Showing papers in "Nuclear Engineering and Design in 1986"

Hydrodynamic models and correlations for bare and wire-wrapped hexagonal rod bundles — Bundle friction factors, subchannel friction factors and mixing parameters

Abstract: Consistent hydrodynamic models for subchannel friction factors and mixing parameters in wire-wrapped rod bundles have been developed for use in subchannel analysis codes. Both flow regime and geometry effects are taken into account in these models. The laminar, transition and turbulent flow regimes are covered for the range of liquid metal fast breeder reactor (LMFBR) rod bundles of design interest. Correlations based on the models for the subchannel friction factor and mixing parameters are calibrated by the available world data. This data includes recent 37-pin hydrodynamic experiments with a geometry between that of typical fuel and blanket assembly design performed by the authors. Specific correlations are presented for subchannel and bundle friction factors, flow split, enhanced eddy diffusivity and the peripheral wire induced swirl velocity.

Turbulence in two-phase bubbly flow

Abstract: Two-dimensional turbulence measurements in air-water two-phase bubbly flow in a pipe using a dual-sensor hot-film anemometry are presented. In contrast to the authors' previous work, the turbulence is highly promoted by the existense of bubbles. And the data confirm the roughly isotropic behaviour for highly turbulent bubbly flow conditions. The effect of bubble-induced velocity fluctuations is discussed based on the turbulence intensity measurements and was found to increase as a 0.8 power of the void fraction. The measured turbulent shear stress shows the highest values in the wall proximity, corresponding to the maxima in the phase distribution. This reflects the enhanced turbulence energy producing there. Eddy diffusivity correlations are proposed to predict profiles of liquid velocity and turbulent shear stress. Finally, the turbulence energy spectra for axial and lateral velocity components u and v , and that for shear stress term uv are calculated, using Fast Fourier Transform techniques. Results show an augmentation of high frequency component for bubbly two-phase flow conditions. Macro and micro scales are also measured and discussed.

A systematic procedure for the incorporation of common cause events into risk and reliability models

Abstract: Common cause events are an important class of dependent events with respect to their contribution to system unavailability and to plant risk. Unfortunately, these events have not been treated with any kind of consistency in applied risk studies over the past decade. Many probabilistic risk assessments (PRA) have not included these events at all, and those that have did not employ the kind of systematic procedures that are needed to achieve consistency, accuracy, and credibility in this area of PRA methodology. In this paper, the authors report on the progress recently made in the development of a systematic approach for incorporating common cause events into applied risk and reliability evaluations. This approach takes advantage of experience from recently completed PRAs and is the result of a project, sponsored by the Electric Power Research Institute (EPRI), in which procedures for dependent events analysis are being developed. Described in this paper is a general framework for system-level common cause failure (CCF) analysis and its application to a three-train auxiliary feedwater system. Within this general framework, three parametric CCF models are compared, including the basic parameter (BP), multiple Greek letter (MGL), and binominal failure rate (BFR) models. Pitfalls of not following the recommended procedure are discussed, and some old issues, such as the benefits of redundancy and diversity, are reexamined.

Some nonlinear dynamics of a heated channel

Abstract: Linear and nonlinear mathematical stability analyses of parallel channel density wave oscillations are reported. The two phase flow is represented by the drift flux model. A constant characteristic velocity v 0 ∗ is used to make the set of equations dimensionless to ensure the mutual independence of the dimensionless variables and parameters: the steady-state inlet velocity v , the inlet subcooling number N sub and the phase change number N pch . The exact equation for the total channel pressure drop is perturbed about the steady-state for the linear and nonlinear analyses. The surface defining the marginal stability boundary (MSB) is determined in the three-dimensional equilibrium-solution/operating-parameter space v − N sub − N pch . The effects of the void distribution parameter C 0 and the drift velocity V g j on the MSB are examined. The MSB is shown to be sensitive to the value of C 0 and comparison with experimental data shows that the drift flux model with C 0 > 1 predicts the experimental MSB and the neighboring region of stable oscillations (limit cycles) considerably better than do the homogeneous equilibrium model ( C 0 = 1, V g j = 0 ) or a slip flow model. The nonlinear analysis shows that supercritical Hopf bifurcation occurs for the regions of parameter space studied; hence stable oscillatory solutions exist in the linearly unstable region in the vicinity of the MSB. That is, the stable fixed point v becomes unstable and bifurcates to a stable limit cycle as the MSB is crossed by varying N sub and/or N pch .

