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At least 163 records · Page 9

Premixed Flame-Vortex Interactions Imaged in Microgravity

A unique experiment makes it now possible to obtain detailed images in microgravity showing how an individual vortex causes the wrinkling, stretching, area increase, and eventual extinction of a premixed flame. The repeatable, controllable flame-vortex interaction represents the fundamental building block of turbulent combustion concepts. New information is provided that is central to turbulent flame models, including measurements of all components of flame stretch, strain, and vorticity. Simultaneous measurements of all components of these quantities are not possible in fully turbulent flames but are possible in the present axisymmetric, repeatable experiment. Advanced PIV diagnostics have been used at one-g and have been developed for microgravity. Numerical simulations of the interaction are being performed at NRL. It is found that microgravity conditions greatly augment the flame wrinkling process. Flame area and the amplitude of wrinkles at zero-g are typically twice that observed at one-g. It is inferred that turbulent flames in microgravity could have larger surface area and thus propagate significantly faster than those in one-g, which is a potential safety hazard. A new mechanism is identified by PIV images that shows how buoyancy retards flame wrinkling at one-g; buoyancy produces new vorticity (due to baroclinic torques) that oppose the wrinkling and the stretch imposed by the original vortex. Microgravity conditions remove this stabilizing mechanism and the amplitude of flame wrinkling typically is found to double. Microgravity also increases the flame speed by a factor of 1.8 to 2.2. Both methane and propane-air flames were studied at the NASA Lewis drop tower. Results indicate that it is important to add buoyancy to models of turbulent flames to simulate the correct flame wrinkling, stretch and burning velocity.

Driscoll, J. F.↗

PIV/HPIV Film Analysis Software Package

A PIV/HPIV film analysis software system was developed that calculates the 2-dimensional spatial autocorrelations of subregions of Particle Image Velocimetry (PIV) or Holographic Particle Image Velocimetry (HPIV) film recordings. The software controls three hardware subsystems including (1) a Kodak Megaplus 1.4 camera and EPIX 4MEG framegrabber subsystem, (2) an IEEE/Unidex 11 precision motion control subsystem, and (3) an Alacron I860 array processor subsystem. The software runs on an IBM PC/AT host computer running either the Microsoft Windows 3.1 or Windows 95 operating system. It is capable of processing five PIV or HPIV displacement vectors per second, and is completely automated with the exception of user input to a configuration file prior to analysis execution for update of various system parameters.

Blackshire, James L.↗

Optical Instrumentation for Temperature and Velocity Measurements in Rig Turbines

Non-intrusive optical measurement techniques have been examined in the context of developing robust instruments which can routinely yield data of engineering utility in high speed turbomachinery test rigs. The engineering requirements of such a measurement are presented. Of particular interest were approaches that provide both velocity and state-variable information in order to be able to completely characterize transonic flowfields. Consideration of all of the requirements lead to the selection of particle image velocimetry (PIV) for the approach to velocity measurement while laser induced fluorescence of oxygen (O2 LIF) appeared to offer the most promise for gas temperature measurement. A PIV system was developed and demonstrated on a transonic turbine stage in the MIT blowdown turbine facility. A comprehensive data set has been taken at one flow condition. Extensive calibration established the absolute accuracy of the velocity measurements to be 3-5 %. The O2 LIF proved less successful. Although accurate for low speed flows, vibrational freezing of O2 prevented useful measurements in the transonic, 300-600 K operating range of interest here.

Ceyhan, I.↗

Investigation of Strain/Vorticity and Large-Scale Flow Structure in Turbulent Nonpremixed Jet Flames

