17 results
An experimental investigation of resonant interaction of a rectangular jet with a flat plate
- K. B. M. Q. Zaman, A. F. Fagan, J. E. Bridges, C. A. Brown
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- Journal:
- Journal of Fluid Mechanics / Volume 779 / 25 September 2015
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- 21 August 2015, pp. 751-775
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The interaction between an 8:1 aspect ratio rectangular jet and a flat plate, placed parallel to the jet, is addressed in this study. At high subsonic conditions and for certain relative locations of the plate, a resonance takes place with accompanying audible tones. Even when the tone is not audible the sound pressure level spectra are often marked by conspicuous peaks. The frequencies of these peaks, as functions of the plate’s length, its location relative to the jet as well as jet Mach number, are studied in an effort to understand the flow mechanism. It is demonstrated that the tones are not due to a simple feedback between the nozzle exit and the plate’s trailing edge; the leading edge also comes into play in determining the frequency. With parametric variation, it is found that there is an order in the most energetic spectral peaks; their frequencies cluster in distinct bands. The lowest frequency band is explained by an acoustic feedback involving diffraction at the plate’s leading edge. Under the resonant condition, a periodic flapping motion of the jet column is seen when viewed in a direction parallel to the plate. Phase-averaged Mach number data on a cross-stream plane near the plate’s trailing edge illustrate that the jet cross-section goes through large contortions within the period of the tone. Farther downstream a clear ‘axis switching’ takes place for the time-averaged cross-section of the jet that does not occur otherwise for a non-resonant condition.
Experimental investigation of the flow field of an oscillating airfoil and estimation of lift from wake surveys
- J. Panda, K. B. M. Q. Zaman
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- Journal:
- Journal of Fluid Mechanics / Volume 265 / 25 April 1994
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- 26 April 2006, pp. 65-95
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The flow field of an airfoil oscillated periodically over a reduced frequency range, 0 ≤ k ≤ 1.6, is studied experimentally at chord Reynolds numbers of Rc = 22000 and 44000. For most of the data, the NACA0012 airfoil is pitched sinusoidally about one quarter chord between angles of attack α of 5° and 25°. The cyclic variation of the near wake flow field is documented through flow visualization and phase-averaged vorticity measurements. In addition to the familiar dynamic stall vortex (DSV), an intense vortex of opposite sign is observed to originate from the trailing edge just when the DSV is shed. The two together take the shape of the cross-section of a large ‘mushroom’ while being convected away from the airfoil. The phase delay in the shedding of the DSV with increasing k, as observed by previous researchers, is documented for the full range of k. It is observed that the sum of the absolute values of all vorticity convected into the wake over a cycle is nearly constant and is independent of the reduced frequency and amplitude of oscillation but dependent on the mean α. The time varying component of the lift is estimated in a novel way from the shed vorticity flux. The analytical foundation of the method and the various approximations are discussed. The estimated lift hysteresis loops are found to be in reasonable agreement with available data from the literature as well as with limited force balance measurements. Comparison of the lift hysteresis loops with the corresponding vorticity fields clearly shows that major features of the lift variation are directly linked to the evolution of the large-scale vortical structures and the phase delay phenomenon.
A natural low-frequency oscillation of the flow over an airfoil near stalling conditions
- K. B. M. Q. Zaman, D. J. Mckinzie, C. L. Rumsey
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- Journal:
- Journal of Fluid Mechanics / Volume 202 / May 1989
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- 26 April 2006, pp. 403-442
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An unusually low-frequency oscillation in the flow over an airfoil is studied experimentally as well as computationally. Wind-tunnel measurements are carried out with two-dimensional airfoil models in the chord Reynolds number (Rc) range of 0.15 × 105−3.0 × 105. During deep stall, at α [gsim ] 18°, the usual ‘bluff-body shedding’ occurs at a Strouhal number, Sts ≈ 0.2. But at the onset of static stall around α = 15°, a low-frequency periodic oscillation is observed, the corresponding Sts being an order of magnitude lower. The phenomenon apparently takes place only with a transitional state of the separating boundary layer. Thus, on the one hand, it is not readily observed with a smooth airfoil in a clean wind tunnel, while on the other, it is easily removed by appropriate ‘acoustic tripping’. Details of the flow field for a typical case are compared with a case of bluff-body shedding. The flow field is different in many ways from the latter case and does not involve a Kármán Vortex street. The origin of the flow fluctuations traces to the upper surface of the airfoil and is associated with a periodic switching between stalled and unstalled states. The mechanism of the frequency selection remains unresolved, but any connection to blower instabilities, acoustic standing waves or structural resonances has been ruled out.
