Subharmonics and vortex merging in mixing layers
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.
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1,750 citations
TL;DR: The micromachining technology that emerged in the late 1980s can provide micron-sized sensors and actuators that can be integrated with signal conditioning and processing circuitry to form micro-electromechanical-systems (MEMS) that can perform real-time distributed control.
Abstract: The micromachining technology that emerged in the late 1980s can provide micron-sized sensors and actuators. These micro transducers are able to be integrated with signal conditioning and processing circuitry to form micro-electromechanical-systems (MEMS) that can perform real-time distributed control. This capability opens up a new territory for flow control research. On the other hand, surface effects dominate the fluid flowing through these miniature mechanical devices because of the large surface-to-volume ratio in micron-scale configurations. We need to reexamine the surface forces in the momentum equation. Owing to their smallness, gas flows experience large Knudsen numbers, and therefore boundary conditions need to be modified. Besides being an enabling technology, MEMS also provide many challenges for fundamental flow-science research.
1,287 citations
TL;DR: In this article, a review of the control of flow separation from solid surfaces by periodic excitation is presented, with an emphasis on experimentation relating to hydrodynamic excitation, although acoustic methods as well as traditional boundary layer control, such as steady blowing and suction are discussed in order to provide an appropriate historical context for recent developments.
1,008 citations
TL;DR: The absolute or convective character of inviscid instabilities in parallel shear flows can be determined by examining the branch-point singularities of the dispersion relation for complex frequencies and wavenumbers.
Abstract: The absolute or convective character of inviscid instabilities in parallel shear flows can be determined by examining the branch-point singularities of the dispersion relation for complex frequencies and wavenumbers. According to a criterion developed in the study of plasma instabilities, a flow is convectively unstable when the branch-point singularities are in the lower half complex-frequency plane. These concepts are applied to a family of free shear layers with varying velocity ratio their average velocity. It is demonstrated that spatially growing waves can only be observed if the mixing layer is convectively unstable, i.e. when the velocity ratio is smaller than Rt = 1.315. When the velocity ratio is larger than Rt, the instability develops temporally. Finally, the implications of these concepts are discussed also for wakes and hot jets.
803 citations
TL;DR: In this paper, the authors present a discussion of different methods which can be used to suppress combustion instabilities using active control, as well as a review of the work which has recently been performed in this area of combustion research.
789 citations
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TL;DR: In this article, Spark shadow pictures and measurements of density fluctuations suggest that turbulent mixing and entrainment is a process of entanglement on the scale of the large structures; some statistical properties of the latter are used to obtain an estimate of entrainedment rates, and large changes of the density ratio across the mixing layer were found to have a relatively small effect on the spreading angle.
Abstract: Plane turbulent mixing between two streams of different gases (especially nitrogen and helium) was studied in a novel apparatus Spark shadow pictures showed that, for all ratios of densities in the two streams, the mixing layer is dominated by large coherent structures High-speed movies showed that these convect at nearly constant speed, and increase their size and spacing discontinuously by amalgamation with neighbouring ones The pictures and measurements of density fluctuations suggest that turbulent mixing and entrainment is a process of entanglement on the scale of the large structures; some statistical properties of the latter are used to obtain an estimate of entrainment rates Large changes of the density ratio across the mixing layer were found to have a relatively small effect on the spreading angle; it is concluded that the strong effects, which are observed when one stream is supersonic, are due to compressibility effects, not density effects, as has been generally supposed
3,339 citations
TL;DR: In this paper, the authors show that a large-scale orderly pattern may exist in the noiseproducing region of a round subsonic jet by observing the evolution of orderly flow with advancing Reynolds number.
