Mean Streamwise Velocity Component Research Articles

Estimation of wind turbine wakes with generative-adversarial networks

The interaction of the atmospheric boundary layer with wind turbines and among wind turbines in a wind farm is a complex phenomenon. Its analysis is fundamental for wind energy development. In this work, a generative adversarial network has been developed to predict the mean streamwise velocity component at hub height in the wake of a wind turbine based on the mean streamwise velocity two rotor diameters upstream. The dataset used to train and test the model is obtained from Large Eddy Simulations (LES) of a wind farm comprising 15 wind turbines under different inlet conditions. The method is able to predict accurately the mean streamwise velocity in the wake of one wind turbine. When the model is used to predict the mean streamwise velocity at hub height of the whole wind farm based on the inlet condition, the difference between the model predictions and LES results are larger as looking downstream.

Effects of unstable thermal stratification on the flow characteristics in an idealized rural-to-urban transition region: A large-eddy simulation study

Large-eddy simulations are performed to study the impacts of unstable thermal stratification on the mean wind and turbulence in an idealized rural-to-urban surface transition region. In the unstable stratification case, a convective boundary layer is developed over the urban region and much longer adjustment distances for the mean wind and turbulence within the canopy are identified compared with that in the neutral case. Moreover, the flow recirculation and turbulence within the canopy are substantially enhanced by the unstable stratification. Specifically, at the far downstream positions of the surface transition, the mean wind is observed to flow at oblique angles through the street channels under the effects of buoyancy, which is qualitatively different from that in the neutral stratification case. Despite the magnitudes of the turbulent and dispersive stresses are significantly larger in the unstable case, the horizontally space-averaged mean streamwise velocity component within the canopy shows similar magnitudes as those in the neutral case. At the downstream region where the flow is already adjusted to the urban surface, the turbulent viscosity and Prandtl mixing length calculated from the horizontally space-averaged quantities are found to be significantly larger in the unstable case than those in the neutral case, while the turbulent Prandtl number is approximately uniform with height with a value of 0.5.

Dynamics of tip vortex flow over three dimensional hydrofoils by LDV measurements

Tip vortices are observed downstream of the flow past the three-dimensional hydrofoils used in propeller, wind and tidal turbines and they largely determine the forces exerted on such structures. In this study, we present the Laser Doppler Velocimetry (LDV) measurements in the flow past three-dimensional hydrofoils namely NACA 4412, NACA 16020, NACA 66(2)415 inclined at an angle of 10° with respect to the free-stream velocity, U∞. The three-dimensional hydrofoils have a semi-span, s = 60 mm, chord lengths, c = 48 mm, 60 mm & 80 mm which correspond to three aspect ratios, ∧ = 2.5, 2.0 & 1.5, respectively, at the chord length based Reynolds number, Re ranging from Re = 1.92 × 105 − 6.39 × 105. LDV measurements were performed at several coordinate points in zy−plane perpendicular to the stream-wise, x direction, measuring the mean stream-wise, u(z, y) and mean velocity component along the z-axis, w(z, y) together with the root-mean square of their fluctuations in the plane located at a stream-wise distance, x/c = 1.0. The swirling strength of the tip vortices are qualitatively evident from the measurements of z− velocity component field, w(z, y) for all the hydrofoils, at various aspect ratios and Reynolds numbers. It is observed that the magnitude of normalized axial velocity deficit, (u(z, y) − U∞)/U∞ and normalized turbulent kinetic energy, TKE(z, y) are dependent on the type of hydrofoil, their aspect ratio, ∧ and the Reynolds number, Re. TKE within the region of the wake and vortex contain about 99% of the peak magnitude of TKE observed in the x/c = 1.0 plane. The vortex center, vortex position and vortex radius are shown to be dependant on the hydrofoil shape, aspect ratio and Reynolds number.

