Analytically-based approach to rotor-stator interaction noise in mean swirling flow

A method for modelling and predicting the noise generated by the interaction between the unsteady wake shed from the rotor and a downstream row of stators in a modern ultra-high bypass ducted turbofan engine is described. An analytically-based model is developed to account for three main features of the problem. First, the way in which a typical unsteady wake disturbance from the rotor interacts and is distorted by the mean swirling flow as it propagates downstream. The analysis allows for the inclusion of mean entropy gradients and entropy perturbations. Second, the effects of real stator-blade geometry and proper representation of the genuinely three-dimensional nature of the problem. Third, to model the propagation of the resulting noise back upstream in mean swirling flow. The analytical nature of the problem allows for the inclusion of all wake harmonics and enables the response at all blade passing frequencies to be determined. Example results are presented for an initial wake distribution corresponding to a genuine rotor configuration. Comparisons between numerical data and the asymptotic model for the wake evolution are made. Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Wave propagation in a slowly-varying duct with mean vortical swirling flow

The propagation of unsteady disturbances in a slowlyvarying cylindrical duct carrying mean swirling flow is investigated using a multiple-scales technique. This is applicable to turbomachinery flow behind a rotor stage when the swirl and axial velocities are of the same order. The presence of mean vorticity couples acoustic and vorticity equations which produces an eigenvalue problem that is not self-adjoint unlike that for irrotational mean flow. In order to determine the amplitude variation along the duct, an adjoint solution for the coupled system of equations is derived. The solution breaks down where a mode changes from cut on to cut off. In this region the amplitude is governed by a form of Airy's equation, and the effect of swirl is to introduce a small shift in the origin of the Airy function away from the turning-point location. The variation of axial wavenumber and amplitude along the duct is calculated. In hard-walled ducts mean swirl is shown to produce much larger amplitude variation along the duct compared with a nonswirling flow. Mean swirl also has a large effect in ducts with finite-impedance walls which differs depending on whether modes are co-rotating with the swirl or counter rotating. © 2001 by A.J. Cooper, Published by the American Institute of Aeronautics and Astronautics, Inc.

The absorption of sound by helmholtz resonators with and without flow

Helmholtz resonators are commonly used as absorbers of incident acoustic power. Theoretical and experimental investigations have been performed in the four cases of no mean flow, grazing mean flow, bias mean flow and a combination of grazing and bias mean flows. In the absence of a mean flow, the absorption coefficient (deflned as the proportion of incident energy absorbed) is a non-linear function of the acoustic pressure and high incident acoustic pressures are required before the absorption becomes signiflcant. In contrast, when there is a mean flow present, either grazing or bias, the absorption is linear and thus absorption coefficient is independent of the magnitude of the acoustic pressure, and absorption is obtained over a wider range of frequencies. Non-linear effects are only discernible very close to resonance and at very-high amplitude. With grazing mean flow, there is the undesirable effect that sound can be generated over a range of frequencies due to the interaction between the unsteadily shed vorticity waves and the downstream edge of the aperture. This production is not observed when there is a bias flow because here the vorticity is shed all around the rim of the aperture and swept away by the mean flow. When there is both a grazing mean flow and a mean bias flow, we flnd that only a small amount of bias mean flow, compared with grazing mean flow, is required to destroy the production of acoustic energy. © 2002 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc.

Generation and scattering of sound in vortical flow

We present solutions to scattering problems for unsteady disturbances to a mean swirling flow in an annular duct with a rigid 'splitter'. This situation has application to rotor-stator interaction noise in aeroengines, where the flow downstream of the fan is swirling and bifurcates into the by-pass duct and the engine core. We also consider the trailing edge extension of this problem. Inviscid mean flow in a cylindrical annulus is considered, with both axial and swirling (azimuthal) velocity components. The presence of vorticity in the mean flow couples the acoustic and vorticity modes of irrotational flow. Instead we have one combined spectrum of acoustic-vorticity waves in which the 'sonic' and 'nearly-convected' modes are fully coupled. In addition to the aeroacoustics application the results offer insight into the behaviour of these acoustic-vorticity waves, and the precise nature of the coupling between the two types of mode. Two regimes are discussed in which progress has been made, one for a specialised mean flow, uniform axial flow and rigid body swirl, and a second regime in which the frequency is assumed large, valid for any axisymmetric mean flow. The Wiener-Hopf technique is used to solve the scattering problems mathematically, and we present numerical evaluations of these solutions. Several new effects are seen to arise due to the mean vorticity, in particular the generation of sound at a trailing edge due to the scattering of a nearly convected disturbance, in contrast to the way a convected gust silently passes a trailing edge in uniform mean flow.

Unsteady ejectors: The effect of driver jet mark-space ratio

mark Unsteady ejectors can be driven by a wide range of driver jets. These vary from pulse detonation engines, which typically have a long gap between each slug of fluid exiting the detonation tube (mark-space ratios in the range 0.1-0.2) to the exit of a pulsejet where the mean mass flow rate leads to a much shorter gap between slugs (mark-space ratios in the range 2-3). The aim of this paper is to investigate the effect of mark-space ratio on the thrust augmentation of an unsteady ejector. Experimental testing was undertaken using a driver jet with a sinusoidal exit velocity profile. The mean value, amplitude and frequency of the velocity profile could be changed allowing the length to diameter ratio of the fluid slugs L/D and the mark-space ratio (the ratio of slug length to the spacing between slugs) L/S to be varied. The setup allowed L/S of the jet to vary from 0.8 to 2.3, while the L/D ratio of the slugs could take any values between 3.5 and 7.5. This paper shows that as the mark-space ratio of the driver jet is increased the thrust augmentation drops. Across the range of mark-space ratios tested, there is shown to be a drop in thrust augmentation of 0.1. The physical cause of this reduction in thrust augmentation is shown to be a decrease in the percentage time over which the ejector entrains ambient fluid. This is the direct result ofthe space between consecutive slugs in the driver jet decreasing. The one dimensional model reported in Heffer et al. [1] is extended to include the effect of varying L/S and is shown to accurately capture the experimentally measured behavior ofthe ejector. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc.

