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lab:zephyr:rotors [2014/11/28 14:35] – [H-Rotor] chrono | lab:zephyr:rotors [2016/07/22 14:00] – [Power Estimation] chrono | ||
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====== Rotors ====== | ====== Rotors ====== | ||
- | Compared to drag-only type rotors (Savonius), | + | Compared to drag-only type rotors (Savonius), lift-only type rotors (Darrieus) |
- | Main focus will be on 3 types: | + | A drag-only type rotor can develop more torque, even at early stages in low wind conditions, but that would require a very specific and resource-intensive generator to accommodate for the very low rotational speed. A typical low end for a direct driven axial flux permanent magnet alternator with many poles is about 100 revolutions per minute. Everything under 100 rpm means huge additional resource investments into rare earth magnets and loads of copper (windings). |
- | * [[lab: | ||
- | * [[lab: | ||
- | * [[lab: | ||
- | Additionally, | ||
+ | ===== VAWT Rotor Types ===== | ||
- | The standardization | + | {{: |
+ | |||
+ | ^ C-Rotor | ||
+ | |{{: | ||
+ | | Laser Cut | 3D Print (complex multipart) | 3D Print (print 2 - assemble 1)| | ||
+ | | 10-50 W | 5-40W | <5 W | | ||
+ | |||
+ | Sources: https:// | ||
+ | |||
+ | The Gorlov Helical blade type is a derivative | ||
+ | developed by its namesake Alexander M. Gorlov to be used in hydro-power applications. It | ||
+ | attempts to solve the problems of vibration | ||
+ | having helical curved blades as opposed to straight blades. In the traditional Darrieus | ||
+ | setup, as the blades rotate the angle of attack will change, resulting in areas throughout the | ||
+ | rotation where the blade is in a stall. This causes vibration which will reduce the life of the | ||
+ | turbine, along with causing noise which is especially unwanted | ||
+ | Gorlov blade type, on the other hand, is curved in a helical fashion, which means that | ||
+ | throughout its rotational path, at least part of the blade will not be in a stall, which greatly | ||
+ | reduces the vibration and the noise generated. | ||
+ | |||
+ | Additionally, | ||
===== Standard-Parameters ===== | ===== Standard-Parameters ===== | ||
+ | |||
+ | Standardization of the system and compatibility of components offers a perfect test environment for different rotor types to see how comparable rotor-surfaces will perform with different rotor-types in the same environment. | ||
==== Maximum wind speed ==== | ==== Maximum wind speed ==== | ||
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Each assembly should have a rotor surface **no larger than 4m²** to avoid possible legal restrictions in Europe. A wind surface of 4 m² equals a 2 m diameter VAWT rotor with a height of 2 m. | Each assembly should have a rotor surface **no larger than 4m²** to avoid possible legal restrictions in Europe. A wind surface of 4 m² equals a 2 m diameter VAWT rotor with a height of 2 m. | ||
- | <WRAP round tip>In every wind condition, a 1 m diameter VAWT with a height of 4 m is more efficient due to the higher rpm and better aerodynamic figures. Industrial VAWTs aim for a large height not for a large diameter. | + | <WRAP round tip>In every wind condition, a 1 m diameter VAWT with a height of 4 m is more efficient due to the higher rpm and better aerodynamic figures. Industrial VAWTs aim for a large height, not for a large diameter. |
</ | </ | ||
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| | ||
FIXME: Define a common rotor to generator-shaft interface for easy rotor type interchangeability | FIXME: Define a common rotor to generator-shaft interface for easy rotor type interchangeability | ||
- | |||
- | ===== C-Rotor ===== | ||
- | * C-type requires lower wind speed, creates higher torque at lower wind speeds | + | ===== Basic Wind Power Calculations |
- | * Usable bandwidth of wind speed is higher | + | |
- | * FIXME: Plans, | + | |
- | {{: | + | Corrections and additional approaches are always welcome. |
- | ===== 3D printable Lenz-Rotor ===== | + | ==== Power Estimation |
- | {{: | + | The following equations provide a means to estimate the approximate amount of kinetic and electric power converted by a wind turbine: |
- | Sources: https:// | + | === Available power in the wind === |
- | ===== 3D printable Gorlov Rotor ===== | + | |
- | {{: | + | <x 20> |
+ | P_{k} ≈ {{1}/{2}} ∗ A ∗ V^3 ∗ ρ | ||
+ | </x> | ||