Large-Eddy Simulation of the Effects of Wind-Direction Fluctuations on Turbulent Flow and Gas Dispersion Within a Cubical Canopy

Large-eddy simulation of turbulent flow and gas dispersion in a cubical canopy is used to investigate the effect of wind-direction fluctuations on gas dispersion. Square blocks are set at regular intervals on the bottom surface, with line sources placed within the first, second, third, fifth and seventh rows. Large-eddy simulation without wind-direction fluctuations produces a good prediction of the mean streamwise velocity component, and the standard deviations of the fluctuations in the streamwise and spanwise velocity components, obtained from a wind-tunnel experiment. Wind-direction fluctuations marginally affect the mean streamwise velocity component above the canopy in the first row, and do not significantly affect the component beyond the third row. The standard deviations of the fluctuations in the streamwise and spanwise velocity components above the canopy are also affected by wind-direction fluctuations, but within the canopy the components are less sensitive to the fluctuations beyond the third row. The spatially-averaged concentrations within the canyon with wind-direction fluctuations before the third row are marginally greater than concentrations without the fluctuations, but they are essentially identical beyond the fifth row. The low-frequency turbulent flow that passes through the canyon is generated with and without wind-direction fluctuations.

Applicability of Taylor’s Hypothesis for Estimating the Mean Streamwise Length Scale of Large-Scale Structures in the Near-Neutral Atmospheric Surface Layer

A field investigation of the mean streamwise length scale Lx of large-scale structures and the convection velocity is performed in a high-Reynolds-number (Reτ ~ 106) atmospheric surface layer (ASL). Based on selected high-quality synchronous data obtained at different streamwise positions, the length scale Lx and global convection velocity Uc are extracted in the logarithmic region of the near-neutral ASL at heights of 0.9 m, 1.71 m, 3.5 m, and 5 m. It is found that Uc values are approximately 16% greater than the local mean streamwise velocity component U, and the value of Lx obtained from spatially-separated measurements is greater than the results estimated from Taylor’s hypothesis using the value of U at the four heights. The mean relative difference between the value of Lx and the results estimated by Taylor’s hypothesis using the value of U is approximately 15%. However, the relative difference between the value of Lx and the results estimated from Taylor’s hypothesis using the convection velocity Uc instead of the mean streamwise velocity component U is reduced to 1 ± 6% (≈ zero). Thus, the convection velocity Uc is more appropriate than the mean streamwise velocity component U in obtaining Lx values in the near-neutral ASL.

Measurement-Based Numerical Study of the Effects of Realistic Land Topography and Stratification on the Coastal Marine Atmospheric Surface Layer

Large-eddy simulations are used to investigate the effects of coastal topography and atmospheric stratification on the coastal marine atmospheric surface layer at the Field Research Facility in Duck, North Carolina, USA. Field measurements obtained from the CASPER-EAST intensive field campaign in autumn 2015 are used to determine the inlet and lower boundary conditions. The simulations are performed using the in-house Virtual Flow Simulator code, with the simulated mean streamwise velocity component, mean temperature, Reynolds shear stress, and turbulent heat flux, shown to be in good agreement with measurements. In the coastal area, the complex coastal topography leads to an enhancement of the Reynolds shear stress for both onshore and offshore flows, while the effect of atmospheric stratification on the momentum transfer is less significant than the topography. In contrast to the momentum flux, the heat flux is influenced by both the coastal topography and stratification. For onshore flow and stable stratification, the heat flux is significantly increased near the sand dune due to the enhanced turbulence and vertical temperature gradient. For onshore flow and unstable stratification, the strong turbulent mixing tends to enhance the heat flux, but is suppressed by the reduced vertical temperature gradient, such that the magnitude of the turbulent heat flux remains almost unchanged in comparison with the upstream flow. For offshore flow in both stable and unstable stratification, the heat flux is enhanced due to the flow separation at the sand dune.