Our study will use the microgravity environment to investigate the underlying flow structure of turbulent nonpremixed round jet flames. In particular, we aim to investigate the large-scale turbulent structure using planar laser Mie scattering (PLMS), and the strain rate and vorticity fields using particle image velocimetry (PIV). This work is motivated by recent studies in our laboratory that have led to several interesting observations of nominally momentum-driven turbulent nonpremixed planar flames. First of all, the organized large-scale turbulent structures that are observed in nonreacting planar jets may be substantially modified or suppressed in nonpremixed planar jet flames. Furthermore, a recent study using PIV and planar laser-induced fluorescence of OH has shown that in transitional and turbulent nonpremixed planar jet flames the presence of the flame seems to greatly influence the underlying vorticity and strain fields, as compared to nonreacting jets. For example, the reaction zones in the jet flames are strongly correlated with regions of high vorticity. A related study has demonstrated that vorticity is not correlated in the same way with either iso-scalar surfaces or scalar dissipation layers in nonreacting planar jets. Furthermore, the relationship between strain and the reaction zone appears to be modified by the presence of high levels of heat release. In particular, the strain rate field in planar jet flames exhibits a preferred direction of principal compressive strain that apparently is related to strong shear across the reaction zone. This preferred direction of strain was not observed in nonreacting jets. One of the major problems encountered when conducting these types of studies is that it is difficult to know to what extent buoyancy influences the results. Therefore, the microgravity environment provides us with an excellent opportunity to explore these issues without the complicating effects of buoyancy. This is particularly the case when studying flames that are transitional between laminar and turbulent states. For example, the strong correlation of vorticity with the reaction zone (discussed above) was observed in both transitional and turbulent planar flames, but the effect was stronger for the transitional case. To date, the reason for the presence of the vorticity-reaction zone correlation is not known, although vorticity production via baroclinic torque is a likely cause. The microgravity environment will allow us to specifically determine whether the vorticity is produced by baroclinic torque resulting from the flame density gradient acting with the hydrostatic pressure gradient.AAdditional details of the planned experiments are provided.

Clemens, N. T.↗

Attenuation of Gas Turbulence by a Nearly Stationary Dispersion of Fine Particles

Turbulence attenuation by greater than a factor of two has been observed in many practical gas flows carrying volume fractions as small as 0.01% of dispersed particles. Particles which cause such attenuation usually are smaller than the smallest scales of the turbulence and have time constants 5 to 10 times greater than the time scale of a typical turbulent eddy. That is, strongly attenuating particles usually have Stokes numbers in the range of 5 to 10, indicating that they do not respond to the turbulent fluctuations, but instead just fall through the flow responding only to the mean flow. There are two mechanisms by which free falling particles may attenuate turbulence. First, the unresponsive particles act as a drag on the turbulent eddies, passing energy from the turbulent eddies to the small scale wakes of the particles where it is quickly dissipated by viscosity. The second mechanism is more complicated. Particles falling under gravity convert gravitational potential energy to turbulent velocity fluctuations. If the particles are large, this mechanism increases the overall turbulence level. However, with moderate size particles, the small scale turbulence generated apparently distorts the turbulent eddies leading to more rapid dissipation. Unfortunately, this conclusion is supported only by circumstantial evidence to date. The objectives of the experiment are to use microgravity to separate the two mechanisms. A region of nearly-isotropic decaying turbulence with zero mean flow will be formed in a box in the microgravity environment. Different sets of particles with Stokes numbers in the range of 2 to 20 will be dispersed in the flow. With zero gravity and no mean fluid velocity the particles will have zero mean velocity. With the large Stokes numbers, the fluctuating velocities will also be small. Therefore, the only attenuation mechanism will be the direct action of the particles on the turbulence. Control experiments will also be done in which the particles fall through the measurement volume. Measurements will be acquired using a high resolution image velocimetry (PIV) system being developed specifically for work in particle-laden flows. The measurements will include the decay of the turbulence kinetic energy under various particle loadings. The spatial spectra of the turbulence will also be measured. In a second set of experiments, the interaction of a single eddy with a collection of nearly stationary particles will be examined. The eddy will be a vortex ring emitted by a jet pulse through an orifice. The distortion of the vortex under the influence of the particles will be examined to gain a better understanding of how fine particles can cause such large reductions in turbulence levels. This experiment could not be conducted in terrestrial gravity because the high particle velocities would overwhelm the relatively low speed motion of the vortex ring. This experimental program is just getting underway. The initial challenge is to build a closed facility containing reasonably homogeneous and isotropic turbulence with zero mean velocity. Our approach is to use a set of synthetic jets mounted on the periphery of a transparent plexiglass box to create the turbulence. A synthetic jet is a plenum chamber with an orifice open to the volume of interest. The volume of the chamber fluctuates periodically so alternately a jet is ejected from the volume or flow is drawn back in as a sink. The asymmetry of this situation results in a net transport of momentum and kinetic energy into the volume of interest. The present apparatus includes eight synthetic jets each powered independently by a six inch loudspeaker. The synthetic jets discharge through ejector tubes to increase the scale of the turbulence. Construction of the apparatus is now complete and preliminary flow visualization studies have been conducted. The PIV system is also under development. A compact dual-pulse YAG laser has been acquired as the light source and special software is under development to allow simultaneous measurements of both the particle phase and the fluid phase (marked by fine tracers).

