Normal Heat Transfer Research Articles

Study on the heat transfer deterioration of supercritical nitrogen in a vertical tube using a pseudo-boiling model

Heat transfer performance of supercritical cryogenic fluid plays a pivotal role in hypersonic vehicle engine cooling and cryogenic fuel vaporization. Heat transfer becomes highly complicated due to the complex physical properties of supercritical fluids (SFs). Heat transfer deterioration (HTD) occurs in SFs similar to the departure from nucleate boiling of subcritical fluids, resulting in a sudden temperature rise. In this study, a pseudo-boiling model is used to investigate HTD of supercritical nitrogen (SCN2) in vertical tubes. The distribution of the pseudo-vapor phase is analyzed to understand the heat transfer behavior in both normal heat transfer (NHT) and HTD regions. Simulation results show that the accumulated pseudo-vapor film weakens the heat transfer from the wall to the mainstream region, resulting in HTD. The critical heat flux (CHF) of SCN2 is observed in the simulation and verified by experimental data. Further investigation into buoyancy and thermal acceleration elucidates the absence of CHF under large mass flux conditions. The forced convection of high turbulent kinetic energy hinders the accumulation of pseudo-vapor film, resulting in NHT under large mass flux conditions. This paper provides a new approach and insights to investigate HTD of SFs using the pseudo-boiling model.

Simulation of blood flow in a tapered artery with ternary hybrid nanofluid and Jeffrey model

This research simulates flow of blood in a tapered peristaltic artery integrating ternary hybrid nanofluid using the Jeffrey fluid model. The simulation examines the effects of Au, Fe3O4, and Ag nanoparticles on the flow. The artery, modeled as a peristaltic channel, is subjected to nonlinear thermal radiation, magnetic forces, and heat source. The problem is formulated using non-linear Cartesian partial differential equations, which are then transformed into dimensionless form without approximations. Adomian Decomposition Method (ADM) is employed to solve these equations, revealing how normal and shear stress, normal and axial velocities, induced magnetic fields, and temperature profiles vary with changes in relevant parameters. Additionally, biological factors are considered to graph streamlines, providing a comprehensive analysis of the flow dynamics. Some notable results include that adding ternary nanoparticles increases the Nusselt number by 26.03% in Newtonian fluids and 158.69% in Jeffrey fluids, and increasing tapering parameters and wavenumber improves axial and normal velocities, heat transfer, and flow complexity.

Experimental investigation of non-uniform heating effect on flow and heat transfer of supercritical carbon dioxide:An application to solar parabolic trough collector

In order to reduce the carbon dioxide emission, the supercritical carbon dioxide (sCO2) Brayton cycle is a good choice to convert solar energy into power using solar parabolic trough collectors (PTCs). Because the earth rotation induced non-uniform flux distribution threatens the safe operation of absorber tubes, we investigate the flow and heat transfer of sCO2 in a horizontal tube under non-uniform heating, with the mass fluxes, average heat fluxes and pressures in the ranges of (397–1244) kg/m2s, (99–413) kW/m2, and (7.5–15.7) MPa, respectively. On the contrary to the classical treatment of supercritical fluid (SCF), SCF is treated in a multiphase framework. It is found that, compared with the sCO2 heat transfer in horizontal tubes under uniform heating, the non-uniform heating not only enhances heat transfer, but also increases friction factors. Besides, the non-uniform heating weakens the stratification effect, but the difference of heat transfer between the top and bottom generatrixes cannot be completed eliminated. It is observed that the larger vapor-like-layer thicknesses on tube walls may switch the sCO2 heat transfer from normal heat transfer (NHT) to heat transfer deterioration (HTD). Three heat transfer mechanisms are commented by using the dimensionless numbers regarding the pseudo-boiling in supercritical pressures.

