Prediction of Noise from High Speed Subsonic Jets Using an Acoustic Analogy

The literature contains various methods for solving the Lilley equation with different types of quadrupole and dipole sources to represent the mixing noise radiated into the far-field by isothermal and heated jets. These include two basic numerical solution methods, the 'direct' and the 'adjoint', and a number of asymptotic, analytic solutions. The direct and adjoint equations are reviewed and it is shown that their solutions are not only related through the adjoint property: the radial ODE for the adjoint displacement Green's function is the same as that governing the direct displacement Green's function because this particular Green's function obeys classical reciprocity with respect to its radial dependence. Further, by comparing the two numerical solution methods within the context of the parallel flow assumption of the Lilley equation, it is shown that the numerical effort for the two methods is equivalent. The numerical solutions are compared with analytic low frequency 'thin shear layer' solutions and WKB solutions, both outside and inside the cone of silence. It is concluded that the former should be used with caution at all angles, while the WKB has some limitations inside the cone of silence. Although numerical solutions can be obtained with little computational effort and are the preferred route for jet mixing noise predictions, the analytic solutions still offer important physical insights as well as verification of numeric results.

Section: Lilley-goldstein Equation Solution Results For Monopole Dipsupporting

confidence: 70%

Solving the Lilley Equation with Quadrupole and Dipole Sources

Tester

Morfey

2010

“…To add to this state of confusion, there have also been notions of "shear noise" and "self noise" source terms. Morris and Farassat (2002), and Raizada and Morris (2006) developed a version of the acoustic analogy based on the linearized Euler equations that permitted the easy identification and interpretation of the source terms in the continuity and the momentum equations. In this formulation, the mean flow properties do not appear in the equivalent sources; these sources have been described as "self noise".…”

Section: Classical Ideas Of Jet Noisementioning

confidence: 99%

Mechanisms of Jet Noise Generation: Classical Theories and Recent Developments

Viswanathan

2009

Lighthill's acoustic analogy and several variants of it have been used to interpret, analyze and explain measured data. In this paper, the validity of the main tenets of the classical theories is examined. This assessment is facilitated by a new comprehensive aeroacoustic database. The overall sound power level does not exactly follow the eighth power of velocity (V j /a), but has a weak dependence on jet temperature. It has been believed that an additional source of noise, with either sixth or fourth power variation with velocity, appears for heated jets; there is also a supposed change in spectral shape at 90°, even though effects associated with convection and flow/acoustic interaction are negligible at that angle. The new data indicate that the velocity exponent for overall power is close to eight even at a very high stagnation temperature ratio of 3.2. Moreover, the spectral shape is invariant with jet Mach number and jet temperature. A careful assessment of Tanna's database, which provided the rationale and justification for many of the theoretical models, reveals that this database is unreliable and exhibits incorrect spectral trends. A fundamental tenet of the classical theories, based on both the formalisms of Lighthill-Ffowcs Williams and Lilley, is the notion of moving sources. This idea immediately leads to a Doppler shift for frequency and a convective amplification factor for the noise radiated to the aft angles. It is demonstrated with the new database that there is no experimental evidence for these conjectured effects of moving sources. The jet temperature ratio (static or stagnation), in addition to jet velocity V j /a, is an independent controlling parameter. New scaling laws that are valid for all angles have been developed with the current database. There are no multiplicative factors with adjustable constants for the spectrum functions; the spectrum function and the velocity exponent depend on the jet temperature ratio and the radiation angle. This relation represents the main difference between the current and the classical formulations. A single exponent collapses the entire spectrum from jets with different V j /a, but at fixed jet temperature ratio. Therefore, there is no experimental evidence for the main classical ideas of jet noise, as consisting of multi

“…the set of equations in favor of ρ′ or p′. Alternatively, Euler equations may be expressed in terms of the logarithm of the pressure, and subsequently variables could be split into their mean and fluctuating components [16,17,18]. The acoustic analogy formulation in that context would produce second-order fluctuations in the momentum and energy equations that are explicitly dependent on the pressure variable, and rather different from sources presented here.…”

Section: Acoustic Analogiesmentioning

confidence: 97%

“…Therefore the actual jet density does not have a place in the source. Similarly, Lighthill's equation [2] for density fluctuations in a quiescent medium (U = 0, , and p -= p ∞ ) is written after eliminating ∂ 2 m j /∂t∂x j between continuity and momentum eqns (6a) and (13) (18) Again ρ should be set equal to the ambient density ρ ∞ . Note that unlike the conventional acoustic analogy, the base-flow is set equal to zero (i.e., v i = v′ i ), and the sources on the right hand side of eqn (18) consist of the fluctuating terms only.…”

Section: Special Cases Of the Acoustic Equationmentioning

confidence: 99%

Hot Jets and Sources of Jet Noise

Khavaran

Kenzakowski

Mielke-Fagan

2010

A prediction method based on the generalized acoustic analogy is presented and used to evaluate aerodynamic noise radiated from high-speed hot jets. The set of Euler equations are divided into two sets of equations that govern what may be considered as a non-radiating base flow plus its residual components. Under certain conditions, the residual equations are rearranged to form a wave equation. This equation consists of a third-order wave operator, plus a number of non-linear terms that are regarded as the equivalent sources of sound and their statistical characteristics are modeled. A specialized RANS solver provides the base flow as well as the variance in both velocity and thermal fluctuations that determine the source strength. The main objective here is to evaluate the relative contribution from various source components to the far-field spectra and to show the significance of temperature fluctuations as a potential source of aerodynamic noise in hot jets.