Stability analysis of a uniformly heated channel with supercritical water

The thermal-hydraulic stability of a uniformly heated channel at supercritical water pressure has been investigated to help understand the system instability phenomena which may occur in supercritical water nuclear reactors (SCWRs). We have extended the modeling approach often used for the stability analysis of phase change systems to supercritical pressure operation conditions and have developed rigorous new non-dimensional groups for the stability maps. We have also shown that while density-wave oscillations (DWO) can occur, Ledinegg excursive instabilities and pressure drop oscillations (PDO) will not occur in supercritical water systems. The linear stability characteristics of a typical uniformly heated channel were computed by evaluating the eigenvalues of a one-dimensional model. An analysis of non-linear instability phenomena was also performed in the time domain and the dynamic bifurcations were evaluated.     

Assessment of flow stability boundaries in a heated channel with different fluids at supercritical pressure

This paper presents results on the stability of a simple heated channel containing fluids at supercritical pressure with an external imposed pressure drop. Basing on a recent work that discussed stability characteristics in a fluid-to-fluid comparison perspective, additional data are presented in order to discuss relevant parametric effects, also including a more accurate fluid-to-fluid comparison.Three different analysis tools, including a system code and in-house linear and transient analysis programs, were adopted to evaluate stability thresholds at different channel throttling conditions and orientations; four different supercritical fluids were considered. The diversity of the adopted tools and the good level of agreement observed in the comparison of their results provide adequate confidence on the general reliability of the obtained information.Among the addressed phenomena, both Ledinegg and density-wave oscillations are considered, pointing out a fundamental continuity between the two phenomena that occur in adjoining regions of the parameter space. Numerical effects are also highlighted, quantifying the impact of truncation error occurring in the use of system codes in the analysis of flow instabilities. The results obtained by different fluids provide further support to the conclusion that, when an appropriate dimensionless formalism is used, the differences obtained in the stability behaviour at imposed heat flux are relatively small for a number of fluids of interest for experimental analyses.     

Experimental study on the density wave oscillation in parallel rectangular channels with narrow gap

An experimental investigation was performed on the density wave oscillation (DWO) with two parallel rectangular channels, which have a cross section of 25 mm × 2 mm and a heated length of 1000 mm. Test parameters are 1 MPa to 10 MPa for pressure, 200–800 kg/m² s for mass velocity, and 10–50 °C for inlet subcooling. The results show that in general the flow becomes more stable while mass velocity, pressure, and inlet subcooling are increased. The period of oscillation becomes shorter if mass velocity is increased or inlet subcooling is decreased. Pressure has little effect on period of the DWO in this research. The dimensionless subcooling number N_sub and phase change number N_pch were adopted to compare results from rectangular channels with those from round tubes. The comparison indicates that the data from rectangular channels agree with those from the round tubes. The RELAP5 software was used to simulate the DWO in rectangular channels. The prediction show good consistency with experimental phenomenon. However, different two-phase flow model behaves differently when pressure changes in prediction.     

Theoretical Study of Two-Phase Flow Oscillation in a Hot Channel, (II)

The kinetic behavior of two-phase flow is considered by conventional linear control theory. This study considers only the essential factors so as to simplify the interpretation of the mechanisms involved in the observed phenomena. A change in heat flux due to a change in coolant velocity is taken into account to study the influence of heat transfer characteristics on the flow stability. While this influence has not appeared as clearly as in the previous numerical experiment⁽¹⁾, agreement was obtained with measurements reported from RWD RL.     

An analysis of interacting instability modes, in a phase change system

This paper presents an analysis of the interaction of pressure-drop oscillations (PDO) and density-wave oscillations (DWO) for a typical NASA type phase change system. A transient lumped parameter model is developed for use in the analysis of the dynamics of this type of system. A compressible volume (e.g., an accumulator vessel) dynamics model was also developed and PDO/DWO interactions are investigated.     