A similar result has been encountered computationally using a two-dimensional Navier–Stokes code. While with the assumption of laminar flow, wake oscillation akin to the bluff-body shedding has been observed previously, the Sts is found to drop to about 0.03 when a ‘turbulent’ boundary layer is assumed. Details of the flow field and unsteady forces, computed for the same conditions as in the experiment, compare reasonably well with the experimental data.
The phenomenon produces intense flow fluctuations imparting much larger unsteady forces to the airfoil than that experienced in bluff-body shedding, and may represent the primary aerodynamics of stall flutter of blades and wings.
Axis switching and spreading of an asymmetric jet: the role of coherent structure dynamics
- K. B. M. Q. Zaman
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- Journal of Fluid Mechanics / Volume 316 / 10 June 1996
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- 26 April 2006, pp. 1-27
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The effects of vortex generators and periodic excitation on vorticity dynamics and the phenomenon of axis switching in a free asymmetric jet are studied experimentally. Most of the data reported are for a 3:1 rectangular jet at a Reynolds number of 450 000 and a Mach number of 0.31. The vortex generators are in the form of ‘delta tabs’, triangular-shaped protrusions into the flow, placed at the nozzle exit. With suitable placement of the tabs, axis switching could be either stopped or augmented. Two mechanisms are identified governing the phenomenon. One, as described by previous researchers, is due to the difference in induced velocities for different segments of a rolled-up azimuthal vortical structure. The other is due to the induced velocities of streamwise vortex pairs in the flow. While the former mechanism, referred to here as the ωθ-dynamics, is responsible for a rapid axis switching in periodically forced jets, e.g. screeching supersonic jets, the effect of the tabs is governed mainly by the latter mechanism, referred to as the ωx-dynamics. Both dynamics can be active in a natural asymmetric jet; the tendency for axis switching caused by the ωθ-dynamics may be, depending on the streamwise vorticity distribution, either resisted or enhanced by the ωx-dynamics. While this simple framework qualitatively explains the various observations made on axis switching, mechanisms actually in play may be much more complex. The two dynamics are not independent as the flow field is replete with both azimuthal and streamwise vortical structures which continually interact. Phase-averaged measurements for a periodically forced case, over a volume of the flow field, are carried out in an effort to gain insight into the dynamics of these vortical structures. The results are used to examine such processes as the reorientation of the azimuthal vortices, the resultant evolution of streamwise vortex pairs, as well as the redistribution of streamwise vortices originating from secondary flow within the nozzle.
Effect of acoustic excitation on the flow over a low-Re airfoil
- K. B. M. Q. Zaman, A. Bar-Sever, S. M. Mangalam
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- Journal:
- Journal of Fluid Mechanics / Volume 182 / September 1987
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- 21 April 2006, pp. 127-148
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Wind-tunnel measurements of lift, drag and wake velocity spectra were carried out under (tonal) acoustic excitation for a smooth airfoil in the chord-Reynolds-number (Rec) range of 4 × 104−1.4 × 105. The data are supported by smoke-wire flowvisualization pictures. Small-amplitude excitation in a wide, low-frequency range is found to eliminate laminar separation that otherwise degrades the airfoil performance at low Rec near the design angle of attack. Excitation at high frequencies, scaling as $U_{\infty}^{\frac{3}{2}}$, eliminates a pre-stall, periodic shedding of large-scale vortices; U∞ is the free-stream velocity. Significant improvement in lift is also achieved during post-stall, but with large-amplitude excitation. Wind-tunnel resonances strongly influence the results, especially in cases requiring large amplitudes. It is shown that large transverse velocity fluctuations, induced near the airfoil by specific cross-resonance modes, lead to the most effective separation control; resonances inducing only large-amplitude pressure fluctuations are demonstrated to be less effective.
