Reynolds Shear Stress Component Research Articles

Design of a bilateral‐symmetric multi‐slot fishway and its comparison with vertical slot fishway in terms of hydraulic properties

AbstractAiming at improving the hydraulic properties and enhancing the fish passage efficiency, this study proposes a novel bilateral‐symmetric multi‐slot fishway (BMSF) by combining the structural features of a double‐sided vertical‐slot fishway, multi‐slot fishway and T‐shape fishway. Eight BMSF cases are further designed by adjusting the slot width and the distance between the short baffle and the front end of the central wall, in order to achieve the relatively best hydrodynamic characteristics. The flow fields of two vertical‐slot fishways and eight BMSF fishways are obtained by numerically solving the Reynolds‐averaged Navier–Stokes equation, the volume‐of‐fluid equation and the k‐ω‐SST turbulence model. Numerical results manifest that the recommended BMSF‐8 provides the smallest values in terms of the maximum time‐averaged velocity magnitude (1.42 m s−1), the maximum time‐averaged turbulent kinetic energy (0.132 m2 s−2), the maximum time‐averaged Reynolds shear stress component (44 Pa), the spatial‐mean time‐averaged velocity magnitude (0.58 m s−1), and the spatial‐mean time‐averaged turbulent kinetic energy (0.042 m2 s−2) in the middle pool at Q = 1000 L/s. Even for the depth‐mean time‐averaged velocity magnitude at the slot and the volume percentages of some critical physical quantities, BMSF‐8 is also superior to the other cases. To sum up, BMSF‐8 leads to the relatively lowest flow velocity and turbulence, being more suitable for the passage of the whole fish community (especially for small‐sized fishes with weaker swimming ability). In addition, the generalizability of the aforementioned superiority of BMSF‐8 is displayed by providing the numerical results of four operating conditions (i.e., Q = 600, 800, 1000 and 1200 L/s).

Dependence of wall jet phenomenology on inlet conditions and near-field flow development

In this paper, the three-dimensional turbulent wall jet flow is investigated for three different developing initial velocity profiles. The developing initial velocity profiles at the nozzle exit are generated by three different lengths (, 50 and 90) of the square nozzle . The velocity profiles at the nozzle exit are measured with the single probe hot-wire anemometer. The Reynolds number based on the bulk mean velocity and nozzle height is 25,000 for all the cases. The measured velocity profiles at the nozzle exit are used as the inlet conditions for the numerical simulations. The results show that the initial velocity profile affects the flow field of the wall jet in near and far-field regions. It is found that the contours of streamwise velocity and turbulent kinetic energy exhibit the effect of initial conditions in the near field. The Reynolds shear stress component dominates in the vertical jet centreline plane, and it increases with a decrease in the nozzle length. The Reynolds shear stress component dominates in the lateral plane, and also exhibit the dependency on initial conditions.

Testing Basic Gradient Turbulent Transport Models for Swirl Burners Using PIV and PLIF

The present paper reports on the combined stereoscopic particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) measurements of turbulent transport for model swirl burners without combustion. Two flow types were considered, namely the mixing of a free jet with surrounding air for different swirl rates of the jet (Re = 5 × 103) and the mixing of a pilot jet (Re = 2 × 104) with a high-swirl co-flow of a generic gas turbine burner (Re = 3 × 104). The measured spatial distributions of the turbulent Reynolds stresses and fluxes were compared with their predictions by gradient turbulent transport models. The local values of the turbulent viscosity and turbulent diffusivity coefficients were evaluated based on Boussinesq’s and gradient diffusion hypotheses. The studied flows with high swirl were characterized by a vortex core breakdown and intensive coherent flow fluctuations associated with large-scale vortex structures. Therefore, the contribution of the coherent flow fluctuations to the turbulent transport was evaluated based on proper orthogonal decomposition (POD). The turbulent viscosity and diffusion coefficients were also evaluated for the stochastic (residual) component of the velocity fluctuations. The high-swirl flows with vortex breakdown for the free jet and for the combustion chamber were characterized by intensive turbulent fluctuations, which contributed substantially to the local turbulent transport of mass and momentum. Moreover, the high-swirl flows were characterized by counter-gradient transport for one Reynolds shear stress component near the jet axis and in the outer region of the mixing layer.

