Transient positively and negatively buoyant turbulent round jets

 The transient character of the jet issuing from an upward nozzle centered at the bottom of a vertical cylindrical tank into bulk liquid of a different density was measured using flow visualization and PIV for varying densimetric Froude numbers by varying the jet Reynolds numbers and the ratios of fluid densities. Positively buoyant jets penetrate to the free surface, driven by both momentum and buoyancy in the upward direction. The lighter jet fluid stratifies in a layer above the bulk liquid. Upon starting, a negatively buoyant jet has three stages. First the jet penetrates to its maximum height in the tank. Then the jet penetration decreases due to the downward backflow of heavier fluid surrounding the jet, which reduces the jet’s upward momentum. Finally the jet penetration height fluctuates around a mean value about 70% the maximum height of penetration. For small negative Froude numbers, the flow is fountain-like. The downward flow turns radially outward as it reaches the bottom of the tank and eventually an annular recirculation zone forms at the bottom of the tank with vortical motion opposite the vorticity of the jet. For large negative Froude numbers, the spreading of the jet extends far enough so the annular downward flow is along the walls of the tank resulting in a large annular recirculation zone. The penetration depth, h, and time, t, scale with buoyancy flux, F, and the jet momentum flux, M, as hM ^-3/4∣F∣^1/2 and t∣F∣/M to collapse the transient jet penetration height data onto a single curve over a wide range of Froude numbers for either positively or negatively buoyant jets. Received: 8 June 1998/Accepted: 3 February 1999     

Computational study of buoyancy effects in a laminar starting jet

Vortical structures formed in evolving jets are important in applications such as fuel injection in diesel engines and fuel leaks. When the jet fluid is different from the ambient fluid, the buoyancy can play an important role in determining the jet flow structure, and hence, the entrainment and fluid mixing processes. In the present study, a jet of helium injected in air is investigated, with emphasis placed on delineating the buoyancy effects on vector–scalar fields during the starting phase. We utilize a computational model, previously validated to predict the flow field of low-density gas jets. The model incorporates finite volume approach to solve the transport equation of helium mass fraction coupled with conservation equations of mixture mass and momentum. Computations were performed for a laminar jet to characterize the advancing jet front, and to capture the formation and propagation of vortex rings and the related pinch-off process. Results show significant effects of buoyancy on jet advancement, as well as on vorticity and helium concentration in the core of the vortex rings.     

Buoyancy effects on turbulent swirling flows

A three-parameter model of turbulence applicable to free boundary layers has been developed and applied for the prediction of axisymmetric turbulent swirling flows in uniform and stagnant surroundings under the action of buoyancy forces. The turbulent momentum and heat fluxes appearing in the time-averaged equations for the mean motion have been determined from algebraic expressions, derived by neglecting the convection and diffusion terms in the differential transport equations for these quantities, which relate the turbulent fluxes to the kinetic energy of turbulence, k, the dissipation length scale of turbulence, L, and the temperature covariance, T ′². Differential transport equations have been used to determine these latter quantities. The governing equations have been solved using fully implicit finite difference schemes. The turbulence model is capable of reproducing the gross features of pure jet flows, buoyant flows and swirling flows for weak and moderate swirl. The behaviour of a turbulent buoyant swirling jet has been found to depend solely on exit swirl and Froude numbers. The predicted results indicate that the incorporation of buoyancy can cause significant changes in the behaviour of a swirling jet, particularly when the buoyancy strength is high. The jet exhibits similarity behaviour in the initial region for weak swirl and weak buoyancy strengths only, and the asymptotic case of a swirling jet under the action of buoyancy forces is a pure plume in the far field. The predicted results have been found to be in satisfactory agreement with the available experimental data and in good qualitative agreement with other predicted results.     

