Centerline Velocity Decay Research Articles

Large-eddy simulation of variable-density round and plane jets

Large-eddy simulations (LES) of heated and cooled plane and round variable-density jets were conducted using a variety of density ratios s = ρ j / ρ co , which relates the jet nozzle density ρ j to the freestream density ρ co . The initial momentum flux was kept constant for better comparison of the resulting data. Both simulations confirm experimental results, in that the jet half-width grows linearly with streamwise coordinate x and the lighter jets decay much faster than the heavy ones. The centerline velocity decay is however different between the plane and round geometries. Whereas the round jets exhibits a decay with 1 / x for all density ratios s, there seem to be two self-similar scalings in plane jets, in the limit of small and large density ratios s. In the limit of small s or for incompressible flow, U c scales as U c ∼ 1 / x , for strongly heated jets on the other hand we find U c ∼ 1 / x . A mixed scaling is proposed and shown to work nicely for both small and large density ratios s. For the round jet simulations, on the other hand, scaling x and U c by s - 1 / 4 ( Chen and Rodi, 1980) collapses the round jet data. Furthermore, it is shown that the streamwise growth in the mean density or the decay of the velocity fluctuations in the quasi-self-similar region, is stronger for round jets. The round jet simulation with a density ratio of s = 0.14 is seen to develop under a global instability. To the author’s knowledge, this is the first LES of a globally unstable round jet at a density ratio of s = 0.14 . The frequency agrees excellently with experimental data and with the new scaling proposed by Hallberg and Strykowski (2006).

An Experimental and Analytical Investigation of Rectangular Synthetic Jets

In this paper the flow field of a rectangular synthetic jet driven by a piezoelectric membrane issuing into a quiescent environment is studied. The similarities exhibited by synthetic and continuous turbulent jets lead to the hypothesis that a rectangular synthetic jet within a limited region downstream of the orifice be modeled using similarity analysis just as a continuous planar jet. Accordingly, the jet is modeled using the classic two-dimensional solution to a continuous jet, where the virtual viscosity coefficient of the continuous turbulent jet is replaced with that measured for a synthetic jet. The virtual viscosity of the synthetic jet at a particular axial location is related to the spreading rate and velocity decay rate of the jet. Hot-wire anemometry is used to characterize the flow downstream of the orifice. The flow field of rectangular synthetic jets is thought to consist of four regions as distinguished by the centerline velocity decay. The regions are the developing, the quasi-two-dimensional, the transitional, and the axisymmetric regions. It is in the quasi-two-dimensional region that the planar model applies, and where indeed the jet exhibits self-similar behavior as distinguished by the collapse of the lateral time average velocity profiles when scaled. Furthermore, within this region the spanwise velocity profiles display a saddleback profile that is attributed to the secondary flow generated at the smaller edges of the rectangular orifice. The scaled spreading and decay rates are seen to increase with stroke ratio and be independent of Reynolds number. However, the geometry of the actuator is seen to additionally affect the external characteristics of the jet. The eddy viscosities of the synthetic jets under consideration are shown to be larger than equivalent continuous turbulent jets. This enhanced eddy viscosity is attributed to the additional mixing brought about by the introduction of the periodic vortical structures in synthetic jets and their ensuing break down and transition to turbulence. Further, a semi-empirical modeling approach is proposed, the final objective of which is to obtain a functional relationship between the parameters that describe the external flow field of the synthetic jet and the input operational parameters to the system.

