Asymptotic approximation of the large-scale structure of turbulence in axisymmetric jets: a first principle jet noise prediction method

轴对称射流中湍流大尺度结构的渐近逼近：第一原理射流噪声预测方法

• 批准号: EP/W01498X/1
• 负责人: Mohammad Koshuriyan
• 金额: $ 45.19万
• 依托单位: University of York
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW01498X%2F1
• 关键词: Asymptotic; approximation; large; scale; structure

Ever since the jet age began in the 1950s, governments, scientists, and engineers have been acutely aware of the health effects created by aircraft noise--the prolonged exposure of which is highly damaging to human health. Increased noise pollution, for example, has been linked to cognitive impairment and behavioural issues in children, sleep disturbance (and consequent health issues therefrom) as well as the obvious hearing damage caused by the repeated intrusion of high levels of noise. The World Health Organization estimates that 1-million healthy life years are lost in Europe due to noise; this is mainly by cardiovascular disease via the persistent increase in stress level-with aviation noise being the largest contributor here. Moreover, the Aviation Environment Federation found that these issues place a £540M/year burden on UK government expenditure. While there has been tremendous progress in understanding aircraft noise, the doubling of flights in the past 20 years to a staggering 40 million (in the pre-Covid year 2019) has heightened the need for research into the physics of jet noise to uncover new reduced-order turbulence models. This proposal develops a novel mathematical model for jet flow turbulence using asymptotic analysis. The re-constructed turbulence structure will be used within a numerical code for fast noise prediction of a high-speed axisymmetric jet flow. Fundamentally, a jet flow breaking down into turbulence creates pressure fluctuations that propagate away as sound. In 1952, Lighthill showed that the Navier-Stokes equations can be exactly re-arranged into a form where a wave operator acting on the pressure fluctuation, is equal to the double-divergence of the jet's Reynolds stress. When the auto-covariance of the Reynolds stress was assumed to be known for a fluid at rest, scaling properties of the acoustic spectrum were obtained such as the celebrated 8th power law. The generalized acoustic analogy formulated by Goldstein in 2003 advanced this idea by dividing the fluid mechanical variables into a steady base flow and its perturbation. The acoustic spectrum per unit volume is a tensor product of a propagator and the auto-covariance of the purely fluctuating Reynolds stress tensor. The propagator can be calculated by determining the Green's function of the Linearized Euler operator for an appropriate jet base flow however, as in Lighthill's theory, the auto-covariance tensor is assumed to be known, which invariably requires the use of Large-Eddy Simulation (LES) and experiments to obtain an approximate functional form for it. But LES data still uses immense computational resources and computing time when different nozzle operating points are needed for design optimization or when complex jets are considered. What makes any alternative to modelling so complex is that the turbulence closure problem precludes a closed-form theory for the auto-covariance tensor. However, our recent work revealed that the peak noise can be accurately predicted when the propagator is determined at low frequencies that are of the same order as the jet spread rate (that is lesser than unity). This proposal, therefore, sets out an alternative, first-of-its-kind, analytical approach to determine the fluctuating Reynolds stress for a given mean flow solution. By solving the governing equations at this asymptotic scaling where the jet evolves temporally at the same rate it spreads in space, we determine the Large-Scale Turbulence (LST) structure in the jet. This approach is defined by a 2-dimensional system of equations for an axisymmetric jet and the computational time is expected to be an order-of-magnitude faster than LES. The LST-based solution of the Reynolds stress auto-covariance for peak jet noise will be compared to LES data provided by our project partners at several jet operating conditions. We aim to show that the LST model of turbulence provides accurate noise predictions and is a viable alternative to LES.

自 20 世纪 50 年代喷气式飞机时代开始以来，政府、科学家和工程师就敏锐地意识到飞机噪音对健康造成的影响——例如，长期暴露在飞机噪音中对人类健康造成严重损害，噪音污染加剧。世界卫生组织估计，噪音与儿童的认知障碍和行为问题、睡眠障碍（以及随之而来的健康问题）以及高强度噪音的反复侵入造成的明显听力损伤有关。迷路了在欧洲，这主要是由于压力水平持续增加而导致的心血管疾病——此外，航空环境联合会发现，这些问题每年给英国政府支出带来 5.4 亿英镑的负担。尽管人们在了解飞机噪音方面取得了巨大进展，但过去 20 年中航班数量翻了一番，达到惊人的 4000 万架次（新冠疫情爆发前的 2019 年），因此迫切需要研究飞机噪音的物理原理，以发现新的降低噪音的方法。 -命令该提案使用渐近分析开发了一种新颖的射流湍流数学模型，该重建的湍流结构将用于高速轴对称射流破坏的快速噪声预测。 1952 年，Lighthill 证明，纳维-斯托克斯方程可以精确地重新排列成：形式，其中波算子作用于压力波动，等于射流雷诺应力的双发散当假设雷诺应力的自协方差对于静止流体而言是已知的，声谱的缩放特性。 Goldstein 在 2003 年提出的广义声学类比通过将流体力学变量划分为稳定的基流及其扰动，得到了著名的八次幂定律。传播因子和纯脉动雷诺应力张量的自协方差 传播因子可以通过确定适当射流基流的线性欧拉算子的格林函数来计算，但是，如莱特希尔理论中，假设自协方差张量为众所周知，这总是需要使用大涡模拟（LES）并通过实验获得其近似函数形式，但是 LES 数据在不同时仍然使用大量的计算资源和计算时间。设计优化或考虑复杂射流时需要喷嘴工作点。使任何替代建模变得如此复杂的原因是湍流闭合问题排除了自协方差张量的封闭形式理论。当传播器在与射流传播速率相同的量级（小于统一）的低频下确定时，可以准确地预测峰值噪声，因此，该提案提出了一种替代方案，史无前例。 、分析方法确定给定平均流解的脉动雷诺应力 通过求解渐近尺度下的控制方程，其中射流在时间上以与在空间中传播的速率相同的速率演化，我们确定了射流中的大尺度湍流 (LST) 结构。该方法由轴对称射流的二维方程组定义，计算时间预计比基于 LST 的雷诺应力求解快一个数量级。我们将把峰值喷射噪声的自协方差与我们的项目合作伙伴在几种喷射操作条件下提供的 LES 数据进行比较，我们的目的是证明湍流的 LST 模型可以提供准确的噪声预测，并且是 LES 的可行替代方案。