Streamwise Turbulence Intensity Research Articles

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.

Large eddy simulation of smooth-wall, transitional and fully rough-wall channel flow

Large eddy simulation (LES) is reported for both smooth and rough-wall channel flows at resolutions for which the roughness is subgrid. The stretched vortex, subgrid-scale model is combined with an existing wall-model that calculates the local friction velocity dynamically while providing a Dirichlet-like slip velocity at a slightly raised wall. This wall model is presently extended to include the effects of subgrid wall roughness by the incorporation of the Hama's roughness function \documentclass[12pt]{minimal}\begin{document}$\Delta U^+(k_{s\infty }^+)$\end{document}ΔU+(ks∞+) that depends on some geometric roughness height ks∞ scaled in inner variables. Presently Colebrook's empirical roughness function is used but the model can utilize any given function of an arbitrary number of inner-scaled, roughness length parameters. This approach requires no change to the interior LES and can handle both smooth and rough walls. The LES is applied to fully turbulent, smooth, and rough-wall channel flow in both the transitional and fully rough regimes. Both roughness and Reynolds number effects are captured for Reynolds numbers Reb based on the bulk flow speed in the range 104–1010 with the equivalent Reτ, based on the wall-drag velocity uτ varying from 650 to 108. Results include a Moody-like diagram for the friction factor f = f(Reb, ε), ε = ks∞/δ, mean velocity profiles, and turbulence statistics. In the fully rough regime, at sufficiently large Reb, the mean velocity profiles show collapse in outer variables onto a roughness modified, universal, velocity-deficit profile. Outer-flow stream-wise turbulence intensities scale well with uτ for both smooth and rough-wall flow, showing a log-like profile. The infinite Reynolds number limits of both smooth and rough-wall flows are explored. An assumption that, for smooth-wall flow, the turbulence intensities scaled on uτ are bounded above by the sum of a logarithmic profile plus a finite function across the whole channel suggests that the infinite Reb limit is inviscid slip flow without turbulence. The asymptote, however, is extremely slow. Turbulent rough-wall flow that conforms to the Hama model shows a finite limit containing turbulence intensities that scale on the friction factor for any small but finite roughness.

Inner-layer intensities for the flat-plate turbulent boundary layer combining a predictive wall-model with large-eddy simulations

Time series velocity signals obtained from large-eddy simulations (LES) within the logarithmic region of the zero-pressure gradient turbulent boundary layer over a smooth wall are used in combination with an empirical, predictive inner-outer wall model [I. Marusic, R. Mathis, and N. Hutchins, “Predictive model for wall-bounded turbulent flow,” Science 329, 193 (2010)10.1126/science.1188765] to calculate the statistics of the fluctuating streamwise velocity in the inner region. Results, including spectra and moments up to fourth order, are compared with equivalent predictions using experimental time series, as well as with direct experimental measurements at Reynolds numbers Reτ = 7300, 13 600, and 19 000. The LES combined with the wall model are then used to extend the inner-layer predictions to Reynolds numbers Reτ = 62 000, 100 000, and 200 000 that lie within a gap in log (Reτ) space between laboratory measurements and surface-layer, atmospheric experiments. The present results support a loglike increase in the near-wall peak of the streamwise turbulence intensities with Reτ and also provide a means of extending LES results at large Reynolds numbers to the near-wall region of wall-bounded turbulent flows.

A new formulation for the streamwise turbulence intensity distribution in wall-bounded turbulent flows

The distribution of the streamwise velocity turbulence intensity has recently been discussed in several papers both from the viewpoint of new experimental results as well as attempts to model its behavior. In the present paper numerical and experimental data from zero pressure-gradient turbulent boundary layers, channel and pipe flows over smooth walls have been analyzed by means of the so called diagnostic plot introduced by Alfredsson & Örlü [P.H. Alfredsson, R. Örlü, The diagnostic plot–a litmus test for wall bounded turbulence data, Eur. J. Mech. B Fluids 29 (2010) 403–406]. In the diagnostic plot the local turbulence intensity is plotted as function of the local mean velocity normalized with a reference velocity scale. Alfredsson et al. [P.H. Alfredsson, A. Segalini, R. Örlü, A new scaling for the streamwise turbulence intensity in wall-bounded turbulent flows and what it tells us about the outer peak, Phys. Fluids 23 (2011) 041702] observed that in the outer region of the boundary layer a universal linear decay of the turbulence intensity independent of the Reynolds number exists. This approach has been generalized for channel and pipe flows as well, and it has been found that the deviation from the previously established linear region appears at a given wall distance in viscous units (around 120) for all three canonical flows. Based on these results, new empirical fits for the streamwise velocity turbulence intensity distribution of each canonical flow are proposed. Coupled with a mean streamwise velocity profile description the model provides a composite profile for the streamwise variance profile that agrees nicely with existing numerical and experimental data. Extrapolation of the proposed scaling to high Reynolds numbers predicts the emergence of a second peak of the streamwise variance profile that at even higher Reynolds numbers overtakes the inner one.

