Kristján Guðmundsson

MY Research

My Ph.D. research is within the area of Jet Aeroacoustics; we seek predict and minimize the aerodynamic noise emitted by jet flows. Of particular interest is the part of the acoustic spectrum where the sound intensity reaches its peak: at low frequencies and downstream angles (shown in blue in fig. 2). This noise is associated with the large scale structures of the flow, in turn related to the instabilities of the inflectional mean velocity profiles.

Figure 2: Qualitative illustration of noise sources and associated directivities.

My work revolves around these instabilities and is an extension of the earlier work by Suzuki and Colonius (JFM, 2006) who showed the hydrodynamic pressure field of the jet (the area just outside the jet shear layer) to be consistent with that of the linear instabilities of the turbulent mean jet flow. I extend their work in two ways:

1. Inclusion of axial asymmetry (e.g. chevron) jets.
2. Inclusion of nonlinear and non-parallel effects for axisymmetric jets.

Linear stability characteristics of asymmetric jets

Figure 3: Chevrons on the B787 (www.boeing.com)

Chevron nozzles create a shift in the acoustic spectrum, reducing peak noise levels (at low-frequencies) while slightly increasing noise at higher frequencies. The chevrons introduce streamwise vorticity into the flow, enhancing mixing and shortening the potential core. The high-frequency penalty is due to increased turbulence intensity near the nozzle while the low-frequency benefit is related to the retardation of the large-scale structures of the flow. Inspired by the success of the linear instability wave as a model for the large scale structures of axisymmetric jets, we extend the theory to asymmetric jets. To summarize our results:

1. The chevron jet is inhomogeneous in both the radial and azimuthal coordinates. This bars the reduction of the governing equations to a single ODE. However, we show that the asymmetric stability problem is reducible to a system of coupled Rayleigh-like ODEs that include the axisymmetric jet as a special case. We solve the resulting Rayleigh system both directly (using Chebyshev polynomials), as well as through multidimensional shooting. The former method gives the entire spectrum of the Rayleigh operator while the latter allows the faster and more accurate tracking of a single mode.




2. We find that the chevron jet gives rise to many more shear-layer modes than the round jet. Only one of the chevron modes is significantly unstable. This mode corresponds most closely to that of the round jet (in terms of growth rate, phase speed, and degree of azimuthal symmetry) and is concentrated on the high-speed side of the shear-layer. Other unstable chevron modes are concentrated further out from the axis, each becoming more stable as its azimuthal complexity increases.




3. We find that chevron growth rate reductions are consistent with far-field noise benefits in that less unstable chevron jets have greater noise reductions.



4. We find that the hydrodynamic pressure field of chevron jets is consistent with that of the instability modes of the turbulent, spreading mean flow.

The concept having been so demonstrated we are now investigating optimization schemes whereby the chevron geometry may be varied to maximally retard large scale structures. The results of this work will be presented at a future date.

• K. Gudmundsson and T. Colonius. "The effects of nozzle serrations on jet stability characteristics," J. Fluid Mech., in preparation, 2009.


• K. Gudmundsson and T. Colonius. "Spatial stability analysis of chevron jet profiles," The 13th AIAA/CEAS Aeroacoustics Conference, Rome, Italy, May 2007. Paper AIAA-2007-3599.


• K. Gudmundsson and T. Colonius. "Linear stability analysis of chevron jet profiles," ASME Joint U.S.-European Fluids Engineering Summer meeting, Miami, Florida, July 2006. Paper FEDSM2006-98485.

Nonlinear and non-parallel stability models for turbulent jets

The modes obtained from linear stability analysis of subsonic flows are non-radiating, meaning that their signature cannot be detected far away from the turbulent region. They do however dominate the linear hydrodynamic region (Suzuki & Colonius, JFM 2006) near the jet. Further out the pressure field is dominated by an algebraicly decaying acoustic field. To obtain a globally valid solution these two fields must be matched up (this is referred to as matched asymptotics, see Tam & Morris, JFM 1980). An alternative is to explicitly include non-parallel effects in the analysis.

The Parabolized Stability Equations (PSE), introduced by Bertolotti & Herbert (TCFD 1991) represent a refinement of the linear stability equations (LST) whereby both non-parallel and nonlinear effects can be considered in the analysis of convectively unstable flows such as boundary layers and free shear-layers. We have implemented the linear and nonlinear PSE in rectangular and cylindrical coordinates, finding significant improvements in near-field predictions, as compared to those of LST (fig. 5).

Figure 5: A comparison of microphone measurements (symbols) to predictions of LST (red) and PSE (blue) for a cold Mach number 0.5 jet.

The predictions shown in fig. 5 are in close agreement with data past saturation after which the measurements decay at a lower rate and have a higher phase-speed as well (as judged from the slope of the phase-curve). This is due to downstream acoustic contamination in the measurements (which consist of both hydrodynamic and acoustic fluctuations, while those predicted by LST/PSE are purely hydrodynamic). Fig. 6 show an analogous comparison where we have filtered the measurements via proper orthogonal decomposition. Excellent comparisons are obtained, even beyond the closure of the potential core.

Figure 6: A comparison of POD-filtered and raw (circles/squares) microphone measurements to predictions of PSE for a cold Mach number 0.5 jet.

The predictions above are obtained via linear PSE. To obtain far-field predictions at low frequencies (below St = 0.2, say), it is imperative that the near-field wave-packet be accurately modeled far downstream. This requires that we account for the nonlinear interactions. Fig. 7 shows example results obtained using the nonlinear PSE on a planar mixing layer, demonstrating well the ability of the nonlinear PSE to model quite complicated physical phenomena.

Figure 7: Spanwise vorticity in a planar mixing layer. Vortex pairing induced via forcing at subharmonic frequencies.

• K. Gudmundsson and T. Colonius. "Nonlinear parabolized stability equation models for turbulent jets and their radiated sound," J. Fluid Mech., in preparation, 2009.


• K. Gudmundsson and T. Colonius. "Parabolized stability equation models for turbulent jets and their radiated sound," The 15th AIAA/CEAS Aeroacoustics Conference, Miami, Florida, May 2009. Paper AIAA-2009-3380.