Wind Farm Optimization with Turbine Placement Using CFD Simulations

BlogCFDWind Farm Optimization with Turbine Placement Using CFD Simulations

Most renewable energy sources come from the sun. Overall, hourly, the sun is estimated to provide the Earth with over 175 trillion kilowatt hours of energy and, of this, approximately 1-2% is converted to wind energy. Wind energy is a renewable, plentiful, and clean alternative to burning fossil fuels, and produces no greenhouse gas emissions. Wind turbines occupy little land and consume no water—inflicting far less damage upon the environment, compared to non-renewable energy sources. In the last decade, an emphasis on renewable energy sources and rapid growth of wind farm numbers has led to significant decreases in associated costs.

In the last decade starting in 1998, MegaWatt-sized turbines and large wind farms have revolutionized the wind energy industry, making it a potent source of renewable energy. Leading this revolution have been Denmark and Germany, who are also the largest wind energy markets.

In this article, we explore the way the SimScale cloud-based 3D simulation software and its features can be used for the design, simulation, and optimization of the power output of a wind farm.

Betz Law and Power Efficiency

The simplest way to assess the efficiency of a wind turbine is through the Betz Law.

Schematic of fluid flow across a wind turbine
Fig 01: Schematic of fluid flow across a wind turbine (Image source: Wikipedia)

Consider the flow of air through an imaginary tube as shown in Fig 01. Initially, the velocity of undisturbed air, downstream, is v1 m/s and upstream; after passing through the wind turbine, is v2 m/s. The average mass of air (m) flowing through an area (A), can be written in terms of density and velocities as:

air mass transfer written in terms of density and velocitiesThe kinetic energy of the originally undisturbed air can be written as:

kinetic energy of originally undisturbed air

This change in velocity, as the wind passes through the rotating turbine blades, signifies the transfer of kinetic energy from the wind to the turbine. Using the above relation for mass, the change in kinetic energy of the wind can thus be written as:

change in kinetic energy of the wind

A simple measure of the efficiency of the wind turbine can be given by the ratio of change in kinetic energy to the undisturbed energy of the wind, as:energy efficiency of the wind turbine given by ratio of change in kinetic energy to undisturbed energy of wind

Optimization Parameters: Wind Farm

There are several aspects that are of importance in designing a wind farm. Some of the most important include:

Power output vs. wind speed of wind turbine on a wind farm
Fig 02: Power output vs. wind speed of wind turbines
park effect, tunnel effect, hill effect in wind farm design
Fig 03: Effects commonly observed in design of a wind farm
Rotor Diameter Hub height vs. Power - Variation of nominal power as a variation of rotor diameter and hub height in a wind farm
Fig 04: Variation of nominal power as a variation of rotor diameter and hub height in a wind farm (Image source: Keiler, J., and Häuser, H. Betreiberdatenbasis. IWET Datenbank)

Simulation of Wind Farm

In this article, wind turbines with a hub height of around 82 m and the rotor diameter of 80 m are considered. Rotor speed is considered to be constant with an angular velocity of 1.8325 rad/s. Such a system is generally rated around 2 MW. The international standard for measurement of wind speeds is at a height of 10 m from the surface and the velocity varies as:

wind velocity variationwhere Z0 refers to the roughness length, Z to the distance from the ground, Zref is the reference height at which the measurements are made (here 10 m) and vref is the wind velocity at the reference height (here 5 m/s). We assume that the roughness is significantly small and of the order of 0.1 m. In the simulations discussed below, in order to avoid the singularities of a log function, the above relation is simplified to an affine function as:

wind linear velocity

The fluid flow can be considered as an incompressible turbulent flow in a steady state. Here the k-omega SST turbulence model is used. The entire project can be accessed in the Public Project Library and can be imported to your account. Different arrangements are considered to analyze their effect on the wind velocity profiles and related turbulence.

Configuration 1: Wind turbines placed one behind the other

Starting with the worst case scenario, where three wind turbines are aligned one behind the other as shown in Fig. 06.

