Directional acoustic radiation from a supersonic jet generated by shear layer instability
TL;DR: In this paper, a theory on the generation mechanism of directional acoustic radiation from a supersonic jet is proposed based on the concept of instability of the shear layer at the boundary of the jet close to the nozzle.
Abstract: A theory on the generation mechanism of directional acoustic radiation from a supersonic jet is proposed. The theory is based on the concept of instability of the shear layer at the boundary of the jet close to the nozzle. Theoretical prediction of the directional wave pattern is found to agree with shadowgraphic observation.
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TL;DR: In this article, a review of recent developments in the hydro- dynamic stability theory of spatially developing flows pertaining to absolute/convective and local/global instability concepts is presented.
Abstract: The goal of this survey is to review recent developments in the hydro dynamic stability theory of spatially developing flows pertaining to absolute/convective and local/global instability concepts. We wish to dem onstrate how these notions can be used effectively to obtain a qualitative and quantitative description of the spatio-temporal dynamics of open shear flows, such as mixing layers, jets, wakes, boundary layers, plane Poiseuille flow, etc. In this review, we only consider open flows where fluid particles do not remain within the physical domain of interest but are advected through downstream flow boundaries. Thus, for the most part, flows in "boxes" (Rayleigh-Benard convection in finite-size cells, Taylor-Couette flow between concentric rotating cylinders, etc.) are not discussed. Further more, the implications of local/global and absolute/convective instability concepts for geophysical flows are only alluded to briefly. In many of the flows of interest here, the mean-velocity profile is non-
1,988 citations
TL;DR: In this paper, it was shown that the spreading rate of a mixing layer can be greatly manipulated at very low forcing level if the mixing layer is perturbed near a subharmonic of the most-amplified frequency.
Abstract: In the present study, it is shown that the spreading rate of a mixing layer can be greatly manipulated at very low forcing level if the mixing layer is perturbed near a subharmonic of the most-amplified frequency. The subharmonic forcing technique is able to make several vortices merge simultaneously and hence increases the spreading rate dramatically. A new mechanism, ‘collective interaction’, was found which can bypass the sequential stages of vortex merging and make a large number of vortices (ten or more) coalesce.A deeper physical insight into the evolution of the coherent structures is revealed through the investigation of a forced mixing layer. The stability and the forcing function play important roles in determining the initial formation of the vortices. The subharmonic starts to amplify at the location where the phase speed of the subharmonic matches that of the fundamental. The position where vortices are seen to align vertically coincides with the position where the measured subharmonic reaches its peak. This location is defined as the merging location, and it can be determined from the feedback equation (Ho & Nosseir 1981).The spreading rate and the velocity profiles of the forced mixing layer are distinctly different from the unforced case. The data show that the initial condition has a longlasting effect on the development of the mixing layer.
808 citations
TL;DR: In this paper, a mathematical model of the cavity tones and pressure oscillation phenomenon based on the coupling between shear layer instabilities and acoustic feedback is developed to help in understanding the tone generation mechanism.
Abstract: Experimental measurements of the frequencies of discrete tones induced by flow over rectangular cavities were carried out over a range of low subsonic Mach numbers to provide a reliable data base for (aircraft wheel well) cavity noise consideration. A mathematical model of the cavity tones and pressure oscillation phenomenon based on the coupling between shear layer instabilities and acoustic feedback is developed to help in understanding the tone generation mechanism. Good agreement is found between discrete tone frequencies predicted by the model and experimental measurements over a wide range of Mach numbers. Evidence of tones generated by the cavity normal mode resonance mechanism at very low subsonic Mach numbers is also presented.
437 citations
TL;DR: In this paper, a solution describing the spatial evolution of small-amplitude instability waves and their associated sound field of axisymmetric supersonic jets is found using the method of matched asymptotic expansions (see Part 1, Tam & Burton 1984).
Abstract: A solution describing the spatial evolution of small-amplitude instability waves and their associated sound field of axisymmetric supersonic jets is found using the method of matched asymptotic expansions (see Part 1, Tam & Burton 1984). The inherent axisymmetry of the problem allows the instability waves to be decomposed into azimuthal wave modes. In addition, it is found that because of the cylindrical geometry of the problem the gauge functions of the inner expansion, unlike the case of two-dimensional mixing layers, are no longer just powers of e. Instead they contain logarithmic terms. To test the validity of the theory, numerical results of the solution are compared with the experimental measurements of Troutt (1978) and Troutt & McLaughlin (1982). Two series of comparisons at Strouhal numbers 0.2 and 0.4 for a Mach-number 2.1 cold supersonic jet are made. The data compared include hot-wire measurements of the axial distribution of root-mean-squared jet centreline mass-velocity fluctuations and radial and axial distributions of near-field pressure-level contours measured by microphones. The former is used to test the accuracy of the inner (or instability-wave) solution. The latter is used to verify the correctness of the outer solution. Very favourable overall agreements between the calculated results and the experimental measurements are found. These very favourable agreements strongly suggest that the method of solution developed in Part 1 paper is indeed valid. Furthermore, they also offer concrete support to the proposition made previously by a number of investigators that instability waves are important noise sources in supersonic jets.
364 citations
TL;DR: By using the triple-deck scaling of Stewartson (1969) and Messiter (1970) it was shown that small but relatively sudden surface geometry variations that produce only very weak static pressure variations can nevertheless produce strong coupling between an externally imposed acoustic disturbance and a spatially growing Tollmien-Schlichting wave as discussed by the authors.
