Thermal hydraulics (also called thermohydraulics) is the study of

hydraulic Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counter ...

flow in

thermal fluids Thermofluids is a branch of science and engineering encompassing four intersecting fields: *Heat transfer *Thermodynamics *Fluid mechanics *Combustion The term is a combination of "thermo", referring to heat, and "fluids", which refers to liquids ...

. The area can be mainly divided into three parts:

thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...

fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and bio ...

, and

heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...

, but they are often closely linked to each other. A common example is

steam Steam is a substance containing water in the gas phase, and sometimes also an aerosol of liquid water droplets, or air. This may occur due to evaporation or due to boiling, where heat is applied until water reaches the enthalpy of vaporization ...

generation in

power plant A power station, also referred to as a power plant and sometimes generating station or generating plant, is an industrial facility for the generation of electric power. Power stations are generally connected to an electrical grid. Many pow ...

s and the associated energy transfer to

mechanical Mechanical may refer to: Machine * Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement * Mechanical calculator, a device used to perform the basic operations of ...

motion and the change of states of the

water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...

while undergoing this process. Thermal-hydraulic analysis can determine important parameters for reactor design such as

plant efficiency The efficiency of a plant is the percentage of the total energy content of a power plant's fuel that is converted into electricity. The remaining energy is usually lost to the environment as heat unless it is used for district heating. Rati ...

and coolability of the system. The common adjectives are "thermohydraulic", "thermal-hydraulic" and "thermalhydraulic".

Thermodynamic analysis

In the thermodynamic analysis, all states defined in the system are assumed to be in

thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermod ...

; each state has mechanical, thermal, and phase equilibrium, and there is no macroscopic change with respect to time. For the analysis of the system, the

first law "First Law" is a science fiction short story by American writer Isaac Asimov, first published in the October 1956 issue of ''Fantastic Universe'' magazine and later collected in ''The Rest of the Robots'' (1964) and ''The Complete Robot'' (1982). ...

and second law of thermodynamics can be applied. In

analysis, a series of states can comprise a

cycle Cycle, cycles, or cyclic may refer to: Anthropology and social sciences * Cyclic history, a theory of history * Cyclical theory, a theory of American political history associated with Arthur Schlesinger, Sr. * Social cycle, various cycles in soc ...

. In this case, each state represents condition at the inlet/outlet of individual component. The example of components are

pump A pump is a device that moves fluids (liquids or gases), or sometimes slurries, by mechanical action, typically converted from electrical energy into hydraulic energy. Pumps can be classified into three major groups according to the method they u ...

compressor A compressor is a mechanical device that increases the pressure of a gas by reducing its volume. An air compressor is a specific type of gas compressor. Compressors are similar to pumps: both increase the pressure on a fluid and both can transp ...

turbine A turbine ( or ) (from the Greek , ''tyrbē'', or Latin ''turbo'', meaning vortex) is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. The work produced by a turbine can be used for generating e ...

, reactor, and

heat exchanger A heat exchanger is a system used to transfer heat between a source and a working fluid. Heat exchangers are used in both cooling and heating processes. The fluids may be separated by a solid wall to prevent mixing or they may be in direct contac ...

. By considering the

constitutive equation In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approx ...

for the given type of fluid, thermodynamic state of each point can be analyzed. As a result, the

thermal efficiency In thermodynamics, the thermal efficiency (\eta_) is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, steam turbine, steam engine, boiler, furnace, refrigerator, ACs etc. For a he ...

of the cycle can be defined. Examples of the cycle include the

Carnot cycle A Carnot cycle is an ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. By Carnot's theorem, it provides an upper limit on the efficiency of any classical thermodynam ...

Brayton cycle The Brayton cycle is a thermodynamic cycle that describes the operation of certain heat engines that have air or some other gas as their working fluid. The original Brayton engines used a piston compressor and piston expander, but modern gas tur ...

, and

Rankine cycle The Rankine cycle is an idealized thermodynamic cycle describing the process by which certain heat engines, such as steam turbines or reciprocating steam engines, allow mechanical work to be extracted from a fluid as it moves between a heat sourc ...

. Based on the simple cycle, modified or combined cycle also exists.

Temperature distribution

Temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...

is an important quantity to know for the understanding of the system. Material properties such as

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

, and

specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...

depend on temperature, and very high or low temperature can bring unexpected changes in the system. In solid, the

heat equation In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat equation was first developed by Joseph Fourier in 1822 for t ...

can be used to obtain the temperature distribution inside the material with given geometries. For steady-state and static case, the heat equation can be written as :

0 =\,\nabla\cdot k \,\nabla T\ \ +q

where Fourier’s law of conduction is applied. Applying

boundary conditions In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to th ...

gives a solution for the temperature distribution.

Single-phase heat transfer

In single-phase heat transfer,

convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...

is often the dominant mechanism of heat transfer. For a diabatic flow where the flow receives heat, the temperature of the coolant changes as it flows. An example of single-phase heat transfer is a

gas-cooled reactor A gas-cooled reactor (GCR) is a nuclear reactor that uses graphite as a neutron moderator and a gas (carbon dioxide or helium in extant designs) as coolant. Although there are many other types of reactor cooled by gas, the terms ''GCR'' and to a l ...

and

molten-salt reactor A molten salt reactor (MSR) is a class of nuclear fission reactor in which the primary nuclear reactor coolant and/or the fuel is a molten salt mixture. Only two MSRs have ever operated, both research reactors in the United States. The 1950's Ai ...