Paris, A. D.↗

An Experimental Study of the Ground Transportation System (GTS) Model in the NASA Ames 7- by 10-Ft Wind Tunnel

The 1/8-scale Ground Transportation System (GTS) model was studied experimentally in the NASA Ames 7- by 10-Ft Wind Tunnel. Designed for validation of computational fluid dynamics (CFD), the GTS model has a simplified geometry with a cab-over-engine design and no tractor-trailer gap. As a further simplification, all measurements of the GTS model were made without wheels. Aerodynamic boattail plates were also tested on the rear of the trailer to provide a simple geometry modification for computation. The experimental measurements include body-axis drag, surface pressures, surface hot-film anemometry, oil-film interferometry, and 3-D particle image velocimetry (PIV). The wind-averaged drag coefficient with and without boattail plates was 0.225 and 0.277, respectively. PIV measurements behind the model reveal a significant reduction in the wake size due to the flow turning provided by the boattail plates. Hot-film measurements on the side of the cab indicate laminar separation with turbulent reattachment within 0.08 trailer width for zero and +/- 10 degrees yaw. Oil film interferometry provided quantitative measurements of skin friction and qualitative oil flow images. A complete set of the experimental data and the surface definition of the model are included on a CD-ROM for further analysis and comparison.

Storms, Bruce L.↗

Liquid Fuels: Pyrolytic Degradation and Fire Spread Behavior as Influenced by Buoyancy

This work is being conducted by the Combustion and Emission Control Lab in the Engineering Department at Clark Atlanta University under NASA Grant No. NCC3-707. The work aims at providing data to supplement the ongoing NASA research activities on fire spread across liquid pools by providing flow visualization and velocity measurements especially in the gas phase and gas-liquid interface. The fabrication, installation, and testing were completed during this reporting period. The system shakedown and detailed quantitative measurements with High Speed Video and Particle Image Velocimetry (PIV) systems using butanol as fuel were performed. New and interesting results, not previously reported in the literature, were obtained from the experiments using a modified NASA tray and butanol as fuel. Three distinct flame spread regimes, as previously reported, were observed. These were the pseudo-uniform regime below 20 C, the pulsating regime between 22 and 30 C and the uniform regime above about 31 C. In the pulsating regime the jump velocity appeared to be independent of the pool temperature. However, the retreat velocity between jumps appeared to depend on the initial pool temperature. The flame retreated before surging forwards with increasing brightness. Previous literature reported this phenomenon only under microgravity conditions. However, we observed such behavior in our normal gravity experiments. Mini-pulsations behind the flame front were also observed. Two or three of these pulsations were observed within a single flame front pulsating time period. The velocity vector maps of the gas and liquid phases ahead, during, and behind the flame front were characterized. At least one recirculation cell was observed right below the flame front.The size of the liquid phase vortex (recirculation cell) below the flame front appeared to decrease with increasing initial pool temperature. The experiments also showed how multiple vortices developed in the liquid phase. A large recirculation cell, which generally spins counterclockwise as the flame spread from right to left, was observed ahead of and near the flame front in the gas phase. Detailed quantitative measurements will be undertaken with the LDV and PIV systems using the modified NASA tray and propanol.

Yeboah, Yaw D.↗

Liquid Fuels: Pyrolytic Degradation and Fire Spread Behavior as Influenced by Buoyancy

This project was conducted by the Combustion and Emission Control Lab in the Engineering Department at Clark Atlanta University under NASA Grant No. NCC3-707. The work aimed at providing data to supplement the ongoing NASA research activities on flame spread across liquid pools by providing flow visualization and velocity measurements especially in the gas phase and gas-liquid interface. During this investigation, the detailed physics of flame spread across liquid pools was revealed using particle image velocimetry (PIV), 3-dimensional Laser Doppler velocimetry (LDV) and high-speed video imaging system (HSVS). Flow fields (front and side views) of both the liquid and gas phases were visually investigated for the three subflash regimes of flame spread behavior. Some interesting findings obtained from the front and side views on flame spread across butanol pools are presented. PIV results showed the size of the transient vortex in the liquid phase near the flame front varied with the initial pool temperature. The transient vortex ahead of the flame front in the gas phase was, for the first time, clearly observed located just within 0-3 mm above the liquid surface and its size was dependent on the initial pool temperature. We calculated the flow velocity at 1 mm below the liquid surface near the flame front and inferred the generation mechanism of the vortex in the gas phase. Finally, after comparison of the flow velocity of the liquid surface and the flame spread rate, a reasonable explanation to the formation mechanism of the pulsating characteristic was proposed. This explanation is compatible with the previous numerical calculations and deductions.

