A general one-dimensional model for conduction-controlled rewetting of a surface

A computer-oriented analytical method for predicting the rewetting rate of a hot dry wall is proposed. The wall, which is modeled as a thin flat plate with internal heat generation, receives a variable heat flux from one side while it is cooled from the other side. The model accounts for the large variations of the heat transfer coefficient near the wet front and for the temperature dependence of the thermal and physical properties of the wall. The one-dimensional heat-conduction equation is solved by dividing the quenching zone into small segments of arbitrary temperature increment and constant properties and heat transfer coefficient. A trial-and-error method is developed to predict the velocity of the wet front, the length of the quenching zone and the temperature profile. The one-dimensional models of other authors can be obtained as particular cases of the present model.     

Analysis of Precursory Cooling in Quenching Phenomena

It has been noted that precursory cooling plays an important role in quenching phenomena. In this work, a new model is presented by assuming that the heat transfer in precursory cooling is mainly due to film boiling, which persists in a finite length. Then the quench velocity and temperature profile are obtained based on the three-region model for one- dimensional axial heat conduction in a heated tube. We applied our model to several existing experimental results and obtained a correlation to predict the effective length of precursory cooling region. It turns out that the correlation takes an identical form for both falling-film rewetting and bottom flooding.     

骤冷前沿区域传热特性实验研究

骤冷过程中骤冷前沿区域的传热特性是研究骤冷过程的主要参数之一，也是研究骤冷前沿移动速度的一个主要输入自变量，本文采用瞬态热块实体验技术和变物性非稳态两维数值分析技术，研究了低压低质量流速条件下管内顶部骤冷过程中骤冷前沿区域的传热特性，以适用的物理模型为基础，采用多元非线性回归分析技术分析了相关参数对骤冷前沿区域传热特性的影响特征。在初始热壁温度为４５０～６００℃，系统压力为０．３１～０．８８ＭＰａ     

过冷度和粗糙度对铁铬铝平板淬冷沸腾影响的实验研究

为了探究过冷度和表面粗糙度对铁铬铝（FeCrAl ）平板淬冷沸腾的影响,对FeCrAl 平板在不同过冷度和表面粗糙度下的淬冷沸腾过程开展了可视化实验研究。采用热电偶测量平板内部温度,并利用导热反问题解析式求解平板表面温度和热流密度;通过对比分析实验现象,探究过冷度和表面粗糙度对平板淬冷沸腾过程的影响,并建立了过冷度与最小膜态沸腾温度的关系式。结果表明,淬冷沸腾过程中,FeCrAl 平板表面形成开尔文一亥姆霍兹（K-H）不稳定波,且气膜破裂后产生的骤冷前沿呈“抛物线”状;随着过冷度的增加,最小膜态沸腾温度增大,临界热流密度增大,平板表面冷却速率加快,淬冷沸腾过程的时长缩短;较大的表面粗糙度可以促进FeCrAl 平板表面淬冷沸腾的进行,但影响微小。      

基于CFD方法的矩形窄缝通道内过冷流动沸腾模型研究

板状燃料元件中的矩形窄缝通道具有宽高比大的几何特征,高度方向速度梯度大、分布陡峭,发生过冷沸腾时,近壁面汽泡运动行为将受其影响而改变,其中汽泡滑移现象对沸腾换热影响较大。本文针对矩形窄缝通道中的汽泡滑移行为,构建了包含滑移热流的壁面热流分配模型,并建立机理性的汽泡受力模型和滑移模型计算汽泡脱离直径、浮升直径和滑移距离等辅助参数,开发了一套适用于矩形窄缝通道内向上流动沸腾的壁面沸腾模型。选用Nuthel窄缝通道沸腾实验进行数值模拟验证,结果表明：本文模型可以较好地预测1～4 MPa中低压工况窄缝通道向上流动沸腾的壁面过热度,最大误差相比RPI模型由80%降低至17%;蒸发热流份额和近壁面空泡份额相比RPI模型更低。     

Evaluation of Heat Transfer Augmentation in a Nanofluid-Cooled Microchannel Heat Sink

Present investigation deals with appraising heat transfer enhancement of single phase microchannel heat sink (MCHS) by ultra fine Cu particle incorporation in base coolant fluid. The particle diameter is of nanometer size and base fluid in combination of nanoparticles is called nanofluid. Governing equations for fluid flow and heat transfer are based on well established “porous medium model” and accordingly, modified Darcy equation and two-equation model are employed. Appropriate equations for both fluid flow and heat transfer are derived and cast into dimensionless form. Velocity profile is obtained analytically and in order to solve conjugate heat transfer problem a combined analytical–numerical approach is employed. For heat transfer analysis, thermal dispersion model is adopted and latest proposed model for effective thermal conductivity – which considers the salient effect of interfacial shells between particles and base fluid – is integrated into model. The effects of dispersed particles concentration, thermal dispersion coefficient and Reynolds number are investigated on thermal fields and on thermal performance of MCHS. Additionally, the impact of turbulent heat transfer on heat transfer enhancement is considered.     

