Numerical Investigation of Vertical Turbulent Jets in Different Types of Waves

The eftects of various types of waves on vertical plane turbulent jets are studied numerically in the paper. A ttn＇ee- dimensional numerical model in a-coordinate is developed to study these problems by use of large eddy simulation method. Turbulence is modeled by a dynamic coherent eddy model. Numerical results including the distribution of veloci- ty, the decay law of the mean velocity along axis, the turbulent Reynolds stresses and the volume flux per unit width without wave, in the first-order Stokes waves, in the second-order Stokes waves, in the fifth-order Stokes waves, in the solitary waves and in random waves are compared and analyzed. A focus on coherent structures, probability density func- tions and correlation functions of jets is also investigated. The numerical results are of great theoretical importance for un- derstanding jet turbulent behaviors in different types of waves.

The Structure of A Turbulent Jet in A Crossflow-Effect of Jet-Crossflow Velocity

A comprehensive numerical study on the three-dimensional structure of a turbulent jet in crossflow is performed. The jet-to-crossflow velocity ratio (R) varies in the range of 2 - 16; both vertical jets and inclined jets without excess streamwise momentum are considered. The numerical results of the Standard two-equation k-ε model show that the turbulent structure can be broadly categorised according to the jet-to-crossflow velocity ratio. For strong to moderate jet discharges, i.e. R> 4, the jet is characterized by a longitudinal transition through a bent-over phase during which the jet becomes almost parallel with the main freestream, to a sectional vortex-pair flow with double concentration maxima; the computed flow details and scalar mixing characteristics can be described by self-similar relations beyond a dimensionless distance of around 20-60. The similarity coefficients are only weakly dependent on R. The cross-section scalar field is kidney-shaped and bifurcated, vvith distinct double concentration maxima; the aspect ratio is found to be around 1.2. A loss in vertical momentum is ob-served and the added mass coefficient of the jet motion is found to be approximately 1. On the other hand, for weak jets in strong crossflow, i. e. R ≥ 2, the lee of the jet is characterized by a negative pressure region. Although the double vortex flow can stili be noted, the scalar field becomes more symmetrical and no longer bifurcated. The similarity coeffcients are al-so noticeably different. The predicted jet flovv characteristics and mixing rates are well supported by experimental and field dala

Coherent structures and wavepackets in subsonic transitional turbulent jets

A large eddy simulation (LES) is performed for two subsonic jets with a Reynolds number of , which have different core temperatures, i.e., the cold and hot jet. The far-field overall sound pressure levels (OASPL) and noise spectra are well validated against previous experimental results. It is found that the OASPL is raised by heating at shallow angles. The most energetic coherent structures are extracted with specified frequencies using the filter based on the frequency domain variant of the snapshot method of proper orthogonal decomposition (POD). The modes have high coherence of near-field pressure for both jets, while the coherence of modes is enhanced greatly by heating. Based on the coherent structures, spatial wavepackets are educed and the characteristics of growth, saturation and decay are analyzed and compared between the two jets in detail. The results show that heating would enhance the linear growth rate for high frequency components, and nonlinear growth rates for low frequency components in general, which are responsible for higher OASPL in the hot jet. The far-field sound generated by wavepackets is computed using the Kirchhoff extrapolation, which matches well with that of LES at shallow angles. This indicates that the wavepackets associated with coherent structures are dominant sound sources in forced transitional turbulent jets. Additionally, the present POD method is proven to be a robust tool to extract the salient features of the wavepackets in turbulent flows.

Direct Numerical Simulation of Particle Dispersion in Gas-Solid Compressible Turbulent Jets

A numerical method was developed to directly simulate the compressible, particle-laden turbulent jets.The fourth order compact finite difference schemes were used to discretize the space derivatives. The Lagrangian method was adopted to simulate the particle motion based on one-way coupling. It is found that the turbulent intensity profiles attain self-similar status in the jet downstream regions. At the Stokes number of 1, particles are concentrated largely in the outer boundaries of the large-scale vortex structures with the most uneven distribution and the widest dispersion in the lateral direction. Particles at the much smaller Stokes numbers are distributed evenly in the flow field, and the lateral dispersion is also considerable. Distribution of particles at much larger Stokes numbers is more uniform and the lateral dispersion becomes small. In addition, the inflow conditions have different effects on the particle dispersion. The direct numerical simulation (DNS) results accord with the previous experiments and numerical studies.

