Stochastic modeling of lift and drag dynamics under turbulent wind inflow conditions

Abstract

We present a new approach to model the complex dynamics of aerodynamic forces on an airfoil in turbulent inflow conditions. Our ansatz is based on stochastic differential equations and aims at replacing traditional look-up table methods used in wind turbine simulation systems by the effective response dynamics of lift and drag forces. The parameters of the model are derived directly from empirical data. Measurements were taken in the closed loop wind tunnel of the University of Oldenburg for an airfoil FX 79-W-151A. The turbulent inflow was generated using a fractal square grid as it is possible to generate in this way wind speed fluctuations with similar statistics as observed in nature. Forces were measured using two strain gauge force sensors at two end points of the vertically installed airfoil. The modeling is performed by applying a stochastic approach on the measured data. By estimating the first two Kramers-Moyal coefficients, a first-order stochastic differential equation called the Langevin equation is obtained. The stochastic model achieved through this approach is extended to account for oscillation effects contained in lift and drag dynamics that probably stem from unsteady aerodynamic effects. The results are optimized by applying a 2 test on the probability density functions (PDFs) of model and measurements. With the knowledge of the Langevin equation, synthetic time series are generated. Their stationary PDFs as well as conditional PDFs show good agreement with the actual measurements. A comparison of classical averaging and the stochastic approach shows that stochastic analysis achieves additional insight into the local dynamics of lift and drag forces.

Parameter-free resolution of the superposition of stochastic signals

“…The algorithm requires solely a standard PC without special software environment and solves the inversion problem within the order of minutes. In the future, it will be applied to various problems that result from the mixing of stochastic processes, such as aerodynamic lift and drag measurements [20].…”

Stochastic Model for Aerodynamic Force Dynamics on Wind Turbine Blades in Unsteady Wind Inflow

“…The model extracts most of the information available in the system dynamics in terms of a dynamic response. The model reads [14] X model (k) =…”

“…The intermediate values can be obtained by linear interpolation. For more details and validation of the model; see [14].…”

“…Since the model is based on aerodynamic characteristics of an FX 79-W-151A, for comparison purpose the airfoil data file of AeroDyn is replaced with measured aerodynamic characteristics of this airfoil (for measurement details see [14]).…”

“…The concept represents a stochastic lift and drag model, which provides the lift and drag forces with local dynamics under unsteady wind inflow conditions. The model estimates the lift and drag coefficients numerically based on the local AOA [14]. The proposed approach thus is a stochastic alternative to the classical BEM and Beddoes-Leishman dynamic stall models.…”