TOSHIBA-WESTINGHOUSE FELLOWS PROGRAM FINAL REPORT AN INVESTIGATION OF GEOMETRIC EFFECTS OF A VERTICAL-DOWNWARD ELBOW ON TWO-PHASE FLOW

Transcription

1 PSU-MNE/AMFL TOSHIBA-WESTINGHOUSE FELLOWS PROGRAM FINAL REPORT AN INVESTIGATION OF GEOMETRIC EFFECTS OF A VERTICAL-DOWNWARD ELBOW ON TWO-PHASE FLOW Submitted to: Seungjin Kim Department of Mechanical and Nuclear Engineering The Pennsylvania State University University Park, PA By: Philip Graybill and Andrew Hardison Toshiba Westinghouse Fellows, 2015 Toshiba-Westinghouse Fellows Program Westinghouse Electric Company The Pennsylvania State University Department of Mechanical and Nuclear Engineering August 2015

2 ii ACKNOWLEDGEMENT This work is made possible by Toshiba Westinghouse through the Toshiba Westinghouse Fellows Program. All research has been conducted at the Advanced Multi-Phase Flow Laboratory at The Pennsylvania State University. This research could not have been performed without the oversight and supervision of Dr. Seungjin Kim, Professor of Mechanical and Nuclear Engineering at The Pennsylvania State University, and Shouxu Qiao, Ph.D. student in the Advanced Multi-Phase Flow Laboratory at The Pennsylvania State University.

3 iii Table of Contents Page ABSTRACT... iv I. INTRODUCTION... 1 Background and Significance... 1 Objective... 3 II. EXPERIMENTAL FACILITY... 4 III. NUMERICAL SIMULATION OF SINGLE-PHASE SECONDARY FLOW... 5 Development of Numerical Mesh... 6 Simulation Configuration... 6 Validity of Simulations... 7 Results... 7 IV. EXPERIMENTS IN TWO-PHASE FLOW... 9 Measurement Methodology... 9 Test Conditions Results V. COMPARISON OF NUMERICAL SIMULATIONS WITH EXPERIMENTAL DATA VI. SUMMARY AND RECOMMENDATIONS Summary Recommendations for Future Work REFERENCES APPENDICES Appendix A: CFD Mesh Sensitivity Study Appendix B: CFD Simulation Results for U bulk = 3 m/s, 2 m/s, and 1m/s Appendix C: CFD Repeatability Study Appendix D: Experimental Repeatability Study Appendix E: Experimental Data Appendix F: CFD Simulation Pressure Distribution... 46

4 iv ABSTRACT The purpose of this study is to investigate the geometric effects of a 90-degree verticaldownward elbow on horizontal-to-vertical-downward two-phase flow. Elbow effects are studied with a two-fold approach: first by performing single-phase computational fluid dynamics (CFD) analysis, and second by conducting two-phase flow experiments. Computational fluid dynamics simulations are performed using ANSYS CFX to study elbow effects downstream of a verticaldownward elbow. Two-phase air-water experiments are conducted at 0 diameters (L=0D) and 3 diameters (L=3D) downstream of the vertical-downward elbow using a four-sensor conductivity probe to obtain local two-phase bubble distribution data. This study examines two flow conditions, both within the bubbly flow regime. Results indicate that downstream of the verticaldownward elbow, void fraction distribution does not closely resemble the secondary flow structure (counter-rotating vortices) of single-phase flow. The local void fraction data downstream of the vertical-downward elbow shows a single-peak distribution. This distribution indicates bubble migration toward the inner wall of the elbow. A comparison between this study and previous research demonstrates that elbow orientation dramatically changes the relationship between void fraction in two-phase flow and single-phase secondary-flow structure.

5 1 I. INTRODUCTION Background and Significance Two-phase flows are encountered in a variety of practical systems, such as the coolant systems of nuclear power plants. In pressurized water reactors (PWRs), two-phase flow conditions are predicted to occur during loss-of-coolant-accidents (LOCA) if the primary loop becomes depressurized. The flow paths in nuclear coolant systems, as with many practical systems, are complex and contain flow restrictions. Accurate two-phase modeling of complex systems requires that the effects of geometry on flow structure be understood. Geometric flow restrictions including elbows, valves, and tees dramatically alter the structure of two-phase flow (Yadav, 2013). The restriction type, orientation, as well as upstream flow conditions must be considered when modeling geometrically restricted two-phase flows. Due to the complex nature of two-phase flows, establishing single-phase computational fluid dynamics (CFD) simulations can provides insight into the physical mechanics which impact two-phase flow, and provide comparison for two-phase flow experimentation. Two-phase CFD simulations are not as well-established as those for single-phase flows, and thus much of the CFD research on geometric flow restrictions has been limited to single-phase flows. Previous CFD research studying elbow restrictions has been performed by Kim et al. (2014), and provides a foundation for the CFD analysis of this study. Kim et al. (2014) performs a comprehensive comparative study of turbulent models for single-phase flow in pipes with elbows. Kim et al. (2014) identifies the RNG k-ε turbulence model (Yakhot & Orszag, 1986) as the best predictor of single-phase flow downstream of an elbow. Kim et al. (2014) also characterizes the dissipation secondary flow using this turbulent model by analyzing swirl intensity in the elbow region. The foundational work by Kim et al. (2014) allows for accurate simulations, which enables comparison between the single-phase secondary flow and two-phase flow characteristics such as local void fraction. Comparison of single-phase simulations with two-phase experimental data provides insight into the mechanisms which govern two-phase flow transport through elbows. Two-phase flow experimental research has been conventionally studied in separate vertical or horizontal orientation in relatively simple channel geometries (i.e. round pipes or rectangular channels) without flow restrictions. Despite the importance of flow restrictions, little research has been conducted on the impacts of geometry on two-phase flow, including the