A comparative study on abnormal heat transfer of supercritical CO2 heated in vertical tubes

The heat transfer characteristics of supercritical CO2 heated in vertical smooth tube are experimentally and numerically investigated. The results show that the M-shaped velocity corresponds to heat transfer enhancement (HTE) at G = 100 kg/m2s, q = 20 kW/m2, and the heat transfer coefficient (HTC) is 15% higher than that of normal heat transfer (NHT). While, the M-shaped velocity causes significant heat transfer deterioration (HTD) before the Tpc at G = 278 kg/m2s, q = 35 kW/m2, and the HTC of HTD is 28%–42% of that in NHT. According to the numerical analysis on the M-shaped flow structure, it reveals that the zero-velocity gradient point of abNHT (HTE and HTD) always falls into the buffer layer (5 < y+ < 30). While, the zero-velocity gradient point of the heat transfer recovery (HTR) is in the log-law region (30 < y+ < 60). The u/u0 of the zero-velocity gradient point of HTE are larger than 1.35. The cross-section turbulent kinetic energy structure shows that smaller TKE in the near-wall region is the dominant factor for HTD and larger TKE in the core region is the dominant factor for HTE.

Effect of flow direction on heat transfer and flow characteristics of supercritical carbon dioxide

This work is devoted to investigating the difference in flow and heat transfer characteristics between vertical upward flow and horizontal flow of supercritical carbon dioxide (&lt;inline-formula&gt;&lt;tex-math id="Z-20240119215215"&gt;\begin{document}$\rm sCO_2$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231142_Z-20240119215215.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231142_Z-20240119215215.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;) based on the pseudo-boiling theory and the experimental parameters: mass flux &lt;i&gt;G&lt;/i&gt; = 496–1100 kg/m&lt;sup&gt;2&lt;/sup&gt;s, heat flux &lt;i&gt;q&lt;/i&gt;&lt;sub&gt;w&lt;/sub&gt; = 54.4–300.2 kW/m&lt;sup&gt;2,&lt;/sup&gt; and pressure &lt;i&gt;P&lt;/i&gt; = 7.531–20.513 MPa. The differences in flow and heat transfer characteristics between horizontal upward tube and vertical upward tube are compared at different mass fluxes, heat fluxes and pressures fully. Finally, unlike the classical treatment of flow and heat transfer for supercritical fluid, single-phase fluid assumption is abandoned, instead, the pseudo-boiling theory is introduced to deal with the flow transfer and heat transfer of &lt;inline-formula&gt;&lt;tex-math id="Z-20240119215113"&gt;\begin{document}$\rm sCO_2 $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231142_Z-20240119215113.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231142_Z-20240119215113.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; in the two tubes. Supercritical fluid is regarded as a multiphase structure in this work, including a vapor-like layer near the wall and a liquid-like fluid in tube core. The results are indicated below. 1) In terms of heat transfer, the inner-wall temperature of the vertical upward tube and the bottom generatrix of horizontal tube are basically the same under normal heat transfer mode. When the heat transfer deterioration occurs in the vertical upward tube, larger supercritical boiling number (&lt;i&gt;SBO&lt;/i&gt;) will cause the wall temperature peak of the vertical upward tube to be much higher than the wall temperature at top generatrix of the horizontal tube at the corresponding enthalpy. The &lt;i&gt;SBO&lt;/i&gt; (&lt;i&gt;SBO&lt;/i&gt; = 5.126×10&lt;sup&gt;–4&lt;/sup&gt;) distinguishes between normal heat transfer deterioration and heat transfer deterioration in the vertical upward tube. In the horizontal tubes, &lt;i&gt;SBO&lt;/i&gt; dominates the maximum wall temperature difference between the top generatrix and the bottom generatrix. Comparing with vertical upward tubes, higher &lt;i&gt;q&lt;/i&gt;&lt;sub&gt;w&lt;/sub&gt;/&lt;i&gt;G&lt;/i&gt; is required for the heat transfer deterioration of supercritical fluid in the horizontal tubes under the same pressure. 2) In terms of flow, the increase in slope of pressure drop in the vertical upward tube is due to the orifice contraction effect. The mechanism that dominates the variation of pressure drop in the horizontal tube is the flow stratification effect, and we show that Froude number &lt;i&gt;Fr&lt;/i&gt;&lt;sub&gt;ave&lt;/sub&gt; can be the similarity criterion number to connect the temperature difference between the top and bottom generatrix of horizontal tube and the pressure drop. The analysis suggests that mechanisms governing horizontal flow and vertical flow of &lt;inline-formula&gt;&lt;tex-math id="Z-20240119215057"&gt;\begin{document}$\rm sCO_2 $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231142_Z-20240119215057.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20231142_Z-20240119215057.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; are different in heat transfer deterioration mode. For the vertical flow, the &lt;i&gt;SBO&lt;/i&gt; plays a leading role, while for the horizontal flow, the &lt;i&gt;Fr&lt;/i&gt; plays an indispensable role.