ROUNDED FLOWING STATES OF OBSTRUCTED BUOYANT JET

The mutual relationships of three effective factors, the diameter D/d (d is the diameter of exit) of obstructed plate, exit densimetric Froude number and the distance H/d of the plate from jet orifice for obstructed buoyant jet in static ambient, are analyzed to explain normal and abnormal rounded flowing (reverberated and bifurcated flowing). The critical Froude numbers for obstructed buoyant jets with H/d=2, 4, 6, 8 which distinguished normal and abnormal flowing pattern are obtained. Normal rounded flowing is found only for a plate under a special value of H/d. A fitted formula of critical Froude numbers with H/d and D/d is presented to distinguish rounded flowing types. The occurring of reverberated or bifurcated flowing in abnormal rounded flow is analyzed. Based on the results of obstructed buoyant jets with D/d=1, normal rounded flowing occurred only for all conditions and axial dilution behind the plate under different H/D is obtained.     

Round gas jets submerged in water

Water submerged gas jets are characterized by the interplay of inertia and buoyancy forces and can exhibit diverse behaviors ranging from bubbly plumes to stable jets. In this work, direct measurements of the interfacial behavior of water-submerged gas jets, with Mach numbers ranging from subsonic to supersonic, were performed using high-speed digital photography and shadowgraphs. The results indicate that the jets have a preferential pinch-off position that can be attributed and correspond to the location of the maximum streamwise-velocity turbulence fluctuations. A new, experimentally determined jet penetration distance is proposed; the jetting length is taken as the jet length corresponding to a 99% probability of the gas-jet outer boundary being attached to the orifice during the sampling period. Using the shadowgraph analysis and this criterion, we determined that the electro-resistivity probe measurements, previously used to determine the jet penetration length, may be significantly biased. This is attributed to the inability of the probe measurements to distinguish between a continuous gas jet and advecting bubbles. In addition, based on a simple force-balance of the jet cross-section, we introduce a new scaling relationship for the jet penetration distance. This relationship shows that the jetting length scales with the square of the Froude number and compares well with the experimental observations. Finally, measurements of the gas jet boundary acceleration coupled with estimations of the internal gas jet velocity suggest that both Rayleigh–Taylor and Kelvin–Helmholtz mechanisms are nearly equally responsible for governing the jet boundary dynamics.     

Color schlieren deflectometry study of jet mixing: effect of buoyancy and perforation

Mixing of jets is crucial for optimal performance of many industrial applications and there is a need to optimize both nozzle geometry and flow conditions. The present study reports the influence of buoyancy and perforation on mixing between a jet and its environment. Optical techniques are ideal for the study of jet mixing due to their non-intrusive and inertia free properties. The present study gives an account of mixing between helium jet and the ambient fluid using a combination of color schlieren deflectometry and radial tomographic mathematics. Four different perforation sizes have been used and the experiments are performed for Reynolds numbers 21–676 and Richardson numbers 3.27–0.0015. Color schlieren images show distinct influence of perforation and flow conditions (Richardson number). Oxygen concentration and jet width quantify effectiveness of jet mixing. Buoyancy plays an important role in mixing at high Richardson number. Perforation improves jet mixing i.e. there is about 120% increase in jet width and the size of perforation plays an important role.     

Concentration measurements in a self-excited jet

The near field of helium-air jets exhausting into an air environment has been experimentally investigated using an aspiration probe and flow visualization. Jets with varying density ratios and Reynolds numbers were studied. Pure helium jets with density ratios of 0.14 were found to display a self-excited behavior characterized by intense mixing. The centerline concentration decay was found to be substantially increased for the self-excited jet. Flow visualization revealed the expulsion of side jets from the potential core region of low density jets. Radial profiles of concentration provide additional evidence that side-jets produce vigorous mixing.     

Axisymmetric large eddy simulation of a circular source of buoyancy

Axisymmetric large-eddy simulations (LES) of published experiments on vertical mixing above a circular source of buoyancy are performed. Numerical results confirm the existence of a mixing boundary layer just above the buoyancy source (freshwater injected into saline water). As experiments suggested, the calculated normalized shape of the boundary layer seems independent of source size, freshwater injection rate and background solute concentration. This validates a restrictive but numerically efficient assumption of axisymmetric turbulence for the LES calculations. It also lends additional credibility to the theoretical boundary-layer analysis of Epstein and Burelbach [Epstein, M., Burelbach, J.P., 2001. Vertical mixing above a steady circular source of buoyancy. Int. J. Heat Mass Trans. 44, 525–536], even at marginally high Froude numbers.     

