Robert Stresing

Gradual wavelet reconstruction of the velocity increments for turbulent wakes

This work explores the properties of the velocity increment distributions for wakes of contrasting local Reynolds number and nature of generation (a cylinder wake and a multiscale-forced case, respectively). It makes use of a technique called gradual wavelet reconstruction (GWR) to generate constrained randomizations of the original data, the nature of which is a function of a parameter, ϑ. This controls the proportion of the energy between the Markov-Einstein length (∼ 0.8 Taylor scales) and integral scale that is fixed in place in the synthetic data. The properties of the increments for these synthetic data are then compared to the original data as a function of ϑ. We write a Fokker-Planck equation for the evolution of the velocity increments as a function of spatial scale, r, and, in line with previous work, expand the drift and diffusion terms in terms up to fourth order in the increments and find no terms are relevant beyond the quadratic terms. Only the linear contribution to the expansion of the drift coefficient is non-zero and it exhibits a consistent scaling with ϑ for different flows above a low threshold. For the diffusion coefficient, we find a local Reynolds number independence in the relation between the constant term and ϑ for the multiscale-forced wakes. This term characterizes small scale structure and can be contrasted with the results for the Kolmogorov capacity of the zero-crossings of the velocity signals, which measures structure over all scales and clearly distinguishes between the types of forcing. Using GWR shows that results for the linear and quadratic terms in the expansion of the diffusion coefficient are significant, providing a new means for identifying intermittency and anomalous scaling in turbulence datasets. All our data showed a similar scaling behavior for these parameters irrespective of forcing type or Reynolds number, indicating a degree of universality to the anomalous scaling of turbulence. Hence, these terms are a useful metric for testing the efficacy of synthetic turbulence generation schemes used in large eddy simulation, and we also discuss the implications of our approach for reduced order modeling of the Navier-Stokes equations.

The Turbulent Flow in the Close-Up Region of Fractal Grids

Turbulence generated by fractal square grids differs substantially from all other documented turbulent flows. Previous experiments indicated that the turbulence intensity reaches its maximum at a position proportional to the length and thickness of the largest bar in the grid [2]. The goal of this work was to investigate the evolution of the flow behind grids with different smallest scales. Hot wire measurements were conducted close to the grid in two different wind tunnels using three different fractal grids. It was found that the positions of the flatness peak and turbulence intensity peak change by altering the numbers of iterations and the blockage ratio respectively. Furthermore, it was shown that this result is invariant to the investigated different boundary conditions.

Towards a stochastic multi-point description of turbulence

In previous work it was found that the multi-scale statistics of homogeneous isotropic turbulence can be described by a stochastic cascade process of the velocity increment from scale to scale, which is governed by a Fokker-Planck equation. We now show how this description for increments can be extended in order to obtain the complete multi-point statistics in real space of the turbulent velocity field (Stresing & Peinke, 2010). We extend the stochastic cascade description by conditioning on an absolute velocity value itself, and find that the corresponding conditioned process is also governed by a Fokker-Planck equation, which contains as a leading term a simple additional velocity-dependent coefficient, d10, in the drift function. Taking the velocity-dependence of the Fokker-Planck equation into account, the multi-point statistics in the inertial range can be expressed by two-scale statistics of velocity increments, which are equivalent to three-point statistics of the velocity field. Thus, we propose a stochastic three-point closure for the velocity field of homogeneous isotropic turbulence. Investigating the coefficient d10 for different flows, we find clear evidence that the multipoint structure of small scale turbulence is not universal but depends on the type of the flow.

Multi-scale Analysis of Turbulence in CFD-Simulations

We performed a 3D DNS simulation using spectral/hpmethod on an fx79- w151a airfoil at a Reynolds number of Re=5000 at an angle of attack of α = 12° Due to a separating flow, an inhomogeneous turbulent field evolved in the wake above the trailing edge. Within this field time series of the flow properties have been gathered at selected points. The data of the time series at one point have been analyzed on the back ground of a multipoint correlation method. From statistics of velocity increments Kramers-Moyal coefficients have been estimated.