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.     

Discussion of heat transfer phenomena in fluids at supercritical pressure with the aid of CFD models

The paper discusses heat transfer enhancement and deterioration phenomena observed in experimental data for fluids at supercritical pressure. The results obtained by the application of various CFD turbulence models in the prediction of experimental data for water and carbon dioxide flowing in circular tubes are firstly described. On this basis, the capabilities of the addressed models in predicting the observed phenomena are shortly discussed.     

Experimental investigation on heat transfer from a heated rod with a helically wrapped wire inside a square vertical channel to water at supercritical pressures

A supercritical water heat transfer test section has been built at Xi’an Jiaotong University to study the heat transfer from a 10 mm rod inside a square vertical channel with a wire-wrapped helically around it as a spacer. The test section is 1.5 m long and the wire pitch 200 mm. Experimental conditions included pressures of 23–25 MPa, mass fluxes of 500–1200 kg/m² s, heat fluxes of 200–800 kW/m², and inlet temperatures of 300–400 °C. Wall temperatures were measured with thermocouples at various positions near the rod surface. The experimental Nusselt numbers were compared with those calculated by empirical correlations for smooth tubes. The Jackson correlation showed better agreement with the test data compared with the Dittus-Boelter correlation but overpredicted the Nusselt numbers almost within the whole range of experimental conditions. Both correlations cannot predict the heat transfer accurately when deterioration occurred at low mass flux and relatively high heat flux in the pseudocritical region. Comparison of experimental data at two different supercritical pressures showed that the heat transfer was more enhanced at the lower supercritical pressure but the deterioration was more likely to occur at the higher pressure, meaning increased safety. Based on a comparison with an identical channel without the helical wrapped wire, it was found that the wire spacer does not enhance the heat transfer significantly under normal heat transfer conditions, but it contributes to the improvement of the heat transfer in the pseudocritical region and to a downstream shift of the onset of the deterioration. The Jackson buoyancy criterion is found to be valid and works well in predicting the onset of heat transfer deterioration occurring in the experiments without wire.     

垂直加热通道内超临界水流动稳定性参数敏感性分析

给出了无量纲分析法与频域法相结合的稳定性分析方法的详细描述,并定义了影响稳定性的关键无量纲数。针对垂直加热通道内超临界水进行了密度波稳定性分析,并建立了稳定性边界。对系统入口阻力因数、出口阻力因数、摩擦因数、进出口压降和流动方向等进行了参数敏感性分析,结果表明高的入口阻力因数有利于系统的稳定,但高的出口阻力因数和高的摩擦因数不利于系统的稳定,系统进出口压差对系统的稳定性影响较小,向上流动比向下流动更有利于系统的稳定。计算结果对超临界水堆的堆芯和系统设计具有指导性作用。     

Sensitivity analysis of numerically determined linear stability boundaries of a supercritical heated channel

The large change in density which occurs when supercritical water is heated above or near to the pseudocritical temperature in a vertical channel can result in the onset of flow instabilities (density wave oscillations). Near to the critical point, substance properties such as enthalpy, density, viscosity, etc. all have larger relative uncertainties compared to subcritical conditions. The goal of this study is to quantify the effect of these property uncertainties and system uncertainties on numerically determined stability boundaries. These boundaries were determined through an eigenvalue analysis of the linearised set of equations. The sensitivity analysis is performed in a forward way. The results show that the impact of the density and viscosity tolerance individually as well as that of the uncertainty of the imposed pressure drop are negligible. The tolerance on the derivative of the density with regard to the enthalpy propagates only noticeably at low N_SUB numbers (T_in > 370 °C). The friction factor and the heat flux distribution uncertainties have a comparable effect, being more pronounced near the bend in the stability curve. The most significant uncertainty was found to be that of the geometry, even a ±25 μm uncertainty on length scales results in a large uncertainty. The results also showed that the stability boundary is linked to the friction distribution rather than its average value, and that different correlations result in strong changes of the predicted boundary. This emphasizes the need for an accurate friction correlation for supercritical fluids. These findings are important to assess the design of experimental facilities which use scaling fluids.     

