Murat Tutkun

Two-point correlations in high Reynolds number flat plate turbulent boundary layers

Two-point correlations of turbulent boundary layer are presented for Reθ of 9800 and 19,100. The results are based on wind tunnel measurements performed in the 30 cm thick boundary layer of the 21.6 m long LML (Laboratoire de Mécanique de Lille) boundary layer research facility. Simultaneous hot-wire probe measurements of the entire boundary layer at 143 different points on an array are used for computation of the two-point correlations. The two-point correlations in the streamwise–spanwise plane at 11 different wall-normal positions covering one boundary layer thickness in the spanwise direction show that the maximal extension of the correlations in the streamwise direction is bounded within ±3.5δ for both of the Reynolds number tested. The shapes of the positive correlations in the streamwise–spanwise plane at different wall-normal positions are similar throughout the boundary layer from nearly the freestream to the wall. The correlations in the streamwise–wall-normal plane for 11 different wall-normal reference positions also show that the correlations in some cases cover the entire boundary layer. The streamwise extent of the correlations in the streamwise–wall-normal plane is about 7–8 boundary layer thicknesses. Two-point correlation maps for the streamwise–wall-normal plane reveal the existence of non-zero correlations between even the intermittent region and near-wall region.

Three-Component Vectorial Proper Orthogonal Decomposition of Axisymmetric Wake Behind a Disk

One-component scalar, two-component vectorial, and three-component vectorial proper orthogonal decompositions of the axisymmetric turbulent wake have been studied to investigate possible effects of the number of components comprising the two-point correlation tensor forming the kernel of the proper orthogonal decompositions integral equation. A wind-tunnel experiment has been performed 50 diameters downstream of the wake generator, which was a disk of 20 mm in diameter. The Reynolds number based on the disk diameter was 20,400. Twelve cross hot wires were used to obtain the simultaneous multipoint measurements. Six of the probes were located on a fixed rake and the other six probes were located on a movable rake, which was traversed from 10 to 180 deg in 10 deg increments. Two experiments were carried out to obtain first the streamwise and azimuthal components of the velocity, and second to obtain the streamwise and radial components of the velocity. Seven out of nine components of the two-point correlation tensor were computed using measured velocities and the remaining two two-point correlations were extracted from the data using the continuity equations. The one-component scalar, and two- and three-component vectorial decomposition results were essentially in agreement. Eigenvalues for the full vector proper orthogonal decompositions integrated over frequency showed that Fourier mode 2 was the largest in both the streamwise and azimuthal velocity. Azimuthal mode 2 peaks at the near-zero frequency, whereas azimuthal mode 1 peaks at a frequency which corresponds to the vortex shedding frequency. Similar features in turbulence kinetic energy distributions were also observed in the modally decomposed two-point cross-spectra and two-point cross-correlations. Copyright

Markovian properties of passive scalar increments in grid-generated turbulence

Recent research (Renner, Peinke and Friedrich 2001 J. Fluid Mech. 433 383) has shown that the statistics of velocity increments in a turbulent jet exhibit Markovian properties for scales of size greater than the Taylor microscale, λ. In addition, it was shown that the probability density functions (PDFs) of the velocity increments, v (r), were governed by a Fokker–Planck equation. Such properties for passive scalar increments have never been tested. The present work studies the (velocity and) temperature field in grid-generated wind tunnel turbulence for Taylor-microscale-based Reynolds numbers in the range 140≤Rλ≤582. Increments of longitudinal velocity were found to (i) exhibit Markovian properties for separations rλ and (ii) be describable by a Fokker–Planck equation because terms in the Kramers–Moyal expansion of order >2 were small. Although the passive scalar increments, δ(r), also exhibited Markovian properties for a similar range of scales as the velocity field, the higher-order terms in the Kramers–Moyal expansion were found to be non-negligible at all Reynolds numbers, thus precluding the PDFs of δ(r) from being described by a Fokker–Planck equation. Such a result indicates that the scalar field is less Markovian than the velocity field—an attribute presumably related to the higher level of internal intermittency associated with passive scalars.

Mind the gap: a guideline for large eddy simulation

This paper briefly reviews some of the fundamental ideas of turbulence as they relate to large eddy simulation (LES). Of special interest is how our thinking about the so-called ‘spectral gap’ has evolved over the past decade, and what this evolution implies for LES applications.

Low-order representations of the canonical wind turbine array boundary layer via double proper orthogonal decomposition

Wind turbine wakes are investigated in order to characterize the development of energetic turbulence structures. Experimental data from stereo particle image velocimetry render the full Reynolds stress tensor accessible in planes parallel to the swept area of the scale model turbine rotor. Proper orthogonal decomposition (POD) is applied to decompose and analyze structures in the wake. The modes resulting from the decomposition demonstrate that structures grow and develop along the streamwise direction. A second iteration of the snapshot POD, otherwise called double proper orthogonal decomposition (DPOD), is applied to modes of common rank from the span of measurement locations yielding an ordered set of projections. The DPOD describes the sub-modal organization in terms of largest common projection and a series of correction modes with coefficients that are functions of the streamwise coordinate. Sub-structures of POD modes that persist through the wake have a dominant projection that accounts for the ch...