Abstract: By using the triple-deck scaling of Stewartson (1969) and Messiter (1970) it is shown that small but relatively sudden surface geometry variations that produce only very weak static pressure variations can nevertheless produce strong, i.e. O(1), coupling between an externally imposed acoustic disturbance and a spatially growing Tollmien-Schlichting wave. The analysis provides a qualitative explanation of the Leehey and Shapiro (1979) boundary-layer receptivity measurements and is in good quantitative agreement with the Aizin and Poliakov (1979) experiment. It may also explain why small 'trip wires' can promote early transition.
334 citations
References
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TL;DR: In this article, the problem of distinguishing between amplifying and evanescent waves is investigated kinematically, without inquiring into the way these disturbances may be set up, and postponing inquiry into the boundary conditions necessary.
Abstract: This paper is concerned with the problem of distinguishing between amplifying and evanescent waves. These have, in the past, been distinguished by considerations of energy transfer or of the initial and boundary conditions with which a wave must be associated. Both procedures are open to criticism.The problem is here interpreted kinematically: we investigate the classes of wave functions which a given propagating system may support, without inquiring into the way these disturbances may be set up, and postponing inquiry into the boundary conditions necessary. In this way, we may distinguish between amplifying and evanescent waves by determining whether a wave function which may be analyzed into "real-frequency" waves may also be analyzed into "real-wave-number" waves. This question may be answered by means of a certain diagram, which may be constructed from knowledge of the dispersion relation.Interchange of the roles of time and space leads to the statement and solution of a further problem. If a propagating system is unstable, the instability may be such that a disturbance grows, but is propagated away from the point of origin: this is termed "convective instability." On the other hand, the instability may be such that the disturbance grows in amplitude and in extent, but always embraces the original point of origin: this is termed "nonconvective instability." The statement that the system supports amplifying waves is synonymous with the statement that the system exhibits convective instability. A system which exhibits nonconvective instability may not be used as an amplifier, but may be used as an oscillator. It is possible to distinguish between convective and nonconvective instability by a further diagram which also may be constructed from knowledge of the dispersion relation.Our theory enables us to make the following assertions. If $\ensuremath{\omega}$ is real for all real $k$, then any complex $k$, for real $\ensuremath{\omega}$, denotes an evanescent wave. Conversely, if $k$ is real for all real $\ensuremath{\omega}$, then any complex $\ensuremath{\omega}$, for real $k$, denotes nonconvective instability.The theory is illustrated by certain simple examples and by discussion of the result of weak coupling between certain types of waves.
264 citations
01 Jan 1958
TL;DR: In this article, the position of the first normal shock in the jet behind a highly underexpanded nozzle is calculated using axial pressure distribution on the centerline of the flow behind the orifice, calculated by the method of characteristics, and the shock is then assumed to exist at that point where atmospheric pressure would be attained behind the shock.
Abstract: A method for calculating the position of the first normal shock, or Mach disc, in the jet behind a highly underexpanded nozzle is presented. In the calculation for a sonic orifice, the axial pressure distribution on the centerline of the flow behind the orifice, calculated by the method of characteristics, is used to define a fictitious nozzle extension, and the shock is then assumed to exist at that point where atmospheric pressure would be attained behind the shock—i.e., the shock is assumed to exist at the end of the fictitious nozzle extension. Physical arguments are then employed to extend this calculation to nozzles with supersonic exit Mach Numbers. The results compare favorably with experimental data. An approximate method for computing the jet boundary up to the point of maximum jet area is given, and the results are compared both with photographs of actual jets and with jet boundaries calculated by the method of characteristics. Favorable agreement exists at relatively low nozzle pressure ratios.
250 citations
TL;DR: In this article, the position of the first normal shock in the jet behind a highly underexpanded nozzle is calculated using axial pressure distribution on the centerline of the flow behind the orifice, calculated by the method of characteristics, and the shock is then assumed to exist at that point where atmospheric pressure would be attained behind the shock.
Abstract: A method for calculating the position of the first normal shock, or Mach disc, in the jet behind a highly underexpanded nozzle is presented. In the calculation for a sonic orifice, the axial pressure distribution on the centerline of the flow behind the orifice, calculated by the method of characteristics, is used to define a fictitious nozzle extension, and the shock is then assumed to exist at that point where atmospheric pressure would be attained behind the shock—i.e., the shock is assumed to exist at the end of the fictitious nozzle extension. Physical arguments are then employed to extend this calculation to nozzles with supersonic exit Mach Numbers. The results compare favorably with experimental data. An approximate method for computing the jet boundary up to the point of maximum jet area is given, and the results are compared both with photographs of actual jets and with jet boundaries calculated by the method of characteristics. Favorable agreement exists at relatively low nozzle pressure ratios.
241 citations
TL;DR: In this paper, a formal solution to the initial value problem for a plane vortex sheet in an inviscid fluid is obtained by transform methods, and the eigenvalue problem is investigated and the stability criterion determined.
Abstract: A formal solution to the initial value problem for a plane vortex sheet in an inviscid fluid is obtained by transform methods. The eigenvalue problem is investigated and the stability criterion determined. This criterion is found to be in agreement with that obtained previously by Landau (1944), Hatanaka (1949), and Pai (1954), all of whom had included spurious eigenvalues in their analyses. It is also established that supersonic disturbances may be unstable; related investigations in hydrodynamic stability have conjectured on this possibility, but the vortex sheet appears to afford the first definite example. Finally, an asymptotic approximation is developed for the displacement of a vortex sheet following a suddenly imposed, spatially periodic velocity.
187 citations