锆-4在冷却水中的骤冷沸腾传热实验研究

为了研究锆-4在冷却水中的骤冷行为与沸腾传热特性,本文采用可视化方法,并测量了锆-4在骤冷过程中的温度变化。基于一维导热反问题求解,计算得到锆-4表面的热流密度和温度。在骤冷过程中锆-4会依次经历膜态沸腾、过渡沸腾、核态沸腾以及单相对流换热4个阶段,并且分析了轴向高度和冷却水过冷度对骤冷行为以及沸腾传热的影响。结果表明,随着过冷度的增大,骤冷时间减小,最小膜态沸腾温度增大,并且核态沸腾与过渡沸腾传热受加热表面局部特性影响显著,并建立了锆-4表面最小膜态沸腾温度的关系式,对反应堆的安全分析具有重要的意义。      

Effect of interfacial wavy motion on film boiling heat transfer from isothermal downward-facing hemispheres

Film boiling heat transfer coefficients for a downward-facing hemispherical surface are measured from the quenching tests in Downward-Boiling Experiment Laminar Transition Apparatus (DELTA). Two test sections are made of copper to maintain low Biot numbers. The outer diameters of the hemispheres are 120 and 294 mm, respectively. The thickness of all the test sections is 30 mm. The effect of diameter on film boiling heat transfer is quantified utilizing results obtained from the test sections. The measured data are compared with the numerical predictions from laminar film boiling analysis. The measured heat transfer coefficients are found to be greater than those predicted by the conventional laminar flow theory on account of the interfacial wavy motion incurred by the Helmholtz instability. Incorporation of the wavy motion model considerably improves the agreement between the experimental and numerical results in terms of heat transfer coefficient. In addition, the film boiling was visualized using a digital camera.     

Assessment of RELAP5/MOD3.2.2 Gamma against ABB Atom 3×3-Rod Bundle Reflooding Tests

The results of the ABB Atom 3×3-Rod Bundle Reflooding Tests were used for assessment of the reflooding model used in RELAP5/MOD3.2.2 Gamma version. The assessment calculations were performed using the default calculation model options implemented in the code.The tests were performed to investigate the effects of different spacer grid designs on heat transfer during the reflooding period of a pressurized water reactor loss-of-coolant accident (LOCA). The tests were conducted under low-pressure and low-flow (LPLF) conditions using a PWR-type 3×3-rod bundle with full-length indirectly electrically heated, stepped cosine axial power-shaped heater rods. Three different spacer grid configurations were studied: spacer grids without mixing vanes, mixing vane spacer grids, and mixing vane spacer grids together with intermediate flow mixers (IFM).A total of 36 tests with different spacer grid configurations were calculated. For two selected basic tests with non-mixing spacer grids an extended comparison of calculated and measured parameters is presented. The comparison of the predicted and measured maximal cladding temperatures and quench times, which are the most important parameters in licensing calculations, is presented for all the performed tests.The assessment calculations were preceded by nodalization, time step, and moving mesh studies.The RELAP5/MOD3.2.2 Gamma code was found to still have several deficiencies in the reflood model. The calculation results show a satisfactory agreement with experimental inner peak cladding temperature, however the predicted temperature turn-around times and quench times are significantly too short. The results also show a significant over-prediction of the reflood heat transfer and the vapour temperatures. The void profile downstream the quench front is not correctly predicted either. Finally, the present reflood model does not properly reflect the effects of spacer grids on the reflood heat transfer.In spite of these deficiencies the improvements incorporated into RELAP5/MOD3.2 by the Paul Scherrer Institute (PSI) eliminated the unphysical behaviors such as continuous cooling without clear turn-around temperature and no visible quenching phenomena, which were shown in the reflood calculations by means of the RELAP5/MOD3.1 code.     

The quenching behavior of aqueous nanofluids around rods with high temperature

The quenching behavior of aqueous nanofluids containing various volume fractions of Al₂O₃, SiO₂, TiO₂ and CuO nanoparticles is experimentally investigated around high temperature brass rod (diameter 20 mm × 75 mm). The experiments are performed at saturated conditions under atmospheric pressure. The results show that the quenching process is strongly dependent on the kind of nanoparticle, as well as its volume fraction. Although it is not observed from the first run in nanofluids, the quenching time is considerably shortened during the repetitive quenching tests. After the repetition tests in nanofluids, a nanoparticles porous layer occurs on the quenched surface and thus, the film boiling vanishes. The surface contact angles and the surface roughness of the quenched surfaces are measured. The results show that contact angles decreases and the surface roughness increases. It can be concluded that the primary reason of critical heat flux enhancement is the change of the surface characteristics due to the porous layer. In addition, the results also showed that there is no significant change in the nucleate boiling heat transfer.     

