Time-averaged Turbulent Kinetic Energy Research Articles

Systematical study on the aerodynamic control mechanisms of a 1:2 rectangular cylinder with Kirigami scales

Biomimetic flow control is being widely applied. In the present study, a biomimetic flow control method, i.e., Kirigami scales, was applied on a 1:2 rectangular cylinder. The effects of scales' shapes and pasting surfaces on the aerodynamics and circumferential flow patterns of a 1:2 rectangular cylinder were studied. Three scale shapes were investigated with different pasting methods, i.e., elliptical, circular, and triangular scales. The Reynolds number (Re) was set at 1.3–3.1 × 104. The surface pressure distributions and the integrated aerodynamic forces were further analyzed at Re = 1.3 × 104. Results show that pasting the elliptical scales on all surfaces performs best, reaching a 2.4% drag reduction and a 76.4% lift reduction. Moreover, the elliptical and triangular scales on the windward and leeward surfaces can significantly reduce the Re effect. To reveal the control mechanism, the particle image velocimetry technique was employed to obtain the circumferential and wake flow fields. The time-averaged and phase-averaged results indicate that the Kirigami scales can push the interactions of shear layers and the shedding vortices further downstream. The Proper orthogonal decomposition analysis and time-averaged turbulent kinetic energy (TKE) results indicate that the wake vortex shedding is significantly suppressed. The spanwise wake flow field was also investigated. Results show that the spanwise TKE values are significantly reduced. This study further deepened the application of Kirigami scales on the common blunt bodies.

Numerical investigation of aero-optical effects around the turret based on delayed detached eddy simulation and unsteady Reynolds averaged Navier-Stokes

Delayed Detached Eddy Simulation (DDES) and Unsteady Reynolds Averaged Navier-Stokes (URANS), based on the two-equation Shear Stress Transport (SST) model, are implemented to investigate the flow features and the aero-optical distortions around the turret. The Mach number is Ma = 0.4 and the Reynolds number is Re = 1.43 × 106. Instantaneous and time-averaged flow fields are presented to compare the ability of DDES and URANS in predicting the flow features. The instantaneous results show that DDES can resolve the abundant flow structures and more disordered density distributions than URANS. The time-averaged pressure coefficient and the density distribution of both methods are generally similar, but the time-averaged turbulent kinetic energy of URANS is far higher than that of DDES. The time-averaged pressure coefficient of DDES is closer to experimental data. In the windward view, typical surface flow features of DDES and URANS are similar. In the leeward view, there are remarkable differences of typical flow features between DDES and URANS. At the six angles of elevation, 60°, 76°, 90°, 103°, 120°, and 132°, the spatial-temporal wavefront distortions are calculated and discussed with the geometric ray-tracing method and the Zernike polynomial fitting, respectively. In spatial distribution, the wavefront distortions of DDES and URANS are slightly different from the experimental data. At the angles of 60°, 76°, 90°, and 103°, the tendencies of wavefront distortion of DDES at different tracing distances are the same with that of URANS, which is due to the same ability of two methods to resolve the density distributions in the attached flow region. However, the results of DDES agree well with the experimental results at the angles of 120° and 132°, which is bigger than the results of URANS. For temporal characteristics, the frequencies of wavefront distortions of DDES are obviously higher than that of URANS. The amplitudes of wavefront distortions by DDES are about 3 to 5 times higher than that by URANS. At the cases of two different FLHs at Ma = 0.4, the flow structures are totally similar, and the tendencies of wavefront distortion with θ are also similar. At the cases of three Mach number, the compression has a big influence on the wavefront distortion.