. The most convenient way for characterizing the single-phase heat transfer is based on an empirical approach, where the temperature difference between the wall and bulk flow can be obtained from the

heat transfer coefficient In thermodynamics, the heat transfer coefficient or film coefficient, or film effectiveness, is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat (i.e., the temperature difference, ). ...

. The heat transfer coefficient depends on several factors: mode of heat transfer (e.g.,

internal Internal may refer to: *Internality as a concept in behavioural economics *Neijia, internal styles of Chinese martial arts *Neigong or "internal skills", a type of exercise in meditation associated with Daoism *''Internal (album)'' by Safia, 2016 ...

external flow In fluid mechanics, external flow is a flow that boundary layers develop freely, without constraints imposed by adjacent surfaces. It can be defined as the flow of a fluid around a body that is completely submerged in it. Examples include fluid moti ...

), type of fluid, geometry of the system, flow regime (e.g.,

laminar Laminar means "flat". Laminar may refer to: Terms in science and engineering: * Laminar electronics or organic electronics, a branch of material sciences dealing with electrically conductive polymers and small molecules * Laminar armour or "band ...

turbulent flow In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...

), boundary condition, etc. Examples of heat transfer correlations are Dittus-Boelter correlation (turbulent

forced convection Forced convection is a mechanism, or type of transport, in which fluid motion is generated by an external source (like a pump, fan, suction device, etc.). Alongside natural convection, thermal radiation, and thermal conduction it is one of the met ...

), Churchill & Chu (

natural convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convect ...

Multi-phase heat transfer

Compared with single-phase heat transfer, heat transfer with a phase change is an effective way of heat transfer. It generally has high value of heat transfer coefficient due to the large value of

latent heat Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a first-order phase transition. Latent heat can be understo ...

of phase change followed by induced mixing of the flow. Boiling and condensation heat transfers are concerned with wide range of phenomena.

Pool boiling

Pool boiling is boiling at a stagnant fluid. Its behavior is well characterized by Nukiyama boiling curve, which shows the relation between the amount of surface superheat and applied heat flux on the surface. With the varying degrees of the superheat, the curve is composed of natural convection, onset of nucleate boiling,

nucleate boiling Nucleate boiling is a type of boiling that takes place when the surface temperature is hotter than the saturated fluid temperature by a certain amount but where the heat flux is below the critical heat flux. For water, as shown in the graph below, n ...

critical heat flux Critical heat flux (CHF) describes the thermal limit of a phenomenon where a phase change occurs during heating (such as bubbles forming on a metal surface used to heat water), which suddenly decreases the efficiency of heat transfer, thus causing ...

, transition boiling, and film boiling. Each regime has a different mechanism of heat transfer and has different correlation for heat transfer coefficient.

Flow boiling

Flow boiling is boiling at a flowing fluid. Compared with pool boiling, flow boiling heat transfer depends on many factors including flow pressure, mass flow rate, fluid type, upstream condition, wall materials, system geometry, and applied heat flux. Characterization of flow boiling requires comprehensive consideration of operating condition. In 2021 a prototype

electric vehicle An electric vehicle (EV) is a vehicle that uses one or more electric motors for propulsion. It can be powered by a collector system, with electricity from extravehicular sources, or it can be powered autonomously by a battery (sometimes cha ...

charging cable using flow boiling was able to remove 24.22 kW of heat, allowing the charging current to reach 2,400 amps, far higher than state of the art charging cables that top out at 520 amps.

Critical Heat Flux

Heat transfer coefficient due to nucleate boiling increases with wall superheat until they reach a certain point. When the applied heat flux exceeds the certain limit, heat transfer capability of the flow decreases or significantly drops. Normally, the critical heat flux corresponds to

DNB Drum and bass (also written as drum & bass or drum'n'bass and commonly abbreviated as D&B, DnB, or D'n'B) is a genre of electronic dance music characterized by fast breakbeats (typically 165–185 beats per minute) with heavy bass and sub-ba ...

in PWR and dryout in

BWR A boiling water reactor (BWR) is a type of light water nuclear reactor used for the generation of electrical power. It is a design different from a Soviet graphite-moderated RBMK. It is the second most common type of electricity-generating nuc ...

. The reduced heat transfer coefficient seen in post-DNB or post-dryout is likely to result in damaging of the boiling surface. Understanding of the exact point and triggering mechanism related to critical heat flux is a topic of interest.

Post-CHF Heat transfer

For DNB type of boiling crisis, the flow is characterized by creeping vapor fluid between liquid and the wall. On top of the convective heat transfer, radiation heat transfer contributes to the heat transfer. After the dryout, the flow regime is shifted from an inverted annular to mist flow.

Other phenomena

Other thermal hydraulic phenomena are subject of interest: * Critical discharge *

Countercurrent flow Countercurrent exchange is a mechanism occurring in nature and mimicked in industry and engineering, in which there is a crossover of some property, usually heat or some chemical, between two flowing bodies flowing in opposite directions to each ...

limitation *

Condensation Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor to ...

* Flow instability * Rewetting

References

{{DEFAULTSORT:Thermal Hydraulics Thermodynamics Fluid dynamics

Thermodynamic analysis

Temperature distribution

Single-phase heat transfer

Multi-phase heat transfer

Pool boiling

Flow boiling

Critical Heat Flux

Post-CHF Heat transfer

Other phenomena

See also

References