Directed percolation in aerodynamics: resolving laminar separation bubble on airfoils

In nature, phase transitions prevail amongst inherently different systems, while frequently showing a universal behavior at their critical point. As a fundamental phenomenon of fluid mechanics, recent studies suggested laminar-turbulent transition belonging to the universality class of directed percolation. Beyond, no indication was yet found that directed percolation is encountered in technical relevant fluid mechanics. Here, we present first evidence that the onset of a laminar separation bubble on an airfoil can be well characterized employing the directed percolation model on high fidelity particle image velocimetry data. In an extensive analysis, we show that the obtained critical exponents are robust against parameter fluctuations, namely threshold of turbulence intensity that distinguishes between ambient flow and laminar separation bubble. Our findings indicate a comprehensive significance of percolation models in fluid mechanics beyond fundamental flow phenomena, in particular, it enables the precise determination of the transition point of the laminar separation bubble. This opens a broad variety of new fields of application, ranging from experimental airfoil aerodynamics to computational fluid dynamics.Comment: 8 pages, 11 figure

Description of laminar-turbulent transition of an airfoil boundary layer measured by differential image thermography using directed percolation theory

Transition from laminar to turbulent flow is still a challenging problem. Recent studies indicate a good agreement when describing this phase transition with the directed percolation theory. This study presents a new experimental approach by means of differential image thermography (DIT) enabling to investigate this transition on the suction side of a heated airfoil. The results extend the applicability of the directed percolation theory to describe the transition on curves surfaces. The experimental effort allows for the first time an agreement between all three universal exponents of the (1+1)D directed percolation for such airfoil application. Furthermore, this study proves that the theory holds for a wide range of flows, as shown by the various conditions tested. Such a large parameter space was not covered in any examination so far. The findings underline the significance of percolation models in fluid mechanics and show that this theory can be used as a high precision tool for the problem of transition to turbulence.Comment: 9 pages, 8 figure

Detailed analysis of the blade root flow of a horizontal axis wind turbine

The root flow of wind turbine blades is subjected to complex physical mechanisms that influence significantly the rotor aerodynamic performance. Spanwise flows, the Himmelskamp effect, and the formation of the root vortex are examples of interrelated aerodynamic phenomena that take place in the blade root region. In this study we address those phenomena by means of particle image velocimetry (PIV) measurements and Reynolds-averaged Navier–Stokes (RANS) simulations. The numerical results obtained in this study are in very good agreement with the experiments and unveil the details of the intricate root flow. The Himmelskamp effect is shown to delay the stall onset and to enhance the lift force coefficient Cl even at moderate angles of attack. This improvement in the aerodynamic performance occurs in spite of the negative influence of the mentioned effect on the suction peak of the involved blade sections. The results also show that the vortex emanating from the spanwise position of maximum chord length rotates in the opposite direction to the root vortex, which affects the wake evolution. Furthermore, the aerodynamic losses in the root region are demonstrated to take place much more gradually than at the tip

On different cascade-speeds for longitudinal and transverse velocity increments

We address the problem of differences between longitudinal and transverse velocity increments in isotropic small scale turbulence. The relationship of these two quantities is analyzed experimentally by means of stochastic Markovian processes leading to a phenomenological Fokker- Planck equation from which a generalization of the Karman equation is derived. From these results, a simple relationship between longitudinal and transverse structure functions is found which explains the difference in the scaling properties of these two structure functions.Comment: 4 pages, 5 figures, now with corrected postscrip

Mandelbrot set in coupled logistic maps and in an electronic experiment

We suggest an approach to constructing physical systems with dynamical characteristics of the complex analytic iterative maps. The idea follows from a simple notion that the complex quadratic map by a variable change may be transformed into a set of two identical real one-dimensional quadratic maps with a particular coupling. Hence, dynamical behavior of similar nature may occur in coupled dissipative nonlinear systems, which relate to the Feigenbaum universality class. To substantiate the feasibility of this concept, we consider an electronic system, which exhibits dynamical phenomena intrinsic to complex analytic maps. Experimental results are presented, providing the Mandelbrot set in the parameter plane of this physical system.Comment: 9 pages, 3 figure

On the universality of small scale turbulence

The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from 8500 to 10^6. The traditional analysis of the statistics of velocity increments by means of structure functions or probability density functions is replaced by a new method which is based on the theory of stochastic Markovian processes. It gives access to a more complete characterization by means of joint probabilities of finding velocity increments at several scales. Based on this more precise method our results call in question the concept of universality.Comment: 4 pages, 4 figure

Stochastic analysis of surface roughness

For the characterization of surface height profiles we present a new stochastic approach which is based on the theory of Markov processes. With this analysis we achieve a characterization of the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method was applied to different road surface profiles which were measured with high resolution. Evidence of Markov properties is shown. Estimations for the parameters of the Fokker-Planck equation are based on pure, parameter free data analysis