The Atmospheric Boundary Layer Over Urban-Like Terrain: Influence of the Plan Density on Roughness Sublayer Dynamics

We investigate the effect of the packing density of cubical roughness elements on the characteristics of both the roughness sublayer and the overlying turbulent boundary layer, in the context of atmospheric flow over urban areas. This is based on detailed wind-tunnel hot-wire measurements of the streamwise velocity component with three wall-roughness configurations and two freestream flow speeds. The packing densities are chosen so as to obtain the three near-wall flow regimes observed in urban canopy flows, namely isolated-wake, wake-interference and skimming-flow regimes. Investigation of the wall-normal profiles of the one-point statistics up to third order demonstrates the impossibility of finding a unique set of parameters enabling the collapse of all configurations, except for the mean streamwise velocity component. However, spectral analysis of the streamwise velocity component provides insightful information. Using the temporal frequency corresponding to the peak in the pre-multiplied energy spectrum as an indicator of the most energetic flow structures at each wall-normal location, it is shown that three main regions exist, in which different scaling applies. Finally, scale decomposition reveals that the flow in the roughness sublayer results from a large-scale intrinsic component of the boundary layer combined with canopy-induced dynamics. Their relative importance plays a key role in the energy distribution and influences the near-canopy flow regime and its dynamics, therefore suggesting complex interactions between the near-wall scales and those from the overlying boundary layer.

A study of geometrical structure of packed beds using flow simulation with the immersed boundary method

In this work, a new method is proposed for calculation of one of the essentials geometrical parameters characterising a packed bed - tortuosity. The geometry of random packings of cylinders and rings (with various packing densities) is numerically generated with Discrete Element Method approach. For flow calculations in a highly complex geometry of a random packed bed, immersed boundary method is employed (with direct forcing variant). The obtained flow velocity field allows for calculation of tortuosity using two methods: by passive advection of massless particles and by comparison of the mean flow velocity magnitude with the mean streamwise velocity component. It is demonstrated that for the packings of low density these two methods are in a good agreement but may diverge for dense packings. Frequency distribution of tortuosity values for individual flow paths is also examined. The results show more frequent occurrence of low-tortuosity paths for coarse packings.

Stable Stratification Effects on Flow and Pollutant Dispersion in Boundary Layers Entering a Generic Urban Environment

Large-eddy simulations (LES) are used to investigate the effect of stable stratification on rural-to-urban roughness transitions. Smooth-wall turbulent boundary layers are subjected to a generic urban roughness consisting of cubes in an in-line arrangement. Two line sources of pollutant are added to investigate the effect on pollutant dispersion. Firstly, the LES method is validated with data from wind-tunnel experiments on fully-developed flow over cubical roughness. Good agreement is found for the vertical profiles of the mean streamwise velocity component and mean Reynolds stress. Subsequently, roughness transition simulations are done for both neutral and stable conditions. Results are compared with fully-developed simulations with conventional double-periodic boundary conditions. In stable conditions, at the end of the domain the streamwise velocity component has not yet reached the fully-developed state even though the surface forces are nearly constant. Moreover, the internal boundary layer is shallower than in the neutral case. Furthermore, an investigation of the turbulence kinetic energy budget shows that the buoyancy destruction term is reduced in the internal boundary layer, above which it is equal to the undisturbed (smooth wall) value. In addition, in stable conditions pollutants emitted above the urban canopy enter the canopy farther downstream due to decreased vertical mixing. Pollutants emitted below the top of the urban canopy are 85 % higher in concentration in stable conditions mostly due to decreased advection. If this is taken into account concentrations remain 17 % greater in stable conditions due to less rapid internal boundary-layer growth. Finally, it is concluded that in the first seven streets the vertical advective pollutant flux is significant, in contrast to the fully-developed case.