6 2 characterization of the elbow-region downstream of 90-degree elbows. The elbow region is defined by Yadav et al. (2014) as the region of flow where the elbow significantly impacts the two-phase flow parameters. Yadav (2013) provides an excellent introduction to two-phase flow experimental research which seeks to characterize effects of vertical elbows in air-water twophase flow. Yadav s (2013) research focuses on characterizing the structure of vertical-upwardto-horizontal two-phase flow through a vertical-upward elbow, and culminates with a one-group interfacial area transport equation (IATE) for the vertical-upward elbow. Additionally, Yadav et al. (2014) characterizes the dissipation of elbow effects in bubbly flows. Yadav (2013) combines single-phase CFD analysis with two-phase experimental data in an analysis of the vertical-upward elbow. Yadav (2013) compares the void fraction distribution and the secondary flow structure at 3 diameters (L=3D) after vertical-upward elbow as shown in Figure 1. Figure 1 is oriented such that the vertical-upward flow would enter the elbow from the bottom of the page, and flow into the page in the horizontal section following the elbow. Because both experimental data and single-phase simulations show symmetry about the vertical axis of Figure 1, a split image comparison is possible. Yadav s (2013) results show that in bubbly flow, bubbles become entrained by the swirling of secondary flow and create a distinct bimodal void fraction distribution in the elbow region after the vertical-upward elbow. Figure 1 clearly shows that regions of the highest void fraction (indicated by dark red in Figure 1 (b)) are centered about core of secondary swirling (indicated by the white arrows in Figure 1 (a)). This research by Yadav (2013) is useful as comparison for the vertical-downward elbow. In view of the limited studies on elbow effects in two-phase flow, continuing study of the elbow effects and other flow restrictions is important for both practical applications and for furthering the scientific understanding of these subjects.

7 3 Figure 1. Previous research by Yadav (2013) showing the effect of a 90-degree vertical-upward elbow on (a) single-phase flow, where contours show the streamwise velocity and white arrows indicate secondary flow velocity, and (b) two-phase flow, where contours show local void fraction (Flow conditions: j f = 3.00 m/s and j g,atm = 0.14 m/s). Objective This research examines the geometric effects of a 90-degree vertical-downward elbow for air-water two-phase flow by performing a two-fold study: single-phase CFD simulations, and two-phase experiments. In this study, single-phase CFD analysis is performed for a verticaldownward elbow to reveal the secondary flow structure downstream of an elbow. Air-water two-phase flow experiments are performed and analyzed downstream of the vertical-downward elbow. Single-phase flow structure and two-phase flow bubble distribution are compared to gain insight into the mechanisms that affect two-phase flow after a vertical-downward elbow. Finally, previous results of Yadav et al. (2014) are compared with the results of this study to analyze the effects of elbows at different orientations.

8 4 II. EXPERIMENTAL FACILITY AND INSTRUMENTATION Experiments are performed in the Combinatorial Two-Phase Flow Test Facility at the Advanced Multi-Phase Flow Laboratory at the Pennsylvania State University. The Combinatorial Two-Phase Flow Test Facility is an adiabatic air-water test facility designed to investigate the effects of orientation change and flow restrictions on two-phase flow transport. This experimental facility, shown in Figure 2, contains a vertically-oriented flow loop. The loop geometry is constructed of acrylic pipes of 50.8 mm inner diameter, which are interconnected via 90-degree glass elbows and have a radius of curvature of 152.4mm. The vertical-upward and vertical-downward glass elbows are positioned at 63 L/D and L/D from the two-phase flow inlet. Filtered water flows from a storage tank (2300 liter capacity) into the inlet. A double-annulus sparger, with a pore size of 10 micrometers, is located at the inlet to generate bubbles. Bubble size is controlled to be uniform at ~2 to 3 mm in diameter at the inlet by fixing the flow rate of the inner annulus to control bubble shear. At the exit of the loop a dual-stage damper-separator system is used to separate the air from the two-phase mixture and return the water back to the storage tank for recirculation. The state-of-the-art four-sensor conductivity probe is used to measure local timeaveraged two-phase flow parameters (Kim et al., 2000). A detailed discussion of the conductivity probe is provided in Section IV. The flow rate of the water is measured with a twowire electromagnetic flowmeter, and the flow rate of the air is controlled by a set of rotameters A differential pressure transducer is used to measure the pressure difference across the elbow.

9 5 Figure 2. Schematic of the experimental facility (Adapted from Yadav (2013)). For the experiments in this study, the red valves are closed to provide two-phase flow through injector A. III. NUMERICAL SIMULATION OF SINGLE-PHASE SECONDARY FLOW The commercially available CFD software ANSYS CFX 14.5 is used to simulate the entire loop geometry of Combinatorial Two-Phase Flow Test Facility at the Advanced Multi- Phase Flow Laboratory as shown in Figure 2. The single-phase CFD simulations in this study extend previous elbow research by Kim et al. (2014) to include a geometry containing three vertical and two horizontal sections interconnected by four vertical elbows; only the verticaldownward elbow, however, is investigated in this study. Single-phase CFD simulations are analyzed in this study because CFD simulations for two-phase flows are not as well-established as those for single-phase flows.