Simple heat transfer model for laminar film condensation in a vertical tube

A new physical model for estimating the liquid film thickness and condensation heat transfer coefficient in a vertical tube, considering the effects of gravity, liquid viscosity, and vapor flow in the core region, is proposed. In particular, for calculating the velocity profile in the liquid film, the liquid is assumed to be in Couette flow forced by the interfacial velocity at the liquid-vapor interface. The interfacial velocity is calculated using an empirical power-law velocity profile. The film thickness and heat transfer coefficient from the new model are compared with existing experimental data and the original Nusslet condensation theory. The new model describes the liquid film thinning effect due to the vapor shear flow and predicts the condensation heat transfer coefficient from experiments reasonably well.     

Understanding decomposition by thermal plasma with supersonic expansion quench

CO2 pyrolysis by thermal plasma was investigated,and a high conversion rate of 33％ and energy efficiency of 17％ were obtained.The high performance benefited from a novel quenching method,which synergizes the converging nozzle and cooling tube.To understand the synergy effect,a computational fluid dynamics simulation was carried out.A quick quenching rate of 107 K s 1 could be expected when the pyrolysis gas temperature decreased from more than 3000 to 1000 K.According to the simulation results,the quenching mechanism was discussed as follows:first,the compressible fluid was adiabatically expanded in the converging nozzle and accelerated to sonic speed,and parts of the heat energy converted to convective kinetic energy;second,the sonic fluid jet into the cooling tube formed a strong eddy,which greatly enhanced the heat transfer between the inverse-flowing fluid and cooling tube.These two mechanisms ensure a quick quenching to prevent the reverse reaction of CO2 pyrolysis gas when it flows out from the thermal plasma reactor.     

A 2D numerical simulation of sub-cooled flow boiling at low-pressure and low-flow rates

The main purpose of this study is to apply a two-fluid mathematical model to numerical simulation of two-phase flow at low-pressure condition. Although models of sub-cooled boiling flow at one-dimension and high-pressure have been studied extensively, there are few equivalent studies for numerical simulation at two-dimension and low-pressure (1-2 bar) conditions. Recent literature studies on sub-cooled boiling flow at low-pressure have shown that empirical models developed for high-pressure situations are not valid at low-pressures. Since the mathematical model used in this study is accomplished at low-pressure, the transport equations for the variables of each phase are substituted in low-pressure. The governing equations of two-phase flow with an allowance to inter-phase transfer of mass, momentum and heat, are solved using a two-fluid; non-equilibrium model. The finite volume discretization scheme is used to create a linearized system of equations that are solved by SIMPLE staggered grid solution technique for a rectangular channel. Improvement of the void fraction prediction of our model for the case of low-pressure sub-cooled flow boiling conditions was achieved. It is found that the heat transfer due to evaporation and surface quenching is higher than that by convection. Good agreement is achieved with the predicted results against the experimental data’s available in the literatures for a number of test cases.     

Possible design of PBR for passive decay heat removal

Conditions for design parameters of above-ground and underground, prismatic high-temperature gas-cooled reactor (HTGR)s for passive decay heat removal based on fundamental heat transfer mechanisms were obtained in the previous works. In the present study, analogous conditions were obtained for pebble bed reactors by performing the same procedure using the model for heat transfer in porous media of COMSOL 4.3a software, and the results were compared. For the power density profile, several approximated distributions together with original one throughout the 10-MWt high-temperature gas-cooled reactor-test module (HTR-10) were used, and it was found that an HTR-10 with a uniform power density profile has the higher safety margin than those with other profiles. In other words, the safety features of a PBR can be enhanced by flattening the power density profile. We also found that a prismatic HTGR with a uniform power density profile throughout the core has a greater safety margin than a PBR with the same design characteristics. However, when the power density profile is not flattened during the operation, the PBR with the linear power density profile has more safety margin than the prismatic HTGR with the same design parameters and with the power density profile by cosine and Bessel functions.     

Numerical computation of a reactor vessel melting under external cooling conditions

Numerical computations are performed for melting and natural convection in the liquefied region of a reactor vessel under external cooling to find more thermal margin for in-vessel retention. Existing typical experiment and calculations for gallium melting are used for the validation. The transient flow field in the liquefied region and the melt front movement analyzed are compared with those from finite-element and finite-volume methods. Reasonable agreements are achieved with respect to melt progression and flow configuration in the liquefied zone. A three-dimensional geometrical model for an azimuthally 3° angular section of the APR1400 pressurized water reactor vessel is prepared based on this verification, and a conservative heat flux profile from the corium inside with a concentrated heat flux from the metallic layer of 2.1 MW/m², which is greater than maximum critical heat flux, is applied to the vessel model assuming constant exterior temperatures of 400 and 1000 K. The results show that even though the vessel inside heat flux is much greater than the critical heat flux, this does not intensively melt a vessel due to combined effects of latent heat absorption during the melting and the remaining heat spreading through the entire vessel.     

