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-hydraulic 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-hydraulic" and "thermalhydraulic".

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 (Sahu et al.[6]) observed that Thermo-hydraulic Parameter (THP) is less sensitive towards the Friction Factor Improvement Factor (FFER). 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)[6].

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

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, [3] 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. [4] 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. [5]

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 in PWR and dryout in 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 hydraulic phenomena are subject of interest:

See also

Related Research Articles

<span class="mw-page-title-main">Heat engine</span> System that converts heat or thermal energy to mechanical work

In thermodynamics and engineering, a heat engine is a system that converts heat to usable energy, particularly mechanical energy, which can then be used to do mechanical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, particularly electrical, since at least the late 19th century. The heat engine does this by bringing a working substance from a higher state temperature to a lower state temperature. A heat source generates thermal energy that brings the working substance to the higher temperature state. The working substance generates work in the working body of the engine while transferring heat to the colder sink until it reaches a lower temperature state. During this process some of the thermal energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid. During this process, some heat is normally lost to the surroundings and is not converted to work. Also, some energy is unusable because of friction and drag.

<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 vapor; 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 convective to conductive heat transfer at a boundary in a fluid. 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.

<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 surface 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.

The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations, named for the eighteenth-century French physicist Jean-Baptiste Biot (1774–1862). The Biot number is the ratio of the thermal resistance for conduction inside a body to the resistance for convection at the surface of the body. This ratio indicates whether the temperature inside a body varies significantly in space when the body is heated or cooled over time by a heat flux at its surface.

<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).

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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 convective heat transfer, the Churchill–Bernstein equation is used to estimate the surface averaged Nusselt number for a cylinder in cross flow at various velocities. The need for the equation arises from the inability to solve the Navier–Stokes equations in the turbulent flow regime, even for a Newtonian fluid. When the concentration and temperature profiles are independent of one another, the mass-heat transfer analogy can be employed. In the mass-heat transfer analogy, heat transfer dimensionless quantities are replaced with analogous mass transfer dimensionless quantities.

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Pillow-plate heat exchangers are a class of fully welded heat exchanger design, which exhibit a wavy, “pillow-shaped” surface formed by an inflation process. Compared to more conventional equipment, such as shell and tube and plate and frame heat exchangers, pillow plates are a quite young technology. Due to their geometric flexibility, they are used as well as “plate-type” heat exchangers and as jackets for cooling or heating of vessels. Pillow plate equipment is currently experiencing increased attention and implementation in process industry.

References

[6] Mukesh Kumar Sahu, Manjeet Kharub, Mahalingam Murugesan Matheswaran. “Nusselt number and friction factor correlation development for arc‑shape apex upstream artificial roughness in solar air heater.” Environmental Science and Pollution Research. Vol. 26, Pages- 65025–65042, 2022.

  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. 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.
  4. 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)
  5. Lavars, Nick (2021-11-16). "Liquid-to-vapor-cooled cable beats the heat for 5-minute EV charging". New Atlas. Retrieved 2021-11-16.