Assessment of turbulence models for single phase CFD computations of a liquid-liquid hydrocyclone using OpenFOAM

ABSTRACT Hydrocyclones are widely used in industry and CFD has been used to compute them. Reynolds stress turbulence models (RSM), which are computationally costly and oftentimes hard to converge, are often recommended in these computations. The present work has selected a liquid-liquid separation hydrocyclone for which single-phase experimental tangential and axial velocity profiles are available. CFD has been employed to test simpler turbulence models than the RSM and results have been compared with experimental data. The turbulence models assessed in the present work were: standard k-ε, standard k-ε with a curvature correction term, RNG k-ε, realizable k-ε, k-ω, SST, a two-time-scale linear eddy viscosity model, nonlinear quadratic and cubic k-ε eddy viscosity models and the Gibson and Launder and LRR Reynolds stress models. Computations have been carried out with OpenFOAM 2.2.2. Results using the Gibson and Launder turbulence model have been compared to some obtained with Ansys Fluent and these were in agreement. Results have shown that all turbulence models, apart from the RSM, returned basically the same tangential velocity profiles as the standard model. All turbulence models have failed in predicting axial velocity. Assessment of the Reynolds stresses has indicated that the internal flow field in hydrocyclones might be shear dominant and that the Reynolds shear stress component is the most relevant to correctly predict tangential velocity. Geometric proportions of hydrocyclones may affect significantly the intensity of rotational and streamline curvature effects. Two-equation eddy-viscosity models are likely to be able to attend such condition, since appropriate levels of eddy viscosity are predicted at free and forced vortexes regions, however further investigation is still needed.

Acoustic and flow characteristics of an airfoil fitted with morphed trailing edges

An experimental study of a simple NACA 0012 airfoil fitted with two different flap profiles was carried out to characterize their aerodynamic and aeroacoustic performance. The airfoil with a flap deflection angle of β = 10° was tested for a wide range of angles of attack at a chord-based Reynolds number of Rec=2.6×105. The aerodynamic lift and drag measurements show improved lift-to-drag performance for the morphed flap airfoil compared to the hinged flap airfoil at low angles of attack. Surface flow visualization and boundary layer measurements on the suction surface of the flap show delayed separation for the morphed flap airfoil. Higher-order moments of the wall pressure fluctuations were also used to observe the flow separation over the flap. Additionally, Particle Image Velocimetry was also used to study the flow over the flap and at the airfoil wake. Flow measurements showed that the downstream wake development could be significantly influenced by the flap camber. The mean velocity contours at the wake showed increased wake velocity deficit and turbulent kinetic energy for the morphed flap airfoil. The turbulent kinetic energy results displayed a characteristic double peak behavior which was also the dominant characteristics of the streamwise Reynolds shear stress component. Near-field unsteady surface pressure fluctuations and far-field noise measurements show reduced point spectra and noise levels for morphed flap configuration at low angles of attack but considerably increased noise levels at high angles of attack compared to hinged flap configuration.

Secondary Flows and Vortex Structure Associated With Isolated and Interacting Barchan Dunes

The three‐dimensional, crescentic morphology of a barchan dune induces secondary flows and a complex vortex structure in its wake. In scenarios where barchans are in close proximity to each other, the flow modifications introduced by the wake of the upstream barchan are important for understanding the morphodynamics of the downstream barchan. The results herein detail the flow structure in a plane normal to the mean flow (cross‐plane) through stereo particle image velocimetry measurements in a refractive‐index‐matching flow facility, utilizing solid, fixed‐bed barchan models. Spatial distributions of streamwise‐oriented swirling motions and Reynolds shear stress components reveal distinct flow regimes in the wake region of an isolated barchan: flow downstream of the horn tips and flow in the separated shear layer closer to the centerline. Streamwise rollers appear downstream of the horns, and measurements upstream demonstrate their origin on the stoss side of the dune in the form of a horseshoe vortex. Flow downstream of the separated shear layer in the wake embodies features consistent with that of hairpin vortices shed from the arched crestline of the barchan. These structures constitute the induction of secondary flows in the flow that, in the case of barchans in close proximity with a lateral offset, are preferentially amplified in accordance with local topography. Further analysis reveals the spatial scales and turbulent stresses associated with these structures, which are discussed in the context of larger fields of bedforms and the formation of protodunes.

