Oscillator-generated perturbations in viscous fluid flow at supercritical frequencies

Bogdanova, E. V.; Ryzhov, O. S.

doi:10.1007/bf00916717

Cited by 12 publications

(8 citation statements)

References 5 publications

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“…Using the triple-deck theory, [Ter84] justified the hypothesis of [BR82]. [AR90] revisited the problem of a vibrating ribbon in a boundary layer at finite Reynolds numbers and resolved the question concerning the contour in the inverse Fourier transform.…”

Section: Discussion Of the Resultsmentioning

confidence: 99%

“…However, the aforementioned results at finite Reynolds numbers suffered due to uncertainty in the path of integration in the inverse Fourier transform at supercritical frequencies of the forcing, and the hypothesis by [BR82] was adopted in order to include the unstable discrete mode into the downstream solution. Using the triple-deck theory, [Ter84] justified the hypothesis of [BR82].…”

Section: Discussion Of the Resultsmentioning

confidence: 99%

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Theoretical and Computational Studies of Stability, Transition and Flow Control in High-Speed Flows

Tumin¹

2011

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Public Reporting burden for this collection of information is estimated to average I hour per response. including the time for reviewing instructions, searching existing data sources. gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comment regarding this burden estimates or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services. Directorate for information Operations and Reports. 1215 AFOSR /t0P(f North Randolph Street AFRL-SR-AR-TR-08-0144Suite 325, Room 3112 Arlington, VA 2299 3-1768 I1. SUPPLEMENTARY NOTESThe views, opinions and/or findings contained in this report are those of the author(s) and should not be construed as an official Department of the Army position, policy or decision, unless so designated by other documentation. Approved for public release; distribution unlimited. ABSTRACT (Maximum 200 words)A comprehensive study of stability and receptivity of hypersonic boundary layers has been carried out. The main results of the project: 1. Mathematical method of the multimode decomposition for three-dimensional perturbations in compressible boundary layers has been developed. The method provides analysis of experimental and computational results for modes of discrete and continuous spectra. 2. Theory of boundary-layer receptivity was developed for roughness-induced perturbations in incompressible and compressible boundary layers. 3. The transient growth phenomenon in compressible boundary layers over flat plate, sphere, and sharp cone has been studied. The work was accompanied by development of solvers for these geometries. IntroductionThe potential of sustained hypersonic flight to revolutionize military and commercial activity is well recognized, and is reflected in recent initiatives such as the National Aerospace Initiative. High-speed vehicles will substantially impact military strategy by providing new defensive options such as a rapid on-demand global strike capability with much shorter response times than currently possible. Furthermore, the development of new technologies based on air-breathing propulsion can be leveraged to considerably reduce the cost of accessto-space, the benefits of which are both military as well as commercial. However, daunting technical challenges remain in realizing such vehicles. The harsh environment imposed by the envelope of such future missions is manifested in the severe anticipated thermo-mechanical loads and various propulsion-related requirements. Although the diversity of the physical phenomena encountered is broad, several key limiting issues have been identified as primary challenges, including both local and global constraints such as, for example, cowl lip loading and airframe balance. A scrutiny of the problems identified reveals the pervasive importance of several basic fluid dynamic phenomena. One of these, and possibly the least understood, is that of high-speed transition.The impact of hypersonic boundary lay...

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Section: Discussion Of the Resultsmentioning

confidence: 99%

Section: Discussion Of the Resultsmentioning

confidence: 99%

Theoretical and Computational Studies of Stability, Transition and Flow Control in High-Speed Flows

Tumin¹

2011

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“…The solution thus supplemented acquires the property of continuity at the intersection of the real axis by the pole. For the problem of instability wave generation considered in [3] the applicability of this principle was established in [4] by solving the inltial-boundary-value problem of the relaxation of the oscillations to a steady re,me. So far, for the problem in question there has been no such proof and this principle is considered to be a hypothesis.…”

Section: Wo (K V)=fwo(t V)"dt § Wo(v)e Wa'(p)=2r Wo(k V)mentioning

confidence: 99%

Generation of secondary instability modes in the interaction of a Tollmien-Schlichting wave with isolated roughness

