The Physical Model Study of the Folsom Dam Auxiliary Spillway System

Transcription

1 ST. ANTHONY FALLS LABORATORY Engineering, Environmental and Geophysical Fluid Dynamics PROJECT REPORT 511 The Physical Model Study of the Folsom Dam Auxiliary Spillway System By Matthew L. Lueker, Omid Mohseni, John S. Gulliver, Harry Schulz, and Richard A. Christopher Prepared for Associates California Engineers LLC, Walnut Creek, CA and Sacramento District of the US Army Corps of Engineers August 28 Minneapolis, Minnesota

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3 The University of Minnesota is committed to the policy that all persons shall have equal access to its programs, facilities, and employment without regard to race, religion, color, sex, national origin, handicap, age or veteran status. ii

4 Abstract Folsom Dam, located on the American River, about 2 miles northeast of Sacramento, CA, was built in 195 for flood control, water supply, electric power, and recreation. A new assessment of the probable maximum flood (PMF) has been made which requires the design and construction of a new outlet system to address dam safety. The new outlet system is an auxiliary spillway which includes a gated control structure, a 2%, 2 ft long chute ending at a stepped spillway and a stilling basin downstream of the spillway. The physical model of the control structure is currently under investigation at the Utah Water Research Laboratory of the Utah State University in Logan, Utah. The focus of this physical model study was the entire auxiliary spillway system, except the control structure. This model utilized a single sluice gate across the entire width for flow control instead of a series of taintor gates, each located in a bay. A 1:26 Froude scaled model of the auxiliary spillway was built in the main channel of the St. Anthony Falls Laboratory (SAFL) to study operation of the stepped spillway and the stilling basin under varying hydraulic conditions by the control structure, headwater elevations in the reservoir and tailwater elevations. The extent of the model was from station 9+15, located 198 ft upstream of the control structure piers, to station 43+52, located 215 feet downstream of the final design of the stilling basin. The initial design of the stilling basin was a 17 ft long basin with a double row of 9 ft tall baffle blocks and a 4.5 ft high end sill. During the testing of the model, this configuration was found to be insufficient for containing the jump inside the stilling basin under design flow conditions. The stilling basin was then modified to be 8 feet longer, with a single row of seven 16 ft high baffle blocks and a 15 foot high solid end sill. Subsequently, hydrostatic and averaged dynamic pressures were measured along the steps, and unsteady dynamic pressures were measured on the floor of the stilling basin and on the baffle blocks to determine if there were low pressures that may be subject to cavitation and to estimate forces on the baffle blocks and the end sill. Water surface elevations were measured along the 2% chute and the stepped spillway for the maximum PMF release of 322, cfs to provide data for determining wall heights. Velocities were measured upstream and downstream of the stepped spillway and the stilling basin to assess the efficiency of the system in dissipating energy. iii

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6 Acknowledgements The work reported herein was funded by Associated California Engineers, LLC, under a contract with the Sacramento District of the US Army Corps of Engineers. Dr. HanBin Liang from the Associated California Engineers, LLC was the project manager, Mr. Nathan Cox and Mr. Harold Huff were the project engineers for the US Army Corps of Engineers (USACE), and Mr. Charles Mifkovic and Drs Henry Falvey and John Cassidy served as consultants to USACE. We would like to thank Chris Ellis, Benjamin Erickson, Mike Plante, Craig Hill, Travis Kluthe, Jim Tucker, Andrew Fyten, Sara Johnson and Alex Ding of St. Anthony Falls Laboratory for their contribution to the model construction, instrumentation, documentation and data collection. v

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8 Table of Contents Abstract...iii Acknowledgements... v List of Figures... xi List of Tables... xvii 1. Introduction The Physical Model Construction Model Scale Model Features Instrumentation Flow Calibration Model Elevation Coordinate System Water Surface Elevation Measurements Velocity Measurements Static Pressure Measurements Dynamic Pressure Measurements Pressure Data Acquisition System Overview of Testing First Test Series: Minimum Tailwater Levels in the Modified Stilling Basin Second Test Series Comparing the Utah State University Model to the SAFL Model Third Test Series Water Surface Elevations Velocity Measurement Station 32+ Prandtl Tube Sampling Station ADV Sampling Energy Loss over the Stepped Spillway Energy Loss through the Stepped Spillway and Stilling Basin Hydrostatic and Average Dynamic Pressure Measurements Unsteady Dynamic Pressure Measurements Baffle Blocks... 5 vii

9 Stilling Basin Floor Maximum Water Surface Elevations at 322, cfs Summary Reference Appendix A. Third Test Series: Water Surface Elevation Data A.1. Discharge of 22,625 cfs A.2. Discharge of 9, cfs A.3. Discharge of 115, cfs A.4. Discharge of 16, cfs A.5. Discharge of 312, cfs Appendix B. Third Test Series: Velocity Profiles B.1. Discharge of 22,625 cfs B.2. Discharge of 9, cfs B.3. Discharge of 115, cfs B.4. Discharge of 16, cfs B.5. Discharge of 312, cfs Appendix C. Third Test Series: Pressure Heads along the Steps and inside the Stilling Basin 115 Appendix D. Third Test Series: Unsteady Dynamic Pressure Measurements D.1. Discharge of 22,625 cfs D.2. Discharge of 9, cfs D.3. Discharge of 115, cfs D.4. Discharge of 16, cfs D.5. Discharge of 312, cfs Appendix E: Estimating the Air Uptake over the Stepped Spillway E.1. Description of the Problem E.2. Application to the Folsom Dam Auxiliary Spillway E.3. How to Aerate E.4. Region of Highest Risk E.4.1. Position of the Bottom Air Inception Point on the Folsom Dam Stepped Spillway 184 E.4.2. Estimating Air Supply E.4.3. Air supply at the Folsom Dam Auxiliary Spillway viii

