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--- lab:zephyr:rotors [2014/11/28 14:35] – [H-Rotor] chrono
+++ lab:zephyr:rotors [2023/04/19 14:18] (current) – [Power Estimation] chrono
@@ Line 1: / Line 1: @@
 ====== Rotors ======
-Compared to drag-only type rotors (Savonius), the lift-only type rotors (Darrieus) haven proven to be generally less suitable for low wind environments. However, the maximum speed of drag-only type rotors is always lower than a comparable lift-only type rotor, because a lift-only type rotor can rotate faster than the wind speed at the tips but with less torque. 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).
+Compared to drag-only type rotors (Savonius), lift-only type rotors (Darrieus) have been proven to be generally less suitable for low wind environments since they're difficult to start up. The maximum speed of drag-only type rotors is always lower than a comparable lift-only type rotor, because a lift-only type rotor can rotate faster than the wind speed at the tips but with less torque. However, the Gorlov rotor with a NACA 0015 airfoil may be a very well suited lift-type rotor for small-scale, low wind environments.
-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:zephyr:rotors#c-rotor|C-Rotor and further development based on it, with less parts if possible]]
-  * [[lab:zephyr:rotors#h-rotor|H-Rotor with NACA profiles or airfoil shaped wings]]
-  * [[lab:zephyr:rotors#v-rotor|V-rotor with airfoil wings]]
-Additionally, there should be a design for a very simple H-Rotor made of half DN100-PE-tubes (standard sewer piping tubes) as wings, preferably three or 3 x n wings for very low resource budget projects.
+===== VAWT Rotor Types =====
-The 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.
+{{:lab:zephyr:3d-print-timelapse-wind_turbine_blade_helix_lenz2_32cm_dia_19cm.mp4|}}
+^  C-Rotor  ^  Lenz-Rotor  ^  Gorlov-Rotor  ^
+|{{:lab:projects:zephyr:zephyr-c-rotor-v1.00.png|}}|{{:lab:zephyr:xt-lenz-mk7-wind-turbine.jpg|}}|{{:lab:zephyr:xt-gorlov-mk7-wind-turbine.jpg|}}|
+| Laser Cut | 3D Print (complex multipart) | 3D Print (print 2 - assemble 1)|
+| 10-50 W | 5-40W | <5 W |
+Sources: https://github.com/apollo-ng/eXperimental-Turbines
+The Gorlov Helical blade type is a derivative of the Darrieus blade type, originally
+developed by its namesake Alexander M. Gorlov to be used in hydro-power applications. It
+attempts to solve the problems of vibration and noise in the original Darrieus design by
+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 in urban settings. The
+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, there should be a design for a very simple H-Rotor made of half DN100-PE-tubes (standard sewer piping tubes) as wings, preferably three or 3 x n wings for very low resource budget projects.
 ===== 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 ====
@@ Line 32: / Line 51: @@
 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.
 </WRAP>
@@ Line 50: / Line 69: @@
 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, Calculations & Prototype Images
-{{:lab:projects:zephyr:zephyr-c-rotor-v1.00.png?300|}}
+Corrections and additional approaches are always welcome.
-===== 3D printable Lenz-Rotor =====
+==== Power Estimation ====
-{{:lab:zephyr:xt-lenz-mk7-wind-turbine.jpg|}}
+The following equations provide a means to estimate the approximate amount of kinetic and electric power converted by a wind turbine:
-Sources: https://github.com/apollo-ng/eXperimental-Turbines
+=== Available power in the wind ===
-===== 3D printable Gorlov Rotor =====
-{{:lab:zephyr:xt-gorlov-mk7-wind-turbine.jpg}}
+<m>P_{k} \approx {{1}/{2}} * A * V^3 * \rho</m>
-Print two times and stack on each other approach. For <1W systems.
+^ Parameter ^ Unit ^ Detail ^
+^ <m 12>P_{k}</m> | Watt | Available power in the wind, as kinetic energy |
+^ <m 12>A</m> | m² | Swept area (turbine/sail etc.) |
+^ <m 12>V</m> | m/s  | Wind speed |
+^ <m 12>\rho</m> | kg/m³ | Density of Air (rho) ~1.225 at 25°C |
-Sources: https://github.com/apollo-ng/eXperimental-Turbines
+**Example: eXperimental Turbine Lenz-Rotor with 0.96 m² surface @ 4 m/s**
+<m>{{1}/{2}} * 0.96 * 4^3 * 1.225 = 36.86 W</m>
-===== Basic Wind Power Calculations =====
+Example values at certain wind speeds:
-Corrections and additional approaches are always welcome.