Effectiveness of secondary tabs for supersonic mixing

The effect of vortex generators, in the form of small tabs projecting into the flow at the nozzle exit, aided by secondary tabs on either side, on the mixing characteristics of an axisymmetric jet at Mach number 1.7 is investigated. Experimental studies on the basic features of the jet from a nozzle with secondary tabs are conducted to assess the free jet characteristics as well as the momentum and thermal mixing behavior. The secondary tabs were found to increase the jet spread and distort the jet cross-section and were found to cause substantial enhancement of mixing of supersonic jets. Jet structure is observed using flow-visualization techniques. LLS images are employed to obtain cross-sectional views of the jet with the introduction of secondary tabs. The ability of secondary tabs to eliminate the screech noise of the supersonic jet is also observed. Received: 3 February 2000/Accepted: 8 February 2001     

Behavior of near-field dilution of thermal buoyant jet discharged horizontally in compound open-channel

The RNG κ-ε model considering the buoyancy effect, which is solved by the hybrid finite analytic method, is used to simulate the mixture of the horizontal round thermal buoyant jet in compound open channel flow. The mixing features near the spout and flowing characteristic of the secondary currents are studied by numerical simulation. Meanwhile, （1） the distribution of the measured isovels for stream-wise velocity, （2） secondary currents, （3） the distribution of the measured isovels for temperature of typical cross-section near the spout, were obtained by the three-dimensional Micro ADV and the temperature measuring device. Compared with experimental data, the RNG κ-ε model based on buoyancy effect can preferably simulate the jet which performs the bifurcation phenomenon, jet reattachment （Conada effect） and beach secondary currents phenomenon with the effect of ambient flow, buoyancy, and secondary currents of compound section and so on.     

Numerical simulations of negatively buoyant jets in an immiscible fluid using the Particle Finite Element Method

Negatively buoyant jets consist in a dense fluid injected vertically upward into a lighter ambient fluid. The numerical simulation of this kind of buoyancy‐driven flows is challenging as it involves multiple fluids with different physical properties. In the case of immiscible fluids, it requires, in addition, to track the motion of the interface between fluids and accurately represent the discontinuities of the flow variables. In this paper, we investigate numerically the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid using the Particle Finite Element Method and compare the two‐dimensional numerical results with experiments on the injection of a jet of dyed water through a nozzle in the base of a cylindrical tank containing rapeseed oil. In both simulations and experiments, the fountain inlet flow velocity and nozzle diameter have been varied to cover a wide range of Froude Fr and Reynolds Re numbers ( 0.1 < Fr < 30, 8 < Re < 1350), reproducing both weak and strong laminar fountains. The flow behaviors observed for the different numerical simulations fit in the regime map based on the Re and Fr values of the experiments, and the maximum fountain height is in good agreement with the experimental observations, suggesting that particle finite element method is a useful tool for the study of immiscible two‐fluid systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of the coflow stream on a plane wall jet

We propose in this work to study an isothermal and a non-isothermal laminar plane wall jet emerging in a coflow steam. The numerical solution of the governing equations was performed by a finite difference method. In this work, we are interested in the study of the influence of Grashof numbers on the wall jet emerging in a medium at rest. Further, we will examine the effect of the coflow stream on the behavior of the dynamic and thermal properties of the wall jet subjected to a constant temperature. A comparison with a simple wall jet is carried out. The results show that for a buoyant wall jet, two parameters can influence the flow: the inertial and buoyancy forces. The velocity effect indicates that the potential core length increases with the velocity ratio. We are also showed that when using a momentum length scale, the normalized longitudinal maximum velocity can reach an asymptotic curve at different velocity ratios.     