Disturbance wave frequencies, velocities and spacing in vertical annular two-phase flow

Abstract: A systematic study of disturbance wave properties in annular flow is reported. Frequencies and velocities were deduced from correlational analysis of film thickness records. The data is shown to agree with the more reliable earlier studies, though these were not so extensive. The spacing between waves has also been deduced. The effects of flow rates on this parameter are explained and its relationship to wave height is examined.

SPORTS - A simple non-linear thermalhydraulic stability code

Abstract: A simple code, called SPORTS ∗ , has been developed for two-phase stability studies. A novel method of solution of the finite difference equations was deviced and incorporated, and many of the approximations that are common in other stability codes are avoided. SPORTS is believed to be accurate and efficient, as small and large time-steps are permitted, and hence suitable for micro-computers.

Automatic identification of flow regimes in vertical two-phase flow using differential pressure fluctuations

Abstract: Differential pressure fluctuations are used to identify the flow regimes of nitrogen gas-water mixtures in a vertical pipe because the fluctuations are determined to be closely connected with the flow configuration. The regimes of vertical two-phase flow are classified by the characteristic features of the statistical properties of differential pressure fluctuations measured at two kinds of rational intervals. The results have shown that it is possible to identify the flow pattern based not on visual observations but on the shape of frequency distributions, the order of variance and the average value of differential pressures, because these statistical properties depend on the flow regimes. Furthermore, to identify the flow patterns automatically, the configuration of frequency distribution is approximated by use of the Gram-Charlier series. Then it is shown that the configuration of fitted frequency curves can be discriminated by the statistical parameters associated with the coefficients of the Gram-Charlier series, such as the mean, standard deviation, coefficient of skewness, and coefficient of excess. On the basis of these data, a flow chart is constructed and an objective and automatic identification technique of flow pattern is proposed.

Strain-induced corrosion cracking of low-alloy steels in LWR systems — case histories and identification of conditions leading to susceptibility☆

Abstract: The term “strain-induced corrosion cracking” (SICC) is introduced to describe crack formation involving dynamic straining, but in the absence of obvious, cyclic loading. Its origins in slow-strain-rate testing and in corrosion failures in boiler systems are described and the links with “classical” stress corrosion cracking and low-cycle corrosion fatigue are identified. Four areas, in which SICC of low-alloy steels in LWR systems has occurred, are described in detail and the typical features are used, together with literature data from laboratory testing, to identify conditions leading to susceptibility. Indications are given of remedial measures and of areas in which further work is necessary.

Current understanding of phase separation mechanisms in branching conduits

Abstract: This paper presents a summary of the state-of-the-art in our understanding of phase separation in branching conduits. The currently existing data base and analytical models are reviewed, and the “lessons learned” are summarized. It is shown that no completely satisfactory model exists for the prediction of phase separation in conduits of untested geometry and/or operating conditions. Nevertheless, based on our current understanding, an interim model is proposed.

Fluid and pressure oscillations occuring at direct contact condensation of steam flow with cold water

Abstract: Pressure and fluid oscillations at pressure suppression containment and cold leg flow oscillations at Emergency Core Cooling Water Injection in water-cooled nuclear power reactors are studied concerning flow oscillations occuring at direct contact condensation of steam flow with cold water. Classifications and mechanisms of these oscillation patterns are presented. Linear frequency analyses are developed in explaining the oscillation frequency and oscillation threshold of both condensation oscillation and plug oscillation. Oscillation frequencies at chugging and at ON-OFF oscillation are examined with analytical models developed for such large amplitude oscillations. Analytical results with these models are compared with the data by simulation experiments. Discussions are made focusing on the applicability of the analyses.

The experimental breeder reactor II inherent shutdown and heat removal tests — results and analysis

Abstract: A test program is being conducted to demonstrate that a power-producing liquid-metal reactor (LMR) can (1) passively remove shutdown heat by natural convection, (2) passively reduce power in response to a loss of reactor flow, and (3) passively reduce power in response to a loss of the balance-of-plant heat sink. Measurements and pretest predictions confirm that natural convection is a reliable, predictable method of shutdown heat removal and suggest that safety-related pumps or pony motors are not necessary for safe shutdown heat removal in an LMR. Measurements from tests in which reactor flow and heat rejection to the balance of plant were perturbed show that reactivity feedbacks can passively control power and temperature. Data from these tests form a basis for additional tests including a complete loss of flow without scram and a complete loss of heat sink without scram.