Scale adaptive simulation of vortex structures past a square cylinder

The scale adaptive simulation (SAS) turbulence model is evaluated on a turbulent flow past a square cylinder using the open-source CFD package OpenFOAM 2.3.0. Two and three-dimensional simulations are performed to determine global quantities like drag and lift coefficients and Strouhal number in addition to mean and fluctuating velocity profiles in the recirculation and wake regions. SAS model is evaluated against the Shear Stress Transport k - ω (SST) model and also compared with previously reported results based on DES, LES and DNS turbulence approaches. Results show that global quantities along with mean velocity profiles are well-captured by 2-D SAS model. The 3-D SAS model also succeeded in providing comparable results with recently published DES study on Reynolds shear stress and velocity fluctuation components using about 12 times lower computational cost. It is shown that large values of the SAS model constant result in too dissipative behavior, so that proper calibration of the SAS model constant for different turbulent flows is vital.

Quantification of Preferential Contribution of Reynolds Shear Stresses and Flux of Mean Kinetic Energy Via Conditional Sampling in a Wind Turbine Array

Conditional statistics are employed in analyzing wake recovery and Reynolds shear stress (RSS) and flux directional out of plane component preference. Examination of vertical kinetic energy entrainment through describing and quantifying the aforementioned quantities has implications on wind farm spacing, design, and power production, and also on detecting loading variation due to turbulence. Stereographic particle image velocimetry measurements of incoming and wake flow fields are taken for a 3 × 4 model wind turbine array in a scaled wind tunnel experiment. Reynolds shear stress component is influenced by ⟨uv⟩ component, whereas ⟨vw⟩ is more influenced by streamwise advection of the flow; u, v, and w being streamwise, vertical, and spanwise velocity fluctuations, respectively. Relative comparison between sweep and ejection events, ΔS⟨uiuj⟩, shows the role of streamwise advection of momentum on RSS values and direction. It also shows their tendency to an overall balanced distribution. ⟨uw⟩ intensities are associated with ejection elevated regions in the inflow, yet in the wake, ⟨uw⟩ is linked with sweep dominance regions. Downward momentum flux occupies the region between hub height and top tip. Sweep events contribution to downward momentum flux is marginally greater than ejection events'. When integrated over the swept area, sweeps contribute 55% of the net downward kinetic energy flux and 45% is the ejection events contribution. Sweep dominance is related to momentum deficit as its value in near wake elevates 30% compared to inflow. Understanding these quantities can lead to improved closure models.

Turbulence Budgets in Buoyancy-affected Vertical Backward-facing Step Flow at Low Prandtl Number

The paper investigates buoyancy impact on the vertical flow over a backward-facing step at low Prandtl number by Direct Numerical Simulation. In particular, the very low Prandtl number of liquid sodium, 0.0088, is considered in the regime of mixed convection, i.e. for Richardson numbers below unity. The effects of buoyancy on mean flow, heat transfer and turbulence are assessed. Buoyancy is found to attenuate recirculation and, consequently, increase heat transfer. Turbulence is decreased in the attached boundary layer for moderate buoyancy impact but surpasses the levels found in forced convection at the largest Richardson number investigated. Beyond the mean flow and second moments, the budgets of turbulent kinetic energy, Reynolds shear stress, temperature variance, and turbulent heat flux components are studied and related to the alterations in the mean field quantities. Due to scale separation, production and dissipation nearly balance for temperature variance while this is not the case for turbulent kinetic energy. Similar findings for the turbulent heat fluxes show that the correlation between temperature and pressure gradient is the most important contribution to the budget aside from production and dissipation. In addition to the physical insight into this flow, the data presented may be used for the validation and improvement of turbulence models for liquid metal flows.