Ross, Howard D.↗

Non-Ballistic Vapor-Driven Ejecta

Impact-induced vaporization is a key component of early-time cratering mechanics. Previous experimental [1,2] and computational [e.g., 3] studies focused on the generation and expansion of vapor clouds in an attempt to better understand vaporization in hypervelocity impacts. Presented here is a new experimental approach to the study of impact-induced vaporization. The three-dimensional particle image velocimetry (3D PIV) system captures interactions between expanding vapor phases and fine particulates. Particles ejected early in the cratering process may be entrained in expanding gas phases generated at impact, altering their otherwise ballistic path of flight. 3D PIV allows identifying the presence of such non-ballistic ejecta from very early times in the cratering process.

Wrobel, K. E.↗

A Separation Control CFD Validation Test Case: Baseline and Steady Suction - Part 1

Low speed flow separation over a wall-mounted hump, and its control using steady suction, were studied experimentally in order to generate a data set for a workshop aimed at validating CFD turbulence models. The baseline and controlled data sets comprised static and dynamic surface pressure measurements, flow field measurements using Particle Image Velocimetry (PIV) and wall shear stress obtained via oil-film interferometry. In addition to the specific test cases studied, surface pressures for a wide variety of conditions were reported for different Reynolds numbers and suction rates. Stereoscopic PIV and oil-film flow visualization indicated that the baseline separated flow field was mainly two- dimensional. With the application of control, some three-dimensionality was evident in the spanwise variation of pressure recovery, reattachment location and spanwise pressure fluctuations. Part 2 of this paper, under preparation for the AIAA Meeting in Reno 2005, considers separation control by means of zero-efflux oscillatory blowing.

David Greenblatt↗

A Separation Control CFD Validation Test Case: Baseline and Steady Suction - Part 1

Low speed flow separation over a wall-mounted hump, and its control using steady suction, were studied experimentally in order to generate a data set for a workshop aimed at validating CFD turbulence models. The baseline and controlled data sets comprised static and dynamic surface pressure measurements, flow field measurements using Particle Image Velocimetry (PIV) and wall shear stress obtained via oil-film interferometry. In addition to the specific test cases studied, surface pressures for a wide variety of conditions were reported for different Reynolds numbers and suction rates. Stereoscopic PIV and oil-film flow visualization indicated that the baseline separated flow field was mainly two-dimensional. With the application of control, some three-dimensionality was evident in the spanwise variation of pressure recovery, reattachment location and spanwise pressure fluctuations. Part 2 of this paper, under preparation for the AIAA Meeting in Reno 2005, considers separation control by means of zero-efflux oscillatory blowing.

Greenblatt, David↗

Modeling of Biological Fluid Systems

This study presents a detailed methodology for modeling and validating three- dimensional fluid flow in realistic reconstructed vasculature geometry. Optical scanned data from a sectioned stenotic lumen having -65% area constriction within an arterial vessel of 9 mm diameter is processed and converted into a finite-element mesh. Mass and momentum transfer equations within the reconstructed stenotic vessel with a-flow rate of 200 ml/rnin is solved using the Galarkin Finite Element formulation. The calculated velocities at several axial locations along the length of the vessel are compared with the Particle Image Velocimetry (PIV) measurements. The computation results are in agreement with the initial steady state PIV measurements. In addition, initial results from pulsatile flow computations at different time points of a pulse cycle will be presented.