Static and dynamic buckling of large thin shells: Design procedure, computation tools, physical understanding of the mechanisms☆

Abstract: During the last ten years, the French Research Institute for Nuclear Energy (Commissariat a l'Energie Atomique) achieved many theoretical as well as experimental studies for designing the first large size pool type fast breeder reactor. Many of the sensitive parts of this reactor are thin shells subjected to high temperatures and loads. Special care has been given to buckling, because it often governs design. Most of the thin shells structures of the French breeder reactor are axisymmetric. However, imperfections have to be accounted for. In order to keep the advantage of an axisymmetric analysis (low computational costs), a special element has been implemented and used with considerable success in the recent years. This element (COMU) is described in the first chapter, its main features are: • — either non axisymmetric imperfection or non axisymmetric load, • — large displacement, • — non linear material behaviour, • — computational costs about ten times cheaper than the equivalent three dimensional analysis. This paper based on a careful comparison between experimental and computational results, obtained with the COMU element, will analyse three problems: • — First: design procedure against buckling of thin shells structures subjected to primary loads. • — Second: static post buckling. • — Third: buckling under seismic loads.

Boiling and fragmentation behaviour during fuel-sodium interactions

Abstract: A selection of the results and subsequent analysis of molten fuel-sodium interaction experiments conducted within the JRC BETULLA I and II facilities are reported. The fuels were copper and stainless steel, at initial temperatures far above their melting points; or urania and alumina, initially at their melting points. For each test, the molten fuel masses were in the lower kilogram range and the subcooled pool mass was either 160 or 4 kg. The sodium pool was instrumented to continually monitor the system temperature and pressure. Post-test examination results of the fragmented fuel debris sizes, shape and crystalline structure are given. The results of this study suggest the following: • - Transition boiling is the dominant boiling mode for the tested fuels in subcooled sodium. • - Two fragmentation mechanisms, vapour bubble formation/collapse and thermal stress shrinkage cracking prevailed for the oxide fuels. This was evidenced by the presence of both smooth and fractured particulate. In contrast, all metal fuel debris was smooth, suggesting fragmentation by the vapour bubble formation/collapse mechanism only during the molten state. • - For each test, there was no evidence of an energetic fuel-coolant interaction.

Probability and uncertainty in nuclear safety decisions

Abstract: In this paper, we examine some problems posed by the use of probabilities in Nuclear Safety decisions. We discuss some of the theoretical difficulties due to the collective nature of regulatory decisions, and, in particular, the calibration and the aggregation of risk information (e.g., experts opinions). We argue that, if one chooses numerical safety goals as a regulatory basis, one can reduce the constraints to an individual safety goal and a cost-benefit criterion. We show the relevance of risk uncertainties in this kind of regulatory framework. We conclude that, whereas expected values of future failure frequencies are adequate to show compliance with economic constraints, the use of a fractile (e.g., 95%) to be specified by the regulatory agency is justified to treat hazard uncertainties for the individual safety goal.

Reconstruction by the synthetic aperture focussing technique (SAFT)

Abstract: A 1-dimensional (Line-) version of the Synthetic Aperture Focussing Technique (LSAFT) was developed at the IzfP during the last 3 years. Experiences and results of this research work are presented and demonstrated on round robin test blocks and components for nuclear power plants.

Uncertainties in systems reliability modelling: Insight gained through European Benchmark exercises

Abstract: Uncertainty ranges associated with systems reliability evaluations take generally into account the mere contributions of the spread in the probability parameters of the events considered in the analysis. As the results of Benchmark Exercises performed in Europe have shown modelling uncertainties may overwhelm data uncertainties. In addition to controversial areas (such as “common cause failures” and “human factors”) other sources of uncertainties arise from the fact that analyst's judgement in the use of the data and available information introduces a significant and not-eliminable degree of subjectivity in the reliability assessments. This, however, does not affect the validity of methodology and analysis results, provided that these are consistently used with respect to the decisional process for which they have been produced.

