Turbulence Descriptors
Turbulence Intensity
Single point longitudinal turbulence intensity is one of the most common predictors of blade loads for wind and tidal turbine applications. This descriptor is determined using the standard deviation of turbulent fluctuations and dividing by mean velocity, as shown below:
Where TI is the Turbulence Intensity (%) σ is the Standard Deviation of Turbulent Fluctuations U is the Mean Flow Velocity |
The average period for turbulence
intensity is typically 10 minutes, during which the mean velocity is considered
constant/quasi-stationary [6].
As the equation takes into account standard deviation of the flow speed, it represents the ‘gustiness’ of the fluid flow around its mean [16].
This is important as tidal turbine loads are highly sensitive to turbulence intensity, because unsteady flow can have a big impact on the extreme loading. The depth-wise turbulence intensity profile for highly energetic flow at the Fall of Warness, Orkney, UK, can vary between 6% near the surface to 13% near the seabed, suggesting the likely turbulence intensity range that a tidal turbine may be exposed to [17].
This is important as tidal turbine loads are highly sensitive to turbulence intensity, because unsteady flow can have a big impact on the extreme loading. The depth-wise turbulence intensity profile for highly energetic flow at the Fall of Warness, Orkney, UK, can vary between 6% near the surface to 13% near the seabed, suggesting the likely turbulence intensity range that a tidal turbine may be exposed to [17].
Length Scales
The length scale is another aspect which is used to define turbulence. This section details a review of the types of length scale.
General Background
Richardson’s notion of turbulence was that a turbulent flow is composed by ‘eddies’ of different sizes [18]. Using Kolmogorov’s theory of 1941, these sizes define a characteristic length scale for eddies. The significance of this is that large eddies are unstable, due to inertial instabilities [19], and break up to form smaller eddies, with the energy stored in the large eddy distributed between smaller eddies [20]. Eventually, energy is passed down to smaller scales until the length scale is such that the viscosity of a fluid can dissipate the kinetic energy into internal (heat) energy [18]. In this section, three branches of length scale are discussed.
Kolmogorov Length Scale
In Kolmogorov’s theory of 1941, he proposed that for very high Reynolds numbers, small scale turbulent motions are statistically isotropic. In this situation, he hypothesised that the statistics of small length scales are universally and uniquely determined by viscosity and rate of energy dissipation [18]. With these two parameters, the length can be calculated:
Integral Length Scale
The integral length scale is a measure of the average size of turbulent eddies; since these eddies obtain energy from the mean flow. Integral length scales have large velocity fluctuation and are low in frequency [6]. Because of this, integral length scales are highly anisotropic. They are defined in terms of the normalized two-point velocity correlations [6]. The integral length scale of the longitudinal velocity component in the direction parallel to the mean flow [6] is defined as:
In the wind context, longitudinal length scales are a secondary driver for blade fatigue loads, being in the order of hundreds of metres [6]. This is not the case for a tidal channel since the length scales will be physically constrained by the seabed and water surface, i.e. channel depth. As a large turbine is likely to impose on a significant portion of the water column, the integral length scale would be much closer to the rotor diameter than for a wind turbine [6].
Taylor Micro Scale
This is an intermediate scale between the two scales mentioned above. This scale specifically corresponds to Kolmogorov’s inertial sub-range [20]. The image below shows a log scale of the length scales describe in terms of their energy content.
Picture Courtesy of McDonough [20]