Ustinov¹

1995

Fluid Dyn

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The infinite plane channel flow arising from the impingement of a plane instability wave of finite amplitude on isolated three-dimensional wall roughness is considered. The problem of the transformation of perturbations developing on the roughness in growing modes of secondary instability is solved. This problem describes the development of perturbations leading to the occurrence of a turbulent wedge. Simple relations describing the flow at large distances from the roughness are obtained. From these relations it follows that the angle at the vertex of the turbulent wedge is determined by the amplitude of the impinging wave, while the value of the perturbations generated is proportional to the roughness wlume.When the free-stream turbulence is fairly low, lzmlnar-turbulent transition starts with the onset and growth of a plane Tollmien-Schlichting wave. When the amplitude of this primary wave reaches a threshold value, secondary three-dimensional perturbations begin to develop rapidly against its background. Once the latter have reached a value comparable with the fundamental wave, the higher harmonics increase very rapidly and turbulent flow develops on a section several boundary-layer thicknesses long. On the basis of this perturbation development we can assume that the position of the transition coincides, with a high degree of accuracy, with the point at which the secondary perturbation amplitude becomes equal to the fundamental wave amplitude. In order to determine this point it is necessary to know the development law of the secondary perturbations and their initial amplitude. The development of the secondary perturbations is well descn'bed by the secondary instability theory [L2], whose conclusions agree with experiment. According to this theory, three-dlmensional perturbations, which are modes of a certain eigenvalue problem, are amplified against the two-dimensional fundamental wave background. There are two types of such modes. Unsteady subharmonic perturbations belong to the first type. Modes of the second type consist of a steady component and an unsteady part with period equal to that of the fundamental wave. The development of perturbations of the first and second types leads to the subharmonic and Klebanoff transitions, respectively. The type of modes amplified in a specific flow is determined by the initial conditions for the secondary perturbations. These initial conditions must be determined from the problem of the transformation of the external three-dimensional perturbations into secondary instability modes. Up till now this problem, similar to the susceptibility problem for the primary instability wave, has been considered only qualitatively [2].In the present paper the problem is solved for the perturbations resulting from the interaction of a primary instability wave with small isolated roughness on the streamlined surface. For the sake of simplicity, we will consider plane channel flow; however, the method of solution and the main results can also be applied to boundary layer flow.1. Consid...

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“…As distinct from the classical inverse Fourier transform, in transform (1.6) integration is carried out along a contour C which, in general, does not coincide with the real axis of the complex plane k. This situation is completely analogous to that encountered in investigating problems of the receptivity of steadystate Poiseuille flow to vibration of the channel walls: in that case, depending on the choice of integration contour, the inverse Fourier transform could describe both the generation of an instability wave by a vibrator [6,10] and the process of suppression of an incident wave by active wall vibration [11]. Thus, a suitable FLUID DYNAMICS Vol.…”

Section: Formulation Of the Receptivity Problem And The Calculation Mmentioning

confidence: 99%

Investigation of Mechanisms of Excitation and Growth of Unstable Perturbations in Pulsating Flows

Manuĭlovich¹

2005

Fluid Dyn

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General laws of the processes of generation and amplification of secondary perturbations in oscillating viscous fluid flows are studied theoretically. The stability and receptivity are analyzed with reference to perturbations generated by fluctuations of the flow rate of Poiseuille flow induced by small two-dimensional roughnesses of the channel walls. It is shown that the presence of roughness leads to excitation in the flow of perturbations at all multiples of the main flow oscillation frequency. Using the Fourier transform along the streamwise coordinate, the problem of calculating the frequency harmonics is reduced to a system of equations of the Orr-Sommerfeld type interrelated via the oscillatory component of the main flow. On the basis of an investigation of the analytic properties of the Fourier-image it is shown that upstream and downstream of the roughness the perturbation can be represented in the form of a superposition of modes of the time-dependent Poiseuille flow. The modes are classified and their spectrum is calculated. The structure of the mean-square fluctuations generated by free perturbations is investigated. Examples of calculating the evolution of forced perturbations are given for cases in which the scattering of the oscillations of the main flow on the roughness leads to the generation of one or two modes growing downstream.

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Oscillator-generated perturbations in viscous fluid flow at supercritical frequencies

Cited by 12 publications

References 5 publications

Theoretical and Computational Studies of Stability, Transition and Flow Control in High-Speed Flows

Theoretical and Computational Studies of Stability, Transition and Flow Control in High-Speed Flows

Generation of secondary instability modes in the interaction of a Tollmien-Schlichting wave with isolated roughness

Investigation of Mechanisms of Excitation and Growth of Unstable Perturbations in Pulsating Flows

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