10 E.5. Summary of Findings Appendix F: Enhancing Self Aeration Using Artificial Roughness F.1. Theoretical Boundary Layer Development F.2. Roughness Strip Design Criteria F.3. Roughness Elements F.4. Results ix

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12 List of Figures Figure 1.1. (a) Satellite photo of the Folsom Dam reservoir and the American River, (b) Aerial photo of the Folsom Dam, and (c) artistic depiction of the Folsom Dam existing and auxiliary spillway System...2 Figure 2.1. Model layout in the main channel of the SAFL shop floor...7 Figure 2.2. Model and prototype roughness and Reynolds numbers...9 Figure 2.3. Head box of the model looking upstream...9 Figure 2.4. Plan and side view of the control structure...1 Figure 2.5. Downstream extent of the model with the original stilling basin design...11 Figure 2.6. Estimates of discharge using the standard (handbook) weir equation versus measured discharge using the SAFL volumetric tanks...12 Figure 2.7. Messa Ultrasonic Sensors M-3/21 installed over the stepped spillway...13 Figure 2.8. A modified United Sensor Prandtl tube was used to measure high flow velocities on the 2% chute and along the stepped spillway Figure 2.9. The PC controlled management system for driving the scanivalves...16 Figure 3.1. The plan and elevation of the new stilling basin at the 1:26 model scale Figure 3.2. Minimum acceptable tailwater elevations in the modified stilling basin...19 Figure 3.3. The minimum tailwater level to confine the hydraulic jump in the modified stilling basin under the 16, cfs flow condition. The tailwater did not overtop the basin walls...2 Figure 3.4. The minimum tailwater level to confine the hydraulic jump in the modified stilling basin under the 22, cfs flow condition. The tailwater overtopped the basin walls...2 Figure 3.5. Locations of pressure taps along the stepped spillway and the stilling basin at the model scale. The pressure taps on the side wall (group #1 and #5) were for measuring hydrostatic pressures, and the pressure taps on the floors (groups #2, 3 and 4), were for measuring time averaged dynamic pressures...22 Figure 3.6. Positions of pressure taps on the steps and the associated labels Figure 3.7. Difference between measured water depths obtained from the Utah State and SAFL models at station 14+ and the associated differences in flow rates Figure 3.8. Typical exit condition from the control structure under the design flow, 135, cfs...26 Figure 3.9. Locations of pressure taps along the stepped spillway and the stilling basin at the model scale during the third test series. The pressure taps on the side wall (group #1 and #5) were for measuring hydrostatic pressures, and the pressure taps on the floor (groups #2, 3,4 and 6), were for measuring time averaged dynamic pressures.3 Figure 3.1. The pressure taps installed on the end sill...31 Figure The pressure transducers installed on the floor of the stilling basin to determine the locations where the pressure drops below vapor pressure, i.e. potential locations for cavitation...31 Figure Mean water surface elevations at a discharge of 135, cfs...33 Figure Maximum and minimum deviations from mean water surface elevations at a discharge of 135, cfs...36 Figure Skewness of water surface elevation data at a discharge of 135, cfs...36 Figure Kurtosis of water surface elevation data at a discharge of 135, cfs...37 xi

13 Figure Location of the sonar at station and the flow conditions at 135, cfs. This is the station where the kurtosis and skewness of the water surface elevation data were large probably due to air entrainment Figure Velocity profiles at station 32+ at a discharge of 135, cfs...39 Figure Velocity profiles at Station at a discharge of 135, cfs...4 Figure Lateral Velocity at Station at a discharge of 135, cfs...4 Figure 3.2. Measured pressure distributions along the steps at 22,6 cfs and 9, cfs Figure Measured pressure distributions along the steps at 115, cfs, 135, cfs, 16, cfs and 312, cfs Figure Locations of pressure measurement (a) on the faces of the baffle block, and (b) on the stilling basin floor Figure Pressure signal from the face of the baffle block at a discharge of 135, cfs...53 Figure Pressure spectrum from the face of the baffle block at a discharge of 135, cfs 53 Figure Pressure signal from right side of the baffle block at a discharge of 135, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F...54 Figure Pressure spectrum from right side of the baffle block at a discharge of 135, cfs54 Figure Pressure signal from left side of the baffle block at a discharge of 135, cfs...55 Figure Pressure spectrum from left side of the baffle block at a discharge of 135, cfs 55 Figure Pressure signal from back of the baffle block at a discharge of 135, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F...56 Figure 3.3. Pressure spectrum from back of the baffle block at a discharge of 135, cfs...56 Figure Pressure signal from sum of the lateral pressures exerted on the baffle block at a discharge of 135, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure Pressure spectrum from sum of the lateral pressures exerted on the baffle block at a discharge of 135, cfs...57 Figure Pressure signal from the floor, 17.9 ft away from steps at a discharge of 135, cfs...6 Figure Pressure spectrum from the floor, 17.9 ft away from steps at a discharge of 135, cfs...6 Figure Pressure signal from the floor, 31.7 ft away from steps at a discharge of 135, cfs...61 Figure Pressure spectrum from the floor, 31.7 ft away from steps at a discharge of 135, cfs...61 Figure Pressure signals from the floor,.54 ft downstream of the face of the baffle block at a discharge of 135, cfs...62 Figure Pressure spectrum from the floor,.54 ft downstream of the face of the baffle block at a discharge of 135, cfs...62 Figure Pressure signals from the basin floor, at the upstream edge of the baffle blocks and centered in the gap between the baffle blocks at a discharge of 135, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F...63 Figure 3.4. Pressure spectrum from the basin floor, at the upstream edge of the baffle blocks and centered in the gap between two baffle blocks at a discharge of 135, cfs..63 xii

