Cross-stream Velocity Components Research Articles

Machine Learning Approach for Flow Fields Over a Circular Cylinder Based on Particle Image Velocimetry Measurements

Flow around a circular cylinder has been experimentally studied at Reynolds numbers of Re = 4 × 103 and Re = 8 × 103 using Particle Image Velocimetry (PIV). The Artificial Neural Network (ANN) method, a subset of machine learning, has been implemented to capture complex flow patterns and relationships within data to estimate the experimental results. Experimental and estimated results regarding instantaneous contour graphics for streamwise (u) and cross-stream (v) velocity components with velocity vector fields have been compared. Furthermore, drag coefficient (CD) and Strouhal number (St) have been validated. In flow features, instantaneous streamwise velocity components indicated a lower pressure zone in the wake region of the cylinder owing to flow separation. The ANN method has predicted the positions of the minimum velocity clusters with 3.2 % for Re = 8 × 103 as a mean relative error compared to the experimental results. Moreover, the average relative difference of 10.82 % between the experimental and the estimated results for the clusters with the minimum streamwise velocity components has been attained at Re = 4 × 103 and Re = 8 × 103. Regarding the cross-stream velocity components, the mean relative difference values have been observed for the clusters with maximum values of 6.83 % and the clusters with minimum values of 3.66 %. Drag coefficients have also been obtained, and these values are very close as CD = 1.090 and CD = 1.084 for PIV and ANN methods at Re = 8 × 103, respectively. Furthermore, St values of the circular cylinder are St = 0.216 at Re = 4 × 103 and St = 0.211 at Re = 8 × 103, which agree with the results of the literature.

NUMERICAL MODELING OF BACKWARD-FACING STEP FLOW VIA COMPUTATIONAL FLUID DYNAMICS

As a fundamental case for problems of fluid mechanics, examination of flow separation and its reattachment is important for engineering applications. Considering the significance of the subject, backward-facing step flow has been modeled via Computational Fluid Dynamics (CFD) based on an experimental study previously done at Re = 5000. Steady simulations have been conducted by k-ε Renormalization Group (RNG) considering the same flow conditions of the reference study. Pressure distributions, streamwise and cross-stream velocity components, velocity magnitude values with streamline patterns and turbulence kinetic energy values have been presented by using contour graphics. Furthermore, the stations for pressure distributions, velocity profiles for streamwise components and turbulence kinetic energy values have been defined for evolution of related data. Lower pressure zone for the wake region of the backward-facing step has been attained due to flow separation. Separation of the upstream boundary layer has been seen and it became a curved one. Moreover, turbulence level of the step wake has been obtained as higher than those of any other points. Transition to core flow has been attained at y* = 1.1 that is above the step height. Flow oscillations have been observed for x* ≥ 2 and y* ≤ 1 since the fluctuations for these values were effective in the wake region. To sum up, the dimensionless reattachment length has been numerically obtained as 5.92 which is very good agreement with the experimental results at same Reynolds number. The deviation from the reference results is from 0.34 % to 1.33 %.

An Observation-Based Study of Gulf Stream Meander Kinematics Offshore of Cape Hatteras

Gulf Stream (GS) meander structure and propagation offshore of Cape Hatteras are investigated by integrating current measurements from a bottom-moored Acoustic Doppler Current Profiler (ADCP) with high-frequency radar (HFR) surface current measurements and satellite Sea Surface Temperature (SST) images during November 2014. The ADCP measurements provide well-resolved current observations throughout most of the water column, while hourly surface current measurements from HF radars and available satellite SST images provide spatial context to the GS orientation, meander propagation, circulation, and shear structure in the region of the ADCP mooring. The observations provide new insights about meander propagation and evolution in this important transition region. ADCP measurements observed that the increase and deepening intervals of the downstream current with approaching meander crests were typically longer than those for the decrease and shoaling of downstream current, consistent with prominent skewed crests near the surface. The transition time from trough to crest is much greater than that from crest to trough, reflecting the asymmetry in the downstream velocity structure. Vertical shears in the downstream and cross-stream velocity components are indicative of a cold dome centered downslope and offshore of the ADCP. Local maxima in downstream current and bottom temperature at the ADCP occur simultaneously, are accompanied by large vertical velocities, and are led by offshore currents in the upper water column. The mean meander phase speed estimated with HFRs is 48 km/day. Meander periods during the month are about 5-6 days. Where the maxima are seen in the water column, downstream currents reach 2.5 m/s, with current reversals sometimes in excess of 0.5 m/s. Downstream currents occupy an increasing portion of the water column as a crest approaches, and a decreasing fraction as a trough approaches. The deepening increase in downstream velocities with approaching crests is often accompanied by an increase in upstream velocities near the bottom.

