# Experimental investigation of the influence of Reynolds number and buoyancy on the flow development of a plane jet in the transitional regime

Abstract: Heated horizontal plane jets find wide applications in engineering appliances such as air curtains and discharge of industrial effluents. In the present study, experimental investigations are condu...

Topics: Jet (fluid) (53%), Reynolds number (52%), Turbulence (52%), Horizontal plane (51%), Buoyancy (51%)

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TL;DR: The concepts presented here were developed in connection with heat transfer and fluid mechanics research experiments of moderately large size and which may frequently require three experiments to be conducted.

Abstract: Uncertainty Analysis is the prediction of the uncertainty interval which should be associated with an experimental result, based on observations of the scatter in the raw data used in calculating the result. In this paper, the process is discussed as it applies to single-sample experiments of the sort frequently conducted in research and development work. Single-sample uncertainty analysis has been in the engineering literature since Kline and McClintock's paper in 1953 [1] and has been widely, if sparsely, practiced since then. A few texts and references on engineering experimentation present the basic equations and discuss its importance in planning and evaluating experiments (see Schenck, for example [2]). Uncertainty analysis is frequently linked to the statistical treatment of the data, as in Holman [3], where it may be lost in the fog for many student engineers. More frequently, only the statistical aspects of data interpretation are taught, and uncertainty analysis is ignored. For whatever reasons, uncertainty analysis is not used as much as it should be in the planning, development, interpretation, and reporting of scientific experiments in heat transfer and fluid mechanics. There is a growing awareness of this deficiency among standards groups and funding agencies, and a growing determination to insist on a thorough description of experimental uncertainty in all technical work. Both the International Standards Organization [4] and the American Society of Mechanical Engineers [5] are developing standards for the description of uncertainties in fluid-flow measurements. The U. S. Air Force [6] and JANNAF [7] each have handbooks describing the appropriate procedures for their classes of problems. The International Committee on Weights and Measures (CIPM) is currently evaluating this issue [8]. The prior references, with the exception of Schenck and, to a lesser extent, Holman, treat uncertainty analysis mainly as a process for describing the uncertainty in an experiment, and end their discussion once that evaluation has been made. The present paper has a somewhat different goal: to show how uncertainty analysis can be used as an active tool in developing a good experiment, as well as reporting it. The concepts presented here were developed in connection with heat transfer and fluid mechanics research experiments of moderately large size (i.e., larger than a breadbox and smaller than a barn) and which may frequently require three

760 citations

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Abstract: Results are presented of measurements on turbulent round jets of air and of helium of the same nozzle momentum efflux, using, for the air jets, x-wire hot-wire probes mounted on a moving shuttle and, for He jets, a composite probe consisting of an interference probe of the Way-Libby type and an x-probe. Current models for scalar triple moments were evaluated. It was found that the performance of the model termed the Full model, which includes all terms except advection, was very good for both the air and the He jets.

648 citations

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Abstract: The axial and radial velocity components w and u, and the concentration c of a Rhodamine 6G dye were measured simultaneously in a turbulent buoyant jet, using laser-Doppler anemometry combined with a recently developed laser-induced-fluorescence concentration measurement technique. These non-intrusive techniques enable measurements in a region of plume motion where conventional probe-based techniques have had difficulties. The results of the study show that the asymptotic decay laws for velocity and concentration of a tracer transported by the flow are verified experimentally in both jets and plumes. The momentum and volume fluxes and the mean dilution factor are determined in dimensionless form as a function of the normalized distance from the flow source. Contradictory results from earlier experimental plume investigations concerning the decay laws of w and c and the plume width ratio b_c/b_w are discussed. The turbulence properties and the transition from momentum-driven jets to buoyancy-driven plumes are presented. The turbulence is found to scale with the mean flow as predicted by dimensional analysis and self-similarity. Buoyancy-produced turbulence is found to transport twice as much tracer as jet turbulence. Although velocity statistics in jets and plumes are found to be highly self-similar there is a strong disparity in the distribution of tracer concentration in the two flows. This occurs in the time-average mean flows as well as the r.m.s. turbulent quantities. Instantaneous concentration fluctuations are found to exceed time averages by as much as a factor of 3. The experimental results should provide a reasonable basis for validation of computer models of axisymmetric plumes.

490 citations

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Abstract: The effects of the mean and turbulence characteristics of the upstream (initial) boundary layer on the evolution of the flow in the near field of a plane jet have been experimentally investigated for four initial conditions. Rates of jet widening and centerline mean velocity decay as well as the kinematic and geometric virtual origins show evidence of systematic dependence on initial conditions. The growth rate of longitudinal turbulence intensity, and the mass flux are higher when the initial boundary layer is laminar than when turbulent. Immediately downstream of the exit, the nondimensional entrainment rates for the laminar initial boundary layer cases reach peak values which are about twice the delayed peak values for the fully turbulent initial boundary layer cases. Within the first 40 slit widths, increases in total average streamwise momentum flux range from 20% to 56%, the larger increases occurring for the laminar initial boundary layers; about 10% of each increase is due to the turbulence field. While such increases violate the traditionally accepted momentum flux invariance, they are consistent with the negative mean static pressure data.

179 citations

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Abstract: A study has been made of the instability and the subsequent breakdown of axisymmetric jets of helium/air mixtures emerging into ambient air. Although the density of the nozzle gas is less than that of the ambient fluid, the jet is essentially nonbuoyant. Two kinds of instability are observed in the near field, depending upon the mean flow parameters. When the ratio of the exiting nozzle fluid density to ambient fluid density is pJp, > 0.6, shear-layer fluctuations evolve in a fashion similar to that observed in constant-density jets: the power spectrum near the nozzle is determined by weak background disturbances whose subsequent spatial amplification agrees closely with the spatial stability theory. When the density ratio is less than 0.6, an intense oscillatory instability may also arise. The overall behaviour of this latter mode (to be called the ‘oscillating’ mode) is shown to depend solely upon the density ratio and upon D/O, where D is the nozzle diameter and 19 is the momentum thickness of the boundary layer at the nozzle exit. The behaviour of this mode is found to be independent of the Reynolds number, within the range covered by the present experiments. This is even true in the immediate vicinity of the nozzle where, unlike in the case of shear-layer modes, the intensity of the oscillating mode is independent of background disturbances. The streamwise growth rate associated with the oscillating mode is not abnormally large, however. The frequency of the oscillating mode compares well with predictions based on a spatio-temporal theory, but not with those of the standard spatial theory. From high-speed films it is found that the overall structure of the oscillating mode repeats itself with extreme regularity. The high degree of repeatability of the oscillating mode, in association with a strong pairing process, leads to abnormally large centreline velocity fluctuation, with its root-mean-square value being about 30 YO of the nozzle exit velocity. Energetic and highly regular pairing is found also to lead to the early and abrupt breakdown of the potential core. The regularity often extends even to the finer structure immediately downstream of the breakdown. An attempt is made to explain these special features both in terms of the large-amplitude vorticity field, and in terms of the theoretically predicted space-time evolution of wave packets.

130 citations