Numerical investigation of upward supercritical water flow with Joule heating effect

By using Joule's Law, resistivity equation, Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) functions, and resistivity-temperature correlation established based on the available experimental data, Joule heating heat flux profiles of upward supercritical water heat transfer in the annular tube are modelled and applied as the boundary condition. The calculated wall temperature result is compared to the Razumovskiy et al. experiment dataset. It is discovered that by using the PCHIP-modelled Joule heating profiles, the estimated wall temperature for both the Normal Heat Transfer (NHT) and Deteriorated Heat Transfer (DHT) regimes is comparable to the experiment in terms of trend and magnitude. However, by using the conventional constant heat flux profiles, the upstream and downstream wall temperatures are overestimated and underestimated respectively. This study demonstrated that CFD can adequately replicate experimental heat flux conditions, hence improving CFD estimates of supercritical heat transfer, particularly for the DHT, which has a substantial heat flux variation. With this fine imitation of the Joule heating heat flux, the critical DHT regime can be more accurately predicted.

Review on Supercritical Fluids Heat Transfer Correlations, Part I: Variants of Fundamental Dimensionless Variables

When supercritical fluids absorb heat energy through channels, their thermophysical properties rapidly change, resulting in an enhanced, deteriorated, or normal heat transfer phenomenon. Understanding the phenomena of heat transfer is essential for applications involving supercritical fluids, particularly nuclear power generation. As a result, the Nusselt number correlation is developed and used to characterize the heat transfer performance under a variety of operating conditions, geometries, and flow directions. Unfortunately, for supercritical fluid heat transfer, there are now over 50 Nusselt number correlations, which create difficulties to comprehend all of the Nusselt number correlations due to their complex structures and distinctive formulations of the modifying factors. Therefore, this review article is devoted to providing a comprehensive yet succinct overview of the key components of the majority of supercritical Nusselt number correlations. The supercritical properties of water, carbon dioxide, and helium are briefly introduced, taking supercritical carbon dioxide as an example. The potential use of supercritical fluid in engineering applications, such as Generation IV nuclear reactors, waste heat recovery, and concentrated solar power, is presented. The origin and properties of the variants of the Reynolds number, the Prandtl number, and the reference temperature modified for the Nusselt number correlation are categorized and examined.

Quantitative thermal-wave depth profiles of solids with spatially variant cooling coefficients imaged using lock-in thermography

A generalized treatment of the thermal-wave boundary-value problem in a solid slab strip with large sidewalls exposed to the ambient and third-kind boundary conditions over the extended sidewall surfaces was presented. Unlike conventional heat conduction theoretical practice, it was found that the cooling coefficient h is not constant and depends on the thermal gradient variation with depth/length. The exponential damping of the TW amplitude with depth presented an ideal condition to reveal the depth dependence of h which under normal steady heat transfer conditions might appear approximately constant in a non-steeply changing thermal field. The observed depth dependence of the heat loss coefficient can be used to establish the physically expected constancy of thermal diffusivity at different modulation frequencies in juxtaposition to some published reports. It is expected that this work can be used to optimize other thermophysical parameters for materials subject to periodic heating.

Experimental investigation on abnormal heat transfer behaviors of hydrocarbon fuel under supercritical condition in a minichannel

The heat transfer characteristics of hydrocarbons in minichannels were studied experimentally, with the heat transfer process divided into four stages: normal heat transfer, heat transfer enhancement, heat transfer weakened, and heat transfer recovery. The onset of heat transfer weakened (OHW) in the process was considered, and the corresponding heat flux (qOHW) was defined. The results show that qOHW is related to the inlet enthalpy, Reynolds number, and working pressure. A dimensional prediction formula for the qOHW was proposed based on the supercritical boiling number, ratio of enthalpy difference to enthalpy at pseudo-critical temperature, Reynolds number, and dimensionless pressure. The average relative deviation of the correlation was 2.01% compared with the experimental results. This study will contribute to the thermal research on supercritical fluids in a minichannel.

