Vortical structure in the wake of a transverse jet
TL;DR: In this article, structural features resulting from the interaction of a turbulent jet issuing transversely into a uniform stream are described with the help of flow visualization and hot-wire anemometry.
Abstract: Structural features resulting from the interaction of a turbulent jet issuing transversely into a uniform stream are described with the help of flow visualization and hot-wire anemometry. Jet-to-crossflow velocity ratios from 2 to 10 were investigated at crossflow Reynolds numbers from 3800 to 11400. In particular, the origin and formation of the vortices in the wake are described and shown to be fundamentally different from the well-known phenomenon of vortex shedding from solid bluff bodies. The flow around a transverse jet does not separate from the jet and does not shed vorticity into the wake. Instead, the wake vortices have their origins in the laminar boundary layer of the wall from which the jet issues. It is argued that the closed flow around the jet imposes an adverse pressure gradient on the wall, on the downstream lateral sides of the jet, provoking 'separation events’ in the wall boundary layer on each side. These result in eruptions of boundary-layer fluid and formation of wake vortices that are convected downstream. The measured wake Strouhal frequencies, which depend on the jet-crossflow velocity ratio, match the measured frequencies of the separation events. The wake structure is most orderly and the corresponding wake Strouhal number (0.13) is most sharply defined for velocity ratios near the value 4. Measured wake profiles show deficits of both momentum and total pressure.
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TL;DR: In this article, a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system, is presented.
Abstract: We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system. These modes, referred to as Koopman modes, are associated with a particular observable, and may be determined directly from data (either numerical or experimental) using a variant of a standard Arnoldi method. They have an associated temporal frequency and growth rate and may be viewed as a nonlinear generalization of global eigenmodes of a linearized system. They provide an alternative to proper orthogonal decomposition, and in the case of periodic data the Koopman modes reduce to a discrete temporal Fourier transform. The Arnoldi method used for computations is identical to the dynamic mode decomposition recently proposed by Schmid & Sesterhenn (Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, 2008), so dynamic mode decomposition can be thought of as an algorithm for finding Koopman modes. We illustrate the method on an example of a jet in crossflow, and show that the method captures the dominant frequencies and elucidates the associated spatial structures.
1,591 citations
Journal Article•
TL;DR: In this article, a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system, is presented.
Abstract: We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system. These modes, referred to as Koopman modes, are associated with a particular observable, and may be determined directly from data (either numerical or experimental) using a variant of a standard Arnoldi method. They have an associated temporal frequency and growth rate and may be viewed as a nonlinear generalization of global eigenmodes of a linearized system. They provide an alternative to proper orthogonal decomposition, and in the case of periodic data the Koopman modes reduce to a discrete temporal Fourier transform. The Arnoldi method used for computations is identical to the dynamic mode decomposition recently proposed by Schmid & Sesterhenn (Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, 2008), so dynamic mode decomposition can be thought of as an algorithm for finding Koopman modes. We illustrate the method on an example of a jet in crossflow, and show that the method captures the dominant frequencies and elucidates the associated spatial structures.
1,412 citations
Cites methods from "Vortical structure in the wake of a..."
...The flow physics of the jet-in-crossflow has been studied extensively (see e.g. Fric & Roshko 1994; Kelso, Lim & Perry 1996; Muppidi & Mahesh 2007) and it is shown that it is mainly characterized by four to five vortical structures depending on R and Re....
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TL;DR: In this article, the structure of round jets in cross-flow was studied using flow visualization techniques and flying-hot-wire measurements, restricted to jet to freestream velocity ratios ranging from 2.0 to 6.0.
