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Validation of IVA Computer Code for Flow Boiling Stability Analysis
Abstract
IVA is a computer code for modeling of transient multiphase, multi-component, non-equilibrium flows in arbitrary geometry including flow boiling in 3D nuclear reactors. This work presents part of the verification procedure of the code. We analyze the stability of flow boiling in natural circulation loop. Experimental results collected on the AREVA/FANP KATHY loop regarding frequencies, mass flows and decay ratio of the oscillations are used for comparison. The comparison demonstrates the capability of the code to successfully simulate such class of processes.
... Analytical studies resulted in the development of models for two-phase flow instability that could be implemented in system codes [19, 20] . Two-phase flow instability was investigated using system codes by Kolev [21], Shiralkar et al. [22], and Rohde et al. [18]. The amplitude and frequency of flashing induced instability at the CIRCUS facility were studied by Schäfer and Manera [23] using ATHLET code. ...
RELAP5 is a system thermal-hydraulic code that is used to perform safety analysis on nuclear reactors. Since the code is based on steady state, two-phase flow regime maps, there is a concern that RELAP5 may provide significant errors for rapid transient conditions. In this work, the capability of RELAP5 code to predict the oscillatory behavior of a natural circulation driven, two-phase flow at low pressure is investigated. The simulations are compared with a series of experiments that were performed in the CIRCUS-IV facility at the Delft University of Technology. For this purpose, we developed a procedure for calibration of the input and code validation. The procedure employs (i) multiple parameters measured in different regimes, (ii) independent consideration of the subsections of the loop, and (iii) assessment of importance of the uncertain input parameters. We found that predicted system parameters are less sensitive to variations of the uncertain input and boundary conditions in high frequency oscillations regime. It is shown that calculation results overlap experimental values, except for the high frequency oscillations regime where the maximum inlet flow rate was overestimated. This finding agrees with the idea that steady state, two-phase flow regime maps might be one of the possible reasons for the discrepancy in case of rapid transients in two-phase systems.
... The schematic loop representation of the geometry is given in Fig. 6.2(a). Figure 6.3 shows the mass flow as a function of time, Kolev (2006). ...
The stronger the driving forces for flow processes the more stable are the resulting phenomena and vice versa. Many of the processes in nuclear thermal hydraulics are associated with low driving forces and tend to instability. This chapter presents a nonlinear stability analysis on some prominent examples in the nuclear thermal hydraulics: the flow boiling and condensation stability analysis. After a state-of-the-art review the AREVA boiling stability data for the ATRIUM 10B fuel bundle are compared with state-of-the-art predictions using the methods presented in this monograph. The classical boiling instability analysis is accomplished with the seldom-presented flow condensation stability analysis in a complex system of emergency condensers consisting of a large number of 1D condensing pipes submerged in a 3D pool. Condensation at the high-pressure side leads to all flow patterns for nearly horizontal pipes with all their instabilities. It is coupled with the 3D boiling of the secondary pool side. The complex picture is very informative for what can be expected and what has to be avoided in such designs.
Creating computer codes for numerical integration of systems of partial differential equations governing multiphase multicomponent flows is an important part of scientific activities in the last 30 years. Whatever the result of such activity is, it has to be validated for a class of practical applications. The validation is a complex process consisting of many elements. The first question asked in this case is: is the adequate equation set solved properly? To answer the question several iteration steps are necessary. The formal check whether the numerical algorithm provides the expected results is usually performed on simplified mathematical benchmarks that possess analytical solutions. Order-of-magnitude estimates and global balances that have to be fulfilled are very important in more complex cases. The verification of computer codes for more complex processes is mainly associated with an experimental data base on two different levels. The closure correlations are usually based on separate effect experiments. The system behavior in which a variety of the elements of the computer code are interacting is checked on system experiments.
Analysis was carried out to predict the threshold of instability for Ledinegg type and density wave oscillations for the Indian Advanced Heavy Water Reactor (AHWR) which is a Natural Circulation Pressure Tube Type Boiling Water Reactor. The mathematical model considers homogeneous two-phase flow and the conservation equations are solved analytically to obtain the steady state thermo-hydraulic characteristics and flow stability map. The model was applied for the AHWR concept after it had been validated with the test data obtained from a simple forced circulation loop with small parallel boiling channels and from the High Temperature Loop (PNC). The results indicate that the proposed design configuration of the AHWR may experience both Ledinegg type (static instability) and Type-I and Type-II density wave oscillations depending on the operating condition. The effects of various geometric and operating parameters on these types of instabilities were studied. It can be seen from the results that the Ledinegg type instability is suppressed with an increase in pressure and disappears when the operating pressure is higher than 0.7MPa. But the density wave instability may occur even at 7 MPa. In addition, it is found that for parallel multiple channels operating under natural circulation condition, the stability of density wave instability is not always enhanced by increasing the throttling coefficients at the inlet of channels.
The effect of gravity on the stability of a single boiling channel is studied.Experiments were performed in a natural circulation loop with a single boiling channel. A region of instability at low powers was identified. The flow evolves in a series of irregular oscillations developing a superposition of two different frequencies.The stability of the system is analyzed using a homogeneous model in the frequency domain. Such an analysis predicts a destabilizing effect of the gravity term of the momentum equation, which is characterized by the Froude number.
The main objective of this paper is to sum up the experimental and theoretical work carried out by the authors and their groups over a period of several years, demonstrating and explaining three different types of two-phase flow oscillations, namely, density-wave type, pressure-drop type oscillations and thermal oscillations, encountered in various boiling flow channel systems.
