Plane Turbulent Wall Jet Research Articles

Experimental investigation of the structure of plane turbulent wall jets. Part 1. Spectral analysis

Plane turbulent wall jets are traditionally considered to be composed of a turbulent boundary layer (TBL) topped by a half-free jet. However, certain peculiar features, such as counter-gradient momentum flux occurring below velocity maximum in experiments and numerical simulations, suggest a different structure of turbulence therein. Here, we hypothesize that turbulence in wall jets has two distinct structural modes, wall mode scaling on wall variables and free-jet mode scaling on jet variables. To investigate this hypothesis, experimental data from our wall jet facility are acquired using single hot-wire anemometry and two-dimensional particle image velocimetry at three nozzle Reynolds numbers 10 244, 15 742 and 21 228. Particle image velocimetry measurements with four side-by-side cameras capture the longest field of view studied so far in wall jets. Direct spatial spectra of these fields reveal modal spectral contributions to variances of velocity fluctuations, Reynolds shear stress, shear force, turbulence production, velocity fluctuation triple products and turbulent transport. The free-jet mode has wavelengths scaling on the jet length scale ${z_{T}}$ , and contains two dominant submodes with wavelengths $5{z_{T}}$ and $2.5{z_{T}}$ . The region of flow above the velocity maximum shows the presence of the outer jet mode whereas the region below it shows robust bimodal behaviour attributed to both wall and inner jet modes. Counter-gradient momentum flux is effected by the outer jet mode intruding into the region below velocity maximum. These findings support the hypothesis of wall and free-jet structural modes, and indicate that the region below velocity maximum could be much complex than a conventional TBL.

Effect of corrugated side-walls on plane turbulent wall jets in narrow channels

An experimental study is presented to investigate the effect of corrugated sidewalls on submerged wall jets in narrow channels. Experiments were performed in a flume 0.3 m wide, 0.5 m deep, and 13.5 m long. Jets issued under the gate with a fixed thickness of 2.5 cm and the tailwater depth was adjusted to 37.5 cm, giving a fixed tailwater depth ratio yt/bo = 15. Experiments were conducted for five slot Froude numbers 2, 3, 4. 5, and 6. The Reynolds number ranged between 24712 and 74136. Three sets of experiments of five runs each, were performed. In Set A, the experiments were performed with smooth sidewalls whereas in Sets B and C, two arrangements of corrugated sidewalls (with gaps and with no gaps) were used, respectively. Velocity profiles along the centerline of the flume, water surface profile and the eddy length were measured for each experiment. It was found that the corrugations with gaps caused the largest decay in the maximum velocity; however, the effect of the presence of the sidewall corrugations on the velocity decay diminishes with the Froude number. Furthermore, the corrugated sidewalls with no gaps were observed to induce more flow entrainment and therefore cause a steep increase in the jet discharge and momentum flux near the slot. However, the corrugated sidewalls with gaps induced more mixing and diffusion, farther downstream from the slot, and caused a faster decay in the jet discharge and momentum. The use of corrugated sidewalls is introduced in this study as an alternative technique, to corrugated beds, to be used for energy dissipation in narrow channels. The sidewall corrugations are easier to maintain as less debris/sediments are trapped in between the corrugations. In addition, if channel maintenance is required, the movement of the maintenance facilities on a smooth bed would be much easier than that on a corrugated bed. Moreover, the sidewall corrugations will not be damaged during the maintenance process.

Layered structure of turbulent plane wall jet

This paper investigates the layered structure of a turbulent plane wall jet at a distance from the nozzle exit. Based on the force balances in the mean momentum equation, the turbulent plane wall jet is divided into three regions: a boundary layer-like region (BLR) adjacent to the wall, a half free jet-like region (HJR) away from the wall, and a plug flow-like region (PFR) in between. In the PFR, the mean streamwise velocity is essentially the maximum velocity, and the simplified mean continuity and mean momentum equations result in a linear variation of the mean wall-normal velocity and Reynolds shear stress. In the HJR, as in a turbulent free jet, a proper scale for the mean wall-normal flow is the mean wall-normal velocity far from the wall and a proper scale for the Reynolds shear stress is the product of the maximum mean streamwise velocity and the velocity scale for the mean wall-normal flow. The BLR region can be divided into four sub-layers, similar to those in a canonical pressure-driven turbulent channel flow or shear-driven turbulent boundary layer flow. Building on the log-law for the mean streamwise velocity in the BLR, a new skin friction law is proposed for a turbulent wall jet. The new prediction agrees well with the correlation of Bradshaw and Gee (1960) over moderate Reynolds numbers, but gives larger skin frictions at higher Reynolds numbers.

