EPSRC Reference: 
EP/W01498X/1 
Title: 
Asymptotic approximation of the largescale structure of turbulence in axisymmetric jets: a first principle jet noise prediction method 
Principal Investigator: 
Koshuriyan, Dr MZA 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
University of York 
Scheme: 
New Investigator Award 
Starts: 
01 February 2023 
Ends: 
31 January 2026 
Value (£): 
354,627

EPSRC Research Topic Classifications: 
Continuum Mechanics 
Nonlinear Systems Mathematics 

EPSRC Industrial Sector Classifications: 
Transport Systems and Vehicles 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
Ever since the jet age began in the 1950s, governments, scientists, and engineers have been acutely aware of the health effects created by aircraft noisethe 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 1million healthy life years are lost in Europe due to noise; this is mainly by cardiovascular disease via the persistent increase in stress levelwith 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 preCovid year 2019) has heightened the need for research into the physics of jet noise to uncover new reducedorder turbulence models. This proposal develops a novel mathematical model for jet flow turbulence using asymptotic analysis. The reconstructed turbulence structure will be used within a numerical code for fast noise prediction of a highspeed 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 NavierStokes equations can be exactly rearranged into a form where a wave operator acting on the pressure fluctuation, is equal to the doubledivergence of the jet's Reynolds stress. When the autocovariance 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 autocovariance 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 autocovariance tensor is assumed to be known, which invariably requires the use of LargeEddy 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 closedform theory for the autocovariance 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, firstofitskind, 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 LargeScale Turbulence (LST) structure in the jet. This approach is defined by a 2dimensional system of equations for an axisymmetric jet and the computational time is expected to be an orderofmagnitude faster than LES. The LSTbased solution of the Reynolds stress autocovariance 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.

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