A novel H-shape fishway with excellent hydraulic characteristics

Abstract Fishway design not only takes into account the swimming abilities of target fishes, but also considers the hydrodynamic characteristics within the fishway. In this study, the flow fields of one vertical-slot fishway (i.e. VSF), five T-shape fishways (i.e. TSF-1~TSF-5) and two H-shape fishways (i.e. HSF-1 and HSF-2) are numerically simulated by solving the three-dimensional Reynolds-averaged Navier-Stokes equations and the K-Omega-SST turbulence model. The numerical results clearly indicate that the hydrodynamic properties of HSF-2 are overall superior to the remaining seven cases, in terms of the time-averaged flow pattern, the time-averaged velocity magnitude, the depth-mean time-averaged velocity magnitude along the vertical-slot section, the volume percentages of the time-averaged velocity magnitude less than some critical values, and the distribution of the time-averaged turbulent kinetic energy. Therefore, HSF-2 is more friendly for fishes with relatively smaller sizes and weaker swimming capacities to transfer upstream. The novel HSF-2 is firstly proposed in this paper, and it is naturally designed during the process of improving the flow regime. Furthermore, the generalizability of the superiority of HSF-2 over VSF and the original T-shape fishway (i.e. TSF-1) has been exhibited with the aid of the numerical results of four operating conditions (i.e. Q = 400 L/s, 600 L/s, 800 L/s and 1000 L/s).

Numerical study on the pulsating energy evolution in the cavitating flow around a mini Cascade

Cavitation is arguably a highly turbulent phenomenon in the liquid flow system. The cavitating flow around a mini cascade was carried out to investigate the turbulent characteristics and pulsation mechanisms. The results demonstrate that cavitation can significantly affect the turbulence velocity fluctuation and turbulence anisotropy, and intensively alter the local turbulent energy. To better provide an understanding of fundamental mechanisms dictating time-averaged pulsating energy, the inhomogeneity of the local concentration of pulsating energy at the vapor–liquid interface and the turbulent vortex core involves different fundamental mechanisms are expounded thoroughly through the ability of the time-averaged turbulent kinetic energy and the time-averaged pulsating entropy. The pulsating energy of cavitating flow around the mini cascade is basically obtained from the time-averaged flow, while the surrounding dissipative mechanisms are driven by the diffusion and dissipation terms. Further, the new definition of viscous diffusion term is derived based on the resolved turbulent kinetic energy, which can also clearly delineate the diffusion effect of turbulent kinetic energy produced by the molecule viscosity. Finally, the turbulent kinetic energy and pulsating enstrophy transport mechanisms inside the shedding vortex are revealed as significant characteristics of the interaction between vortex dynamics and turbulence–cavitation.

Structured porous surface for drag reduction and wake attenuation of cylinder flow

In the current study, a new passive flow control strategy characterized by 3D printing structured porous surface was introduced and experimentally investigated to manipulate the dynamic wake evolution and flow characteristics around a circular cylinder at a Reynolds number of 2.02×104. With the 3D printing structured porous surface, parts of the incoming flow could go through the cylinder and communicate with the wake flow spontaneously. As a result, the vortex shedding was suppressed and the drag was reduced. From POD analysis results, we observed shifted modes and decreased vorticity distribution, indicating that the periodic vortex shedding process was weakened. This was also verified by the analysis of dynamic wake evolution and by the power spectrum analysis. In addition, experimental results showed that the time-averaged turbulent kinetic energy (TKE) and the Reynolds shear stress (RSS) distributions were restrained in the wake of the porous cylinder. Moreover, the mean estimated drag coefficients witnessed a significant decrease up to 49.47%.

Measurement and prediction of bottom boundary layer hydrodynamics under modulated oscillatory flows

Velocities are measured using LDA within the bottom boundary layer for 10 oscillatory flow tunnel experiments involving regular and amplitude modulated oscillatory flows over a gravel-rough bed and a sand-rough bed. Corresponding regular and modulated flows were equivalent in terms of rms velocity, oscillatory flow period, skewness and asymmetry. The experimental results are compared with predictions based on a 1DV RANS model with k−ϵ turbulence closure. The effects of modulation on the hydrodynamics of individual flow half-cycles and on the time-averaged hydrodynamics are analysed. Turbulence is carried over from one half-cycle to the following half-cycle but the main hydrodynamic properties within a half-cycle (boundary layer thickness, peak turbulent kinetic energy, peak turbulent stress) show little or no dependence on prior half-cycle flow conditions. Turbulence propagation from the bed and vertical profiles of skewness, asymmetry, time-averaged turbulent kinetic energy and time-averaged turbulent stress show remarkably little effect of modulation. Modulation does not affect the shape of the time-averaged velocity profile generated by the non-symmetric flows, but it does reduce the magnitude. The RANS model shows generally good agreement with the measured hydrodynamics above about one grain diameter from the bed, but, because of its assumption of rough turbulent flow, poorly predicts the hydrodynamics of the low-velocity half-cycles of the modulated flows over the sand-rough bed.

