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

L’équation du moment de la quantité de mouvement analyse le couple produit par les pales en rotation d’une éolienne.
L'équation du moment de la quantité de mouvement est trouvée en appliquant la deuxième loi de Newton à une petite particule de fluide. Cette loi stipule que le taux de variation de la quantité de mouvement linéaire est égal à la force externe qui agit sur elle.
Le moment de force est calculé en considérant la position de la particule de fluide pour déterminer le couple.
Le vecteur position est combiné à la force externe pour trouver le couple agissant sur la particule.
La dérivée temporelle est ensuite développée en deux parties. Une partie représente le taux de variation du moment angulaire dû à la vitesse du fluide, tandis que l'autre tient compte de la façon dont le fluide se déplace dans l'espace.
Le changement de position au fil du temps est égal à la vitesse de la particule, ce qui simplifie l'expansion.
L’équation du moment de la quantité de mouvement est obtenue en intégrant ces termes sur le volume de contrôle.
Cette équation relie le couple sur le système au moment angulaire entrant et sortant du volume de contrôle et aux forces externes agissant sur celui-ci.

Équation du moment d’impulsion

L'équation du moment d'impulsion est un outil essentiel pour analyser le couple produit par les pales rotatives d'une éolienne. Cette équation est dérivée de l'application de la deuxième loi de Newton à une particule fluide, qui stipule que le taux de variation de l'impulsion linéaire est égal à la force externe agissant sur la particule.

<img alt="Equation 1" src="/files/ftp_upload/18053/18053_Equation_1.svg" style="text-align: center; height: 48px;">


Dans le cas de systèmes rotatifs comme les éoliennes, le moment de cette force, ou couple, est déterminé en considérant la position de la particule fluide par rapport à l'axe de rotation.

Pour calculer le couple, le vecteur de position de la particule fluide est combiné à la force externe agissant sur elle. Cette combinaison donne le couple subi par la particule.

<img alt="Equation 2" src="/files/ftp_upload/18053/18053_Equation_2.svg" style="text-align: center; height: 52px;">


L'étape suivante consiste à développer la dérivée temporelle du moment d'impulsion. Cette expansion est divisée en deux parties: l’une représente le taux de variation du moment angulaire dû à la vitesse de la particule, et l’autre représente le mouvement du fluide dans l’espace.

<img alt="Equation 3" src="/files/ftp_upload/18053/18053_Equation_3.svg" style="text-align: center; height: 96px;">


Étant donné que le changement de position au fil du temps est égal à la vitesse de la particule, l’expansion mathématique se simplifie, ce qui permet de mieux comprendre comment les forces agissent au sein du système rotatif.

La forme finale de l’équation du moment d’impulsion est obtenue en intégrant les termes pertinents sur le volume de contrôle, qui englobe la région du fluide interagissant avec la turbine.

<img alt="Equation 4" src="/files/ftp_upload/18053/18053_Equation_4.svg" style="text-align: center; height: 62px;">

Cette équation fournit une relation entre le couple exercé sur le système et le moment angulaire entrant et sortant du volume de contrôle, ainsi que les forces externes agissant sur le système. Dans le contexte des éoliennes, cela permet une analyse détaillée de la manière dont les pales génèrent de l’énergie de rotation à partir du vent, améliorant ainsi l’efficacité et les performances de l’éolienne.

L’équation du moment de la quantité de mouvement analyse le couple produit par les pales en rotation d’une éolienne.
L’équation du moment de la quantité de mouvement est déterminée par ...

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Civil Engineering

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Finite Control Volume Analysis

Analyse par volumes de contrôle finis

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

Moment-of-Momentum Equation

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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moment-of-momentum equation

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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Learn how the moment-of-momentum equation links wind turbine torque, angular momentum, and control volume forces in rotating fluid systems for high school science.

Wind Turbine Torque and Angular Momentum | JoVE K12

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civil engineering

Wind Turbine Torque and Angular Momentum

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