Characteristics of the Wind - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 525

Table 8-6.
Turbulence Simulations Using the Transformation Technique

Reference No. of

components

Spectrum
model

Probability
distribution

Coherence

Neuman and Foster [1970] 1 Dryden Gaussian NA

Reeves et al. [1976] 1 Dryden Non-Gaussian NA

Perlmutter et al. [1977] 3 Dryden Gaussian Vertical

Campbell [1984] 3 von Karman Gaussian NA

Frost and Wang [1980] 1 Dryden,

von Karman,
and Kaimal

Gaussian Vertical

Arman and Frost [1986a] 3 Kaimal Gaussian Vertical

Arman and Frost [1986b] 3 Hojstrup Gaussian Vertical, plus

cross-correlation

Correlation Techniques

Most applications of the correlation technique to turbulence simulation are based on
the Markov hypothesis [ e.g. Cliff and Hall 1980, Lee and Stone 1983, Legg and Raupach
1982]. The velocity of a small volume of air at a future time is represented by the sum of
a velocity correlated with the velocity at the present time and a purely random, uncorrelated
increment of velocity. For a stationary, homogeneous turbulent flow the correlated part is
given mathematically by the Lagrangian velocity auto-correlation function. An application
of this technique to wind turbine design is that by Cliff and Hall [1980].

Harmonic Series Techniques

Two turbulence simulations which use harmonic series have been reported in the wind
energy literature. That of Sundar and Sullivan [1981] simulates a random process by a
series of cosine waves at almost evenly spaced frequencies and with amplitudes weighted
according to the spectral energy at the wave frequency, and the authors report that with as
few as 50 frequencies one can obtain a fairly good representation of the spectrum. Their
procedure has been expanded to three-dimensions using a composite of the Davenport
spectrum and the Fourier transform of the coherence function. Because direct evaluation
of the three-dimensional spectrum is time consuming, a fast Fourier transform technique
was applied to decrease the computational time. A second harmonic series technique is that
developed by Powell and Connell [1986a].

Turbulence Simulation in Lagrangian (Rotating) Coordinates

Powell and Connell [1986b] provide a comparison of the following three turbulence
simulation models based on rotating coordinates: Connell [1982], Sundar and Sullivan
[1983], and Veers [1984]. All three models are based on the harmonic series technique,
which the authors recommend over the transformation (white noise) technique. However,
comparisons of the time series produced by the different models showed that significant
differences can occur, and recommendations were made for improving simulation methods.
More recent models proposed by Veers [1988] and expanded by Kelley [1993] are now
widely used and reported.