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.

Control of a plane turbulent wall jet by means of a micro jet from the wall

Control of a plane turbulent wall jet by means of a micro jet from the wall

Multi-time-scale turbulent heat transfer model for predictions of various turbulent heat transfer phenomena

The turbulent heat transfer model has been a useful and powerful tool in the calculation of turbulence heat transfer for designs of equipment with engineering and industrial problems. Among turbulent heat transfer models, two-equation turbulence models for both velocity and thermal fields are one of the best models because they have more accurate prediction performance and can carry out turbulence calculations at the proper calculation costs. In this study, in order to improve the prediction performance of two-equation heat transfer turbulence model in more complex problems of turbulent heat transfer, a turbulence model based on the multi-time-scale model proposed by Nagano and Hattori (Int J Heat Fluid Flow 51:221, 2015) for predictions of a velocity field is modified, and a turbulent heat transfer model with the multi-time-scale is newly proposed. The proposed turbulent heat transfer models are evaluated in complex fields of turbulent heat transfer problem such as a T-junction turbulent thermal mixing channel flow, a turbulent plane impinging jet with heat transfer and a turbulent plane wall jet with heat transfer, where databases of these complex turbulent heat transfer phenomena are obtained by our DNS. Based on the results, adequate improvement of the prediction performance of a proposed turbulent heat transfer model is validated.

A numerical study of a confined turbulent wall jet with an external stream

Wall jet flow exists widely in engineering applications, including the simulation of thunderstorm downburst outflows, and has been investigated extensively by both experimental and numerical methods. Most previous studies focused on the scaling laws and self-similarity, while the effect of lip thickness and external stream height on mean velocity has not been examined in detail. The present work is a numerical study, using steady Reynolds-Averaged Navier Stokes (RANS) simulations at a Reynolds number of 3.5 X 104, of a turbulent plane wall jet with an external stream to investigate the influence of the wall jet domain on downstream development of the flow. The comparisons of flow characteristics simulated by the Reynolds stress turbulence model closure (Stress-omega, SWRSM) and experimental results indicate that this model may be considered reasonable for simulating the wall jet. The confined wall jet is further analyzed in a parametric study, with the results compared to the experimental data. The results indicate that the height and the width of the wind tunnel and the lip thickness of the jet nozzle have a great effect on the wall jet development. The top plate of the tunnel does not confine the development of the wall jet within 200b of the nozzle when the height of the tunnel is more than 40b (b is the height of jet nozzle). The features of the centerline flow in the mid plane of the 3D numerical model are close to those of the 2D simulated plane wall jet when the width of the tunnel is more than 20b.

A plane turbulent wall jet on a fully rough surface

The mean velocity field and skin friction characteristics of a plane turbulent wall jet on a smooth and a fully rough surface were studied using Particle Image Velocimetry. The Reynolds number based on the slot height and the exit velocity of the jet was Re= 13,400 and the nominal size of the roughness was k = 0.44mm. For this Reynolds number and size of roughness element, the flow was in the fully rough regime. The surface roughness results in a distinct change in the shape of the mean velocity profile when scaled in outer coordinates, i.e. using the maximum velocity and outer half-width as the relevant velocity and length scales, respectively. Using inner coordinates, the mean velocity in the lower region of the inner layer was consistent with a logarithmic profile which characterizes the overlap region of a turbulent boundary layer; for the rough wall case, the velocity profile was shifted downward due to the enhanced wall shear stress. For the fully rough flow, the decay rate of the maximum velocity of the wall jet is increased, and the skin friction coefficient is much larger than for the smooth wall case. The inner layer is also thicker for the rough wall case. The effects of surface roughness were observed to penetrate into the outer layer and slightly enhance the spread rate for the outer half-width, which was not observed in most other studies of transitionally rough wall jet flows.