10 6 Development of Numerical Mesh A structured topology is used to discretize the loop geometry. Meshing is performed in ANSYS ICEM CFD. Hexahedral cells, with grid lines aligned with the axial flow, comprise the mesh. The non-dimensional distance from the pipe wall based on friction velocity, the y+ value, is targeted to be 50, and controlled to be within 40 to 100. A mesh-sensitivity test has been performed to determine a suitable mesh and demonstrate grid-independence of the CFD solutions. The detailed results of the mesh sensitivity study are given in Appendix A. The mesh that is used for the remainder of this investigation contains 4.46 million cells. Images of a section of the mesh are shown in Figure 3. (a) (b) Figure 3. (a) A cross-section showing grid geometry and spacing of mesh. (b) Image of mesh showing axial cell spacing relative to cross-sectional spacing. Simulation Configuration Research by Kim et al. (2014) indicates that the RNG k-ε turbulence model (Yakhot & Orszag, 1986) best predicts single-phase flow conditions after an elbow. Thus, this study exclusively studies the RNG k-ε model for numerical simulations. Simulations are configured as follows: The flow of water is solved at 25 C, under steady state conditions. Advection fluxes and turbulence numerics are determined with a high-resolution scheme (ANSYS Inc., 2013). Scalable wall functions are employed to accurately model the near-wall turbulence of boundary layer region. ANSYS CFX implements a coupled solver to iteratively solve the Navier-Stokes

11 7 equations (ANSYS Inc., 2013). All simulations are iteratively solved until the root mean square of the residuals have converged below 1e-7. The boundary conditions used for simulations are specified as follows: The inlet velocity is fixed at a uniform value, referred to as the bulk velocity. Four simulations are performed, with bulk velocities of 1, 2, 3, and 4 m/s respectively. Simulation results for 4 m/s are presented in this report. Simulation results for bulk velocities of 1 m/s, 2 m/s, and 3 m/s are presented in Appendix B, and show nearly identical trends as the 4 m/s simulation. The inlet turbulent intensity is estimated to be of medium intensity, and set to be 5% of the bulk velocity. The outlet boundary condition is specified as a pressure outlet. Validity of Simulations To assess the accuracy of our models, the CFX simulation results from the current study are compared against OpenFOAM CFD results of Kim et. al (2014), and the LDA experimental results of Sudo et al. (1998). The CFX simulations are well within ±5% of previous simulations, and are roughly within ±10% of the experimental data of Sudo et al. (1998). Figure C-1 and C-2 in Appendix C presents the CFX simulations velocity profiles compared to previous work of Kim et al. (2014) and Sudo et al. (1998). Validation of the CFX models is also conducted by comparing the dissipation of swirl intensity after an elbow. Swirl Intensity is a metric which quantifies the magnitude secondary flow, and is defined in more detail in Appendix C. The dissipation of swirl intensity downstream of an elbow is used to assess the consistency of our simulations with previous research. The comparison of swirl intensity dissipation for current and previous simulation of an inlet velocity of 1 m/s and 4 m/s is presented in Appendix C Figure C- and C-4. When compared against previous research, the dissipation rates of the CFX simulations of this study match the findings of Kim et al. (2014). Both velocity profile and dissipation of swirl intensity results suggest our model accurately predicts the single-phase flow conditions of the vertical-upward elbow. By confirming our results agree with previous simulation research, the simulation analysis can be confidently extended to the vertical-downward elbow. Results The vertical-downward elbow is analyzed at L=0D, 3D, 10D, 50D after the elbow. Figure 4 presents the cross-sectional simulation results for a bulk velocity of 4 m/s. The contours show streamwise velocity. The arrows which overlay the contours show the direction

12 8 and magnitude of the tangential velocity, which represents the secondary flow or swirl. Figure 4 cross sections are oriented such that the horizontal flow would enter the elbow from the left side of the page, and flow into the page in the vertical-downward section following the elbow. Figure 4. Results of CFD analysis shown at 0D, 3D, 10D, and 50D after the vertical-downward elbow with a bulk velocity of 4 m/s. The contours show streamwise velocity. The arrows which overlay the contours show the direction and magnitude of the tangential velocity, which is known as the secondary flow or swirl. As evidenced by the tangential velocity vectors in Figure 4, the elbow geometry causes two counter-rotating vortices to develop downstream of the elbow. At L=0D, the tangential velocity vectors reveal kidney-bean-shaped vortices (seen at the top left and bottom left in Figure 4, at L=0D). The maximum tangential velocity at L=0D is 1.2 m/s. The counter-rotating vortices decrease in intensity further downstream of the elbow. At L=3D, the vortex shape is

13 9 more circular than at L=0D, and the vortex has migrated closer to the centerline of the pipe that is perpendicular to curvature of the elbow. Streamwise velocity near the outer wall increases from 0D to 3D. The higher streamwise velocity in 3D is complemented by a larger region of low velocity. This region of low velocity has propagated outward (relative to 0D) due swirling. By L=10D, the vortex core has almost reached the centerline of the pipe that is perpendicular to curvature of the elbow. The tangential velocity vectors also have decreased in size, indicating dissipation of secondary flow. The streamline velocity has become significantly more uniform. Analysis of our simulations show that by 15D, swirl Intensity has decreased by 90% (see Appendix C). By 50D, the flow remains undeveloped; swirl intensity, however, has decayed to a negligible amount. When CFD simulations are compared between the vertical-upward and verticaldownward elbow, the results are nearly identical. This result confirms that single-phase flow structure is independent of elbow orientation, as detailed in Appendix C. IV. EXPERIMENTS IN TWO-PHASE FLOW Measurement Methodology To obtain detailed measurements of local time-averaged two-phase flow parameters, the state-of-the-art four-sensor conductivity probe is employed. The four-sensor conductivity probe accurately measures local two-phase flow parameters such as bubble frequency (f b ), bubble velocity (v g ), void fraction (α), and interfacial area concentration (a i ). A complete description of the conductivity probe is provided by Kim et al. (2000). A traversing unit is used to position the probe at points within the pipe cross-section to an accuracy of 0.01 mm. Data is sampled at 50 khz for 30 seconds for each measurement point in the pipe cross-section. This sampling rate and measurement duration ensures that the signals from the bubbles are adequately resolved and that a significant number of bubbles (~2000) are measured by the probe to obtain accurate timeaveraged data. The conductivity probe can be installed in the flow loop using a measurement port as shown in Figure 5. Because the flow downstream of a vertical-downward elbow is not axisymmetric, the measurement ports are designed to rotate at 22.5 degree intervals without stopping the flow. In this experiment, the azimuthal directions θ = 0 and 90 degrees are defined