Experimental investigation on natural circulation heat transfer of supercritical CO2 in a closed loop

The natural circulation system based on supercritical CO2 has attracted attention due to its simple structure and safety compared with the forced circulation system. This work presented an experimental investigation of the heat transfer characteristics of CO2 based on natural circulation. Two heat transfer modes can also be observed in supercritical CO2 natural circulation, normal heat transfer and heat transfer deterioration. The development of heat transfer deterioration criterion and heat transfer correlation is significant for the application of supercritical CO2 natural circulation, but there are few related studies. Direct adoption of the supercritical CO2 forced convective criteria and heat transfer correlations to natural circulation introduces large deviations. By analyzing the existing research results of forced convection in supercritical CO2 and introducing new dimensionless parameters SBO and K, a deterioration criterion and a heat transfer correlation suitable for natural circulation of supercritical CO2 are developed based on experimental data. The new criterion can well distinguish the two heat transfer modes, and the new correlation improves markedly. The results can benefit engineering applications in advanced power cycles.

Look-up table for wall temperature of vertically-upward round tube with heat transfer to supercritical water

Wall temperature of heat transfer tubes is one of the most important parameters indicating the operation safety of various heat transfer facilities, and as a result, estimation of the wall temperature becomes one of the main tasks in the design of heat transfer facilities. The wall temperature look-up table (Tw-LUT) can be established directly from experimental data and can be then used to estimate the wall temperature of the heat transfer tubes, avoiding the approximation or extrapolation of fluid properties that inevitably exists in the heat transfer correlations. In view of the problems existing in applications with wall temperature estimations of the heat transfer tube, such as limited data points and the limited application scopes of parameters, a look-up table is built in this paper for wall temperatures of vertically-upward round tubes of 10 mm tube diameter with heat transfer to supercritical water (SCW), under conditions with pressure in the range from 22.5 to 31 MPa, the mass velocity in the range from 200 to 3000 kg·m−2·s−1, the heat flux in the range from 200 to 1800 kW·m−2, and the bulk fluid enthalpy in the range from 1000 to 3000 kJ·kg−1. In order to cover the gaps between the experimental data points, and to improve the prediction accuracy of the Tw-LUT, the best heat transfer correlation is selected for each local area of interest in the LUT based on its prediction accuracy in the corresponding local area, and then the best heat transfer correlation is adopted to supplement wall temperature results to fill up the Tw-LUT. The comparison between the wall temperatures by the Tw-LUT and the experimental wall temperatures is carried out to verify the accuracy of the Tw-LUT, and it is shown that the mean absolute deviation of the results is 0.87%, and 87.81% of the results fall into the ±3% error band, indicating that the Tw-LUT has a good accuracy for wall temperature prediction and the establishment method is reliable and can be used to build other look-up tables. The Tw-LUT can be applied not only to normal heat transfer conditions but also to deteriorated heat transfer conditions and enhanced heat transfer conditions with a satisfactory accuracy.