Thermal-hydraulic modeling and analysis of a tank in pool reactor for normal operation and loss of flow transient

A transient thermal-hydraulic model entitled Tank in Pool Reactor Thermal-Hydraulic Analysis (TPRTHA) has been developed to simulate the steady-state operation and loss of flow transient for a tank in pool type research reactor. The model solves the momentum equation, energy equation and general conduction equation in cylindrical coordinates in order to predict the coolant velocity, coolant temperature and fuel rod temperature distribution respectively. The analytical solution is utilized for steady-state calculation while the finite difference technique with implicit scheme is adopted for transient calculation. The model divides the active core into a specified axial regions and the fuel rod into a specified radial zones, then a nodal calculation is performed for both average and hottest rods with a chopped cosine shaped heat generation flux. The model also predicts the heat flux leading to onset of nucleate boiling and the critical heat flux as well as the flow inversion phenomenon. The model is used to simulate a 2 MW reactor with downward flow direction and different types of fuel bundles of different powers and different flow rates. The best-estimate thermal-hydraulic safety margins are determined and the model results are analyzed and discussed.     

Bubble Lift-off Diameter and Nucleation Frequency in Vertical Subcooled Boiling Flow

A series of experiments were carried out to investigate phenomena from bubble nucleation to lift-off for a subcooled boiling flow in a vertical annulus channel. A high-speed digital video camera was used to capture the bubble dynamics. The bubble lift-off diameter and bubble nucleation frequency were evaluated in terms of heat flux, mass flux, and degree of subcooling. The fundamental features of the lift-off diameter and nucleation frequency (i.e., the variations across nucleation sites and the dependence on the flow and heat flux conditions) were addressed based on the present observation. A database for the bubble lift-off diameter was built by gathering and summarizing the data of Prodanovic et al., Situ et al., and the present experiments. We evaluated the predictive capabilities of Unal's model, Situ et al.'s model, and Prodanovic et al.'s correlation against the database. We obtained the best prediction results by modifying the wall superheat correlation in Unal's model. In addition, we suggested a new correlation for a combined parameter of the bubble nucleation frequency and bubble lift-off diameter.     

Characteristic features of the radiolysis of water irradiated under strictly fixed conditions and under conditions varying over a small range

A qualitative mathematical analysis of the system of differential equations that describes the radiolysis of pure water and water solutions of hydrogen, hydrogen peroxide, and oxygen is performed. It is established that in a closed volume with fixed values of external parameters (dose rate, temperature, and others) a steady state characterized by a stable singular point-type attractor is unavoidably reached. The type of attractor does not depend on the values of the external parameters, i.e., in principle the system possesses self-regulation properties with respect to them. It is shown that under real conditions, when the external parameters cannot be strictly fixed, the existence of a stationary state and a stationary concentration of the products of radiolysis of water are determined not only by the specific values of the external parameters but also by their variation in the time required to establish a stationary state. 3 figures, 1 table, 10 references. OKB “Gidropress.” Translated from Atomnaya énergiya, Vol. 87, No. 1, pp. 39–48, July, 1999.     

Evaluation of Cooling Capability in a Heated Narrow Flow Passage

A numerical method for the thermal hydraulic phenomena in a narrow flow passage is developed to evaluate the gap cooling capability. Based on a drift flux model, the two-dimensional gas-liquid two-phase flow in the annular and hemispherical heated narrow flow passages is modeled. The drift velocity correlation is combined with the flooding correlation, which describes physical phenomena under cooling limits. Experiment on thermal hydraulic phenomena in the heated narrow flow passage is performed. Boiling two-phase flow behavior and dryout phenomena are observed. The critical heat flux data is obtained from measurement of the heating surface temperature. Counter-current two-phase flow, which is a key phenomenon in the gap cooling mechanism, is reproduced by the numerical analysis appropriately. The critical heat flux is predicted by assuming that deficiency of the liquid supply against the gas upward flow leads to occurrence of dryout. Validity of the newly developed numerical method is demonstrated through comparison of the predicted critical heat flux with the present and existing data in the gap width range from 0.5 to 5 mm and the pressure range from 1 to 50 bar.     