14 10 along the axes perpendicular to the elbow curvature (designated as (r/r) p ) and parallel to the axis of curvature (designated as (r/r) c ) respectively. For convenience, the inner wall will refer to the wall associated with the inner curvature of the elbow; likewise the outer wall refers to the wall associated with the outer curvature of the elbow, as shown in Figure 5 (b). The measurement port used for experimentation after the vertical-downward elbow is located 3D after the verticaldownward elbow. During each experiment, the probe is traversed in the radial direction to 15 different positions across the entire diameter of the pipe, and rotated between 0 and degrees at 22.5 degree increments. Figure 5 (b) shows the measurement grid employed during experimentation; each gray circle represents a measurement location. Thus, a total of 120 data points are collected per cross-section. The radial coordinates of the measurement points in the cross section are non-dimensionalized where r/r=0 is defined as the center of the pipe and r/r=±1 correspond to the pipe walls at opposite ends of a given diameter. (a) (b) Figure 5. (a) Photograph of the measurement port. (b) The measurement grid and corresponding coordinate system used for local conductivity probe measurements in the verticaldownward section. Gray circles indicate measurement locations. Test Conditions Previous research within the Advanced Multi-Phase Flow Laboratory by Yadav (2013) has resulted in the development of a database to categorize two-phase flow conditions. Table 1 displays the established flow conditions designated for two-phase flow research. The established flow conditions are known as Runs. The experiments performed in this study extend the

15 11 existing database to include Run 7 and Run 8 flow conditions for the vertical-downward elbow. Conductivity probe measurements are performed for both conditions at L=0D and L=3D after the vertical-downward elbow of the test facility. To confirm repeatability, conductivity probe data from this study at L=3D for Runs 5, 7, and 8 are compared to existing data from the Advanced Multi-Phase Flow Laboratory. The details of the repeatability analysis are presented in Appendix D. The experiments are performed at 20 C. Table 1. The two-phase flow conditions used for experimentation at the Advanced Multi-phase Fluids Laboratory. This study focuses on Run 7 and Run 8 flow conditions, denoted by a gray shading. jf: volumetric liquid flux jg: volumetric gas flux Results Figure 6 and Figure 7 plot void fraction measurements obtained with the conductivity probe for Run 7 and Run 8 respectively at 0D and 3D after the vertical-downward elbow. These surface plots are created in MATLAB using third-order interpolation of local data collected during experimentation. Local data used to generate the results of this study can be found in Appendix E. The void fraction is plotted on the vertical axis in Figures 6 and 7. Under Run 7 conditions at 0D after the elbow, a prominent single-peak distribution of the void fraction is evident near the inner wall. A ridge of high void fraction circles the pipe near the wall (at approximately r/r=0.7). At 3D, the void fraction distribution is still single-peaked, but has significantly dissipated in magnitude in comparison with 0D. The ridge feature of 0D has disappeared by 3D. The data from 3D shows evidence of a slightly bimodal distribution, with two minor peaks located near the wall of inner curvature. Similar to the Run 7, a pronounced single-peak void fraction distribution is shown at 0D for Run 8. This void fraction peak of Run 8 is higher than the peak of Run 7, reaching a maximum value of 0.14 as compared For Run 8, the ridge feature seen in Run 7 is no longer distinct. By 3D, the distribution of the void fraction remains single-peaked, but has dissipated from the upstream conditions at 0D. A bimodal peaking is not shown by this data,

16 12 however the single-peak distribution is elongated in the direction perpendicular to the axis of curvature. (a) (b) Figure 6. Run 7 void fraction surface plots at (a) L/D=0 and (b) L/D=3. (a) (b) Figure 7. Run 8 void fraction surface plots at (a) L/D=0 and (b) L/D=3.

17 13 V. COMPARISON OF NUMERICAL SIMULATIONS WITH EXPERIMENTAL DATA Single-phase liquid velocity is compared with two-phase void fraction in Figure 8 for Run 7 and Figure 9 for Run 8. Single-phase and two-phase results are compared for 0D and 3D after the vertical-downward elbow. The upper half of Figures 8 and 9 show the CFD simulation results. The contours show streamwise velocity, and the arrows show the direction and magnitude of the tangential velocity. The lower half of Figures 8 and 9 show contour plots of the void fraction. Because both simulation and experimental results show symmetry about the axis parallel with curvature, (r/r) p, the overlaid results of Figures 8 and 9 allow for easy comparison. The results of Run 7 show that void fraction distribution does not closely resemble the secondary flow structure. The void fraction distribution is primarily single-peaked near the inner wall at both 0D and 3D. Oppositely, the swirling associated with the coupled vortices is centered near the pipe walls perpendicular to the axis of curvature of the elbow. This difference in structure is most evident at 0D. Likewise, Run 8 does not show an obvious relationship between void fraction distribution and secondary flow structure. Results show that swirling does not entrain a significant amount of bubbles after the vertical-downward elbow. The results of the current study which compare single-phase and two-phase show significantly different relationships between secondary flow and void fraction distribution than are seen for the vertical-upward elbow studied by Yadav (2013). Recall that Yadav s (2013) results presented in Figure 1 show a distinct bimodal void fraction distribution which peaks at the vortex centers of the secondary flow. The difference between the results for the verticaldownward elbow and the vertical-upward elbow are largely due to the flow conditions upstream of the elbows, as well as the differing effects of buoyancy caused by the different orientations. Flow conditions upstream of the vertical-downward elbow and the vertical-upward elbow are quite different, and consequently cause different elbow effects. Upstream flow conditions act as the inlet conditions to the elbows. The previous study by Yadav (2013) found that in bubbly flow, bubbles are well distributed prior to entering the vertical-upward elbow. Conversely, the inlet conditions of the vertical-downward elbow are characterized by a poorly-distributed inlet of bubbles; the majority of bubbles enter the elbow near the upper wall as a result of buoyancy. In two-phase flow, liquid which enters the elbow tends to follow the outside curvature due to a greater inertia than the gas phase, and as a result pushes the gas phase toward the inner curvature.