14 Figure Pressure signal from the basin floor inside the separation zone of the baffle block at a discharge of 135, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure Pressure spectrum from the basin floor inside the separation zone of the baffle block at a discharge of 135, cfs...64 Figure Pressure signal from the basin floor at the downstream edge of the baffle blocks and centered in the gap between two baffle blocks at a discharge of 135, cfs. The solid red line represents gauge water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F...65 Figure Pressure spectrum from the basin floor at the downstream edge of the baffle blocks and centered in the gap between two baffle blocks at a discharge of 135, cfs..65 Figure 4.1. Sonar cart and rails used to measure water surface elevations at a discharge of 322, cfs...68 Figure 4.2. Maximum water surface elevations along the chute and spillway at a discharge of 322, cfs...69 Figure 4.3. Change in discharge over the period of the test at a discharge of 322, cfs...7 Figure 4.4. Water flowing upstream over the stilling basin walls back into the stepped spillway at a discharge of 322, cfs...7 Figure A.1. Mean water surface elevations at a discharge of 22,625 cfs...79 Figure A.2. Maximum and minimum deviations from mean water surface elevations at a discharge of 22,625 cfs...82 Figure A.3. Skewness of water surface elevations measured at a discharge of 22,625 cfs...82 Figure A.4. Kurtosis of water surface elevations measured at a discharge of 22,625 cfs...83 Figure A.5. Mean water surface elevations at a discharge of 9, cfs...84 Figure A.6. Maximum and minimum deviations from mean water surface elevations at a discharge of 9, cfs...87 Figure A.7. Skewness of water surface elevation measured at a discharge of 9, cfs...87 Figure A.8. Kurtosis of water surface elevation measured at a discharge of 9, cfs...88 Figure A.9. Mean water surface elevations measured at a discharge of 115, cfs...89 Figure A.1. Maximum and minimum deviations from mean water surface elevations at 115, cfs...92 Figure A.11. Skewness of water surface elevations measured at 115, cfs...92 Figure A.12. Kurtosis of water surface elevations measured at 115, cfs...93 Figure A.13. Mean water surface elevations at 16, cfs...94 Figure A.14. Maximum and minimum deviations from mean water surface elevations at 16, cfs...97 Figure A.15. Skewness of water surface elevations measured at 16, cfs...97 Figure A.16. Kurtosis of water surface elevations measured at 16, cfs...98 Figure A.17. Mean water surface elevations at 312, cfs...99 Figure A.18. Maximum and minimum deviations from mean water surface elevations at 312, cfs...12 Figure A.19. Skewness of water surface elevations measured at 312, cfs...12 Figure A.2. Kurtosis of water surface elevations measured at 312, cfs...13 Figure B.1. Velocity profiles at 22,625 cfs at station Figure B.2. Velocity profiles at 22,625 cfs at station Figure B.3. Lateral velocities at 22,625 cfs at station xiii

15 Figure B.4. Velocity profiles at a discharge of 9, cfs at station Figure B.5. Velocity profiles at a discharge of 9, cfs at station Figure B.6. Lateral velocities at a discharge of 9, cfs at station Figure B.7. Velocity profiles at a discharge of 115, cfs at station Figure B.8. Velocity profiles at a discharge of 115, cfs at station Figure B.9. Lateral velocities at a discharge of 115, cfs at station Figure B.1. Velocity profiles at a discharge of 16, cfs at station Figure B.11. Velocity profiles at a discharge of 16, cfs at station Figure B.12. Lateral velocities at a discharge of 16, cfs at station Figure B.13. Velocity profiles at a discharge of 312, cfs at station Figure B.14. Velocity profiles at a discharge of 312, cfs at station Figure B.15. Lateral velocities at a discharge of 312, cfs at station Figure B.16. Energy loss over the Folsom Dam stepped spillway and the stilling basin as a function of a dimensionless discharge Figure D.1. Pressure on the face of the baffle block at 22,625 cfs Figure D.2. Pressure on right side of the baffle block at 22,625 cfs Figure D.3. Pressure on left side of the baffle block at 22,625 cfs Figure D.4 Pressure on the back side of the baffle block at 22,625 cfs Figure D.5. Lateral pressure on the baffle block at 22,625 cfs (limited by vapor pressure) Figure D.6. Pressures on the basin floor, 17.9 ft from steps at 22,635 cfs Figure D.7. Pressures on the basin floor, 31.7 ft from steps at 22,625 cfs Figure D.8. Pressure on the basin floor,.54 ft upstream of the baffle block at 22,625 cfs...13 Figure D.9. Pressure on the basin floor inside the separation zone at 22,625 cfs Figure D.1. Pressure on the basin floor along the downstream edge of the baffle blocks at 22,625 cfs Figure D.11. Pressure on the face of the baffle block at 9, cfs Figure D.12. Pressure on the right side of the baffle block at 9, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure D.13. Pressure on the left side of the baffle block at 9, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure D.14. Pressure on the back side of the baffle block at 9, cfs Figure D.15. Lateral pressure on the baffle block at 9, cfs (limited by vapor pressure) Figure D.16. Pressure on the basin floor, 17.9 ft from steps at 9, cfs...14 Figure D.17. Pressure on the basin floor, 31.7 ft from steps at 9, cfs Figure D.18. Pressure on the basin floor,.54 ft upstream of the baffle block at 9, cfs Figure D.19. Pressure on the basin floor, inside the separation zone at 9, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure D.2. Pressure on the basin floor along the downstream edge of the baffle blocks at 9, cfs Figure D.21. Pressure on the face of the baffle block at 115, cfs Figure D.22. Pressure on the right side of the baffle block at 115, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F xiv