ЭКСПЕРИМЕНТАЛЬНОЕ ОБОСНОВАНИЕ ПРОЕКТНЫХ ХАРАКТЕРИСТИК ПАРОГЕНЕРАТОРА РУ БРЕСТ-ОД-300

The project BREST-OD-300 reactor plant (RP) with a fast neutron reactor and a lead coolant in the primary circuit is being developed in NIKIET JSC. As a steam generator (SG), a helical-type steam generator with coiled tubes with subcritical pressure water in the second circuit is considered. To substantiate the design characteristics of the secondary coolant at the State Research Center of the Russian Federation - IPPE, thermohydraulic tests of various SG models were carried out at the SPRUT stand Initially, tests were carried out on a model of a coiled steam generator consisting of two three-tube modules with a longitudinal lead flow around a three-tube bundle of coiled tubes. The influence of operating parameters on thermohydraulic characteristics and hydrodynamic stability is shown in the case of operation of one module, as well as in the joint operation of two models in the investigated range of operating parameters. At the second stage, tests of a standard steam generator model were carried out with lead flowing around 18 heat exchange tubes. In the multitube model, the downward movement of the heating coolant took place with the flow around the bundle of heat transfer tubes close to the transverse flow. Data were obtained on the hydrodynamic stability of steam generating tubes and the entire model as a whole when operating in the entire range of changes in operating parameters, which are necessary for creating a databank and further verification of calculation codes describing the ongoing thermohydraulic processes. During the tests in both models of the steam generator, there were no noises inherent in unstable operating modes of the circuit. No pulsations of water and steam temperature were found, respectively, in the inlet and outlet collectors. At high lead temperatures, the temperature of the superheated steam was always close to the lead inlet temperature. A series of works devoted to the study of heat transfer from the side of a lead coolant with a transverse flow around a package of heat exchange tubes in normal heat transfer modes and with freezing of lead has been completed. Studies have been carried out on the effect of oxygen concentration in lead on heat transfer.

Multiple wall temperature peaks during forced convective heat transfer of supercritical carbon dioxide in tubes

Heat transfer deterioration (HTD) is defined as having one or multiple wall temperature peaks along the flow length for supercritical heat transfer. The single-peak phenomenon has been widely reported in the literature, but the multi-peak phenomenon is seldomly studied and not well understood. Here, the convective heat transfer of supercritical carbon dioxide in vertical tubes is investigated, with pressure, mass flux, and heat flux in the ranges of 7.5~23 MPa, 400~1500 kg/m2s, and 25~450 kW/m2, respectively, and inner tube diameter covering 8, 10, and 12 mm. Sudden changes are observed between normal heat transfer (NHT) without wall temperature peak and HTD by crossing a global critical supercritical boiling number (SBO) based on the pseudo-boiling theory. For HTD, we show that inner diameter and pressure have significant influences on whether the multi-peak phenomenon occurs: it takes place for inner diameter of 12 mm only and under pressure of ~8 and ~12.5 MPa. It is found that friction factors for multi-peak cases are obviously larger than those for single-peak or NHT cases, which is successfully explained by the orifice contraction effect due to the strong “vapor” expansion at the tube cross-section corresponding to the sharp wall temperature peak. The multi-peak phenomenon is shown to be governed by the competition between the local evaporation momentum force and inertia force along the flow length. Our work enhances the understanding of supercritical heat transfer and verifies the validity of pseudo-boiling assumption, and can also benefit engineering applications in advanced power cycles.

On the Use of a Buoyancy Parameter for Distinguishing Deteriorated From Normal Heat Transfer in Upward Flows at Supercritical Pressures

Abstract An extensive analysis of two versions of a buoyancy parameter as supercritical heat transfer deterioration (DHT) identifiers was conducted for large databases obtained in carbon dioxide flowing through three electrically heated tubes with internal diameters equal to 4.6, 8.0, and 22.0 mm and in Refrigerant R134a through an 8.0 mm tube. For the first time, buoyancy parameter profiles along each tube were considered for wide ranges of closely incremented operating conditions. The occurrence of DHT in each test section was first assessed confidently by observation of wall temperature profiles and comparison of measurements with wall temperature predictions of a correlation for normal heat transfer (NHT). The objective of this work was to determine whether a universal buoyancy parameter threshold could be used as a means for identifying DHT in a test section. It was found that correction factors were required for both parameters to account for an observed shift of the threshold for DHT occurrence, as the mass flux was changed. The resulting threshold for one of the buoyancy parameters identified correctly DHT for cases having a mass flux up to a certain value, but failed to do so for cases with a higher mass flux.

