Two-dimensional Turbulent Jet Research Articles

Two-Dimensional Turbulent Thermal Free Jet: Conservation Laws, Associated Lie Symmetry and Invariant Solutions

The two-dimensional turbulent thermal free jet is formulated in the boundary layer approximation using the Reynolds averaged momentum balance equation and the averaged energy balance equation. The turbulence is described by Prandtl’s mixing length model for the eddy viscosity νT with mixing length l and eddy thermal conductivity κT with mixing length lθ. Since νT and κT are proportional to the mean velocity gradient the momentum and thermal boundaries of the flow coincide. The conservation laws for the system of two partial differential equations for the stream function of the mean flow and the mean temperature difference are derived using the multiplier method. Two conserved vectors are obtained. The conserved quantities for the mean momentum and mean heat fluxes are derived. The Lie point symmetry associated with the two conserved vectors is derived and used to perform the reduction of the partial differential equations to a system of ordinary differential equations. It is found that the mixing lengths l and lθ are proportional. A turbulent thermal jet with νT≠0 and κT≠0 but vanishing kinematic viscosity ν and thermal conductivity κ is studied. Prandtl’s hypothesis that the mixing length is proportional to the width of the jet is made to complete the system of equations. An analytical solution is derived. The boundary of the jet is determined with the aid of a conserved quantity and found to be finite. Analytical solutions are derived and plotted for the streamlines of the mean flow and the lines of constant mean thermal difference. The solution differs from the analytical solution obtained in the limit ν→0 and κ→0 without making the Prandtl’s hypothesis. For ν≠0 and κ≠0 a numerical solution is derived using a shooting method with the two conserved quantities as targets instead of boundary conditions. The numerical solution is verified by comparing it to the analytical solution when ν→0 and κ→0. Because of the limitations imposed by the accuracy of any numerical method the numerical solution could not reliably determine if the jet is unbounded when ν≠0 and κ≠0 but for large distance from the centre line, ν>νT and κ>κT and the jet behaves increasingly like a laminar jet which is unbounded. The streamlines of the mean flow and the lines of constant mean temperature difference are plotted for ν=0 and κ=0.

Simulation of the flow field and scour evolution by turbulent wall jets under a sluice gate

This numerical study of scour process tested the skills of computational fluid dynamics in modeling the unsteady flow field during the scour development stage by two-dimensional turbulent wall jets under a sluice gate. The modeling was found to well describe the experimentally observed flow patterns, that is, the main jet diverged to a returning jet and a tail jet. The model also correctly predicts the evolution of the scour depth and length. We examined the self-similarity of the profiles of scour bed and overlying velocities throughout the entire scour development and equilibrium stages. We found self-preserved profiles of velocities and scour beds using local jet parameters. Four growth curves were compared in describing the temporal evolution of scour depth. Finally, non-dimensional scaling of the equilibrium maximal scour depth was investigated. We used the theory of wall jet, and suggested that a modified jet Froude number can be used to predict the equilibrium scour depth, which accounts for the attenuation of the jet velocities along the apron.

Numerical simulation of reynolds number effect of a free incompressible isothermal turbulent coaxial jet

This paper studies the effect of Reynolds number on a two-dimensional free incompressible isothermal coaxial turbulent jet over a range of high Reynolds numbers. This is necessary because of its application in noise control and mixing. The Reynolds numbers at the nozzle exit were 9824, 19648, 29472, 39296 and 49120. The models were designed in ANSYS Design Modeler and the numerical simulation was done using a finite volume based Computational Fluid Dynamics (CFD) in ANSYS FLUENT using the two-dimensional Realizable turbulence model. The Governing equations were discretized using the finite volume method with the solution based on the PISO algorithm. The decay of centerline velocity, turbulent kinetic energy profile, the radial profile of axial velocity and similarity profile were investigated along the flow direction. Contour plot indicates that the velocity is high at the jet exit and decreases downstream due to the rapid mixing of the inner and outer jet and the surrounding fluid. It is found generally that Reynolds number plays significant role especially before self-similarity region. The result shows that increasing the Reynolds number give rise to more turbulence which in turn decreases the potential core length, turbulent kinetic energy and enhances the mixing of the fluid. However, at the jet exit, the flow with the lowest Reynolds number has the highest turbulent kinetic energy because it suffers the greater shear. The spreading of the jet was more or less independent of the Reynolds number beyond the self-similarity region. It is also found that the velocity profile is brought to congruence at about z/D=25 for the Reynolds numbers considered

