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

모멘텀 방정식은 풍력 터빈의 회전 블레이드에서 생성되는 토크를 분석합니다.
운동량 모멘텀 방정식은 뉴턴의 제2법칙을 작은 유체 입자에 적용하여 찾을 수 있습니다. 이 법칙은 선형 운동량의 변화율이 선형 운동량에 작용하는 외력과 같다고 말합니다.
힘의 모멘트는 토크를 결정하기 위해 유체 입자의 위치를 고려하여 계산됩니다.
위치 벡터는 입자에 작용하는 토크를 찾기 위해 외부 힘과 결합됩니다.
그런 다음 시간 도함수는 두 부분으로 확장됩니다. 한 부분은 유체의 속도로 인한 각운동량의 변화율을 나타내고 다른 부분은 유체가 공간을 통해 이동하는 방식을 나타냅니다.
시간에 따른 위치 변화는 입자의 속도와 같아서 팽창을 단순화합니다.
모멘텀 방정식은 제어 볼륨에 대해 이러한 항을 적분하여 얻습니다.
이 방정식은 시스템의 토크를 제어 볼륨에 들어오고 나가는 각운동량 및 이에 작용하는 외부 힘과 관련시킵니다.

모멘트-오브-모멘텀 방정식

모멘트-오브-모멘텀 방정식은 풍력 터빈의 회전 날개에서 생성되는 토크를 분석하는 데 중요한 도구입니다. 이 방정식은 뉴턴의 제2법칙을 유체 입자에 적용하여 도출한 것으로, 선형 운동량의 변화율은 입자에 작용하는 외부 힘과 같다고 명시합니다.

<img alt="Equation 1" src="/files/ftp_upload/18053/18053_Equation_1.svg" style="text-align: center; height: 48px;">

풍력 터빈과 같은 회전 시스템의 경우, 이 힘의 모멘트 또는 토크는 회전 축에 대한 유체 입자의 위치를 ​​고려하여 결정됩니다.

토크를 계산하려면 유체 입자의 위치 벡터를 유체 입자에 작용하는 외부 힘과 결합합니다. 이 조합을 통해 입자가 경험하는 토크가 생성됩니다.

<img alt="Equation 2" src="/files/ftp_upload/18053/18053_Equation_2.svg" style="text-align: center; height: 52px;">

다음 단계는 모멘트의 시간 미분을 확장하는 것입니다. 이 확장은 두 부분으로 나뉩니다. 하나는 입자의 속도로 인한 각운동량의 변화율을 나타내고, 다른 하나는 공간을 통한 유체의 움직임을 설명합니다.

<img alt="Equation 3" src="/files/ftp_upload/18053/18053_Equation_3.svg" style="text-align: center; height: 96px;">

시간에 따른 위치의 변화는 입자의 속도와 같으므로 수학적 확장이 간소화되어 회전 시스템 내에서 힘이 작용하는 방식을 더 명확하게 이해할 수 있습니다.

모멘트-오브-모멘텀 방정식의 최종 형태는 터빈과 상호 작용하는 유체 영역을 포함하는 제어 볼륨에 대한 관련 용어를 적분하여 얻습니다.

<img alt="Equation 4" src="/files/ftp_upload/18053/18053_Equation_4.svg" style="text-align: center; height: 62px;">

이 방정식은 시스템에 가해지는 토크와 제어 볼륨에 들어오고 나가는 각운동량, 그리고 시스템에 작용하는 외부 힘 간의 관계를 제공합니다. 풍력 터빈의 맥락에서 이를 통해 블레이드가 바람으로부터 회전 에너지를 생성하는 방식을 자세히 분석하여 터빈의 효율성과 성능을 개선할 수 있습니다.

모멘텀 방정식은 풍력 터빈의 회전 블레이드에서 생성되는 토크를 분석합니다.
모멘텀 방정식은 다음과 같이 구합니다.