- | Print two times and stack on each other approach. For <1W systems. | + | ^ Parameter ^ Unit ^ Detail ^ |
+ | ^ <x 12> | ||
+ | ^ <x 12> | ||
+ | ^ <x 12> | ||
+ | ^ <x 12>\rho</x> | kg/m³ | Density of Air (rho) ~1.225 at 25°C | | ||
- | Sources: https:// | + | **Example: eXperimental Turbine Lenz-Rotor with 0.96 m² surface @ 4 m/s** |
+ | <x 16> | ||
+ | {{1}/{2}} ∗ 0.96 ∗ 4^3 ∗ 1.225 = 36.86 W | ||
+ | </x> | ||
- | ===== Basic Wind Power Calculations ===== | + | ^ Windspeed ^ 1 m/s ^ 2 m/s ^ 4 m/s ^ **8 m/s** ^ **16 m/s** ^ |
+ | ^ Power | 0.57 W| 4.60 W| **36.68 W** | **294.91 W** | **2.36 kW** | | ||
- | Corrections | + | Basically, power scales linearly with the area swept out by the turbine blades |
+ | |||
+ | === Conversion Efficiency === | ||
- | **Power in the wind**\\ | ||
<x 20> | <x 20> | ||
- | P_{wind} = A_{wind} * (v_{wind})^3 * {{1}/{2}} \rho | + | P_{r} ≈ P_{k} ∗ C_{P} |
</x> | </x> | ||
- | * <x 12>P_{wind}</x> -> Available power in the wind, as kinetic | + | * <x 12>P_{r}</x> -> Converted rotational |
- | * <x 12>A_{wind}</x> -> Area of surface (turbine/ | + | * <x 12>P_{k}</x> -> Available power in the wind, as kinetic energy in Watt |
- | * <x 12>V_{wind}</ | + | * <x 12>C_{P}</x> -> Power coefficient |
- | * <x 12> | + | |
- | Example: | + | **Example: |
+ | |||
+ | <x 16> | ||
+ | 36.86 ∗ 0.25 = 9.21 W | ||
+ | </ | ||
+ | |||
+ | The power coefficient accounts for the efficiency of the turbine in converting the wind’s kinetic energy into rotational energy. According to [[https:// | ||
+ | |||
+ | ^ Turbine Type ^ Power Coefficient ^ | ||
+ | | Simple drag VAWT | 0.20 | | ||
+ | | Decent VAWT | 0.30 | | ||
+ | | Good VAWT | 0.35 | | ||
+ | | Superb | ||
+ | | Superb | ||
+ | |||
+ | === Torque === | ||
+ | |||
+ | For turbines which use drag forces (not lift forces), the following equation can be used to estimate the amount of torque in the system, where R is the radius of turbine in meters((Brandmaier, | ||
<x 20> | <x 20> | ||
- | (0.75 * 0.8) * 5.4^3 * {{1}/ | + | τ ≈ {{1}/ |
</x> | </x> | ||
- | **Estimated Wind-Power conversion | + | === Tip Speed Ratio === |
+ | |||
+ | The tip speed ratio (λ) defines the relationship between blade tip speed and incident | ||
+ | wind speed((Deisadze, | ||
<x 20> | <x 20> | ||
- | P_{mech} | + | λ = {{ω ∗ R}/{V}} |
</x> | </x> | ||
- | | Simple drag VAWT | 20% | | + | This equation shows the relationship between the tip speed ratio and the power |
- | | Decent VAWT | 30% | | + | coefficient for various blade types. For each type, there is a unique curve, and therefore a |
- | | Good VAWT | 30% | | + | unique optimal tip speed ratio which corresponds to the maximum power coefficient that |
- | | Superb | + | can be achieved. |
- | | Superb | + | |
+ | For example, a Savonius rotor will produce a maximum power coefficient | ||
+ | of about 0.31 at a tip speed ratio of about 0.9. However, a Darrieus rotor produces a | ||
+ | maximum power coefficient of around 0.35 at a much higher tip speed ratio of around 5.8. | ||
+ | |||
+ | To be most efficient, a blade and rotor should be designed to perform near its optimal tip | ||
+ | speed ratio at wind speeds it is likely to encounter((Ragheb and Ragheb, Wind Turbines Theory - The Betz Equation and Optimal Rotor Tip Speed Ratio 2011)). | ||
+ | |||
+ | === Reynolds Number === | ||
+ | |||
+ | The Reynolds number range for small-scale gorlov VAWTs is quite | ||
+ | low. In comparison, the Reynolds number operating regime of most airfoils used for aircrafts ranges from **6.3e6 for a small Cessna** to **2.0e9 for a Boeing 747**. | ||
+ | |||
+ | <x 20> | ||
+ | Re = {{V ∗ D ∗ \rho}/ | ||
+ | </ | ||
+ | |||
+ | ^ Parameter ^ Unit ^ Detail ^ | ||
+ | ^ <x 12> | ||
+ | ^ <x 12> | ||
+ | ^ <x 12> | ||
+ | ^ <x 12> | ||
+ | |||
+ | **Example: Helical Gorlov-Rotor with 35 cm radius @ 4 m/s** | ||
+ | |||
+ | <x 16> | ||
+ | {{4 ∗ 0.7 ∗ 1.225}/ | ||
+ | </ | ||
- | You can watch these calculations in action, applied to reference wind speed measurements on the [[https:// | + | You can watch these calculations in action, applied to reference wind speed measurements on the [[https:// |
- | A tuned VAWT probably has a best-case efficiency of 40%, while a simple drag-based turbine with no optimization nor special aerodynamics may have an efficiency of about 20%. | + | A tuned VAWT probably has a best-case efficiency of 35%, while a simple drag-based turbine with no optimization nor special aerodynamics may have an efficiency of about 20%. |
{{tag> | {{tag> |