Effect of Application of Electric Force to Diesel Fuel Droplets Charged Through Millikan Oil-Drop Experiment on Physical and Thermal Characteristics of Flame

Abstract This paper proposes a new feasible method to allow continuous change in the primary injection spray cone angle of liquid fuel droplets, which are injected from nozzles in liquid fuel combustion systems, to control the flame shape and thermal characteristics of the flame. The method is based on electric force applied to fuel droplets charged through frictional effects between the internal surface of the nozzle and the fuel flow as the liquid fuel is sprayed (based on the Millikan oil-drop experiment). A sprint computational fluid dynamics code was developed to investigate the effect of application of electric force to charged diesel fuel droplets, which were injected from a pressure swirl atomizer, on physical and thermal characteristics of a two-dimensional axisymmetric turbulent jet diffusion flame. The results show that an electric field applied to charged fuel droplets (electric force) changes the spatial distribution of the liquid fuel droplets in the flame reaction zone. An applied electric force in (−y) direction diverts the fuel droplets towards the axis centerline of the furnace and, consequently, decreases the primary injection cone angle and increases the concentration of the evaporated droplets around the axis centerline, which enhances the fuel-oxidant mixing rate and raises the flame temperature. Unlike an applied electric force in (−y) direction, an applied electric force in (+y) direction decreases the flame temperature. However, as the primary injection cone angle is decreased, an applied electric force in (+y) direction increases the flame temperature.

Scaling mean velocity in two-dimensional turbulent wall jets

Studies in the literature on plane turbulent wall jets on flat surfaces, have invariably considered either the nozzle initial conditions or the asymptotic conditions far downstream, as scaling parameters for the streamwise variations of length and velocity scales. These choices, however, do not square with the notion of self similarity which is essentially a "local" concept. We first demonstrate that the streamwise variations of velocity and length scales in wall jets show remarkable scaling with local parameters i.e. there appear to be no imposed length and velocity scales. Next, it is shown that the mean velocity profile data suggest existence of two distinct layers - the wall (inner) layer and the full-free jet (outer) layer. Each of these layers scales on the appropriate length and velocity scales and this scaling is observed to be universal i.e. independent of the local friction Reynolds number. Analysis shows that the overlap of these universal scalings leads to a Reynolds-number-dependent power-law velocity variation in the overlap layer. It is observed that the mean-velocity overlap layer corresponds well to the momentum-balance mesolayer and there appears to be no evidence for an inertial overlap; only the meso-overlap is observed. Introduction of an intermediate variable absorbs the Reynolds-number dependence of the length scale in the overlap layer and this leads to a universal power-law overlap profile for mean velocity in terms of the intermediate variable.

Comparing selected parameters of a two-dimensional turbulent free jet on the basis of experimental results, digital simulations, and theoretical analyses

The presented experimental and digital examinations of a two-dimensional turbulent free jet are a first phase of in the study of the Coandă effect and its hysteresis. Additionally, basing on theoretical analyses, selected results for a turbulent jest have been also mentioned, considering theoretical assumptions for the wall layer. As the result, on the basis of experimental, digital, and analytical methods, a review of characteristic jet properties has been prepared, which includes a jet spreading ratio, its cross and longitudinal sections, and turbulence level. The jet spreading radio has been expressed as a non-linear function of the x : b relative length.

Scour due to turbulent wall jets downstream of low-/high-head hydraulic structures

AbstractTo overcome over-prediction of the scour depths by existing methods, a mathematical model is developed based on a work transfer theory. This model predicts the equilibrium scour hole’s depth and length due to two-dimensional turbulent wall jets downstream of low-/high-head hydraulic structures. The work transfer theory states that the work done by the attacking jet flow is transferred to work done to remove the volume of the scoured bed material out of the scour hole. This results in an analytical nonlinear equation for predicting the equilibrium scour depth. This unique feature of the nonlinearity of the developed equation shows the mutual dependence of the scour geometry and flow hydrodynamics on each other. Non-circulating wall jet flows and re-circulating jet flows within the scour hole are both considered. A separate equation is developed for predicting the length of the scour hole. Field data at the Nile Grand Barrages in Egypt and the Shimen Arch Dam in China are used to validate the develo...