Transient pool boiling heat transfer during rapid cooling under saturated water condition

The transient pool boiling heat transfer during rapid cooling was investigated under the saturated water condition. The quenching method was applied, and the vertical rodlet was used as the test specimen. The effects of material property, test specimen size, groove structure, and chromium coating were studied. The small heat capacity and small volume-to-area ratio (VAR) made the quenching duration shorter. In the groove-structured test specimen, the vapor film on the structured portion collapsed earlier than on the plain portion, which could be due to the small local VAR of the structured portion. It caused the groove-structured test specimen to exhibit a shorter quenching duration than the plain test specimen, though both test specimens had almost the same averaged VAR. This implies that the quenching duration and position of the vapor film rupture can be actively controlled by the surface structure. The influence of chromium coating on the quenching duration was preliminarily tested using niobium for accident tolerant fuel (ATF) application in a nuclear light water reactor. The chromium-coated niobium test specimen exhibited a somewhat longer quenching duration than the non-coated one.     

Dependency of Doppler Factors on Resonance Self-Shielding Factors for Gold and Silver

A simple model was developed to evaluate the effect of the radial power profile on the thermo-hydraulics in the core during reflood phase of loss-of-coolant accident in PWRs. It was incorporated into REFLA code, a reflood analysis code.

The model assumes that the fluid mixes completely among subchannels and additionally that the fuel temperature is not affected each other among fuels. This model is featuring no three-dimensional treatment for the evaluation on effect of the radial power profile.

The model improved the predictability of clad temperature and gave a better prediction than a method which is generally used in the safety analysis. The model predicted a poorer core cooling in high radial power region than data. The error of the prediction increased with the increase in radial power ratio. These indicates the conservativeness of the model on the maximum clad temperature prediction. The reason of the conservativeness is due to the neglection of the heat transfer enhancement by two-dimensional effect in high power region.     

Understanding CO_2 decomposition by thermal plasma with supersonic expansion quench

CO_2 pyrolysis by thermal plasma was investigated,and a high conversion rate of 33% and energy efficiency of 17% were obtained.The high performance benefited from a novel quenching method,which synergizes the converging nozzle and cooling tube.To understand the synergy effect,a computational fluid dynamics simulation was carried out.A quick quenching rate of 10~7Ks(-1) could be expected when the pyrolysis gas temperature decreased from more than 3000 to 1000 K.According to the simulation results,the quenching mechanism was discussed as follows: first,the compressible fluid was adiabatically expanded in the converging nozzle and accelerated to sonic speed,and parts of the heat energy converted to convective kinetic energy; second,the sonic fluid jet into the cooling tube formed a strong eddy,which greatly enhanced the heat transfer between the inverse-flowing fluid and cooling tube.These two mechanisms ensure a quick quenching to prevent the reverse reaction of CO_2 pyrolysis gas when it flows out from the thermal plasma reactor.     

Quench front propagation during bottom reflooding of a heated annular channel

A time-dependent two-dimensional conduction model of quenching, via bottom reflood, of hot, dry cylindrical tube of finite length in an annulus is presented. The method of finite integral transform is used in the solution. Multiregion heat transfer is considered at the heater surface, and no a priori assumption is made in regard to the quench front velocity. A possible mode of variation of the quench temperature with coolant inlet velocity is proposed. Predictions of the quench front velocity are compared with a few experimental data for Zircaloy-2 tube available in the literature.     

Innovative production of nuclear fuel by microwave internal gelation: Heat transfer model of falling droplets

Based on closed packed microspheres produced by internal gelation, the Sphere-pac concept provides a safer and cleaner process and better remote production capability compared to the traditional production of nuclear fuels. Whereas classical reactor fuel rods are fed with UO₂ pellets, this advanced concept is suggested for minor actinide bearing fuels.This paper focuses on the thermal analysis of the microspheres during their preparation by microwave-assisted internal gelation (MIG). Internal gelation is a sol-gel process initiated by a temperature shift within aqueous droplets. Alternatively this critical temperature increase takes place by contact heat transfer from a hot silicon-oil bath. Microwave heating of the droplets during their free fall provides a simpler and cleaner process, where the experimental parameters have to be carefully optimized.A matlab model is developed to study the thermal behaviour of a droplet during processing inside a microwave resonant cavity. This finite elements model takes into account the most relevant parameters (size of droplet, thermal properties of the solution, heat and mass transfer …) and calculates the temperature profile inside the droplet. The model is validated with experimental data from literature. The influence of each parameter on the temperature profile is investigated and the optimal microwave power can then be determined and applied to the production unit.