Abstract: Past evidence suggests that a large-scale orderly pattern may exist in the noiseproducing region of a jet. Using several methods to visualize the flow of round subsonic jets, we watched the evolution of orderly flow with advancing Reynolds number. As the Reynolds number increases from order 102 to 103, the instability of the jet evolves from a sinusoid to a helix, and finally to a train of axisymmetric waves. At a Reynolds number around 104, the boundary layer of the jet is thin, and two kinds of axisymmetric structure can be discerned: surface ripples on the jet column, thoroughly studied by previous workers, and a more tenuous train of large-scale vortex puffs. The surface ripples scale on the boundary-layer thickness and shorten as the Reynolds number increases toward 105. The structure of the puffs, by contrast, remains much the same: they form at an average Strouhal number of about 0·3 based on frequency, exit speed, and diameter.To isolate the large-scale pattern at Reynolds numbers around 105, we destroyed the surface ripples by tripping the boundary layer inside the nozzle. We imposed a periodic surging of controllable frequency and amplitude at the jet exit, and studied the response downstream by hot-wire anemometry and schlieren photography. The forcing generates a fundamental wave, whose phase velocity accords with the linear theory of temporally growing instabilities. The fundamental grows in amplitude downstream until non-linearity generates a harmonic. The harmonic retards the growth of the fundamental, and the two attain saturation intensities roughly independent of forcing amplitude. The saturation amplitude depends on the Strouhal number of the imposed surging and reaches a maximum at a Strouhal number of 0·30. A root-mean-square sinusoidal surging only 2% of the mean exit speed brings the preferred mode to saturation four diameters downstream from the nozzle, at which point the entrained volume flow has increased 32% over the unforced case. When forced at a Strouhal number of 0·60, the jet seems to act as a compound amplifier, forming a violent 0·30 subharmonic and suffering a large increase of spreading angle. We conclude with the conjecture that the preferred mode having a Strouhal number of 0·30 is in some sense the most dispersive wave on a jet column, the wave least capable of generating a harmonic, and therefore the wave most capable of reaching a large amplitude before saturating.
2,108 citations
TL;DR: A mixing layer is formed by bringing two streams of water, moving at different velocities, together in a lucite-walled channel as mentioned in this paper, where dye is injected between the two streams just before they are brought together, marking the vorticitycarrying fluid.
Abstract: A mixing layer is formed by bringing two streams of water, moving at different velocities, together in a lucite-walled channel. The Reynolds number, based on the velocity difference and the thickness of the shear layer, varies from about 45, where the shear layer originates, to about 850 at a distance of 50 cm. Dye is injected between the two streams just before they are brought together, marking the vorticity-carrying fluid. Unstable waves grow, and fluid is observed to roll up into discrete two-dimensional vortical structures. These turbulent vortices interact by rolling around each other, and a single vortical structure, with approximately twice the spacing of the former vortices, is formed. This pairing process is observed to occur repeatedly, controlling the growth of the mixing layer. A simple model of the mixing layer contains, as the important elements controlling growth, the degree of non-uniformity in the vortex train and the ‘lumpiness’ of the vorticity field.
1,335 citations
TL;DR: In this paper, the structure of the flat plate incompressible smooth-surface boundary layer in a low-speed water flow is examined using hydrogen-bubble measurements and also hot-wire measurements with dye visualization.
Abstract: The structure of the flat plate incompressible smooth-surface boundary layer in a low-speed water flow is examined using hydrogen-bubble measurements and also hot-wire measurements with dye visualization. Particular emphasis is placed on the details of the process of turbulence production near the wall. In the zone 0 < y+ < 100, the data show that essentially all turbulence production occurs during intermittent ‘bursting’ periods. ‘Bursts’ are described in some detail.The uncertainties in the bubble data are large, but they have the distinct advantage of providing velocity profiles as a function of time and the time sequences of events. These data show that the velocity profiles during bursting periods assume a shape which is qualitatively distinct from the well-known mean profiles. The observations are also used as the basis for a discussion of possible appropriate mathematical models for turbulence production.
1,004 citations
TL;DR: In this paper, the authors used the hyperbolic-tangent velocity profile of the disturbed shear layer to obtain better agreement with experimental results by means of the inviscid linearized stability theory of spatially growing disturbances.
Abstract: Experimental investigations of shear layer instability have shown that some obviously essential features of the instability properties cannot be described by the inviscid linearized stability theory of temporally growing disturbances. Therefore an attempt is made to obtain better agreement with experimental results by means of the inviscid linearized stability theory of spatially growing disturbances. Thus using the hyperbolic-tangent velocity profile the eigenvalues and eigenfunctions were computed numerically for complex wave-numbers and real frequencies. The results so obtained showed the tendency expected from the experiments. The physical properties of the disturbed flow are discussed by means of the computed vorticity distribution and the computed streaklines. It is found that the disturbed shear layer rolls up in a complicated manner. Furthermore, the validity of the linearized theory is estimated. The result is that the error due to the linearization of the disturbance equation should be larger for the vorticity distribution than for the velocity distribution, and larger for higher disturbance frequencies than for lower ones. Finally, it can be concluded from the comparison between the results of experiments and of both the spatial and temporal theory by Freymuth that the theory of spatially-growing disturbances describes the instability properties of a disturbed shear layer more precisely, at least for small frequencies.
837 citations