Axisymmetric Synthetic Jets: An Experimental and Theoretical Examination

The flowfield of a round synthetic jet driven by a piezoelectric membrane issuing into a quiescent environment is studied in this paper. The self-similar behavior exhibited by both synthetic and continuous turbulent jets leads to the hypothesis that synthetic jetsmay bemodeled using similarity analysis, just as continuous turbulent jets aremodeled. Accordingly, synthetic jets are modeled using both the Schlichting solution to boundary-layer equations in cylindrical coordinates and the Landau–Squire solution to the Navier–Stokes equations in spherical coordinates, for which the virtual viscosity coefficient of a continuous turbulent jet is replaced with that measured for a synthetic jet. The virtual viscosity of the synthetic jet for bothmodels is obtained from the spreading rate and velocity decay rate of the jet. Hot-wire anemometry is used to characterize the flow downstream of the orifice. The flowfield is observed to consist of two regions, as distinguished by the centerline velocity decay: namely, a developing and adeveloped region. The developing region is characterized by a velocity increase followed by a plateau, for which the axial extent of this region scales with the stroke length L. The developed region is identified by the centerline velocity decaying as x , and it is within this region that the jet models are applicable. The velocity decay rate and spreading rate of synthetic jets are observed to increase with stroke ratio L=d, while being independent of the Reynolds number Re. This dependency on stroke ratio is attributed to the increase in impulse and energy of the emerging vortex rings as the stroke ratio increases and their subsequent enhanced interaction. The geometry of the actuator is additionally seen to impact the spreading and decay rates by means of influencing the initial conditions at the orifice. The experiments verify that byusing the adjusted value of the virtual viscosity, the theoreticalmodels of a continuous turbulent jetmay still be used to model a periodic synthetic jet. The virtual viscosity of the synthetic jets under test proves to be larger than that of equivalent turbulent continuous jet based on the same momentum flux. The enhanced viscosity is attributed to the additional momentum transfer and mixing brought about by the periodic introduction and breakdown of the vortex rings in synthetic jets.

Axial plus tangential entry swirling jet

This paper presents an experimental investigation on swirling jets with well-defined initial conditions. The axial, radial, and azimuthal velocity components, with their respective fluctuations were measured using high spatial–resolution particle image velocimetry. These detailed measurements allow the initial conditions of the swirling jets to be established and the jets to be characterized using various swirl number definitions. The significance of each term in the swirl number calculations are quantified, and the effect of the common assumptions and simplifications are examined. The characteristics of the jets in relation to the initial conditions are then investigated and compared with the previous studies using similar characterization parameters. Jets with Reynolds number of approximately 5700 and swirl conditions ranging from a non-swirling reference case to high swirl are studied. General properties of swirling jets such as higher spreading rate, higher centerline velocity decay, and higher turbulence level are observed. When the degree of swirl is sufficiently high, vortex breakdown occurs. A swirl number of 0.94 is recorded for a high swirl case prior to vortex breakdown, much higher than the critical swirl number reported in the literature. This behavior is attributed to the effect of the initial conditions on the swirl number calculation.

Experimental investigation of axisymmetric coaxial synthetic jets

Measurements were made in the near field of piston driven axisymmetric coaxial synthetic jets emanating from an orifice and a surrounding annulus of equal exit areas and cavity volumes. Piston velocity, amplitude, radial spacing between the orifice and the annulus, and exit angles had a strong influence on the dominant features of the flow. Flow visualization revealed three distinct topologies of the jet consisting of expanding, contracting and recirculating regions and doubling of the number of foci inside of the cavity compared to jet from the orifice alone. The direction of the swirl/rotation imposed on the mean flow was also dependent on the direction of the rotation of dominant foci. Interaction between flow from the orifice and the annulus amplified the azimuthal instability of ring vortices due to the periodic axial stretching and compression of the streamwise vortex filaments. Bifurcation of ring vortices into elliptical lobes reported earlier [S.V. Gaimella, V.P. Schroeder, Local heat transfer distributions in confined multiple air impingement, ASME Journal of Electronic Packaging 123 (3) (2001) 165–172] for single cavity jet was also observed in the coaxial jet. The number of cellular structures however was considerably larger than the single jet case. Large excursions of the jets from the plane of symmetry were observed. Power spectra exhibited sub-harmonic distribution of energy due to coalescence of the vortices. Growth of jet width and decay of centerline velocity were strongly influenced by the spacing and forcing frequency.

