William A. McMullan

Jet Noise: Acoustic Analogy informed by Large Eddy Simulation

A novel approach to the development of a hybrid prediction methodology for jet noise is described. Modeling details and numerical techniques are optimized for each of the three components of the model. Far-field propagation is modeled by solution of a system of adjoint linear Euler equations, capturing convective and refraction effects using a spatially developing jet mean flow provided by a Reynolds-averaged Navier―Stokes computational fluid dynamics solution. Sound generation is modeled following Goldsteins acoustic analogy, including a Gaussian function model for the two-point cross correlation of the fourth-order velocity fluctuations in the acoustic source. Parameters in this model describing turbulent length and time scales are assumed to be proportional to turbulence information also taken from the Reynolds-averaged Navier―Stokes computational fluid dynamics prediction. The constants of proportionality are, however, not determined empirically, but extracted by comparison with turbulence length and time scales obtained from a large eddy simulation prediction. The large eddy simulation results are shown to be in good agreement with experimental data for the fourth-order two-point cross-correlation functions. The large eddy simulation solution is then used to determine the amplitude parameter and also to examine which components of the cross correlation are largest, enabling inclusion of all identified dominant terms in the Gaussian source model. The acoustic source description in the present approach is therefore determined with no direct input from experimental data. This model is applied to the prediction of sound to the experimental configuration of the European Union JEAN project, and gives encouraging agreement with experimental data across a wide spectral range and for both sideline and peak noise angles. This paper also examines the accuracy of various commonly made simplifications, for example: a locally parallel mean flow approximation rather than consideration of the spatially evolving mean jet flow and scattering from the nozzle; the assumption of small radial variation in Green function over the turbulence correlation length; the application of the far-field approximation in the Green function; and the impact of isotropic assumptions made in previous acoustic source models.

Large Eddy Simulation of a High Reynolds Number Subsonic Turbulent Jet for Acoustic Source Capture

Large Eddy Simulations of a Mach 0.75 isothermal jet at a Reynolds number of 1 million have been generated to allow analysis of acoustic noise sources. Two simulations are presented: one starting at the nozzle exit plane with 5% inlet perturbations and one including the upstream development of the ow in the nozzle. Analysis of the former results shows the ow to become fully turbulent by 0.5 nozzle diameters, whereas in the latter case the inlet perturbations have decayed before reaching the nozzle exit and consequently it does not become fully turbulent until 2.5 nozzle diameters. Comparison with LDV data shows good prediction of the potential core length, jet centreline axial uctuation and mean velocity proles, but generally an over-prediction of resolved normal and shear stresses. Fourth order two-point two-time correlations are important for modelling of noise sources and comparison of the shape and decay of the LES predicted correlations with experimental data show good agreement. To reduce the noise modelling eort, it is important to know the relative magnitudes of these correlation terms and comparison with recent PIV data shows reasonable agreement although some terms appear to be anomalously high, and further investigations are necessary

Initial condition effects on large scale structure in numerical simulations of plane mixing layers

In this paper, Large Eddy Simulations are performed on the spatially developing plane turbulent mixing layer. The simulated mixing layers originate from initially laminar conditions. The focus of this research is on the effect of the nature of the imposed fluctuations on the large-scale spanwise and streamwise structures in the flow. Two simulations are performed; one with low-level three-dimensional inflow fluctuations obtained from pseudo-random numbers, the other with physically correlated fluctuations of the same magnitude obtained from an inflow generation technique. Where white-noise fluctuations provide the inflow disturbances, no spatially stationary streamwise vortex structure is observed, and the large-scale spanwise turbulent vortical structures grow continuously and linearly. These structures are observed to have a three-dimensional internal geometry with branches and dislocations. Where physically correlated provide the inflow disturbances a “streaky” streamwise structure that is spatially stationary is observed, with the large-scale turbulent vortical structures growing with the square-root of time. These large-scale structures are quasi-two-dimensional, on top of which the secondary structure rides. The simulation results are discussed in the context of the varying interpretations of mixing layer growth that have been postulated. Recommendations are made concerning the data required from experiments in order to produce accurate numerical simulation recreations of real flows.