Visualization and Measurement of Flow over a Cylindrical Surface with a Bump

The complex flowfield around a cylindrical bump with a hemispherical free end mounted on a cylindrical surface has been studied by means of liquid-crystal flow visualization, surface-pressure measurements, and cross-hot-wire anemometry. This setup constitutes a prototype of a typical wall-mounted sensor on an aircraft. The slenderness parameter of the bump is one and the curvature of the hemispherical ending starts at the half-height of the bump. The radii of both the cylindrical and hemispherical parts of the bump are equal. The thickness of the turbulent boundary layer over the cylindrical surface, which controls the location of the separation over the bumps surface, is smaller than the bump height at the position at which the bump is located. The flow over the hemispherical free end separates further downstream than does the flow over the cylindrical part of the bump. The size of the recirculation region downstream of the bump is larger than the recirculating region of a finite cylinder with a flat end. A Reynolds number dependence of the reattachment point behind the bump is observed. Large turbulence fluctuations exist because of the interaction between the downwash and the turbulent boundary layer developing over the ground surface. The upstream disturbance of the bump, retardation due to an adverse pressure gradient, and push up of the flow due to the finite length of the bump are also captured by the velocity measurements. Effects due to the curvature of the surface plane are not detectable far downstream of the bump.

Identification of Markov process within a wind turbine array boundary layer

The Markovian properties within a wind turbine array boundary layer are explored for data taken in a wind tunnel containing a model wind turbine array. A stochastic analysis of the data is carried out using the mathematics of Markov processes. The data were obtained using hot-wire anemometry thus providing point velocity statistics. The theory of Markov process is applied to obtain a statistical description of longitudinal velocity increments inside the turbine wake. Comparison of two- and three-scale conditional probability density functions indicates the existence of Markovian properties in longitudinal velocity increments for scale differences larger than the Taylor microscale. This result is quantified by use of the Wilcoxon rank-sum test which verifies that this relationship holds independent of initial scale selection outside of the near-wake region behind a wind turbine. Furthermore, at the locations which demonstrate Markovian properties, there appears to be a well defined inertial subrange which ...

Energy-scale aware feature extraction for flow visualization

In the visualization of flow simulation data, feature detectors often tend to result in overly rich response, making some sort of filtering or simplification necessary to convey meaningful images. In this paper we present an approach that builds upon a decomposition of the flow field according to dynamical importance of different scales of motion energy. Focusing on the high‐energy scales leads to a reduction of the flow field while retaining the underlying physical process. The presented method acknowledges the intrinsic structures of the flow according to its energy and therefore allows to focus on the energetically most interesting aspects of the flow. Our analysis shows that this approach can be used for methods based on both local feature extraction and particle integration and we provide a discussion of the error caused by the approximation. Finally, we illustrate the use of the proposed approach for both a local and a global feature detector and in the context of numerical flow simulations.

The WALLTURB Joined Experiment to Assess the Large Scale Structures in a High Reynolds Number Turbulent Boundary Layer

Experiments, involving the joint effort of three European teams and aiming at using the state-of-the-art techniques to study the dynamics of the high Reynolds turbulent boundary layer, have been performed in June 2006 in the LML large wind tunnel. A set of four stereoscopic PIV systems and a rake of 143 hot wires were used to provide synchronised measurements. This paper summarises these experiments, presents sample results of both PIV and hot-wire rake data and illustrates the complementarity of such a coupled approach that combines the advantages of each technique.

Structural impact assessment of low level jets over wind turbines

High-frequency (50 Hz) observational data from the 200-m tower data (Reese Technology Center, Texas) have been prescribed as inflow conditions into the NREL FAST code in order to evaluate the structural impacts of Low Level Jets (LLJs) on a typical commercial wind turbine. A vertical region of interest for the analysis of interaction LLJ–wind turbine has been delimited, and the LLJ length scales have been calculated. The analysis of power spectra exhibited a deviation within the inertial subrange from the classical −5/3 slope in a log-log representation towards a lower slope, which indicated a lower rate of energy transfer when the LLJ was present. It has been observed that during a LLJ event the turbulence intensity and turbulence kinetic energy were significantly lower than those during unstable conditions; and cyclical aerodynamic loads on the turbine blades produced a negative impact on the wind turbine, mainly due to the enhanced wind shear. Dominant frequencies present in the power spectra of the incoming wind were also observed in frequencies related to the dynamic loads of the turbines. It was found that the wind turbine can mimic the signals from the approaching inlet flow, although some of the replication can be altered or annulled in a wind farm.