In order to explore the influence of combustion-induced thermal expansion on turbulence, a new research method is introduced. The method consists in jointly applying Helmholtz-Hodge decomposition and conditioned structure functions to analyzing turbulent velocity fields. Opportunities offered by the method are demonstrated by using it to process Direct Numerical Simulation data obtained earlier from two statistically 1D, planar, fully-developed, weakly turbulent, single-step-chemistry, premixed flames characterized by two significantly different (7.52 and 2.50) density ratios, with all other things being approximately equal. To emphasize the influence of combustion-induced thermal expansion on turbulent flow of unburned mixture upstream of a premixed flame, the focus of analysis is placed on structure functions conditioned to the unburned mixture in both points. Two decomposition techniques, i.e. (i) a widely used orthogonal Helmholtz-Hodge decomposition and (ii) a recently introduced natural Helmholtz-Hodge decomposition, are probed, with results obtained using them being similar in the largest part of the computational domain with the exception of narrow zones near the inlet and outlet boundaries. Computed results indicate that combustion-induced thermal expansion can significantly change turbulent flow of unburned mixture upstream of a premixed flame by generating anisotropic potential velocity fluctuations whose spatial structure differ substantially from spatial structure of the incoming turbulence. The magnitude of such potential velocity fluctuations is greater than the magnitude of the solenoidal velocity fluctuations in the largest part of the mean flame brush in the case of the high density ratio. In the case of the low density ratio, the latter magnitude is larger everywhere, but the two magnitudes are comparable in the middle of the mean flame brush. Contrary to the potential velocity fluctuations, the influence of the thermal expansion on the solenoidal velocity field in the unburned mixture is of minor importance under conditions of the present study.

为了探讨燃烧引起的热膨胀对湍流的影响，提出了一种新的研究方法。该方法包括联合应用Helmholtz-Hodge分解和条件结构函数来分析湍流场。通过使用该方法处理较早的直接数值模拟数据，展示了该方法的机会，这些直接数值模拟数据是从两个统计学上一维的，平面的，完全展开的，弱湍流的，单步化学的，预混火焰，其特征是两个明显不同（7.52和2.50）密度比，其他所有条件都大致相等。为了强调燃烧引起的热膨胀对预混火焰上游未燃烧混合物湍流的影响，分析的重点放在两个点都适合未燃烧混合物的结构功能上。探索了两种分解技术，即（i）广泛使用的正交Helmholtz-Hodge分解和（ii）最近引入的自然Helmholtz-Hodge分解，使用它们获得的结果在计算域的最大部分中相似，除了入口和出口边界附近的狭窄区域。计算结果表明，燃烧引起的热膨胀可通过产生各向异性的势速波动来显着改变预混火焰上游未燃烧混合物的湍流，其空间结构与传入湍流的空间结构明显不同。在高密度比的情况下，这种潜在的速度波动的幅度大于平均火焰刷的最大部分中螺线管速度波动的幅度。在低密度比的情况下，后者的大小在每个地方都较大，但是在平均火焰刷的中间，这两个大小是可比较的。与潜在的速度波动相反，在本研究条件下，热膨胀对未燃烧混合物中螺线管速度场的影响较小。