Large Eddy Simulation of Free and Impinging Subsonic Jets and their Sound Fields

Abstract

Evaluating aerodynamic noise from aircraft engines is a design stage process, so that it conform to regulations at airports. Aerodynamic noise is also a principal source of structural vibration and internal noise in short/vertical take off and landing and rocket launches. Acoustic loads may be critical for the proper functioning of electronic and mechanical components. It is imperative to have tools with capability to predict noise generation from turbulent flows. Understanding the mechanism of noise generation is essential in identifying methods for noise reduction. Lighthill (1952) and Lighthill (1954) provided the first explanation for the mechanism of aerodynamic noise generation and a procedure to estimate the radiated sound field. Many such procedures, known as acoustic analogies are used for estimating the radiated sound field in terms of the turbulent fluid flow properties. In these methods, the governing equations of the fluid flow are rearranged into two parts, the acoustic sources and the propagation terms. The noise source terms and propagation terms are different in different approaches. A good description of the turbulent flow field and the noise sources is required to understand the mechanism of noise generation. Computational aeroacoustics (CAA) tools are used to calculate the radiated far field noise. The inputs to the CAA tools are results from CFD simulations which provide details of the turbulent flow field and noise sources. Reynolds-Averaged Navier Stokes (RANS) solutions can be used as inputs to CAA tools which require only time-averaged mean quantities. The output of such tools will also be mean quantities. While complete unsteady turbulent flow details can be obtained from Direct Numerical Simulation (DNS), the computation is limited to low or moderate Reynolds number flows. Large eddy simulations (LES) provide accurate description for the dynamics of a range of large scales. Most of the kinetic energy in a turbulent flow is accounted by the large-scale structures. It is also the large-scale structures which accounts for the maximum contribution towards the radiated sound field. The results from LES can be used as an input to a suitable CAA tool to calculate the sound field. Numerical prediction of turbulent flow field, the acoustic sources and the radiated sound field is at the focus of this study. LES based on explicit filtering method is used for the simulations. The method uses a low-pass compact filter to account for the sub-grid scale effects. A one-parameter fourth-order compact filter scheme from Lele (1992) is used for this purpose. LES has been carried out for four different flow situations: (i) round jet (ii) plane jet (iii) impinging round jet and (iv) impinging plane jet. LES has been used to calculate the unsteady flow evolution of these cases and the Lighthill’s acoustic sources. A compact difference scheme proposed by Hixon & Turkel (1998) which involves only bi-diagonal matrices are used for evaluating spatial derivatives. The scheme provides similar spectral resolution as standard tridiagonal compact schemes for the first spatial derivatives. The scheme is computationally less intensive as it involves only bi-diagonal matrices. Also, the scheme employs only a two-point stencil. To calculate the radiated sound field, the Helmholtz equation is solved using the Green’s function approach, in the form of the Kirchhoff-Helmholtz integral. The integral is performed over a surface which is present entirely in the linear region and covers the volume where acoustic sources are present. The time series data of pressure and the normal component of the pressure gradient on the surface are obtained from the CFD results. The Fourier transforms of the time series of pressure and pressure gradient are then calculated and are used as input for the Kirchhoff-Helmholtz integral. The flow evolution for free jets is characterised by the growth of the instability waves in the shear layer which then rolls up into large vortices. These large vortical structures then break down into smaller ones in a cascade which are convected downstream with the flow. The rms values of the Lighthill’s acoustic sources showed that the sources are located mainly at regions immediately downstream of jet break down. This corresponds to the large scale structures at break down. The radiated sound field from free jets contains two components of noise from the large scales and from the small scales. The large structures are the dominant source for the radiated sound field. The contribution from the large structures is directional, mainly at small angles to the downstream direction. To account for the difference in jet core length, the far field SPL are calculated at points suitably shifted based on the jet core length. The peak value for the radiated sound field occurs between 30°and 35°as reported in literature. Convection of acoustic sources causes the radiated sound field to be altered due to Doppler effect. Lighthills sources along the shear layer were examined in the form of (x, t) plots and phase velocity pattern in (ω, k) plots to analyse for their convective speeds. These revealed that there is no unique convective speeds for the acoustic sources. The median convective velocity Uc of the acoustic sources in the shear layer is proportional to the jet velocity