Orderly structure in jet turbulence

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.

Effect of background turbulence on an axisymmetric turbulent jet

“…The constant of proportionality in the fully developed region for the nondimensionalized mass flow rate was estimated to be 0.32 by Ricou & Spalding (1961). ( The experimental results of Falcone & Cataldo (2003) and Crow and Champagne (1971) found c to be 0.297 and 0.292, respectively. The entrainment rate of the jet (c = dm/dx) decreases as the Reynolds number increases.…”

Scanning tomographic particle image velocimetry applied to a turbulent jet

“…The round jet is a widely studied canonical turbulent free-shear flow, [20][21][22][23] as it is relatively simple to set up experimentally and exhibits self-similar statistical structure, evolving downstream at a constant Reynolds number. An analytical solution of the boundary layer approximation to the incompressible turbulent jet mean momentum equations also exists.…”

Annular impinging jet with recirculation zone expanded by acoustic excitation

“…The value of 0.3 is in tune with the most preferred mode (i.e. the most amplified mode obtained by an artificial external excitation) according to Crow and Champagne [17]. Moreover, Cho et al [30] observed a non-pairing advection of vortices for higher Strouhal number from 0.6 to 0.9.…”

“…The highest sensitivity of round jets to excitation (i.e. the most amplified mode under small artificial excitations) is known be at the most preferred mode, at Strouhal number of 0.3-0.35 [17]. As mentioned above, the situation in annular jets is governed by two scales, e.g., Strouhal numbers for intermediate merging zone of the outer mixing region of annular jets are comparable or slightly smaller than those of jets, a very gradual decrease around 0.35 was presented, e.g., by Chan and Ko [49].…”

“…Steady turbulent impinging jets can achieve very high heat/mass transfer rate--the term "steady" meant in the time-mean-flow sense. In fact, the processes in turbulent impinging jet flows are significantly influenced by inherent oscillations and large vortex structures--as described e.g., by Crow and Champagne [17], Hussain [18], and Kataoka et al [19]. Despite this fact, a possibility to intensify transport process to obtain even higher performance by excitation remains a great challenge for researchers.…”