Characteristics of a Jet in the Vicinity of a Free Surface

In this study, the characteristics of a round turbulent jet in the vicinity of a free surface are investigated. The jet issued from a nozzle located at a depth five times the nozzle diameter (d = 10 mm) below and parallel to the free surface. The jet exit velocity was 2.8 m/s and the resulting Reynolds number was 28,000. Instantaneous two-dimensional PIV measurements were obtained in the vertical central plane and in several horizontal planes at various distances (y/d = 0,±1,±2,±3± 4) from the axis of the nozzle. All fields-of-view were positioned at streamwise locations in the range of 28 < x/d < 62, where the jet interacts significantly with the free surface. The results reveal that the behavior of the surface jet is very similar to that of the free jet before it interacts with the free surface which occurs at about x/d = 30. Beyond this, the velocity normal to the free surface is diminished and those parallel to the free surface are enhanced in the region near the free surface. In the horizontal plane near the free surface (y/d = +4), the spreading of the surface jet is significantly greater than that of the free jet. The mean lateral flow in this region tends to be outward everywhere for the surface jet, while the opposite trend occurs in the free jet. Turbulence intensities in all three directions are reduced by the effect of the free surface confinement. Near the free surface, at y/d = +4, unlike the single peak streamwise turbulence intensity profile noticed in the case of the free jet, the off-axis double peaks reappear in the case of the surface jet. The magnitude of shear stress in the vertical central plane of the surface jet is smaller than that noticed in the free jet near the free surface. In identical horizontal planes, the shear stress (-uw¯) profiles are similar in both free jets and surface jets in regions where the interaction with the free surface is not significant (x/d ≈ 30). As the downstream distance increases near the free surface, the magnitudes of the shear stress profiles are larger compared to that of the free jet. An increase in the normal component of vorticity is observed in the horizontal planes near the free surface.

Mixing in turbulent free jets issuing from isosceles triangular orifices with different apex angles

This paper reports the results of an experimental investigation on mixing in turbulent free air jets issuing from isosceles triangular orifices with apex angles of 10°, 20° and 30°. The results obtained in a contoured nozzle round jet are also presented for comparison. The measurements were made with an x-array hot-wire probe and a pitot-static tube in isothermal, incompressible jets issuing into still surrounding air. The Reynolds number, based on the equivalent diameter of the triangular orifices (the same as the diameter of the contoured round nozzle), was on average 1.69×105 for all jets. The results of the mean streamwise centreline velocity decay, mass entrainment and jet spreading suggest that the 10° jet has the highest mixing rate among all the test jets and that the contoured nozzle round jet has the lowest mixing rate. The high mixing rate of the 10° jet is supported by the jet centreline profile of the streamwise turbulence intensity and the one-dimensional energy spectra, which develop much more rapidly in this jet than in any of the other jets.

Scaling Law of the Turbulent Field for the Approximate Equilibrium Boundary Layer in an Adverse Pressure Gradient

The scaling laws of streamwise turbulent intensity and turbulent energy spectrum profiles have been investigated experimentally for the approximate equilibrium boundary layer subjected to an adverse pressure gradient. Non-dimensional pressure gradient parameters P+ and β are 2.74×10-3 and 1.32, respectively. The momentum thickness Reynolds number Rθ is 10,200. The velocity scales ues derived analytically from the boundary layer equation and us a limiting case with respect to P+→0 of ues are used instead of the friction velocity uτ. Streamwise and normal turbulent intensity profiles scaled with us collapse on those of zero pressure gradient case. With experimental data by Monty et al., the streamwise turbulent intensity scaled with us and ues takes almost constant value to P+ in the local similarity region for 0≦ P+ <3.00×10-3 and 0≦ P+ ≦6.17×10-3, respectively. Also, turbulent energy spectrum in the inertial sub-range are well scaled with us rather than uτ. Accordingly, it is expected that ues and us are suitable for the scaling of the turbulent intensity and turbulent energy spectrum.