Turbulence suppression in free shear flows by controlled excitation
- K. B. M. Q. Zaman, A. K. M. F. Hussain
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- Journal:
- Journal of Fluid Mechanics / Volume 103 / February 1981
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- 20 April 2006, pp. 133-159
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In an attempt to explain the mechanics of turbulence suppression previously observed by us in jets under controlled excitation, the near fields of four circular jets, a plane jet and a plane mixing layer, all with laminar efflux boundary layers, have been explored through hot-wire measurements. It is shown that controlled excitation, induced acoustically as well as by vibrating ribbons, can reduce turbulence intensities in all these flows. Reduction by as much as 80% is observed, the maximum decrease occurring at about 400θe downstream from the exit; θe is the initial shear-layer momentum thickness. The suppression effect is a maximum for excitation at the Strouhal number Stθ(≡ fθe/Ue) of about 0.017. In the jets, the turbulence suppression is observed over the range 0·75 ≤ x/D ≤ 8, while for the plane mixing layer it could be detected as far downstream as x ≅ 6000θe.
The flow-fields with and without excitation for a typical case of turbulence suppression have been studied in detail. Spectra of the u signal and time-averaged field data indicate that excitation at Stθ ≅ 0·017 suppresses the formation of naturally occurring energetic vortices - an observation confirmed by flow-visualization experiments and by study of the large-scale coherent structures of the shear layer, educed through conditional-sampling measurements. Excitation at Stθ ≅ 0·017 produces a rapid growth of the shear layer instability mode, and consequently, its saturation, roll-up and breakdown occurs much earlier in x than is found to occur naturally (at Stθ ≅; 0·012). The suppression effect is apparently a consequence of earlier transition of the shear layer vortices, which otherwise naturally grow to larger sizes and survive for larger x, as well as being due to the prevention of successive pairing of these structures.
The ‘preferred mode’ of the axisymmetric jet
- A. K. M. F. Hussain, K. B. M. Q. Zaman
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- Journal:
- Journal of Fluid Mechanics / Volume 110 / September 1981
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- 20 April 2006, pp. 39-71
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The ‘preferred mode’ of an incompressible axisymmetric free jet has been organized through controlled perturbation, and spatial distributions of time-average as well as phase-average flow properties in the near field are documented. The excitation produces noticeable changes in the time-average measures of the jet, although these changes are less dramatic than those for the excitation producing stable vortex pairing. For different stages in the evolution of the preferred-mode coherent structure, the phase-average vorticity, coherent Reynolds stress, and incoherent turbulence intensities and Reynolds stress have been educed through phase-locked hot-wire measurements, over the spatial extent of the structure and without invoking the Taylor hypothesis. For a particular stage of the evolution (i.e. when the structure is centred at x/D ≃ 3) the distributions of these quantities have been compared for both initially laminar and fully turbulent exit boundary layers, and for four jet Reynolds numbers. The relative merits of the coherent structure streamline and pseudo-stream-function patterns, as compared with phase-average velocity contours, for structure boundary identification have been discussed. The structure shape and size agree closely with those inferred from the average streamline pattern of the natural structure educed by Yule (1978).
These data as well as τ-spectra show that even excitation at the preferred mode cannot sustain the initially organized large-scale coherent structure beyond eight diameters from the jet exit. The background turbulence is organized by the coherent motions in such a way that the maximum rate of decrease of the coherent vorticity occurs at the structure centres which are the saddle points of the background-turbulence Reynolds-stress distributions. The structure centres are also the locations of peak phase-average turbulence intensities. The evolving shape of the structure as it travels downstream helps explain the transverse variations of the wavelength and convection velocity across the mixing layer. The coherent structure characteristics are found to be independent of whether the initial boundary layer is laminar or turbulent, but depend somewhat on the jet Reynolds number. With increasing Reynolds number, the structure decreases in the streamwise length and increases in the radial width and becomes relatively more energetic, and more efficient in the production of coherent Reynolds stress.
Taylor hypothesis and large-scale coherent structures
- K. B. M. Q. Zaman, A. K. M. F. Hussain
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- Journal:
- Journal of Fluid Mechanics / Volume 112 / November 1981
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- 20 April 2006, pp. 379-396
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The applicability of the Taylor hypothesis to large-scale coherent structures in turbulent shear flows has been evaluated by comparing the actual spatial distributions of the structure properties with those deduced through the use of the hypothesis. This study has been carried out in the near field of a 7[sdot ]62 cm circular air jet at a jet Reynolds number of 3[sdot ]2 x 104, where the coherent structures and their interactions have been organized through controlled excitation. Actual distributions of the structure properties have been obtained through phase-average hot-wire data, the measurements having been repeated at different spatial points over the extents of the structure crosssections at a fixed phase. The corresponding ‘spatial’ distributions of these properties obtained (by using the Taylor hypothesis) from the temporal data at appropriate phases and locations, show that the hypothesis works quite well for an isolated coherent structure if a constant convection velocity, equal to the structure centre velocity, is used in the hypothesis everywhere across the shear flow. The popular use of the local time-average or even the instantaneous streamwise velocity produces unacceptably large distortions. When structure interactions like pairing are involved, no convection velocity can be found with which the hypothesis works. Distributions of the terms in the Navier–Stokes equation contributing to the phase-average vorticity, but neglected by the hypothesis, have been quantitatively determined. These show that the terms associated with the background turbulence field, but not those associated with the coherent motion field, can be neglected. In particular, the pressure term due to the coherent motion field is large and cannot be neglected.
