Gary J. Page

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.

Finite Volume Discretization Aspects for Viscous Flows on Mixed Unstructured Grids

A solution method for compressible turbulent flows on unstructured grids in two dimensions is described. The method can be used on grids consisting of triangular and/or quadrilateral cells. Control volumes are constructed from dual cells, and the solution variables are stored at the vertices of the grid. Grid-transparent algorithms are developed that do not require knowledge of cell types, leading to simple discretization schemes on mixed grids. The inviscid fluxes are computed from limited high-resolution schemes originally developed for unstructured triangular grids. They are easily applied to quadrilateral or mixed grids and are grid transparent. The discretization of the viscous fluxes is studied in detail. A positive, grid-transparent discretization of Laplaces equation is developed. The existence of tangential derivatives in the viscous terms prevents grid transparency. By neglecting tangential derivatives, an approximate form of the viscous fluxes is developed, which recovers grid transparency. The approximate form is shown to be similar to the thin-shear-layer approximation. Results are obtained for a transonic inviscid flow, a laminar separated flow, and a transonic turbulent flow

Shock capturing using a pressure-correction method

A new pressure-correction scheme has been developed, which is suitable for the calculation of a flow containing a wide range of Mach numbers such as a transonic impinging jet. The method uses equations based on properties per unit volume so that momentum is retained as a basic dependent variable rather than velocity. This simplifies the discretization of the time-dependent flow equations and allows a direct relationship to be determined between pressure and mass flux. The hyperbolic nature of the system of equations is obtained by using the retarded pressure approach. This is a transformation of the real pressure based on local Mach number and is used in the momentum and pressure-correction equations. The shocked quasi-one-dimensional flow in a nozzle is used as a test of shock capturing properties and speed of computation. The new method gives precise shock capturing over two nodes with no over or under-shoots; it is also significantly faster than the MacCormack and Jameson explicit schemes tested for this problem. Finally, a turbulent, under-expanded, axisymmetric, impinging jet calculation is presented. The correct periodic under/over-expansions of the jet are predicted, and the normal standoff shock is cleanly captured.

Numerical predictions of turbulent underexpanded sonic jets using a pressure-based methodology:

Abstract The objective of this work is to model underexpanded turbulent sonic jets. A pressure-based computational fluid dynamics methodology has been employed, incorporating extensions to handle high speed flows. A standard two-equation turbulence model is used, with an optional compressibility correction. Comparison with experimental jet centre-line Mach number showed the correct shock cell wavelength but a too rapid decay. The compressibility correction had no effect on the shock cell decay but increased the potential core length to give better agreement with experiment. Calculations for nozzle pressure ratios up to 30 showed the variation of Mach disc location in good agreement with experiment. For nozzle pressure ratios above 6, unsteady solutions were observed, emanating from the intersection of the Mach disc with the shear layer. Experimental work has identified similar large-scale instabilities; the peak mode of the prediction had a Strouhal number of 0.16, close to experimental values.

Large-eddy simulation of twin impinging jets in cross-flow

The flow-field beneath a jet-borne vertical landing aircraft is highly complex and unsteady. large-eddy simulation is a suitable tool to predict both the mean flow and unsteady fluctuations. This work aims to evaluate the suitability of LES by applying it to two multiple jet impingement problems: the first is a simple twin impinging jet in cross-flow, while the second includes a circular intake. The numerical method uses a compressible solver on a mixed element unstructured mesh. The smoothing terms in the spatial flux are kept small by the use of a monitor function sensitive to vorticity and divergence. The WALE subgrid scale model is utilised. The simpler jet impingement case shows good agreement with experiment for mean velocity and normal stresses. Analysis of time histories in the jet shear layer and near impingement gives a dominant frequency at a Strouhal number of 01, somewhat lower than normally observed in free jets. The jet impingement case with an intake also gives good agreement with experimental velocity measurements, although the expansion of the grid ahead of the jets does reduce the accuracy in this region. Turbulent eddies are observed entering the intake with significant swirl. This is in qualitative agreement with experimental visualisation. The results show that LES could be a suitable tool when applied to multiple jet impingement with realistic aircraft geometry.

A CFD Coupled Acoustics Approach for Coaxial Jet Noise

Whilst the most general methodology to predict jet noise utilises Direct Numerical Simulation or Large Eddy Simulation to model the full unsteady ∞owfleld, such an approach is unfeasible in an engineering context. A method is proposed to couple a standard Reynolds Averaged Navier-Stokes CFD method with a Lighthill based noise model for coaxial jets. This has relatively low computational resource requirements, whilst possessing the physical mechanisms to re∞ect how changes in nozzle geometry modify the noise spectra. The three parameters in the noise model were calibrated using single stream jet noise data and then applied to coaxial jet ∞ows. Coplanar coaxial jet problems for difiering area and velocity ratios showed reasonable agreement with measured noise spectra. However, a three-quarter cowl nozzle conflguration showed poor agreement with experiment. Serrations added to the nozzle produced only small changes in the turbulence intensity and length scale predicted by the RANS CFD model and consequently only minor changes were observed in the spectra - a reduction in low frequency noise coupled with an increase at higher frequencies.

A model for international teaming in aircraft design education

Abstract This paper describes the nature and development of an undergraduate aircraft design course involving students in US and UK universities working in an integrated team that models the international collaboration commonplace in the aerospace industry. The reasoning that led to this collaboration is outlined and details of the organisation and management of the programme described. Observations from the three years of experience with running the programme are made and some overall conclusions given. Some of the design projects are illustrated including the roadable aircraft design which won the 1999/2000 NASA/FAA AGATE National General Aviation Design Competition. The collaboration has been successful from an educational standpoint and would serve as an effective model that could be adopted by other pairs of universities.

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

LES of Impinging Jet Flows Relevant to Vertical Landing Aircraft

The flow-field due to multiple impinging jets from a vertical landing aircraft is highly complex and unsteady. The ability to predict both the mean flow and unsteady excursions is important for the design and development of future aircraft. A Large Eddy Simulation (LES) technique is used to compute two simplified twin impinging jet in cross flow problems. The LES solutions give good agreement with experiment and are a significant improvement over Reynolds Averaged Navier-Stokes solutions. The interaction of the wall jets to form an unsteady fountain that can sometimes reach the intake is observed. There is a disparity in time scales between that needed to resolve the smallest eddies and that for flow to travel through the domain, resulting in the computation needing a large number of time steps to achieve statistically meaningful results. The LES results indicate considerable promise for this type of flow problem, and work is underway to extend the application to full aircraft geometries.

Large Eddy Simulation of a complete Harrier aircraft in ground effect

This paper aims to demonstrate the viability of using the large eddy simulation (LES) CFD methodology to model a representative, complete STOVL aircraft geometry at touch down. The flowfield beneath such a jet-borne vertical landing aircraft is inherently unsteady. Hence, it is argued in the present work that the LES technique is the most suitable tool to predict both the mean flow and unsteady fluctuations, and, with further development and validation testing, this approach could be a replacement, and certainly a complementary aid, to expensive rig programmes. The numerical method uses a compressible solver on a mixed element unstructured mesh. Examination of instantaneous flowfield predictions from these LES calculations indicate close similarity with many flow features identified from ground effect flow visualisations, which are well known to be difficult to model using RANS-based CFD. Whilst significant further work needs to be carried out, these calculations show that LES could be a practical tool to model, for example, Hot Gas Ingestion for the Joint Strike Fighter aircraft.