Banerjee, Rupak↗

Measurements of Unsteady Wake Interference Between Tandem Cylinders

A multi-phase, experimental study in the Basic Aerodynamics Research Tunnel at the NASA Langley Research Center has provided new insight into the unsteady flow interaction around cylinders in tandem arrangement. Phase 1 of the study characterized the mean and unsteady near-field flow around two cylinders of equal diameter using 2-D Particle Image Velocimetry (PIV) and hot-wire anemometry. These measurements were performed at a Reynolds number of 1.66 x 10(exp 5), based on cylinder diameter, and spacing-to-diameter ratios, L/D, of 1.435 and 3.7. The current phase, Phase 2, augments this dataset by characterizing the surface flow on the same configurations using steady and unsteady pressure measurements and surface flow visualization. Transition strips were applied to the front cylinder during both phases to produce a turbulent boundary layer upstream of the flow separation. For these flow conditions and L/D ratios, surface pressures on both the front and rear cylinders show the effects of L/D on flow symmetry, pressure recovery, and the location of flow separation and attachment. Mean streamlines and instantaneous vorticity obtained from the PIV data are used to explain the flow structure in the gap and near-wake regions and its relationship to the unsteady surface pressures. The combination of off-body and surface measurements provides a comprehensive dataset to develop and validate computational techniques for predicting the unsteady flow field at higher Reynolds numbers.

Jenkins, Luther N.↗

Phased-Array Study of Dual-Flow Jet Noise: Effect of Nozzles and Mixers

A 16-microphone linear phased-array installed parallel to the jet axis and a 32-microphone azimuthal phased-array installed in the nozzle exit plane have been applied to identify the noise source distributions of nozzle exhaust systems with various internal mixers (lobed and axisymmetric) and nozzles (three different lengths). Measurements of velocity were also obtained using cross-stream stereo particle image velocimetry (PIV). Among the three nozzle lengths tested, the medium length nozzle was the quietest for all mixers at high frequency on the highest speed flow condition. Large differences in source strength distributions between nozzles and mixers occurred at or near the nozzle exit for this flow condition. The beamforming analyses from the azimuthal array for the 12-lobed mixer on the highest flow condition showed that the core flow and the lobe area were strong noise sources for the long and short nozzles. The 12 noisy spots associated with the lobe locations of the 12-lobed mixer with the long nozzle were very well detected for the frequencies 5 KHz and higher. Meanwhile, maps of the source strength of the axisymmetric splitter show that the outer shear layer was the most important noise source at most flow conditions. In general, there was a good correlation between the high turbulence regions from the PIV tests and the high noise source regions from the phased-array measurements.

Soo Lee, Sang↗

Microvascular Branching as a Determinant of Blood Flow by Intravital Particle Imaging Velocimetry

The effects of microvascular branching on blood flow were investigated in vivo by microscopic particle imaging velocimetry (micro-PIV). We use micro-PIV to measure blood flow by tracking red blood cells (RBC) as the moving particles. Velocity flow fields, including flow pulsatility, were analyzed for the first four branching orders of capillaries, postcapillary venules and small veins of the microvascular network within the developing avian yolksac at embryonic day 5 (E5). Increasing volumetric flowrates were obtained from parabolic laminar flow profiles as a function of increasing vessel diameter and branching order. Maximum flow velocities increased approximately twenty-fold as the function of increasing vessel diameter and branching order compared to flow velocities of 100 - 150 micron/sec in the capillaries. Results from our study will be useful for the increased understanding of blood flow within anastomotic, heterogeneous microvascular networks.

Parsons-Wingerter, Patricia↗

Active-Adaptive Control of Inlet Separation Using Supersonic Microjets

Flow separation in internal and external flows generally results in a significant degradation in aircraft performance. For internal flows, such as inlets and transmission ducts in aircraft propulsion systems, separation is undesirable as it reduces the overall system performance. The aim of this research has been to understand the nature of separation and more importantly, to explore techniques to actively control it. In this research, we extended our investigation of active separation control (under a previous NASA grant) where we explored the use of microjets for the control of boundary layer separation. The geometry used for the initial study was a simple diverging Stratford ramp, equipped with arrays of microjets. These early results clearly show that the activation of microjets eliminated flow separation. Furthermore, the velocity-field measurements, using PIV, also demonstrate that the gain in momentum due to the elimination of separation is at least an order of magnitude larger (two orders of magnitude larger in most cases) than the momentum injected by the microjets and is accomplished with very little mass flow through the microjets. Based on our initial promising results this research was continued under the present grant, using a more flexible model. This model allows for the magnitude and extent of separation as well as the microjet parameters to be independently varied. The results, using this model were even more encouraging and demonstrated that microjet control completely eliminated significant regions of flow separation over a wide range of conditions with almost negligible mass flow. Detailed studies of the flowfield and its response to microjets were further examined using 3-component PIV and unsteady pressure measurements, among others. As the results presented this report will show, microjets were successfully used to control the separation of a much larger extent and magnitude than demonstrated in our earlier experiments. In fact, using the appropriate combination of control parameters (microjet, location, angle and pressure) separation was completely eliminated for the largest separated flowfield we could generate with the present model. Separation control also resulted in a significant reduction in the unsteady pressures in the flow where the unsteady pressure field was found to be directly responsive to the state of the flow above the surface. Hence, our study indicates that the unsteady pressure signature is a strong candidate for a flow state sensor , which can be used to estimate the location, magnitude and other properties of the separated flowfield. Once better understood and properly utilized, this behavior can be of significant practical importance for developing and implementing online control.