Integrated Quadrant Analysis: A New Method for Analyzing Turbulent Coherent Structures

Integrated quadrant analysis is a novel technique to identify and to characterize the trajectory and strength of turbulent coherent structures in the atmospheric surface layer. By integrating the three-dimensional velocity field characterized by traditional quadrant analysis with respect to time, the trajectory history of individual coherent structures can be preserved with Eulerian turbulence measurements. We develop a method to identify the ejection phase of coherent structures based on turbulence kinetic energy (TKE). Identifying coherent structures within a time series using TKE performs better than identifying them with the streamwise and vertical velocity components because some coherent structures are dominated by the cross-stream velocity component as they pass the sensor. By combining this identification method with the integrated quadrant analysis, one can animate or plot the trajectory of individual coherent structures from high-frequency velocity measurements. This procedure links a coherent ejection with the subsequent sweep and quiescent period in time to visualize and quantify the strength and the duration of a coherent structure. We develop and verify the method of integrated quadrant analysis with data from two field studies: the Eclipse Boundary Layer Experiment (EBLE) in Corvallis, Oregon in August 2017 (grass field) and the Vertical Cherry Array Experiment (VACE) in Linden, California in November 2019 (cherry orchard). The combined TKE identification method and integrated quadrant analysis are promising additions to conditional sampling techniques and coherent structure characterization because the identify coherent structures and couple the sweep and ejection components in space. In an orchard (VACE), integrated quadrant analysis verifies each coherent structure is dominated by a sweep. Conversely, above the roughness sublayer (EBLE), each coherent structure is dominated by an ejection.

Electrical switching of a surfactant coated drop in Poiseuille flow

Electrical effects can impart a cross-stream component to drop motion in a pressure-driven flow, due to either an asymmetric charge distribution or shape deformation. However, surfactant-mediated alterations in such migration characteristics remain unexplored. By accounting for three-dimensionality in the drop motion, we analytically demonstrate here a non-trivial switching of drop migration with the aid of a surfactant coating on its surface. We establish this phenomenon as controllable by exploiting an interconnected interplay between the hydrodynamic stress, electrical stress and Marangoni stress, manifested so as to achieve a net interfacial force balance. Our results reveal that under different combinations of electrical conductivity and permittivity ratios, the relative strength of the electric stress with respect to the hydrodynamic stress, the applied electric field direction and the surfactants alter the longitudinal and cross-stream velocity components of the droplets differently. The effect of drop deformation on its speed is found to be altered with the increased sensitivity of the surface tension to the surfactant concentration, depending on the competing effects of the electrohydrodynamic flow modification and the tip stretching phenomenon. Further, with a suitable choice of electrical property ratios, the Marangoni effects can be exploited to direct the drop in reaching a final transverse position towards or away from the channel centreline. These results may turn out to be of immense consequence in providing an insight to the underlying complex physical mechanisms dictating an intricate control on the drop motion in different directions.

An Interpretation of the Laminar-Turbulent Transition Startup against the Consideration of the Transverse Viscosity Factor

This paper proposes a rheological model of a fluid having the Newtonian model applicability limit and a potential for further “addition” of the transverse viscosity factor. The dynamic equations for a fluid that has such rheological model are discussed, the analysis of which demonstrates the possibility of “generating” the cross stream velocity components. The transition to the dimensionless notation introduces four dimensionless complexes of local characterization for the transition conditions in the neighborhood of the flow region point in question. Based on such dimensionless complexes and using the known experimental data, the empiric conditions of “generating” the cross stream velocity components and starting the laminar-turbulent transition are proposed.

Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

The motion of a viscous droplet in unbounded Poiseuille flow under the combined influence of bulk-insoluble surfactant and linearly varying temperature field aligned in the direction of imposed flow is studied analytically. Neglecting fluid inertia, thermal convection and shape deformation, asymptotic analysis is performed to obtain the velocity of a force-free surfactant-laden droplet. The droplet speed and direction of motion are strongly influenced by the interfacial transport of surfactant, which is governed by surface Péclet number. The present study is focused on the following two limiting situations of surfactant transport: (i) surface-diffusion-dominated surfactant transport considering small surface Péclet number, and (ii) surface-convection-dominated surfactant transport considering high surface Péclet number. Thermocapillary-induced Marangoni stress, the strength of which relative to viscous stress is represented by the thermal Marangoni number, has a strong influence on the distribution of surfactant on the droplet surface. The present study shows that the motion of a surfactant-laden droplet in the combined presence of temperature and imposed Poiseuille flow cannot be obtained by a simple superposition of the following two independent results: migration of a surfactant-free droplet in a temperature gradient, and the motion of a surfactant-laden droplet in a Poiseuille flow. The temperature field not only affects the axial velocity of the droplet, but also has a non-trivial effect on the cross-stream velocity of the droplet in spite of the fact that the temperature gradient is aligned with the Poiseuille flow direction. When the imposed temperature increases in the direction of the Poiseuille flow, the droplet migrates towards the flow centreline. The magnitude of both axial and cross-stream velocity components increases with the thermal Marangoni number. However, when the imposed temperature decreases in the direction of the Poiseuille flow, the magnitude of both axial and cross-stream velocity components may increase or decrease with the thermal Marangoni number. Most interestingly, the droplet moves either towards the flow centreline or away from it. The present study shows a critical value of the thermal Marangoni number beyond which the droplet moves away from the flow centreline which is in sharp contrast to the motion of a surfactant-laden droplet in isothermal flow, for which the droplet always moves towards the flow centreline. Interestingly, we show that the above picture may become significantly altered in the case where the droplet is not a neutrally buoyant one. When the droplet is less dense than the suspending medium, the presence of gravity in the direction of the Poiseuille flow can lead to cross-stream motion of the droplet away from the flow centreline even when the temperature increases in the direction of the Poiseuille flow. These results may bear far-reaching consequences in various emulsification techniques in microfluidic devices, as well as in biomolecule synthesis, vesicle dynamics, single-cell analysis and nanoparticle synthesis.

Three-Dimensional Boundary Layer in a Turbine Blade Passage

The boundary layer on the end wall of a turbine blade cascade is subject to cross-stream pressure gradients in the blade passage, which generate a cross-stream velocity component to make it three dimensional. This distorts the turbulence relative to a two-dimensional boundary layer and impacts the end wall heat transfer. This study presents measurements of the three-dimensional boundary layer in a turbine cascade obtained with a laser Doppler velocimeter. In addition, two types of Reynolds-averaged Navier–Stokes models are compared to the measurements: the Shear Stress Transport model using the isotropic eddy viscosity assumption and a Reynolds stress model that allows for anisotropy of the Reynolds stress. Neither model fully captures the complexity of the three-dimensional boundary layer in a turbine blade passage, particularly for turbulence associated with the cross-stream flow and for the highly accelerated three-dimensional boundary layer at the passage exit. Measurements at the passage exit indicate a very thin boundary layer with laminarlike qualities. Because of the boundary-layer complexity, end wall heat transfer is not well predicted toward the pressure side and the exit of the blade passage.