CFD analysis of thermal-hydraulic behavior of supercritical water in sub-channels

Investigations on the thermal-hydraulic behavior in the supercritical water-cooled reactor (SCWR) fuel assembly have obtained a significant attention in the international SCWR community. However, there is still a lack of understanding and ability to predict the heat transfer behavior of supercritical fluids. In this paper, computational fluid dynamics (CFD) analysis is carried out to study the thermal-hydraulic behavior of supercritical water flows in sub-channels of a typical SCWR fuel assembly using commercial CFD code CFX-5.6. Three types of sub-channels, e.g. regular sub-channel, wall sub-channel and corner sub-channel, are analyzed. Effects of various parameters, such as boundary conditions and pitch-to-diameter ratios, on the mixing phenomenon in sub-channels and heat transfer are investigated. The turbulent mixing in tight lattice (P/D = 1.1) is lower than that in wide lattice (P/D > 1.1), whereas, the effect of pitch-to-diameter ratio on the turbulent mixing is slight at P/D > 1.1. The amplitude of turbulent mixing in wall sub-channel is slightly higher than that in regular sub-channel and is close to that in corner sub-channel. The mixing coefficient in the sub-channel at P/D ≥ 1.2 is in the range from 0.022 to 0.028. The results also show unusual behavior of turbulent mixing in the vicinity of the pseudo-critical point, and further investigation is needed. The mass mixing due to cross flow in wall sub-channel is much stronger than that in regular sub-channel at a same pitch-to-diameter ratio. The mass mixing in wall and regular sub-channels, especially at small pitch-to-diameter ratio, brings an unfavorable feedback to the heat transfer and strengthens the non-uniformity of the circumferential distribution of heat transfer. The strong mass mixing in corner sub-channel should be paid attention.     

On the analogies in the dynamic behaviour of heated channels with boiling and supercritical fluids

In this paper, the origin and the consequences of a new dimensionless formalism recently introduced for analysing the dynamic behaviour of heated channels with fluids at supercritical pressures are discussed. A unified view of boiling and supercritical fluid instabilities is proposed, basing on the argument that, despite the strong differences in their operating conditions, in both cases the relevant dynamics results from the changes in density that the fluid undergoes along the channel.The discussion is presently supported only by modelling, performed both by a simplified program and a system code; however, considering the complete independence of these modelling tools, the close agreement observed between their results provides a reasonable level of confidence in the proposed conclusions.Interesting thermodynamic relationships, devised as a by-product of the introduction of the new dimensionless parameters, are also presented, in the aim to stimulate further studies capable to provide greater insight into the fascinating aspects raised by recognising the intimate similarity of these two classes of phenomena, which have such a remarkable relevance for present and future nuclear reactor technology.     

Dimensionless parameters in stability analysis of heated channels with fluids at supercritical pressures

The paper proposes dimensionless parameters for the analysis of stability in heated channels with supercritical fluids. The parameters are devised basing on the classical phase change and sub-cooling numbers adopted in the case of boiling channels, proposing a novel formulation making use of fluid properties at the pseudo-critical temperature as a function of pressure. The adopted formulation for dimensionless density of a given fluid provides a unique dependence with respect to dimensionless enthalpy, in a reasonably wide range of system pressures, thus giving generality to the predictions of unstable conditions obtained as a function of dimensionless parameters. It is shown that these parameters allow setting up quantitative stability maps for a single heated channel with imposed overall pressure drop, in analogy with the ones proposed in previous work concerning boiling channels. Similarities with the boiling channel stability phenomena are pointed out, also supporting the conclusions with system code predictions.     

Discussion on the stability of heated channels with different fluids at supercritical pressures

The paper extends previous work on the stability of heated channels with fluids at supercritical pressure as predicted by available models.A set of dimensionless numbers proposed to predict the threshold of instabilities is further discussed to highlight their capabilities and possible improvements. In particular, it is shown that the choice made for the reference value of the derivative of specific volume with respect to specific enthalpy is justified as an extension of classical formulations adopted for boiling channels. Moreover, the degree of universality to be expected by the use of these dimensionless numbers while using different fluids is clarified; in this aim four different fluids are considered: water, carbon dioxide, ammonia and refrigerant R23.In order to provide a clear perspective of the usefulness of the proposed dimensionless numbers for dealing with different fluids, linear stability maps generated by a previously developed in-house code, making use of balance equations in dimensionless form, are then compared with the results obtained by computations performed in dimensional terms. In this aim, both an in-house code and RELAP5 are used. The reference considered system is a long circular channel with uniform heating and no singular pressure drops, already addressed in previous analyses, here assumed both in vertical upward and in horizontal flow conditions. The comparison of the predictions obtained for the different fluids allows to ascertain the level of applicability of the dimensionless numbers and, as an interesting by-product, confirms the possibility to encounter static instabilities also in systems at supercritical pressure.     

Computational estimate of the corrosion resistance of fuel microelements with silicon carbide cladding in a water medium at supercritical pressure

A computational estimate of the corrosion resistance of a silicon carbide coating on spherical fuel microelements in a supercritical-pressure water medium at 350–700°C is made for the nominal operating regime of the core of a light-water nuclear reactor. A model of the thermal dissociation of water and dissolution of a silicon oxide film is used to estimate the corrosion resistance of silicon carbide. An expression describing the dependence of the corrosion depth of a silicon carbide layer on the temperature and pressure of the medium (concentration of the products of dissociation of water) and the operating time of the fuel microelements is obtained on the basis of the model developed. __________ Translated from Atomnaya énergiya, Vol. 102, No. 3, pp. 168–173, March, 2007. An erratum to this article is available at .     

