Distribution parameter and drift velocity for two-phase flow in a large diameter pipe

In view of practical importance of the drift flux model for two-phase flow analysis in general, and in the analysis of nuclear reactor transients and accidents in particular, the distribution parameter, and the drift velocity have been studied for two-phase flow in a vertical large diameter pipe. In this, study, local measurements were performed on flow parameters, such as void fraction, gas velocity and, liquid velocity in a vertical upward air–water two-phase flow in a pipe of 200 mm inner diameter and, 25 m in height by using the local sensor techniques such as hot-film probes, optical multi-sensor, probes and differential pressure gauges. Two-phase flow regimes in a vertical large diameter pipe, were classified into bubbly, churn and slug flows according to the visual observation. The values of the, distribution parameter and the mean drift velocity were determined directly by their definition using experiment data of the local flow parameters in a two-phase flow in a large diameter pipe. Various existing drift flux correlations were compared with the present experimental results and experimental data obtained by other researchers. A detailed discussion on the problems of these correlations was presented in this paper.     

Two phase flow 1D turbulence model for poly-disperse upward flow in a vertical pipe

A 1D test-solver was developed in recent years for modeling of two phase bubbly flows in pipe geometry. The solver considers a number of bubble classes and calculates bubble-size resolved void fraction profiles in the radial direction. A successful implementation was achieved regarding bubble forces models (non-drag forces). Discrepancies appeared when coalescence and breakup rates were significant. These rates depend upon local turbulence quantities, which are possible reason for discrepancies. Originally the test-solver is equipped by Sato model (Sato, Y., Sadatomi, M., Sekoguchi, K., 1981. Momentum and heat transfer in two-phase bubble flow. I. International Journal Multiphase Flow 7, 167–177 .) which accounts for turbulence via shear- and bubble-induced viscosities calculated out of empirical correlations. One equation for the turbulent kinetic energy was solved, while the dissipation rate was calculated out of a correlation. In order to improve calculation of the local turbulence parameters, a two-phase k– turbulence model was adopted instead. The account for the bubble-induced turbulence was made via a source term taken out of literature. Comparisons between new and old turbulence modeling against experimental data showed better agreement for the new model. The experiments covered a wide range of water and air superficial velocities for upward bubbly flow in two pipe's diameters: 50 and 200 mm. The main feature of the new model is providing more reliable values of turbulence parameters for application in coalescence and breakup models. A comparison with CFX 5.7 calculations in a 50 mm pipe showed better calculation results when the source term was considered in the k– equations. An implementation into CFX is planned.     

A finite element LES for high-Re flow in a short-elbow pipe with undisturbed inlet velocity

The paper is concerned with a large-eddy simulation (LES) for a high-Reynolds-number flow in a short-elbow pipe, which can potentially be employed in the primary piping system of the Japan Sodium-cooled Fast Reactor (JSFR). The basic performance of the LES is studied for an elbow pipe flow without turbulence at inlet boundary at Re = 1.2 × 10⁶ by comparison with a flow observed in a 1/3-scale water experiment, where the flow disturbance at the pipe inlet is small. In setting up the computational conditions, special care was taken to ensure that the mesh subdivision was suitable for the simulation of the pipe flow through a theoretical consideration. We discuss the effects of the turbulence model (Smagorinsky model, WALE model) and the inlet velocity profile on the results. The mechanism of the pressure fluctuation and the origin of the fluid force are also discussed with the aid of spectral analysis and the visualization of essential hydraulic quantities.     

