Synthetic turbulence generation methods for numerical

Synthetic turbulence generation methods for numerical
investigations of turbulent wind fields
PO. ID
307
B. Roidl, S. Wellenberg, M. Marnett, W. Schröder
Chair of Fluid Mechanics and Institute of Aerodynamics, RWTH Aachen
Abstract
Results
The dynamics of power extraction and the structural loads of a wind energy system
are defined by the spatial and temporal behavior of a turbulent atmospheric
boundary layer. In the development process of wind turbines computational fluid
dynamics (CFD) methods and stand-alone turbulence models are applied to
predict those dynamic processes. A synthetic turbulence model is presented which
includes the significant impact of organized patterns of coherent turbulent
structures to further analyze the turbulent mechanisms in atmospheric boundary
layers and their impact on the structure and power extraction of future wind
turbines.
 Vortical structures presented in Figure 2 (left) imply rapid convergence to
physical turbulence using the RSTGN approach.
 Figure 2 (right) shows that the solution of the RSTGN approach converges to the
reference RANS solution within 2 boundary-layer thicknesses.
 The results of the RSTGN2 method do not converge to the reference solutions
within the computational domain, neither at Reθ=7000, nor at Reθ=700.
Objectives
 Many structural features are not explicitly included in contemporary simulations
of synthetic turbulent wind fields. The focus is set to meet prescribed energy
spectra or second-order statistics.
 The presented ansatz based on the reformulated synthetic turbulence generation
(RSTG) method [1] is extended to mimic length scales, structural patterns, and
arbitrary energy spectra to meet the requirements of variable wind fields.
 The synthetic turbulence generation method can be used as an inflow condition
for a large-eddy simulation (LES).
 The method shall also be applied in the future as a stand-alone turbulence model
similar to those of [2] and [3].
Methods
 The flow solver applies a mixed centered/upwind advective upstream splitting
method (AUSM) scheme to solve the Navier-Stokes equations [4].
 The Reynolds-averaged Navier-Stokes (RANS) simulations apply a oneequation turbulence model [5]. MILES approach is used for the LES [4].
Figure 2: Turbulent structures (left) and skin-friction distribution for a flat-plate
boundary layer at Reθ=7000 (top) and Reθ=700 (bottom)
 Coherent structures are generated satisfying implicitly the auto-two point
correlation.
 The mean velocity profile is needed at the inflow boundary, i.e. from RANS.
 Each eddy core i has individual spectral properties f(σ) that are associated with
turbulent anisotropic length and time scales which depend on the location of the
core in the boundary layer. The velocity signal is computed by Equation 1.

N
uj x, y, z, t   ak j  ij f1 j  1  f 2 j  2  f 3 j  3  with f nj  exp iq j  qn  qk

(1)
i 1
where σ, a, ν, q describe a distance function, correlated Reynolds stresses,
random signs and spatial framework of the shape functions.
.
Figure 3: Development of the Reynolds-stress distribution for flat-plate boundary
layer at Reθ=700
 Figure 3 shows a good agreement of RSTGN method with reference DNS
solution within a very short transition time. RSTGN2 configuration does not
yield satisfying results.
Conclusions
Figure 1: Schematic of the computational domain
Computational Setup:
 Two self similar zero-pressure gradient boundary layers are used as validation
cases of the RSTGN method.
 Reynolds number based on the momentum thickness θ is about 7000 and 700.
 Domain size is 8δx5δx2δ (12δx5δx2δ) and 1000x118x220 (200x71x51) grid points
at Reθ=7000 (Reθ=700).
 Configuration RSTGN contains features such as organized turbulent patterns,
Reynolds stresses, proper turbulent length and time scales
 Configuration RSTGN2 is computed with a simplified STG method without proper
spatial turbulent patterns, but with proper Reynolds stresses and length and time
scales.
 Setup is shown in Figure 1.
 Organized patterns of a fully turbulent boundary layer were extracted from the
analysis of a pure LES solution of self-similar boundary layers to be
reconstructed in a STG method.
 The promising RSTGN approach reduces computational resources in case of
pure LES simulation due to rapid transition from synthetic to physical turbulence
(about 2 boundary-layer thicknesses). The proper description of organized
patterns of coherent turbulent structures can improve existing turbulence
models to enhance the development process of future wind turbines.
 The RSTGN method shall also be applicable as a prospective stand-alone
turbulence model for rapid evaluation of arbitrary wind fields.
References
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method and its application to zero-pressure gradient boundary layers. Int. J. Heat Fluid Flow, Vol. 44, pp. 28-40, 2013
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Meteorol. Soc., Vol. 98, pp. 563-598, 1972
3. J. Mann: Wind field simulation. Prob. Eng. Mech., Vol. 13, No. 4, pp. 269-282, 1998
4. M. Meinke, W. Schröder, E. Krause, T. Rister: A comparison of second- and sixth-order methods for large-eddy
simulations. Comput. Fluids, Vol. 31, pp. 695-718, 2002
5. E. Fares, W. Schröder: A General One-Equation Turbulence Model for Free Shear and Wall-Bounded Flows. Flow
Turbul. Combust, Vol. 73, pp. 187-215, 2004
6. P. Schlatter, R. Örlü, R. Li, G. Brethouwer, J. H. M. Fransson, A. V. Johansson, P. H. Alfredsson, D. Henningson:
Turbulent boundary layers up to Reθ=2500 studied through simulation and experiment. Phys. Fluids, Vol. 21, 051702,
2009
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