Theoretical study of flashing and water hammer in a supercritical water cycle during pressure drop

During a loss of coolant accident (LOCA) the pressure of the coolant can drop significantly in the vicinity of the leak. It will be shown that unlike in pressurized water reactors (PWRs) where this pressure drop can cause only sudden vaporization - also called flashing - in supercritical water cooled reactors (SCWRs) it can cause sudden condensation (condensation-induced water hammer), too. The reason is that from supercritical state the system can go to metastable liquid as well as to metastable vapour state after LOCA. Relaxation from metastable fluid states is a fast process, followed by a local positive or negative pressure-jump, which might increase the damage around the leak. Conservative estimation will be given for the magnitude of these pressure jumps caused by the flashing or water hammer by assuming various initial pressure losses. In our calculations, three different equations of state are used: the simple van der Waals EoS; the Redlich-Kwong as an empirical development; and the more sophisticated non-cubic Deiters equation of state. These equations are able to describe metastable states qualitatively but with different accuracy. These calculations can help us to map the local immediate effect of any sudden pressure drop and therefore it can help to design better safety protocols.     

The light water integral reactor with natural circulation of the coolant at supercritical pressure B-500 SKDI

Pressure increase in the primary circuit over the critical value gives a possibility to construct the B-500SKDI (500 MWe) lightwater integral reactor with natural circulation of the coolant in the vessel with a diameter less than 5 m. The given reactor has a high safety level, simple operability, its specific capital cost and fuel expenditure being lower as compared to a conventional PWR. The development of the B-500SKDI reactor is carried out taking into consideration verified technical decisions of current NPPs on the basis of Russian LWR technology.     

Analysis of the unstable behaviour of a single-phase natural circulation loop with one-dimensional and computational fluid-dynamic models

This paper discusses the results obtained using one-dimensional and three-dimensional computational fluid-dynamic codes for the prediction of the dynamic behaviour observed in experiments carried out in a single-phase natural circulation apparatus. The loop is made of glass and is equipped with vertical and horizontal heaters and coolers that can be separately operated, thus obtaining different working configurations.     

CFD code application: calculating heat transfer in a reactor with supercritical parameters

Thermohydraulic calculations of isolated and communicating cells of a rod bundle were performed by the channel method for CANDU-X fuel assemblies and by a three-dimensional method. It was established that in solving the problem for the tightest cell in the case q = const the azimuthal nonuniformity of the temperature was found to decrease by 77°C but it too was inadmissibly large. The temperature distribution along the surface of a fuel element in the case q = const was found to be different from the solution of the adjoint problem. A region with elevated coolant temperature, impeding heat exchange between two neighboring cells, was found between two adjoining cells. It was found that to evaluate computational reliability an experimental study must be performed on rod assemblies with supercritical coolant parameters.     

Temperature-viscosity induced laminar instabilities in a gaseous heated channel

Laminar flow instability exhibits itself as a flow rate excursion in single isolated tubes having negative pressure-drop-flow-rate derivative at constant heat addition in a gas which has a viscosity increasing with temperature in the laminar Reynolds number range. An application is in laminar flow nuclear rocket reactors. The constitutive equations for such a system were solved using seven different forms of the energy equation in a steady state isolated channel. An equation for flow rate at neutral stability is given. Parametric results are presented for a range of heat flux, flow rate and fluid state conditions. Closed form solutions and existing experimental findings were verified using numerical analysis.     

The effect of low-concentration inorganic materials on the behaviour of supercritical water

Supercritical water is a promising working fluid in the new Generation IV nuclear power plants. Due to the presence of the pseudo-critical line, the thermo-hydraulics (thermal and flow properties) and the physical chemistry of the supercritical water differ significantly from the pressurized hot water used in pressurized water reactors. In this study we would like to analyse the effect of small amount of inorganic material on the thermo-hydraulics of the supercritical water cooled nuclear reactors and other, non-nuclear supercritical water loops.     

Analysis of Ledinegg flow instability in natural circulation at supercritical pressure

Since the thermophysical properties of water change dramatically at near-critical and pseudocritical point, the instability of natural circulation at supercritical pressure may occur in a loop. To predict the region of instability of natural circulation at supercritical pressure, a test loop was built at Tsinghua University. The paper presents the information of the test loop and a numerical analysis model for the loop. The paper verified the numerical analysis code by experiment results and using the code to analyze the instability of the loop. The paper concludes conclusion that there will be no Ledinegg instability occurring at supercritical pressure in the loop.