湍流燃烧是一种重要的能源利用方式，锅炉、内燃机、燃气轮机等燃烧设备中化学反应都发生在湍流流动中。高效高精度数值模拟能揭示湍流燃烧中内在的复杂物理化学过程。输运概率密度函数方法（TPDF）因为精确封闭了非线性化学反应源项，所以对于湍流-化学反应强相互作用的湍流燃烧问题能够实现准确预测。但是TPDF方法面临着两方面的挑战，一方面，TPDF方法中由分子扩散所导致的小尺度混合过程未封闭，混合模型对于TPDF预测精度有显著影响；另一方面，作为TPDF方法的一种常用数值实现方法，蒙特卡洛随机颗粒法需要求解大量计算颗粒，由此带来的巨大计算开销使得TPDF方法难以应用于实际燃烧室模拟中。因此，本文围绕TPDF方法，以提升精度和降低开销为目标，开展了混合过程差异扩散建模、标量混合时间尺度建模、空间分区自适应燃烧建模的研究。在TPDF方法中考虑差异扩散效应对于提升预测精度十分重要，差异扩散效应对于小尺度混合过程的影响体现为不同组分有着不同的混合时间尺度。本文在颗粒成对混合模型的总框架下提出一种通用的基于颗粒物质质量的混合模型实现方法，能够以多种不同的混合时间尺度作为输入参数，并且自然地满足了可实现性条件。用该方法改进了广为应用的平均交换相互作用模型和修正Curl模型。标量混合时间尺度模型是小尺度混合模型的关键组成部分。在湍流预混燃烧中，反应标量的局部梯度由反应-扩散平衡来驱动，而传统的常数混合速率参数模型无法考虑火焰结构的影响且模型参数须人为给定。本文在湍流预混火焰的大涡/过滤密度函数模拟中提出了动态hybrid混合时间尺度模型，动态地考虑了由湍流和火焰结构分别引起的亚网格标量混合，且不需要人为选取混合模型参数。面向工程燃烧室数值仿真需求，需发展兼顾仿真精度和计算效率的自适应燃烧建模方法。目前，基于TPDF方法的自适应燃烧模型的研究鲜有报道。本文发展了基于TPDF方法与组分输运类燃烧模型的自适应燃烧模型，构建了包括动态空间分区、子模型耦合、化学组分表示转化在内的一系列核心模块。将所发展的自适应燃烧模型应用于模拟实验室尺度代表性火焰，结果表明自适应燃烧模型对真实燃烧系统的预测精度可以达到与TPDF模型相同的水平。本文的研究成果有助于从提升混合过程建模精度和降低计算开销两方面推动TPDF方法在湍流燃烧高效高精度数值模拟中发挥越来越重要的作用。

Turbulent combustion is an important way of energy utilization. Chemical reactions occur in turbulent flow in various combustion equipments, such as boiler, internal combustion engine, and gas turbine. Efficiently and accurately numerical simulations can reveal the complex physical and chemical processes in turbulent combustion. Since the transported probability density function (TPDF) method treats the nonlinear chemical reaction term exactly, it can accurately predict turbulent combustion problems with strong turbulence-chemistry interaction. However, there remains two challenges faced by the TPDF method. On the one hand, the micro-mixing process caused by molecular diffusion is unclosed in the TPDF method. Micro-mixing models affect the prediction accuracy of the TPDF method significantly. On the other hand, a huge number of Monte Carlo nominally compuational particles are needed to numerically solve the evolution of composition fields in the TPDF method. So the large compuational cost caused by the huge number of Monte Carlo particles hinders the application of the TPDF method in simulations of practical combustion chambers. In order to improve the accuracy and reduce the compuational cost of the TPDF method, the present work has carried out researches in following aspects: considering the effect of differential diffusion in mixing models, modelling the scalar mixing timescale in turbulent premixed flames, and modelling combustion in a zone-adaptive way.Accounting for the effect of differential diffusion helps to improve accuracy of the TPDF method. Mixing timescales of different species are different due to differential diffusion. In this work, a mass-based implementation is formulated in the context of a general pair-wise mixing formulation. Different mixing timescales among species can be incorporated and the realizability condition of the species mass fractions summing to unity is met naturally in the mass-based implementation. According to the proposed implementation, the interaction by exchange with the mean (IEM) model and the modified Curl (MC) model have been augmented to incorporate different mixing timescales.Scalar mixing timescale is a key component of a micro-mixing model. In turbulent premixed combustion, the local gradient of a reactive scalar is driven by the reaction–diffusion balance. The conventional mechanical-to-scalar timescale model which is solely based on turbulence-induced mixing can't incorporate the effect of flame structure and requires manual tuning for the mixing rate parameter. A dynamic hybrid closure method of the scalar mixing timescale is formulated in large eddy/filtered density function simulations (LES/FDF) for turbulent premixed flames. The new model adaptively adjusts the relative contributions to the subgrid scalar mixing from turbulence and reaction according to the local state of combustion and requires no tuning for the mixing rate parameter.By urgent demand for numerical simulations of practical combustors, it is necessary to develop an adaptive combustion modelling method to take into account accuracy and efficiency simultaneously. Up to now, there are few researches on adaptive combustion modelling which incorporates the TPDF method. In this paper, a zone-adaptive combustion modelling strategy based on the TPDF method and a species-transported combustion model is proposed. Several core components of the adaptive model are constructed elaborately including adaptively spatial partition, submodels coupling, composition transformation between representations and so on. The proposed adaptive combustion model is applied to typical flames in a laboratory scale. Results show that the adaptive combustion model is as accurate as the stand-alone TPDF model for this real combustion system.By improving accuracy of micro-mixing models and reducing computational overhead via adaptive combustion modelling, the present research helps to promote the TPDF method to play a more and more important role in efficiently and accurately numerical simulations of turbulent combustion.