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.

自从20世纪50年代喷气式飞机时代开始以来，政府、科学家和工程师们就已经敏锐地意识到飞机噪音对健康的影响--长期暴露在飞机噪音中对人类健康的危害非常大。例如，噪音污染的增加与儿童的认知障碍和行为问题、睡眠障碍（以及由此产生的健康问题）以及高水平噪音的反复侵入造成的明显听力损伤有关。世界卫生组织估计，欧洲因噪音损失了100万健康寿命年;这主要是由于压力水平持续增加导致的心血管疾病，其中航空噪音是最大的贡献者。此外，航空环境联合会发现，这些问题给英国政府支出带来了每年5.4亿英镑的负担。虽然在了解飞机噪音方面取得了巨大进展，但过去20年来，航班数量翻了一番，达到惊人的4000万次（在2019年前的新冠肺炎疫情中），这增加了对喷气噪音物理学研究的需求，以发现新的降阶湍流模型。本文提出了一种新的射流湍流数学模型，并采用渐近分析法。重构的湍流结构将用于高速轴对称射流的快速噪声预测的数值代码中。从根本上说，射流分解成湍流会产生压力波动，并以声音的形式传播出去。1952年，莱特希尔指出，Navier-Stokes方程可以精确地重新排列成一种形式，其中作用于压力波动的波算子等于射流雷诺应力的双散度。当雷诺应力的自协方差被假定为已知的流体在休息时，声学频谱的标度特性，如著名的8次幂定律。Goldstein在2003年提出的广义声学类比通过将流体力学变量分为定常基流及其扰动来推进这一思想。每单位体积的声谱是传播子和纯波动雷诺应力张量的自协方差的张量积。对于适当的喷流底流，通过确定线性化欧拉算子的绿色函数，可以计算传播算子。然而，与Lighthill的理论一样，自协方差张量假定是已知的，这总是需要使用大涡模拟（LES）但是对于不同的喷管，大涡模拟数据仍然需要耗费大量的计算资源和计算时间，对于设计优化或当考虑复杂射流时，需要工作点。使任何替代建模如此复杂的是，湍流闭合问题排除了自协方差张量的闭合形式理论。然而，我们最近的工作表明，峰值噪声可以准确地预测时，传播是在低频确定的，是相同的顺序作为喷流扩散率（小于1）。因此，本提案提出了一种替代的、首创的分析方法，以确定给定平均流解的脉动雷诺应力。通过求解控制方程在这个渐近缩放射流演变的时间在空间中传播的相同的速度，我们确定的大尺度湍流（LST）结构的射流。这种方法是由一个2维系统的方程轴对称射流和计算时间预计将是一个数量级的速度比LES。基于LST的解决方案的雷诺应力自协方差峰值喷气噪声将比较LES数据提供的几个喷气操作条件下，我们的项目合作伙伴。我们的目标是表明，湍流的LST模型提供了准确的噪声预测，是一个可行的替代LES。