An experimental study of organized motions in the turbulent plane mixing layer
- A. K. M. F. Hussain, K. B. M. Q. Zaman
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- Journal:
- Journal of Fluid Mechanics / Volume 159 / October 1985
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- 20 April 2006, pp. 85-104
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Large-scale coherent structures in a large, single-stream plane mixing layer of air have been investigated experimentally. The unforced, initially fully turbulent mixing layer rolls up into organized structures whose average passage frequency fm at any downstream distance x from the lip depends on x. These structures are detected for the entire length of the measurement, i.e. up to x = 3 m or 5000θe. The Strouhal number Stθ (= fm θ/Ue) is observed to be a constant (≈ 0.024) at all x. θe and θ are, respectively, the exit and local momentum thicknesses of the mixing layer, and Ue is the free-stream velocity. (The entrainment velocity on the zero-speed side is found to be 0.032 Ue.) The coherent-structure properties are educed in the developing and self-preserving regions of the mixing layer using an optimized conditional-sampling method, triggered on the peaks of a local reference ũ-signal obtained from the high-speed edge of the layer. Sectional-plane contours of the properties of the structure such as coherent vorticity, Reynolds stress and production reveal that the structure formation and evolution are complete by x ≅ 500θe, beyond which the structure achieves an ‘equilibrium’ state as defined by the structure properties.
Natural large-scale structures in the axisymmetric mixing layer
- K. B. M. Q. Zaman, A. K. M. F. Hussain
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- Journal:
- Journal of Fluid Mechanics / Volume 138 / January 1984
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- 20 April 2006, pp. 325-351
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This paper summarizes results of our investigations on: optimization of conditional sampling technique for eduction of naturally occurring large-scale structures in an axisymmetric mixing layer, comparison of the natural structure with that induced via controlled excitation, and the sensitivity of the educed structure to the excitation amplitude and of the natural coherent structure to Reynolds number and initial condition. Measurements include sectional-plane contours of various structure properties; however, coherent vorticity is the principal measure used in these considerations. All plausible alternative triggering criteria, based on reference velocity signals from fixed probes, were considered in order to arrive at the best practical eduction technique. It is shown that the simple criterion of triggering on the positive peaks of the longitudinal velocity signal derived from the high-speed edge of the mixing layer results in the optimum eduction. The characteristics of the natural structures, educed by the optimum detection criterion, are found to be independent of ReD over the measurement range 5.5 × 104−8 × 105. A mild dependence on the initial condition (viz laminar vs. turbulent) is observed, the structures being more disorganized for the initially laminar boundary-layer case. The educed natural structures agree well with those induced by controlled sinusoidal excitation at low excitation levels; higher levels, however, produce considerably stronger structures.
Far-field noise of a subsonic jet under controlled excitation
- K. B. M. Q. Zaman
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- Journal:
- Journal of Fluid Mechanics / Volume 152 / March 1985
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- 20 April 2006, pp. 83-111
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The phenomena of excitation-induced suppression and amplification of broadband jet noise have been experimentally investigated in an effort to understand the mechanisms, especially in relation to the near flow-field large-scale structure dynamics. Suppression is found to occur only in jets at low speeds with laminar exit boundary layers, the optimum occurring for excitation at Stθ ≈ 0.017, where Stθ is the Strouhal number based on the initial shear-layer momentum thickness. The suppression mechanism is linked to an initial-condition effect on the large-scale structure dynamics. The interaction and evolution of laminar-like structures at low jet speeds produce more (normalized) noise and turbulence, compared to asymptotically lower levels at high speeds when the initial shear layer is no longer laminar. The effect of initial condition has been demonstrated by tripped versus untripped jet data. The excitation at Stθ ≈ 0.017 results in a quick roll-up and transition of the laminar shear-layer vortices, yielding coherent structures which are similar to those at high speeds. Thus, the broadband noise and turbulence are suppressed, but at the most to the asymptotically lower levels. When at the asymptotic level, the broadband jet noise can only be amplified by the excitation; the amplification is found to be maximum for excitation in the StD range of 0.65–0.85, StD being the Strouhal number based on the jet diameter. Excitation in this StD range also produces strongest vortexpairing activity. From spectral analysis of the flow-field and the near sound-pressure field, it is inferred that the pairing process induced by the excitation is at the origin of the broadband noise amplification.