Influences of free surface jump conditions and different [formula omitted] SST turbulence models on breaking wave modelling

A two-phase flow Computational Fluid Dynamics (CFD) model is employed for both spilling and plunging breaking wave simulations. A numerical wave tank is built to evaluate the performance of two different free surface modelling approaches (i.e., continuous free surface conditions and free surface jump conditions) and three k−ω SST turbulence models (i.e., the original k−ω SST, the buoyancy modified k−ω SST and the free surface k−ω SST (a newly proposed model)). The influences of the free surface modelling approaches and the turbulence models are investigated by comparing with the published experimental measurements in terms of breaking point, free surface elevations, time-averaged velocity field, time-averaged turbulent kinetic energy and general turbulent behaviour, respectively. Overall, the free surface k−ω SST with the free surface jump conditions performs best in terms of the accuracy of the predictions against the experimental data and the capture of the physical breaking phenomena, for instance, the trapped air pocket and the development of the free surface in the surf zone.

Experimental study of near-bed concentration and sediment vertical mixing parameter for vertical concentration distribution in the surf zone

Two formulae for the near-bed concentration (C¯a) and the sediment vertical mixing parameter (m) are established based on a large scale wave flume experiment. The advantage of the new formulae is that the turbulent kinetic energy induced by wave breaking can be taken into account; the formula for C¯a is in terms of the near-bed, time-averaged turbulent kinetic energy, and the formula for m is in terms of depth- and time-averaged turbulent kinetic energy. A new expression for suspended sediment load also is established by depth integration of the vertical distribution of the suspended sediment concentration obtained on basis of the new formulae. Equation validation is done by comparing the predicted C¯a and m to measurements for different types of waves (regular wave, wave group, and irregular wave), and good agreement is found. The advantages of the proposed formulae over previous formulae also are discussed.

A method for reducing mean flow in oscillating-grid turbulence

Oscillating-grid turbulence (OGT) is an experimental tool that has been widely used to study the role of turbulent fluctuations under conditions of small mean flow. We report experiments to investigate the structure of the turbulent flow produced by an oscillating grid, using velocity measurements obtained through the application of two-dimensional particle image velocimetry in the vertical plane through the centre of the grid. Ensemble averages of the fluid velocity measurements at specific stages of the grid’s oscillation indicate that mean flow is induced in OGT by the merging of grid-induced jets close to the tank sidewalls. The installation of an open-ended ‘inner box’ (with its top edge positioned just below the bottom of the grid’s oscillation) is shown to inhibit the merging of the jets, thereby resulting in a reduction in the magnitude of the mean flow within the interior of the inner box region. Measurements of the time-averaged root-mean-square turbulent velocity components and the time-averaged turbulent kinetic energy flux indicate that the installation of the inner box results in turbulence that is in good agreement with the well-established models of OGT across the central 50% of the inner box’s width, but that distinct anisotropic regions exist adjacent to the vertical sidewalls. We anticipate that this simple amendment to reduce the mean flow present in OGT can be readily used in future work that utilises OGT to isolate the effects of turbulent fluctuations from those of the mean flow.Graphical abstract

