In this study, liquid-vapor vertical upflow has been research with the intent of finding an improved method of modelling the interphase friction in two-phase vertical flow in nuclear thermal-hydraulic codes. An improved method of modelling interphase friction should allow for better prediction of pressure gradient, void fraction and the phasic velocities. Data has been acquired from several available published resources and analyzed to determine the interphase friction using a force balance between the liquid and vapor phases. Using the Buckingham Pi Theorem, a dimensionless interphase friction force was tested and refined before being compared against seven other dimensionless parameters. Three correlations have been developed that establish a dimensionless interphase friction force as a function of the Weber number, the Froude number and the mixture Froude number. Statistical analysis of the three correlations shows that the mixture Froude number correlation should be the most accurate correlation. The correlations have a weakness that makes them ineffective mostly for bubbly flow and some slug flow scenarios, while they should perform significantly better for annular flow cases. Comparisons have been made against the interphase friction calculations published in the manuals of RELAP5/MOD2, RELAP5/MOD3.3, RELAP5-3D and TRACE. The findings have generally shown that the equations in the manuals provide very inaccurate approximations of the interphase friction compared to the interphase friction that was found via force balance. When analyzing the source code of RELAP5/MOD3.3, several differences were noticed between the source code and manual, which have been discussed. Calculations with the source code equations reveal that the source code provides a modestly improved prediction of the interphase friction force, but still has significant errors. Despite the fact that the manual and source code equations indicate that RELAP5/MOD3.3 should perform poorly in modelling interphase friction, actual RELAP5/MOD3.3 model runs perform very well in predicting pressure gradient, void fraction, the liquid and vapor velocities and the interphase friction force. This is largely due to RELAP5/MOD3.3 being able to adjust parameters to converge to a solution that fits within the boundary conditions established in the input file. Modifications to the RELAP5/MOD3.3 code were first made with the three correlations developed using dimensionless parameters, and were tested with data points that the RELAP5/MOD3.3 flow regime map had predicted would be annular flow. While the mixture Froude number correlation has been analyzed to be the most statistically accurate of the three correlations, it was found that the Weber number correlation performed best when implemented into RELAP5/MOD3.3. In a parametric study of the Weber number correlation, it performed optimally at 150% of the original correlation, improving upon the original RELAP model in almost every metric examined. Additional investigations were performed with individual annular flow correlations that model specific physical parameters. Results with the annular flow physical models were inconclusive as no particular model provided a significant improvement over the original RELAP5/MOD3.3 model, and there was no clear indication that combining the models would provide significant improvement. / Ph. D.

The purpose of this study is to develop an accurate model of the downcomer of the once-through steam generator (OTSG) developed by Babcock & Wilcox, using RELAP5/MOD2. While the physical model can be easily developed, several parameters are left to be adjusted to optimally model the downcomer and match data that was retrieved in a first-of-a-kind (FOAK) study conducted at Oconee Unit I in Oconee, South Carolina. Once the best-fit set of parameters has been determined, then the model must be tested for power levels exceeding that for which the steam generator was originally designed, so as to determine the power level at which a phenomenon known as flood-back becomes a concern. All known previous studies that have been conducted using RELAP5/MOD2 have shown that RELAP over-predicts interphase friction. However, all of those studies focused on heated two-phase upflow, whereas the downcomer is modeled as adiabatic two-phase downflow. In this study, it is found that the original slug drag model for RELAP5/MOD2 developed by Idaho National Engineering Laboratory (INEL) under-predicts the interphase friction between the liquid and vapor phase within the downcomer. Using a modified version of the original slug drag model created by Babcock & Wilcox (B&W), an optimum multiplier is found for each power level. An increase of 1181% in interphase friction over the INEL slug drag model, which equals an increase of 4347% for the default B&W model provides the most accurate results for all power levels studied. Emphasis is also placed on modeling the orifice plate of the OTSG downcomer which has been added to stabilize pressure fluctuations between the downcomer and tube bundle of the OTSG. While several different schemes are explored for modeling the orifice plate, a branch connection with an inlet area 14.22% of that of the downcomer is used to model the orifice plate along with the volume that transitions the two-phase downflow to horizontal flow into the tube nest of the OTSG. Power levels exceeding that for which the steam generator was designed are tested in RELAP using the slug drag multiplier to determine at which power level a liquid level would occur and would flood-back become a concern. In this study, it is determined that a liquid level would form at 135% power and that at any higher power level, flood-back would be of concern for any user of the steam generator. / Master of Science

The performance of a flashing flow nozzle was quantified by efficiency and metastability measurements. Efficiency was calculated over a range of operating conditions, by using both inlet and exit conditions and the nozzle thrust. Metastability was quantified by a parameter that compared the experimental mass flow rate with homogeneous equilibrium and frozen state flow rates. The efficiency of the flashing flow nozzle was found to be less than half the efficiency of the nozzle while operating at near thermodynamic equilibrium. Attempts were made to improve nozzle performance by lowering the piping diameter immediately upstream of the nozzle to increase flow turbulence and encourage a uniform bubbly flow. Bubbly flow helps two-phase flows become less metastable, by generating a uniform distribution of bubbles that act as nucleation sites for flashing inception. Low flow metastabilities were found with high inlet qualities and small upstream piping diameters. These conditions also resulted in the highest flashing flow nozzle efficiencies; however, the efficiency showed a much less pronounced response to upstream piping diameter. The homogeneous equilibrium model was found to be an inaccurate predictor of nozzle performance. To satisfy this model, a shock must be positioned in the nozzle's divergent section, severely limiting nozzle efficiency. The effects of phase slip on nozzle efficiency were investigated with recommendations made for further research in this area. / Master of Science