Application of various RANS based models towards predicting turbulent slot jet impingement

Numerical simulation near the stagnation zone for an impinging jet is challenging because of the presence of sharp gradient due to the change of velocity from zero to the system scale velocity. A comparative study of four Reynolds averaged Navier–Stokes (RANS) based turbulence models has been done by numerically simulating a two-dimensional turbulent slot jet impinging air normally on a flat plate. Nozzle-to-plate spacings equal to 4 and 9.2 have been taken as two test cases with nozzle exit Reynolds number of 2×104. The turbulence intensity at the exit of the nozzle is kept constant at 1%. The capability to predict the fluid flow of the standard k−ε model, the low Reynolds number (LRN) k−ε models proposed by Launder and Sharma (LS) and Yang and Shih (YS), and the standard k−ω model have been evaluated by comparing the computational results with the experimental data available in the literature. The numerically obtained results have been compared with the experimental results on impingement surface pressure, free jet mean velocity profiles, spanwise velocity profiles, spanwise distribution of root mean square velocity fluctuation, skin friction coefficient distribution, non-dimensional velocity profile in wall coordinates. The standard k−ε model predicted the largest recirculation loop among the turbulence models used. The skin friction coefficient distribution is reproduced by YS and k−ω model for both the spacings whereas the other LRN model LS and the standard k−ε model are unable to predict the results. The linear law of the wall is found to be valid up to Y+≃4.0 in the recirculation region. The velocity profiles in wall coordinates in the recirculation region are behaving similar to those in the wall jet region of an impinging jet and the developed region of a wall jet.

228 二次元乱流噴流における線形撹乱に対する撹乱方程式を用いた理論的裏付け(OS13-4 乱流現象の実験と数値シミュレーション(4),OS13 乱流現象の実験と数値シミュレーション)

228 二次元乱流噴流における線形撹乱に対する撹乱方程式を用いた理論的裏付け(OS13-4 乱流現象の実験と数値シミュレーション(4),OS13 乱流現象の実験と数値シミュレーション)

Numerical Simulation of Free Surface in the Case of Plane Turbulent Wall Jets in Shallow Tailwater

Wall-jet flow is an important flow field in hydraulic engineering, and its applications include flow from the bottom outlet of dams and sluice gates. In this paper, the plane turbulent wall jet in shallow tailwater is simulated by solving the Reynolds Averaged Navier-Stokes equations using the standard turbulence closure model. This study aims to explore the ability of a time splitting method on a non-staggered grid in curvilinear coordinates for simulation of two-dimensional (2D) plane turbulent wall jets with finite tailwater depth. In the developed model, the kinematic free-surface boundary condition is solved simultaneously with the momentum and continuity equations, so that the water surface elevation can be obtained along with the velocity and pressure fields as part of the solution. 2D simulations are carried out for plane turbulent wall jets free surface in shallow tailwater. The comparison undertaken between numerical results and experimental measurements show that the numerical model can capture the velocity field and the drop in the water surface elevation at the gate with reasonable accuracy.

1217 Comparison of linear disturbance in a two-dimensional turbulent jet with a linear stability theory

It is recently revealed that there exists a linear disturbance in a two-dimensional turbulent jet. In this study, theoretical explanation for the linear disturbance was attempted based on disturbance equations, and velocity measurements using an x-type hot-wire anemometer and their comparison to a linear stability theory based on the parallel flow assumption were performed. An periodical-average was applied for the velocity data to extract a disturbance excited by a periodical initial disturbance, then it was confirmed linearity of the excited disturbance to the initial disturbance for low intensity of the initial disturbance. The growth rate of the excited disturbance is in qualitative agreement with the linear stability theory as well as the disturbance distribution. The disturbance equations for the periodic components of disturbances includes the second-order product terms of the random components, and the third-order and the fourth-order product terms appear in the high-order disturbance equations. The experimental data indicate that these terms are proportional to the initial disturbance amplitude until the initial disturbance is so strong that the excited disturbance is non-linear behavior, indicating that the disturbance equations are linear for an infinitesimal periodic component. This well explains existence of the linear disturbance in the turbulent flows.

