Wake Width: Discussion of Several Methods How to Estimate It by Using Measured Experimental Data

Several methods of defining and estimating the width of a turbulent wake are presented and tested on the experimental data obtained in the wake past an asymmetric prismatic airfoil NACA 64(3)-618, which is often used as tip profile of the wind turbines. Instantaneous velocities are measured by using the Particle Image Velocimetry (PIV) technique. All suggested methods of wake width estimation are based on the statistics of a stream-wise velocity component. First, the expansion of boundary layer (BL) thickness is tested, showing that both displacement BL thickness and momentum BL thickness do not represent the width of the wake. The equivalent of 99% BL thickness is used in the literature, but with different threshold value. It is shown that a lower threshold of 50% gives more stable results. The ensemble average velocity profile is fitted by Gauss function and its σ-parameter is used as another definition of wake width. The profiles of stream-wise velocity standard deviation display a two-peak shape; the distance of those peaks serves as wake width for Norberg, while another tested option is to include the widths of such peaks. Skewness (the third statistical moment) of stream-wise velocity displays a pair of sharp peaks in the wake boundary, but their position is heavily affected by the statistical quality of the data. Flatness (the fourth statistical moment) of the stream-wise velocity refers to the occurrence of rare events, and therefore the distance, where turbulent events ejected from the wake become rare and can be considered as another definition of wake width. The repeatability of the mentioned methods and their sensitivity to Reynolds’ number and model quality are discussed as well.

Dynamics of the nonequilibrium flow in a duct with obstruction

This work aims to numerically simulate the dynamics of a channel flow with an obstruction since the moment we inject a fluid with an homogeneous velocity profile. The simulations uses the open source tools of the OpenFOAM platform, the pisoFoam and the LES turbulence model, describing in detail the velocity profiles of laminar and turbulent flows. We also perform a boundary layer mapping in the presence of an obstacle. We used three different domains to follow the evolution of the velocity profile while the fluid progresses downstream and passes the obstruction. The results reproduce the well-known results of laminar flow in a channel, as well as the average velocity profile in the turbulent regime and the occurrence of attachments by the obstruction. These preliminary results are used to validate the solvers and the mesh used. Next, an analysis of the velocity profile dynamics resulted in determining an exponential decay of the root mean square deviations of the homogeneous to the parabolic, and to the turbulent regime in the channel.

Turbulent Flow Over a Facing Step at Several Reynolds Numbers

An experimental study was performed over forward facing step (FFS). It was located within a transparent rectangular acrylic channel (1.4 m in length, 0.1 m in width and 0.02 m in height). The step is 0.01 m in height and 0.1 m in width, and was located 0.7 m downstream (fully developed region); a spanwise aspect ratio, w/h = 10 was used. The experiments were carried out using particle image velocimetry (PIV), which is a non intrusive experimental technique. The experimental water flow conditions include three Reynolds numbers based on the step height, Reh = 1124, 1404 and 1685. These flow conditions correspond to turbulent flow. Measurements were carried out in two zones; zone A begins at x = 8 cm (measured from the step base), and zone B starts at x = 0, y = 0, the visualization region corresponds to an area of 22.76 mm × 16.89 mm. 100 instantaneous velocity fields were obtained for each Reh. A temporal and spatial average was performed to obtain a velocity profile in zone A; likewise, the corresponding turbulence intensity and shear stress distribution were evaluated. The average velocity profile was evaluated for each Reh. Regarding the vortex center location, it was observed that as Reh increases, the y-direction coordinate moves towards bottom of wall channel. For zone B, it was also observed a reduction of the shear stress as Reh increases.

A determination of the effective viscosity for the Brinkman–Forchheimer flow model

The effective viscosity μe for the Brinkman–Forchheimer flow (BFF) model has been determined experimentally for steady flow through a wall-bounded porous medium. Nuclear magnetic resonance (NMR) techniques were used to measure non-invasively the ensemble-average velocity profile of water flowing through a tube filled with an open-cell rigid foam of high porosity (ϕ = 0.972). By comparing these data with the BFF model, for which all remaining parameters were measured independently, it was determined that μe = (7.5+3.4−2.4)μf, where μf was the viscosity of the fluid. The Reynolds number, based upon the square root of the permeability, was 17.