Direct Numerical Simulation of Transitional Noncircular Buoyant Reactive Jets

The near field dynamics of transitional buoyant reactive jets established on noncircular geometries, including a rectangular nozzle with an aspect ratio of 2:1 and a square nozzle with the same cross-sectional area, are investigated by three-dimensional spatial direct numerical simulations. Without applying external perturbations at the inflow boundary, large vortical structures develop naturally in the flow field due to buoyancy effects. Simulation results and analysis describe the details and clarify mechanisms of vortex dynamics of the noncircular buoyant reactive jets. The interaction between density gradients and gravity initiates the flow vorticity. Among the major vorticity transport terms, the gravitational term mainly promotes flow vorticity in the cross-streamwise direction. For the baroclinic torque, it can either create or destroy flow vorticity depending on the local flow structure. The vortex stretching term has different effects on the streamwise and cross-streamwise vorticity. Streamwise vorticity is mainly created by vortex stretching, while this term can either create or destroy cross-streamwise vorticity. Under the coupling effects of buoyancy and noncircular nozzle geometry, three-dimensional vortex interactions lead to the transitional behavior of the reactive jets. Simulations also show that the rectangular jet is more vortical than the square jet. The rectangular jet has a stronger tendency of transition to turbulence at the downstream due to the aspect ratio effect. Mean flow property calculations show that the rectangular buoyant reactive jet has a higher entrainment rate than its square counterpart. Received 13 December 2000 and accepted 24 July 2001     

An effect of a horizontal buoyant jet on the temperature distribution inside a hot water storage tank

The hot water storage tank (for stratified thermal storage) with a heat pump draws a lot of attention nowadays due to its high performance. In Japan, reheating of the bath is commonly used, and as this mode, the jet injects horizontally at the middle of the tank, so the temperature distribution of the tank changes complexly with time. Hence a model is needed to simulate this phenomenon, precisely. Additionally, in the process of designing a hot water storage system, it is necessary to simulate temperature distribution quickly, since a test run itself is a time consuming process.In this study, visualization experiments were performed using tracer particles and thermo-sensitive liquid crystals. Experiments were also carried out to find the unsteady temperature distribution in a tank when the positively or negatively buoyant jet was injected horizontally in the middle of the tank whose size is limited and has an influence from the opposite wall.If the momentum effect of the buoyant jet is stronger than that of buoyancy, the buoyant jet impinge against the opposite wall of the tank, and a vortex was observed near the opposite wall. Empirical formulas were proposed to predict the height of the vortex “Z_b” under various conditions, such as the momentum and the buoyancy of the buoyant jet, and the Prandtl number of the tank water. Furthermore, the 3D-CFD was carried out to supplement the 3D behavior of the inner tank fluid.A one dimensional model, “uniformly distributed injection model”, for simulating temperature distribution was proposed. The performance of the model was verified by comparing the results with the unsteady temperature distribution obtained experimentally. The model was also compared with the measurements obtained using a commercially available hot water storage system. Both results showed good agreements. Hence adequacy of the model was clarified.     

Visualization of coherent structure in scalar fields of unsteady jet flows with interferometric tomography and proper orthogonal decomposition

Proper orthogonal decomposition (POD) is a method of examining spatial coherence in unsteady flow fields from an ensemble of multidimensional measurements. When applied to experimental data, the proper orthogonal decomposition is generally restricted to data sets with low spatial resolution. This is because of the inherent difficulties in generating an ensemble of measurements that contain a large number of data points. In this paper, a system for obtaining a large ensemble of three-dimensional scalar measurements using interferometric tomography is presented. The proper orthogonal decomposition is applied in three spatial dimensions to experimental data of two jet-like flows. The coherent structure present in the near field of a neutrally buoyant, helium–argon jet and the far field of a buoyant helium jet into air is visualized. The POD results of the helium–argon jet clearly reveal the breakdown region of a sequence of vortex rings and a large-scale flapping motion in the jet far field. The POD of the buoyant helium jet shows a number of competing modes with varying degrees of helicity. Received: 14 January 2000/Accepted: 26 September 2000     

An experimental study of vertical turbulent jet with negative buoyancy

A jet discharged upward into an ambient of higher temperature than that of the jet fluid was investigated experimentally. The width of the upflow spread linearly to the distance from the nozzle exit, whereas the width of the whole jet was almost constant. The height of top of jet varied in proportion to the square root of the discharge Froude number. The time-averaged velocities and temperatures as well as the intensities of their fluctuations at the jet axis were well correlated with the same scaling law as that used for the buoyant jet. The radial distributions showed no similarity profiles for the timeaveraged velocities and temperatures, and the intensities of their fluctuations.     

