Airfoil Noise in a Turbulent Jet
By Lilla Edit Koloszár, Patrick Rambaud, Jérôme Anthoine, von Karman Institute for Fluid Dynamics (VKI), Rhode-Saint-Genèse 1640, Belgium
Numerical models for sound prediction involve the solution of fluid equations. Due to the non-linearity of these equations and the importance of different scales, it is a difficult task to predict the sound produced by fluid flows, especially for high Reynolds number, subsonic conditions. Since the sound field associated with subsonic flows represents only a minute fraction of the energy in the flow, the accuracy of numerical simulations must be very high to capture the sound generation. This is particularly dramatic in free space and at low subsonic speeds. However, the fact that the sound field is in some sense a small perturbation of the flow can be used to obtain approximate solutions. Aeroacoustic analogies, which allow sound generation mechanisms to be separated from sound propagation, have been developed for this purpose.
 Pressure fluctuations at a listener position of 3 wavelengths from the transversely oscillating sphere |
Progress in computational aeroacoustics (CAA) nowadays allows a direct numerical simulation of the hydrodynamic and acoustic fields at once. The Reynolds numbers that can be achieved (at reasonable computational costs) by these accurate numerical approaches are still below the range that corresponds to practical engineering applications, however, and acceptable accuracy on the calculated sound field occurs only for Mach numbers in the high subsonic range.
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 Computational domain and mesh in the wing region |
At the opposite end of the spectrum is a low Mach number turbulent jet at a relatively large Reynolds number. Of particular interest is the noise produced when an airfoil is placed into the oncoming flow from a jet under these conditions. A numerical investigation of this aerodynamic noise source has been performed using a multi-domain hybrid method, which consists of two steps:
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Near the noise source, the flow field is obtained from LES computations performed using FLUENT.
- In the far field, the Ffowcs-Williams Hawkings (FW-H) integral method is used to predict the sound propagation. This aeroacoustic analogy allows for predictions of the sound produced by solid surfaces immersed in the unsteady flow field.
Even though FLUENT has the FW-H capability, an acoustic postprocessing module based on this method has been developed at VKI as part of an academic research project during the nine-month Diploma Course postgraduate program.The postprocessing module is implemented in FLUENT through user-defined functions (UDFs). The primary advantage of this approach, compared to writing a postprocessing module using separate software such as Matlab for example, is that the variables from the solver can be accessed and, therefore, used directly in the noise calculation.
The new acoustic module takes into consideration only the noise induced by vibrating body forces on a surface, namely the dipole source. It was first validated through a basic acoustic test case: a transversely oscillating rigid sphere that serves as a pure dipole source. The results were compared to the analytical solution of the problem and to the acoustic module in FLUENT (6.1.22 and 6.2.3). The implemented module showed good agreement with the analytical solution and with the solution obtained with FLUENT in the far-field region where the method is valid. It revealed however that the user should be careful to define the listener position to guarantee that it lies in the far field, a position that depends on the distance from, and the frequency governing the sound source. Otherwise the predictions of pressure fluctuations were found to be questionable. This is due to the fact that the FW-Hmethod assumes plane wave propagation while, in the mid field, the wave propagation is between the ideal spherical and plane wave forms.
 Instantaneous flow field from the jet outlet to the leading edge of the wing; coherent structures visualized with Q = 30000 colored by pressure (Q is the second invariant of the velocity gradient tensor) |
Once the implemented acoustic module was validated, it was applied to the case of a wing in a turbulent jet flow of Mach number M = 0.1. A 2D NACA0012 wing is placed into the jet flow at a distance of 6 times the jet diameter downstream of the jet outlet. The chord of the wing profile is equal to the jet diameter, so the Reynolds number based on either the jet diameter or the wing chord is the same (36,000).
The unsteady aerodynamics of airfoils involves two phenomena. One is the flow separation, either at the trailing edge or, if the wing is stalled, on the suction side.The other is the interaction with oncoming vortical, periodic, or random disturbances. Such effects influence the sound field. This basic investigation of airfoil-vortex interaction can be used in two major areas of industrial applications. First, such a phenomenon governs the noise propagation from a helicopter rotor blade. The second major application of airfoil induced noise propagation is related to turbomachinery. Here the blades are always submerged in a turbulent flow, so sound production due to the fluctuating pressure is encountered.
 Pressure fluctuations at a listener position of 4 wavelengths from the wing |
For the jet flow over the wing, the noise is primarily due to the interaction of large eddies with the body, so the pressure fluctuations on the body surface are needed for the acoustic module. The flow calculation in the source region is performed using the large eddy simulation (LES) approach in FLUENT. The mesh is refined near the solid boundaries, in order to reach y+ values less than 5. A very fine mesh is used at the leading edge where most of the vortex dynamics occurs,to give enough resolution for noise prediction. The number of faces on the wing surface is 12,000 and the total mesh size is about 913,000. Because of the large number of cells, statistically fully converged data are not yet available, since only five flow-through calculations have been performed to date.
The results at one instant in time show that the wing has a strong effect on the flow field and that the leading edge plays a key role in the evolution of the incoming coherent structures. These structures either have to deviate from their original path in order to bend away from the wing or impact the leading edge,which tears them apart. Such a vortical flow induces pressure fluctuations on the wing surface. The fluctuating pressure level at the leading edge is around 100times higher than that at the trailing edge, so the strongest acoustic source is likely to be found near the airfoil leading edge.
 Directivity of sound pressure level at a listener position of 4 wavelengths from the wing |
The prediction of noise propagation is determined at a given far-field position, just above the wing, using the implemented UDF and the FW-H module in FLUENT. The same background LES calculation is used as the source, and the pressure fluctuations at a listener position of 4 wavelengths from the wing (in the far field) are in excellent agreement. The close results show that the assumption of considering only the dipole source term is valid for noise prediction in the far field. The directivity of the acoustic signal was also computed. The predicted null region in the vicinity of ±90 degrees is typical of acoustic scattering by a finite streamlined body.
More.info: www.vki.ac.be
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