Measurements of Turbulent Jet Mixing in a Turbulent Co-Flow Including the Influence of Periodic Forcing and Heating

In this work, the turbulent mixing of a confined coaxial jet in air is investigated by means of simultaneous particle image velocimetry and planar laser induced fluorescence of the acetone seeded flow injection. The jet is injected into a turbulent duct flow at atmospheric pressure through a 90 ∘ pipe bend. Measurements are conducted in a small scale windtunnel at constant mass flow rates and three modes of operation: isothermal steady jet injection at a Dean number of 20000 (Red=32000), pulsed isothermal injection at a Womersley number of 65 and steady injection at elevated jet temperatures of ΔT=50 K and ΔT=100 K. The experiment is aimed at providing statistically converged quantities of velocity, mass fraction, turbulent fluctuations and turbulent mass flux at several downstream locations. Stochastic error convergence over the number of samples is assessed within the outer turbulent shear layer. From 3000 samples the statistical error of time-averaged velocity and mass fraction is below 1 % while the error of Reynolds shear stress and turbulent mass flux components is in the of range 5-6 %. Profiles of axial velocity and turbulence intensity immediately downstream of the bend exit are in good agreement with hot-wire measurements from literature. During pulsed jet injection strong asymmetric growing of shear layer vortices lead to a skewed mass fraction profile in comparison with steady injection. Phase averaging of single shot PLIF-PIV measurements allows to track the asymmetric shear layer vortex evolvement and flow breakdown during a pulsation cycle with a resolution of 10∘. Steady injection with increased jet temperature supports mixing downstream from 6 nozzle diameters onward.

Reynolds Stress Structures in the Hybrid RANS/LES of a Planar Channel

The near-wall cycle of hybrid RANS/LES is studied by calculating the flow through a planar channel. Statistical results are commented on and related to instantaneous structures which are extracted from the flow field. The problematic structures in the artificial near-wall cycle, well known to be super-streaks, are identified and quantified. The calibration of such closures provides a correct mixing length argument in the logarithmic layer. However because of these overly intense streamwise streaks, it is impossible to simultaneously predict the Reynolds streamwise normal and shear stress components correctly. Further, because the location of the RANS-LES interface changes spatially and temporally, we see these structures are more free to move vertically and this further worsens statistical results.

Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture

Direct numerical simulations of turbulent flow in a channel with superhydrophobic surfaces (SHS) were performed, and the effects of the surface texture on the turbulence and skin-friction coefficient were examined. The SHS is modeled as a planar boundary comprised of spanwise-alternating regions of no-slip and free-slip boundary conditions. Relative to the reference no-slip channel flow at the same bulk Reynolds number, the overall mean skin-friction coefficient is reduced by 21.6%. A detailed analysis of the turbulence kinetic energy budget demonstrates a reduction in production over the no-slip phases, which is explained by aid of quadrant analysis of the Reynolds shear stresses and statistical analysis of the turbulence structures. The results demonstrate a significant reduction in the strength of streamwise vortical structures in the presence of the SHS texture and a decrease in the Reynolds shear-stress component ⟨R12⟩ which has a favorable influence on drag over the no-slip phases. A secondary flow which is set up at the edges of the texture also effects a beneficial change in drag. Nonetheless, the skin-friction coefficient on the no-slip features is higher than the reference levels in a simple no-slip channel flow. The increase in the skin-friction coefficient is attributed to two factors. First, spanwise diffusion of the mean momentum from free-slip to no-slip regions increases the local skin-friction coefficient on the edges of the no-slip features. Second, the drag-reducing capacity of the SHS is further reduced due to additional Reynolds stresses, ⟨R13⟩.

LES Study of 3D Incompressible Temporal Mixing Layer Using Different Well-Known Subgrid Scale (SGS) Models

In this paper, 3D incompressible temporal mixing layer at three different Reynolds numbers has been investigated using large eddy simulation (LES) turbulence model. To consider the effects of the subgrid scales, six different well-known SGS models, Smagorinsky, dynamic Smagorinsky, Yoshizava one equation, Spalart–Allmaras one equation, Lagrangian dynamic Smagorinsky two equation (LDS) and six-equations Reynolds stress (RSM) were applied. The computed LES results for vorticity thickness, average total kinetic energy, and Reynolds shear stress components of stress tensor revealed that the LDS and RSM models agree well with DNS data. Different steps of forming of coherent flow structures at different times were also discussed.