Numerical modeling of a two-dimensional vertical turbulent two-phase jet

The results of numerically modeling two-dimensional two-phase flow of the “gas-solid particles” type in a vertical turbulent jet are presented for three cases of its configuration, namely, descending, ascending, and without account of gravity. Both flow phases are modeled on the basis of the Navier-Stokes equations averaged within the framework of the Reynolds approximation and closed by an extended k-ɛ turbulence model. The averaged two-phase flow parameters (particle and gas velocities, particle concentration, turbulent kinetic energy, and its dissipation) are described using the model of mutually-penetrating continua. The model developed allows for both the direct effect of turbulence on the motion of disperse-phase particles and the inverse effect of the particles on turbulence leading to either an increase or a decrease in the turbulent kinetic energy of the gas. The model takes account for gravity, viscous drag, and the Saffman lift. The system of equations is solved using a difference method. The calculated results are in good agreement with the corresponding experimental data which confirms the effect of solid particles on the mean and turbulent characteristics of gas jets.

Study on the Interfacial Layer between the Turbulent/Non-Turbulent Region in a Two-Dimensional Turbulent Jet

The interface between the turbulent and non-turbulent region in a two-dimensional turbulent jet is investigated by the simultaneous measurement of velocity and pressure. The measurements are performed using a combined probe comprising an X-type hot-wire probe and a static pressure probe. The measurement data are analyzed by the conditional sampling technique and an ensemble averaging technique on the basis of the intermittency function for the turbulent/non-turbulent decision. The measurement results at the cross-streamwise edge of the turbulent region show that there is a thin interfacial layer associated with a sharp jump of physical quantities (such as mean streamwise velocity) at the cross-streamwise edge of the turbulent region, and the thickness of interfacial layer is found to be 0.08 times the half-width of the cross-streamwise profile of the mean streamwise velocity. Moreover, the possibilities that there are small vortices in the middle of the interfacial layers and the existence of these vortices contributes to the transport of fluctuation pressure to the non-turbulent region are shown.

Jet-cavity interaction: effect of the cavity depth

A two-dimensional turbulent wall jet over a shallow cavity is studied numerically. The present paper investigates the wall jet outer layer effect on a shallow cavity flow structure. This layer is an important turbulence source which is added to that of the inner shear layer. It was found that the reattachment process seems to be accelerated in the turbulent wall jet incoming flow compared to that of the cavity in duct flow. The present study shows that the flow structure is very sensitive to the cavity depth to nozzle height ratio; the increasing of this ratio induces a reattachment length decrease.

Characteristics of Two-Dimensional Turbulent Jet in Flapping Motion

The characteristics of a two-dimensional turbulent jet in the flapping motion are investigated by simultaneously measuring the velocity and pressure. The simultaneous measurements are performed by using a combined probe that consists of an X-type hot-wire probe and a static pressure tube. The measurement data are analyzed by using a conditional sampling technique and the ensemble-averaging technique, on the basis of an intermittency function. This function is used to determine whether the jet is in the flapping motion or not. The measurement results of two hot-wire probes set in the self-preserving region of the jet are analyzed by performing a wavelet transform. The experimental results show that the ensemble-averaged velocity field during the flapping motion shows a good agreement with the measurement result obtained by Sakai, et al. (2006) through multi-point simultaneous measurement of velocity. Further, the ensemble-averaged static pressure field during the flapping motion indicates the pressure of a vortex coherent structure, interpreted as a combination of flapping and puffing motions in the self-preserving region of the jet. In addition, the estimation of the turbulent energy budget shows that the turbulent energy production and its transportation from the inner region to the outer region of the jet by the diffusion are enhanced during the flapping motion. In particular, this enhancement of the turbulent energy transportation is caused by the combination of the increasing of the turbulent diffusion to the outer region of the jet and the decreasing of the pressure diffusion to the inner region of the jet.

