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.

本文的目的是证明由于放热化学反应产生的热释放而引起的热膨胀对湍流预混燃烧情况下潜在的湍流流体动力学及其模型的影响。由放热引起的热膨胀在湍流预混火焰内产生主要为正的膨胀率值，这已显示出对流动拓扑分布，湍动能和涡旋演变有重大影响。已经证明主要为正的膨胀率的大小提供了热膨胀强度的量度。已经表明，随着Karlovitz数和特征Lewis数的减小，热膨胀对流体湍流的影响会增强，并且随着未燃烧气体与已燃烧气体之间的密度比增加。这反映在流拓扑的贡献减弱的情况下，这仅对于扩张率的正值会随Karlovitz数的增加而获得。预混湍流火焰中的热膨胀不仅会引起大部分正膨胀率，而且还会由于火焰法向加速度而引起火焰引起的压力梯度。压力和膨胀波动之间的相关性，以及密度和压力梯度之间的矢量积，分别通过压力膨胀和斜压转矩项显着影响了湍流预混火焰中湍动能和涡流的演变。与卡洛维兹值和特征性刘易斯值的减小相比，湍流动能和回旋方程中压力膨胀和斜压扭矩相对于其他项的大小的相对贡献分别增强。对于较小的Karlovitz值和特征性Lewis数，这会导致火焰刷内的湍动能和涡流显着增加，但是对于Karlovitz的较大值，湍流动能和涡流都会从未燃烧的燃烧侧向燃烧的气体侧衰减。和特征的刘易斯数。预混火焰中的热量释放还引起子网格应力的显着各向异性，并影响其与解析应变率的对准。这种各向异性在子网格应力的建模中起关键作用，并且已证明子网格应力各向同性部分的显式闭合可改善子网格应力和湍动能闭合的性能。而且，已经显示出用于非反应性湍流的常规动态建模技术不适用于湍流的预混火焰。此外，在某些情况下，由于预混合湍流火焰中火焰的法向加速度引起的火焰速度增加可能会引起湍流动能，反应性标量，标量梯度和标量变化的反梯度传输。反梯度传输的倾向随着均方根湍流速度值和特征路易斯数的减小而增加。已经发现，涡度主要与中间主应变率本征方向对准，但是具有最广泛和最压缩的主应变率本征方向的涡旋对准的相对程度响应于热膨胀的强度而变化。已经发现，对于小亚单位Lewis数以及对于大Damöhler和小Karlovitz数的组合，膨胀率几乎等于最广泛的应变率，并且在这些条件下，涡度与最广泛的主应变率本征方向不对齐。但是获得了具有最大压缩主应变率本征方向的增加的共线对准。相比之下，对于在火焰中具有较高的Karlovitz数和较低的Damköhler数且Lewis数接近于1的组合，涡度显示出在放热效果强的反应区域中，与最广泛的主方向的共线排列增加。与密度增加，Damköhler数增加和Lewis数减少的湍流应变相比，火焰法向加速度的增强使反应性标量梯度优先与最广泛的主应变率特征方向对准，这与优先的共线对准相反。具有最大压缩主应变率特征方向的被动标量梯度。对于高卡洛维兹数，反应性标量梯度对齐方式开始类似于在被动标量混合情况下观察到的行为。热膨胀对具有局部主应​​变率特征方向的涡度和反应性标量梯度的对准特性的影响，决定了涡流传递方程中涡流拉伸项的统计量，以及标量耗散率和火焰表面密度传递方程中法向应变率的贡献。 ， 分别。基于上述关于预混合燃烧中的热膨胀对流体湍流的影响的基本物理信息，已经提出在湍流预混合燃烧中湍流和燃烧模型是紧密联系的。所以，