窄通道自然循环临界热流密度的非线性分析

通过自然循环流动实验,取得5 mm间隙窄矩形通道的自然循环临界热流密度（CHF）发生时的可视化图片,以及流量、壁温和实验段压差信号,并运用非线性分析技术对CHF发生过程进行了定性和定量研究。研究发现：自然循环压差时间序列的功率谱在半对数坐标中呈指数下降;自相关系数逐渐下降;三维吸引子相图表现出奇怪吸引子的特点。这表明了自然循环系统CHF的发生过程具有非线性混沌特性。自然循环CHF发生的初始阶段,由于流量脉动和流型往复变迁,流动和换热表现出一定的周期性;随着热流密度的提高,周期性减小,随机性增大,但总能达到一个确定的状态,体现了混沌运动的特点。     

Frequency of Undulations on a Falling Water Film

An experimental study has been undertaken on the frequency of presented by the undulations occurring on the surface of a falling liquid film. The configuration of the film surface was observed by measuring the changes in the film thickness by means of a capacitometer. The flow regime was in the range of turbulent flow region, in which the undulations occur prominently and travel down along with the fluid film. The undulations proceed downward in an almost fixed pattern. The frequency of the passage of crests observed from a fixed point was evaluated from power spectral analysis to be about 20–30Hz, and this value changed very little with the Reynolds number and with heat flux applied to the falling liquid film. It is shown that this constancy of observed frequency is related to the fact that the large undulations move at the same velocity as the bulk of the fluid film, and that the speed of propagation is corresponding to a group velocity for ripples on the film surface.     

Two-phase instability analysis in natural circulation loops of China advanced research reactor

In this paper, two-phase flow instability in natural circulation loops of China Advanced Research Reactor (CARR) has been investigated. CARR is a low pressure and low power density research reactor. A natural circulation instability analysis model is developed for the natural circulation loop of CARR. The homogeneous flow model is used to establish the system control equations. The non-uniform heating and subcooled boiling heat transfer is included. The accumulation heat of the wall is also included. Numerical method of Gear is employed to solve the system equations documented in terms of ordinary differential equations. According to the calculation results, stability maps of the natural circulation loop, which confirm the presence of an instability region under the conditions of low equilibrium quality in the outlet and low pressure, are obtained. It is a special kind of density wave oscillation (DWO) that occurs in very low equilibrium quality region with the characteristics of geysering and ‘Type-I’ DWO at the same time. The calculation results show such oscillation course clearly. The variations of the mass flow rate, the pressure drop and the boiling boundary are analyzed separately. Especially, the phase-space trajectory of the boiling boundary and the mass flow rate is discussed. Finally the oscillation frequency is discussed. The calculated results have important significance for the safety operation and accidental analysis of CARR.     

Development of Discrete Ordinates SN Code in Three-Dimensional (X,Y, Z) Geometry for Shielding Design

A discrete ordinates transport code ENSEMBLE in (X, Y, Z) geometry has been developed for the purpose of shielding calculations in three-dimensional geometry. The code has some superior features, compared with THREETRAN which is the only code of the same kind so far developed. That is, the code can treat higher order anisotropic scattering and employs a coarse mesh rebalancing method. Moreover it has a negative flux fix-up routine using a variable weight diamond difference equation scheme and has a ray-effect fix-up option using a fictitious source based on S_N→P_N-1 conversion technique. Formulations for these advanced features in three-dimensional space have been derived.

As the demonstration of the capabilities of the code, several numerical analyses and an analysis of an annular duct streaming experiment in JRR-4 at Japan Atomic Energy Research Institute, have been performed.

As a result of these analyses, confirmation has been obtained for the prospect of applicability of ENSEMBLE to practical shielding design.     

