Thermal hydraulics

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Thermal hydraulics (also called thermohydraulics) is the study of hydraulic flow in thermal fluids. The area can be mainly divided into three parts: thermodynamics, fluid mechanics, and heat transfer, but they are often closely linked to each other. A common example is steam generation in power plants and the associated energy transfer to mechanical motion and the change of states of the water while undergoing this process. Thermal-hydraulics analysis can determine important parameters for reactor design such as plant efficiency and coolability of the system. [1]

Contents

The common adjectives are "thermohydraulic", "thermal-hydraulics" and "thermalhydraulics".

Thermodynamic analysis

In the thermodynamic analysis, all states defined in the system are assumed to be in thermodynamic equilibrium; 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 and second law of thermodynamics can be applied. [2]

In power plant analysis, a series of states can comprise a cycle. In this case, each state represents condition at the inlet/outlet of individual component. The example of components are pump compressor, turbine, reactor, and heat exchanger. By considering the constitutive equation for the given type of fluid, thermodynamic state of each point can be analyzed. As a result, the thermal efficiency of the cycle can be defined.

Examples of the cycle include the Carnot cycle, Brayton cycle, and Rankine cycle. Based on the simple cycle, modified or combined cycle also exists.

Thermo-Hydraulic Improvement Parameter (THIP)

Authors observed that Thermo-hydraulic Parameter (THP) is less sensitive towards the Friction Factor Improvement Factor (FFER) [3] . The deviation between the terms (fR/fS) and (fR/fS)0.33 has been found 48 % to 64 % for the range of roughness and other parameters with (Re) 2900 – 14,000, which has been used for the present study. Therefore, to evaluate in equal proportions of enhancement in heat transfer (Nu) and friction factor (f) in the thermal systems a new parameter has been proposed and introduced using the present work which is more realistic and it is named as Thermo-hydraulic Improvement Parameter (THIP), and it can be evaluated as the ratio of (NNIF) to (FFIF) [3] .

Where (NNIF)=Nusselt Number Improvement Factor and (FFIF)=Friction Factor Improvement Factor

Temperature distribution

Temperature is an important quantity to know for the understanding of the system. Material properties such as density, thermal conductivity, viscosity, and specific heat depend on temperature, and very high or low temperature can bring unexpected changes in the system. In solid, the heat equation 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

where Fourier’s law of conduction is applied.

Applying boundary conditions gives a solution for the temperature distribution.

Single-phase heat transfer

In single-phase heat transfer, convection is often the dominant mechanism of heat transfer. For adiabatic 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 and molten-salt reactor.

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. The heat transfer coefficient depends on several factors: mode of heat transfer (e.g., internal or external flow), type of fluid, geometry of the system, flow regime (e.g., laminar or turbulent flow), boundary condition, etc.

Examples of heat transfer correlations are Dittus-Boelter correlation (turbulent forced convection), Churchill & Chu (natural convection).

Multi-phase heat transfer

Different two-phase flow regimes Two-phase Flow.svg
Different two-phase flow regimes

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 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, [4] 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, critical heat flux, 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. [5] In 2021 a prototype electric vehicle 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. [6]

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 (CHF) corresponds to departure from nucleate boiling (DNB) in pressurized water reactor (PWR) and dryout in boiling water reactor (BWR). 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 hydraulics phenomena are subject of interest:

See also

Related Research Articles

<span class="mw-page-title-main">Convection</span> Fluid flow that occurs due to heterogeneous fluid properties and body forces

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. When the cause of the convection is unspecified, convection due to the effects of thermal expansion and buoyancy can be assumed. Convection may also take place in soft solids or mixtures where particles can flow.

<span class="mw-page-title-main">Boiling</span> Rapid phase transition from liquid to gas or vapour

Boiling or ebullition is the rapid phase transition from liquid to gas or vapour; the reverse of boiling is condensation. Boiling occurs when a liquid is heated to its boiling point, so that the vapour pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding atmosphere. Boiling and evaporation are the two main forms of liquid vapourization.