Suspended sediment transport around a large-scale laboratory breaker bar

This paper presents novel insights into suspended sediment concentrations and fluxes under a large-scale laboratory plunging wave. Measurements of sediment concentrations and velocities were taken at 12 locations around an evolving breaker bar, covering the complete breaking region from shoaling to inner surf zone, with particular high resolution near the bed using an Acoustic Concentration and Velocity Profiler. Wave breaking evidently affects sediment pick-up rates, which increase by an order of magnitude from shoaling to breaking zone. Time-averaged reference concentrations correlate poorly with periodic and time-averaged near-bed velocities, but correlate significantly with near-bed time-averaged turbulent kinetic energy. The net depth-integrated suspended transport is offshore-directed and primarily attributed to current-related fluxes (undertow) at outer-flow elevations (i.e. above the wave bottom boundary layer). The wave-related suspended transport is onshore-directed and is generally confined to the wave bottom boundary layer. Cross-shore gradients of sediment fluxes are quantified to explain spatial patterns of sediment pick-up and deposition and of cross-shore sediment advection. Suspended particles travel back and forth between the breaking and shoaling zones following the orbital motion, leading to local intra-wave concentration changes. At locations between the breaker bar crest and bar trough, intra-wave concentration changes are due to a combination of horizontal advection and of vertical exchange with the bedload layer: sediment is entrained in the bar trough during the wave trough phase, almost instantly advected offshore, and deposited near the bar crest during the wave crest phase. Finally, these results are used to suggest improvements for suspended sediment transport models.

Large‐scale laboratory study of breaking wave hydrodynamics over a fixed bar

AbstractA large‐scale wave flume experiment has been carried out involving a T = 4 s regular wave with H = 0.85 m wave height plunging over a fixed barred beach profile. Velocity profiles were measured at 12 locations along the breaker bar using LDA and ADV. A strong undertow is generated reaching magnitudes of 0.8 m/s on the shoreward side of the breaker bar. A circulation pattern occurs between the breaking area and the inner surf zone. Time‐averaged turbulent kinetic energy (TKE) is largest in the breaking area on the shoreward side of the bar where the plunging jet penetrates the water column. At this location, and on the bar crest, TKE generated at the water surface in the breaking process reaches the bottom boundary layer. In the breaking area, TKE does not reduce to zero within a wave cycle which leads to a high level of “residual” turbulence and therefore lower temporal variation in TKE compared to previous studies of breaking waves on plane beach slopes. It is argued that this residual turbulence results from the breaker bar‐trough geometry, which enables larger length scales and time scales of breaking‐generated vortices and which enhances turbulence production within the water column compared to plane beaches. Transport of TKE is dominated by the undertow‐related flux, whereas the wave‐related and turbulent fluxes are approximately an order of magnitude smaller. Turbulence production and dissipation are largest in the breaker zone and of similar magnitude, but in the shoaling zone and inner surf zone production is negligible and dissipation dominates.

Time-averaged near-wake of a yawed cylinder

The present study focused on time-averaged near-wake (up to four diameters downstream) of a cylinder with yaw angles from 0° to 45° by 5° steps at a Reynolds number (Re) of 5000 based on the cylinder diameter. Two complementary techniques was employed to identify the flow patterns i.e. dye injection flow visualization and particle image velocimetry (PIV). Two different flow patterns with respect to the direction of streamlines between the cylinder and the bifurcation line in the near-wake, flow pattern A (FP-A) and B (FP-B), and one bistable pattern were observed in the near-wake as yaw angle is varied. The underlying mechanism of transition was demonstrated. The breakdown of the limited validity of the independence principle (IP) was attributed to this three-dimensional transition in the near-wake. The time-averaged and rms velocity distributions, time-averaged streamline topologies, parallel shedding phenomena, time-averaged vorticity patterns, time-averaged turbulent kinetic energy fields, drag estimations and vortex shedding frequencies have been experimentally investigated using the PIV technique in both streamwise-transverse (x–y) and streamwise-spanwise (x–z) planes.

Parameterization of Time-Averaged Suspended Sediment Concentration in the Nearshore

To quantify the effect of wave breaking turbulence on sediment transport in the nearshore, the vertical distribution of time-averaged suspended sediment concentration (SSC) in the surf zone was parameterized in terms of the turbulent kinetic energy (TKE) at different cross-shore locations, including the bar crest, bar trough, and inner surf zone. Using data from a large-scale laboratory experiment, a simple relationship was developed between the time-averaged SSC and the time-averaged TKE. The vertical variation of the time-averaged SSC was fitted to an equation analogous to the turbulent dissipation rate term. At the bar crest, the proposed equation was slightly modified to incorporate the effect of near-bed sediment processes and yielded reasonable agreement. This parameterization yielded the best agreement at the bar trough, with a coefficient of determination R2 ≥ 0.72 above the bottom boundary layer. The time-averaged SSC in the inner surf zone showed good agreement near the bed but poor agreement near the water surface, suggesting that there is a different sedimentation mechanism that controls the SSC in the inner surf zone.