0122 順圧力勾配下の乱流境界層における壁面せん断応力の計測(OS1 噴流,後流および剥離流れ現象の探求と技術革新,オーガナイズドセッション)

Applicability of law of the wall to turbulent boundary layers under favorable pressure gradient has been studied using direct measurement of the wall shear stress. The effect of lip pressure that would produce extra force acting on a floating element of the direct measurement has been investigated for improving reliability of measured wall shear stress. The experimental results suggest that the lip pressure is unable to be ignored in the direct measurement. The logarithmic mean velocity profile using friction velocity determined by the direct measurement is disagreed with the standard log-law. The favorable pressure gradient reduces magnitude of the streamwise turbulent intensity normalized with the friction velocity compared with that of zero pressure gradient.

A new formulation for the streamwise turbulence intensity distribution

Numerical and experimental data from zero pressure-gradient turbulent boundary layers over smooth walls have been analyzed by means of the so called diagnostic plot introduced by Alfredsson & Örlü [Eur. J. Fluid Mech. B/Fluids, 42, 403 (2010)]. In the diagnostic plot the local turbulence intensity is shown as a function of the local mean velocity normalized with a reference velocity scale. In the outer region of the boundary layer a universal linear decay of the turbulence intensity is observed independent of Reynolds number. The deviation from this linear region appears in the buffer region and seems to be universal when normalized with the friction velocity. Therefore, a new empirical fit for the streamwise velocity turbulence intensity distribution is proposed and the results are compared with up to date reliable high-Reynolds number experiments and extrapolated towards Reynolds numbers relevant to atmospherical boundary layers.

A method to estimate turbulence intensity and transverse Taylor microscale in turbulent flows from spatially averaged hot-wire data

A new approach to evaluate turbulence intensity and transverse Taylor microscale in turbulent flows is presented. The method is based on a correction scheme that compensates for probe resolution effects and is applied by combining the response of two single hot-wire sensors with different wire lengths. Even though the technique, when compared to other correction schemes, requires two independent measurements, it provides, for the same data, an estimate of the spanwise Taylor microscale. The method is here applied to streamwise turbulence intensity distributions of turbulent boundary layer flows but it is applicable generally in any turbulent flow. The technique has been firstly validated against spatially averaged DNS data of a zero pressure-gradient turbulent boundary layer showing a good capacity to reconstruct the actual profiles and to predict a qualitatively correct and quantitatively agreeing transverse Taylor microscale over the entire height of the boundary layer. Finally, the proposed method has been applied to available higher Reynolds number data from recent boundary layer experiments where an estimation of the turbulence intensity and of the Taylor microscale has been performed.

A new scaling for the streamwise turbulence intensity in wall-bounded turbulent flows and what it tells us about the “outer” peak

One recent focus of experimental studies of turbulence in high Reynolds number wall-bounded flows has been the scaling of the root mean square of the fluctuating streamwise velocity, but progress has largely been impaired by spatial resolution effects of hot-wire sensors. For the near-wall peak, recent results seem to have clarified the controversy; however, one of the remaining issues in this respect is the emergence of a second (so-called outer) peak at high Reynolds numbers. The present letter introduces a new scaling of the local turbulence intensity profile, based on the diagnostic plot by Alfredsson and Örlü [Eur. J. Mech. B/Fluids 42, 403 (2010)], which predicts the location and amplitude of the “outer” peak and suggests its presence as a question of sufficiently large scale separation.

Effects of Splitter Plates on Turbulent Quantities on a Boundary Layer Developing on a Flat Plate near the Trailing Edge

An experimental investigation was made on a turbulent boundary layer near the trailing edge on a long flat plate with a blunt trailing edge. The flow was controlled by an additional splitter plate attached to the trailing edge along the wake center line. The length of the splitter plate, l, was varied from 0.3 to 3 times the trailing edge thickness, h. Measurement of fluctuating velocity was made under the freestream zero pressure gradient. Almost independent of the installation of the splitter plate, the turbulent intensity and the Reynolds shear stress in the inner layer decreased when approaching the trailing edge of the flat plate (x/h=0), compared with that in the fully-developed turbulent boundary layer under the zero pressure gradient. The only exception was the distribution at x/h=0 near the wall in the case without the splitter plate (l/h=0), where the degree of the decrease in urms/Ue was relatively small, and vrms/Ue and -uv / Ue2 were larger than those of the zero pressure gradient. The effect of l/h on turbulent quantities was shown just upstream of the trailing edge upon close comparison, and was classified into two groups: l/hl/h≧1. The tendency of the turbulent energy production terms approaching x/h=0 coincided with the decrease in the streamwise turbulent intensity and in the Reynolds shear stress.