18 14 This creates a pressure distribution in the pipe. Because the pressure distribution acts similarly for the vertical-upward and vertical-downward elbow, it is therefore not a mechanism which causes void fraction distribution differences. (However it does provide insight on the pressure forces acting on bubbles, and explains why a slightly bimodal peaking at L=3D after the verticaldownward elbow might occur. For more detail, see Appendix F.) Because gas enters the vertical-downward elbow nearly exclusively in one region of pipe (the upper wall), the elbow swirling acts on the gas in a uniform manner, and pushes nearly all bubbles toward the inner wall of the elbow. For the vertical-upward elbow, which has a well-dispersed bubble distribution within the pipe at the elbow inlet, bubbles located at different radial and azimuthal positions experience different forces and effects from the secondary flow (both direction and magnitude differences). Thus, bubbles move differently depending on their original position in the pipe at the inlet to the elbow. This keeps bubbles distributed more evenly throughout the pipe (where bubbles become entrained by swirl), and does not cause the dramatic single-peak that is seen in the vertical-downward elbow. Elbow orientation and buoyancy effects contribute to bubble distribution. As mentioned previously, the high inertia water forces gas to swirl toward the inner wall of the pipe. For the vertical-upward elbow, buoyancy opposes bubble accumulation near the inner wall of the elbow. Instead, buoyancy causes an upward force on the bubbles which spreads the bubbles in the cross section at the exit of the vertical-upward elbow. The secondary flow is then able to influence the bubble distribution, which results in the bimodal peaking of void fraction. Quite differently, in the vertical downward elbow, buoyancy acts in a direction opposite the flow direction (orthogonal to the transverse direction) after the elbow. Consequently buoyancy no longer helps bubbles spread in the pipe, and bubbles become entrained significantly less by the secondary flow. Additionally, buoyancy forces oppose the fluid velocity, and allow bubbles to accumulate in the region following the vertical-upward elbow. This is accumulation is aided by the low velocity water located at the inner wall of the elbow. As seen at 0D after the elbow lowest streamwise velocity corresponds to the region of highest void fraction.

19 15 (a) (b) Figure 8. Figure 8 shows a comparison of single-phase CFD liquid velocity (upper crosssection) with void fraction distribution (lower cross-section) for Run 7 conditions at (a) L=0D and (b) L=3D after the elbow. (a) (b) Figure 9. Figure 9 shows a comparison of single-phase CFD liquid velocity (upper crosssection) with void fraction distribution (lower cross-section) for Run 8 conditions at (a) L=0D and (b) L=3D after the elbow.

20 16 VI. SUMMARY AND RECOMMENDATIONS Summary and Conclusion This study presents an analysis of the geometric effects of a vertical-downward elbow on bubbly air-water two-phase flow. Two-phase flow experiments are performed at 0D and 3D after the vertical-downward elbow. The experimental facility consists of three vertical and two horizontal sections, interconnected by four vertical elbows. A state-of-the-art four-sensor conductivity probe was used to obtain detailed measurements of local two-phase flow parameters. The computational fluid dynamics solver ANSYS CFX is used to perform simulations of single-phase flow of the test facility, and the simulation results are analyzed at 0D, 3D, 10D, and 50D after the vertical-downward elbow. The simulation results for single-phase flow show the secondary flow characteristics of elbows, and confirm that single-phase flow structure is independent of elbow orientation. Twophase flow experimental results show a sharp, single-peaked void fraction distribution at 0D. At 3D, the experimental results show a less extreme single-peaked distribution, with some evidence of a secondary bimodal peaking. A comparison of the single-phase results and the two-phase results demonstrates that void fraction distribution does not closely resemble the secondary flow structure after the verticaldownward elbow. This suggests other dominant effects such as upstream flow conditions and buoyancy effects. The secondary flow structure of single-phase flow and the void fraction of two-phase flow of this study differ significantly in nature from similar comparisons made by Yadav et al. (2013) for the vertical-upward elbow. In the elbow region after a vertical-upward elbow, the secondary flow entrains the bubbles, and causes a distinct bimodal-peaked distribution centered about the vortex cores. However, in the vertical-downward elbow, a strong correlation between swirl and void fraction does not exist. Recommendations for Future Work The current research helps develop the database needed to model geometric effects on two-phase flow, specifically elbow effects downstream of a vertical-downward elbow. Only two new flow conditions are presented in this study. There is a need for more data collection at different flow conditions and locations downstream of the vertical-downward elbow. It is recommended to continue collecting more flow conditions and locations in order to develop a

21 17 strong database to accurately model geometric effects on two-phase flow. Suggested locations of data to be taken are at 9D, 12D, 15D, and 20D. Conductivity probe data should be collected at a variety of flow rates. It is recommended that following additional data collection, new predictive models for two-phase flow around restrictions should be created. Finally, after predictive models have been in developed, the predictive models should be implemented to reactor system safety analysis code for improved modeling of disaster-type situations. This improved modeling will improve the safety of reactors, which is ultimately of primary importance.

