected in the weakening of the contributions of fow topologies, which are obtained only for positive values of dilatation rate, with increas- ing Karlovitz number. The thermal expansion within premixed turbulent fames not only induces mostly positive dilatation rate but also induces a fame-induced pressure gradi- ent due to fame normal acceleration. The correlation between the pressure and dilatation fuctuations, and the vector product between density and pressure gradients signifcantly afect the evolutions of turbulent kinetic energy and enstrophy within turbulent premixed fames 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, respec- tively strengthen with decreasing values of Karlovitz and characteristic Lewis numbers. This leads to signifcant augmentations of turbulent kinetic energy and enstrophy within the fame 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 fame brush for large values of Karlovitz and characteristic Lewis numbers. The heat release within premixed fames also induces signifcant anisotropy of sub-grid stresses and afects 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 tur- bulent kinetic energy closures. Moreover, the usual dynamic modelling techniques, which are used for non-reacting turbulent fows, have been shown to not be suitable for turbulent Extended author information available on the last page of the article Vol.:(0123456789)1 3 754 Flow, Turbulence and Combustion (2021) 106:753–848 premixed fames. Furthermore, the velocity increase across the fame due to fame normal acceleration may induce counter-gradient transport for turbulent kinetic energy, reactive scalars, scalar gradients and scalar variances in premixed turbulent fames under some con- ditions. 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 eigendirec- tion 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 ther- mal 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 fames with Lewis number close to unity, vorticity shows an increased collinear alignment with the most extensive principal direction in the reaction zone where the efects of heat release are strong. The strengthening of fame normal acceleration in comparison to turbulent strain- ing with increasing values of density ratio, Damköhler number and decreasing Lewis num- ber makes the reactive scalar gradient align preferentially with the most extensive princi- pal 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 behav- iour observed in the case of passive scalar mixing. The infuence 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 fame surface density transport equations, respectively. Based on the aforementioned fun- damental physical information regarding the thermal expansion efects on fuid 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. Keywords Premixed fame · Turbulence · Heat release · Thermal expansion · Flow topology · Scalar gradient alignment · Vorticity alignment · Sub-grid fux closure · Sub- grid stress closure 1 Introduction In spark ignition engines and industrial gas turbines fuel and oxidiser are homogeneously mixed prior to the combustion and the corresponding fames are commonly referred to as premixed fames. In premixed combustion, the fame moves normal to itself and the fow accelerates in the fame normal direction due to thermal expansion. Moreover, thermal expansion gives rise to mostly positive values of dilatation rate. In premixed combustion, the heat release rate due to exothermal chemical reaction gives rise to signifcant changes in density across the fame, even under moderate values of Mach number. This leads to a signifcant amount of thermal expansion characterised by predominantly positive values 1 3 Flow, Turbulence and Combustion (2021) 106:753–848 755 of dilatation rate, which makes the underlying turbulent fuid motion in premixed turbu- lent combustion diferent from non-reacting compressible fow turbulence. The infuence of heat release and thermal expansion on turbulence in premixed fames has been indicated by Karlovitz et al. (1953) in their pioneering analysis. The hypothesis of fame-generated turbulence by Karlovitz et al. (1953) was subsequently explained based on physical argu- ments by Bray and Libby (1976). The hypothesis by Karlovitz et al. (1953) was confrmed by Moreau and Boutier (1977) based on experimental data which revealed that the self- induced pressure gradient within the fame acts to preferentially accelerate lighter combus- tion products more than the heavier reactants. Borghi and Escudie (1984) and Chomiak and Nisbet (1995) provided further experimental evidence of the important role played by the self-induced pressure gradient in premixed turbulent combustion. This self-induced pres- sure gradient has been demonstrated to play a key role in non-gradient turbulent transport, which has implications in the modelling of turbulent scalar fuxes and Reynolds stresses (Kuznetsov 1979; Bray et al. 1980; Moss 1980; Shepherd et al. 1982; Strahle 1983; Cheng and Shepherd 1991; Rutland and Cant 1994; Zhang and Rutland 1995; Veynante et al. 1997; Veynante and Poinsot 1997; Frank et al. 1999; Swaminathan et al. 2001; Kalt et al. 2002; Nishiki et al. 2002, 2006; Chakraborty and Cant 2009a, 2009b, 2009c; Chakraborty et al. 2011a, e). Moreover, the self-induced pressure gradient within the fame is respon- sible for the baroclinic torque which acts to generate vorticity and plays a key role in the enstrophy transport in turbulent premixed fames (Lipatnikov et al. 2014; Chakraborty et al. 2016, 2017; Dopazo et al. 2017; Papapostolou et al. 2017). It has recently been reported that the heat release due to combustion modifes the spec- tra of turbulent kinetic energy (Kolla et al. 2014) and its dissipation rate (Kolla et al. 2016) in turbulent premixed fames in comparison to the corresponding results obtained for turbulent non-reacting fows. The two-point velocity correlations for the velocity feld in turbulent premixed fames need to account for density diferences between two points in question due to thermal expansion efects. This type of spectral analysis has the potential to provide insights into the scales where the correlation between pressure and dilatation remains important, which, in turn, afect the spectral energy transfer from lower to higher
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