Quantifying error of lidar and sodar Doppler beam swinging measurements of wind turbine wakes using computational fluid dynamics

Abstract. Wind-profiling lidars are now regularly used in boundary-layer meteorology and in applications such as wind energy and air quality. Lidar wind profilers exploit the Doppler shift of laser light backscattered from particulates carried by the wind to measure a line-of-sight (LOS) velocity. The Doppler beam swinging (DBS) technique, used by many commercial systems, considers measurements of this LOS velocity in multiple radial directions in order to estimate horizontal and vertical winds. The method relies on the assumption of homogeneous flow across the region sampled by the beams. Using such a system in inhomogeneous flow, such as wind turbine wakes or complex terrain, will result in errors. To quantify the errors expected from such violation of the assumption of horizontal homogeneity, we simulate inhomogeneous flow in the atmospheric boundary layer, notably stably stratified flow past a wind turbine, with a mean wind speed of 6.5 m s−1 at the turbine hub-height of 80 m. This slightly stable case results in 15° of wind direction change across the turbine rotor disk. The resulting flow field is sampled in the same fashion that a lidar samples the atmosphere with the DBS approach, including the lidar range weighting function, enabling quantification of the error in the DBS observations. The observations from the instruments located upwind have small errors, which are ameliorated with time averaging. However, the downwind observations, particularly within the first two rotor diameters downwind from the wind turbine, suffer from errors due to the heterogeneity of the wind turbine wake. Errors in the stream-wise component of the flow approach 30% of the hub-height inflow wind speed close to the rotor disk. Errors in the cross-stream and vertical velocity components are also significant: cross-stream component errors are on the order of 15% of the hub-height inflow wind speed (1.0 m s−1) and errors in the vertical velocity measurement exceed the actual vertical velocity. By three rotor diameters downwind, DBS-based assessments of wake wind speed deficits based on the stream-wise velocity can be relied on even within the near wake within 1.0 m s−1 (or 15% of the hub-height inflow wind speed), and the cross-stream velocity error is reduced to 8% while vertical velocity estimates are compromised. Measurements of inhomogeneous flow such as wind turbine wakes are susceptible to these errors, and interpretations of field observations should account for this uncertainty.

Turbulent flow over the trough region formed by a pair of forward-facing bedform shapes

The present paper explores the turbulent flow characteristics and overall drag over the trough region of a pair of adjacent 2-D forward-facing dune-shaped artificial structures with two different stoss-side slopes and aims to make a comparative study. Structures considered here were of equal base length (λ) with a common gentle slope of 6°at the downstream face. The stoss-side angles were respectively 50°and 90°. Experiments were conducted at the Fluvial Mechanics Laboratory (FML) of Indian Statistical Institute (ISI), Kolkata. The velocity data were collected using a 3-D Micro-Acoustic Doppler Velocimeter (ADV) at the flume centerline to analyze the mean flows, Reynolds stresses and the overall drag at a Reynolds number, Reh≈1.44×105. One-dimensional profiles of turbulent flow parameters demonstrate that the flow separation bubble and a thin perturbed shear layer between the negative velocity region and outer layer with high velocity are the main sources of turbulence production. A change in turbulence characteristics between the two crest positions is identified. A greater amount of flow resistance is observed in the case of the structure having higher stoss-side slope. The spectral analysis reveals that peak power spectral density generally occurs at 0.25–1 Hz for the stream-wise velocity component and at 0.9–3.0 Hz for the cross-stream and vertical velocity components. Power spectra showed better defined peaks near the shear layer in the separation cell where it reaches to maximum which is two to three times greater than its values in the upstream and further downstream region. Strouhal numbers are calculated using the frequencies of eddies and vortices with different sets of characteristic length and velocity scales; and compared with the previous results of other researchers.

Droplet–turbulence interaction in a confined polydispersed spray: effect of droplet size and flow length scales on spatial droplet–gas velocity correlations

