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Open LANE Dissertation FINAL.Pdf The Pennsylvania State University The Graduate School College of Engineering THE DEVELOPMENT OF A COMPREHENSIVE ANNULAR FLOW MODELING PACKAGE FOR TWO-PHASE THREE-FIELD TRANSIENT SAFETY ANALYSIS CODES A Dissertation in Nuclear Engineering by Jeffrey W. Lane © 2009 Jeffrey W. Lane Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2009 The dissertation of Jeffrey W. Lane was reviewed and approved* by the following: Lawrence E. Hochreiter Professor of Mechanical and Nuclear Engineering Dissertation Co-Advisor Co-Chair of Committee Fan-Bill Cheung Professor of Mechanical and Nuclear Engineering Dissertation Co-Advisor Co-Chair of Committee Kostadin Ivanov Distinguished Professor of Nuclear Engineering John H. Mahaffy Associate Professor Emeritus of Nuclear Engineering Gita Talmage Professor of Mechanical Engineering Ali Borhan Professor of Chemical Engineering David L. Aumiller, Jr. Fellow Engineer, Bechtel Marine Propulsion Corporation Special Member Jack S. Brenizer Professor of Mechanical and Nuclear Engineering Program Chair of Nuclear Engineering *Signatures are on file in the Graduate School. Abstract The annular two-phase flow regime is important to several applications and most notably the safety analysis of nuclear reactors. Such analyses require an accurate prediction of the phenomena associated with this regime, including the pressure gradient as well as the distribution of liquid and the interfield rate of exchange between the film and dispersed droplet fields. In general, the nuclear industry uses transient safety analysis codes, such as COBRA-TF, to predict phenomena of interest for various reactor accident scenarios and ensure the safe design of the system. COBRA-TF is a best-estimate thermal-hydraulic analysis tool developed for Light Water Reactors (LWR) and the primary feature of COBRA-TF is that it provides a three-field representation of two-phase flow (vapor/non-condensable gases, continuous liquid or films, and dispersed liquid or droplets). This representation is regarded as the most physically accurate approach for analyzing situations where liquid can coexist in both continuous and discrete forms, as is the case for annular-mist and counter-current flow situations, since substantial differences can exist in the velocity and flow direction for these two fields. The prediction of annular flow situations requires a variety of constitutive relationships to describe the mass, momentum, and energy exchange that occurs between the flow fields and provide closure to the set of momentum equations. An initial assessment of the predictive capability of COBRA-TF indicated that the modeling package that was used in the baseline version of the code did not provide adequate predictions when a variety of annular flow experiments were simulated. As a result, the goal of the current study was to assemble a physically-based and self-consistent annular flow modeling package that is amenable to implementation in three-field analysis environments and accurately captures the variation in entrainment and interfacial drag within co-current and counter-current regimes over the pressure range of interest (atmospheric to 2000-psia). The constitutive relations available in the open- literature were assessed relative to the models employed in the modeling package that was applied in the baseline version of COBRA-TF. Where necessary, model upgrades were made in an effort to utilize the most appropriate models that are based on either the physics of the flow or developed from experimental data collected over the desired range of conditions. The models that were incorporated into the newly proposed modeling package were either based on those developed in previous studies or developed uniquely within the current study. It is important to iii note that the current study used COBRA-TF to provide the baseline modeling package as a means for comparison and as a vehicle for assessing the newly proposed modeling packages; however, the proposed packages are amenable to implementation into any other three-field analysis tool. The proposed modeling packages for co-current and counter-current annular flow are outlined in Chapters 4 and 5, respectively. The co-current modeling package: 1) applies an interfacial shear model that explicitly accounts for the presence of interfacial waves, 2) idealizes the structure of the interface in a manner that is consistent with both the interfacial shear model and other visual observations, 3) includes three mechanistic-based entrainment rate models (roll wave stripping, Kelvin-Helmholtz lifting, and liquid bridge breakup) that calculate a theoretical entrainment rate for a single wave based on the physical structures and controlling phenomena as they are currently understood for each mechanism, and 4) provides a functional relationship between the actual and theoretical entrainment rates based on comparisons to experimental data to account for any deficiencies that exist in the theoretical model. This methodology improves the physical basis of the modeling package while simultaneously leveraging the available experimental data to ensure the modeling package is able to accurately reflect the experimental data. Meanwhile, the three-field Counter-Current Flow Limitation (CCFL) model developed in the current study is based on an empirical model that has been shown to suitably correlate specific sets of data over a wide range of flow path dimensions and geometries. The resulting correlation provides a quantitative description of the experimentally determined flooding curve. The proposed model compares the flow conditions predicted by the code to the results of the user- specified CCFL correlation to determine if the standard set of momentum equations should be replaced with a newly developed set of CCFL momentum equations. The proposed model also provides appropriate entrainment rate models (pool and excess film) and necessary criterion to exit the model in a stable manner. In general, this approach provides flexibility to the code user and again leverages the available experimental data to improve the predictive capability of the code since a universal model has yet to be determined for this phenomenon. While not entirely mechanistic, this approach ensures the proper amount of liquid flow can penetrate these regions, which is preeminent to achieving accurate predictions of coolant and temperature distributions for Loss-of-Coolant Accident (LOCA) scenarios. Overall the development of this model is a unique aspect of the current study because of the explicit treatment of the entrained field, which iv previously suggested models did not consider because they were aimed at two-field analysis environments. The results of the current study indicate that the inclusion of these newly proposed modeling packages for both co-current and counter-current annular flow has provided increased accuracy in the predictions of phenomena that are of interest to reactor safety analyses. In particular, the mean relative error in entrained fraction was reduced from 20.2% (underprediction) to 4.5% (overprediction) and the mean relative error in axial pressure gradient was reduced from 108.2% to 7.6% (both overprediction) for co-current upward annular flow situations following the implementation of these packages into COBRA-TF and the code-to-data agreement of several different parameters within the counter-current flow regime was improved significantly. It was also shown that the proposed co-current annular modeling package: 1) provided reasonable estimates of a variety of more fundamental annular flow parameters such as wave spacing, velocity, and intermittency, and 2) was able to capture the general behavior within the developing flow region. Both these results provide confidence that the proposed modeling package reasonably reflects the underlying physics of the annular regime. Moreover, the current study is one of the few works that has examined the predictive capabilities of transient analysis codes within the developing, or non-equilibrium, annular flow region. The methodology employed in the current study is not meant to provide a final solution to this complex problem; however, given the importance of these phenomena to the safety analysis of various reactor accident scenarios and the abundance of available experimental data, it would be inopportune not to employ this modeling methodology and improve the predictive capabilities of three-field transient analysis codes until a more viable approach is ascertained. Regardless, the current study has both provided a functional modeling package that has presently improved the predictive capabilities of three-field analysis tools and established a new baseline for future research and model development activities in this area. v Table of Contents List of Figures .................................................................................................................x List of Tables................................................................................................................xix Nomenclature ................................................................................................................xx Acknowledgements .....................................................................................................xxv 1. Introduction ...........................................................................................................1 1.1. Overview of Annular Flow....................................................................................2
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