22 18 REFERENCES ANSYS Inc. (2013). ANSYS CFX-Solver Modeling Guide. Crawford, N. M., Cunningham, G., & Spence, S. W. T. (2007). An Experimental Investigation Into the Pressure Drop for Turbulent Flow in 90 Elbow Bends. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 221(2), doi: / jpme84 Hibiki, T., & Ishii, M. (2000). Two-group interfacial area transport equations at bubbly-to-slug flow transition. Nuclear Engineering and Design, 202(1), doi: /s (00) Ishii, M., & Hibiki, T. (2006). Thermo-Fluid Dynamics of Two-Phase Flow. New York, N.Y: Springer Science+Business Media. Kim, J., Yadav, M., & Kim, S. (2014). Characteristics of Secondary Flow Induced by 90-degree Elbow in Turbulent Pipe Flow. Engineering Applications of Computational Fluid Mechanics, 8(2), doi: / Kim, S., Fu, X. Y., Wang, X., & Ishii, M. (2000). Development of the Miniaturized Four-Sensor Conductivity Probe and the Signal Processing Scheme. International Journal of Heat and Mass Transfer, 43(22), doi: /s (00) Mena, D., Personal Communication (2015), Department of Mechanical and Nuclear Engineering, The Pennsylvania State University. Yadav, M. S. (2013). Interfacial Area Transport Across Vertical Elbows in Air-Water Two- Phase Flow. Pennsylvania State University. University Park, Pa. Yadav, M. S., & Kim, S. (2013). EFFECTS OF 90-deg VERTICAL ELBOWS ON THE DISTRIBUTION OF LOCAL TWO-PHASE FLOW PARAMETERS. Nuclear Technology, 181(1), Yadav, M., Worosz, T., Kim, S., Tien, K., & Bajorek, S. (2014). Characterization of the Dissipation of Elbow Effects in Bubbly Two-Phase Flows. International Journal of Multiphase Flow, 66, doi: /j.ijmultiphaseflow Yakhot V, Orszag SA (1986). Renormalization Group Analysis of Turbulence: I. Basic Theory. Journal of Scientific Computing 1(1):1-51.

23 19 APPENDICES Appendix A: CFD Mesh Sensitivity Study Appendix B: CFD Simulation Results for U bulk = 3 m/s, 2 m/s, and 1m/s Appendix C: CFD Repeatability Study Appendix D: Experimental Repeatability Study Appendix E: Experimental Data Appendix F: CFD Simulation Pressure Distribution... 46

24 20 Appendix A: CFD Mesh Sensitivity Study A mesh sensitivity test was conducted to ensure a grid-independent solution is obtained. A mesh sensitivity test is performed by refining a mesh until the CFD solution changes negligibly between refinements. Figure A-1 shows the three meshes tested for this sensitivity study, and have 0.70, 3.02, and 4.46 million cells. Presented in Figure A-2 are partial results from the mesh sensitivity test. Figure A-2 displays the streamwise velocity profile at 3D after the vertical-downward elbow for theta=0 and theta=90 and an inlet velocity 4m/s. As seen in Figure A-2, the velocity profile of the meshes with 3.02 and 4.46 million cells changes negligibly. Thus, the solution is no longer gird dependent, and the 4.46 million cell mesh can be confidently analyzed. Figure A-1. This figure shows cross sectional views of the three meshes with 0.70, 3.02, and 4.46 million cells which are used in the mesh sensitivity test.

25 Figure A-2. This figure presents the streamwise velocity profile at 3D after the verticaldownward elbow for theta=0 and theta=90 and for an inlet velocity 4m/s. The legend labels of y50_4_46m, y50_3_02m, and y50_0_70m correspond to mesh with 4.46, 3.02, and 0.70 million cells respectively. 21

26 22 Appendix B: CFD Simulation Results for U bulk = 3 m/s, 2m/s, and 1 m/s CFD simulations are performed for ANSYS CFX 14.5 for bulk velocities of 1, 2, 3, and 4 m/s. Presented in this appendix are simulation results for bulk velocities of 1 m/s, 2 m/s, and 3 m/s. The trends seen in Figures B-1 to B-3 are identical to the trends previously identified in this report for an inlet velocity of 4 m/s. Figure B-1 Results of CFD analysis shown at 0D, 3D, 10D, and 50D after the verticaldownward elbow at a bulk velocity of 3 m/s. The contours show streamwise velocity. The arrows which overlay the contours show the direction and magnitude of the tangential velocity, which is known as the secondary flow or swirl.

27 Figure B-2. Results of CFD analysis shown at 0D, 3D, 10D, and 50D after the verticaldownward elbow at a bulk velocity of 2 m/s. The contours show streamwise velocity. The arrows which overlay the contours show the direction and magnitude of the tangential velocity, which is known as the secondary flow or swirl. 23

28 Figure B-3. Results of CFD analysis shown at 0D, 3D, 10D, and 50D after the verticaldownward elbow at a bulk velocity of 1 m/s. The contours show streamwise velocity. The arrows which overlay the contours show the direction and magnitude of the tangential velocity, which is known as the secondary flow or swirl. 24

29 25 Appendix C: CFD Repeatability Study To assess the accuracy of our models, the CFX simulation results of this study are first compared against the OpenFOAM CFD results of Kim et. al (2014), and the LDA experimental results of Sudo et al. (1998). The comparison is made for the elbow region after the verticalupward elbow. The velocity profiles of the CFX simulations closely match that of the previous OpenFOAM simulations by Kim et al. (2014). The CFX simulations in this study are well within ±5% of previous simulations (average of 4.35% difference), and are roughly within ±10% of the experimental data of Sudo et al. (2013). In the experiment of Sudo et al. (1998), a elbow with a radius of curvature of 2D and a Reynold s number 60,000 based on pipe diameter and bulk velocity were analyzed. For the current CFX studies, a bulk velocity of 1m/s results in a Reynold s number of the 50,800. This Reynold s number is comparable to Reynold s number in the research done by Sudo et al. (1998). Thus, these experimental and CFD results can be compared. Figure C-1 and Figure C-2 are a comparison the CFX simulations to previous work at L=3D, 10D, and 50D for both theta=0 and theta= 90 degrees with a bulk velocity of 1m/s and 4 m/s respectively.