16 Figure D.23. Pressure on the left side of the baffle block at 115, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure D.24. Pressure on the back side of baffle block at 115, cfs Figure D.25. Lateral pressure on the baffle block at 115, cfs (limited by vapor pressure)...15 Figure D.26. Pressure on the basin floor, 17.9 ft from steps at 115, cfs Figure D.27. Pressure on the basin floor, 31.7 Feet from steps at 115, cfs Figure D.28. Pressure on the basin floor,.54 ft upstream of the baffle block at 115, cfs Figure D.29. Pressure on the basin floor inside the separation zone at 115, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure D.3. Pressure on the basin floor along the downstream edge of the baffle blocks at 115, cfs Figure D.31. Pressure on the face of the baffle block at 16, cfs Figure D.32. Pressure on the right side of the baffle block at 16, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure D.33. Pressure on the left side of the baffle block at 16, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F...16 Figure D.34. Pressure on the back side of the baffle block at 16, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure D.35. Lateral Pressure on the baffle block at 16, cfs (limited by vapor pressure)..162 Figure D.36. Pressure on the basin floor, 17.9 ft from steps at 16, cfs Figure D.37. Pressure on the basin floor, 31.7 ft from steps at 16, cfs Figure D.38. Pressure on the basin floor,.54 ft upstream of the baffle block at 16, cfs Figure D.39. Pressure on the basin floor inside the separation zone at 16, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure D.4. Pressure on the basin floor along the downstream edge of the baffle blocks at 16, cfs Figure D.41. Pressure on the face of the baffle block at 312, cfs...17 Figure D.42. Pressure on the right side of the baffle block at 312, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure D.43. Pressure on the left side of the baffle block at 312, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure D.44. Pressure on the back side of the baffle block at 312, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure D.45. Lateral pressure on the baffle block at 312, cfs (limited by vapor pressure) Figure D.46. Pressure on the basin floor, 17.9 ft from steps at 312, cfs Figure D.47. Pressure on the basin floor, 31.7 ft from steps at 312, cfs Figure D.48. Pressure on the basin floor,.54 ft upstream of the baffle block at 312, cfs xv

17 Figure D.49. Pressure on the basin floor inside the separation zone at 312, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure D.5. Pressure on the basin floor along the downstream edge of the baffle blocks at 312, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F Figure E.1. Geometrical arrangement of the bottom aerator considered here Figure E.2. Variation of L i in terms of the discharge per unit width, q w Figure E.3. Critical cavitation index σ bi versus discharge per unit width q w. Assuming s=.91m (3 ft), φ = 21.8 o, and temperature of 25 o C (77 o F), then σ bi =.33 for q w =8 m 3 /s/m (86 ft 2 /s) Figure F.1. Inner vertex datum, outer vertex datum and the tangential step height Figure F.2. Semi-log plot of the prototype velocity profile at step Figure F.3. Positions of rectangular ribs in the second configuration tested Figure F.4. Second configuration of roughness ribs looking downstream Figure F.5. Second configuration of roughness ribs looking upstream Figure F.6. Third configuration of roughness ribs, side view Figure F.7. Visual assessment of the air entrainment point of inception at Q = 89,62 cfs, HW = ft Figure F.8. Visual assessment of the air entrainment point of inception at Q = 133,43 cfs, HW = ft Figure F.9. Visual assessment of the air entrainment point of inception at Q = 33,329 cfs, HW = 481 ft Figure F.1. Visual assessment of the air entrainment point of inception using configuration 3, i.e. an extended rough chute at Q = 135, cfs, HW = 466 ft....2 xvi

18 List of Tables Table 1.1. Initial hydraulic conditions under which the testing of the physical model was planned...1 Table 2.1. Froude similarity relationships and scaling between the model and prototype. Length ratio is given as r....5 Table 3.1. Summary of the minimum acceptable tailwater levels for an acceptable performance of the modified stilling basin...19 Table 3.2. Summary of hydraulic conditions for all flows...21 Table 3.3. Prototype water depths measured in the Utah State model at station Table 3.4. Prototype water depths measured in the SAFL model at station Table 3.5. Difference between measured water depths obtained from the Utah State and SAFL models at Station Table 3.6. Summary of the hydraulic conditions in the third test series...27 Table 3.7. Third test series: water surface measurement stations. Where depths were recorded sonar angle was perpendicular, where water surface elevations were recorded, sonar angle was vertical...29 Table 3.8. Summary of Mean, Minimum, and Maximum Water Surface Elevations at 135, cfs...34 Table 3.9. Energy loss over the stepped spillway for the target 135, cfs flow condition (Test 1). Elevations given in the table are from the stilling basin invert...43 Table 3.1. Energy loss over the stepped spillway for the target 135, cfs flow condition Table 3.11 (Test 2). Elevations given in the table are from the stilling basin invert...43 Energy loss over the stepped spillway for the target 312, cfs flow condition (Test 3). Elevations given in the table are from the stilling basin invert...44 Table Energy loss over the stepped spillway for the target 312, cfs flow condition (Test 4). Elevations given in the table are from the stilling basin invert...44 Table Total energy loss along the stepped spillway and the stilling basin under different flow conditions. Total energy, H, given in column 5 has been calculated from the stilling basin invert Table Pressure heads recorded at the pressure taps at a discharge of 135, cfs...48 Table Mean dynamic pressure heads measured on the baffle block at 135, cfs...5 Table Mean dynamic pressure heads measured on the stilling basin floor at a discharge of 135, cfs...58 Table 4.1. Table 4.2. Maximum water surface elevations measured along the 2% chute and the stepped spillway at a discharge of 322, cfs. LDS stands for looking downstream...71 Maximum water surface elevations measured at a discharge of 322, cfs at the last station over the stepped spillway. Because of the steep angle of flow and the observed variability in the water surface elevation, the sonar was slightly adjusted at each location, thus the correct station associated with each reading along the width of the stepped spillway is tabulated below Table A.1. Summery of mean, minimum, and maximum water surface elevations at 22,625 cfs8 Table A.2. Summery of mean, minimum, and maximum water surface elevations at 9, cfs85 Table A.3. Summery of mean, minimum, and maximum water surface elevations at 115, cfs...9 Table A.4. Summery of mean, minimum, and maximum water surface elevations at 16, xvii