Investigation of Coherent Structures in Turbulent Mixing Layers using Large Eddy Simulation

Large Eddy Simulation (LES) of two- and three-dimensional spatially-developing mixing layers are presented. The maximum Reynolds number obtained in the simulations is Re ∼ 70, 000 based on the visual thickness of the layer and the velocity difference across it. The purpose of this research is to assess the capability of two- and three-dimensional LES to replicate the features found in the plane mixing layer that originates from initially laminar conditions. Two dimensional simulations offer a poor representation of the real flow; the obtained velocity fluctuation statistics do not achieve similarity and the lack of spanwise dimension prevents the formation of streamwise vortex structures. This prevents the flow from undergoing transition to turbulence and the flow remains in an unsteady laminar state. Three-dimensional simulations produce flow statistics that agree very well with experimental data, and replicate many of the salient features of the laboratory flow. Streamwise vortex structure is observed to develop in the flow, and a transition to turbulence in the flow is recorded. Careful inspection of flow visualisation reveals the presence of quasi-two-dimensional coherent structures embedded within the turbulent flow, the topography of which bears remarkable resemblance to comparable experimental flow visualisation. In order to produce a credible numerical representation of the flow, it is essential to perform well-resolved, fully three-dimensional simulations that are initialised from boundary conditions that mimic those found in the real flow.

Spanwise domain effects on the evolution of the plane turbulent mixing layer

Large Eddy Simulation is used to simulate a series of plane mixing layers. The influence of the spanwise domain on the development of the mixing layer, and the evolution of the coherent structures, are considered. The mixing layers originate from laminar conditions, and an idealised inflow condition is found to produce accurate flow predictions when the spanwise computational domain extent is sufficient to avoid confinement effects. Spanwise domain confinement of the flow occurs when the ratio of spanwise domain extent to local momentum thickness reaches a value of ten. Flow confinement results in changes to both the growth mechanism of the turbulent coherent structures, and the nature of the interactions that occur between them. The results demonstrate that simulations of the two-dimensional mixing layer flow requires a three-dimensional computational domain in order that the flow will evolve in a manner that is free from restraints imposed by the spanwise domain.

Investigation of Streamwise and Transverse Instabilities on Swept Cylinders and Implications for Turbine Blading

The starting point for this investigation was the observation of robust streamwise streaks in flow visualization on the suction surfaces of blades in a turbine cascade at subsonic and transonic speeds. The spanwise wavelength of an array of streamwise vortices had been predicted and is here confirmed experimentally. Observations of streaks on unswept turbine blades and on circular cylinders confirmed these earlier predictions, providing a firm basis for referencing the new measurements of vortical behavior. The observations made it clear that the boundary layers are highly three dimensional. In this paper observations of streamwise and transverse instabilities on swept circular cylinders, over a range of inclinations, are presented. The circular cylinder is a canonical case and observations relate the streamwise vorticity of the unswept case to the more aggressive crossflow instability at high sweep angles. Introducing sweep brings consideration of a wide range of instabilities. Prominent is crossflow instability resulting from the inflectional behavior of a three-dimensional boundary layer.