Abstract: The structure of round jets in cross-flow was studied using flow visualization techniques and flying-hot-wire measurements. The study was restricted to jet to freestream velocity ratios ranging from 2.0 to 6.0 and Reynolds numbers based on the jet diameter and free-stream velocity in the range of 440 to 6200.Flow visualization studies, together with time-averaged flying-hot-wire measurements in both vertical and horizontal sectional planes, have allowed the mean topological features of the jet in cross-flow to be identified using critical point theory. These features include the horseshoe (or necklace) vortex system originating just upstream of the jet, a separation region inside the pipe upstream of the pipe exit, the roll-up of the jet shear layer which initiates the counter-rotating vortex pair and the separation of the flat-wall boundary layer leading to the formation of the wake vortex system beneath the downstream side of the jet.The topology of the vortex ring roll-up of the jet shear layer was studied in detail using phase-averaged flying-hot-wire measurements of the velocity field when the roll-up was forced. From these data it is possible to examine the evolution of the shear layer topology. These results are supported by the flow visualization studies which also aid in their interpretation.The study also shows that, for velocity ratios ranging from 4.0 to 6.0, the unsteady upright vortices in the wake may form by different mechanisms, depending on the Reynolds number. It is found that at high Reynolds numbers, the upright vortex orientation in the wake may change intermittently from one configuration of vortex street to another. Three mechanisms are proposed to explain these observations.
720 citations
TL;DR: In this article, a review of the physical behavior of this important class of flow in the incompressible and compressible regimes is presented, and a general consensus on the qualitative structure of the flow at low velocity ratios (jet speed/crossflow speed) is established.
Abstract: It is common for jets of fluid to interact with crossflow. This article reviews our understanding of the physical behavior of this important class of flow in the incompressible and compressible regimes. Experiments have significantly increased in sophistication over the past few decades, and recent experiments provide data on turbulence quantities and scalar mixing. Quantitative data at high speeds are less common, and visualization still forms an important component in estimating penetration and mixing. Simulations have progressed from the Reynolds-averaged methodology to large-eddy and hybrid methodologies. There is a general consensus on the qualitative structure of the flow at low speeds; however, the flow structure at low-velocity ratios (jet speed/crossflow speed) might be fundamentally different from the common notion of shear-layer vortices, counter-rotating vortex pairs, wakes, and horseshoe vortices. Fluid in the near field is strongly accelerated, which affects the jet trajectory, entrainment, ...
465 citations
TL;DR: In this paper, the authors measured the instantaneous instantaneous velocity fields of a jet in crossflow with PIV and found that the wake vortices are the dominant dynamic flow structures and that they interact strongly with the jet core.
Abstract: Detailed instantaneous velocity fields of a jet in crossflow have been measured with stereoscopic particle image velocimetry (PIV). The jet originated from a fully developed turbulent pipe flow and entered a crossflow with a turbulent boundary layer. The Reynolds number based on crossflow velocity and pipe diameter was 2400 and the jet to crossflow velocity ratios were R=3.3 and R=1.3. The experimental data have been analysed by proper orthogonal decomposition (POD). For R=3.3, the results in several different planes indicate that the wake vortices are the dominant dynamic flow structures and that they interact strongly with the jet core. The analysis identifies jet shear-layer vortices and finds that these vortical structures are more local and thus less dominant. For R=1.3, on the other hand, jet shear-layer vortices are the most dominant, while the wake vortices are much less important. For both cases, the analysis finds that the shear-layer vortices are not coupled to the dynamics of the wake vortices. Finally, the hanging vortices are identified and their contribution to the counter-rotating vortex pair (CVP) and interaction with the newly created wake vortices are described.
402 citations
Cites background or methods or result from "Vortical structure in the wake of a..."
...However, as pointed out by Fric & Roshko (1994), there are fundamental differences....
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...The visualizations by Fric & Roshko (1994) show that the wake vortices connect to the jet core with an angle of about 90◦ to the jet trajectory....
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...From the visualizations of both Fric & Roshko (1994) and Kelso et al. (1996), we note two observations....
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...This observation is consistent with the fact that the Strouhal number of the wake vortices (reported for example by Fric & Roshko 1994) is different from that of the jet shear-layer vortices reported by Shapiro et al. (2006)....
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...Fric & Roshko (1994) found that they could only visualize the vortex when the tracer was released in the incoming boundary layer and not when released in the jet....
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References
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TL;DR: Experiments on turbulent circular jets issuing into cross flow from both heated and unheated jets were conducted in this paper, where the authors showed that turbulent circular planes can be generated by both heating and cooling.