ASTEC application to in-vessel corium retention

This paper summarizes the work done in the SARNET European Network of Excellence on Severe Accidents (6th Framework Programme of the European Commission) on the capability of the ASTEC code to simulate in-vessel corium retention (IVR). This code, jointly developed by the French Institut de Radioprotection et de Sûreté Nucléaire (IRSN) and the German Gesellschaft für Anlagen und Reaktorsicherheit mbH (GRS) for simulation of severe accidents, is now considered as the European reference simulation tool.First, the DIVA module of ASTEC code is briefly introduced. This module treats the core degradation and corium thermal behaviour, when relocated in the reactor lower head. Former ASTEC V1.2 version assumed a predefined stratified molten pool configuration with a metallic layer on the top of the volumetrically heated oxide pool. In order to reflect the results of the MASCA project, improved models that enable modelling of more general corium pool configurations were implemented by the CEA (France) into the DIVA module of the ASTEC V1.3 code.In parallel, the CEA was working on ASTEC modelling of the external reactor vessel cooling (ERVC). The capability of the ASTEC CESAR circuit thermal-hydraulics to simulate the ERVC was tested. The conclusions were that the CESAR module is capable of simulating this system although some numerical and physical instabilities can occur. Developments were then made on the coupling between both DIVA and CESAR modules in close collaboration with IRSN. In specific conditions, code oscillations remain and an analysis was made to reduce the numerical part of these oscillations. A comparison of CESAR results of the SULTAN experiments (CEA) showed an agreement on the pressure differences.The ASTEC V1.2 code version was applied to IVR simulation for VVER-440/V213 reactors assuming defined corium mass, composition and decay heat. The external cooling of reactor wall was simulated by applying imposed coolant temperature and heat transfer coefficient (HTC). The obtained results (pool temperatures, heat flux distribution, reactor wall ablation) were compared with available predictions of other codes. The agreement was correct, in particular on the shape and depth of ablation, as well as the maximum heat flux in case of a thick metallic layer, while ASTEC calculated a lower maximum heat flux for a thin metallic layer.     

Comparison of ELM-Filament Mitigation Between Supersonic Molecular Beam Injection and Pellet Injection on HL-2A

On HL-2A,two different injections(supersonic molecular beam injection(SMBI)and pellet injection(PI)) are used to mitigate edge localized mode(ELM)-filament convective transport.The changes of their characteristics are studied in this paper.A high spatiotemporal resolution probe shows there are many similar phenomena,and the filament density amplitude and radial velocity are both suppressed.Our statistical results indicate that:the velocity suppression comes from the decrease of filament density and temperature;the transient particle and heat fluxes drop strongly;and long-range correlation along a magnetic flux surface also decreases,when the electron-ion collisionality increases significantly,which may have a role on the filament parallel current during ELM mitigation.     

窄矩形通道污垢沉积数值仿真

为研究窄矩形通道内CaSO4溶液由于析晶沉积产生的污垢及对换热的影响,本研究基于合理的污垢沉积、污垢剥蚀与污垢热阻模型,利用FLUENT软件结合用户自定义函数（UDF）对一定热流密度、入口流速、入口温度和流体浓度的流体进行了析晶沉积模拟计算。研究结果表明了此工质的污垢产生情况和对换热的影响,同时得到热流密度、入口流速和流体浓度3种影响因素对污垢沉积的影响：污垢热阻随热流密度增大而增大,随入口流速增大而减小,随流体浓度增大而增大。本研究可用于模拟板状燃料元件窄矩形通道由于析晶导致的污垢沉积过程。     

Transient film boiling under transient conditions related to vapor explosion (effects of transient flow and fragmentation under a shock pressure)

Two fundamental phenomena are significant when a shock pressure interacts with the large scale coarse mixing state. One is an intensive flow and the other is the surface area enhancement due to the disintegration of the hot drops. The effects of these phenomena on the transient heat transfer and behavior of vapor film under a shock pressure are investigated. Transient heat transfer of film boiling from an electrically heated platinum ribbon 2.5 mm wide and 0.15 mm thick was measured immediately after passage of a shock pressure from 0.1 to 0.7 MPa. The heater was set horizontally in a vertical shock tube which was filled with vapor liquid bubbly mixture and kept initially in the film boiling state. That is, the heater corresponds to a typical hot drop and the bubbles around it correspond to the coarse mixture around the drop. The liquid was Freon-113 with an initial void fraction in the range from 0 to 3%. When the shock wave arrives at the heater, intensive transient flow occurs due to collapse of bubbles around the heater. First, the effects of the initial void fraction, the intensity of the shock and the heated wall temperature on the transient heat fluxes and collapse of the vapor film were investigated experimentally and analytically under the shock pressure. Compared with a heated wall in the liquid alone, the transient heat flux at the heated wall increases and the collapse of the vapor film becomes easier in the bubbly mixture due to the transient flow. Effects of surface enhancement during the fragmentation process on the heat transfer rate and transient behavior of vapor film are investigated analytically by application of the newly proposed surface stretch model. It is made clear when the surface area is increasing, the vapor film is apt to collapse and the transient heat transfer is enhanced by the surface stretch.     

