Name: wind turbine torque and angular momentum
Uploaded: 2025-02-13T15:43:22.000Z
Duration: 1 min 9 s
Channel: JoVE

Die Moment-of-Moment-Gleichung analysiert das Drehmoment, das von den rotierenden Flügeln einer Windkraftanlage erzeugt wird.
Die Moment-des-Impuls-Gleichung wird gefunden, indem man das zweite Newtonsche Gesetz auf ein kleines Fluidteilchen anwendet. Dieses Gesetz besagt, dass die Änderungsrate des linearen Impulses gleich der äußeren Kraft ist, die auf ihn wirkt.
Das Kraftmoment wird berechnet, indem die Position des Flüssigkeitspartikels berücksichtigt wird, um das Drehmoment zu bestimmen.
Der Positionsvektor wird mit der externen Kraft kombiniert, um das auf das Partikel wirkende Drehmoment zu ermitteln.
Die Zeitableitung wird dann in zwei Teile erweitert. Ein Teil stellt die Änderungsrate des Drehimpulses aufgrund der Geschwindigkeit des Fluids dar, während der andere Teil angibt, wie sich das Fluid durch den Raum bewegt.
Die Positionsänderung im Laufe der Zeit entspricht der Geschwindigkeit des Teilchens, wodurch die Expansion vereinfacht wird.
Die Moment-des-Impuls-Gleichgewichts erhält man, indem man diese Terme über das Kontrollvolumen integriert.
Diese Gleichung setzt das Drehmoment am System in Beziehung zum Drehimpuls, der in das Steuervolumen ein- und ausgeht, und den externen Kräften, die darauf wirken.

impulsgleichung

Die Impulsgleichung ist ein wichtiges Werkzeug zur Analyse des Drehmoments, das von den rotierenden Rotorblättern einer Windturbine erzeugt wird. Diese Gleichung wird abgeleitet, indem Newtons zweites Gesetz auf ein Fluidelement angewendet wird, wobei gilt, dass die Änderungsrate des linearen Impulses gleich der auf das Element wirkenden äußeren Kraft ist.

<img alt="Equation 1" src="/files/ftp_upload/18053/18053_Equation_1.svg" style="text-align: center; height: 48px;">

Bei rotierenden Systemen wie Windturbinen wird das Drehmoment berechnet, indem die Position des Fluidelements relativ zur Rotationsachse einbezogen wird.

Um das Drehmoment zu berechnen, wird der Positionsvektor des Fluidelements mit der auf es wirkenden äußeren Kraft kombiniert. Diese Kombination ergibt das auf das Fluidelement wirkende Drehmoment.

<img alt="Equation 2" src="/files/ftp_upload/18053/18053_Equation_2.svg" style="text-align: center; height: 52px;">

Der nächste Schritt besteht darin, die zeitliche Ableitung des Impulses zu erweitern. Diese Erweiterung ist in zwei Teile unterteilt: Der eine stellt die Änderungsrate des Drehimpulses aufgrund der Geschwindigkeit des Partikels dar, der andere berücksichtigt die Bewegung der Flüssigkeit durch den Raum.

<img alt="Equation 3" src="/files/ftp_upload/18053/18053_Equation_3.svg" style="text-align: center; height: 96px;">

Da die Positionsänderung im Laufe der Zeit der Geschwindigkeit des Partikels entspricht, vereinfacht sich die mathematische Erweiterung, was zu einem klareren Verständnis der Wirkung von Kräften innerhalb des rotierenden Systems führt.

Die endgültige Form der Momentengleichung erhält man durch Integration der relevanten Terme über das Kontrollvolumen, das den Bereich der Flüssigkeit umfasst, die mit der Turbine interagiert.

<img alt="Equation 4" src="/files/ftp_upload/18053/18053_Equation_4.svg" style="text-align: center; height: 62px;">

Diese Gleichung stellt eine Beziehung zwischen dem auf das System ausgeübten Drehmoment und dem Drehimpuls her, der in das Kontrollvolumen eintritt und es verlässt, sowie den auf das System wirkenden externen Kräften. Im Zusammenhang mit Windturbinen ermöglicht dies eine detaillierte Analyse, wie die Rotorblätter Rotationsenergie aus dem Wind erzeugen, wodurch die Effizienz und Leistung der Turbine verbessert wird.

Impulsgleichung

Die Moment-of-Moment-Gleichung analysiert das Drehmoment, das von den rotierenden Flügeln einer Windkraftanlage erzeugt wird.
Die Moment-des-Moment-Gleichung wird durch ...

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wind turbine torque and angular momentum

The moment-of-momentum equation helps explain how wind turbine blades create torque. Torque is the turning effect of a force around an axis. In rotating systems, this equation links the motion of the wind with the force acting on it.

The equation begins with Newton's second law for a fluid particle. That law says the rate of change of linear momentum equals the external force on the particle. To find torque, the position of the particle relative to the rotation axis is combined with that force.

The next step is to expand the time derivative of the moment of momentum. One part describes the change in angular momentum caused by the particle's own velocity. The other part accounts for the fluid moving through space.

Because the change in position over time equals the particle's velocity, the expression simplifies. The final form is found by integrating over the control volume, which is the region of fluid that interacts with the turbine. This relationship connects torque with the angular momentum entering and leaving the control volume and with the external forces acting on the system.

For wind turbines, this equation helps show how the blades turn wind energy into rotational energy. It also supports more detailed analysis of turbine performance. That makes it useful for improving efficiency and understanding how the blades work.

Wind Turbine Torque and Angular Momentum

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The moment-of-momentum equation helps explain how wind turbine blades create torque. Torque is the turning effect of a force around an axis. In rotating systems, this equation links the motion of the wind with the force acting on it. The equation begins with Newton's second law for a fluid particle. That law says the rate of change of linear momentum equals the external force on the particle. To find torque, the position of the particle relative to the rotation axis is combined with that force.

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Wind Turbine Torque and Angular Momentum

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