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Fluid Dynamics

What is fluid dynamics?

In physics, fluid dynamics is a subdiscipline of fluid mechanics that deals with fluid flow. Fluid dynamics is one of the most important of all areas of physics.

Key Facts

  • Conservation of mass in fluid dynamics states that all mass flow rates into a control volume are equal to all mass flow rates out of the control volume plus the rate of mass change within the control volume.
  • Bernoulli’s equation can be considered a statement of the conservation of energy principle appropriate for flowing fluids.
  • The Reynolds number is one of the characteristic numbers used for predicting whether a flow condition will be laminar or turbulent. It is defined as the ratio of inertial forces to viscous forces.
  • Head loss of the hydraulic system is divided into two main categories:
  • Darcy’s equation can be used to calculate major losses. The friction factor for fluid flow can be determined using a Moody chart.
  • In fluid dynamicsdrag is a force acting opposite to the relative motion of any moving object. The force a flowing fluid exerts on a body in the flow direction.
  • By definition, multiphase flow is the interactive flow of two or more distinct phases with common interfaces in, say, a conduit.
  • Centrifugal pumps are devices used to transport fluids by converting rotational kinetic energy to the hydrodynamic energy of the fluid flow.
What is difference between fluid mechanics and fluid dynamics?
What is the difference between fluid mechanics and fluid dynamics?

Fluid mechanics is the study of the forces on fluids. These fluids can be either gas or liquid. In physics, fluid dynamics is a subdiscipline of fluid mechanics that deals with fluid flow. Fluid mechanics include fluid statics (the study of fluids at rest) and fluid dynamics (the study of fluids in motion).

What is the definition of fluid?
What is the definition of fluid?

In physics, a fluid is a substance that continually deforms (flows) under applied shear stress. The characteristic that distinguishes a fluid from a solid is its inability to resist deformation under applied shear stress (a tangential force per unit area). Fluids are a subset of the phases of matter and include liquids, gases, plasmas, and, to some extent, plastic solids.

What is fluid dynamics used for?
What is fluid dynamics used for?

Fluid dynamics are an important part of most industrial processes, especially those involving the
transfer of heat. In nuclear reactors, the heat removal from the reactor core is accomplished by passing a liquid or gaseous coolant through the core and other regions where heat is generated.

Thermodynamics

What is thermodynamics?

Thermodynamics is the science that deals with energy production, storage, transfer, and conversion. It studies the effects of workheat, and energy on a system. Despite the fact it is a very broad subject that affects most fields of science, including biology and microelectronics, we will concern mostly with large-scale observations.

Key Facts

  • In physics and everyday life, a temperature is an objective comparative measurement of hot or cold based on our sense of touch. This definition is not a simple matter. The kinetic theory of gases provides a microscopic explanation of temperature. It is based on the fact that during an elastic collision between a molecule with high kinetic energy and one with low kinetic energy, part of the energy will transfer to the molecule of lower kinetic energy.
  • Energy is generally defined as the potential to do work or produce heat. Sometimes it is like the “currency” for performing work. You must have the energy to accomplish work. To do 1 kilojoule of work, you must expend 1 kilojoule of energy.
  • The enthalpy is the sum of the internal energy E plus the product of the pressure p and volume V.
  • Four laws of thermodynamics define fundamental physical quantities (temperature, energy, and entropy) and characterize thermodynamic systems at thermal equilibrium.
  • The ideal gas model is used to predict the behavior of gases and is one of the most useful and commonly used substance models ever developed.
  • thermodynamic process is defined as a change from one equilibrium macrostate to another macrostate. The initial and final states are the defining elements of the process.
  • The typical thermodynamic cycle consists of a series of thermodynamic processes transferring heat and work while varying pressure, temperature, and other state variables, eventually returning a system to its initial state.
  • Today, the Rankine cycle is the fundamental operating cycle of all thermal power plants where an operating fluid is continuously evaporated and condensed.
What are the four laws of thermodynamics?
What are the four laws of thermodynamics?

The laws are as follows:

  1. Zeroth law of thermodynamics: If two systems are both in thermal equilibrium with a third, then they are in thermal equilibrium with each other.
  2. The first law of thermodynamics: The increase in internal energy of a closed system is equal to the heat supplied to the system minus work done by it. 
  3. The second law of thermodynamics: The entropy of any isolated system never decreases. In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases.
  4. Third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero.
What is the definition of fluid?
What is thermodynamics used for?

Despite the fact it is a very broad subject that affects most fields of science, including biology and microelectronics, we will concern mostly with large-scale observations. Knowledge of thermodynamics is essential to engineers who deal with power plants. Our goal here will be to introduce thermodynamics as the energy conversion science and introduce some of the fundamental concepts and definitions used in the study of engineering thermodynamics. These fundamental concepts and definitions will be further applied to energy systems and finally to thermal or nuclear power plants.

What is the thermal efficiency of nuclear power plant?
What is the thermal efficiency of nuclear power plants?

In modern nuclear power plants, the overall thermal efficiency is about one-third (33%), so 3000 MWth of thermal power from the fission reaction is needed to generate 1000 MWe of electrical power.

Heat Transfer

What is heat transfer?

Heat transfer is an engineering discipline that concerns the generation, use, conversion, and exchange of heat (thermal energy) between physical systems.  In power engineering, it determines key parameters and materials of heat exchangers.