19 cfs...95 Table A.5. Summery of mean, minimum, and maximum water surface elevations at 312, cfs...1 Table C.1. Locations of pressure taps throughout the model during the third test series Table C.2. Results of the pressure head measurements during the third test series Table D.1. Average dynamic pressure heads on the baffle block at 22,625 cfs Table D.2. Average dynamic pressure heads on the basin floor at 22,625 cfs Table D.3. Average dynamic pressure heads on the baffle block at 9,cfs Table D.4. Average dynamic pressure heads on the basin floor at 9, cfs Table D.5. Average dynamic pressure heads on the baffle block at 115, cfs Table D.6. Average dynamic pressure heads on the basin floor at 115, cfs Table D.7. Average dynamic pressure heads on the baffle block at 16, cfs Table D.8. Average dynamic pressure heads on the basin floor at 16, cfs Table D.9. Average dynamic pressure heads on the baffle block at 312, cfs Table E.1. Vapor pressure as a function of temperature Table F.1. Model and prototype parameters at the downstream end of the 2% chute (no roughness elements added) at a discharge of 135, cfs...19 xviii

20 1. Introduction The Folsom Dam, located on the American River, about 2 miles northeast of Sacramento, CA, was built in 195 for flood control, water supply, electric power, and recreation (Figure 1.1a and b). Due to changes in land use in the past 6 years and subsequent flood records since the completion of the dam, a new assessment of the probable maximum flood (PMF) has been made which requires the design and construction of a new outlet system to address dam safety. The new outlet system is an auxiliary spillway which includes a gated control structure, a 2 ft, 2% chute ending at a stepped spillway and a stilling basin (Figure 1.1c). The1:3 scale model of the control structure is currently under investigation at the Utah Water Research Laboratory (UWRL) at USU (Utah State University), located in Logan, Utah. In addition, a 1:48 scale model of the existing spillway, the stepped spillway, the stilling basin, the confluence of the two waterways and the downstream channel geometry is being studied at the U.S. Bureau of Reclamation (USBR) Hydraulic Investigations and Laboratory Services Group in Denver, Colorado. The USBR model was used for helping define tested hydraulic conditions. The focus of the SAFL model study was on the physical model study of the entire auxiliary spillway system, except the control structure. This model utilizes a single sluice gate across the width for flow control instead of a series of taintor gates each located in a bay. The hydraulic conditions for the entire discharge system, including both existing and new auxiliary spillways, are given in Table 1.1. The bold flow rates were used for testing in the SAFL model. All prototype elevations given in this report are based on the NGVD 29 Datum. Table 1.1. Initial hydraulic conditions under which the testing of the physical model was planned. Return Period Total Flow Reservoir Elevation Flow in Auxiliary Spillway Flow in Main Dam (not modeled) Tailwater (years) (cfs) (feet) (cfs) (cfs) (feet) 2-yr 22, , yr 115, , 25, & yr 115, , yr 16, , 25, & yr 16, , PMF 88, ,5 496,

21 (a) (b) (c) Figure 1.1. (a) Satellite photo of the Folsom Dam reservoir and the American River, (b) Aerial photo of the Folsom Dam, and (c) artistic depiction of the Folsom Dam existing and auxiliary spillway System. The objectives of this physical model study were to test the effectiveness of the designed stilling basin under a wide range of flow 2

22 conditions and tailwater levels, to test modifications to the stilling basin needed to provide for effective energy dissipation, to measure water surface elevations along the 2% chute and the stepped spillway under the probable maximum flood (PMF) condition, to determine the effectiveness of the system in dissipating the energy along the stepped spillway and the stilling basin by measuring flow velocities, to investigate potential cavitation along the steps or in the stilling basin by measuring dynamic pressure, to investigate the potential effects of bulking of the flow along the stepped spillway, to investigate how to increase self aeration at the downstream end of the 2% chute and the upstream end of the stepped spillway to negate potential cavitation damage along the steps. This report summarizes the physical model and the results of the tests and analysis conducted at SAFL. Section 2 of the report is on Froude scaling parameters, model construction and instrumentation. Section 3 is on the overall test series performed and the minimum tailwater testing, the data collected for estimating energy dissipation, and the static and dynamic pressure datasets. Section 4 is on the results of the water surface profile measurements, for the PMF maximum discharge of 322, cfs. Appendices A to D contain documentation of the measurements reported. Appendices E and F will be helpful if cavitation is found to be of concern on the stepped spillway. Appendix E presents an analytical method to estimate the required air supply and Appendix F gives the results of roughness elements designed and installed at the end of the model chute and on the first few steps of the stepped spillway to enhance self-aeration. 3

