Abstract All models invoke assumptions that result in model errors. The objective of model form uncertainty quantification is to translate these assumptions into mathematical statements of uncertainty. If each assumption in a model can be isolated, then the uncertainties associated with each assumption can be independently assessed. In situations where a series of assumptions leads to a hierarchy of models with nested assumptions, physical principles from a higher-fidelity model can be used to directly estimate a physics-based uncertainty in a lower-fidelity model. Turbulent nonpremixed combustion models fall into a natural hierarchy from the full governing equations to Conditional Moment Closure to flamelet-like models to thermodynamic equilibrium, and, at each stage of the hierarchy, a single assumption can be isolated. In this work, estimates are developed for the uncertainties associated with each assumption in the hierarchy. The general method identifies a trigger parameter that can be obtained with information only from the lower-fidelity model that is used to estimate the error in the lower-fidelity model using only physical principles from the higher-fidelity model. Starting from the lowest fidelity model, the trigger parameters identified in this work are the product of a chemical time scale and the scalar dissipation rate for the equilibrium chemistry model, which characterizes the errors associated with neglecting finite-rate chemistry and transport; the reciprocal of the product of a generalized Lagrangian flow time and the scalar dissipation rate for the steady flamelet model, which characterizes the errors associated with neglecting flow history effects; and the relative magnitude of the conditional fluctuations for Conditional Moment Closure. The approach is applied in LES to a turbulent nonpremixed simple jet flame to quantify the errors associated with the equilibrium chemistry model and the steady flamelet model. The results indicate that errors associated with neglecting finite-rate chemistry and transport in the equilibrium chemistry model are dominant upstream while errors associated with neglecting flow history in the steady flamelet model become more important downstream.

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分层模型形成湍流燃烧建模的不确定性量化

Abstract 所有模型都会调用导致模型错误的假设。模型形式不确定性量化的目标是将这些假设转化为不确定性的数学陈述。如果模型中的每个假设都可以隔离，则可以独立评估与每个假设相关的不确定性。在一系列假设导致具有嵌套假设的模型层次结构的情况下，来自高保真模型的物理原理可用于直接估计低保真模型中基于物理的不确定性。湍流非预混燃烧模型属于一个自然层次，从完整的控制方程到条件力矩闭合，再到类火焰模型再到热力学平衡，并且在层次结构的每个阶段，可以隔离单个假设。在这项工作中，估计是针对与层次结构中每个假设相关的不确定性进行的。通用方法识别可以仅使用来自低保真模型的信息获得的触发参数，该信息用于仅使用来自高保真模型的物理原理来估计低保真模型中的误差。从最低保真度模型开始，这项工作中确定的触发参数是平衡化学模型的化学时间尺度和标量耗散率的乘积，它表征与忽略有限速率化学和输运相关的误差；广义拉格朗日流动时间与稳态火焰模型的标量耗散率的乘积的倒数，它表征与忽略流动历史效应相关的误差；以及条件矩闭包的条件波动的相对幅度。该方法在 LES 中应用于湍流非预混简单喷射火焰，以量化与平衡化学模型和稳定火焰模型相关的误差。结果表明，与忽略平衡化学模型中的有限速率化学和输运相关的错误在上游占主导地位，而与忽略稳定小火焰模型中的流动历史相关的错误在下游变得更加重要。