On the use of notched collars on an axisymmetric jet

This paper reports an experimental study conducted on the use of circular, V- and A-notched collars with the expansion-ratio of 3 for a Re = 20,000 axisymmetric jet by using hot-wire anemometry. Results show that limited specific differences in the centerline velocity decay and turbulent intensity levels arise from the use of notched collars. The overall flow field of the collared-jets and their self-excitation mechanisms are also not significantly influenced by modifications to the axial distance distribution of the collars, at least for the notch configurations used in the present study. Observations gathered in the present study suggest that altering the collar cross-sectional geometry, length and expansion-ratio remains to be more effective control techniques for collared-jets.

Velocity and concentration measurements in initial region of submerged round jets in stagnant environment and in coflow

Velocity and concentration fields are measured in submerged round jets in a stagnant environment and in coflow using laser Doppler anemometry and laser-induced fluorescence. Measurements are made in the initial region within distances of 40 jet exit diameter at jet Reynolds number between 1000 and 5000 and coflow-to-jet velocity ratio from 0 to 0.43. Different behaviors of jet spreading and dilution are found in jets at three different ranges of Reynolds number in which the jets are classified as initially laminar, transitional or turbulent. In the zone of established flow, the jet centerline velocity and concentration decay with downstream distance at different rates in the three groups of jets. For jets in coflow, axial development of normalized forms of centerline mean excess velocity and mean concentration at different velocity ratios can be reasonably well collapsed onto universal trends through the use of momentum length scale. Turbulence properties inside a jet are increased by the presence of a strong coflow. Inside the zone of flow establishment, some strange features are observed on jet turbulence properties. The length of zone of flow establishment increases from the turbulent jets, to the transition jets and to the laminar jets. The zone lengths for concentration are shorter than those for velocity by one to two jet exit diameters. Both lengths are shortened further in the presence of a coflow. For jets a stagnant environment and in the strong jet flow region of jets in coflow, jet widths increase linearly with downstream distance in transitional and turbulent jets. Self-similarity of radial profiles of mean velocity or excess velocity, mean concentration, turbulence intensities and concentration fluctuation level is explored in the zone of established flow.

NUMERICAL SIMULATION ON FLAPPING MOTION OF SUBMERGED PLANE WATER JETS

Based on volume of fluid (VOF) technique, the flapping motion of submerged turbulent plane jet in shallow water impinging vertically onto the free water surface was simulated. To study further on the flapping motion, the power spectrum density, the centerline velocity decay, as well as the mean velocity profiles of the jet were all investigated in this paper. The results are in great agreement with those of theoretical analyses, and the results show that the flapping motion is a new flow pattern of submerged turbulent plane jets.

Aerodynamics of an isolated slot-burner from a tangentially-fired boiler

The aerodynamic development of fully turbulent isothermal jets issuing from rectangular slot-burners was modelled by obtaining a solution to the Reynolds averaged Navier–Stokes equations. A finite-volume method was used with the standard k–ε, RNG k–ε and Reynolds stress turbulence models. The slot-burners were based on physical models, which were designed to be representative of typical burner geometries found in tangentially-fired coal boilers. Two cases were investigated, in which jets from three vertically stacked rectangular nozzles discharged at 90° and then 60° to the wall containing the burner. The nozzle angle had little effect on jet centreline velocity decay, with the 60° nozzle showing a marginally higher rate of decay. The jets from the 60° nozzles were found to deviate slightly from their geometric axis slightly due to internal pressure redistribution in the flow at the nozzles. The simulations were validated against the physical models and were found to reproduce the flow field of the jets accurately with the Reynolds stress model producing the best results.

Improved noise predictions from subsonic jets at Mach 0.75 using URANS calculations

Numerical simulations of round, compressible, turbulent jets at Mach 0.75 have been carried out. Two jets, one cold and hot, have been simulated. Overall Sound Pressure Levels (SPL) at far-field observer locations have been calculated using Ffowcs Williams-Hawkings equation. Axial and radial variation of the mean axial velocity, axial variation of u′u′½, v′v′½, radial variation of u′v′ and overall SPL levels are compared with experimental data reported in the literature. The potential core length is predicted well, but the predicted centreline velocity decay is faster than the measured value. The URANS calculations are able to predict the absolute values for the overall SPL, and the trends to within ±4dB of the experimental value for most of the receivers. The calculations predict the trends as well as absolute values of the variations of the spectral amplitude for receivers at 30Dj but not 50Dj.