Evaluation of check valve monitoring methods

Check valves are used extensively in nuclear plant safety systems and balance-of-plant (BOP) systems. Their failures have resulted in significant maintenance efforts and, on occasion, have resulted in water hammer, overpressurization of low-pressure systems and damage to flow system components. Consequently, in recent years check valves have received considerable attention by the Nuclear Regulatory Commission (NRC) and the nuclear power industry. Oak Ridge National Laboratory (ORNL) is carrying out a comprehensive two phase aging assessment of check valves in support of the Nuclear Plant Aging Research (NPAR) program. As part of the second phase, ORNL is evaluating several developmental and/or commercially available check valve diagnostic monitoring methods; in particular, those based on measurements of acoustic emission, ultrasonics, and magnetic flux. These three methods were found to provide different (and complementary) diagnostic information. The combination of acoustic emission with either ultrasonic or magnetic flux monitoring yields a monitoring system that succeeds in providing sensitivity to detect all major check valve operating conditions. The three check valve monitoring methods described in this paper are still under development and are presently being tested as part of a program directed by the Nuclear Industry Check Valve Group (NIC) in conjunction with the Electric Power Research Institute (EPRI). Phase 1 of this program (water testing) is being carried out at the Utah Water Research Laboratory located on the Utah State University campus.     

Development of design guidance for low velocity impacts on concrete floors

It has been recognised in the UK, that where designers or safety assessors have to consider the effects of dropped loads on various targets, there is uncertainty associated with the fact that these are low velocity impacts. This uncertainty arises for a variety of load/target combinations, but in this paper we concern ourselves with loads which are massive and with reinforced concrete floor targets.The major uncertainty for dropped load assessments, lies in the fact that the designer does not have access, in general, to relevant data. Instead, it is usual, for design purposes, to make use of empirical formulae which are intended for high velocity missiles. The design process involves using the empirical formulae not only for the local damage which they are intended to address, but also to define a load-time history or impulse for the purposes of determining slab response.This paper indicates the range of events that need to be considered, the manner in which the designer approaches the task of making his assessment of the target and the limits of applicability of the available empirical methods. The programme now in progress in the UK is outlined and some of the results emerging are presented.     

An analysis of check valve performance characteristics based on valve design

Although it had been theorized by nuclear industry valve experts that the two most significant factors in assessing check valve performance were valve type (or design) and operating conditions, until recently, no data was available to support their assumptions. In co-operation with the Nuclear Industry Check Valve Group (NIC), Oak Ridge National Laboratory (ORNL) undertook a review and analysis of check valve failures recorded in the Institute of Nuclear Power Operations’ (INPO) Nuclear Plant Reliability Data System (NPRDS). This study involved the characterization of failures according to several parameters, including valve design (e.g. swing check, lift check). Since the valve design is not inherently included within the NPRDS engineering record for each component in the database, ORNL relied on input from NIC, valve manufacturers and catalogs to supply the missing information. As a result, nearly 60% of the 21 000 check valves listed in the NPRDS component database and 85% of the 838 failures occurring during 1991–1992 were identified according to valve design. This data provided the basis to perform previously unavailable cross-correlations between parameters such as valve design versus failure mode, valve design versus failure discovery method, population/failure distributions by valve design, etc. Performance assessments and predictions based on more specific sets of parameters (as opposed to generic check valve failure rates obtained from standard reference sources that generally ignore the valve design) should result in a significant impact on future nuclear plant operations, including inservice testing (IST) practices, maintenance, and probabilistic risk assessments (PRAs) by providing a means to calculate more appropriate relative (and ultimately absolute) failure rates for check valves.     

Development of diagnosis algorithm for the check valve with spectral estimations and neural network models using acoustic signals

We have developed a method for detecting and diagnosing a disk wear failure and a foreign object failure among the various failure modes of check valves. The method is based on the acoustic emission sensors which can detect the sound wave of the leakage flow and the estimation of the power spectral densities with an auto-regressive model. For validating the method, we implemented a hydraulic test loop with an artificially failed check valve. We have found that the frequency spectrums from the acoustic signals are strongly dependent on the failure modes of the check valve and that they are nearly independent of the failure size and operating pressure through an estimation of the power spectral density with an auto-regressive signal processing model. In addition, the root mean square values of the acoustic signal and the amplitudes of the power spectral density as well as the loop pressure have a strong dependency on the failure size in each failure mode of the check valve. We developed a diagnosis algorithm by using neural network models in order to identify the type and size of the failure in the check valve. The diagnosis algorithm consists of a hierarchical model composed of three back-propagation neural networks. The results of our research and the experiments show that the diagnosis algorithm is proven to be a good solution for identifying the failures of the check valves without any disassembling work.     