A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient

A novel two-equations model for computing the flow properties of a spatially-developing, incompressible, zero-pressure-gradient, turbulent boundary layer over a smooth, flat wall is developed. The mean streamwise velocity component inside the boundary layer is described by the Reynolds-averaged Navier–Stokes equation where the Reynolds shear stress is given by an extended mixing-length model. The nondimensional form of the mixing length is described by a polynomial function in terms of the nondimensional wall normal coordinate. Moreover, a stream function approach is applied with a leading-order term described by a similarity function. Two ordinary differential equations are derived for the solution of the similarity function along the wall normal coordinate and for its streamwise location. A numerical integration scheme of the model equations is developed and enables the solution of flow properties. The coefficients of the mixing-length polynomial function are modified at each streamwise location as part of solution iterations to satisfy the wall and far-field boundary conditions and adjust the local boundary layer thickness, δ99.4, to a location where streamwise speed is 99.4% of the far-field streamwise velocity. The elegance of the present approach is established through the successful solution of the various flow properties across the boundary layer (i.e., mean streamwise velocity, viscous stress, Reynolds shear stress, skin friction coefficient, and growth rate of boundary layer among others) from the laminar regime all the way to the fully turbulent regime. It is found that results agree with much available experimental data and direct numerical simulations for a wide range of Reθ based on the momentum thickness (Reθ) from 15 up to 106, except for the transition region from laminar to turbulent flow. Furthermore, results shed light on the von Kármán constant as a function of Reθ, the possible four-layer nature of the mean streamwise velocity profile, the universal profiles of the streamwise velocity and the Reynolds shear stress at high Reθ, and the scaling laws at the outer region.

Streamwise development of the wind turbine boundary layer over a model wind turbine array

The streamwise development of turbulence statistics and mean kinetic energy in a model wind farm consisting of 3 × 5 wind turbines is studied experimentally in a wind tunnel. The analysis uses planar Particle Image Velocimetry data obtained at the centerline plane of the wind farm, covering the inflow as well as four planes in between five downstream wind turbines. The data analysis is organized by dividing these measurement planes into three regions: the above-rotor, rotor-swept, and below-rotor regions. For each field, flow development is quantified using a properly defined relative difference norm based on an integration over each of the regions. Using this norm, it is found that the mean streamwise velocity approaches a fully developed state most rapidly, whereas the flow development is more gradual for the second-order statistics. The vertical entrainment flux of the mean kinetic energy by the Reynolds shear stress, ⟨U⟩⟨u′v′⟩, is observed to develop at a rate similar to that of the Reynolds shear stress rather than the mean streamwise velocity component. Its development is slowest in the layer nearest to the ground. Analysis of various terms in the mean kinetic energy equation shows that the wind turbine boundary layer has not yet reached fully developed conditions by the fifth turbine but that it is approaching such conditions. By comparing the vertical entrainment flux with the horizontal flux due to the mean flow, it is found that the former increases, whereas the latter decreases, as function of downstream distance, but that the former is already an important contributor in the developing region.

Modified ‘closure’ constants of the Standard k–ε turbulence model for the prediction of wind-induced natural ventilation

In this study, wind-driven natural ventilation in buildings is investigated by means of computational fluid dynamics. The airflow in and around three pilot buildings, which correspond to the most common natural-ventilation designs, i.e. cross-, windward- and leeward- single-sided ventilation, is simulated by applying both the Standard and a modified k–ε turbulence model. The latter represents a Prandtl number-modified version of the Standard k–ε model, based on the flow-variable (velocity and turbulence variables) distributions and on the atmospheric boundary layer (ABL) assumptions. Numerical results of streamwise and vertical velocity components, as well as of pressure coefficients at the facades, obtained by both turbulence models are compared with available wind tunnel experimental data found in literature. It is concluded that both models applied are in acceptable agreement with measurements, especially for the mean streamwise velocity component, while the proposed modified model is more accurate as far as flow within the windward and the internal parts (i.e. within the building) of the domain is concerned. Practical application: This study focuses on the development of a modified k–ε turbulence model for the prediction of wind-driven natural ventilation. The analysis described represents a methodology to produce ‘closure’ parameters, such as Prandtl numbers, compatible with the incoming wind characteristics (ABL). It was found that for all ventilation cases studied, i.e. cross- and single-sided ventilation, the proposed modified model is more accurate compared with the Standard k–ε model, and it accounts for the dumping effect near the walls and for kinetic energy reduction in the impinging region adequately. It is satisfying that the modified k–ε model leads to acceptable engineering results within relatively practical computer resources.