Numerical and experimental investigation of the mean and turbulent characteristics of a wing-tip vortex in the near field

The near-field (up to three chord lengths) development of a wing-tip vortex is investigated both numerically and experimentally. The research was conducted in a medium speed wind tunnel on a NACA 0012 square tip half-wing at a Reynolds number of 3.2 × 105. A full Reynolds stress turbulence model with a hybrid unstructured grid was used to compute the wing-tip vortex in the near field while an x-wire anemometer and five-hole probe recorded the experimental results. The mean flow of the computed vortex was in good agreement with experiment as the circulation parameter was within 6% of the experimental value at x/ c = 0 for α = 10° and the crossflow velocity magnitude was within 1% of the experimental value at x/ c = 1 for α = 5°. The trajectory of the computed vortex was also in good agreement as it had moved inboard by the same amount (10% chord) as the experimental vortex at the last measurement location. The axial velocity excess is under predicted for α = 10°, whereas the velocity deficit is in relatively good agreement for α = 5°. The computed Reynolds shear stress component 〈 u′v′〉 is in good agreement with experiment at x/ c = 0 for α = 5°, but is greatly under predicted further downstream and at all locations for α = 10°. It is thought that a lack of local grid refinement in the vortex core and deficiencies in the Reynolds stress turbulence model may have led to errors in the mean flow and turbulence results respectively.

Large-Eddy Simulation of Film Cooling in an Adverse Pressure Gradient Flow

In order to analyze the interaction of multiple rows of film cooling holes in flows at adverse pressure gradients, large-eddy simulations (LESs) are performed. The considered three-row cooling configuration consists of inclined cooling holes at an angle of 30 deg with a lateral pitch of p/D=3 and a streamwise spacing of l/D=6. The cooling holes possess a fan-shaped exit geometry with lateral and streamwise expansions. For each cooling row the complete internal flow is computed. Air and CO2 are injected in order to investigate the influence of an increased density ratio on the film cooling physics at adverse pressure gradients. The CO2 injected at the same blowing rate as air shows a higher magnitude of the Reynolds shear stress component and, thus, an enhanced mixing downstream of the cooling holes. The LES results of the air and CO2 configurations are compared to the corresponding particle-image velocimetry (PIV) measurements and show a convincing agreement in terms of the averaged streamwise velocity and streamwise velocity fluctuations. Furthermore, the cooling effectiveness is investigated for a zero and an adverse pressure gradient configuration with a temperature ratio at gas turbine conditions. For the adverse pressure gradient case, reduced temperature levels off the wall are observed. However, the cooling effectiveness shows only minor differences compared to the zero pressure gradient flow. The turbulent Schmidt number at CO2 injection shows large variations. Just downstream of the injection it attains low values, whereas high values are detected in the upper mixing zone of the cooling flow and the freestream at each film cooling row.

Relaminarization of turbulent channel flow using traveling wave-like wall deformation

Effect of traveling wave-like wall deformation (i.e. peristalsis) in a fully developed turbulent channel flow is investigated by means of direct numerical simulation. We not only demonstrate that the friction drag is reduced by wave-like wall deformation traveling toward the downstream direction, but also show that the turbulence is completely suppressed (viz. the flow is relaminarized) under some sets of parameters. It is also found that at higher amplitude of actuation the relaminarized flow is unstable and exhibits a periodic cycle between high and low drag. The drag reduction is caused by suppression of random Reynolds shear stress component due to stabilization. The quadrant analysis reveals that traveling wave-like wall deformation makes strongly negative random Reynolds shear stress in the converging region.

