Elliptic jets. I - Characteristics of unexcited and excited jets
TL;DR: Experimental studies of incompressible elliptic jets of different aspect ratios and initial conditions are summarized along with the effects of excitations at selected frequencies and amplitudes in this paper, where the experimental facilities and procedures are described and jet spread and decay are discussed.
Abstract: Experimental studies of incompressible elliptic jets of different aspect ratios and initial conditions are summarized along with the effects of excitations at selected frequencies and amplitudes. The experimental facilities and procedures are described and jet spread and decay are discussed. The instability of elliptic shear layers, the behavior of the jet column under controlled excitation, and the time-average measures of unexcited jets are addressed.
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TL;DR: Noncircular jets have been identified as an efficient technique of passive flow control that allows significant improvements of performance in various practical systems at a relatively low cost because noncircular jet rely solely on changes in the geometry of the nozzle as discussed by the authors.
Abstract: Noncircular jets have been the topic of extensive research in the last fifteen years. These jets were identified as an efficient technique of passive flow control that allows significant improvements of performance in various practical systems at a relatively low cost because noncircular jets rely solely on changes in the geometry of the nozzle. The applications of noncircular jets discussed in this review include improved large- and small-scale mixing in low- and high-speed flows, and enhanced combustor performance, by improving combustion efficiency, reducing combustion instabilities and undesired emissions. Additional applications include noise suppression, heat transfer, and thrust vector control (TVC). The flow patterns associated with noncircular jets involve mechanisms of vortex evolution and interaction, flow instabilities, and fine-scale turbulence augmentation. Stability theory identified the effects of initial momentum thickness distribution, aspect ratio, and radius of curvature on the initial flow evolution. Experiments revealed complex vortex evolution and interaction related to selfinduction and interaction between azimuthal and axial vortices, which lead to axis switching in the mean flow field. Numerical simulations described the details and clarified mechanisms of vorticity dynamics and effects of heat release and reaction on noncircular jet behavior.
537 citations
TL;DR: In this article, the effect of vortex generators at the nozzle exit on the evolution of a jet was investigated, and the results of an experimental investigation on the effect on the vortex generators were reported.
Abstract: The results of an experimental investigation on the effect of vortex generators, in the form of small tabs at the nozzle exit on the evolution of a jet, are reported in this paper. Primarily tabs of triangular shape are considered, and the effect is studied up to a jet Mach number of 1.8. Each tab is found to produce a dominant pair of counter‐rotating streamwise vortices having a sense of rotation opposite to that expected from the wrapping of the boundary layer. This results in an inward indentation of the mixing layer into the core of the jet. A triangular‐shaped tab with its apex leaning downstream, referred to as a delta tab, is found to be the most effective in producing such vortices, with a consequential large influence on the overall jet evolution. Two delta tabs, spaced 180° apart, completely bifurcate the jet. Four delta tabs stretch the mixing layer into four ‘‘fingers,’’ resulting in a significant increase in the jet mixing downstream. For six delta tabs the mixing layer distortion settles back to a three finger configuration through an interaction of the streamwise vortices. The tabs are found to be equally effective in jets with turbulent or laminar initial boundary layers. Two sources of streamwise vorticity are postulated for the flow under consideration. One is the upstream ‘‘pressure hill,’’ generated by the tab, which constitutes the main contributor of vorticity to the dominant pair. Another is due to vortex filaments shed from the sides of the tab and reoriented downstream by the mean shear of the mixing layer. Depending on the orientation of the tab, the latter source can produce a vortex pair having a sense of rotation opposite to that of the dominant pair. In the case of the delta tab, vorticity from the two sources add, explaining the strong effect in that configuration.
420 citations
TL;DR: The effect of vortex generators, in the form of small tabs projecting normally into the flow at the nozzle exit, on the characteristics of an axisymmetric jet is investigated experimentally over the jet Mach number range of 0.3-1.81 as discussed by the authors.
Abstract: The effect of vortex generators, in the form of small tabs projecting normally into the flow at the nozzle exit, on the characteristics of an axisymmetric jet is investigated experimentally over the jet Mach number range of 0.3-1.81. The tabs eliminate screech noise from supersonic jets and alter the shock structure drastically. They distort the jet cross section and increase the jet spread rate significantly. The distortion produced is essentially the same at subsonic and underexpanded supersonic conditions. Thus, the underlying mechanism must be independent of compressibility effects. A tab with a height as small as 2 percent of the jet diameter, but larger than the efflux boundary-layer thickness, is found to produce a significant effect. Flow visualization reveals that each tab introduces an 'indentation' into the high speed side of the shear layer via the action of streamwise vortices. These vortices are inferred to be of the 'trailing vortex' type rather than of the 'necklace vortex' type. It is apparent that a substantial pressure differential must exist between the upstream and the downstream sides of the tab to effectively produce these trailing vortices. This explains why the tabs are ineffective in the overexpanded flow, as in that case an adverse pressure gradient exists near the nozzle exit which reduces the pressure differential produced by the tab.
346 citations
TL;DR: In this article, a monotonically integrated large eddy simulation (MILES) approach is introduced for closure of the low-pass filtered Navier-Strokes equations (NSE) using high-resolution monotone algorithms.
326 citations
TL;DR: In this article, the mixing augmentation methods employed efficiently in sub- sonic flows failed to work at elevated Mach numbers, and some were inefficient because they were utilized outside their effective range.