Uj at the center of the nozzle as Uc ≈ 0.6Uj. Simulations of the round jet at Mach number 0.9 were used for validating the LES approach. Five different cases of the round jet were used to understand the effect of Reynolds number and inflow perturbation on the flow, acoustic sources and the radiated sound field. Simulations were carried out for an Euler and LES at Reynolds number 3600 and 88000 at two different inflow perturbations. The LES results for the mean flow field, turbulence profiles and SPL directivity were compared with DNS of Freund (2001) and experimental data available in literature. The LES results showed that an increase in inflow forcing and higher Reynolds number caused the jet core length to reduce. The turbulent energy spectra showed that the energy content in smaller scale is higher for higher Reynolds number. LES of plane jets were carried out for two different cases, one with a co-flow and one without co-flow. LES of plane jets were carried out to understand the effect of co-flow on the sound field. The plane jets were of Mach number 0.5 and Reynolds number of 3000 based on center-line velocity excess at the nozzle. This is similar to the DNS by Stanley et al. (2002). It was identified that the co-flow leads to a reduction in turbulence levels. This was also corroborated by the turbulent energy spectrum plots. The far field radiation for the case without co-flow is higher over all angles. The contribution from the low frequencies is directional, mainly towards the downstream direction. The range of dominant convective velocities of the acoustic sources were different along shear layers and center-line. The plane jet results were also used to bring out a qualitative comparison of flow and the radiation characteristics with round jets. For the round jet, the center-line velocity decays linearly with the stream-wise distance. In the plane jet case, it is the square of the center-line velocity excess which decays linearly with the stream-wise distance. The turbulence levels at any section scales with the center-line stream-wise velocity. The decay of turbulence level is slower for the plane jet and hence the acoustic sources are present for longer distance along the downstream direction. Subsonic impinging jets are composed of four regions, the jet core, the fully developed jet, the impingement zone and the wall jet. The presence of the second region (fully developed free jet) depends on the distance of the wall from the nozzle and the length of the jet core. In impinging jets, reflection from the wall and the wall jet are additional sources of noise compared to the free jets. The results are analysed for the contribution of the different regions of the flow towards the radiated sound field. LES simulations of impinging round jets and impinging plane jet were carried out for this purpose. In addition, the results have been compared with equivalent free jets. The directivity plots showed that the SPL levels are significantly higher for the impinging jets at all angles. For free jets, a typical time scale for the acoustic sources is the ratio of the nozzle size to the jet velocity. This is ro/Uj for round jets and h/Uj for plane jets. For impinging jets, the non-dimensionlised rms of Lighthill’s source indicates that the time scale for acoustic sources is the ratio of the height of the nozzle from the wall to the jet velocity be L/Uj. LES of impinging round jets was carried out for two cases with different inflow perturbations. The jets were at Reynolds number of 88000 and Mach number of 0.9, same as the free jet cases. The impingement wall was at a distance L = 24ro from the nozzle exit. For impinging round jets, the SPL levels are found to be higher than the equivalent free jets. From the SPL levels and radiated noise spectra it was shown that the contribution from the large scale structures and its reflection from the wall is directional and at small angles to the wall normal. The difference in the range of angles where the radiation from the large scale structures were observed shows the significance of refraction of sound waves inside the flow. The rms values of the Lighthill’s sources indicate two dominant regions for the sources, just downstream of jet breakdown and in the impingement zone. The LES of impinging plane jet was done for a jet of Mach number 0.5 and Reynolds number of 6000. The impingement wall was at a distance L = 10h from the nozzle exit. The radiated sound field appears to emanate from this impingement zone. The directivity and the spectrum plots of the far field SPL indicate that there is no preferred direction of radiation from the impingement zone. The Lighthill’s sources are concentrated mainly in the impingement zone. The rms values of the sources indicate that the peak values occur in the impingement zone. The results from the different flow situations demonstrates the capability of LES with explicit filtering method in predicting the turbulent flow and radiated noise field. The method is robust and has been successfully used for moderate Reynolds number and an Euler simulation. An important feature is that LES can be used to identify acoustic sources and its convective speeds. It has been shown that the Lighthill source calculations, the calculated sound field and the observed radiation patterns agree well. An explanation for these based on the different turbulent flow structures has also been provided.