Classification of two-phase flow instabilities is summarized first. Three distinct types of two-phase flow oscillations and their mechanisms are explained. Since 1950’s with the beginning of commercialization of nuclear reactors, the interest in two-phase flow instability studies started to grow in the western countries followed by the Soviet Union and China. Hence, in the literature review, the most available work to our knowledge is cited. The results of our experimental work on transient and sustained instabilities in single, double channel, cross-connected double channel, four parallel channel and four cross-connected parallel channel upflow systems are presented. The effects of heat flux variations, inlet subcoo1ing, flow rate, inlet and exit restrictions are indicated. The effect of heat transfer augmentation on two-phase flow instabilities in a vertical single channel is also included. Numerical models which are based on the assumption of homogeneous two-phase flow and thermodynamic equilibrium of the two phases to predict both the steady state and transient behavior of forced convection boiling upflow two-phase flow in a single channel are summarized and some of the results of these solutions are presented. Two different two-phase flow models, namely a constantproperty homogeneous flow model and a variable property-flux model which are used for the prediction of the pressure-drop and density wave instability thresholds in a single boiling channel upflow system are mentioned and some of the solution results are presented.
Bifurcation analyses of the impact of the void distribution parameter C0 and the axial power profile on the stability of boiling water reactors (BWRs) are reported. Bifurcation characteristics of heated channels (without nuclear feedback) appear to be very sensitive to the axial power profile. A turning point bifurcation was detected for a (symmetrically) peaked axial power profile. This kind of bifurcation does not occur for a uniformly heated channel.
Both supercritical and subcritical Hopf bifurcations were encountered in a (nuclear-coupled) reactor system, depending on the strength of the void reactivity feedback. Subcritical bifurcations become less likely to occur as C0 is significantly larger than unity. In BWRs with a strong nuclear feedback, the oscillation amplitude of limit cycles caused by a supercritical bifurcation is very sensitive to both C0 and the axial power profile.
Instability of two-phase flow at low flow rate conditions is investigated analytically and experimentally. By applying the drift flux model, a linear analysis is conducted to study the effect of slip which is considered to play an important role at low flow rate conditions. Results obtained are compared with those of other analytical works and the reason for apparent variations is discussed. Some notes are also given on the lumped parameters which govern instability characteristics, and on the often-observed relation between the period of oscillation and the transit time.
The main objective of this paper is to present the validity of using a homogeneous flow model which predicts density-wave oscillation of water in a natural-circulation boiling-fluid channel. The seven different homogeneous flow models presented here are all based on linearized approximation, and the transient responses of the pressure drop as to the inlet flow rate are calculated by the Laplace transformation technique. The major differences between these seven models are in their heat capacities in the subcooling region and in their frictional coefficients. The test results using the analytical models are then compared with the data obtained from two different apparatuses: one apparatus is for the data in the region up to 2.94 MPa of pressure, and a second larger apparatus in the region up to 11.8 MPa of pressure. Furthermore, they are evaluated with some other authors' work to make the generalization.The model which best predicts the onset of oscillation is finally selected by carefully comparing the results of these comparisons.
A state-of-the-art one-dimensional thermal-hydraulic model has been developed to be used for the linear analysis of nuclear-coupled density-wave oscillations in a boiling water nuclear reactor (BWR). This model accounts for phasic slip, distributed spacers, subcooled boiling, space/time-dependent power distributions and distributed heated wall dynamics. In addition to a parallel channel stability analysis, a detailed model was derived for the BWR loop analysis of both the natural and forced circulation modes of operation.The model for coolant thermal-hydraulics has been coupled with the point kinetics model of reactor neutronics. Kinetics parameters for use in the neutronics model have been obtained by utilizing self-consistent nodal data and power distributions.The computer implementation of this model, NUFREQ-N, was used for the parametric study of a typical BWR/4, as well as for comparisons with existing in-core and out-of-core data. Also, NUFREQ-N was applied to analyze the expected stability characteristics of a typical BWR/4.
Natural circulation is an important passive heat-removal mechanism in both existing and next-generation light water reactors. Thermal and stability analyses are performed for a two-phase natural circulation loop. The homogeneous equilibrium model is employed to describe the two-phase flow in the loop. Subsequently, a linear stability analysis is performed in the frequency domain to establish the stability map of a natural circulation loop. The mass flow rate increases rapidly with increasing heater power until it reaches a maximum and then decreases slowly with increasing heating power. The maximum flow rate may be obtained for a riser with length and diameter two to three times that of the heater. Stability analyses indicate that in addition to the unstable region for density-wave oscillations at high power levels, there is an unstable region at low power levels. The existence of this unstable region is supported by several experimental observations. The area of the unstable region at low power levels increases with decreasing riser diameter, with increasing riser length, and with decreasing system pressure.
This paper describes the instability maps for the excursive and the density wave instabilities which may occur in an open two-phase natural circulation loop. Criteria for the excursive and the density wave instability were obtained from the steady loopwise momentum equation and the characteristic equation, respectively. A simple, one-dimensional two-phase homogeneous equilibrium flow was assumed. Heat flux, inlet subcooling, inlet- and exit-line restrictions, condenser liquid level, loop height and the heater section length were taken as parameters. The results were summarized on the instability map in the plane of vs. Nsub. The stable region appears at the lower left part of the map, bounded by two boundaries; the excursive instability region appears at the upper right part of the map. From the map, it can be readily confirmed that the dynamic stability criterion automatically satisfies the excursive stability criterion. Effects of parameters on the stability of the system were also discussed in this paper. The upper boundary of the stable region was compared with the experimental results reported previously.