Effect of Local Periodic Disturbance on Mixing Layer Downstream of Two-Dimensional Jet (Spatial Structure and Quantitative Representation of Laminar-Turbulent Transition Process)

The laminar-turbulent transition of a mixing layer induced by oscillating flat plates at an exit of a two-dimensional nozzle was experimentally investigated. The mixing layer was formed between the jet, which issued from the nozzle and the surrounding quiescent fluid. The plates oscillated vertically in relation to the mean flow. The oscillation frequency was two orders of magnitude smaller than the fundamental frequency of the velocity fluctuation. Mean and fluctuating velocity components in the streamwise and normal directions were measured by hot-wire anemometers. In the oscillating state, the same phenomenon as in the natural transition process appeared more upstream. In the early stage within the nonlinear region, the growth of fluctuating velocity attenuated and the Reynolds shear stress component decreased. The decrease in their production rate due to the expansion of the mixing layer contributed to the attenuation and decrease. The probability of the streamwise and normal fluctuating velocity components taking the same sign, increased or decreased in accordance with the increase and decrease of the Reynolds shear stress component. The randomness factor, which had been proposed by Sato, appeared to be a reasonable indicator of the present transition process, especially in the process in which the periodic velocity fluctuation became irregular. However, this factor certainly indicated the same value at two streamwise positions.

Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface

The geostrophic Ekman boundary layer for large Rossby number (Ro) has been investigated by exploring the role played by the mesolayer (intermediate layer) lying between the traditional inner and outer layers. It is shown that the velocity and Reynolds shear stress components in the inner layer (including the overlap region) are universal relations, explicitly independent of surface roughness. This universality of predictions has been supported by observations from experiment, field and direct numerical simulation (DNS) data for fully smooth, transitionally rough and fully rough surfaces. The maxima of Reynolds shear stresses have been shown to be located in the mesolayer of the Ekman boundary layer, whose scale corresponds to the inverse square root of the friction Rossby number. The composite wall-wake universal relations for geostrophic velocity profiles have been proposed, and the two wake functions of the outer layer have been estimated by an eddy viscosity closure model. The geostrophic drag and cross-isobaric angle predictions yield universal relations, which are also supported by extensive field, laboratory and DNS data. The proposed predictions for the geostrophic drag and the cross-isobaric angle compare well with data for Rossby number Ro ≥ 105. The data show low Rossby number effects for Ro < 105 and higher-order effects due to the mesolayer compare well with the data for Ro ≥ 103.

Robust evaluation of the dissimilarity between interrogation windows in image velocimetry

Image velocimetry techniques, which extract motion information by comparison of image regions, typically make use of cross-correlation to measure the degree of matching. In this work, a novel measure of the dissimilarity between interrogation windows is proposed which is based on a more robust estimator than cross-correlation. The method is validated on synthetic images and on two experimental data sets obtained from a periodically pulsed jet and a backward-facing step. The former is a basically laminar flow, whereas the latter is fully turbulent. Both of them are characterized by regions of high velocity gradients. The efficiency of the robust image velocimetry (RIV) is compared with a cross-correlation algorithm (PIV). The analysis of results shows that the RIV is less sensitive to the appearance and disappearance of particles, and to high velocity gradients and, in general, to noise, generating less spurious velocity vectors. As a consequence RIV resolves better the vorticity peaks at the center of the vortex rings generated by the pulsed jet, obtaining, for a given interrogation window size, a higher spatial resolution. Moreover, in the analysis of the flow field generated by the backward-facing step, the RIV performs better in the shear layer at the border of the recirculation region, leading to a more reliable estimation of Reynolds shear stress and horizontal velocity component.

Management of Stronger Wall Jet by a Streamwise Vortex with Periodic Perturbation (Analysis by Phase Averaging)

In a stronger wall jet managed by a streamwise vortex, effect of periodic perturbation on the interaction and evolution processes has been investigated in the equations derived from phase averaging and triple decomposition. Transverse and spanwise locations of vortex center have time variations associated with variation in strength of streamwise vortex. Normal Reynolds stress difference (V2-W2) and shear stress VW generated by periodic perturbation reduce decay rate of maximum vorticity and accelerate growth rate of spanwise vortex radius in terms of production terms in transport equation for streamwise vorticity. Prediction of Reynolds shear stress component VW by taking account of time variation of both vortex center and strength successfully explains experimental data of conventional time average stress of vw.