Vortex pairing in a circular jet under controlled excitation. Part 2. Coherent structure dynamics
- A. K. M. F. Hussain, K. B. M. Q. Zaman
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- Journal:
- Journal of Fluid Mechanics / Volume 101 / Issue 3 / 11 December 1980
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- 19 April 2006, pp. 493-544
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The coherent structure dynamics in the near field of a circular jet has been experimentally explored by inducing ‘stable’ vortex pairing through controlled excitation (see Zaman & Hussain 1980) and applying phase-averaging techniques. Hot-wire measurements were made in a 7·62 cm air jet with laminar exit boundary layer at the Reynolds number ReD = 3·2 × 104, excited at the Strouhal number StD = 0·85. At a particular phase during the pairing process, spatial distributions of the phase-average longitudinal and lateral velocity perturbations (〈u)〉, 〈v〉), vorticity, streamlines, the coherent and background Reynolds stresses and turbulence intensities have been educed. These data have been obtained for four different locations occupied by the vortices at the same phase (preceding, during, and following the pairing event), in the region 0 < x/D < 5. Spatial distributions of these measures at four successive phases during the pairing process are also educed in an attempt to further understand the vortex-pairing dynamics. The flow physics is discussed on the basis of measurements over the physical extent of the vortical structures, phase-locked to specific phases of the pairing event and thus do not involve use of the Taylor hypothesis.
The computed pseudostream functions at particular phases are compared with the corresponding streamlines drawn by the method of isoclines. Transition of the vortices is examined on the basis of vorticity diffusion, the superimposed random fluctuation field intensities and Reynolds stress and phase-locked circumferential correlation measurements. The peak vorticity drops rapidly owing to transition and interaction of the vortices during pairing but, farther downstream, the decay can be attributed to destruction of the coherent vorticity by the background turbulence Reynolds stress, especially at the locations of the latter's ‘saddle points’. Controlled excitation enhances the initial circumferential coherence of the vortical structures, but is ineffective in delaying turbulent breakdown near the end of the potential core; the breakdown appears to occur through evolution of the circumferential lobe structures. The coherent structure Reynolds stress is found to be much larger than the background turbulence Reynolds stress for 0 < x/D [lsim ] 3, but these two are comparable near the end of the jet potential core. The zone average of the coherent structure Reynolds stress over the cross-section of the merging vortex pair is much larger than that over a single vortical structure either before or after the completion of pairing. During the pairing process, such average correlations are found to be the largest at an early phase of the process while entrainment, turbulent breakdown as well as rapid diffusion of vorticity occur at a later phase. The regions of alternate positive and negative coherent Reynolds stresses associated with the structures and their interactions help explain ‘negative production’.
Vortex pairing in a circular jet under controlled excitation. Part 1. General jet response
- K. B. M. Q. Zaman, A. K. M. F. Hussain
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- Journal:
- Journal of Fluid Mechanics / Volume 101 / Issue 3 / 11 December 1980
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- 19 April 2006, pp. 449-491
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Hot-wire and flow-visualization studies have been carried out in three air jets subjected to pure-tone acoustic excitation, and the instability, vortex roll-up and transition as well as jet response to the controlled excitation have been investigated. The centreline fluctuation intensity can be enhanced by inducing stable vortex pairing to a level much higher than even that at the ‘preferred mode’, but can also be suppressed below the unexcited level under certain conditions of excitation. The conditions most favourable to vortex pairing were determined as a function of the excitation Strouhal number, the Reynolds number (ReD), and the initial shear-layer state, i.e. laminar or turbulent. It is shown that the rolled-up vortex rings undergo pairing under two distinct conditions of excitation: ‘the shear layer mode’ when the Strouhal number based on the initial shear-layer momentum thickness (Stθ) is about 0·012, and ‘the jet column mode’ when the Strouhal number based on the jet diameter (StD) is about 0·85. The former involves pairing of the near-exit thin vortex rings when the initial boundary layer is laminar, irrespective of the value of StD. The latter involves pairing of the thick vortex rings at x/D ≅ 1·75, irrespective of Stθ or whether the initial boundary layer is laminar or turbulent. For laminar exit boundary layer, pairing is found to be stable, i.e., occurring regularly in space and time, for ReD < 5 × 104, but becomes intermittent with increasing ReD or fluctuation intensity in the initial boundary layer.