Alvi, Farrukh S.↗

Validating LES for Jet Aeroacoustics

Engineers charged with making jet aircraft quieter have long dreamed of being able to see exactly how turbulent eddies produce sound and this dream is now coming true with the advent of large eddy simulation (LES). Two obvious challenges remain: validating the LES codes at the resolution required to see the fluid-acoustic coupling, and the interpretation of the massive datasets that result in having dreams come true. This paper primarily addresses the former, the use of advanced experimental techniques such as particle image velocimetry (PIV) and Raman and Rayleigh scattering, to validate the computer codes and procedures used to create LES solutions. It also addresses the latter problem in discussing what are relevant measures critical for aeroacoustics that should be used in validating LES codes. These new diagnostic techniques deliver measurements and flow statistics of increasing sophistication and capability, but what of their accuracy? And what are the measures to be used in validation? This paper argues that the issue of accuracy be addressed by cross-facility and cross-disciplinary examination of modern datasets along with increased reporting of internal quality checks in PIV analysis. Further, it is argued that the appropriate validation metrics for aeroacoustic applications are increasingly complicated statistics that have been shown in aeroacoustic theory to be critical to flow-generated sound.

Bridges, James↗

Establishing Consensus Turbulence Statistics for Hot Subsonic Jets

Many tasks in fluids engineering require knowledge of the turbulence in jets. There is a strong, although fragmented, literature base for low order statistics, such as jet spread and other meanvelocity field characteristics. Some sources, particularly for low speed cold jets, also provide turbulence intensities that are required for validating Reynolds-averaged Navier-Stokes (RANS) Computational Fluid Dynamics (CFD) codes. There are far fewer sources for jet spectra and for space-time correlations of turbulent velocity required for aeroacoustics applications, although there have been many singular publications with various unique statistics, such as Proper Orthogonal Decomposition, designed to uncover an underlying low-order dynamical description of turbulent jet flow. As the complexity of the statistic increases, the number of flows for which the data has been categorized and assembled decreases, making it difficult to systematically validate prediction codes that require high-level statistics over a broad range of jet flow conditions. For several years, researchers at NASA have worked on developing and validating jet noise prediction codes. One such class of codes, loosely called CFD-based or statistical methods, uses RANS CFD to predict jet mean and turbulent intensities in velocity and temperature. These flow quantities serve as the input to the acoustic source models and flow-sound interaction calculations that yield predictions of far-field jet noise. To develop this capability, a catalog of turbulent jet flows has been created with statistics ranging from mean velocity to space-time correlations of Reynolds stresses. The present document aims to document this catalog and to assess the accuracies of the data, e.g. establish uncertainties for the data. This paper covers the following five tasks: Document acquisition and processing procedures used to create the particle image velocimetry (PIV) datasets. Compare PIV data with hotwire and laser Doppler velocimetry (LDV) data published in the open literature. Compare different datasets acquired at roughly the same flow conditions to establish uncertainties. Create a consensus dataset for a range of hot jet flows, including uncertainty bands. Analyze this consensus dataset for self-consistency and compare jet characteristics to those of the open literature. One final objective fulfilled by this work was the demonstration of a universal scaling for the jet flow fields, at least within the region of interest to aeroacoustics. The potential core length and the spread rate of the half-velocity radius were used to collapse of the mean and turbulent velocity fields over the first 20 jet diameters in a highly satisfying manner.

Bridges, James↗