Heat transfer effects on flow past an impulsively started semi-infinite vertical plate with uniform heat flux

An implicit finite-difference technique is employed to derive a solution to the flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with uniform heat flux. Transient and steady-state velocity and temperature profiles, the local and average skin-friction and the Nusselt number are shown graphically. The velocity profiles at small values of time t are shown to agree with theoretical solution of the flow past an impulsively started infinite vertical plate with uniform heat flux. The effect of different parameters Pr (the Prandtl number) and Gr (the Grashof number) are studied. It is found that the number of time steps to reach steady-state depends strongly on Grashof number.     

Flow and pressure drop fluctuations in a vertical tube subject to low frequency oscillations

Heat transfer and other equipment mounted on off-shore platforms may be subjected to low frequency oscillations. The effect of these oscillations, typically in the frequency range of 0.1–1 Hz, on the flow rate and pressure drop in a vertical tube has been studied experimentally in the present work. A 1.75 m-long vertical tube of inner diameter 0.016 m was mounted on a plate and the whole plate was subjected to oscillations in the vertical plane using a mechanical simulator capable of providing low frequency oscillations in the range of 8–30 cycles/min at an amplitude of 0.125 m. The effect of the oscillations on the flow rate and the pressure drop has been measured systematically in the Reynolds number range 500–6500. The induced flow rate fluctuations were found to be dependent on the Reynolds number with stronger fluctuations at lower Reynolds numbers. The effective friction factor, based on the mean pressure drop and the mean flow rate, was also found to be higher than expected. Correlations have been developed to quantify this Reynolds number dependence.     

Experiments on flows, boiling and heat transfer in porous media: Emphasis on bottom injection

This paper deals with basic experiments conducted to analyse the effect of the particles’ shape and size distribution on intrinsic properties of porous beds as well as two-phase flow and heat transfer in these porous media.Structural, transport properties, flow laws and heat transfer with phase-change phenomena in several kinds of porous media are presented and discussed. The porosity of stacks constituted by spheres of various sizes is analysed. A variation law of the porosity as a function of the standard deviation of the particle size distribution is proposed. The porosity, tortuosity, permeability and inertial coefficient of the flow law in randomly stacked fibres are established experimentally and theoretically. The porosity of such media is found to vary from 0.35 to 0.92 according to the fibre aspect ratio. Tortuosity and Kozeny–Carman parameters are determined by both electric and hydrodynamic methods. These parameters are found to vary with the porosity of the fibrous bed. New relations of permeability and inertial coefficient are derived from experimental results. Finally, a pressure drop relation is proposed for fibrous beds.Convective boiling phenomena, with emphasis to application on bottom injection, are experimentally determined for fibrous porous media. Temperature field determination evidences the formation of three distinct zones in the porous medium: a liquid zone, a two-phase zone and a superheated zone. For higher heat flux density, a fourth zone is found in which vapour and liquid are in thermal non-equilibrium. A one-dimensional analytical model of pressure drop in two-phase configuration has been performed. Comparisons with experimental data are found in good agreement with the results of this model for moderate heat fluxes. For higher heat flux values, discrepancies are found. These cases correspond to the appearance and the evolution of the thermal non-equilibrium two-phase zone. Heat transfer characteristics at the heated walls are analysed. Formation of vapour in the neighbourhood of the heated walls has a strong influence on the heat transfer coefficient. This behaviour may be related to the critical heat flux phenomenon encountered in usual ducts.