Education

교육

JoVE Core

Civil Engineering

토목공학

Unit 1

제1단원

Finite Control Volume Analysis

유한 제어 체적 해석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

conservation of mass in finite cotrol volume

conservation-of-mass-in-finite-cotrol-volume

Continuity Equation for a Fixed Control Volume

The continuity equation describes conservation of mass for a fixed control volume. In fluid mechanics, a system is a collection of the same contents over time, and its mass stays constant. That idea is the starting point for deriving the equation. To analyze flow, a fixed, non-deforming control volume is chosen so it matches the system at one instant. The Reynolds transport theorem then links the system to the control volume. It shows that the rate of change of system mass has two parts: mass...

conservation of mass in fixed, nondeforming control volume

conservation-of-mass-in-fixed-nondeforming-control-volume

Continuity and Velocity in Pipe Flow

Conservation of mass explains how fluid moves through a fixed control volume such as a pipe or duct. In a fixed, nondeforming control volume, the total mass stays constant unless mass enters or leaves through the control surfaces. For steady, incompressible flow, the mass entering the system equals the mass leaving it. A sewer pipe is a useful example of this idea. It can be treated as a fixed control volume with inlet and outlet control surfaces around the flow region. Because the fluid is...

conservation of mass in moving, nondeforming control volume

conservation-of-mass-in-moving-nondeforming-control-volume

Stormwater Detention Basin Mass Balance

Stormwater detention basins use mass balance to manage runoff during heavy rainfall. These basins are especially important in urban areas, where impervious surfaces can increase flooding risk. Engineers use the conservation of mass to track how water enters, is stored in, and leaves the basin. In a detention basin, the control volume is the water inside the basin. Its boundaries are the basin walls, the inflow pipes, and the outflow structures. During a rain event, water comes in through the...

linear momentum in control volume

Momentum Balance for Fluid Control Volumes

Linear momentum balance for a fluid control volume links Newton’s second law to moving fluid. The law says that the rate of change of linear momentum equals the sum of the external forces acting on the system. In a fluid system, this idea helps explain how motion and force are related. A control volume can match the fluid system at a specific moment. When that happens, the forces on the control volume and the system are the same. Reynolds transport theorem explains this connection by splitting...

application of the linear momentum equation

application-of-the-linear-momentum-equation

Forces in a 180° Pipe Bend

Forces in a 180-degree pipe bend can be found by applying the linear momentum equation to flowing water. The pipe has a constant cross-sectional area of 0.01 square meters, and the water moves at 15 meters per second. The pressure at the inlet is 0.2 megapascals, and the pressure at the outlet is 0.16 megapascals. The goal is to find the force components in the x and y directions that hold the bend in place. In this case, the flow is only in the y direction at both the entrance and the exit.

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.

conservation of energy in control volume

Turbine Work from Energy Changes

A turbine can turn fluid energy into shaft work when flow passes through a control volume. The fluid enters the turbine at one point and leaves at another. Under steady-flow conditions, there is no energy buildup inside the control volume, so the stored energy does not change with time. This steady-flow setup makes the energy equation simpler. The turbine is treated as doing mechanical work, and heat transfer is taken as negligible, so Q̇ is approximately zero. The flow at the inlet and outlet...

application of the energy equation

Centrifugal Pump Flow Rate Calculation

Centrifugal pump flow rate can be calculated with the energy equation. In this problem, water moves between two reservoirs at different elevations, and the pump provides the energy needed for the transfer. The pump input is 7500 joules per second, the elevation difference is 10 meters, and the head loss from friction and other resistances is 5 meters. Both reservoirs are open to the atmosphere, so the pressure at the inlet and outlet is the same. That means the pressure terms in the energy...

design example: forces in sluice gate

Sluice Gate Water Pressure and Reaction Force

Sluice gates control water flow in channels, reservoirs, and irrigation systems. They work as vertical barriers with an opening that can be raised or lowered. Changing the opening height changes the water velocity and pressure below the gate. The forces on a sluice gate depend on the water depths upstream and downstream, written as z1 and z2. When the gate is closed, the upstream water depth is greater. That creates a strong pressure difference across the gate and a net force toward the...

key terms and concepts

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

JoVE Core Civil Engineering offers a foundational exploration of essential construction materials such as bricks, stones, steel, wood, and concrete, along with fluid mechanics topics like flow over immersed bodies, open channel flow, and dimensional modeling. It also covers key surveying concepts, including leveling, traverse adjustments, curve design, topographic mapping, and geospatial technologies (GPS & GIS). Science-in-action videos showcase laboratory research on materials, fluids, and surveying practices in real-world engineering systems.

civil engineering

Wind Turbine Torque and Angular Momentum

Description

Transcript

Tags