The trajectories of the vortex centres and their convection velocities during a pairing event have been recorded through phase-locked measurements. In the presence of stable vortex pairing, the time average profiles of fluctuation intensities and Reynolds stress show noticeable deviations from those in the unexcited jet. The vortex pairing phenomenon produce considerably larger excursions of the $\widetilde{uv}(t)$ signal than the time-average Reynolds stress reveals, suggesting that only certain phases of the pairing process may be important in entrainment, and production of Reynolds stress and jet noise.
The free shear layer tone phenomenon and probe interference
- A. K. M. F. Hussain, K. B. M. Q. Zaman
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- Journal:
- Journal of Fluid Mechanics / Volume 87 / Issue 2 / 26 July 1978
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- 12 April 2006, pp. 349-383
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Free shear layer stability measurements with a hot wire revealed that the probe itself can trigger and sustain upstream instability modes like the slit jet-wedge edge tones. The flow fields associated with the free shear layer tones induced in axisym-metric and plane air shear layers by a hot-wire probe and by a plane wedge were then explored experimentally, and found to be different in many ways from the widely investigated jet edge tone phenomenon.
As many as four frequency stages have been identified, there being a fifth stage associated with the subharmonic attributed to vortex pairing in the free shear layer. No evidence of hysteresis could be found in the shear layer tone. In the interstage jump (i.e. bimodal) regions, the tone occurred in only one mode at a time while intermittently switching from one to the other. Frequency variations in each stage are shown to collapse on a single curve when non-dimensionalized with the initial momentum thickness θe or with the lip-wedge distance h, and plotted as a function of h/θe.
Phase average measurements locked onto the tone fundamental show that the phase velocity and wavelength of the tone-induced velocity fluctuation are essentially independent of the stage of tone generation; in each stage, both phase velocity and wavelength decrease with increasing frequency but undergo jumps at starts of new stages. The measured amplitude and phase profiles, as well as the variations of the shear tone wavenumber and phase velocity with the Strouhal number, show reasonable agreement with the predictions of the spatial stability theory. The wavelength λ bears a unique relation to h, this h, δ relation being different from the Brown-Curle equation for the jet edge tone.
Shear layer tones would be typically induced in near-field shear layer measurements involving invasive probes, and can produce misleading results. A method for determining the true free shear layer natural instability frequency is recommended.
Investigation of a ‘transonic resonance’ with convergent–divergent nozzles
- K. B. M. Q. ZAMAN, M. D. DAHL, T. J. BENCIC, C. Y. LOH
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- Journal of Fluid Mechanics / Volume 463 / 25 July 2002
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- 31 July 2002, pp. 313-343
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Experimental studies have shown that convergent–divergent nozzles, when run at low pressure ratios, often undergo a flow resonance accompanied by emission of acoustic tones. The phenomenon, different in characteristics from conventional ‘screech’ tones, is addressed in this paper. Unlike screech, the resonant frequency (fN) increases with increasing supply pressure. There is a ‘staging’ behaviour; odd-harmonic stages resonate at lower pressures while the fundamental occurs in a wide range of higher pressures corresponding to a ‘fully expanded Mach number’ (Mj) around unity. Within a stage, fN varies approximately linearly with Mj; the slope of the variation steepens when the angle of divergence of the nozzle is decreased. Based on the data, correlation equations are provided for the prediction of fN. A companion computational study captures the phenomenon and predicts the frequencies, including the stage jump, quite well. While the underlying mechanisms are not completely understood yet, it is clear that the unsteadiness of a shock occurring within the divergent section plays a direct role. The shock drives the flow downstream like a vibrating diaphragm, and resonance takes place similarly to the (no-flow) acoustic resonance of a conical section having one end closed and the other end open. Thus, the fundamental is accompanied by a standing one-quarter wave within the divergent section, the next stage by a standing three-quarter wave, and so on. The distance from the foot of the shock to the nozzle exit imposes the pertinent length scale. The principal trends in the frequency variation are explained qualitatively from the characteristic variation of that length scale. A striking feature is that tripping of the nozzle's internal boundary layer tends to suppress the resonance. It is likely that the trip effect occurs due to a break in the azimuthal coherence of the unsteady flow.