TIME-AVERAGED TURBULENT MIXING AND VERTICAL CONCENTRATION DISTRIBUTION OF HIGH-DENSITY SUSPENSIONS FORMED UNDER WAVES

We analyzed oscillating flow data from U-tube experiments by Lamb et al. (2004) and found that the time-averaged turbulent kinetic energy (TKE) near bed decreased exponentially with height above the bed in high-density-suspension (HDS) flows under waves, and that the ratios of TKE distributions in the streamwise, cross-stream, and vertical dimensions were constant. Based on the finite-mixing-length theory, a semi-theoretical time-averaged suspended sediment concentration model for HDS was developed. To avoid the stability problems with the numerical solution, a simplified model was also formulated through combing the apparent Fickian diffusivity and the damping function. The comparison between the calculated results and measurements shows both models consider the effect of the sediment-induced stratification well.

Large-scale laboratory observations of turbulence on a fixed barred beach

The details of a large-scale laboratory experiment to study the turbulence generated by waves breaking on a fixed barred beach are presented. The data set includes comprehensive measurements of free surface displacement and fluid velocity for one random and one regular wave case. Observations of the time-averaged turbulent kinetic energy per unit mass, , show that the turbulence generated by wave breaking was greatest at the bar crest and did not fully dissipate prior to reaching the bed. This indicates that, even in a time-averaged sense, wave breaking turbulence may be important for near-bed processes. Onshore of the bar, turbulence was generally confined to the upper part of the water column and had dissipated once the waves reformed (approximately 1.5 wavelengths onshore of the bar crest). The turbulent structure was the same in the random and regular wave cases; however, the magnitude of was much less in the random wave case, despite similar offshore wave conditions. Additionally, three methods were used to separate the wave-induced and turbulent components of velocity:. ensemble averaging, high-pass filtering and a differencing method proposed by Trowbridge (1998 J. Atmos. Ocean. Technol. 15 290–8). The magnitude of varied by as much as a factor of 5 among these methods, but qualitatively, the cross-shore and vertical structure were independent of the method used. The differencing method agreed closely with ensemble averaging in terms of the magnitude and structure of time-averaged quantities and in the signature of the time-dependent turbulent kinetic energy. Given this agreement, the differencing method appears to be the most suitable for application to random waves, such as those observed in the field.

Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone

The characteristics of wave and turbulence velocities created by a broad-banded irregular wave train breaking on a 1:35 slope were studied in a laboratory wave flume. Water particle velocities were measured simultaneously with wave elevations at three cross-shore locations inside the surf zone. The measured data were separated into low-frequency and high-frequency time series using a Fourier filter. The measured velocities were further separated into organized wave-induced velocities and turbulent velocity fluctuations by ensemble averaging. The broad-banded irregular waves created a wide surf zone that was dominated by spilling type breakers. A wave-by-wave analysis was carried out to obtain the probability distributions of individual wave heights, wave periods, peak wave velocities, and wave-averaged turbulent kinetic energies and Reynolds stresses. The results showed that there was a consistent increase in the kurtosis of the vertical velocity distribution from the surface to the bottom. The abnormally large downward velocities were produced by plunging breakers that occurred from time to time. It was found that the mean of the highest one-third wave-averaged turbulent kinetic energy values in the irregular waves was about the same as the time-averaged turbulent kinetic energy in a regular wave with similar deep-water wave height to wavelength ratio. It was also found that the correlation coefficient of the Reynolds stress varied strongly with turbulence intensity. Good correlation between u′ and w′ was obtained when the turbulence intensity was high; the correlation coefficient was about 0.3–0.5. The Reynolds stress correlation coefficient decreased over a wave cycle, and with distance from the water surface. Under the irregular breaking waves, turbulent kinetic energy was transported downward and landward by turbulent velocity fluctuations and wave velocities, and upward and seaward by the undertow. The undertow in the irregular waves was similar in vertical structure but lower in magnitude than in regular waves, and the horizontal velocity profiles under the low-frequency waves were approximately uniform.