Statistical Properties of a Turbulent Boundary Layer Affected by Grid-Generated Turbulence (Analysis of Spatial Development by Means of Direct Numerical Simulation)

The effects of grid-generated turbulence on a turbulent boundary layer are investigated by means of a direct numerical simulation (DNS). A square turbulence-generating grid, on which the velocity components are set to zero, is numerially constructed near the entrance to a rectangular parallelepiped domain. The nonslip condition is applied to the lower boundary to develop a turbulent boundary layer downstream of the turbulence-generating grid. The fractional step method is used to solve the governing equations. The results show that streamwise and vertical turbulence intensities and Reynolds stress normalized by the inner parameters are suppressed in the log-law region by the grid turbulence.

Spatial resolution correction for hot-wire anemometry in wall turbulence

We investigate spatial resolution issues in hot-wire anemometry measurements of turbulence intensity and energy spectra. Single normal hot-wire measurements are simulated by means of filtering direct numerical simulation (DNS) of turbulent channel flow at \(Re_\tau = 934\). Through analysis of the two-dimensional energy spectra from the DNS, the attenuation of the small-scale energy levels is documented, especially in the near-wall region. The missing energy displays anisotropic characteristics, and an attempt is made to model this using an empirical equation, thus providing a correction scheme for all wall normal locations. The empirical model is assessed using experimental boundary layer data and shown to effectively correct both the streamwise one-dimensional energy spectra and turbulence intensity at a Reynolds number significantly above that of the DNS.

The Physical Mechanism of Heat Transfer Augmentation in Stagnating Flows Subject to Freestream Turbulence

Experiments have been performed in a water tunnel facility to examine the physical mechanism of heat transfer augmentation by freestream turbulence in classical Hiemenz flow. A unique experimental approach to studying the problem is developed and demonstrated herein. Time-resolved digital particle image velocimetry (TRDPIV) and a new variety of thin-film heat flux sensor called the heat flux array (HFA) are used simultaneously to measure the spatiotemporal influence of coherent structures on the heat transfer coefficient as they approach and interact with the stagnation surface. Laminar flow and heat transfer at low levels of freestream turbulence (Tux¯=0.5–1.0%) are examined to provide baseline flow characteristics and heat transfer coefficients. Similar experiments using a turbulence grid are performed to examine the effects of turbulence with mean streamwise turbulence intensity of Tux¯=5.0% and an integral length scale of Λx¯=3.25 cm. At a Reynolds number of ReD¯=U∞¯D/υ=21,000, an average increase in the mean heat transfer coefficient of 64% above the laminar level was observed. Experimental studies confirm that coherent structures play a dominant role in the augmentation of heat transfer in the stagnation region. Calculation and examination of the transient physical properties for coherent structures (i.e., circulation, area averaged vorticity, integral length scale, and proximity to the surface) shows that freestream turbulence is stretched and vorticity is amplified as it is convected toward the stagnation surface. The resulting stagnation flow is dominated by dynamic, counter-rotating vortex pairs. Heat transfer augmentation occurs when the rotational motion of coherent structures sweeps cooler freestream fluid into the laminar momentum and thermal boundary layers into close proximity of the heated stagnation surface. Evidence in support of this mechanism is provided through validation of a new mechanistic model, which incorporates the transient physical properties of tracked coherent structures. The model performs well in capturing the essential dynamics of the interaction and in the prediction of the experimentally measured transient and time-averaged turbulent heat transfer coefficients.