AbstractThis paper discusses the interaction between droplets and entrained turbulent air flow in the far-downstream locations of a confined polydispersed isothermal spray. Simultaneous and planar measurements of droplet and gas velocities in the spray along with droplet size are obtained with the application of a novel experimental technique, developed by Hardalupaset al. (Exp. Fluids, vol. 49, 2010, pp. 417–434), which combines interferometric laser imaging for droplet sizing (ILIDS) with particle image velocimetry (PIV). These measurements quantified the spatial correlation coefficients of droplet–gas velocity fluctuations ($R_{dg}$) and droplet–droplet velocity fluctuations ($R_{dd}$) conditional on droplet size classes, for various separation distances, and for axial and cross-stream velocity components. At the measurement location close to the spray edge, with increasing droplet size,$R_{dg}$was found to increase in axial direction and decrease in cross-stream direction. This suggests that as the gas-phase turbulence becomes more anisotropic away from the spray axis, the gravitational influence on droplet–gas correlated motion tends to increase. The effective length scales of the correlated droplet–gas motion were evaluated and compared with that for gas and droplet motion. The role of different turbulent eddies of the gas flow on the droplet–gas interaction was examined. The flow structures were extracted using proper orthogonal decomposition (POD) of the instantaneous gas velocity data, and their contribution on the spatial droplet–gas velocity correlation was evaluated, which quantified the momentum transfer between the two phases at different length scales of the gas flow. The droplets were observed to augment turbulence for the first three POD modes (larger scales) and attenuate it for the rest of the modes (smaller scales). It has been realized that apart from droplet Stokes number and mass loading, the dynamic range of length scales of the gas flow and the relative turbulent kinetic energy content of the flow structures (POD modes) must be considered in order to conclude if the droplets enhance or reduce the carrier-phase turbulence especially at the lower wavenumbers.

Characterizing spatial variability in velocity and turbulence intensity using 3-D acoustic Doppler velocimeter data in a plane-bed reach of East St. Louis Creek, Colorado, USA

We investigated the influence on flow resistance of flow structure and turbulence at the reach scale in a mountain channel using 3-D velocity measurements and geostatistical analysis to understand the complexity of the flow structure in a reach with limited bed irregularities. The increase in flow resistance at low flows in a plane-bed reach was not fully explained by grain resistance, therefore detailed 3-D velocity measurements were made to investigate spatial variability in velocity and turbulence components and potential controls on flow resistance. One plane-bed reach was surveyed over two stages in Fraser Experimental Forest, Colorado, using a combination of a total station, LiDAR (Light Detection and Ranging), and a SonTek Flowtracker handheld ADV (acoustic Doppler velocimeter). LiDAR was used to capture bank and channel geometry at low flows, whereas the water surface and bed data were collected with the total station at all flows. We used the standard deviation of bed elevation (σb) within a moving window as an index of roughness height (ks) and calculated the relative submergence of the bed at different stages as h/ks, where h is the local flow depth. ADV measurements were collected on a grid with a 0.3m to 0.5m spacing. Geostatistical analysis of the velocity data indicated that the flow was highly three-dimensional and varied based on stage, demonstrating that even small irregularities in the bed have a significant influence on the flow characteristics. The streamwise component was the largest at both low and high flow, but varied more throughout the reach at low flow. At high flow, the greatest streamwise velocities were located within the thalweg. Areas of upwelling and downwelling also varied based on stage, with this component being strongly influenced by small changes in the morphology at high flow, and by protuberant grains at low flows. The cross-stream velocity and turbulence components were controlled by the flow structure and less by the roughness of the bed. The turbulence intensity is significant when considering hydraulics for predicting sediment transport and for habitat assessment.The plane-bed flow patterns were compared to results from a pool-riffle reach in the North Fork Cache La Poudre River, a step-pool reach in East St. Louis Creek, and a step-pool reach in Italy on the Rio Cordon. The comparison of the 3-D velocities among channel types showed that the plane-bed reach has higher streamwise velocities, but similar values of cross-stream and transverse velocities. Streamwise turbulence intensities were similar in both the plane-bed and step-pool reach in East St. Louis Creek. The analysis revealed that the connection between the flow characteristics and the channel was not only related to the gross morphology and location of larger clasts, but also to the development of shear layers from the convergence of flow. Therefore, it is essential to understand how water moving in one direction can alter the characteristics of another component of flow and how this interaction is connected to the bed morphology.