Numerical analysis of heat transfer and hydraulic resistance during an upward turbulent flow of supercritical pressure carbon dioxide in a heated tube

This paper presents the wall temperature distribution, averaged velocity, turbulent statistics, and hydraulic resistance investigated using large eddy simulation for CO2 at supercritical pressure flowing upward in a heated vertical tube for the deteriorated heat transfer regimes simulated by Bae et al. using a direct numerical simulation (DNS). Numerical simulations were performed using the “in-house” computational fluid dynamics code ANES. We discuss the reasons for certain inconsistencies in wall temperature distribution between the DNS data of Bae et al. and others, the mechanism of formation of an M-shaped profile of the averaged axial velocity, and the features of turbulent kinetic energy generation due to deformation of the averaged velocity field and buoyancy forces. We show that the return to the normal heat transfer regime after the wall temperature reaches its local peak is due to the action of buoyancy forces.

Evaluation and development of heat transfer model for supercritical water flowing in 2 × 2 rod bundles with spacer grid

Supercritical water has excellent heat transfer abilities that allows higher power density and smaller structure in power plants. However, due to the large variation of the fluid thermal-physical properties near pseudo-critical point, heat transfer to supercritical water shows abnormal behavior at certain points. Thus, an accurate prediction model of heat transfer to fluid is very important to the supercritical energy system design. The present studies performed an experiment of 2 × 2 rod bundles with spacer effect at supercritical pressure and more than 5000 data pointes were obtained. A thorough analysis and assessment of the heat transfer models was carried out, to give an insight into the characters of the present heat transfer models for the fully-developed flow and spacer grid influenced flow. The result shows that the Watts-Chou correlation can predict the so-called normal heat transfer regions without spacer grid effects. For the enhancement heat transfer region in consequence of the spacer grid, all the existing models underestimate the heat transfer abilities at supercritical condition. In addition, the enhancement factor of spacer grid design and flow conditions were evaluated. Based on these enhancement factors, a new heat transfer model for space grid effect was developed and the accuracy of heat transfer in the downstream of spacer grid was significantly improved.

Heat Transfer and Hydraulic Resistance in Turbulent Flow in Vertical Round Tubes at Supercritical Pressures—Part II: Results From Numerical Simulation With Differential Turbulent Viscosity Models

Abstract The review of numerical studies on the turbulent flow and heat transfer of supercritical pressure (SCP) coolants in heated vertical round tubes, which were conducted using different differential turbulent viscosity models, is presented. The results of predictions are compared with the experimental data on wall temperature and heat transfer rate. It is shown that most often the turbulent viscosity models only qualitatively (but not quantitatively) predict the deteriorated heat transfer effects, which appear due do buoyancy forces and thermal acceleration effects at strongly variable physical properties of a coolant. At the same time, the regimes of normal heat transfer are successfully reproduced by “standard” k–ε and RNG models with wall functions (WFs), as well as by two-layer models. The conclusion is made that none of the presently known turbulent viscosity models can be confidently recommended for predicting any flow regimes and heat transfer of SCP coolants. Strongly variable properties of SCP coolant stipulate more strict demands for validating mesh independence of the obtained results and for an accuracy of approximation of the tabulated values of the coolant properties. It was ascertained that using more and more numerous calculation codes and the results from their application requires certain caution and circumspection. Sometimes, the energy transport equations were erroneously written for temperature or temperature variance rather than for enthalpy. Crying discrepancy in the predictions of different authors conducted using the same CFD codes and turbulence models and possible reasons for such a discrepancy are not analyzed.

О ВЛИЯНИИ СОДЕРЖАНИЯ КИСЛОРОДА НА ТЕПЛООБМЕН ПРИ ПОПЕРЕЧНОМ ОБТЕКАНИИ ПАРОГЕНЕРИРУЮЩИХ ТРУБ В РЕЖИМАХ НОРМАЛЬНОГО ТЕПЛООБМЕНА И С ЗАМОРАЖИВАНИЕМ СВИНЦА

