Abstract
Goldstein, Sescu & Afsar (J. Fluid Mech., vol. 695, pp. 199234, 2012) formulated an asymptotic theory in nonparallel flows for the vector Green’s function that enters adjoint linearized Euler equations in the generalized acoustic analogy formulation (Goldstein. J. Fluid Mech. 488, pp. 315333, 2003). The theory introduced a new distinguished scaling at low frequencies for a slowlydiverging mean flow that showed how the leading order nonparallel flow Green’s function solution would be (mathematically) different to the same parallel flow result at all points in the jet. The theory gave qualitative agreement with the full numerical calculation of the Linearized Euler Equations in Karabasov et al. (2011, AIAA2929). The present paper follows on from this work and is concerned with assessing the predictive capability of the Goldstein et al. (2012) asymptotic theory for low frequency jet noise. Using Goldstein’s generalized acoustic analogy formulation we determine the propagator (that depends on the adjoint vector Green’s function) using a steady ReynoldsAveraged NavierStokes (RANS) calculation to obtain the mean flow field for the asymptotic theory. The jet is axisymmetric and unheated with an acoustic Mach number of 0.9. We recover the basic structure of the Goldstein et al. (2012) qualitative analysis by showing the large increase in magnitude of the low frequency dominant propagator component when the true nonparallel flow is used. Our main result shows that this asymptotic solution can predict the jet noise spectrum at 30 degees to the jet axis remarkably well up to the peak noise when a suitably constructed axisymmetric turbulence model is used within the acoustic analogy. Since the calculation time for this approach is considerably faster than solving the full Linearized Euler equations, the merits for doing this are immediately clear.
Original language  English 

Pages  132 
Number of pages  32 
DOIs  
Publication status  Published  30 May 2016 
Event  22nd AIAA/CEAS Aeroacoustics Conference  Lyon, France Duration: 30 May 2016 → 1 Jun 2016 Conference number: eISBN: 9781624103865 http://arc.aiaa.org/doi/book/10.2514/MAERO16 
Conference
Conference  22nd AIAA/CEAS Aeroacoustics Conference 

Country  France 
City  Lyon 
Period  30/05/16 → 1/06/16 
Internet address 
Keywords
 Green’s function
 nonparallel flow
 low frequency jet noise
 asymptotic theory
 ReynoldsAveraged NavierStokes
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Profiles

Mohammed Afsar
Person: Academic