Spinodal lines and equations of state: A review

Abstract: The importance of knowing superheated liquid properties, and of locating the liquid spinodal line, is discussed. The measurement and prediction of the spinodal line, and the limits of isentropic pressure undershoot, are reviewed. Means are presented for formulating equations of state and fundamental equations to predict superheated liquid properties and spinodal limits. It is shown how the temperature dependence of surface tension can be used to verify p - v - T equations of state, or how this dependence can be predicted if the equation of state is known.

The development of a closed-form analytical model for the stability analysis of nuclear-coupled density-wave oscillations in boiling water nuclear reactors

Abstract: 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.

The prediction of fully developed axial turbulent flow in rod bundles

Abstract: Results are presented from the application of a finite-volume calculation method to fully-developed axial turbulent flow in various smooth rod bundle arrangements. Simplified algebraic versions of the Reynolds stress transport equations are used in the calculation of the full three dimensional velocity field, without any special adjustments for each geometry. The predictions obtained for different rod spacings compare favourably with experiment and reveal the significant role of the cross-plane turbulence-driven secondary flow in shaping the mean flow and turbulence distributions. The success of the results obtained establish the effectiveness of the method and encourage further applications and development.

Post dryout heat transfer prediction

Abstract: A mechanistic model of post dryout heat transfer has been developed involving momentum and energy equations for both vapor and liquid, average drop diameter at the dryout location, and using heat transfer correlations for vapor-to-drop, wall-to-drop, and wall-to-vapor. This involves a computer calculation stepwise down the tube from dryout. This calculation was simplified making possible the heat transfer prediction at any position down the tube without the stepwise solution. The two solutions agree well with other. To make the predictions agree with data it was found necessary to multiply the wall-to-vapor heat transfer coefficient by a factor ranging from around 0.7 to about 2. At present this factor is found to be a function of bulk-to-wall viscosity ratio and quality. It may also be a function of liquid and vapor densities, tube and particle diameters and Reynolds number. A similar effect on wall-to-gas heat transfer is found in solid particle-gas flowing mixtures. The detailed explanation is a yet unknown, but appears to be due to turbulence suppression and enhancement resulting from particle motion.

Hidden sources of uncertainty: Judgment in the collection and analysis of data

Abstract: This paper investigates several sources of uncertainty that are not usually quantified explicitly in the analysis of data for probabilistic risk assessments (PRA). These uncertainties stem from the judgments that the analyst has to make in collecting as well as in analyzing the data to estimate the PRA parameters. It is shown that “objective” data are nonexistent even when data is collected through detailed and careful review of plant operating records. Several examples from real experience are cited to support the argument. The paper also discusses a framework for incorporating uncertain evidence and describes how various types of judgments and uncertainties can be represented explicitly in the assessment of common cause failure rates.

Validity of homogeneous flow model for instability analysis

Abstract: 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.

Response spectrum method for nonclassically damped systems

Abstract: For nonclassically damped systems a modal superposition method which makes use of complex mode shapes and frequencies is presented in a companion paper [1]. The method is extended into a response spectrum formulation in this paper. Each complex mode shape and its conjugate result in two real vectors. These vectors, when multiplied, to the displacement spectral value and the velocity spectral value, respectively, give two response vectors. A method of combining these responses from various modes is presented. It is shown that the velocity spectrum is approximately equal to the displacement spectrum, when expressed in the same units, in the intermediate frequency range only. A method of estimating the velocity spectrum from the displacement spectrum is presented. Nine coupled primary-secondary systems subjected to 12 earthquake ground motions were analyzed using the proposed response spectrum method, and the results were compared against those from the direct time history method. From the 108 analyses, 8 displacements and 9 forces per analysis, the mean error was found to be less than 1%, and the standard deviation of the percent error in the order of 10. The error is of the same order as is normally encountered in the response spectrum analysis of the classically damped systems.

Physical properties of nodular cast iron for shipping containers and safety analysis by fracture mechanics

Abstract: Recently, the dry-storage technique for storing spent fuels or radioactive wastes in shipping containers has been improved as one of the new technologies in the nuclear-fuel cycle. Mitsui Engineering and Shipbuilding has engaged for 5 years in the development of a radioactive waste container made of modular cast iron. This paper describes the physical properties of nodular cast iron and a fracture mechanical study of the container made of this material. The material is equivalent to FCD 37 in the JIS Standard. Many tests were carried out to obtain the mechanical properties, the fracture toughness and other characteristics using specimens machined from a thick-walled casting block. Then, the structural integrity of the cubic-type container made of this material was estimated on the basis of fracture mechanics. The critical flaw sizes regarding stresses occurred during a 9-meter drop test and a 1-meter punch-drop test were calculated. The results indicate that these sizes can be determined by a nondestructive inspection. Consequently, it has been analytically confirmed that nodular cast iron containers are strong enough to withstand an impact load during drop tests if the applied stresses are less than the yield stress.