The BREST-OD-300 steam generator project being developed at NIKIET is pioneering both in terms of the heat carrier used (lead) and in design implementation (coils of helical heat transfer tubes). The advantages of the designs of steam generators made in the form of helical coiled tubes, in comparison with straight tube designs are obvious. Helical coiled tubes are used in heat exchange equipment not only to increase the heat transfer surface, to solve the problem of thermal expansion, but also to increase the coefficient of heat transfer to the fluid flowing inside the tubes. In 2011-2017 years the thermohydraulic tests of various models of lead-heated steam generator were carried out at the IPPE SPRUT facility (IPPE). The test program was aimed to study the heat transfer and the thermal-hydraulic stability of the steam generating tubes. Throughout the entire range of changes in operating parameters, no pulsating modes were detected with overturn of circulation in the water circuit. The design temperatures of superheated steam were obtained in nominal operation. The results provide extensive information on water heat transfer in different zones of the steam generating channel under various operating conditions (nominal and partial modes, starting modes). However, to verify the computer codes, experimental data on the heat transfer of lead coolant around the bundles of heat transfer tubes are necessary. Due to the small twist angle of the tubes in a full-scale steam generator, it can be said that heat transfer is close to heat transfer during transverse flow. A model with a transverse flow of lead coolant around steam-generating tubes was developed at the SSC RF - IPPE. The main goal of the research was to obtain data on the effect of oxygen concentration in lead on heat transfer in normal heat transfer modes and with lead freezing. Throughout the entire range of changes in the initial temperature values of lead and water, blocking of the annular space by frozen lead was not recorded.

The K number, a new analogy criterion number to connect pressure drop and heat transfer of sCO2 in vertical tubes

Pressure drop and heat transfer are important for design and operation of power plant using supercritical fluid, but they were investigated independently previously. The objective of this paper is to make a connection between pressure drop and heat transfer for supercritical carbon dioxide (sCO2). Experimental data of pressure drop and heat transfer were obtained in our sCO2 convective test loop, covering pressures, mass fluxes and heat fluxes in the ranges of 7.5–23 MPa, 500–1500 kg/m2s and 15–400 kW/m2, respectively. Different from classical single-phase fluid assumption for supercritical fluid, pseudo-boiling is introduced to deal with flow and heat transfer in supercritical domain, including a wall-attached gas-like layer and a liquid-like fluid in tube core. Supercritical boiling number SBO and K number are developed to characterize the gas-like layer thickness. Friction factors and heat transfer are found to display the two regimes distribution: a normal heat transfer (NHT) regime with smaller friction factors at smaller SBO, and a heat transfer deterioration (HTD) regime accompanying sharply increased pressure drops beyond a critical SBO. We conclude an orifice contraction effect due to the strong vapor expansion, explaining the HTD induced rise of pressure drops. We show that K can be the similarity criterion number to connect pressure drops and heat transfer. A new correlation of friction factors is developed for sCO2, which is suitable for NHT and HTD, having mean relative error, mean absolute relative error and root-mean-square relative error of −6.2%, 18.1% and 21.2%, respectively, which are significantly smaller than those predicted by the correlations in the literature.

Effect of non-uniform heating on scCO2 heat transfer deterioration

The accurate prediction of heat transfer deterioration (HTD) is important to ensure the safe operation of scCO2 cycles driven by various heat sources. Here, the scCO2 heat transfer experiment is performed in a 10 mm diameter vertical tube, covering the ranges of pressures 7.51–21.1 MPa, mass fluxes 488–1500 kg/m2s and heat fluxes 43.7–488 kW/m2. Both uniform heating and non-uniform heating cases are dealt with, but more attention is paid on non-uniform heating. We show that non-uniform heating displays strong circumference angles dependent heat transfer characteristic. Normal heat transfer (NHT) displays gentle rise of wall temperatures along flow length, but for HTD, wall temperature peak is detected ahead of pseudo-critical point. Pseudo-boiling is introduced to deal with scCO2 heat transfer. Heat added to scCO2 is decoupled into a temperature rise part and a phase change part. Flow structure includes a vapor-like fluid near tube wall and a liquid-like fluid in tube core. The analogy between subcritical boiling and supercritical heat transfer results in a supercritical-boiling-number SBO to govern the vapor layer thickness. Sudden change from NHT to HTD is found when crossing a critical SBOcr, which is 5.126 × 10−4 for uniform heating based on our experimental data and other data in the literature, but becomes 8.908 × 10−4 for non-uniform heating using our experimental data. Compared to uniform heating, non-uniform heating is found to delay the occurrence of HTD. The criterion presented here is useful to avoid the occurrence of HTD in the design and operation of scCO2 cycles.