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

Первый закон термодинамики гласит, что скорость изменения общей накопленной энергии в системе равна чистой скорости теплоты и работы, передаваемых в систему.
Для контрольного объема, который совпадает с системой в данный момент, чистая теплота и работа, поступающие в систему, равны чистой тепло и работе, поступающей в контрольный объем.
Для этой системы и совпадающего объема управления применяется теорема Рейнольдса о транспорте.
Общая скорость изменения энергии в пределах управляющего объема определяется как скоростью изменения накопленной энергии, так и чистым потоком энергии через границу.
Энергия, протекающая через границу, включает в себя вклад тепла и работы, таких как работа шахты и работа под давлением.
Работа вала является результатом вращения компонентов, таких как турбины, в то время как напряжения жидкости создают работу под давлением.
Общее уравнение энергии объединяет все элементы: накопленную энергию, тепло, работу вала и работу под давлением из-за нормальных напряжений.
Это уравнение представляет собой экономию энергии в жидкостных и газовых системах, включая теплопередачу, работу вала и силы давления на поверхности управления.

Сохранение энергии в контрольном объеме

Рассмотрим турбину, работающую в условиях установившегося потока. Контрольный объем очерчен вокруг турбины, при этом жидкость входит в одной точке и выходит в другой. Турбина извлекает энергию из жидкости, которая выполняет механическую работу (работу вала).

 Для систем с установившимся потоком производная по времени от сохранённой энергии становится равной нулю, поскольку в контрольном объеме нет накопления энергии. Это упрощает уравнение энергии до следующего вида:

<img alt="Equation 1" src="/files/ftp_upload/18054/18054_Equation_1.svg" style="text-align: center; height: 27px;">

 Поскольку мы концентрируемся на работе, выполняемой валом турбины, и предполагаем незначительную теплопередачу, . Таким образом, уравнение энергии упрощается еще больше:

<img alt="Equation 2" src="/files/ftp_upload/18054/18054_Equation_2.svg" style="text-align: center; height: 27px;">


 Поток делится на две составляющие: жидкость, входящую в турбину (вход) и жидкость, выходящую из турбины (выход). Массовый расход в обеих точках постоянен, а поток энергии на входе и выходе определяется как:

<img alt="Equation 3" src="/files/ftp_upload/18054/18054_Equation_3.svg" style="text-align: center; height: 27px;">


 Где:

-ṁ — массовый расход,

-ũ1 , V_1 и z_1 относятся к внутренней энергии, скорости и высоте на входе,

-ũ2 , V_2 и z_2 относятся к внутренней энергии, скорости и высоте на выходе,

 В типичной турбине внутренняя и кинетическая энергия жидкости уменьшается при прохождении через турбину, что приводит к выполнению полезной работы вала. Предположим, что турбина работает на входе со скоростью V_1=50 м/с, на выходе со скоростью V_2=20 м/с, с высотой на входе z_1=100 м и с высотой на выходе z_2=90 м. Предположим, что изменение внутренней энергии мало по сравнению с изменениями кинетической и потенциальной энергии, а массовый расход ṁ составляет 10 кг/с.

<img alt="Equation 4" src="/files/ftp_upload/18054/18054_Equation_4.svg" style="text-align: center; height: 27px;">

 В результате турбина вырабатывает приблизительно 11,48 кВт механической мощности, извлекая энергию из текущей жидкости.

Первый закон термодинамики гласит, что скорость изменения общей накопленной энергии в системе равна чистой скорости теплоты и работы, передаваемых в ...

Education

JoVE Core

Civil Engineering

Unit 1

Раздел 1

Finite Control Volume Analysis

Анализ методом конечных контрольных объемов

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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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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.

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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