Numerical predictions of noise due to subsonic jets from nozzles with and without chevrons

Numerical simulations of round, compressible, turbulent jets using the Shear Stress Transport (SST k– ω) model have been carried out. The three-dimensional calculations have been done on a tetrahedral mesh with 0.9 million cells. Two jets, one cold and hot, have been simulated. The Mach number for both the cases is 0.75. Overall sound pressure levels (SPL) at far-field observer locations have been calculated using Ffowcs Williams–Hawkings equation. The numerical predictions have been compared with experimental results available in the literature. Axial and radial variation of the mean axial velocity, axial variation of u ′ u ′ ¯ 1 / 2 , v ′ v ′ ¯ 1 / 2 , radial variation of u ′ v ′ ¯ and overall SPL levels are compared. The potential core length is predicted well, but the predicted centerline velocity decay is faster than the measured value. The URANS calculations are not able to predict the absolute values for the overall SPL, but predict the trends reasonably well. The calculations predict the trends and absolute values of the variations of the spectral amplitude well for the aft receivers, but not for the forward receivers. Effect of chevrons on the noise from the jet is also investigated for cold and hot jets. In each case, two chevron taper angles, namely, 0° and 5° are considered. The latter nozzle produces the most significant modification to the baseline spectra and is less effective at high frequencies in abating the noise. The present calculations predict a reduction in the overall SPL for the chevron nozzle with 0° taper angle and a slight increase for chevron nozzle with 5° taper angle, for both cold and hot jets.

Numerical Simulation of Turbulent Jets

In this study, plane and circular turbulent non-buoyant jets are simulated numerically using a three-dimensional computational model. The aim of the study is to evaluate the accuracy of turbulent closure schemes employed in three-dimensional models. In particular, standard k–ε and renormalized group k–ε schemes with standard coefficients are evaluated. The modeled jets are deeply submerged, that is the impact of free surface and solid boundaries on jets are eliminated. The accuracy of the turbulent schemes is assessed by analyzing the decay of centerline velocity, jet growth rates, similarity of longitudinal and vertical velocity profiles, and turbulent kinetic energy profiles. The results from the two turbulent closure schemes are compared with accepted experimental and theoretical studies to determine their accuracy. It is found that the k—ε scheme with standard coefficient performs equally well and in some cases better than the renormalized group k—ε scheme. Finally, the model is applied to analyze flow pattern in the Sampit River, South Caroline, USA, resulting from stormwater discharge in a recreational area. Various inlet designs are investigated and box inlet is found to provide a practical means of localizing high surface currents.

Simultaneous velocity and passive scalar concentration measurements in low Reynolds number neutrally buoyant turbulent round jets

Velocity and scalar concentration characteristics of low Reynolds number (Re) neutrally buoyant turbulent round jets were studied using coupled particle image velocimetry and laser induced fluorescence. Experiments were conducted on a jet with a fully developed pipe exit profile at Re = 1,500 and Re = 4,000. Measurements were made in the far field (60 < x/D < 80). Results show that the centerline velocity decay constant increases with Re and the virtual origin is located far from the jet exit. The Re does not have such an influence on the scalar concentration decay constant and scalar field virtual origin. Centerline turbulent intensities show evidence of becoming self-similar past x/D ≈ 75 but the same is not observed in the scalar fluctuations. The latter are strongly influenced by the Re, increasing as entrainment of ambient flow on the jet axis increases as the flow approaches laminar conditions. Scalar fluxes showed a marked Re dependence as well. Results were used to estimate the turbulent Schmidt number which decreases as the Re decreases.

