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

La première loi de la thermodynamique stipule que le taux de variation de l’énergie totale stockée dans un système est égal au taux net de chaleur et de travail transféré dans un système.
Pour un volume de contrôle qui coïncide avec le système à un moment donné, la chaleur nette et le travail entrant dans le système sont égaux à la chaleur nette et au travail entrant dans le volume de contrôle.
Pour ce système et le volume de contrôle coïncident, le théorème de transport de Reynolds est appliqué.
Le taux total de variation d’énergie à l’intérieur du volume de contrôle est déterminé à la fois par le taux de variation temporelle de l’énergie stockée et le flux d’énergie net à travers la limite.
L’énergie qui circule à travers la frontière comprend les contributions de la chaleur et du travail, comme le travail de puits et le travail sous pression.
Le travail de l’arbre résulte de composants rotatifs tels que les turbines, tandis que les contraintes des fluides produisent un travail sous pression.
L’équation énergétique générale combine tous les éléments : l’énergie stockée, la chaleur, le travail dans l’arbre et le travail sous pression dû à des contraintes normales.
Cette équation représente la conservation de l’énergie dans les systèmes fluides, intégrant le transfert de chaleur, le travail de l’arbre et les forces de pression sur la surface de contrôle.

conservation de l'énergie dans le volume de contrôle

Considérons une turbine fonctionnant dans des conditions d'écoulement stable. Le volume de contrôle est dessiné autour de la turbine, le fluide entrant à un point et sortant à un autre. La turbine extrait de l'énergie du fluide, qui effectue un travail mécanique (travail de l'arbre).

Pour les systèmes à écoulement stable, la dérivée temporelle de l'énergie stockée devient nulle puisqu'il n'y a pas d'accumulation d'énergie dans le volume de contrôle. Cela simplifie l'équation énergétique à:

<img alt="Equation 1" src="/files/ftp_upload/18054/18054_Equation_1.svg" style="text-align: center; height: 27px;">


Étant donné que nous nous concentrons sur le travail effectué par l'arbre de la turbine et que nous supposons un transfert de chaleur négligeable, Q̇ ≈ 0. Par conséquent, l'équation énergétique se simplifie encore davantage à:

<img alt="Equation 2" src="/files/ftp_upload/18054/18054_Equation_2.svg" style="text-align: center; height: 27px;">


L'écoulement est divisé en deux composants: le fluide entrant dans la turbine (entrée) et sortant de la turbine (sortie). Le débit massique aux deux points est constant et le flux d'énergie à l'entrée et à la sortie est donné par:

<img alt="Equation 3" src="/files/ftp_upload/18054/18054_Equation_3.svg" style="text-align: center; height: 27px;">


Où:

-ṁ est le débit massique,

- ũ1 , V_1 et z_1 font référence à l'énergie interne, à la vitesse et à la hauteur à l'entrée,

- ũ2 , V_2 et z_2 font référence à l'énergie interne, à la vitesse et à la hauteur à la sortie,

Dans une turbine typique, les valeurs internes et cinétiques du fluide L'énergie diminue à mesure qu'elle traverse la turbine, ce qui entraîne un travail utile sur l'arbre. Supposons qu'une turbine fonctionne avec une vitesse d'entrée de V_1=50 m/s, une vitesse de sortie de V_2= 20 m/s, une hauteur d'entrée z_1=100 m et une hauteur de sortie z_2=90m. Supposons que le changement d'énergie interne est faible par rapport aux changements d'énergie cinétique et potentielle, et que le débit massique est de 10 kg/s.

<img alt="Equation 4" src="/files/ftp_upload/18054/18054_Equation_4.svg" style="text-align: center; height: 27px;">

En conséquence, la turbine produit environ 11,48 kW de puissance mécanique en extrayant de l'énergie du fluide en écoulement.

Conservation de l'énergie dans le volume de contrôle

La première loi de la thermodynamique stipule que le taux de variation de l’énergie totale stockée dans un système est égal au taux net de chaleur et de travail transféré dans un ...

Education

Enseignement

JoVE Core

Civil Engineering

Génie civil

Unit 1

Unité 1

Finite Control Volume Analysis

Analyse par volumes de contrôle finis

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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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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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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.

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Turbine Work from Energy Changes

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