Key Facts

  • Heat is the amount of energy flowing from one body to another spontaneously due to their temperature difference. Heat is a form of energy, but it is energy in transit.
  • Heat transfer is usually classified into various mechanisms, such as:
    • Heat Conduction. Heat conduction, also called diffusion, occurs within a body or between two bodies in contact. It is the direct microscopic exchange of kinetic energy of particles through the boundary between two systems.
    • Heat Convection. Heat convection depends on the motion of mass from one region of space to another. Heat convection occurs when the bulk flow of a fluid (gas or liquid) carries heat along with the flow of matter in the fluid.
    • Thermal Radiation. Radiation is heat transfer by electromagnetic radiation, such as sunshine, with no need to be present in the space between bodies.
  • Fourier’s law of thermal conduction states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and the area, at right angles to that gradient, through which the heat flows.
  • Newton’s law of cooling states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings provided the temperature difference is small, and the nature of radiating surface remains the same.
  • Stefan–Boltzmann law states that radiation heat transfer rate, q [W/m2], from a body (e.g.,, a black body) to its surroundings is proportional to the fourth power of the absolute temperature.
  • Boiling and condensation differ from other forms of convection in that they depend on the latent heat of vaporization, which is very high for common pressures. Therefore large amounts of heat can be transferred during boiling and condensation essentially at a constant temperature.
  • Heat exchangers are devices used to transfer thermal energy from one fluid to another without mixing the two fluids.
  • To minimize heat losses in industry and also in the construction of buildings, thermal insulation is widely used. Thermal insulation aims to reduce the overall heat transfer coefficient by adding material with low thermal conductivity.
What are the three mechanisms of heat transfer?
What are the three mechanisms of heat transfer?

Heat transfer is usually classified into various mechanisms, such as:

  • Heat Conduction. Heat conduction, also called diffusion, occurs within a body or between two bodies in contact. It is the direct microscopic exchange of kinetic energy of particles through the boundary between two systems.
  • Heat Convection. Heat convection depends on the motion of mass from one region of space to another. Heat convection occurs when the bulk flow of a fluid (gas or liquid) carries heat along with the flow of matter in the fluid.
  • Thermal Radiation. Radiation is heat transfer by electromagnetic radiation, such as sunshine, with no need to be present in the space between bodies.
What is heat transfer used for?
What is heat transfer used for?

Heat transfer is commonly encountered in engineering systems and other aspects of life, and one does not need to go very far to see some application areas of heat transfer. Detailed knowledge of heat transfer mechanisms is also essential for reactor engineers as well as all other engineers.

What are the main parameters of heat exchangers?
What are the main parameters of heat exchangers?

Heat transfer in a heat exchanger usually involves convection in each fluid and thermal conduction through the wall separating the two fluids. In analyzing heat exchangers,  it is often convenient to work with an overall heat transfer coefficientknown as a U-factor. The U-factor is defined by an expression analogous to Newton’s law of cooling.

Moreover, engineers also use the logarithmic mean temperature difference (LMTD) to determine the temperature driving force for heat transfer in heat exchangers.

Nuclear engineering is the branch of engineering concerned with applying nuclear fission and nuclear fusion and applying other sub-atomic physics based on nuclear physics principles. Nuclear engineering generally deals with applying nuclear energy in various branches, including nuclear power plants, naval propulsion systems, food production, or medical diagnostic equipment such as MRI machines.

Our goal here will be to introduce the engineering of nuclear reactors, and deal with topics like fluid dynamics, power plant thermodynamics, reactor heat generation and removal (single-phase and two-phase coolant flow and heat transfer), materials in nuclear engineering, and structural mechanics.

Thermal-Hydraulic Considerations

A nuclear power plant (nuclear power station) looks like a standard thermal power station with one exception. The heat source in the nuclear power plant is a nuclear reactor. As is typical in all conventional thermal power stations, the heat is used to generate steam which drives a steam turbine connected to a generator that produces electricity. But in nuclear power plants, reactors produce an enormous amount of heat (energy) in a small volume. The density of the energy generation is very large, which puts demands on its heat transfer system (reactor coolant system). Therefore we have to start with the reactor heat generation and removal from the reactor.

For a reactor to operate in a steady state, all of the heat released in the system must be removed as fast as it is produced. This is accomplished by passing a liquid or gaseous coolant through the core and through other regions where heat is generated. The heat transfer must be equal to or greater than the heat generation rate or overheating, and possible damage to the fuel may occur. The nature and operation of this coolant system are some of the most important considerations in designing a nuclear reactor.

Material Considerations

The temperature in an operating reactor varies from point to point within the system. Consequently, there is always one fuel rod and one local volume hotter than all the rest. Peak power limits must be introduced to limit these hot places. The peak power limits are associated with a boiling crisis and conditions that could cause fuel pellet melt. However, metallurgical considerations place upper limits on the temperature of the fuel cladding and the fuel pellet. Above these temperatures, there is a danger that the fuel may be damaged. One of the major objectives in the design of nuclear reactors is to remove the heat produced at the desired power level while assuring that the maximum fuel temperature and the maximum cladding temperature are always below these predetermined values.

It must be noted that theoretically, there is no upper limit to the power level (from the criticality point of view), which can be attained by any critical reactor having sufficient excess of reactivity to overcome its negative temperature coefficient. Nuclear reactors must be equipped with proper safety systems to avoid undesirable power changes.

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2, and 3. June 1992.

See above:

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