Probability of pipe breakage regarding transient flow in a small pipe network

A reliability model was developed for the calculations of the probability of pipe breakage associated with transient effect. The statistical distribution for the maximum pressure wave heights was determined from the results of 168 transient analyses. It was found that the statistical distribution for internal pressure among the random variables of reliability function is well matched with the Gumbel distribution. The probability of pipe breakage in a small pipe network was calculated according to pipe diameter, thickness, allowable stress, and internal pressure. From the results, it was found that transient effect significantly increases the probability of pipe breakage. Using the present reliability model, it could be possible to find a pipe that contains the high probability of pipe breakage in a water distribution system. If the reliability model developed in the present study is applied for the design, a safe design will be accomplished. Furthermore, it can be effectively used for the management and maintenance of a water distribution system.     

Reversal of laminar flow in a circular pipe

In the analysis of the loss of coolant accident (LOCA) in water reactors, the frictional resistance is treated in a one-dimensional sense using the quasi-steady state approximation for evaluation of the friction factor. The calculation has predicted one or more flow reversals. The present paper examines the limits of validity of the quasi-steady approximation by comparing with a new exact solution assuming no flow separation. Radial velocity distributions, mean flowrate and friction coefficients are compared for the specific case of a ramp change in pressure gradient including the limiting step. For low ramp rates with transient laminar flow in circular pipes the quasi-steady approximation is found valid; for high ramp rates the time to zero bulk flow is underestimated by 22.2%.     

Mitigating check valve slamming and subsequentwater hammer events for PPFS using MOC

The method of characteristic (MOC) was adopted to analyze the check valve-induced water hammer behaviors for a Parallel Pumps Feedwater System (PPFS) during the alternate startup process. The motion of check valve disc was simulated using inertial valve model. Transient parameters including the pressure oscillation, local flow velocity and slamming of the check valve disc etc. have been obtained. The results showed that severe slamming between the valve disc and valve seat occurred during the alternate startup of parallel pumps. The induced maximum pressure vibration amplitude is up to 5.0 MPa. The scheme of appending a damping torque to slow down the check valve closing speed was also performed to mitigate of water hammer. It has been numerically approved to be an effective approach.     

Two-phase flow patterns in turbulent flow through a dose diffusion pipe

A numerical investigation is carried out for turbulent particle-laden flow through a dose diffusion pipe for a model reactor system. A Lagrangian stochastic Monte-Carlo particle-tracking approach and the averaged Reynolds equations with a k– turbulence model, with a two-layer zonal method in the boundary layer, are used for the disperse and continuous phases. The flow patterns coupled with the particle dynamics are predicted. It is observed that the coupling of the continuous phase with the particle dynamics is important in this case. It was found that the geometry of the throat significantly influences the particle distribution, flow patterns and length of the recirculation region. The accuracy of the simulations depends on the numerical prediction and correction of the fluid phase velocity during a characteristic time interval of the particles. A numerical solution strategy for the computation of two-way momentum coupled flow is discussed. The three test cases show different flow features in the formation of a recirculation region behind the throat. The method will be useful for the qualitative analysis of conceptual designs and their optimisation.     

Design and test of hydraulic vacuum breaker check valve for simplified boiling water reactor

In the current design of the simplified boiling water reactor, the vacuum breaker check valve is an important safety component. The vacuum breaker check valve is the only key safety components which is not passive in nature. Failure of this mechanical valve drastically reduces the passive containment cooling system cooling capability and hence containment pressure may exceed the design pressure. To eliminate this problem novel vacuum breaker check valve was developed to replace the mechanical valve. This new design is based on a passive hydraulic head, which is fail-safe and is truly passive in operation. Moreover this new design needs only one additional tank and one set of piping each to the wetwell and drywell. This system is simple in design and hence is easy to maintain and to qualify for operation. The passive vacuum breaker check valve performance was first evaluated using RELAP5. Then the passive vacuum breaker check valve was constructed and implemented in the PUMA integral test facility. Its performance was studied in a large break loss of coolant accident simulation test performed in PUMA facility.     