+^ 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 ===
+<m>
+P_{r} \approx P_{k} * C_{P}
+</m>
+  * <m 12>P_{r}</m> -> Converted rotational energy in Watt
+  * <m 12>P_{k}</m> -> Available power in the wind, as kinetic energy in Watt
+  * <m 12>C_{P}</m> -> Power coefficient
+**Example: eXperimental Turbine Lenz-Rotor with 0.96 m² surface @ 4 m/s**
+<m>
+.86 * 0.25 = 9.21 W
+</m>
+The power coefficient accounts for the efficiency of the turbine in converting the wind’s kinetic energy into rotational energy. According to [[https://en.wikipedia.org/wiki/Betz%27s_law|Betz's law]], no wind turbine can capture more than 16/27 (59.3%) of the available kinetic energy in wind. This theoretical maximum power limit is also known as Betz's coefficient (0.593) or Betz-Limit. However, most wind turbines operate at a power coefficient of less than 0.45:
+^ Turbine Type ^ Power Coefficient ^
+| Simple drag VAWT | 0.20 |
+| Decent VAWT | 0.30 |
+| Good VAWT | 0.35 |
+| Good HAWT | 0.40 |
+| Big Grid MW+ HAWT | 0.45 |
+=== 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, et al. 2013)).
+<m>
+\tau \approx {{1}/{2}} * R * A * V^2 * \rho
+</m>
+=== Tip Speed Ratio ===
+The tip speed ratio (λ) defines the relationship between blade tip speed and incident
+wind speed((Deisadze, et al. 2013)).
+<m>
+\lambda = {{\omega * R}/{V}}
+</m>
+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 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)).
-**Power in the wind**\\
+=== Reynolds Number ===
-<x 20>
-P_{wind} = A_{wind} * (v_{wind})^3 * {{1}/{2}} \rho
-</x>
-  * <x 12>P_{wind}</x> -> Available power in the wind, as kinetic energy in Watt
+The Reynolds number range for small-scale gorlov VAWTs is quite
-  * <x 12>A_{wind}</x> -> Area of surface (turbine/sail etc.) in m²
+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 12>V_{wind}</x>  -> Wind speed in m/s
-  * <x 12>\rho</x> -> (rho) Density of air (about 1.2 Kg/m³)
-Example: Test Turbine MK7
+<m>
+Re = {{V * D * \rho}/{\nu}}
+</m>
-<x 20>
+^ Parameter ^ Unit ^ Detail ^
-(0.75 * 0.8) * 5.4^3 * {{1}/{2}} \rho = 56.68 W
+^ <m 12>V</m> | m/s | Incoming flow velocity |
-</x>
+^ <m 12>D</m> | m | Turbine Diameter |
+^ <m 12>\rho</m> | kg/m³ | Density of Air (rho) ~1.225 at 25°C |
+^ <m 12>\nu</m> | m²/s | Kinematic viscosity of Air (nu) ~1.57e-5 at 25 °C |
-**Estimated Wind-Power conversion (mechanical)**
+**Example: Helical Gorlov-Rotor with 35 cm radius @ 4 m/s**
-<x 20>
+<m>
-P_{mech} = P_{wind} * Conv_{Eff}
+{{4 * 0.7 * 1.225}/{0.0000157}} \approx 218471
-</x>
+</m>
-| Simple drag VAWT | 20% |
-| Decent VAWT | 30% |
-| Good VAWT | 30% |
-| Superb  VAWT | 40% |
-| Superb  HAWT | 50% |
-You can watch these calculations in action, applied to reference wind speed measurements on the [[https://apollo.open-resource.org/flight-control/vfcc/#/dashboard/db/wind-power-simulation|Wind Power]] VFCC Dashboard
+You can watch these calculations in action, applied to reference wind speed measurements on the [[https://apollo.open-resource.org/flight-control/vfcc/#/dashboard/db/wind-power-simulation|Wind Power]] VFCC Dashboard.
-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>zephyr wind energy research vawt turbine rotor c-rotor h-rotor}}

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