Large eddy simulation of vertical turbulent jets under JONSWAP waves

The effect of random waves on vertical plane turbulent jets is studied numerically and the mechanism behind the interaction of the jet and waves is analyzed. The large eddy simulation method is used and the σ-coordinate system is adopted. Turbulence is modeled by a dynamic coherent eddy model. The σ-coordinate transformation is introduced to map the irregular physical domain with a wavy free surface and an uneven bottom onto a regular computational domain. The fractional step method is used to solve the filtered Navier–Stokes equations. Results presented include the distribution of velocity, the decay law of the mean velocity along the jet axis, self-similar characteristics and volume flux per unit width. In particular, the role of coherent structures on the momentum transfer along the jet centerline and the jet instantaneous characteristics in JONSWAP waves are a special focus of this research. The numerical results obtained are of great theoretical importance in understanding the behavior of turbulent jets in random wave environments.

Mean and fluctuating velocity fields of a diamond turbulent jet

The present paper reports the first investigation on a turbulent jet issuing from a diamond orifice（hereafter termed a ＂diamond jet＂） with an aspect ratio of 1.7.Velocity measurements were conducted in the transitional region,and the exit Reynolds number of the jet was 50000.For comparison,a round jet with identical normalized boundary conditions was also measured.It is shown that the diamond jet decays and spreads faster than the round jet does over the measured flow region.The axis-switching phenomenon is observed in the diamond jet.Although both jets display primary coherent structures in the near field,these structures are found to break down more rapidly in the diamond jet,due to the higher three-dimensionality of the flow.Moreover,the streamwise components of the Reynolds normal stress and all the shear stresses reach their maxima around the location of the maximal mean shear while the maxima of the lateral components of the Reynolds normal stresses occur around the centreline of the jet.

Flapping Characteristics of 2D Submerged Turbulent Jets in Narrow Channels

Flapping characteristics of the self-excited flapping motion of submerged vertical turbulent jet in narrow channels are studied theoretically and experimentally.It is found that the water depth is a most important parameter to the critical jet exit velocity and the jet flapping frequency.The results indicate that the critical jet exit velocity increases with water depth and the jet flapping frequency is inversely proportional to the water depth.Meanwhile,experimental result also shows that the surface disturbance wave changes the frequency of flapping motion,i.e.the flapping frequency locks-in the disturbing frequency when the disturbing frequency is near and less than the natural flapping frequency.

FLOW CHARACTERISTICS OF TURBULENT JETS INJECTED OBLIQUELY IN CROSSFLOW

Numerical simulation has been performed to investigate the characteristics ofthe turbulent jet issuing obliquely into a crossflow, at the injection angles of 90° and 60°. TheSIMPLEC algorithm in the body-fitted coordinates and the wall-function method using the RNG k-εturbulence model have been adopted to simulate this flow at two jet-to-crossflow velocity ratios, 2and 4. The numerical results are good agreement with the experimental measurements, the jettrajectories have been given, the separation events in the lee of the jet exit have been found, andthe forming mechanism has been analyzed.

THE MERGING OF TWO UNEQUAL AXISYMMETRIC PARALLEL TURBULENT JETS

Results of an experimental study of the merging of unequal parallel round turbulent jets are presented.Experiments were conducted for a jet axial separation to nozzle diameter ratio of 3.0 and the Reynolds numbers ranging from 8 000 to 15 000.The distance to the point where the jets are merged was measured for a range of jet source momentum flux ratios.Three different merger criteria were used based on the mean velocity profile,mean passive tracer concentration profile,and Reynolds stress profile.The results show that the concentration profile merges closest to the jet sources followed by the velocity profile with the Reynolds stress profile merging furthest from the nozzles.For all three profiles the merge distance is relatively insensitive to the momentum flux ratio,consistent with previous findings for slot jets and buoyant round jets.The measured merge distances are consistent with previously published results for equal round jets,though the poor spatial resolution of data in the literature means that limited comparison is possible.There are no studies of unequal jet merger currently in the literature that could be used for comparison.

Visualization of a Turbulent Jet Using Wavelets

An application of multiresolution image analysis to turbulence was investigated in this paper, in order to visualize the coherent structure and the most essential scales governing turbulence. The digital imaging photograph of jet slice was decomposed by two-dimensional discrete wavelet transform based on Daubechies, Coifman and Baylkin bases. The best choice of orthogonal wavelet basis for analyzing the image of the turbulent structures was first discussed. It is found that these orthonormal wavelet families with index N<10 were inappropriate for multiresolution image analysis of turbulent flow. The multiresolution images of turbulent structures were very similar when using the wavelet basis with the higher index number, even though wavelet bases are different functions. From the image components in orthogonal wavelet spaces with different scales, the further evident of the multi-scale structures in jet can be observed, and the edges of the vortices at different resolutions or scales and the coherent structure can be easily extracted.