Numerical Modeling of a Round Jet Discharged into Random Waves

Coastal disposal of waste water can be idealized as the problem of a jet under random waves. Understanding of this phenomenon is important for engineering design and environmental impact assessment. The present study aims to simulate such phenomenon by using a 3D numerical model based on the solution of the spatially filtered and σ-transformed Navier–Stokes equations with dynamic sub-grid scale model of turbulence. The numerical solution procedures are split into three steps: advection, diffusion and pressure propagation, and a Lagrange–Euler method is used to track the free surface. Cases of vertical jet in stagnant water, pure random waves and vertical jet in random waves are simulated with the same grid system for comparative study. Different methods of generating jet inflow turbulence have been tested and the method of jet azimuthal modes is found to be the optimum. The numerical results reproduce the distinct characteristics of jet in waves, including faster decay of centerline velocity, wider lateral spreading and the occurrence of wave tractive mechanism.

Effects of noncircular collars on an axisymmetric jet

An experimental investigation was carried out to study the effects of noncircular collars on an axisymmetric jet using surface flow visualization and hot-wire anemometry. Circular, square, and triangular collars with expansion ratios of 1.20, 1.35, and 1.54, respectively, with collar lengths of up to two jet diameters were used. Flow visualization shows that circular collars led to equidistant flow reattachments along the collar wall, while square and triangular collars resulted in the formation of a pair of counter-rotating vortex-pairs on each side of the collar wall. These vortex-pairs are caused by the presence of the three-dimensional velocity gradients between locations of minimum and maximum step-heights, which drove fluid from the collar wall centerlines towards the corners. Time-averaged velocity measurements show that the circular collar required the shortest collar length to achieve maximum centerline velocity decay, followed by square and triangular collars. Centerline turbulence intensity and velocity spectra results reveal that all three collars were able to suppress vortex-pairing events when they were sufficiently long with the triangular collar being the most effective. Furthermore, the triangular collar also produces the widest overall jet-spread, ahead of square and circular collars, respectively, even though it demonstrates significantly different jet-spreads along planes of minimum and maximum step-height. Self-excitation frequencies from all three collars could be distinguished into distinct frequency bands with changes in the collar lengths. Within each band, the circular collar results in the largest variation of excitation frequency over the square and triangular collars, respectively. Lastly, square and triangular collars require wider ranges of collar lengths for each of the frequency bands, as compared to the circular collar.

Active control of high-speed and high-Reynolds-number jets using plasma actuators

Localized arc filament plasma actuators are used to control an axisymmetric Mach 1.3 ideally expanded jet of 2.54 cm exit diameter and a Reynolds number based on the nozzle exit diameter of about 1.1×106. Measurements of growth and decay of perturbations seeded in the flow by the actuators, laser-based planar flow visualizations, and particle imaging velocimetry measurements are used to evaluate the effects of control. Eight actuators distributed azimuthally inside the nozzle, approximately 1 mm upstream of the nozzle exit, are used to force various azimuthal modes over a large frequency range (StDF of 0.13 to 1.3). The jet responded to the forcing over the entire range of frequencies, but the response was optimum (in terms of the development of large coherent structures and mixing enhancement) around the jet preferred Strouhal number of 0.33 (f = 5 kHz), in good agreement with the results in the literature for low-speed and low-Reynolds-number jets. The jet (with a thin boundary layer, D/θ ∼ 250) also responded to forcing with various azimuthal modes (m = 0 to 3 and m = ±1, ±2, ±4), again in agreement with instability analysis and experimental results in the literature for low-speed and low-Reynolds-number jets. Forcing the jet with the azimuthal mode m = ±1 at the jet preferred-mode frequency provided the maximum mixing enhancement, with a significant reduction in the jet potential core length and a significant increase in the jet centreline velocity decay rate beyond the end of the potential core.