Spreading characteristics of compressible jets from nozzles of various geometries
- K. B. M. Q. ZAMAN
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- Journal:
- Journal of Fluid Mechanics / Volume 383 / 25 March 1999
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- 25 March 1999, pp. 197-228
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The spreading characteristics of jets from several asymmetric nozzles, and a set of rectangular orifices are compared, covering a jet Mach number range of 0.3–2.0. The effect of ‘tabs’ for a rectangular and a round nozzle is also included in the comparison. Compared to a round jet, the jets from the asymmetric nozzles spread only slightly more at subsonic conditions whereas at supersonic conditions, when ‘screech’ occurs, they spread much more. The dynamics of the azimuthal vortical structures of the jet, organized and intensified under the screeching condition, are thought to be responsible for the observed effect at supersonic conditions. Curiously, the jet from a ‘lobed’ nozzle spreads much less at supersonic condition compared to all other cases; this is due to the absence of screech with this nozzle. Screech stages inducing flapping, rather than varicose or helical, flow oscillation cause a more pronounced jet spreading. At subsonic conditions, only a slight increase in jet spreading with the asymmetric nozzles contrasts previous observations by others. The present results show that the spreading of most asymmetric jets is not much different from that of a round jet. This inference is further supported by data from the rectangular orifices. In fact, jets from the orifices with small aspect ratio (AR) exhibit virtually no increase in the spreading. A noticeable increase commences only when AR is larger than about 10. Thus, ‘shear layer perimeter stretching’, achieved with a larger AR for a given cross-sectional area of the orifice, by itself, proves to be a relatively inefficient mechanism for increasing jet spreading. In contrast, the presence of streamwise vortices or ‘natural excitation’ can cause a significant increase – effects that might explain the observations in the previous investigations. Thus far, the biggest increase in jet spreading is observed with the tabs. This is true in the subsonic regime, as well as in the supersonic regime, in spite of the fact that screech is eliminated by the tabs. The characteristic spreading of the tabbed jets is explained by the induced motion of the tab-generated streamwise vortex pairs. The tabs, however, incur thrust loss; the flow blockage and loss in thrust coefficient, vis-à-vis the spreading increase, are evaluated for various configurations.
Large- and small-scale vortical motions in a shear layer perturbed by tabs
- JUDITH K. FOSS, K. B. M. Q. ZAMAN
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- Journal:
- Journal of Fluid Mechanics / Volume 382 / 10 March 1999
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- 10 March 1999, pp. 307-329
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The large- and small-scale vortical motions produced by ‘delta tabs’ in a two-stream shear layer have been studied experimentally. An increase in mixing was observed when the base of the triangular shaped tab was affixed to the trailing edge of the splitter plate and the apex was pitched at some angle with respect to the flow axis. Such an arrangement produced a pair of counter-rotating streamwise vortices. Hot-wire measurements detailed the velocity, time-averaged vorticity (Ωx) and small-scale turbulence features in the three-dimensional space downstream of the tabs. The small-scale structures, whose scale corresponds to that of the peak in the dissipation spectrum, were identified and counted using the peak-valley-counting technique. The optimal pitch angle, θ, for a single tab and the optimal spanwise spacing, S, for a multiple tab array were identified. Since the goal was to increase mixing, the optimal tab configuration was determined from two properties of the flow field: (i) the large-scale motions with the maximum Ωx, and (ii) the largest number of small-scale motions in a given time period. The peak streamwise vorticity magnitude [mid ]Ωx−max[mid ] was found to have a unique relationship with the tab pitch angle. Furthermore, for all cases examined, the overall small-scale population was found to correlate directly with [mid ]Ωx−max[mid ]. Both quantities peaked at θ≈±45°. It is interesting to note that the peak magnitude of the corresponding circulation in the cross-sectional plane occurred for θ≈±90°. For an array of tabs, the two quantities also depended on the tab spacing. An array of contiguous tabs acted as a solid deflector producing the weakest streamwise vortices and the least small-scale population. For the measurement range covered, the optimal spacing was found to be S≈1.5 tab widths.