Investigation of a turbulent wall jet in forced convection issuing into a directed coflow stream

ABSTRACTIn the present paper, we have studied numerically the directed coflow stream effects on mean and turbulent flow properties of a turbulent plane wall jet in forced convection emerging into a directed coflow stream. The system of equations governing the studied configuration is solved with a finite difference scheme using a staggered grid for numerical stability, not uniform in the two directions of the flow. The modified version of the first-order low Reynolds number k–ϵ turbulence model is used and compared to existing experimental findings. It is found that predicted results are in satisfactory agreement with the experimental data and that the wall jet fluid decays faster in presence of a directed coflow stream. Results show also that the increase of coflow deviation angles causes an increase of the growth rates of the dynamic and thermal half-width of the jet and enhances the turbulent mixing. It is found that the longitudinal development of normalised forms of the jet characteristics parameters at different directed coflow velocity ratios can be reasonably well collapsed onto universal trends through the use of momentum length scale.

Direct numerical simulation of particle-laden plane turbulent wall jet and the influence of Stokes number

The distribution and motion of inertial particles in plane turbulent wall jet are investigated using direct numerical simulation, under the assumption of one-way coupling. To our knowledge, this appears to be the first direct numerical simulation of a particle-laden plane turbulent wall jet. It is shown that, in outer part of the wall jet, the behaviour of particles closely resembles that of a free plane jet. Due to the streamwise decay of particle Stokes number, the particle streaks formed in the near wall region of the wall jet are characterized by their intensity variation, which differs significantly from those in the channel flow. The streamwise growth of the particle velocity half-width is approximately equal to that of the fluid velocity half-width and the maximum velocity of particles decays slower than that of fluid due to inertia. The outer scaling can collapse the mean particle velocity in both the inner and outer region for heavier particles. In the buffer region, the particle–fluid velocity difference can be negative or positive depending on the Stokes number since there are two competing effects, namely the memory effect and turbophoresis. In the viscous region, the larger particles are on average faster than fluid and the velocity difference is found to be self-similar depending on outer Stokes number. The near-wall distribution of velocity difference is significantly correlated with the presence of high-momentum particles which are entrained by vortical structures generated in the outer region of the wall jet. These results are useful for environmental and engineering applications.

Review of literature on local scour under plane turbulent wall jets

Stability of hydraulic structures is threatened by persistent scour downstream of the apron, which renders their foundations exposed. Jets issuing under the sluice gate are turbulent enough to cause significant scour. Extensive study of the jets is, therefore, necessary in order to understand the underlying hydraulics and provide remedial measures. In this paper, a comprehensive review of the investigations on local scour caused by wall jets is presented, including both the classical as well as the prevalent approach. Various aspects of the scour under wall jets have been explained, including the process of scouring, different parameters affecting the maximum scour depth, analysis of flow characteristics within the scour hole and on the apron, time variation of scour depth, rate of sediment removal, and scour depth estimation formulae.

A numerical study of a plane turbulent wall jet in a coflow stream

This work is a numerical study of an isothermal and a non-isothermal turbulent plane wall jet emerging in a coflow stream with different velocity ratios ranging from 0 to 0.2. Turbulence modeling is performed by using a modified low-Reynolds number k–ε model. The numerical resolution of the governing equations was carried out via finite difference method. The present predictions are compared with those suggested in the literature. It was found that the studied model reasonably predicts the mean flow proprieties of the flow field. The main purpose of this work is to determine the influence of the velocity ratio on the dynamic, thermal and turbulent characteristics of the flow. A comparison with a simple wall jet is made. Besides, the influence of Reynolds and Richardson numbers on the wall jet emerging in a coflowing stream is examined. As far as the isothermal flow is concerned, results show that the potential core length decreases in accordance with the velocity ratio. It was also found that, downstream from the jet exit (in the established region), the longitudinal distributions of the normalized forms of the excess maximum x-velocity and the turbulent maximum kinetic energy converge to a single curve at different velocity ratios. The present investigation suggests that the effect of coflowing jet on the dynamic, thermal and turbulent parameters is negligible in the potential core area (ZFE) and the jet is similar to that of a simple jet. Further downstream of this region, the velocity ratio affects the flow as far as the high coflow streams are concerned.