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24 2. The Physical Model Construction 2.1. Model Scale The proposed model scale by the USACE was 1:24. In order to maintain the maximum discharge (PMF) the model was built in the SAFL main channel, which has a maximum discharge capacity of 3 cfs, a length of 275 ft and a width of 9 ft. To fit the model in the SAFL main channel, the model scale was set to 1:26. The constraints were the channel width at the downstream end of the model and the height to model the elevation difference between the reservoir and the stilling basin invert. The layout of the model in the SAFL main channel is shown in Figure 2.1. Geometric and Froude similarity were used to scale the other parameters used in the model and summarized in Table 2.1. Table 2.1. Froude similarity relationships and scaling between the model and prototype. Length ratio is given as r. Parameter Relationship Scale Length r 1:26 Velocity r 1/2 1:5.1 Frequency r -1/2 5.1:1 Discharge r 5/2 1:3447 Manning s Coefficient of Roughness r 1/6 1:1.72 Froude similarity was determined to be adequate for modeling due to fully rough flow throughout the model. However, for the physical model study, it was necessary to select a lining material along the 2% chute and the stepped spillway to model the head loss correctly through the use of similar Darcy-Weisbach friction factors. The Reynolds Number and relative roughness under the PMF condition were estimated to be and (using four times the channel hydraulic radius), respectively. The Darcy-Weisbach friction factor was determined from the Moody Diagram to be.1 (Figure 2.2). By using PVC lining with an absolute roughness of.7 ft, under the PMF condition, the model Reynolds Number and relative roughness were estimated to be and , respectively, which give a friction factor of about.11. Therefore, PVC lining was used for the entire model. Surface tension, bubble rise velocity and viscous forces are determining factors for bulking the flow and cannot be correctly modeled in a Froude scale model. Any results from the model 5

25 concerning flow aeration and bulking are considered qualitative when applied to the prototype. Under the PMF condition, which is used to determine the channel wall height, initial estimates indicate that aeration cannot occur and water surface elevations can be used for the wall height design Model Features The extent of the model was from station located 75 ft upstream of the piers, to station 43+59, located 222 feet downstream of the end of the final designed stilling basin. Flow rate was controlled using the SAFL main channel intake gate which draws water directly from the Mississippi River. The flow was then directed into a pressurized head box of the model which was about 14 feet long, 7.6 feet wide and 12 feet high. Flow entered a pressurized head box through a 7.5 foot by 5 foot port at the bottom of the head box and exited at the top of its downstream end (Figure 2.3). The head box was sealed and finished with paint. Four lid sections were constructed for the head box, two of which were made of Plexiglas for observing the flow inside the head box. Two clear ports were then added to the top of the head box for air release and headwater measurements. From the head box, the flow entered the control structure. The extent of the control structure is shown in Figure 2.4. Plywood was used for the construction and the lining of the floor and side curved walls upstream of the piers. The rest of the control structure, i.e. the piers, side walls and the sluice gate, were made of Plexiglas with the exception of the upstream curved ceiling which was made of sheet metal. The control structure was built with an accuracy of 1/32. The only geometric difference between the model control structure and the prototype is a single sluice gate extending across all six bays instead of taintor gates in each bay of the structure. The sluice gate was used to control headwater levels after setting the flow rate. The remainder of the model was geometrically similar to the prototype and was finished with PVC sheeting. The accuracy of the model where lumber and plywood were used for the construction was at 1/8. At the downstream end of the model, the flow discharged into the SAFL main channel, as shown in Figure 2.5. Tailwater was controlled by the main channel weir type tailgate located about 1 ft downstream of the model (Figure 2.1). Tailwater measurement was performed at station 43+59, at the downstream end of the model. 6

26 FLOW Figure 2.1. Model layout in the main channel of the SAFL shop floor 7

27 (This is a blank page) 8

28 Figure 2.2. Model and prototype roughness and Reynolds numbers Top of Head box Head box Inlet Figure 2.3. Head box of the model looking upstream. 9

29 Control Structure Plan View 2 2 ( X ) ( Y ) + = SECTION F F Figure 2.4. Plan and side view of the control structure 1

30 Figure 2.5. Downstream extent of the model with the original stilling basin design 2.3. Instrumentation Flow Calibration Flow rate was measured at the weir-type tailgate. The data acquisition system was comprised of a gate elevation sensor, an Ultrasonic sensor measuring water surface, and a computer in place to estimate the flow rate at the weir using the head upstream of the gate and the gate height. The following weir equation, with no contractions, was used. The units of the original equation were in the System International, however, herein the equation is presented in the US Customary units Q = * L* H (cfs) (2.1) In equation 2.1, Q is the flow rate in cfs, L is the crest length in ft, and H is the head over weir in ft. Flow rate as estimated by equation 2.1 was plotted versus actual flow as measured by the SAFL volumetric tanks (Figure 2.6). It is evident from Figure 2.6 that equation 2.1 consistently underestimated the discharge by about 1%. The discharge equation was then adjusted using the multiplier, to result in a calibrated weir coefficient. Finally, the adjusted discharge equation was checked against the PMF, i.e. 9.5 cfs at the model scale, and the error was 1 cfs, i.e..3 cfs at the model scale. 11

31 Main Channel Weir Calibration 7 SAFL Volumetric Tank Measurement (cfs) y = 1.956x R 2 = Handbook Weir Equation (cfs) Figure 2.6. Estimates of discharge using the standard (handbook) weir equation versus measured discharge using the SAFL volumetric tanks Model Elevation Coordinate System The model elevation benchmark (BM) was set at the top of one of the eight inch I-beams supporting the model chute above the SAFL main channel. This elevation was set to 1 feet, which corresponds to the prototype elevation of 292 feet Water Surface Elevation Measurements All water surface measurements made during testing were performed using arrays of Massa Ultrasonic Sensors M-3/21 (Figure 2.7). These sensors measure distance through air to a reflecting surface (water in this case) using an ultrasonic pulse. The only relevant specification that Massa provides for this sensor is a measurement resolution of.1 inches (.25mm) with an accuracy of about 1 mm, which is air temperature dependent. The sensors have internal temperature compensation, echo return processing, and output an 8 conical beam. The range of 12