Abstract: Experiments on turbulent circular jets issuing into cross flow from both heated and unheated jets
541 citations
"Vortical structure in the wake of a..." refers background in this paper
...…1, and becomes dominant in the far field, where it is synonymous with the jet'^ A partial list of the numerous experimental studies of the vortex-pair structure of the jet includes the following: Keffer & Baines (1963), Pratte & Baines (1967), Kamotani & Greber (1972), and Fearn & Weston (1974)....
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TL;DR: In this article, it is suggested that extremely low-level spatially coherent disturbances in individual facilities change the initial conditions of a laminar shear layer and result in the discrepancies reported in the literature.
Abstract: For about a decade it has been noticed from the measurements of many jets that the value of the preferred mode and the spreading rate vary within a range of about 100%. In the present paper it is suggested that extremely low‐level spatially coherent disturbances in individual facilities change the initial conditions of a laminar shear layer. The various initial conditions are able to cause different downstream developments of the jet and result in the discrepancies reported in the literature.
453 citations
"Vortical structure in the wake of a..." refers background in this paper
...These structures are of the same type as the vortex ring structures of free jets (Freymuth 1966; Becker & Massaro 1968; Gutmark & Ho 1983)....
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TL;DR: In this article, the position of a jet in space, when stretched by the ratio of jet to cross-wind momenta, is described by a single function, where a natural system of axes is used to define important directions of the flow.
Abstract: The flow of a jet directed normal to a uniform, steady cross-wind is considered. Experimental results show that for various jet strengths, the position of the jet in space, when stretched by the ratio of jet to cross-wind momenta, is described by a single function. Exceptions exist at very low velocity ratios where a shift of the potential core is evident. A natural system of axes is used to define important directions of the flow. The integrated equation of motion along the primary jet flow direction is made dimensionless after the general method of Morton (1961) and a virtual source is defined for the flow. It is shown that a single functional behaviour of the axial jet velocity exists for various velocity ratios if the jet is considered to originate from this source. Lateral velocity profiles show a similarity when scaled by appropriate lengths and velocities but true self-preservation is not attained.
412 citations
"Vortical structure in the wake of a..." refers background in this paper
...…1, and becomes dominant in the far field, where it is synonymous with the jet'^ A partial list of the numerous experimental studies of the vortex-pair structure of the jet includes the following: Keffer & Baines (1963), Pratte & Baines (1967), Kamotani & Greber (1972), and Fearn & Weston (1974)....
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TL;DR: The steady two-dimensional flow of viscous incompressible fluid in the boundary layer along a solid boundary, which is governed by Prandtl's approximation to the full equations of motion, presents a problem which in general is as intractable as any in applied mathematics.
Abstract: The steady two-dimensional flow of viscous incompressible fluid in the boundary layer along a solid boundary, which is governed by Prandtl's approximation to the full equations of motion, presents a problem which in general is as intractable as any in applied mathematics. The problem, however, has such an immediate and necessary application that approximate methods of varying accuracy which go beyond the formal processes of expansions in series and so on, have been devised for the rapid calculation of the principal characteristics of the laminar boundary-layer, the variation of pressure along the surface being known. Such methods usually represent approximately the boundary-layer velocity distribution at any point by one of a known family of distributions whose spacing along the surface is determined by some means, often by the use of Karman's momentum equation.
376 citations
TL;DR: In this article, the Strouhal number was used to measure the growth of small disturbances in a separated laminar boundary layer for high Reynolds numbers as a function of the dimensionless flow parameters.
Abstract: This paper deals with the growth of small disturbances in a separated laminar boundary layer for high Reynolds numbers as a function of the dimensionless flow parameters. Using a hot-wire technique, the experiments show that spatially growing disturbances are only affected by the Strouhal number. Thus the basic equations of the process become relatively simple. The experiments show good agreement with theoretical results obtained by means of hydrodynamic stability theory for spatially growing disturbances.
375 citations
"Vortical structure in the wake of a..." refers background in this paper
...These structures are of the same type as the vortex ring structures of free jets (Freymuth 1966; Becker & Massaro 1968; Gutmark & Ho 1983)....
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