Kelvin-Helmholtz-like instabilities in turbulent flows over complex surfaces

Riblets are small surface protrusions aligned with the flow direction, which confer an anisotropic roughness to the surface [6]. We have recently reported that the transitional-roughness effect in riblets, which limits their performance, is due to a Kelvin–Helmholtz-like instability of the overlying mean flow [7]. According to our DNSs, the instability sets on as the Reynolds number based on the roughness size of the riblets increases, and coherent, elongated spanwise vortices begin to develop immediately above the riblet tips, causing the degradation of the drag-reduction effect. This is a very novel concept, since prior studies had proposed that the degradation was due to the interaction of riblets with the flow as independent units, either to the lodging of quasi-streamwise vortices in the surface grooves [2] or to the shedding of secondary streamwise vorticity at the riblet peaks [9]. We have proposed an approximate inviscid analysis for the instability, in which the presence of riblets is modelled through an average boundary condition for an overlying, spanwise-independent mean flow. This simplification lacks the accuracy of an exact analysis [4], but in turn applies to riblet surfaces in general. Our analysis succeeds in predicting the riblet size for the onset of the instability, while qualitatively reproducing the wavelengths and shapes of the spanwise structures observed in the DNSs. The analysis also connects the observations with the Kelvin–Helmholtz instability of mixing layers. The fundamental riblet length scale for the onset of the instability is a ‘penetration length,’ which reflects how easily the perturbation flow moves through the riblet grooves. This result is in excellent agreement with the available experimental evidence, and has enabled the identification of the key geometric parameters to delay the breakdown. Although the appearance of elongated spanwise vortices was unexpected in the case of riblets, similar phenomena had already been observed over other rough [3], porous [1] and permeable [11] surfaces, as well as over plant [5,14] and urban [12] canopies, both in the transitional and in the fully-rough regimes. However, the theoretical analyses that support the connection of these observations with the Kelvin–Helmholtz instability are somewhat scarce [7, 11, 13]. It has been recently proposed that Kelvin–Helmholtz-like instabilities are a dominant feature common to “obstructed” shear flows [8]. It is interesting that the instability does not require an inflection point to develop, as is often claimed in the literature. The Kelvin-Helmholtz rollers are rather triggered by the apparent wall-normal-transpiration ability of the flow at the plane immediately above the obstructing elements [7,11]. Although both conditions are generally complementary, if wall-normal transpiration is not present the spanwise vortices may not develop, even if an inflection point exists within the roughness [10]. REFERENCES [1] Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 J. Fluid Mech. 562, 35–72. [2] Choi, H., Moin, P. & Kim, J. 1993 J. Fluid Mech. 255, 503–539. [3] Coceal, O., Dobre, A., Thomas, T. G. & Belcher, S. E. 2007 J. Fluid Mech. 589, 375–409. [4] Ehrenstein, U. 2009 Phys. Fluids 8, 3194–3196. [5] Finnigan, J. 2000 Ann. Rev. Fluid Mech. 32, 519–571. [6] Garcia-Mayoral, R. & Jimenez, J. 2011 Phil. Trans. R. Soc. A 369, 1412–1427. [7] Garcia-Mayoral, R. & Jimenez, J. 2011 J. Fluid Mech. doi: 10.1017/jfm.2011.114. [8] Ghisalberti, M. 2009 J. Fluid Mech. 641, 51–61. [9] Goldstein, D. B. & Tuan, T. C. 1998 J. Fluid Mech. 363, 115–151. [10] Hahn, S., Je, J. & Choi, H. 2002 J. Fluid Mech. 450, 259–285. [11] Jimenez, J., Uhlman, M., Pinelli, A. & G., K. 2001 J. Fluid Mech. 442, 89–117. [12] Letzel, M. O., Krane, M. & Raasch, S. 2008 Atmos. Environ. 42, 8770–8784. [13] Py, C., de Langre, E. & Moulia, B. 2006 J. Fluid Mech. 568, 425–449. [14] Raupach, M. R., Finnigan, J. & Brunet, Y. 1996 Boundary-Layer Meteorol. 78, 351–382.

Rotor - Stator broadband noise prediction

In this paper a semi analytic model for rotor - stator broadband noise is presented. The work can be split into two sections. The first examines the distortion of the rotor wake in mean swirling flow, downstream of the fan. Previous work by Cooper and Peake4 is extended to include dissipative effects. In the second section we consider the interaction of this gust with the downstream stator row. We examine the way in which an unsteady pressure field is generated by the interaction of this wake flow with the stator blades and obtain estimates for the radiated noise. A new method is presented to extend the well known LINSUB code to the third dimension to capture the effect of the spanwise wavenumber and stator lean and sweep. Copyright © 2008 by Adrian Lloyd and Nigel Peake.