Modelling and experimental investigation of horizontal buoyant gas jets injected into stagnant uniform ambient liquid

In this article, an experimental and theoretical study on the buoyant non-condensable gas jet that is injected horizontally into a high-density liquid ambient at different initial conditions is performed. Direct and instantaneous global measurements of the interface were performed using a high-speed photography. The position and motion of the entire gas jet were captured by a high-velocity camera and the images were processed, averaged and analyzed to extract the jet parameters and interface position. In the mathematical model, the rate of entrainment is assumed to be a function of the jet centerline velocity, the ratio of the mean jet and the ambient densities, while the entrainment coefficient depends on the local Froude number at the jet region. An interfacial shear stress acting at the interface between the jet flow and the water ambient in the opposed direction to the main jet momentum flux is considered. The results showed that the model is able to accurately predict the jet parameters: trajectory, spread, jet angles and penetration lengths as well as the jet regimes. An overall good agreement was obtained between the simulation and experimental results over a large range of Froude numbers and jet diameters. The developed model has proven to be an adequate tool to predict the different jet parameters.     

Characteristics of Sonic Jets with Tabs

The results of an experimental investigation on the effect of a vortex generator in the form of a mechanical tab placed at the nozzle exit on the evolution of jet and its decay are reported in this paper. Jets from a sonic nozzle with and without tabs operated at nozzle pressure ratios from 2 to 7 were studied. Tabs with two combinations of length-to-width ratio were investigated by keeping the blockage area constant. The tabs offered a blockage of 10.18% of the nozzle exit area. The centerline pitot pressure decay shows that for the tabbed jet a maximum core reduction of about 75% can be achieved at a nozzle pressure ratio (NPR) 7 compared to an uncontrolled jet. The shadowgraph pictures show that the tabs drastically weaken the shock structure in the jet core and disperse the supersonic zone of the flow making them occupy a greater zone of the flow field compared to the plain nozzle. This causes the waves to become weaker and the jet to spread faster. The tabs are found to shed counter-rotating vortices all along the edges, resulting in enhanced mixing. Isobaric contours reveal that the streamwise vortices cause an inward indentation of the entrained mass into the jet core and an outward ejection of core flow. To understand the distortion introduced by tabs on the jet cross-section and its growth leading to bifurcation of the jet, a surface coating visualization method was developed and employed.     

Buoyancy effects on flow transition in low-density inertial gas jets

Effects of buoyancy on transition from laminar to turbulent flow are presented for a momentum-dominated helium jet injected into ambient air. The buoyancy was varied in a 2.2 s drop tower facility without affecting the remaining operating parameters. The jet flow in Earth gravity and microgravity was visualized using the rainbow schlieren deflectometry apparatus. Results show significant changes in the flow structure and transition behavior with change of buoyancy.     

Control of diffuser jet flow: turbulent kinetic energy and jet spreading enhancements assisted by a non-thermal plasma discharge

An axisymmetric air jet exhausting from a 22-degree-angle diffuser is investigated experimentally by particle image velocimetry (PIV) and stereo-PIV measurements. Two opposite dielectric barrier discharge (DBD) actuators are placed along the lips of the diffuser in order to force the mixing by a co-flow actuation. The electrohydrodynamic forces generated by both actuators modify and excite the turbulent shear layer at the diffuser jet exit. Primary air jet velocities from 10 to 40 m/s are studied (Reynolds numbers ranging from 3.2 to 12.8 × 10⁴), and baseline and forced flows are compared by analysing streamwise and cross-stream PIV fields. The mixing enhancement in the near field region is characterized by the potential core length, the centreline turbulent kinetic energy (TKE), the integrated value of the TKE over various slices along the jet, the turbulent Reynolds stresses and the vorticity fields. The time-averaged fields demonstrate that an effective increase in mixing is achieved by a forced flow reattachment along the wall of the diffuser at 10 m/s, whereas mixing enhancement is realized by excitation of the coherent structures for a primary velocity of 20 and 30 m/s. The actuation introduces two pairs of contra-rotating vortices above each actuator. These structures entrain the higher speed core fluid toward the ambient air. Unsteady actuations over Strouhal numbers ranging from 0.08 to 1 are also studied. The results suggest that the excitation at a Strouhal number around 0.3 is more effective to enhance the turbulence kinetic energy in the near-field region for primary jet velocity up to 30 m/s.