Heavy water moderator surrounding each fuel channel is one of the important safety features in CANDU reactors since it provides an in-situ passive heat sink for the fuel in situations where other engineered means of heat removal from fuel channels have failed. In a critical break LOCA scenario, fuel cooling becomes severely degraded due to rapid flow reduction in the affected flow pass of the heat transport system. This can result in pressure tubes experiencing significant heat-up during early stages of the accident when coolant pressure is still high, thereby causing uniform thermal creep strain (ballooning) of the pressure tube (PT) into contact with its calandria tube (CT). The contact of the hot PT with the CT causes rapid redistribution of stored heat from the PT to CT and a large heat flux spike from the CT to the moderator fluid. For conditions where subcooling of the moderator fluid is low, this heat flux spike can cause dryout of the CT. This can detrimentally affect channel integrity if the CT post-dryout temperature becomes sufficiently high to result in continued thermal creep strain deformation of both the PT and the CT. A comprehensive mechanistic model is developed to predict the critical heat flux (CHF) variations along the downward facing outer surface of calandria tube. The model is based on the hydrodynamic model of \cite{Cheung/Haddad1997} which considers a liquid macrolayer beneath an elongated vapor slug on the heated surface. Local dryout is postulated to occur whenever the fresh liquid supply to the macrolayer is not sufficient to compensate for the liquid depletion within the macrolayer due to boiling on the heating surface. A boundary layer analysis is performed, treating the two phase motion as an external buoyancy driven flow, to determine the liquid supply rate and the local CHF. The model takes into account different types of flow regime or slip ratio. It is applicable for a calandria vessel as well, under a sever accident condition where a thermal creep failure is postulated to occur if sustained CHF is instigated in the surrounding shield tank water. Model shows good agreement with the available experimental CHF data. The model has been modified to take into account the effect of subcooling and has been validated against the empirical correction factors. / Dissertation / Doctor of Philosophy (PhD)

Three existing pressure-drop models are validated and analyzed with experimental data compiled from the research database. From the analysis, it was found that the pressure-drop prediction results from the models are not very accurate and not consistent with all experimental datasets. A new pressure-drop model was consequently created based on the findings from the study, and experimental data from the database were used to validate the model to produce more accurate and consistent predictions. The new pressure-drop model was tested on experimental datasets that were in the database and also with experimental datasets that were not in the database. Good and consistent results were achieved, and the new model proved capable of predicting pressure drops for different pure refrigerants and refrigerant mixtures flowing inside different configurations of microin tubes for both condensation and evaporation.

This report presents experimental results for the pressure drop across a restriction of annular geometry used in a typical pressurized water reactor steam generator. The pressure drops were obtained for air, water, and the corresponding two-phase mixtures. The loss coefficients associated with these pressure drops were experimentally determined and empirical relations correlating the results were developed. The tests were performed at atmospheric conditions (atmospheric temperature and pressure), and the two-phase flow mass velocity ranged from 236 to 711 1bm/s-ft2.

This research is concerned with the presentation of pressure drop experimental results across a restriction of trefoil geometry (tube support plate) used in steam generators. The pressure drops were obtained for single-phase and two-phase of air, water, and their mixtures. The tests were performed at atmospheric conditions (pressure and temperature). The loss coefficients associated with these pressure drops were experimentally determined, and empirical correlations for the results were developed. The results were compared with previous studies done on other geometries with air-water mixtures, and also to a similar geometry with steam-water mixture.

Based on a two-phase boundary layer approach, a computational model is proposed to estimate the thickness of the waterfilm due to rain on the upper surface of an airfoil. The coupling between the air boundary layer and the water film is established by the conservation of mass and momentum at the interface. By a simple coordinate transformation, the interface is conformed to the finite difference grid system. Trajectory analysis of a raindrop of 1 mm diameter shows that the impingement of drops is high near the leading edge of the airfoil and decreases downstream. The finite difference equations of air/waterfilm are based on a Crank Nicholson scheme. The solution of finite difference equations at the initial station indicates a film thickness of 0.01 mm. Marching downstream along the surface of the airfoil gives raise to stability problems in the finite difference equations.

A counter-current two-phase flow under an applied electric field has been studied theoretically using potential flow equations. A flooding correlation has been derived taking account of applied electric field on the interface for both adiabatic and condensing system. It is found that the electric field enhances flooding phenomena in case of adiabatic system. In the case with system involving condensation the electric field enhances flooding at low liquid flow rates and at high liquid flow rates the flooding point decreases under electric field depending on the rate of subcooling. / Thesis / Master of Engineering (ME)

A method has been developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier Stokes equations. The entire calculation is performed in the physical domain. The method is currently limited to the calculation of attached flows. The features of the current method can be summarized as follows. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is not needed. Different time steps are used in the different governing equations to improve the convergence speed of the viscous calculations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes (length/height ≅ 1000). A special discretization technique is also used to stabilize these calculations which use long and thin control volumes. A special formulation of the energy equation is used to provide improved transient behavior of solutions which use the full energy equation. The method is then compared with a wide variety of test cases. The freestream Mach numbers range from 0.075 to 2.8 in the calculations. Transonic viscous flow in a converging diverging nozzle is calculated with the method; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good. Essentially incompressible turbulent boundary layer flow in an adverse pressure gradient is calculated and the computed distribution of mean velocity and shear stress are in good agreement with the measurements. At the other end of the Mach number range, a flat plate turbulent boundary layer with a freestream Mach number of 2.8 is calculated using the full energy equation; the computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer. / Ph. D.