Prediction of mass and momentum transport in turbulent plane wall jets over smooth and transitionally rough surfaces

This paper is concerned with the prediction of mass and momentum transport in turbulent wall jets developing over smooth and transitionally rough plane walls. The ability to accurately predict the resulting wall shear stresses and vertical profiles of the Reynolds stresses in these flows is prerequisite to the accurate prediction of bed scour, sediment re-suspension and transport by turbulent diffusion. The computations were performed by solving the Reynolds-averaged forms of the equations describing conservation of mass, momentum and concentration. The unknown correlations that arise from the averaging process (the Reynolds stresses in the case of the momentum equation, and the turbulent mass fluxes in the case of concentration) were obtained from the solution of modeled differential equations that describe their conservation. Since these models are somewhat more complex than those typically used in practice, their benefits are demonstrated by comparisons with results obtained from simpler, eddy-viscosity based closures. Comparisons with experimental data show that results of acceptable accuracy can be obtained only by using the appropriate combination of models for the turbulent fluxes of mass and momentum that properly account for the reduction of the Reynolds stresses due to wall damping effects, and for the modification of the mass transfer rates due to interactions with the mean rates of strain.

The asymptotic downstream flow of plane turbulent wall jets without external stream

The plane turbulent wall-jet flow without externally imposed stream is considered. It is assumed that the wall jet does not emerge from a second wall perpendicular to the velocity vector of the initial wall jet. The (kinematic) momentum flux$K(x)$of the wall jet decreases downstream owing to the shear stress at the wall. This investigation is based on the hypothesis that the total friction force on the wall is smaller than the total inflow momentum flux. In other words, the turbulent wall jet tends to a turbulent ‘half-free jet’ with a non-zero momentum flux$K_{\infty }\;(\text{m}^{3}~\text{s}^{-2})$far downstream. The fact that the turbulent half-free jet is the asymptotic form of a turbulent wall jet is the basis for a singular perturbation method by which the wall-jet flow is determined. It turns out that the ratio between the wall distance$y_{m}$of the maximum velocity and the wall distance$y_{0.5}$of half the maximum velocity decreases downstream to zero. Dimensional analysis leads immediately to a universal function of the dimensionless momentum flux$K(\mathit{Re}_{x})/K_{\infty }$that depends asymptotically only on the local Reynolds number$\mathit{Re}_{x}=\sqrt{(x-x_{0})K_{\infty }}/{\it\nu}$, where$x_{0}$denotes the coordinate of the virtual origin. When the values$K$and${\it\nu}$at the position$x-x_{0}$are known, the asymptotic momentum flux$K_{\infty }$can be determined. Experimental data on all turbulent plane wall jets (except those emerging from a second plane wall) collapse to a single universal curve. Comparisons between available experimental data and the analysis make the hypothesis$K_{\infty }\neq 0$plausible. A convincing verification, however, will be possible in the future, preferably by direct numerical simulations.

Incomplete similarity of a plane turbulent wall jet on smooth and transitionally rough surfaces

This study assesses the hypothesis of incomplete similarity for a plane turbulent wall jet on smooth and transitionally rough surfaces. Typically, a wall jet is considered to consist of two regions: an inner layer and an outer layer. The degree to which these two regions reach equilibrium with each other and interact to produce the property of self-similarity remains an open question. In this study, the analysis of the outer and inner regions indicates that each region is characterised by a half-width which exhibits its own distinct dependence on the streamwise distance x from the slot, and a single self-similar structure for both regions does not exist. More specifically, the inner and outer layers of the wall jet exhibit different scaling laws, which results in two self-similar mean velocity profiles, both of which retain a dependence on the slot height H. As such, incomplete similarity of the wall jet on smooth and transitionally rough surfaces is confirmed by this study. In addition, comparison of the experimental results for the transitionally rough surface with the smooth wall case indicates that the surface roughness modifies the development of the mean velocity profile in both the inner and outer regions, although the effect on the outer region is relatively small and close to the experimental uncertainty.