Influence of a Numerical Boundary Layer Trips on Spatio-Temporal Correlations within LES of a Subsonic Jet

Large eddy simulation is a useful tool for jet noise prediction, and in particular its ability to predict two-point two-time fourth order correlations to guide jet noise modelling is promising. However, many predictions suffer from poor development of the initial jet shear layer and consequent incorrect prediction of critical parameters such as jet potential core length. In this work a simple numerical trip is introduced into the simulation of the convergent part of the upstream nozzle of a subsonic circular free jet with a Reynolds number of 1 million. After an initial decay, realistic turbulence is sustained to the nozzle exit. This then excites a rapid growth in the free shear layer giving a fully turbulent shear layer within 0.5Dj of the nozzle exit plane. When compared to an untripped simulation this gives an accurate prediction of potential core length and realistic growth of turbulent fluctuations along the nozzle lip-line. Flow visualisation and spectra show the untripped case to produce unrealistic vortex ring structures whereas the tripped case has a rapid onset of three-dimensionality. Similar benefits are found when analysing the second and fourth order space-time correlations at the early x/Dj = 1.5 station. The tripped correlations show good agreement with experimental PIV data. A complete map of correlation data is available for jet noise modelling.

Analysis of the variable density mixing layer using Large Eddy Simulation

In this paper Large Eddy Simulations of mixing layer flows with Reynolds numbers of up to 80,000, based on the velocity difference across the layer and its visual thickness are presented. Mixing layers over a wide range of density ratios are simulated. Several of the simulations are performed at conditions which match reference experimental data. Analysis of the mean velocity statistics shows that the simulations produce very reasonable predictions when compared to the experimental data. In addition the mean growth rates of the simulated flows agree well with the accepted entrainment model of the flow. Spanwise- and cross-stream-averaged flow visualisations are used to illustrate the quasi-two-dimensional coherent structures present in the flow. The simulated flows are observed to undergo the mixing transition, and that coherent structures persist in the turbulent flow for all density ratios. The topography of the flow is analysed in detail, and it is shown that the mean visual thickness, coherent structure convection velocity and coherent structure spacing are all functions of the density ratio between the freestreams. The simulation results provide evidence that the variation in the spatial growth rate with density ratio is a consequence of the density ratio dependence of the convection velocity, whilst the temporal growth rates for all density ratios are the same.

Large eddy simulation of a compressor cascade and the influence of spanwise domain

A controlled diffusion compressor cascade is studied using large eddy simulation (LES). The aim of this study is to assess the capability of LES to be used in an industrial context. The Reynolds number is approximately 700 000 based on chord length and inlet velocity. A ‘thin-slice’ representation of the cascade is used as the reference grid, and the influence of a narrow span is studied by comparison simulations with a domain that has a span five times larger than the thin-slice grid. While the instantaneous flow-fields of the thin-slice and wide-domain simulations are qualitatively similar, the thin-slice simulations suffer from flow confinement problems caused by the imposition of the narrow span. The non-unity axial velocity density ratio of the flow enforces the use of inviscid wall spanwise boundaries, which have a parasitic influence on the development of the flow in the thin-slice simulations. The resultant data obtained from the thin-slice simulations are therefore compromised and the computed loss estimation is considered unreliable. However, when comparing mean quantities such as surface pressure and boundary layer growth the narrow does give reasonable predictions. While the inviscid spanwise walls also affect the flow near the boundaries in the wide domain simulations, there is sufficient region of span from which reliable flow data and loss estimations can be obtained. For blade flows at off-design conditions, a span of 20 per cent of the blade chord is sufficient to give good agreement with experimental data. This incurs a computational cost that may be too high to incorporate parametric LES studies into the design cycle of turbomachinery components with current computers.

The Effect of Initial Conditions on Streamwise Vortices in the Plane Turbulent Mixing Layer

In this research we investigate the effect of inflow conditions on the streamwise vortices that exist in the plane turbulent mixing layer. Both initially-laminar and initially-turbulent mixing layers are considered here. The effect of the imposed fluctuations is assessed in the initially-laminar mixing layer simulations through the use of a white noise disturbance environment, and a physically-correlated fluctuation environment produced by an inflow generation method. The initially-turbulent mixing layer has its inflow condition produced by the inflow generation method. Each simulation produces good statistical agreement with the experimental data. The initially-laminar simulation with correlated fluctuations predicts the presence of statistically stationary streamwise vortices, whilst the other two simulations do not.