NUMERICAL SIMULATION OF TURBULENT JETS WITH LATERAL INJECTION INTO A CROSSFLOW

In this paper, Numerical simulations of mean velocity and turbulent kinetic energy fields are presented for three-dimensional lateral jet in crossflow, at the injection angles of -60° and -30 °. The RNG κ- ε turbulence model, with the two-layer wall function method, is adopted to simulate the characteristics of this flow at the jet-to-crossflow velocity ratios, 1, 2 and 4. The results show that the injection angle and jet-to-crossflow velocity ratio can change the flow fields, and the range upstream affected by jet injected laterally increase and the curvature of jet trajectories varies along the flow direction. Furthermore, the separation events in the lee of the jet exit and behind the jet bending-segment have been found, and the mechanisms of two vortex systems are analyzed.

Influences of initial velocity,diameter and Reynolds number on a circular turbulent air/air jet

This paper assesses the suitability of the inflow Reynolds number defined by Reo -- UoD/v （here Uo and D are respectively the initial jet velocity and diameter while v is kinematic viscosity） for a round air/air jet. Specifically an experimental investigation is performed for the influences of Uo, D and Reo on the mean-velocity decay and spread coefficients （Ku, Kr） in the far field of a circular air jet into air from a smoothly contracting nozzle. Present measurements agree well with those previously obtained under similar inflow conditions. The relations Ku ∝ Uo and Kr ∝ 1/Uo for Uo 〈 5 m/s appear to work, while each coefficient approaches asymptotically to a constant for Uo 〉 6 m/s, regardless of the magnitudes of Reo and D. It is revealed that Reo may not be an appropriate dimensionless parameter to characterize the entire flow of a free air/air jet. This paper is the first paper that has challenged the suitability of Reo for turbulent free jets.

Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet

A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric.The proper orthogonal decomposition(POD)analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1%of the turbulent kinetic energy,and hence their impact on the wake dynamics is studied.The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point.The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction.In addition,the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.

Analytical investigation on mean and turbulent velocity fields of a plane jet

This paper analyses the downstream developments of the mean and the turbulent velocity fields of a plane jet. Based on the conservation of mass and the conservation of momentum, the mean-velocity half width （reflecting the jet spread rate） and the relative mass flow rate （jet entrainment） are related to the decay rate of the centreline mean velocity. These relations are not subject to self-preservation. Both analytical and experimental results suggest that the jet spread rate （K1） and the entrainment rate （K3） （and thus the decay rate K2） can be well estimated from the centreline velocity, i.e., K1 ≈ 0.6K2 and K3 ∝K2. The effect of initial mean velocity and RMS velocity profiles on the downstream mean velocity field appears to be embodied in the constants K1 K2 and K3. The analytical relationship for the self-preserving Reynolds shear stress, obtained for the first time, works well.

On two distinct Reynolds number regimes of a turbulent square jet

The effects of Reynolds number on both large-scale and small-scale turbulence properties are investigated in a square jet issuing from a square pipe. The detailed velocity fields were measured at five different exit Reynolds numbers of 8 × 10^3 〈 Re 〈 5 × 10^4. It is found that both large-scale properties （e.g,, rates of mean velocity decay and spread） and small-scale properties （e.g., the dimensionless dissipation rate constant A = εL/（u^2）^3/2） are dependent on Re for Re ≤ 3 ×10^4 or Reλ ≤ 190, but virtually become Re-independent with increasing Re or Reλ. In addition, for Reλ 〉 190, the value ofA = εL/（u^2）^3/2 in the present square jet converges to 0.5, which is consistent with the observation in direct numerical simulations of box turbulence, but lower than that in circular jet, plate wake flows, and grid turbulence. The discrepancies in critical Reynolds number and A = εL/（u^2）^3/2 among different turbulent flows most likely result from the flow type and initial conditions.