30 Figure C-1. This figure illustrates streamwise velocity profiles at 3D, 10D, and 50D after the vertical-downward elbow at theta=0 and theta=90 for an inlet velocity 4m/s. The vertical axis displays non-dimensionalized radius, while the horizontal axis displays non-dimensionalized velocity (streamwise velocity divided by bulk velocity) 26

31 27 Figure C-2. This figure illustrates streamwise velocity profiles at 3D, 10D, and 50D after the vertical-downward elbow at theta=0 and theta=90 for an inlet velocity 4m/s. The vertical axis displays non-dimensionalized radius, while the horizontal axis displays non-dimensionalized velocity (streamwise velocity divided by bulk velocity) Validation of the CFX models with previous research is also conducted by comparing the dissipation of swirl intensity after an elbow. Swirl Intensity is a metric which quantifies the magnitude secondary flow. The dissipation of swirl intensity is also compared with previous research. Swirl intensity (I s ) is defined by Kim et al (2013) to be the following: (1) where U is a vector of flow velocity and n is a unit normal vector to the pipe section area. When compared against previous research, the dissipation rate found in this study matches the findings of Kim et al. (2014). The comparison of swirl intensity dissipation results for simulations with a bulk velocity of 4 m/s are presented in Figure B-2. Figure B-3 presents swirl intensity decay for

32 28 simulations with 1, 2, and 4 m/s bulk velocity conditions. Swirl intensity has been normalized for comparison. When compared against previous research, the dissipation rates of the CFX simulations of this study match the findings of Kim et al. (2014). Both velocity profile and dissipation of swirl intensity results suggest our model accurately predicts the single-phase flow conditions of the vertical-upward elbow. By confirming our results agree with previous simulation research, the simulation analysis can be confidently extended to the verticaldownward elbow. Additionally, Figure C-3 shows that for single-phase flow, swirl intensity dissipation is independent of orientation. Figures C-3 and C-4 show that by 15D, 90% of the swirl has dissipated. At 90% dissipation, the elbow region is considered to have ended. Figure C-3. This figure displays a comparison swirl intensity dissipation after the upwarddownward elbow (CFX simulation and Kim et al. (2014) OpenFOAM simulation) and after a vertical-downward elbow (CFX simulation) for an inlet velocity 4m/s. The vertical axis displays normalized swirl intensity, while the horizontal axis displays the non-dimensionalized development length in diameters after the vertical-downward elbow.

33 Figure C-4. This figure displays swirl intensity dissipation after the vertical-upward elbow for inlet velocities of 1, 2, and 4m/s. The vertical axis displays normalized swirl intensity, while the horizontal axis displays the non-dimensionalized development length in diameters after the vertical-downward elbow. 29

34 30 Appendix D: Experimental Repeatability Study To confirm repeatability, experimental conditions were tested to determine if the new results are consistent with the existing database. The existing database for the verticaldownward elbow contains data for L=3D at Run 7 and Run 8 conditions (Mena, Personal Communication), and data by Yadav (2013) at L=3D for Run 5. Figure D-1 compares the local void fraction data measured in the current study with existing data collected by Mena (2015). Table D-1 shows the void fraction and elbow strength values for Run 7 at 3D after the verticaldownward elbow. Likewise, Figure D-2 and Table D-2 compare local void fraction and elbow strength for Run 8 conditions. Figure D-3 and Table D-3 compare local void fraction and elbow strength for Run 5 conditions. The comparison results for Run 7 and Run 8 show excellent agreement (within ±10%). The comparison for Run 5 shows a lesser agreement; however it still suggest repeatability of the data. (a) Current (b) Mena, (2015) Figure D-1 This figure compares conductivity probe data taken at L=3D after the verticaldownward elbow for Run 7 flow conditions. Void fraction is plotted on the vertical axis for (a) data of the current study and (b) Mena s (2015) data.

35 31 Table D-1 This Table displays the area averaged void fraction and elbow strength at 3D after the verticaldownward elbow for current data and previous data (Mena, 2015) for Run 7. (a) Current (b) Mena, (2015) Figure D-2 This figure compares conductivity probe data taken at L=3D after the verticaldownward elbow for Run 8 flow conditions. Void fraction is plotted on the vertical axis for (a) data of the current study and (b) Mena s (2015) data. Table D-2 This Table displays the area averaged void fraction and elbow strength at 3D after the verticaldownward elbow for current data and previous data (Mena, 2015) for Run 8.

36 32 (a) Current (b) Yadav, (2013) Figure D-3 This figure compares conductivity probe data taken at L=3D after the verticaldownward elbow for Run 8 flow conditions. Void fraction is plotted on the vertical axis for (a) data of the current study and (b) Yadav s (2013) data. Table D-3 This Table displays the area averaged void fraction and elbow strength at 3D after the verticaldownward elbow for current data and previous data (Yadav, 2013) for Run 5.