Numerical investigation of a water flow in a rib-roughened channel by using Reynolds stress model

In this paper, water flow in a rib-roughened channel is investigated numerically by using Reynolds stress turbulence models (RSM) on a three-dimensional (3-D) domain. Computational results for mean streamwise velocity component and turbulent kinetic energy show good agreements with available experimental data. Five rib pitch-to-height ratios (p/h) of 1, 5, 10, 15 and 20 are analysed for six different Reynolds numbers (Re) of 3000, 7000, 12,000, 20,000, 40,000 and 65,000. Velocity vectors, streamlines and Reynolds stresses are showed for these ratios and Re numbers. Streamlines revealed that Reynolds numbers do not affect flowfield but play an important role in the Reynolds stresses.

Reverse flow regions in three-dimensional backward-facing step flow

Laser-Doppler velocity measurements adjacent to the bounding walls of three-dimensional (3-D) backward-facing step flow are performed for the purpose of mapping the boundaries of the reverse flow regions that develop in this geometry (adjacent to the sidewalls, the flat wall and the stepped wall) as a function of the Reynolds number. The backward-facing step geometry is configured by a step height ( S) of 1 cm, which is mounted in a rectangular duct having an aspect ratio (AR) of 8:1 and an expansion ratio (ER) of 2.02:1. Results are presented for a Reynolds number range between 100 and 8000, thus covering the laminar, transitional and turbulent flow regimes. The boundaries of the reverse flow regions are identified by locating the streamwise coordinates on a plane adjacent to the bounding walls where the mean streamwise velocity component is zero. The size of the reverse flow regions increases and moves further downstream in the laminar flow regime; decreases and moves upstream in the transitional flow regime; and remains almost constant or diminishes in the turbulent flow regime; as the Reynolds number increases. The spanwise distribution of the boundary line for the reverse flow region adjacent to the stepped wall develops a minimum near the sidewall in the laminar flow regime, but that minimum in the distribution disappears in the turbulent flow regime. Predictions agree well with measurements in the laminar flow regime and reasonably well in the turbulent flow regime.

Reattachment of Three-Dimensional Flow Adjacent to Backward-Facing Step

Numerical simulations for incompressible three-dimensional laminar forced convection flow adjacent to backward-facing step in rectangular duct are performed to examine the reattachment region of the separated flow on the stepped wall. The feasibility of utilizing the two-dimensional flow definition and the limiting streamline definition for identifying the reattachment line/region was examined. The downwash and the “jet-like” flow that develops near the sidewall creates significant spanwise flow adjacent to the stepped wall, making it difficult to identify a reattachment line/region both numerically and experimentally. The use of the line/region that identifies the location on a plane adjacent to the stepped wall where the gradient of the mean streamwise velocity component is zero ∂u/∂y|y=0=0 is recommended for code and apparatus validation of three-dimensional separated flow.

The Effects of Surface Roughness on the Mean Velocity Profile in a Turbulent Boundary Layer

Experimental measurements of the mean velocity profile in a canonical turbulent boundary layer are obtained for four different surface roughness conditions, as well as a smooth wall, at moderate Reynolds numbers in a wind tunnel. The mean streamwise velocity component is fitted to a correlation which allows both the strength of the wake, Π, and friction velocity, Uτ, to vary. The results show that the type of surface roughness affects the mean defect profile in the outer region of the turbulent boundary layer, as well as determining the value of the skin friction. The defect profiles normalized by the friction velocity were approximately independent of Reynolds number, while those normalized using the free stream velocity were not. The fact that the outer flow is significantly affected by the specific roughness characteristics at the wall implies that rough wall boundary layers are more complex than the wall similarity hypothesis would allow.

