ABSTRACT

The chemical time scale can be used to characterize a reactive system(’s behavior). In addition, various dimensionless numbers (e.g. Damköhler number) rely on a characteristic chemical time scale. The inverse eigenvalues of a system are regarded as the system’s time scales. This means, the number of time scales is equal the numbers of eigenvalues. A formulation for a single characteristic time scale is required for the system characterization and to calculate dimensionless numbers. Recently proposed modifications of the Eddy Dissipation Concept (a turbulence-chemistry interaction model) also incorporate the Damköhler number in their formulation. Besides accuracy, the numerical efficiency is important, since the chemical time scale needs to be computed in each cell at every time step. We present different chemical time scale definitions found in literature, evaluate them on simple test problems and use them for flame simulations in conjunction with the modified Eddy Dissipation Concept. For the simple test case, most formulations give satisfactory results. The complexity of the chemical reaction mechanism greatly impacts the calculated time scale values. Therefore, we suggest to use a simple global mechanism for the calculation of chemical time scales to ensure reproducibility and consistency of the results.

摘要

化学时间尺度可用于表征反应系统（的行为）。此外，各种无量纲数（例如 Damköhler 数）依赖于特征化学时间尺度。系统的逆特征值被视为系统的时间尺度。这意味着，时间尺度的数量等于特征值的数量。系统表征和计算无量纲数需要一个单一特征时间尺度的公式。最近提出的对涡流耗散概念（湍流-化学相互作用模型）的修改也在其公式中加入了 Damköhler 数。除了准确性之外，数值效率也很重要，因为需要在每个时间步长的每个单元格中计算化学时间尺度。我们提出了文献中发现的不同化学时间尺度定义，在简单的测试问题上对其进行评估，并将它们与修改后的涡流耗散概念结合用于火焰模拟。对于简单的测试用例，大多数公式都给出了令人满意的结果。化学反应机制的复杂性极大地影响了计算的时间尺度值。因此，我们建议使用简单的全局机制来计算化学时间尺度，以确保结果的可重复性和一致性。