1101 複数の長方形切欠を用いた二次元噴流の操縦 (二次流れによる寄与)(流体力学IV)

1101 複数の長方形切欠を用いた二次元噴流の操縦 (二次流れによる寄与)(流体力学IV)

Modeling heat transfer in dilute two-phase flows using the Mesoscopic Eulerian Formalism

In dilute two-phase flows, the accurate prediction of the temperature of the dispersed phase can be of paramount importance. Indeed, processes such as evaporation or chemical reactions are strongly non-linear functions of heat transfer between the carrier and dispersed phases. This study is devoted to the validation of an Eulerian description of the dispersed phase – the Mesoscopic Eulerian Formalism (MEF) – in the case of non-isothermal flows. Direct Numerical Simulations using the MEF are compared to a reference Lagrangian simulation for a two-dimensional non-isothermal turbulent jet laden with solid particles. The objectives of this paper are (1) to study the influence of the thermal inertia of particles on their temperature distribution and (2) conduct an a posteriori validation of the MEF, which was recently extended to non-isothermal flows. The focus is on the influence of additional terms in the MEF governing equations, namely heat fluxes arising from the Random Uncorrelated Motion (RUM). Results show that mean and rms of particle temperature are strongly dependent of the thermal Stokes number. The mean temperature is satisfactorily predicted by the MEF, comparing to the Lagrangian reference. Under the conditions of the present study, the RUM heat fluxes have a marginal influence on the mean particle temperature. However, a significant impact was observed on the magnitude of particle temperature fluctuations. Neglecting the RUM heat fluxes leads to erroneous results while the Lagrangian statistics are recovered when it is accounted for in the regimes of low to moderate thermal Stokes number.

Dissipation element analysis of scalar field in turbulent jet flow

For better understanding of turbulence, the geometry of turbulent structures in turbulent jet flow should be analyzed. The aim of the present work was to experimentally verify the dissipation element theory on highly resolved two-dimensional measurements turbulent jets using Rayleigh scattering technique. The statistical analysis of the characteristic parameters of dissipation elements; namely the linear length connecting the extremal points and the absolute value of the scalar difference at these points, respectively was also investigated. Rayleigh scattering was used to topographically produce 2D images of turbulent mixing to obtain the concentration distribution of two gases in a turbulent shear flow. The scalar field obtained was subdivided into numerous finite size regions. In each of these regions local extremal points of the fluctuating scalar are determined via gradient trajectory method. Gradient trajectories starting from any point in the scalar field ϕ( x, y) in the directions of ascending and descending scalar gradients will always reach a minimum and a maximum point where ∇ ϕ = 0. The dissipation element has two extremal points (one maximal and one minimal) and two saddle points at the boundaries.

Measurements of roughness noise

Experiments have been performed on the roughness noise produced by a two-dimensional turbulent wall jet boundary layer flowing over short fetches of sandpaper roughness. A range of rough surface sizes were studied from hydrodynamically smooth through fully rough. Velocity measurements were made to document the form of the wall jet boundary layer and the influence of the roughness upon it. Acoustic measurements showed background noise levels to be very low so that the sound produced by the rough surfaces could be clearly detected with signal to noise ratios as large as 20 dB. Even hydrodynamically smooth roughness was found to produce noise, conclusively indicating the presence of scattering as a source mechanism. Variations of the roughness noise spectra with flow speed and roughness size are found to be inconsistent with any simple parameter scaling. Boundary layer wall pressure fluctuation measurements made within the roughness fetches reveal a spectral form quite different than the roughness noise, and fluctuation levels some 50–70 dB higher. Despite these differences the wall pressure and roughness noise are found to be very simply related, at least at lower frequencies (<6 kHz). The roughness noise spectrum varies closely as the product of the wall pressure spectrum, the frequency squared, and the mean-square roughness height. This is the scaling predicted by scattering theory and implies a major simplification to the problem of roughness noise prediction for stochastic surfaces.

The Statistical Evaluation of the Flapping Motion in a Two-Dimensional Turbulent Jet

The flapping motion in a two-dimensional turbulent jet is analyzed statistically. The analysis is done by applying a continuous wavelet transform with Gabor mother wavelet to the experimental result of hot-wire anemometer. The analysis results show that the flapping motion is clearly recognized by the present new method. The flapping motion occurs at random, and the average time interval of flapping motion is about 6.1 times the flapping periods (0.24 sec). The average duration time of the flapping motion is about 1.7 times the flapping period (0.07 sec) and the one that continues over 3.0 times the flapping period is very few. The negative value of the two-point spatial velocity correlation substantially depends on whether the flapping motion arises or not. From these results, it is found that the flapping motion in a two-dimensional turbulent jet has a very important role to the properties of the jet though the flapping motion is a rare phenomenon.