Investigation of the effect of external periodic flow pulsation on a cylinder wake using linear stability analysis

The aim of this paper is to investigate the receptivity of cylinder wake to external periodic flow pulsation at low Reynolds number using linear stability analysis. The inlet flow pulsation appears as a forcing term in the linearised equation set. The full non-linear N-S equations as well as the linearised set for small perturbations around the time-averaged flow are solved using an in-house finite volume solver. The results are first validated against reference data for growth rate and frequency of the most unstable eigenmode for flow past a fixed cylinder with steady base flow at various Reynolds numbers. A special numerical technique is developed to separate the components of the solution in the wake that vary with the natural shedding frequency and the external pulsating frequency. The developed approach requires temporal integration over one period of vortex shedding and solution of a 4×4 linear system at every cell of the domain. The results show that both cross-stream and streamwise velocity components in the near cylinder region are strongly affected by flow pulsation, and its effect is spatially localised in the near wake. Increasing the pulsation frequency reduces the spatial extent within which pulsation plays an important role. A symmetric shedding pattern is established and at every period of external pulsation, two pairs of symmetric vortices are shed from the top and bottom of the cylinder. The width of the wake periodically widens and narrows, which is similar to “wake breathing” observed in a streamwise oscillating cylinder.

Experimental study of an active grid-generated shearless mixing layer and comparisons with large-eddy simulation

A shearless mixing layer characterized by interactions between two regions with different turbulence intensities but without mean shear is investigated experimentally in a wind tunnel. Reynolds numbers higher than those of prior studies [B. Gilbert, “Diffusion mixing in grid turbulence without mean shear,” J. Fluid Mech. 100, 349 (1980); S. Veeravalli and Z. Warhaft, “The shearless turbulent mixing layer,” J. Fluid Mech. 207, 191 (1989); B. Knaepen, O. Debliquy, and D. Carati, “Direct numerical simulation and large-eddy simulation of a shear-free mixing layer,” J. Fluid Mech. 514, 153 (2004); D. Tordella and M. Iovieno, “Numerical experiments on the intermediate asymptotics of shear-free turbulent transport and diffusion,” J. Fluid Mech. 549, 429 (2006); D. A. Briggs, J. H. Ferziger, J. R. Koseff, and S. G. Monismith, “Entrainment in a shear-free turbulent mixing layer,” J. Fluid Mech. 310, 215 (1996)] are achieved by using an active grid with rotating winglets on one-half of its cross section. Stationary flow-conditioning fine meshes are used to avoid mean velocity gradients. Measurements are performed at five different downstream wind-tunnel locations using an X-type hot-wire probe and a stereoscopic particle image velocimetry system. The Reynolds numbers based on the Taylor microscale in the high- and low-kinetic energy regions are 170 and 88, respectively. The energy and integral length-scale ratios between the two regions are 4.27 and 1.73, respectively. The inlet turbulence in the upper and lower portions of the shearless mixing layer is not fully isotropic, with the streamwise velocity fluctuations being between 6% and 13% higher than the cross-stream ones. Fundamental statistical properties of the flow are documented and analyzed at various scales using band-pass box-filtered velocities. Downstream evolution of variance and half-width of the mixing layer, skewness and flatness factors, as well as the statistics of two-point velocity increments at various displacements are presented. It is found that much of the deviations from Gaussian statistics originate from large-scale motions. The data are well suited to be used as initial condition for simulations and as test for large-eddy simulation (LES) models and codes. Comparison studies for three LES models including Smagorinsky, dynamic Smagorinsky, and dynamic mixed nonlinear models are implemented in simulations of temporally decaying shearless mixing layer using a pseudospectral code. Initial conditions are prescribed by matching the longitudinal energy spectra at all heights across the layer for both streamwise and cross-stream velocity components. LES with all three subgrid scale models tested underpredicts the kinetic energy and exhibits deviations from the measured non-Gaussian behaviors. Overall, the dynamic Smagorinsky model predicts statistics slightly better than the other two models.