Linear and nonlinear model large-eddy simulations of a plane jet

The mixed-nonlinear Kosović, Leray and LANS- α subgrid scale models are contrasted with linear Smagorinsky and Yoshizawa large-eddy simulations for a Re = 4000 plane jet simulation. Comparisons are made with direct numerical simulation data and reliable measurements. Global properties of the jet such as the spreading and centerline velocity decay rates are investigated. The mean-flow and turbulence parameters in the self-similar region are also studied. Mixed models developed for boundary layers compare well with the benchmark jet data and the linear model predictions. Differences between the models are minor and none showed any clear advantage in all the data comparisons.

PIV measurements of a turbulent jet issuing from round sharp-edged plate

An experimental investigation is presented of a turbulent jet issuing from a round sharp-edged orifice plate (OP) into effectively unbounded surroundings. Planar measurements of velocity were conducted using Particle Image Velocimetry (PIV) in the near and transition regions. The Reynolds number, based on the jet initial diameter and velocity, is approximately 72,000. The instantaneous and mean velocities, Reynolds normal and shear stresses were obtained. The centerline velocity decay and the half-velocity radius were derived from the mean velocity. It is revealed that primary coherent structures occur in the near field of the OP jet and that they are typically distributed asymmetrically with respect to the nozzle axis. Comparison of the present PIV and previous hot-wire measurements for the OP jet suggests that high initial turbulence intensity leads to reduced rates of decay and spread of the mean flow field and moreover a lower rate of variation of the turbulence intensity. Results also show that self-similarity of the mean flow is well established from the transition region while the turbulent statistics are far from self-similar within the measured range to 16 diameters.

Scale model study of airflow performance in a ceiling slot-ventilated enclosure: Non-isothermal condition

Scale-model study of a non-isothermal ceiling slot-ventilated enclosure was investigated in both airspeed and thermal fields. Results of airflow pattern, centerline velocity and centerline temperature decay, velocity and temperature profile, airflow boundary layer and thermal boundary layer growth, floor velocity, and floor temperature difference were analyzed to establish semi-empirical prediction equations. Results also compared with previous researches to validate the physical behavior of air-jet. Data of centerline velocity decay showed similar airflow characteristics as isothermal air-jet with Archimedes number ( Ar ) < 0.004 , which performed as pseudo-isothermal airflow. Air-jet fell on entry with Ar > 0.018 . A single circulation airflow existed at 0.004 < Ar < 0.011 and two-circulation airflow occurred at 0.011 < Ar < 0.018 . The centerline velocity decay was fitted well as similar form of an isothermal condition. The centerline temperature decay was fitted well as the form of centerline velocity decay in both ceiling and floor regions. Both the velocity and temperature profiles agreed with results obtained from literature. Both airflow boundary layer and thermal boundary layer growths increased with traveling distance of air-jet. Maximum floor velocity and floor temperature difference were fitted well with different parameters. Analysis of airflow performance in a non-isothermal condition makes progress in predicting air quality inside the enclosures and guides the design concepts of ventilation system for an indoor environment.

Effects of cross-stream radial injections on a round jet

An experimental study has been carried out to investigate cross-stream radial injections into a round jet using laser-induced fluorescence technique and a hot-wire anemometry. The aim is to study the fundamental interaction behavior and resultant flow structures caused by the presence of the radial injections. Flow visualization results show that radial injections lead to enhanced shear layer perturbations and instabilities, as well as improved transition to turbulence. For each radial injection, a counter-rotating vortex pair (CVP) is formed which aligns in the streamwise direction shortly after its inception and penetrates the round jet core progressively downstream. Their presence along the round jet peripheral region affects the jet cross-section shape and influences the jet width, depending on their exact locations. The quasi-steady nature of the CVP was investigated and deduced to be an effect of the transverse orientation of the injection. The formation of recursive flow structures imparted flow oscillations which accounted for the quasi-steadiness as well as other observed secondary flow structures. Hot-wire measurements showed that radial injections enhance centerline velocity decay and turbulence levels, effective up to fifty jet diameters downstream. Also, half-jet-width comparisons between measurements taken along injection planes and non-injection planes confirmed that jet-width alterations are possible across an appreciable range of Reynolds number with an appropriate positioning of the radial injection ports.