32 the sensors is 4 to 4 inches. The sensors prove to be quite rugged and robust with the exception of poor echo returns on angled flat flows such as those found at high flows on the steepest portion of the stepped spillway. A program was written to be able to interface with up to 15 sensors at once and save data to file. The sampling frequency of each probe was 1 hertz and in almost all cases 6 second data sets were collected. Any suspicious data caught by the probes was immediately deleted. After each dataset was collected, the program generated a histogram constructed of 1% bin sizes of the remaining good samples. The sensors were placed in numerous locations of the model and output was given in model elevation coordinates. Figure 2.7. Messa Ultrasonic Sensors M-3/21 installed over the stepped spillway Velocity Measurements High flow velocities at the end of the chute and along the stepped spillway were measured using a type PA United Sensors modified Prandtl tube connected to a Rosemount 351S_CD Coplanar Differential pressure transducer using 1/16 inch plastic tubing. The tubing, Prandtl tube and transducer were all filled with water and purged of air (Figure 2.8). The pressure transducer was factory calibrated from -125 to 125 inches H 2 O and was set to 1 second damping to eliminate any fluctuations and get a true mean reading. The stated total accuracy 13

33 performance is.55% of the span, or.1375 inches H 2 O. The Prandtl tube was mounted on a modified point gage with a precision of.1 ft for accurate depth measurements. Low flow velocities at the downstream end of the model were measured using a 2-D Sontek/YSI Inc. Acoustic Doppler Velocimeter (ADV). The stated specifications were: Velocity range: ±.1 to 4. m/s (±.3 to 13 ft/s) Velocity resolution:.1 m/s Velocity accuracy: ±1% of measured velocity, ±.25 cm/s Sampling volume location: 1 cm from the center transducer The ADV was mounted on a steel rod looking sideways. The rod had a depth indicator having a precision of.1 feet (3 inches for the prototype). Thirty second samples were taken to ensure true mean readings. Figure 2.8. A modified United Sensor Prandtl tube was used to measure high flow velocities on the 2% chute and along the stepped spillway Static Pressure Measurements Static gage pressure measurements were placed throughout the stepped spillway and stilling 14

34 basin. A total of 66 taps were constructed of 1/16 inch steel tubing and flush mounted, and glued into surfaces in the model. One-sixteenth inch tubes were then connected to the back side of the taps and routed to the PC-controlled Scanivalve hydraulic switches. Five additional tubes were connected to vials of known elevations over a range of 94.8 inches of water, +/ inches of water as seen by the transducer, for calibration and quality control purposes. The common port of the hydraulic switches was connected to a three way valve leading to either a pressure transducer or a purge water source, depending on valve direction. Using LabView, automated processes for tap purging, pressure transducer calibration, and tap pressure measurement were constructed. Purges and transducer calibration were performed before every data collection. Pressure output was saved in the model elevation coordinate system and was later converted to static pressure exerted at each tap. The pressure transducer was an Endevco Model 851B Dynamic Pressure Measurements Dynamic gage pressure measurements in the stilling basin were sampled using eight Endevco Model 851B-2 and one Endevco 851B-5 pressure transducers. They were flush mounted to surfaces in the middle baffle block and on the floor. These transducers have a range of +/- 2 psi (55.4 inches of water), and +/-5 psi (138.4 inches of water), respectively. The stated combined maximum error is 1.5% and.75% of their full scale output (FSO), respectively. Two thirds of this error is attributed to the non-linearity of the calibration (a 3 rd order calibration was performed on each transducer). Thus, the accuracy of the transducers non-linearly calibrated is less than.5% and.25% of FSO, or.1 psi (.28 inches of water) and.125 psi (.35 inches of water), respectively. One of the transducers with a range of +/-5 psi was installed in the face of one of the baffle blocks. The calibration procedure for the stilling basin transducers involved filling the stilling basin with quiescent water and entering values of tailwater elevations given by the sonar located at the downstream end of the model. The first elevation was under atmospheric pressure and was given as the model elevation of the transducers. In addition, prior to each test series, a secondary calibration routine was performed by calculating and applying an offset to the calibration curve to account for a zero shift. Calibration, raw voltage, and pressure datasets were all saved to a file. The pressure datasets were saved in the model elevation coordinate system. 15

35 Pressure Data Acquisition System Data acquisition was performed by a PC based system running LabView and using two Measurement Computing Corporation PCI-DAS652 A/D cards. These A/D cards are 16 bit boards with programmable gain. All of the Endevco transducers used for this model study were set for a resolution of.15 mv with a stated accuracy of.371% of the reading. The A/D cards were about 6 times more accurate than the pressure transducers in the worst case scenario and were never a significant contributor to the overall error. The A/D cards were set to capture frequencies as small as 1 khz. In addition to performing the measurement of the pressure, the A/D board also monitored the Scanivalve positions. A PC controlled Measurement Computing USB-PDIS8 relay board was used for driving the Scanivalves. The LabView application allowed the operator to hit virtual buttons to initiate the automated measurement routines including the purging, transducer calibration, pressure measurement, and data storage (Figure 2.9). Figure 2.9. The PC controlled management system for driving the scanivalves. 16

36 3. Overview of Testing After building the model and evaluating the performance of the stilling basin under the flow conditions given in Table 1.1, it was determined that the original design of the stilling basin, with two rows of 9-ft tall baffle blocks and a 4.5-ft high solid end sill was inadequate to confine the hydraulic jump under the designed flow (135, cfs). Therefore, the stilling basin was modified as follows: The basin length was extended by 8 ft; the two rows of 9-ft baffle blocks were replaced with one row of 16-ft high baffle blocks; and the 4.5 ft high end sill was replaced with a 15-ft high solid end sill. The new stilling basin at the model scale is shown in Figure 3.1. The first test series was to determine the minimum tailwater levels under which the stilling basin would function appropriately and the hydraulic jump would be confined in the stilling basin. The second test series was based on a new set of tailwater levels supplied by the USCOE. The third test series, which included water surface elevations, head loss over the steps and along the stilling basin and pressure measurements were based on the minimum tailwater elevations. Figure 3.1. The plan and elevation of the new stilling basin at the 1:26 model scale. 17