Vertical wind turbine configuration and wind turbine wakes simulation with cfd software
Fig 06: Configuration of the wind turbines (left); Wake observed downstream and its interference with the subsequent turbines (right)

Fig. 06 also shows a cut slice of the simulation box and the influence of the first turbine on the subsequent turbines upstream is visually evident. A simple estimate shows that the input velocity for the first turbine is around 20 m/s and the output is around 10 m/s. On the contrary, the velocities downstream and upstream of the second and third turbines are almost same and leading to nearly zero power efficiency in them.

wind turbine turbulence simulation with cfd software
Fig 07: Velocity profile downstream and upstream (top-left); Velocity (u-y) depicting turbulence (top-right); Velocity (u-x) upstream from first turbine (bottom-left) and third turbine (bottom-right) shows changes in turbulence profiles

The above velocity profiles in Fig. 07 confirm the conventional knowledge that such a placement is highly undesirable. There is a significant influence of wakes and turbulence from the turbines in front. However, if the turbines are placed reasonably far away, the effects of such wakes can still be negotiated.

Configuration 2: Wind turbines placed one beside the other

Alternatively, it is possible to place the turbines one beside the other, to the direction of the headwind, as shown in Fig. 08.

Horizontal placement of wind turbines and wind turbine wakes simulation with cfd software
Fig 08: Configuration of turbines (left); Velocity (u-z) profile downstream and upstream including depiction of wakes (right)

Unlike the previous configuration, now if the wind turbines are placed beside each other as seen in Fig. 08, all the turbines are faced with the same wind speeds. Thus, as the air flows across the turbines, the turbines can be equally effective.

wind turbine CFD analysis
Fig 09: Downstream wind velocity profile u-x (top-left) and u-y (top-right) demonstrate the influence of turbulence caused by each turbine; velocity profile (u-z) upstream (bottom-left) and downstream (bottom-right) of each turbine

Fig. 09 depicts the velocity profiles. The downstream velocity profiles for u-x and u-y show minor interaction between the turbines. The turbines are just placed about three rotor diameters away in these simulations and such an interaction should be expected. At double these distances, such interactions tend to zero. Such simulations can be easily performed with SimScale with much larger distances to optimize the wind farm.

Configuration 3: Wind turbines placed along a diagonal

The last configuration is to place the turbines one beside the other, along a diagonal, to the direction of the headwind, as shown in Fig. 10. Most commercial wind farms use such configurations.

wind turbine placement in diagonal wind farms cfd simulation
Fig 10: Downstream wind velocity profile u-x (top-left) and u-y (top-right) demonstrate the influence of turbulence caused by each turbine; velocity profile (u-z) upstream (bottom-left) and downstream (bottom-right) of each turbine

Wind turbines need to always face the direction of the wind since any wind from the side will not cause the rotation of the turbines. Thus, the turbines are allowed to “yaw” or rotate towards the direction of the wind. Placing the turbines along a diagonal can also result in much smaller areas required. As shown in Fig. 11, as long as sufficient distances are maintained along the two directions, it can provide a compact way of packing more turbines in the same area.

Velocity profiles - wind turbine placement on a wind farm simulation
Fig 11: Downstream wind velocity profile u-x (top-left) and u-y (top-right) demonstrate the influence of turbulence caused by each turbine; velocity profile (u-z) upstream (bottom-left) and downstream (bottom-right) of each turbine

As shown in Fig. 11, the diagonal distance between the turbines is the same as the horizontal distance in the previous configuration. Yet, just assessing pictorially, the interaction of wakes generated by the turbines are much smaller.

It’s important to note that a simulation does not necessarily need to have the same number of turbines as the real farm. Using periodic boundary conditions that couple two opposite faces will allow the simulation of a wind farm of any size.

This is just a glimpse of how SimScale could be used to simulate various practical problems related to wind engineering. A much larger wind farm can easily be considered to test the fluid flow patterns and optimize the turbine placements. In addition to the park effect discussed above, hill and tunnel effects, the effect of rotor diameter and/or hub height could also be explored using SimScale. The next time you plan to build a wind farm, take advantage of the SimScale simulation environment.

wind turbine cfd simulation


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