Correcting hot-wire measurements of stream-wise turbulence intensity in boundary layers

The current experimental activity aimed at resolving the scaling of stream-wise turbulence intensity profiles uu¯+(y+) with Reynolds number in turbulent flat plate boundary layers has brought the largely unresolved issue of correcting systematic errors in hot-wire measurements of uu¯+(y+) into focus. Here, a heuristic scheme is proposed to generate unique uu¯+(y+;Reδ∗) profiles from data obtained with single hot wires of widely different length, aspect ratio and construction over a large Reynolds number range of 4000≲Reδ∗≲50 000. A comparison with LDA data and other checks suggest that the present correction scheme produces uu¯+(y+;Reδ∗) profiles close to the (unknown) true profiles.

The intermediate wake of a body of revolution at high Reynolds numbers

Results are presented on the flow field downstream of a body of revolution for Reynolds numbers based on a model length ranging from 1.1 × 106 to 67 × 106. The maximum Reynolds number is more than an order of magnitude larger than that obtained in previous laboratory wake studies. Measurements are taken in the intermediate wake at locations 3, 6, 9, 12 and 15 diameters downstream from the stern in the midline plane. The model is based on an idealized submarine shape (DARPA SUBOFF), and it is mounted in a wind tunnel on a support shaped like a semi-infinite sail. The mean velocity distributions on the side opposite the support demonstrate self-similarity at all locations and Reynolds numbers, whereas the mean velocity distribution on the side of the support displays significant effects of the support wake. None of the Reynolds stress distributions of the flow attain self-similarity, and for all except the lowest Reynolds number, the support introduces a significant asymmetry into the wake which results in a decrease in the radial and streamwise turbulence intensities on the support side. The distributions continue to evolve with downstream position and Reynolds number, although a slow approach to the expected asymptotic behaviour is observed with increasing distance downstream.

Fine particle turbulence modulation

Streamwise turbulence intensities of fine particulate suspensions were studied in a 26 mm N.B. horizontal pipe loop. Colloidal silica spheres were prepared in 10−4M and 1M KNO3 solutions to control the degree of aggregate formation in the suspension. Using an ultrasonic Doppler velocity profiling sensor, the turbulence intensities of the fine particle suspensions were compared with those of a particle-free flow over a range of Reynolds numbers. At low electrolyte concentration, the silica particles remain dispersed, with the turbulence intensity of the suspension flow comparable with that of the particle-free flow. At high electrolyte concentration, increased particle-particle interaction leads to the formation of particle aggregates which support turbulence augmentation over a critical Reynolds number range. The range of Reynolds numbers over which this turbulence enhancement is observed is limited by both fluid dynamic effects at low Reynolds numbers (Re ≈ 5500) and aggregate breakup at high Reynolds numbers (Re ≈ 8000). © 2010 American Institute of Chemical Engineers AIChE J, 2011

Coherent flow structures in a depth‐limited flow over a gravel surface: The influence of surface roughness

Turbulent flows moving over a gravel bed develop large‐scale, macroturbulent flow structures that are initiated at anchor clasts in the bed and grow and dissipate as they move upward through the flow depth. This paper extends previous research in which we investigated the influence of the Reynolds number on coherent flow structures generated over a gravel bed by assessing the importance of effective bed roughness. Here, we report on flume experiments in which flows over beds of decreasing surface roughness have been quantified through the application of digital particle imaging velocimetry, which allows study of the downstream and vertical components of velocity over the entire flow field. These results indicate that as the effective roughness increases (1) the visual distinctiveness of the coherent flow structures becomes more defined throughout the flow depth, (2) the upstream angle of slope of the coherent flow structure increases, and (3) the reduction in streamwise flow velocity and turbulence intensity toward the upstream side of the structure becomes greater. Applying standard scaling laws, these structures appear shear‐generated and form through a combination of both wake flapping and the reattachment of localized shear layers associated with flow separation around individual topographic protrusions. As the effective protrusion decreases, the scale of these coherent flow structures also decreases.

Calculation of time-varying mean velocity by different methods and determination of turbulence intensities

The raw velocity data for both stream-wise and transversal directions in unsteady flows, which are formed by generating input hydrograph, are obtained by using a flow tracker. The same hydrograph is generated 15 times and the mean values are found by calculating the average of all hydrographs. The time varying mean is obtained by using FFT, moving average, wavelet and EMD methods. The best time varying mean is selected according to prescribed criteria. Then, the 15 time series are processed and the stream-wise and transversal turbulence intensities are obtained. The mean of the product of fluctuations is also determined. Key words: Unsteady flow, instantaneous velocity measurement, flow tracker, data processing.