Turbulent plane wall jets over smooth and rough surfaces

Large-eddy simulations were carried out to study the effects of surface roughness on a plane wall-jet using the Lagrangian dynamic eddy-viscosity subgrid-scale model, at Re = 7500 (based on the jet bulk velocity and height). Results over both smooth and rough surfaces were validated by experimental data at the same Reynolds number. As the jet is injected into the still environment, large-scale rollers are generated in the shear layer between the high-momentum fluid of the jet and the surrounding and are convected downstream with the flow. To understand the extent to which the outer-layer structures modify the flow in the inner layer and the extent to which the effect of roughness spreads away from the wall, both instantaneous and mean flow fields were investigated. The results revealed that, for the Reynolds number and roughness height considered in this study, the effect of roughness is mostly confined to the near-wall region of the wall jet. There is no structural difference between the outer layer of the wall jet over the smooth and rough surfaces. Roughness does not affect the size of the outer-layer structures or the scaling of the profiles of Reynolds stresses in the outer layer. However, in the inner layer, roughness redistributes stresses from streamwise to wall-normal and spanwise directions toward isotropy. Contours of joint probability-density function of the streamwise and wall-normal velocity fluctuations at the bottom of the logarithmic region match those of the turbulent boundary layer at the same height; while the traces of the outer-layer structure were detected at the top of the logarithmic region, indicating that they do not affect the flow very close to the wall, but still modify a major portion of the inner layer. This modification must be taken into consideration when the inner layer of a wall jet is compared with the conventional turbulent boundary layer.

On determining wall shear stress in spatially developing two-dimensional wall-bounded flows

A full momentum integral-based method for determining wall shear stress is presented. The method is mathematically exact and has the advantage of having no explicit streamwise gradient terms. It is applicable for flows that change rapidly in the streamwise direction and, in particular, to flows with ill-defined outer boundary conditions or when the measurement grid does not extend over the whole boundary layer thickness. The method is applied to two different experimental plane turbulent wall jet data sets for which independent estimates of wall shear stress were known, and the different results compare favorably. Complications owing to experimental limitations and measurement error in determining wall shear stress from the proposed method are presented, and mitigating strategies are described.

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.

On the Structure of a Plane Turbulent Wall Jet

The present study proposes two interactive eddy viscosities for the two layers of a plane wall jet where the influence of one layer is considered on the eddy viscosity of the other layer. Using these viscosities, the equations governing the wall jet flow are solved numerically. The flow structure extracted from the numerical solution is found in excellent agreement with the existing literature that justifies a two-layered structure of plane turbulent wall jet.

Flow Field in a Skimming Flow Over a Vertical Drop Without End-Sill

ABSTRACTThe flow structure in the shear layer and in the recirculation zone of a skimming flow downstream of a vertical drop without end-sill measured using high speed particle image velocimetry (HSPIV) and flow visualization method is presented. The interface between the sliding jet and the recirculation zone (zone below sliding jet) was enhanced through non-ventilation condition between the drop structure and the jet. The flow field measured through HSPIV was used to represent the characteristics of mean streamwise velocity in the shear layer and mean horizontal velocity in the recirculation zone. With the growth of shear layer as the jet slides down over the recirculation zone, the momentum exchange from the sliding jet into the recirculation zone via the shear layer increases along with energy loss. Hence, it was observed that the amount of energy dissipated in the skimming flow at the drop structure without ventilation is greater than that with ventilation by an average value of 50% forYc/H≥ 0.2 (whereYc= critical depth andH= drop height). However, the flow structure in the recirculation zone is found to be analogous to that of turbulent plane wall jet. The nonlinear regression analysis is used to fit the regressed velocity profiles to the measured HSPIV mean velocity distributions. Further, the appropriate characteristic velocity and length scales are selected to attain the unique similarity profiles both in the shear layer and in the recirculation zone of the skimming flow. The selection of the characteristic scales is also discussed. The similarity profiles are well comparable with those of napped flow without end-sill and with ventilation as well as of skimming flow with end-sill and without ventilation. It is interesting to observe that, the proposed similarity profiles for the shear layer also map the data of backward-facing step flow and cavity shear flow. In addition, the turbulence characteristics in the shear layer, including turbulence intensities, turbulent kinetic energy, viscous and Reynolds shear stresses, and turbulence energy-budget balance, are illustrated in detail. From the variation of turbulence production it is observed that near the drop structure the energy exchange is from the chaotic recirculation zone to the sliding-jet flow, while in the later part it is reversed. Furthermore, the analysis of turbulence energy-budget balance indicates very significant role of turbulence production, pressure diffusion and turbulence diffusion as compared with turbulence advection that has very minor role in turbulence energy-budget balance for the central part of the shear layer.