It is known that turhulent mixing noise from high-speed jets consists of two components. They are the noise from large turbulent structures in the form of Mach wave radiation and the less directional fine-scale turbulence noise. The Mach wave radiation dominates in the downstream direction. The fine-scale turbulence noise dominates in the sideline and upstream directions. A semiempirical theory is developed for the prediction of the spectrum, intensity, and directivity of the fine-scale turhulence noise. The prediction method is self-contained. The turbulence information is supplied by the k-e turhulence model. The theory contains three empirical constants beyond those of the k-e model. These constants are determined by best fit of the calculated noise spectra to experimental measurements. Extensive comparisons between calculated and measured noise spectra over a wide range of directions of radiation,jet velocities, and temperatures have heen carried out. Excellent agreements are found. It is believed that the present theory offers significant improvements over current empirical or semiempirical jet noise prediction methods in use. There is no first principle jet noise theory at the present time.

Jet Mixing Noise from Fine-Scale Turbulence

Several methods for the prediction of jet noise are described. All but one of the noise prediction schemes are based on Lighthill's or Lilley's acoustic analogy, whereas the other is the jet noise generation model recently proposed by Tam and Auriault. In all of the approaches, some assumptions must be made concerning the statistical properties of the turbulent sources. In each case the characteristic scales of the turbulence are obtained from a solution of the Reynolds-averaged Navier-Stokes equation using a kappa-sigma turbulence model. It is shown that, for the same level of empiricism, Tam and Auriault's model yields better agreement with experimental noise measurements than the acoustic analogy. It is then shown that this result is not because of some fundamental flaw in the acoustic analogy approach, but instead is associated with the assumptions made in the approximation of the turbulent source statistics. If consistent assumptions are made, both the acoustic analogy and Tam and Auriault's model yield identical noise predictions. In conclusion, a proposal is presented for an acoustic analogy that provides a clearer identification of the equivalent source mechanisms, as is a discussion of noise prediction issues that remain to be resolved.

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Acoustic Analogy and Alternative Theories for Jet Noise Prediction

Broadband shock noise from supersonic jets is investigated through acoustic measurements in both the near and far fields. The peak Helmholtz number of broadband shock noise from unheated convergent nozzles is found to be independent of nozzle pressure ratio when based on the length of the shock cells and the ambient speed of sound. Excellent agreement between power spectral densities measured at various far-field angles is obtained at and above the peak shock noise frequency when source convection and directivity effects are included. The directivity of broadband shock noise is found to be pointed in the upstream direction, with omnidirectionality being approached only at high pressure ratios. For both convergent and convergent-divergent nozzles, the relative importance of shock noise with respect to jet-mixing noise is found to be maximum near the pressure ratio at which a Mach disk begins to form in the jet. Near-field measurements point to a limited portion of the shock cell system as the region of dominant broadband noise emission from a highly underexpanded convergent nozzle.

Broadband Shock Noise from Supersonic Jets

There is now a substantial body of theoretical and experimental evidence that the dominant part of the turbulent noise of supersonic jets is generated directly by the large turbulence structures/instability waves of the jet flow. Earlier, Tam and Burton provided a description of the physical mechanism by which supersonically traveling instability waves can generate sound efficiently. They used the method of matched asymptotic expansions to construct an instability wave solution which is valid in the far field. The present work is an extension of the theory of Tam and Burton. It is argued that the instability wave spectrum of the jet may be regarded as generated by stochastic white noise excitation at the nozzle lip region. The reason why the excitation has white noise characteristics is that near the nozzle lip region the flow in the jet mixing layer has no intrinsic length and time scales. The present stochastic wave model theory of supersonic jet noise contains a single unknown multiplicative constant. Comparisons between the calculated noise directivities at selected Strouhal numbers and experimental measurements of a Mach 2 jet at different jet temperatures have been carried out. Favorable agreements are found.

Turbulent Mixing Noise from Supersonic Jets

Subsonic jet noise from nonaxisymmetric and tabbed nozzles are investigated experimentally and theoretically. It is shown that the noise spectra of these jets are in good agreement with the similarity spectra found empirically earlier by Tam et al. through a detailed analysis of supersonic jet noise data (Tam, C. K. W., Golebiowski, M., and Seiner, J. M., On the Two Components of Turbulent Mixing Noise from Supersonic Jets, AIAA Paper 96-1716, 1996). Furthermore, the radiated noise fields of the jets under study, including elliptic and large-aspect-ratio rectangular jets, are found to be quite axisymmetric and are practically the same as that of a circular jet with the same exit area. These experimental results strongly suggest that nozzle geometry modification into elliptic or rectangular shapes is not an effective method for jet noise suppression. A lobed nozzle, on the other hand, is found to impact significantly the noise field. Noise from large-scale turbulent structures, radiating principally in the downstream direction, is effectively suppressed. Tabs also impact the noise field, primarily by shifting the spectral peak to a higher frequency. A jetlets model is developed to provide a basic understanding of the noise from tabbed jets. The model predicts that the noise spectrum from a jet with N tabs (N ≥ 2) can he obtained from that of the original jet (no tab) by a simple frequency shift. The shifted frequency is obtained by multiplying the original frequency by N 1/2 . This result is in fairly good agreement with experimental data.

Subsonic Jet Noise from Nonaxisymmetric and Tabbed Nozzles

: The characteristics, both spectral and directivity, of the sound field of supersonic shock-free jets are studied by measuring the turbulent mixing noise in the far field from four two-inch diameter nozzles, namely a convergent nozzle for pressure ratios up to critical and three convergent- divergent nozzles having nominal design Mach numbers of 1.4, 1.7, and 2.0, respectively. The measurements were conducted in a free-field environment. The results from 75 jet exit conditions are presented in a systematic manner in the form of tabulated one-third octave spectra. The test program was carefully planned in order to obtain results (i) at constant jet efflux temperature with varying jet velocity, and conversely (ii) at constant exit velocity while varying jet efflux temperature. The effects of jet velocity and exhaust temperature on turbulent mixing noise can therefore be assessed independently.

The Generation and Radiation of Supersonic Jet Noise. Volume 3. Turbulent Mixing Noise Data

: The characteristics of the sound field of shock-containing under- expanded jets are studied by measuring the noise from a two-inch diameter convergent nozzle over an extensive envelope of supercritical jet operating conditions. The measurements, which are accurate and comprehensive, were conducted in the Lockheed anechoic facility. The results are presented in this Volume in a systematic manner in the form of narrowband spectra. The details pertinent to the experimental program and the data presentation format are summarized below. The total noise spectrum from an incorrectly expanded jet flow contains discrete components (or screech) in addition to the basic turbulent mixing noise and the broadband shock-associated noise. In order to study the trends and dependencies of the broadband component accurately, it is vital to keep the contamination by screech to a minimum in the experimental program. In the present experiments, screech suppression was successfully achieved by wrapping all surfaces surrounding the nozzle exit with sound absorbing material, and incorporating a small projection inside the nozzle lip. This projection interrupts the feedback loop between the first shock and the nozzle exit plane, which has been previously proposed and verified as the physical mechanism of screech generation. The detailed calibration tests, conducted prior to the main shock-associated noise experiments, established that all results are essentially uncontaminated by the presence of screech.

Peter D. Dean

Papers

The Generation and Radiation of Supersonic Jet Noise. Volume 3. Turbulent Mixing Noise Data

The Generation and Radiation of Supersonic Jet Noise. Volume 4. Shock-Associated Noise Data