Name: turbine work from energy changes
Uploaded: 2025-02-13T15:43:22.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

High School

Chemistry

Energy

C-PS3-4

Conservation of Energy in Control Volume

熱力学の第一法則は、システム内に蓄積されたエネルギーの総変化率は、システムに伝達される熱と仕事の正味の速度に等しいと述べています。
特定の瞬間にシステムと一致する制御ボリュームの場合、システムに入る正味の熱と仕事は、制御ボリュームに入る正味の熱と仕事と等しくなります。
このシステムと一致制御ボリュームには、レイノルズ輸送定理が適用されます。
制御ボリューム内のエネルギー変化の合計速度は、蓄積されたエネルギーの時間変化率と境界を通る正味のエネルギーの流れの両方によって決まります。
境界を越えて流れるエネルギーには、シャフトワークや圧力ワークなどの熱とワークからの寄与が含まれます。
シャフトの仕事はタービンのような回転部品から生じますが、流体の応力は圧力の仕事を生み出します。
一般エネルギー方程式は、蓄積されたエネルギー、熱、シャフトの仕事、および垂直応力による圧力の仕事というすべての要素を組み合わせたものです。
この方程式は、熱伝達、シャフトワーク、および制御面の圧力を組み込んだ流体システムのエネルギー保存を表しています。

制御体積におけるエネルギーの保存

定常流条件下で動作するタービンを考えてみましょう。制御体積はタービンの周囲に描かれ、流体は 1 つの点から流入し、別の点から流出します。タービンは流体からエネルギーを抽出し、流体は機械的な作業 (シャフト作業) を実行します。

 定常流系の場合、制御体積内にエネルギー蓄積がないため、蓄積されたエネルギーの時間微分はゼロになります。これにより、エネルギー方程式は次のように簡略化されます。

<img alt="Equation 1" src="/files/ftp_upload/18054/18054_Equation_1.svg" style="text-align: center; height: 27px;">

 タービンシャフトによって行われる作業に焦点を合わせ、熱伝達が無視できると仮定するため、Q̇ ≈ 0。したがって、エネルギー方程式はさらに次のように簡略化されます。

<img alt="Equation 2" src="/files/ftp_upload/18054/18054_Equation_2.svg" style="text-align: center; height: 27px;">

 流れは、タービンに入る流体 (入口) とタービンから出る流体 (出口) の 2 つの要素に分割されます。両点の質量流量は一定で、入口と出口のエネルギー流束は次のように表されます:

<img alt="Equation 3" src="/files/ftp_upload/18054/18054_Equation_3.svg" style="text-align: center; height: 27px;">

 ここで:

-ṁ は質量流量です。

-ũ1 、V_1、および z_1 は入口での内部エネルギー、速度、および高さを表します。

- ũ2 、V_2、および z_2 は出口での内部エネルギー、速度、および高さを表します。

 一般的なタービンでは、流体の内部および運動エネルギーはタービンを通過するとエネルギーが減少し、その結果、有効なシャフト作業が行われます。タービンが、入口速度 V_1 = 50 m/s、出口速度 V_2 = 20 m/s、入口高さ z_1 = 100 m、出口高さ z_2 = 90m で動作しているとします。内部エネルギーの変化は運動エネルギーと位置エネルギーの変化に比べて小さく、質量流量 は 10 kg/s であると仮定します。

<img alt="Equation 4" src="/files/ftp_upload/18054/18054_Equation_4.svg" style="text-align: center; height: 27px;">

 その結果、タービンは流れる流体からエネルギーを抽出して、約 11.48 kW の機械力を生成します。

熱力学の第一法則は、システム内に蓄積された総エネルギーの変化率は、熱と仕事の正味の変換率に等しいと述べています...

Education

JoVE Core

Civil Engineering

土木工学

Unit 1

ユニット1

Finite Control Volume Analysis

有限コントロールボリューム法による解析

KEY TERMS AND CONCEPTS

主要用語と概念

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 is then described by the mass flow rate and by the fluid’s internal energy, velocity, and height at each location.

For the inlet and outlet, the mass flow rate is constant. The energy flux depends on ṁ, u1, V1, and z1 at the inlet, and on ṁ, u2, V2, and z2 at the outlet. Here, u is internal energy, V is velocity, and z is height.

In a typical turbine, the fluid loses internal energy and kinetic energy as it moves through the device. That energy loss becomes useful shaft work. For example, if V1 = 50 m/s, V2 = 20 m/s, z1 = 100 m, z2 = 90 m, and the mass flow rate is 10 kg/s, with a small internal energy change, the turbine produces about 11.48 kW of mechanical power.

Turbine Work from Energy Changes

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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.

conservation of energy in control volume

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...

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Centrifugal Pump Flow Rate Calculation

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key terms and concepts

Learn how a steady-flow turbine uses changes in velocity, height, and internal energy to produce shaft work, with a worked 11.48 kW example.

Turbine Work from Energy Changes | JoVE K12

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Turbine Work from Energy Changes

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