Prediction of Flow and Heat Transfer through Stationary and Rotating Ribbed Ducts Using a Non-linear k−ε Model

The present paper deals with the prediction of three-dimensional fluid flow and heat transfer in rib-roughened ducts of square cross-section, which are either stationary, or rotate in orthogonal mode. The main objective is to assess how a recently developed variant of a cubic non-linear k−e model (proposed by Craft et al. Flow Turbul Combust 63:59–80, 1999) can predict three-dimensional flow and heat transfer characteristics through stationary and rotating ribbed ducts. The present paper discusses turbulent air flow and heat transfer through two different configurations, namely: (I) a stationary square duct with “in-line” normal and (II) a square duct with normal ribs in a “staggered” arrangement under stationary and rotating conditions, with the axis of rotation normal to the flow direction and parallel to the ribs. In this paper the flow and thermal predictions of the linear k−e model (EVM) are also included, as a set of baseline predictions. The mean flow predictions show that both linear and non-linear k−e models can successfully reproduce most of the measured data for stream-wise and cross-stream velocity components. Moreover, the non-linear model is able to produce better results for the turbulent stresses. The heat transfer predictions show that both EVM and NLEVM2, the more recent variant of the non-linear k−e, with the algebraic length-scale correction term, overestimate the measured Nusselt numbers for both geometries examined. While the EVM with the differential length-scale correction term underestimates heat transfer levels, the Nusselt number predictions with the NLEVM2 and the ‘NYP’ term are in close agreements with the measured data. Comparisons with our earlier work, Iacovides and Raisee (Int J Heat Fluid Flow, 20:320–328, 1999), show that the NLEVM2 thermal predictions are of similar quality to those of a second-moment closure.

Mean flow and turbulence characteristics of a full-scale spiral corrugated culvert with implications for fish passage

A micro-acoustic Doppler velocimeter (ADV) was used to measure three-dimensional mean velocity and turbulence characteristics in a full-scale culvert with spiral corrugations. The culvert was set up in a test bed constructed to examine juvenile salmon passage success in various culvert types. The test culvert was 12.2 m long and 1.83 m in diameter and set at a 1.14% slope. The corrugations were 2.54 cm deep by 7.62 cm peak to peak with a 5° right-handed pitch. Cross-sectional grids of ADV measurements were taken at discharges of 0.028, 0.043, 0.071, 0.099, 0.113, 0.227, and 0.453 m 3/s at nine locations. In the uniform flow region, the centerline velocity profiles were consistent with fully rough turbulent flows and the friction factor was independent of Reynolds number and was very close to theoretical results. Secondary flow induced by the spiral corrugations caused asymmetries in the velocity and turbulence distributions creating a reduced velocity zone (RVZ) on the right side of the culvert as seen looking upstream, which small fish could utilize to aid their upstream passage. Velocity and axial components of turbulence in the RVZ were found to be much less than in mid-channel or on the left of the culvert, and the difference became greater at increased flow rates. In addition, cross-stream and vertical velocity components within the RVZ were small relative to the downstream axial component, while lateral and vertical turbulence intensities were comparable to the axial component. Observations from a concurrent fish passage study showed that more juvenile fish migrate through the right side of the culvert within the RVZ.

Field measurements of three-dimensional hydraulics in a step-pool channel

We investigated the effects of morphologic position and discharge on flow structure in a steep (0.10 m/m) mountain channel by collecting three-dimensional measurements of time-averaged and turbulent velocity components with a SonTek FlowTracker Handheld ADV (acoustic Doppler velocimeter) on a 30-m reach of a step-pool channel in the Colorado Rockies. Velocity profiles were measured at morphologic positions characteristic of steep channels (above steps, step lips, base of steps, pools, cascades, runs), and at five different discharges. A marked three-dimensionality of flow structure was documented in East St. Louis Creek. Velocities in the streamwise component were the largest contributors to overall velocity vector magnitudes; cross-stream and vertical components contributed averages of 20% and 15%, respectively, to overall vector magnitudes. Turbulence intensities were especially multi-dimensional, however, with large contributions to turbulent kinetic energy from the vertical component of velocity. Analysis of variance indicated that discharge and morphologic position significantly affected mean streamwise velocities, with substantially higher velocities upstream from steps than in pools. Discharge and morphology effects on cross-stream and vertical velocity components, however, were not significant. Discharge and morphologic position also significantly affected turbulence intensities for all flow components, with the greatest turbulence intensities occurring in pools and at high discharges. These results illustrate the strong discharge-dependence of hydraulics in step-pool channels, where relative submergence of bedforms changes rapidly with discharge, and the substantial spatial variation in hydraulics created by step-pool sequences.