Abstract: Recent interest in supersonic combustion (scramjets) and noise reduction for the high speed civil transport (HSCT) plane prompted renewed research in supersonic mixing processes and means to control them. The scramjet propulsion concept requires rapid mixing between fuel and air in order to minimize the size of the combustor and affect the performance of the entire vehicle system. Also, accelerated mixing of exhaust plumes with coflowing air has been shown to lead to jet noise reduction. Other examples of technological applications requiring control of mixing in compressible flows include thrust augmenting ejectors, thrust vector control, metal deposition, and gas dynamic lasers. The technological challenge of mixing enhancement in compressible flows stems from the inherently low growth rates of supersonic shear layers. Many mixing augmentation methods employed efficiently in sub sonic flows failed to work at elevated Mach numbers, and some were inefficient because they were utilized outside their effective range. Never-
316 citations
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01 Jan 1967TL;DR: The dynamique des : fluides Reference Record created on 2005-11-18 is updated on 2016-08-08 and shows improvements in the quality of the data over the past decade.
Abstract: Preface Conventions and notation 1. The physical properties of fluids 2. Kinematics of the flow field 3. Equations governing the motion of a fluid 4. Flow of a uniform incompressible viscous fluid 5. Flow at large Reynolds number: effects of viscosity 6. Irrotational flow theory and its applications 7. Flow of effectively inviscid liquid with vorticity Appendices.
11,187 citations
TL;DR: In this paper, the Navier-Stokes equation is derived for an inviscid fluid, and a finite difference method is proposed to solve the Euler's equations for a fluid flow in 3D space.
Abstract: This brief paper derives Euler’s equations for an inviscid fluid, summarizes the Cauchy momentum equation, derives the Navier-Stokes equation from that, and then talks about finite difference method approaches to solutions. Typical texts for this material are apparently Acheson, Elementary Fluid Dynamics and Landau and Lifschitz, Fluid Mechanics. 1. Basic Definitions We describe a fluid flow in three-dimensional space R as a vector field representing the velocity at all locations in the fluid. Concretely, then, a fluid flow is a function ~v : R× R → R that assigns to each point (t, ~x) in spacetime a velocity ~v(t, ~x) in space. In the special situation where ~v does not depend on t we say that the flow is steady. A trajectory or particle path is a curve ~x : R→ R such that for all t ∈ R, d dt ~x(t) = ~v(t, ~x(t)). Fix a t0 ∈ R; a streamline at time t0 is a curve ~x : R→ R such that for all t ∈ R, d dt ~x(t) = ~v(t0, ~x(t)). In the special case of steady flow the streamlines are constant across times t0 and any trajectory is a streamline. In non-steady flows, particle paths need not be streamlines. Consider the 2-dimensional example ~v = [− sin t cos t]>. At t0 = 0 the velocities all point up and the streamlines are vertical straight lines. At t0 = π/2 the velocities all point left and the streamlines are horizontal straight lines. Any trajectory is of the form ~x = [cos t + C1 sin t + C2] >; this traces out a radius-1 circle centered at [C1 C2] >. Indeed, all radius-1 circles in the plane arise as trajectories. These circles cross each other at many (in fact, all) points. If you find it counterintuitive that distinct trajectories can pass through a single point, remember that they do so at different times. 2. Acceleration Let f : R × R → R be some scalar field (such as temperature). Then ∂f/∂t is the rate of change of f at some fixed point in space. If we precompose f with a 1 Fluid Dynamics Math 211, Fall 2014, Carleton College trajectory ~x, then the chain rule gives us the rate of change of f with respect to time along that curve: D Dt f := d dt f(t, x(t), y(t), z(t)) = ∂f ∂t + ∂f ∂x dx dt + ∂f ∂y dy dt + ∂f ∂z dz dt = ( ∂ ∂t + dx dt ∂ ∂x + dy dt ∂ ∂y + dz dt ∂ ∂z ) f = ( ∂ ∂t + ~v · ∇ ) f. Intuitively, if ~x describes the trajectory of a small sensor for the quantity f (such as a thermometer), then Df/Dt gives the rate of change of the output of the sensor with respect to time. The ∂f/∂t term arises because f varies with time. The ~v ·∇f term arises because f is being measured at varying points in space. If we apply this idea to each component function of ~v, then we obtain an acceleration (or force per unit mass) vector field ~a(t, x) := D~v Dt = ∂~v ∂t + (~v · ∇)~v. That is, for any spacetime point (t, ~x), the vector ~a(t, ~x) is the acceleration of the particle whose trajectory happens to pass through ~x at time t. Let’s check that it agrees with our usual notion of acceleration. Suppose that a curve ~x describes the trajectory of a particle. The acceleration should be d dt d dt~x. By the definition of trajectory, d dt d dt ~x = d dt ~v(t, ~x(t)). The right-hand side is precisely D~v/Dt. Returning to our 2-dimensional example ~v = [− sin t cos t]>, we have ~a = [− cos t − sin t]>. Notice that ~v · ~a = 0. This is the well-known fact that in constant-speed circular motion the centripetal acceleration is perpendicular to the velocity. (In fact, the acceleration of any constant-speed trajectory is perpendicular to its velocity.) 3. Ideal Fluids An ideal fluid is one of constant density ρ, such that for any surface within the fluid the only stresses on the surface are normal. That is, there exists a scalar field p : R × R → R, called the pressure, such that for any surface element ∆S with outward-pointing unit normal vector ~n, the force exerted by the fluid inside ∆S on the fluid outside ∆S is p~n ∆S. The constant density condition implies that the fluid is incompressible, meaning ∇ · ~v = 0, as follows. For any region of space R, the rate of flow of mass out of the region is ∫∫ ∂R ρ~v · ~n dS = ∫∫∫
9,804 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
1,750 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