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lab:zephyr:rotors [2016/07/14 21:34] – [Power Estimation] chrono | lab:zephyr:rotors [2016/07/25 13:46] – [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) |
+ | |||
+ | 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). | ||
+ | |||
===== VAWT Rotor Types ===== | ===== VAWT Rotor Types ===== | ||
Line 72: | Line 76: | ||
==== Power Estimation ==== | ==== Power Estimation ==== | ||
- | The following | + | The following |
- | converted by a wind turbine | + | |
+ | === Available power in the wind === | ||
<x 20> | <x 20> | ||
- | P ≈ {{1}/{2}} ∗ A ∗ V^3 ∗ ρ ∗ C_{P} | + | P_{k} ≈ {{1}/{2}} ∗ A ∗ V^3 ∗ ρ |
</x> | </x> | ||
- | * <x 12>P</ | + | ^ Parameter ^ Unit ^ Detail ^ |
- | | + | ^ <x 12>P_{k}</ |
- | | + | ^ <x 12> |
- | * <x 12> | + | ^ <x 12> |
+ | ^ <x 12> | ||
+ | |||
+ | **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> | ||
+ | |||
+ | ^ 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** | | ||
+ | |||
+ | Basically, power scales linearly with the area swept out by the turbine blades and cubically with the speed of the wind as it sweeps the blades. However, these relationships have some variation depending on the design of each particular turbine. | ||
+ | |||
+ | === Conversion Efficiency === | ||
+ | |||
+ | <x 20> | ||
+ | P_{r} ≈ P_{k} ∗ C_{P} | ||
+ | </ | ||
+ | |||
+ | * <x 12> | ||
+ | * <x 12> | ||
* <x 12> | * <x 12> | ||
- | Ideally, power scales linearly | + | **Example: eXperimental Turbine Lenz-Rotor |
- | The power coefficient | + | <x 16> |
- | coefficient, | + | 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 | ||
+ | ^ Turbine Type ^ Power Coefficient ^ | ||
| Simple drag VAWT | 0.20 | | | Simple drag VAWT | 0.20 | | ||
| Decent VAWT | 0.30 | | | Decent VAWT | 0.30 | | ||
| Good VAWT | 0.35 | | | Good VAWT | 0.35 | | ||
- | | Superb | + | | Good HAWT | 0.40 | |
- | | Superb | + | | Big Grid MW+ HAWT | 0.45 | |
- | **Example: eXperimental Turbine Lenz-Rotor with 0.96 m² surface @ 4 m/s** | + | === 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> | ||
- | 0.96 * 4^3 * {{1}/ | + | τ ≈ {{1}/ |
</x> | </x> | ||
- | ^ Windspeed ^ 1 m/s ^ 2 m/s ^ 4 m/s ^ **8 m/s** ^ **16 m/s** ^ | + | === Tip Speed Ratio === |
- | ^ Power | 0.57 W| 4.60 W| **36.68 W** | **294.91 W** | **2.36 kW** | | + | |
- | ==== Estimated Wind-Power conversion | + | The tip speed ratio (λ) defines the relationship between blade tip speed and incident |
+ | wind speed((Deisadze, | ||
- | According to [[https://en.wikipedia.org/ | + | <x 20> |
+ | λ = {{ω ∗ R}/{V}} | ||
+ | </x> | ||
+ | |||
+ | This equation shows the relationship between the tip speed ratio and the power | ||
+ | coefficient for various blade types. For each type, there is a unique curve, and therefore a | ||
+ | unique optimal tip speed ratio which corresponds to the maximum power coefficient that | ||
+ | can be achieved. | ||
+ | |||
+ | 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 | ||
+ | |||
+ | 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 | ||
+ | |||
+ | === Reynolds Number === | ||
+ | |||
+ | The Reynolds number range for small-scale gorlov VAWTs is quite | ||
+ | low. In comparison, | ||
<x 20> | <x 20> | ||
- | P_{mech} | + | Re = {{V ∗ D ∗ \rho}/{\nu}} |
</x> | </x> | ||
- | | Simple drag VAWT | 20% | | + | ^ Parameter ^ Unit ^ Detail ^ |
- | | Decent VAWT | 30% | | + | ^ <x 12> |
- | | Good VAWT | 35% | | + | ^ <x 12> |
- | | Superb | + | ^ <x 12> |
- | | Superb | + | ^ <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> |