Low-dimensional models for turbulent plane Couette flow in a minimal flow unit

We model turbulent plane Couette flow in the minimal flow unit (MFU) – a domain whose spanwise and streamwise extent is just sufficient to maintain turbulence – by expanding the velocity field as a sum of optimal modes calculated via proper orthogonal decomposition from numerical data. Ordinary differential equations are obtained by Galerkin projection of the Navier–Stokes equations onto these modes. We first consider a 6-mode (11-dimensional) model and study the effects of including losses to neglected modes. Ignoring these, the model reproduces turbulent statistics acceptably, but fails to reproduce dynamics; including them, we find a stable periodic orbit that captures the regeneration cycle dynamics and agrees well with direct numerical simulations. However, restriction to as few as six modes artificially constrains the relative magnitudes of streamwise vortices and streaks and so cannot reproduce stability of the laminar state or properly account for bifurcations to turbulence as Reynolds number increases. To address this issue, we develop a second class of models based on ‘uncoupled’ eigenfunctions that allow independence among streamwise and cross-stream velocity components. A 9-mode (31-dimensional) model produces bifurcation diagrams for steady and periodic states in qualitative agreement with numerical Navier–Stokes solutions, while preserving the regeneration cycle dynamics. Together, the models provide empirical evidence that the ‘backbone’ for MFU turbulence is a periodic orbit, and support the roll–streak–breakdown–roll reformation picture of shear-driven turbulence.

Flow Conditioning Design in Thick Liquid Protection

The HYLIFE-II conceptual design proposed using arrays of high-speed oscillating and stationary slab jets, or turbulent liquid sheets, to protect the reactor chamber first walls from damaging neutrons, ions and X-rays. Flow conditioning can be used to reduce turbulent fluctuations in these liquid sheets and thereby reduce surface ripple, or free-surface fluctuations, and delay jet breakup. Several flow conditioning configurations are studied experimentally for vertical turbulent sheets of water issuing downwards from nozzles of thickness (small dimension) δ = 1 cm into ambient air for Reynolds numbers Re = 5.0 × 104 and 1.2 × 105. In particular, the role of one or more fine screens in the flow conditioner was studied. As the flow conditioning element immediately upstream of the nozzle inlet, fine screens have been shown to have a major impact upon the sheet free-surface geometry. Planar laser-induced fluorescence was used to measure the free-surface geometry of the liquid sheet and its fluctuations in the near field at streamwise distances downstream of the nozzle exit x ≤ 25δ. Laser-Doppler velocimetry was used to quantify the impact of different conditioning configurations on the cross-stream velocity component and its fluctuations just upstream of the nozzle exit. The results indicate that minor differences in velocity and velocity fluctuations near the nozzle exit can lead to major variations in free-surface geometry, and that free-surface fluctuations are strongly affected by changes in flow conditioner design, even in the near-field region of the flow. A single-screen configuration was shown to produce the smoothest jets at both Reynolds numbers, with fluctuations of 3.3% at Re = 1.2 × 105 and x = 25δ.

Velocity and turbulence distribution around lotic macrophytes

Flow velocity and turbulence patterns were measured in and around a common lotic macrophyte, Ranunculus penicillatus subspecies pseudofluitans (stream water-crowfoot), using a two-dimensional electromagnetic current meter (EMCM). Due to the high shooting density of this species, there was a sharp velocity gradient at the plant boundary, with velocities dropping to a constantly low value after no more than 5 cm into the plant, thus forcing most of the flow over and around the macrophyte. There was a dead-water zone immediately downstream of the plant, beyond which the current moved in from the sides to allow flow under the trailing shoots. High turbulence intensities were recorded for both downstream and cross-stream velocity components at the lateral margins and downstream of the plant. Meanwhile, pulses of water upstream of the plant produced turbulence in the downstream component, but not in the cross-stream component.