This paper focusses on the relationship between the heat release rate and the acoustic field, which is a crucial element in modelling thermoacoustic instabilities. The aim of the paper is twofold. The first aim is to develop a transformation tool, which makes it easy to switch between the time-domain representation (typically a heat release law involving time-lags) and the frequency-domain representation (typically a flame transfer function) of this relationship. Both representations are characterised by the same set of parameters n₁, n₂, …, n_k. Their number is quite small, and they have a clear physical meaning: they are time-lag dependent coupling coefficients. They are closely linked to the impulse response of the flame in the linear regime in that they are proportional to the discretised (with respect to time) impulse response. In the nonlinear regime, the parameters n₁, n₂, …, n_k become amplitude-dependent. Their interpretation as time-lag dependent coupling coefficients prevails; however, the link with the impulse response is lost. Nonlinear flames are commonly described in the frequency-domain by an amplitude-dependent flame transfer function, the so-called flame describing function. The time-domain equivalent of the flame describing function is sometimes mistaken for a ‘nonlinear impulse response’, but this is not correct. The second aim of this paper is to highlight this misconception and to provide the correct interpretation of the time-domain equivalent of the flame describing function.

本文着重于放热率与声场之间的关系，这是模拟热声不稳定性的关键因素。本文的目的是双重的。第一个目标是开发一种转换工具，该工具可以轻松地在这种关系的时域表示（通常是涉及时滞的放热定律）和频域表示（通常是火焰传递函数）之间进行切换。两种表示都具有相同的一组参数n ₁，n ₂，…，n _k。它们的数量非常小，并且具有明确的物理含义：它们是时滞相关的耦合系数。它们与线性状态下火焰的脉冲响应紧密相关，因为它们与离散的（相对于时间）脉冲响应成比例。在非线性状态下，参数n ₁，n ₂，…，n _k变得与振幅有关。他们解释为时滞相关的耦合系数。但是，与脉冲响应的链接丢失了。非线性火焰通常在频域中通过振幅相关的火焰传递函数（即所谓的火焰描述函数）进行描述。有时将火焰描述函数的时域等效物误认为是“非线性脉冲响应”，但这是不正确的。本文的第二个目的是强调这种误解，并对火焰描述函数的时域等效性提供正确的解释。