Hydrodynamic characterization and optimization of Contra-push check valve by numerical simulation

This paper introduced the structure and working principle of a new designed check valve, Contra-push check valve (CPCV), which can release water hammer and valve slam in accidents and special working status of nuclear power systems. The steady and transient characteristics of CPCV are simulated by CFD codes. Based on the experimental data, it is shown that the result is highly dependent on the turbulence model. The renormalization group theory (RNG) k–ε model is proved to be more accurate to describe the flow inside the valve. Steady hydraulic characteristics computed with RNG k–ε model agreed well with the experimental data at different positions of the plug. The Sensitivity analysis of structure parameters of CPCV were carried out in this study and two key factors were revealed.     

One-dimensional three-field model of condensation in horizontal countercurrent flow with supercritical liquid velocity

A one-dimensional three-field model was developed to predict the flow of liquid and vapor that results from countercurrent flow of water injected into the hot leg of a PWR and the oncoming steam flowing from the upper plenum. The model solves the conservation equations for mass, momentum, and energy in a continuous-vapor field, a continuous-liquid field, and a dispersed-liquid (entrained-droplet) field. Single-effect experiments performed in the upper plenum test facility (UPTF) of the former SIEMENS KWU (now AREVA) at Mannheim, Germany, were used to validate the countercurrent flow limitation (CCFL) model in case of emergency core cooling water injection into the hot legs. Subcooled water and saturated steam flowed countercurrent in a horizontal pipe with an inside diameter of 0.75 m. The flow of injected water was varied from 150 kg/s to 400 kg/s, and the flow of steam varied from 13 kg/s to 178 kg/s. The subcooling of the liquid ranged from 0 K to 104 K. The velocity of the water at the injection point was supercritical (greater than the celerity of a gravity wave) for all the experiments. The three-field model was successfully used to predict the experimental data, and the results from the model provide insight into the mechanisms that influence the flows of liquid and vapor during countercurrent flow in a hot leg. When the injected water was saturated and the flow of steam was small, all or most of the injected water flowed to the upper plenum. Because the velocity of the liquid remained supercritical, entrainment of droplets was suppressed. When the injected water was saturated and the flow of steam was large, the interfacial shear stress on the continuous liquid caused the velocity in the liquid to become subcritical, resulting in a hydraulic jump. Entrainment ensued, and the flow of liquid to the end of the hot leg was greatly reduced.The influence of condensation on the transition from supercritical to subcritical flow as observed in the experimental data is also predicted with the three-field model. When the injected water was subcooled, condensation on the flow of continuous liquid caused a reduction in the flow of vapor and, consequently, a reduction in the interfacial shear stress. Therefore, the flow of liquid remained supercritical to the end of the hot leg at the upper plenum. The entire flow of injected water flowed to the end of the hot leg at higher flows of steam when the injected water was subcooled than when it was saturated. When the flow of vapor was large enough to cause a hydraulic jump in the subcooled liquid, the rate of entrained droplets was greatly increased. The interfacial surface area of the droplets was several orders of magnitude greater than for the continuous-liquid field, and condensation rate on the droplet field was also several orders of magnitude greater. When the flow of vapor from the upper plenum was at its greatest, most of the flow in the continuous liquid was entrained before reaching the upper plenum. The large flow of subcooled droplets caused three-quarters of the steam to condense.     