In thermal fluid dynamics, the Nusselt number is the ratio of total heat transfer to conductive heat transfer at a boundary in a fluid. Total heat transfer combines conduction and convection. Convection includes both advection and diffusion (conduction). The conductive component is measured under the same conditions as the convective but for a hypothetically motionless fluid. It is a dimensionless number, closely related to the fluid's Rayleigh number.

In the study of heat transfer, Newton's law of cooling is a physical law which states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its environment. The law is frequently qualified to include the condition that the temperature difference is small and the nature of heat transfer mechanism remains the same. As such, it is equivalent to a statement that the heat transfer coefficient, which mediates between heat losses and temperature differences, is a constant.

<span class="mw-page-title-main">Leidenfrost effect</span> Physical phenomenon

The Leidenfrost effect is a physical phenomenon in which a liquid, close to a solid surface of another body that is significantly hotter than the liquid's boiling point, produces an insulating vapor layer that keeps the liquid from boiling rapidly. Because of this repulsive force, a droplet hovers over the surface, rather than making physical contact with it. The effect is named after the German doctor Johann Gottlob Leidenfrost, who described it in A Tract About Some Qualities of Common Water.

<span class="mw-page-title-main">Boiling water reactor</span> Type of nuclear reactor that directly boils water

A boiling water reactor (BWR) is a type of light water nuclear reactor used for the generation of electrical power. It is the second most common type of electricity-generating nuclear reactor after the pressurized water reactor (PWR), which is also a type of light water nuclear reactor.

<span class="mw-page-title-main">Heat transfer</span> Transport of thermal energy in physical systems

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, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.

<span class="mw-page-title-main">Heat pipe</span> Heat-transfer device that employs phase transition

A heat pipe is a heat-transfer device that employs phase transition to transfer heat between two solid interfaces.

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. It is used in calculating the heat transfer, typically by convection or phase transition between a fluid and a solid. The heat transfer coefficient has SI units in watts per square meter per kelvin (W/m2K).

A coolant is a substance, typically liquid, that is used to reduce or regulate the temperature of a system. An ideal coolant has high thermal capacity, low viscosity, is low-cost, non-toxic, chemically inert and neither causes nor promotes corrosion of the cooling system. Some applications also require the coolant to be an electrical insulator.

<span class="mw-page-title-main">Supercritical water reactor</span> Concept nuclear reactor whose water operates at supercritical pressure

The supercritical water reactor (SCWR) is a concept Generation IV reactor, designed as a light water reactor (LWR) that operates at supercritical pressure. The term critical in this context refers to the critical point of water, and should not be confused with the concept of criticality of the nuclear reactor.

A zeotropicmixture, or non-azeotropic mixture, is a mixture with liquid components that have different boiling points. For example, nitrogen, methane, ethane, propane, and isobutane constitute a zeotropic mixture. Individual substances within the mixture do not evaporate or condense at the same temperature as one substance. In other words, the mixture has a temperature glide, as the phase change occurs in a temperature range of about four to seven degrees Celsius, rather than at a constant temperature. On temperature-composition graphs, this temperature glide can be seen as the temperature difference between the bubble point and dew point. For zeotropic mixtures, the temperatures on the bubble (boiling) curve are between the individual component's boiling temperatures. When a zeotropic mixture is boiled or condensed, the composition of the liquid and the vapor changes according to the mixtures's temperature-composition diagram.

In the study of heat transfer, critical heat flux (CHF) is the heat flux at which boiling ceases to be an effective form of transferring heat from a solid surface to a liquid.

<span class="mw-page-title-main">Reaction calorimeter</span> Apparatus for measuring reaction energy

A reaction calorimeter is a calorimeter that measures the amount of energy released or absorbed by a chemical reaction. It does this by measuring the total change in temperature of an exact amount of water in a vessel.

Micro heat exchangers,Micro-scale heat exchangers, or microstructured heat exchangers are heat exchangers in which fluid flows in lateral confinements with typical dimensions below 1 mm. The most typical such confinement are microchannels, which are channels with a hydraulic diameter below 1 mm. Microchannel heat exchangers can be made from metal or ceramic.