Research on the jet characteristics of the deflector–jet mechanism of the servo valve

In view of the complicated structure of the deflector-jet mechanism,a mathematical model based on the turbulent jet flow theory in the deflector-jet amplifier is proposed.Considering the energy transformation and momentum variation,an equation of the flow velocity distribution at the key fluid region is established to describe the morphological changes of the fluid when it passes through the deflector and jets into the receiver.Moreover,the process is segmented into four stages.According to the research results,the oil enters the deflector and impinges with the side wall.Then one part of the oil＇s flow velocity decreases and a high pressure zone is formed by the oil accumulation,the other part of the oil reverses out of the deflector along the side wall.Prior to entering the receiver,the flow is a kind of plane impinging jet.Virtually,the working pressure of the receiver is generated by the impact force,while the high speed fluid flows out of the receiver and forms a violent vortex,which generates negative pressure and causes the oil to be gasified.Compared with the numerical simulation results,the turbulent jet model that can effectively describe the characteristics of the deflector-jet mechanism is accurate.In addition,the calculation results of the prestage pressure characteristic have been verified by experiments.

Initial Dilution of A Vertical Round Non-Buoyant Jet in Wavy Cross-Flow Environment

The phenomenon of wastewater discharged into coastal waters can be simplified as a turbulent jet under the effect of waves and currents. Previous studies have been carried out to investigate the jet behaviors under the current only or the wave only environment. To obtain better understanding of the jet behaviors in a realistic situation, a series of physical experiments on the initial dilution of a vertical round jet in the wavy cross-flow environment are conducted. The diluted processes of the jet are recorded by a high-resolution camcorder and the concentration fields of the jet are measured with a peristaltic suction pumping system. When the jet is discharged into the wavy cross-flow environment, a distinctive phenomenon, namely ＂effluent clouds＂, is observed. According to the quantitative measurements, the jet width in the wavy cross-flow environment increases more significantly than that does in the cross-flow only environment, indicating that the waves impose a positive effect on the enhancement of jet initial dilution. In order to generalize the experimental findings, a comprehensive velocity scale ua and a characteristic length scale l are introduced. Through dimensional analysis, it is found that the dimensionless centerline concentration trajectories cy/l is in proportion to 1/3 power of the dimensionless downstream distance x/l, and the dimensionless centerline dilution 2c aS Q/（u l） is proportional to the square of the dimensionless centerline trajectory cy/l. Several empirical equations are then derived by using the Froude number of cross-flow Frc as a reference coefficient. This paper provides a better understanding and new estimations of the jet initial dilution under the combined effect of waves and cross-flow current.

Particle modulations to turbulence in two-phase round jets

The particle modulations to turbulence in round jets were experimentally studied by means of two-phase velocity measurements with Phase Doppler Anemometer （PDA）. Laden with very large particles, no significant attenuations of turbulence intensities were measured in the farfields, due to small two-phase slip velocities and particle Reynolds number. The gas-phase turbulence is enhanced by particles in the near-fields, but it is significantly attenuated by the small particles in the far-fields. The smaller particles have a more profound effect on the attenuation of turbulence intensities. The enhancements or attenuations of turbulence intensities in the far-fields depends on the energy production, transport and dissipation mechanisms between the two phases, which are determined by the particle prop- erties and two-phase velocity slips. The non-dimensional parameter CTI is introduced to represent the change of turbulence intensity.

Numerical simulation of flow field of single-hole oxygen lance jet

The numerical simulation of jet flow field in Laval tube was carried out first by commercial software CFX4.4, and it is used to determine inlet pressure condition out of nozzle in order to its numerical simulation. The decay rule of jet middle line velocity of axial symmetry turbulence jet and cross section＇s expand situation out of the tube in different stagnation pressure and surrounding temperature were analyzed systematically. The result showed that K-e model is suitable for numerical simulation. The conclusion will have important guide and referent function to research of two important craft parameters, impact depth and the impact area which are related to steel-making production practice.

AN INVESTIGATION OF TURBULENT RECTANGULAR JET DISCHARGED INTO A NARROW CHANNEL WEAK CROSSFLOW

A computational investigation of the mean flow field of turbulent rectangular jets issuing into a narrow channel crossflow is presented. The length of the jet slot spans more than 55% of the crossflow channel bed, leaving a small clearance between the jet edge and sidewalls. A finite volume code employing the standard k-εmodel is used to predict the mean, three-dimensional flow field. The mean flow field is investigated for two velocity ratios （6 and 9）. Important flow features, such as the formation of different vortical structures and their characteristics owing to different values of the velocity ratio, are discussed. Some predicted results are compared with the experimental data reported in the literature. The predicted mean and turbulent flow properties are shown to be in good agreement with the experimental data.