LDA-Measurements of Transitional Flows Induced by a Square Rib

New fundamental measurements are presented for the transition process in flat plate boundary layers downstream of two-dimensional square ribs. By use of laser Doppler anemometry (LDA) and a large Matched-Index-of-Refraction (MIR) flow system, data for wall-normal fluctuations and Reynolds stresses were obtained in the near wall region to y+<0.1 in addition to the usual mean streamwise velocity component and its fluctuation. By varying velocity and rib height, the experiment investigated the following range of conditions: k+=5.5 to 21, 0.3<k/δ1<1,180<Rek<740,6×104<Rex,k<1.5×105,ReΘ660,−125<x−xk/k<580. Consequently, results covered boundary layers which retained their laminar characteristics through those where a turbulent boundary layer was established shortly after reattachment beyond the forcing rib. For “large” elements, evolution of turbulent statistics of the viscous layer for a turbulent boundary layer y+<∼30 was rapid even in flows where the mean velocity profile still showed laminar behavior.

Turbulent properties in a homogeneous tidal bottom boundary layer

Profiles of mean and turbulent velocity and vorticity in a tidal bottom boundary layer are reported. Friction velocities estimated (1) by the profile method using the time mean streamwise velocity, (2) by the eddy‐correlation method using the turbulent Reynolds stress, and (3) by the dissipation method using the turbulent kinetic energy dissipation rate ε are in good agreement. The mean streamwise velocity component exhibits two distinct log layers. In both layers, ε is inversely proportional to the distance from the bottom Z. The lower log layer occupies the bottom 3 m. In this layer, the turbulent Reynolds stress is nearly constant. The dynamics in the lower log layer are directly related to the stress induced by the seabed. The upper log layer spans 5 to 12 m above the bottom. In this layer, the turbulent Reynolds stress decreases toward the surface. The friction velocity estimated by the profile method in the upper log layer is about 1.8 times of that estimated in the lower log layer. Form drag might be important in the upper log layer. A detailed study of upstream topography is required for the bed stress estimate. The mean profile of vertical flux of spanwise vorticity is nearly uniform with Z and is at least a factor of 5 larger than the vertical divergence of turbulent Reynolds stress to which it may be compared. A new method of estimating the friction velocity is proposed that uses the vertical flux of turbulent spanwise vorticity. This is supported by the fact that the vertical eddy diffusivity for the turbulent vorticity is about equal in magnitude and vertical structure to the eddy viscosity for the turbulent momentum. The friction velocity calculated from the vorticity flux is equal to that estimated by the other three methods. Turbulent enstrophy, corrected for the sensor response function, is proportional to Z−1 for the entire water column. The relation between ε and enstrophy for high‐Reynolds‐number flows is confirmed by our observations.

An experimental and numerical study of a 90° bifurcation

The flow field of a 90° square duct bifurcation was examined both experimentally and numerically for a Reynolds number of 1200 and equal branch flow rates. Velocity measurements were carried out with a one-component LDV, recording, besides the time mean streamwise velocity component, its time variation due to vortex shedding which took place in the extension of the main duct, as well as secondary flow velocities in the 90° branch. Flow visualization provided additional information about the three-dimensional character of the flow field by recording the paths of neutrally buoyant solid particles. The experimental data were compared with the results of a numerical method, constituting an extension of the well-known SOLA method to a 3-D generalized coordinate system, presented here for the first time. These comparisons were very successful in the vertical branch but less satisfactory in the horizontal branch where unsteadiness was very strong. The characteristic frequency of the velocity fluctuations in the detached shear layer of the horizontal branch was very well predicted but the velocity amplitudes were underestimated. The predicted secondary flow in the vertical branch was compared well with the experimental data presenting maximum values close to the inlet mean velocity.

The Flow Over Two-Dimensional Surface-Mounted Obstacles at Low Reynolds Numbers

The flow over a fence and a block mounted in a fully developed channel flow is experimentally investigated as a function of the Reynolds number, blockage ratio and length-to-height ratio using a laser-Doppler-anemometer. The information obtained includes the location and size of the primary and secondary recirculation zones, and profiles of the mean streamwise velocity component. The experiments were carried out in a channel for a Reynolds number in the range 150 < ReH < 4500. Comparisons are drawn between the obstacle flow and the backward-facing step flow.