In fluid thermodynamics, 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, nucleate boiling occurs when the surface temperature is higher than the saturation temperature by between 10 and 30 °C. The critical heat flux is the peak on the curve between nucleate boiling and transition boiling. The heat transfer from surface to liquid is greater than that in film boiling.

In engineering, physics, and chemistry, the study of transport phenomena concerns the exchange of mass, energy, charge, momentum and angular momentum between observed and studied systems. While it draws from fields as diverse as continuum mechanics and thermodynamics, it places a heavy emphasis on the commonalities between the topics covered. Mass, momentum, and heat transport all share a very similar mathematical framework, and the parallels between them are exploited in the study of transport phenomena to draw deep mathematical connections that often provide very useful tools in the analysis of one field that are directly derived from the others.

In fluid dynamics, the entrance length is the distance a flow travels after entering a pipe before the flow becomes fully developed. Entrance length refers to the length of the entry region, the area following the pipe entrance where effects originating from the interior wall of the pipe propagate into the flow as an expanding boundary layer. When the boundary layer expands to fill the entire pipe, the developing flow becomes a fully developed flow, where flow characteristics no longer change with increased distance along the pipe. Many different entrance lengths exist to describe a variety of flow conditions. Hydrodynamic entrance length describes the formation of a velocity profile caused by viscous forces propagating from the pipe wall. Thermal entrance length describes the formation of a temperature profile. Awareness of entrance length may be necessary for the effective placement of instrumentation, such as fluid flow meters.

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The removal of heat from nuclear reactors is an essential step in the generation of energy from nuclear reactions. In nuclear engineering there are a number of empirical or semi-empirical relations used for quantifying the process of removing heat from a nuclear reactor core so that the reactor operates in the projected temperature interval that depends on the materials used in the construction of the reactor. The effectiveness of removal of heat from the reactor core depends on many factors, including the cooling agents used and the type of reactor. Common liquid coolants for nuclear reactors include: deionized water, heavy water, the lighter alkaline metals, lead or lead-based eutectic alloys like lead-bismuth, and NaK, a eutectic alloy of sodium and potassium. Gas cooled reactors operate with coolants like carbon dioxide, helium or nitrogen but some very low powered research reactors have even been air-cooled with Chicago Pile 1 relying on natural convection of the surrounding air to remove the negligible thermal power output. There is ongoing research into using supercritical fluids as reactor coolants but thus far neither the supercritical water reactor nor a reactor cooled with supercritical Carbon Dioxide nor any other kind of supercritical-fluid-cooled reactor has ever been built.

References

  1. Akimoto, Hajime; Anoda, Yoshinari; Takase, Kazuyuki; Yoshida, Hiroyuki; Tamai, Hidesada (2016). Nuclear Thermal Hydraulics. An Advanced Course in Nuclear Engineering. Vol. 4. doi:10.1007/978-4-431-55603-9. ISBN   978-4-431-55602-2. ISSN   2195-3708.
  2. No, Hee Cheon (1989). 핵기계공학. Seoul: Korean Nuclear Society.
  3. 1 2 Sahu, Mukesh Kumar; Kharub, Manjeet; Matheswaran, Mahalingam Murugesan (2022-09-01). "Nusselt number and friction factor correlation development for arc-shape apex upstream artificial roughness in solar air heater". Environmental Science and Pollution Research. 29 (43): 65025–65042. doi:10.1007/s11356-022-20222-0. ISSN   1614-7499. PMID   35482237.
  4. Nukiyama, Shiro (December 1966). "The maximum and minimum values of the heat Q transmitted from metal to boiling water under atmospheric pressure". International Journal of Heat and Mass Transfer. 9 (12): 1419–1433. doi:10.1016/0017-9310(66)90138-4. ISSN   0017-9310.
  5. E., Todreas, Neil (2011). Nuclear Systems Volume I : Thermal Hydraulic Fundamentals, Second Edition. CRC Press. ISBN   9781439808887. OCLC   910553956.{{cite book}}: CS1 maint: multiple names: authors list (link)
  6. Lavars, Nick (2021-11-16). "Liquid-to-vapor-cooled cable beats the heat for 5-minute EV charging". New Atlas. Retrieved 2021-11-16.