37 33 Appendix E: Experimental Data Appendix E provides the database of local two-phase flow parameters measured along the vertical-downward section studied in this research. The measured parameters include local time-averaged void fraction (α), interfacial area concentration (a i ), bubble velocity (v g ), bubble Sauter mean diameter (D sm ), and bubble frequency (f b ). Tables present both group-i and group- II bubbles (Hibiki & Ishii, 2000). Because the flow conditions examined in this study are within bubbly flow, few group-ii bubbles are measured.

38 34 Table E.1.1. Experimental data obtained by four-sensor conductivity probe for Run 7 (j f = 4.00 m/s, j g,atm = 0.23 m/s) at L/D]H = 0. Void Fraction, α-i [-] Interfacial Area Concentration, a i -I [1/m] r/r Void Fraction, α-ii [-] Interfacial Area Concentration, a i -II [1/m] r/r

39 35 Table E.1.2. Experimental data obtained by four-sensor conductivity probe for Run 7 (j f = 4.00 m/s, j g,atm = 0.23 m/s) at L/D]H = 0. Bubble Velocity, v g -I [m/s] Sauter Mean Diameter, D sm -I [mm] r/r Bubble Velocity, v g -II [m/s] Sauter Mean Diameter, D sm -II [mm] r/r

40 36 Table E.1.3. Experimental data obtained by four-sensor conductivity probe for Run 7 (jf = 4.00 m/s, jg,atm = 0.23 m/s) at L/D]H = 0. Bubble Frequency, fb-i [Hz] Bubble Frequency, fb-ii [Hz] r/r

41 37 Table E.2.1. Experimental data obtained by four-sensor conductivity probe for Run 7 (jf = 4.00 m/s, jg,atm = 0.23 m/s) at L/D]H = 3. Void Fraction, α-i [-] Interfacial Area Concentration, a i -I [1/m] r/r Void Fraction, α-ii [-] Interfacial Area Concentration, a i -II [1/m] r/r

42 38 Table E.2.2. Experimental data obtained by four-sensor conductivity probe for Run 7 (jf = 4.00 m/s, jg,atm = 0.23 m/s) at L/D]H = 3. Bubble Velocity, v g -I [m/s] Sauter Mean Diameter, D sm -I [mm] r/r Bubble Velocity, v g -II [m/s] Sauter Mean Diameter, D sm -II [mm] r/r

43 39 Table E.2.3. Experimental data obtained by four-sensor conductivity probe for Run 7 (jf = 4.00 m/s, jg,atm = 0.23 m/s) at L/D]H = 3. Bubble Frequency, fb-i [Hz] Bubble Frequency, fb-ii [Hz] r/r

44 40 Table E.3.1 Experimental data obtained by four-sensor conductivity probe for Run 8 (jf = 4.00 m/s, jg,atm = 0.35 m/s) at L/D]H = 0. Void Fraction, α-i [-] Interfacial Area Concentration, a i -I [1/m] r/r Void Fraction, α-ii [-] Interfacial Area Concentration, a i -II [1/m] r/r

45 41 Table E.3.2. Experimental data obtained by four-sensor conductivity probe for Run 8 (jf = 4.00 m/s, jg,atm = 0.35 m/s) at L/D]H = 0. Bubble Velocity, v g -I[m/s] Sauter Mean Diameter, D sm -I [mm] r/r Bubble Velocity, v g -II [m/s] Sauter Mean Diameter, D sm -II [mm] r/r

46 42 Table E.3.3. Experimental data obtained by four-sensor conductivity probe for Run 8 (jf = 4.00 m/s, jg,atm = 0.35 m/s) at L/D]H = 0. Bubble Frequency, fb-i [Hz] Bubble Frequency, fb-ii [Hz] r/r

47 43 Table E.4.1. Experimental data obtained by four-sensor conductivity probe for Run 8 (jf = 4.00 m/s, jg,atm = 0.35 m/s) at L/D]H = 3. Void Fraction, α-i [-] Interfacial Area Concentration, a i -I [1/m] r/r Void Fraction, α-ii [-] Interfacial Area Concentration, a i -II [1/m] r/r

48 44 Table E.4.2. Experimental data obtained by four-sensor conductivity probe for Run 8 (jf = 4.00 m/s, jg,atm = 0.35 m/s) at L/D]H = 3. Bubble Velocity, v g -I[m/s] Sauter Mean Diameter, D sm -I [mm] r/r Bubble Velocity, v g -II [m/s] Sauter Mean Diameter, D sm -II [mm] r/r

49 45 Table E.4.3. Experimental data obtained by four-sensor conductivity probe for Run 8 (jf = 4.00 m/s, jg,atm = 0.35 m/s) at L/D]H = 3. Bubble Frequency, fb-i [Hz] Bubble Frequency, fb-ii [Hz] r/r

50 46 Appendix F: CFD Simulation Pressure Distribution Local pressure data is obtained from the CFD simulations to help understand the physical mechanisms driving flow structure. Presented in Figure D-1 are local pressure distributions for 0D and 3D after the vertical-downward elbow for an inlet velocity of 4 m/s. Note that the scales in Figure D-1 (a) and Figure D-1 (b) are unique. Figure D-1 (a) shows an 8.6% absolute pressure difference between the high pressure region located along the outer wall of the pipe and the low pressure region located near the inner wall of the pipe. This pressure distribution is caused by the inertia of the water, and is a significant factor bubble in distribution. As seen in Figure D-1 (b), a 1.3% absolute pressure difference occurs between the low pressure regions at the center of swirling and the high pressure regions located at the inner wall of curvature where the swirling water meets. Swirling is the primary cause of this pressure difference at 3D, and while small, this pressure difference can explain the appearance of a slight bimodal distribution. (a) (b) Figure F-1. This figure displays the local pressure distributions for 0D and 3D after the vertical-downward elbow for an inlet velocity of 4 m/s. Note the scales in (a) and (b) are unique.