Direct contact condensation of steam on slowly moving water

Abstract: A study of direct contact condensation of stagnant saturated steam on slowly moving subcooled water has been performed with reference to a horizontal flat geometry. Inlet water mass flowrate and temperature together with inlet steam temperature have been investigated, as experimental variables, in the following ranges: 1. (a) pressure up to 6 bar, 2. (b) inlet steam temperature up to 160°C 3. (c) inlet water mass flowrate up to 120 kg/h, 4. (d) inlet water temperature up to 70°C, 5. (e) available steam mass flowrate up to 20 kg/h. Condensation heat transfer coefficients have been determined as functions of inlet water mass flowrate, inlet water and steam temperature. Heat transfer coefficient does not show, practically, dependence either on inlet water temperature or inlet steam temperature but only on inlet water mass flowrate. Correlations are given for the Nusselt number, as a function of Reynolds and Prandtl numbers. An evaluation of thermal non-equilibrium degree between the phases is also presented, together with a correlation for its prediction.

Steady-state creep of orthotropic rotating disks of variable thickness

Abstract: Creep analysis of orthotropic rotating disks with variable thickness has been carried out for secondary stage of creep. Norton's power law of creep is employed to derive general expressions for stresses and strain rates in the disks. These expressions have been utilized to find stress and strain rate distributions for disks with the following types of thicknesses - (i) constant thickness, (ii) linearly varying thickness, and (iii) hyperbolically varying thickness. The numerical computations to study the effects of anisotropy and the profile of the disks on stresses and strains have been carried out employing the method of successive approximations. Five different cases of anisotropy have been considered. Selecting a certain type of material anisotropy and an optimum profile for the disk may result in a better design for the turbine disks.

Seismic response of nonclassically damped systems

Abstract: There are many practical problems in which the damping matrix cannot be represented in a classical form, thus leading to complex mode shapes and frequencies. A modal superposition method making use of the complex mode shapes is presented. In the method a complex mode shape is replaced by two real modal vectors. The modal equations are integrated in the same fashion as in the classically damped systems, except we now also use the modal velocities in addition to the usual modal displacements. It is shown that the modal superposition method for the nonclassically damped system gives response values almost identical to those given by the direct integration method. A method of constructing the damping matrix for a coupled primary and secondary system is also presented.

Flow Regime Transition and Interfacial Characteristics of Inverted Annular Flow

Abstract: Among various two-phase flow regimes, the inverted flow in the post-dryout region is relatively less well understood due to its special heat transfer conditions. The review of existing data indicates further research is needed in the areas of basic hydrodynamics related to liquid core disintegration mechanisms, slug and droplet formations, entrainment, and droplet size distributions. In view of this, the inverted flow is studied in detail both analytically and experimentally. Criteria for initial flow regimes in the post-dryout region are given. Preliminary models for subsequent-flow regime transition criteria are derived together with correlations for a mean droplet diameter based on the adiabatic simulation data.

Decision analytic tools for resolving uncertainty in the energy debate

Abstract: Within the context of a Social Compatibility Study on Energy Supply Systems a complex decision making model was used to incorporate scientific expertize and public participation into the process of policy formulation and evaluation. The study was directed by the program group “Technology and Society” of the Nuclear Research Centre Julich. It consisted of three parts: First, with the aid of value tree analysis the whole spectrum of concern and dimensions relevant to the energy issue in Germany was collected and structured in a combined value tree representing the values and criteria of nine important interest groups in the Federal Republic of Germany. Second, the revealed criteria were translated into indicators. Four different energy scenarios were evaluated with respect to each indicator making use of physical measurement, literature review and expert surveys. Third, the weights for each indicator were elicited by interviewing randomly chosen citizens. Those citizens were informed about the scenarios and their impacts prior to the weighting process in a four day seminar. As a result most citizens favoured more moderate energy scenarios assigning high priority to energy conservation. Nuclear energy was perceived as necessary energy source in the long run, but should be restricted to meet only the demand that cannot be covered by other energy means.