The triple decomposition of a fluctuating velocity field in a multiscale flow

A new method for the triple decomposition of a multiscale flow, which is based on the novel optimal mode decomposition (OMD) technique, is presented. OMD provides low order linear dynamics, which fits a given data set in an optimal way and is used to distinguish between a coherent (periodic) part of a flow and a stochastic fluctuation. The method needs no external phase indication since this information, separate for coherent structures associated with each length scale introduced into the flow, appears as the output. The proposed technique is compared against two traditional methods of the triple decomposition, i.e., bin averaging and proper orthogonal decomposition. This is done with particle image velocimetry data documenting the near wake of a multiscale bar array. It is shown that both traditional methods are unable to provide a reliable estimation for the coherent fluctuation while the proposed technique performs very well. The crucial result is that the coherence peaks are not observed within the spectral properties of the stochastic fluctuation derived with the proposed method; however, these properties remain unaltered at the residual frequencies. This proves the method’s capability of making a distinction between both types of fluctuations. The sensitivity to some prescribed parameters is checked revealing the technique’s robustness. Additionally, an example of the method application for analysis of a multiscale flow is given, i.e., the phase conditioned transverse integral length is investigated in the near wake region of the multiscale object array

A robust post-processing method to determine skin friction in turbulent boundary layers from the velocity profile

The present paper describes a method to extrapolate the mean wall shear stress, , and the accurate relative position of a velocity probe with respect to the wall, Δ, from an experimentally measured mean velocity profile in a turbulent boundary layer. Validation is made between experimental and direct numerical simulation data of turbulent boundary layer flows with independent measurement of the shear stress. The set of parameters which minimize the residual error with respect to the canonical description of the boundary layer profile is taken as the solution. Several methods are compared, testing different descriptions of the canonical mean velocity profile (with and without overshoot over the logarithmic law) and different definitions of the residual function of the optimization. The von Kármán constant is used as a parameter of the fitting process in order to avoid any hypothesis regarding its value that may be affected by different initial or boundary conditions of the flow. Results show that the best method provides an accuracy of Δ≤0.6% for the estimation of the friction velocity and Δ+≤0.3 for the position of the wall. The robustness of the method is tested including unconverged near-wall measurements, pressure gradient, and reduced number of points; the importance of the location of the first point is also tested, and it is shown that the method presents a high robustness even in highly distorted flows, keeping the aforementioned accuracies if one acquires at least one data point in +<10. The wake component and the thickness of the boundary layer are also simultaneously extrapolated from the mean velocity profile. This results in the first study, to the knowledge of the authors, where a five-parameter fitting is carried out without any assumption on the von Kármán constant and the limits of the logarithmic layer further from its existence

Flow characteristics and scaling past highly porous wall-mounted fences

An extensive characterization of the flow past wall-mounted highly porous fences based on single- and multi-scale geometries has been performed using hot-wire anemometry in a low-speed wind tunnel. Whilst drag properties (estimated from the time-averaged momentum equation) seem to be mostly dependent on the grids’ blockage ratio; wakes of different size and orientation bars seem to generate distinct behaviours regarding turbulence properties. Far from the near-grid region, the flow is dominated by the presence of two well-differentiated layers: one close to the wall dominated by the near-wall behaviour and another one corresponding to the grid’s wake and shear layer, originating from between this and the freestream. It is proposed that the effective thickness of the wall layer can be inferred from the wall-normal profile of root-mean-square streamwise velocity or, alternatively, from the wall-normal profile of streamwise velocity correlation. Using these definitions of wall-layer thickness enables us to collapse different trends of the turbulence behaviour inside this layer. In particular, the root-mean-square level of the wall shear stress fluctuations, longitudinal integral length scale, and spanwise turbulent structure is shown to display a satisfactory scaling with this thickness rather than with the whole thickness of the grid’s wake. Moreover, it is shown that certain grids destroy the spanwise arrangement of large turbulence structures in the logarithmic region, which are then re-formed after a particular streamwise extent. It is finally shown that for fences subject to a boundary layer of thickness comparable to their height, the effective thickness of the wall layer scales with the incoming boundary layer thickness. Analogously, it is hypothesized that the growth rate of the internal layer is also partly dependent on the incoming boundary layer thickness

Downstream evolution of perturbations in a zero pressure gradient turbulent boundary layer

This paper examines the evolution of perturbations generated by various trips in a zero pressure gradient turbulent boundary layer. Measurements taken using hot-wire anemometry show that the evolution of the boundary layer towards the natural state is strongly dependent on the trip geometry. In particular the mechanisms creating the boundary layer appear to depend primarily on the wall normal distribution of blockage ratio, recovering the natural properties more rapidly for a uniform distribution of blockage (wall normal cylinders) than for non-uniform blockage (sawtooth fence). The relative size of the trip with respect to the boundary layer is shown to be a second order effect. Standard behaviour (characterized by the skin friction coefficient, CfCf, the wake component, ΠΠ, and the shape factor, H) is recovered successfully 500D∼75h500D∼75h downstream, presenting 175%175% higher momentum thickness, θθ, than the natural case for the same downstream distance

Experimental measurement of wall shear stress in strongly disrupted flows

Mean and fluctuating wall shear stress is measured in strongly disrupted cases generated by various low-porosity wall-mounted single- and multi-scale fences. These grids generate a highly turbulent wake which interacts with the wall-bounded flow modifying the wall shear stress properties. Measurement methods are validated first against a naturally growing zero pressure gradient turbulent boundary layer showing accuracies of 1% and 4% for extrapolation and direct measurement of the mean shear stress respectively. Uncertainty associated with the root mean square level of the fluctuations is better than 2% making it possible to measure small variations originating from the different fences. Additionally, probability density functions and spectra are also measured providing further insight into the flow physics. Measurement of shear stress in the disrupted cases (grid+TBL) suggest that the flow characteristics and turbulence mechanisms remain unaltered far from the grid even in the most disrupted cases. However, a different root mean square level of the fluctuations is found for different grids. Study of the probability density functions seem to imply that there are different degrees of interaction between the inner and outer regions of the flow

Passive scalar dispersion in the near wake of a multi-scale array of rectangular cylinders

The near wakes of flows past single- and multi-scale arrays of bars are studied by means of planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV). The aim of this research is to better understand dispersion of passive scalar downstream of the multi-scale turbulence generator. In particular, the focus is on plausible manifestations of the space-scale unfolding (SSU) mechanism, which is often considered in the literature as the reason for the enhancement of the turbulent scalar flux in flows past fractal grids (i.e. specific multi-scale turbulence generators). The analysis of qualitative and quantitative PLIF results, as well as the simultaneously acquired PIV results, confirms the appearance of a physical scenario resembling the SSU mechanism. Unlike the anticipation of the literature, however, this scenario applies to some extent also to the flow past the single-scale obstacle. Application of a triple decomposition technique (which splits the acquired fields into their means, a number of coherent fluctuations and their stochastic parts) and a conditional-averaging technique reveals that the SSU mechanism is active in the vicinity of an intersection point between two adjacent wakes and is driven almost exclusively by coherent fluctuations associated with the larger of the intersecting wakes. This suggests that the SSU mechanism is related to the coherent fluctuations embedded in the flow rather than to the fine-scale turbulence and its underlying integral length scale, as proposed in previous works