Development of a database of pipe fracture experiments

Over the last 35 years, researchers worldwide have conducted hundreds—if not thousands—of pipe fracture experiments. In the early years, researchers focused their attention on studying the failure pressure and crack propagation behavior of axially cracked pipe loaded by internal pressure. The earliest work was sponsored by the oil and gas industry and, as such, involved relatively thin-walled, low toughness carbon steel pipes. This work was eventually followed up by efforts in the USA and Germany on nuclear piping with axial cracks. In recent years, attention has turned to understanding the behavior of circumferentially cracked nuclear piping subjected to both pressure and bending loads. The loading histories for these experiments range from the relatively simple case of quasi-static, monotonic displacement control to the more complex cases of dynamic cyclic loading, and pipe system experiments. In this paper, two of the leaders in this research, i.e. Battelle in the USA and MPA Stuttgart in Germany, have collaborated to develop a database of pipe fracture experiments. The database includes data from other organizations as well as the data from Battelle and MPA. In addition, as part of this paper, an example of how the database was used to assess the failure pressure of axially cracked pipe is given.     

Numerical prediction of stratified pipe flows in PWRs

The phenomenon of thermal stratification has been analysed on the l'EXPRESS experimental facility representing the pressurizer surge line of a Framatome PWR. This experimental approach has allowed to characterize flow regimes for different operating conditions. A numerical simulation approach has been performed by the TRIO code. The measured fluid temperatures have been compared to calculated values. A first validation of the numerical simulation was realized by comparing steady state results to experimental values, the second one by comparing transient conditions. Also the stratification onset has been estimated and compared to the experiment. The numerical simulation has allowed to obtain a good prediction of the quantities representative of the thermal loading.     

Annular flow entrainment rate experiment in a small vertical pipe

Two-fluid model predictions of film dryout in annular flow, leading to nuclear reactor fuel failure, are limited by the uncertainties in the constitutive relations for the entrainment rate of droplets from the liquid film. The main cause of these uncertainties is the lack of separate-effects experimental data in the range of the operating conditions in nuclear power reactors. An air–water experiment has been performed to measure the entrainment rate in a small pipe. The current data extend the available database in the literature to higher gas and liquid flows and also to higher pressures. The measurements were made with the film extraction technique. A mechanistic model was obtained based on Kelvin–Helmholtz' instability theory. The dimensionless model includes the Weber number of the gas and the liquid film Reynolds number. Kataoka and Ishii's correlation (Kataoka, I., Ishii, M., 1982. NUREG/CR-2885, ANL-82-44) is modified based on this model and the new data. The new correlation collapses the present air–water data and Cousins and Hewitt's data (Cousins, L.B., Hewitt, G.F., 1968. UKAEA Report AERE-R5657) The effects of pressure and surface tension were considered in the derivation so it may be applied for boiling water reactor operating conditions.     

Numerical solutions for the kinematic model of pebble flow velocity profiles and its applications in pebble-bed nuclear reactor

The modular pebble-bed nuclear reactor (PBR) is a candidate Generation IV reactor being developed. The pebble flow in the very slow draining of fuel pebbles draws attention for its implications on core physical design and reactor physics analysis. One of the effective and simplified methods to address this problem is the kinematic model which is based on continuous theory to derive a diffusion equation for vertical velocity. This paper investigates the appropriate numerical solutions for the kinematic model of pebble flow velocity profiles in PBR geometry. Our method is based on a previously proposed transformed Cartesian coordinates and uses the implicit Crank–Nicholson integration scheme with two different treatments of the boundary conditions. Validations show that this numerical solution gives preferable agreements with the experimental results in the reference. Finally, the simulated velocity profiles are applied in the investigation of two pebble burnup-related issues, which are the pebble residence time prediction and the channel scheme in realistic high-temperature reactor pebble-bed modules reactor core geometry.     

Temperature distributions in liquid metals for turbulent flow in a horizontal pipe with free convection

A general method is developed for utilizing limited experimental data to obtain velocity or temperature distributions over the cross-section of a heated horizontal pipe, under conditions where distortion occurs due to superimposed free convection effects. The method is applied to available temperature data for five cases of constant-flux heating of liquid metals in turbulent flow, and the resulting isotherms and wall temperature distributions are presented. Substantial asymmetry is demonstrated for Reynolds numbers as high as 10⁵, with a corresponding distortion of the wall temperature distribution, and it is found that local heat transfer coefficients may be as low as 30% of predicted values.