37 3.1. First Test Series: Minimum Tailwater Levels in the Modified Stilling Basin After the completion of the new stilling basin, the model was run under different flow conditions and it was noticed by the SAFL researchers as well as the representatives from USCOE and Associates California Engineers LLC that the performance of the stilling basin was highly sensitive to the tailwater levels. Therefore, it was decided to conduct a series of tests to determine minimum acceptable tail water levels to confine the hydraulic jump within the basin. Flow conditions through the stilling basin were recorded during these tests. Requirements for acceptable tail water levels were as follows: 1. The jump had to start before the baffle blocks and the location of the toe of the hydraulic jump needed to be stabilized. To satisfy the stability requirement, the toe of the jump was usually located at or slightly upstream of the stepped spillway. This avoided the instability of a jump located on the flat surface of the stilling basin. 2. Under low flow conditions, 22,625 cfs, the tail water level had to be high enough to prevent a secondary jump downstream of the end sill. However, a standing wave was allowed to form just downstream of the end sill. The water surface elevations measured directly upstream of the end sill indicate the prototype water surface drop from the end sill to the tail water measurement location was 2.1 feet. This was recorded during the minimum tail water rising condition of 15.8 feet (elevation). These tests were performed in November 27 and were repeated in February 28 for video recording. Another flow rate of 22, cfs was added to the test series to fill the gap between the 16, and 312, cfs flow conditions. The results are shown in Figure 3.2 and Table 3.1. In Figure 3.2, minimum tailwater levels when the tailwater was rising and falling are plotted as two different series. The difference between the two seems to be insignificant. The results of this test series can be approximated by a linear relationship between discharge and minimum tailwater level (the line was fitted to all the data in Figure 3.2). High discharges, however, slightly deviate from this linear trend. It is important to note that under the PMF flow condition (312, cfs), the test was constrained by the height of the SAFL main channel. 18

38 For the 22, cfs flow condition, the deviation from the linear relationship between the tailwater and discharge can be attributed to the change in channel geometry when the tailwater overflows the basin walls. Figures 3.3 and 3.4 show the difference in outlet geometries for the 16, cfs and 22, cfs flow conditions, respectively Minimum TW Elevations (ft) y =.3x R 2 = , 1, 15, 2, 25, 3, 35, Discharge (cfs) Min TW Falling Min TW Rising Figure 3.2. Minimum acceptable tailwater elevations in the modified stilling basin Table 3.1. Summary of the minimum acceptable tailwater levels for an acceptable performance of the modified stilling basin Return Period Total Discharge Main Spillway Target Auxiliary Spillway Actual Auxiliary Spillway Target Headwater Actual Headwater Min Tailwater Falling Min Tailwater Rising cfs cfs cfs cfs ft ft ft ft 2-yr 22,625 22,625 22, yr 115, 115, 115, yr 115, 25, 9, 9, yr 16, 16, 17, yr 16, 25, 135, 135, N/A N/A N/A 22, 212, PMF 562, 25, 312, 311,

39 Figure 3.3. The minimum tailwater level to confine the hydraulic jump in the modified stilling basin under the 16, cfs flow condition. The tailwater did not overtop the basin walls. Figure 3.4. The minimum tailwater level to confine the hydraulic jump in the modified stilling basin under the 22, cfs flow condition. The tailwater overtopped the basin walls. 2

40 3.2. Second Test Series The second test series was performed under the flow rate and headwater conditions given in Table 1.1. The tailwater levels, however, were revised by the USCOE and were based on the results of a modified HEC-RAS model of the American River. The target and actual hydraulic conditions in the second test series are summarized in Table 3.2. Return Period Total Discharge Table 3.2. Main Spillway Summary of hydraulic conditions for all flows Target Aux Spillway Actual Aux Spillway Target Head water Actual Head water Target Tailwater Actual Tailwater Original Tailwater cfs cfs cfs cfs ft ft ft ft ft 2-yr 22,625 22,625 22, yr 115, 115, 115, yr 115, 25, 9, 89, yr 16, 16, 16, yr 16, 25, 135, 134, , 25, 312, 31, During the second test series, the following data were collected. Water surface elevations at stations14+, 18+9, 25+5, 32+1, 34+4, 35+15, 36+74, 41+13, and in the reservoir, which mostly represented the water elevation in the approach channel upstream of the control structure. Velocity measurements at station 32+ using a Prandtl tube and a pressure transducer. Velocity measurements taken at station using ADV. Hydrostatic and averaged dynamic pressure measurements at a total of 57 locations throughout the model, of which one was located on the wall just upstream of the stepped spillway at station 32+, 44 on the first ten steps, seven along the remaining steps, three on the north wall of the stilling basin, and two on the north wall downstream of the stilling basin (Figures 3.5 and 3.6). Unsteady dynamic pressures on the four sides of the center baffle block. Since all the tests of the second test series were repeated more extensively during the third test series with minimum tail water levels downstream of the stilling basin, the results of this test series are not presented in this report. 21

41 (2) Pressure taps on the floor A B C D Figure 3.5. Locations of pressure taps along the stepped spillway and the stilling basin at the model scale. The pressure taps on the side wall (group #1 and #5) were for measuring hydrostatic pressures, and the pressure taps on the floors (groups #2, 3 and 4), were for measuring time averaged dynamic pressures. 22

42 L b d.8 ft.8 ft 6% of L a c 4.5 ft e Figure 3.6. Positions of pressure taps on the steps and the associated labels Comparing the Utah State University Model to the SAFL Model The focus of the Folsom Dam physical model study done at the Utah State University was the control structure and its approach channel while the focus of the SAFL model was the stepped spillway and the stilling basin. Therefore, the extent of the two models was different. However, both models included the control structure as well as part of the 2% chute. It was decided to compare the water depths measured at station 14+ in both models. Those data are given in Tables 3.3 and 3.4. The differences between the two datasets are given in Table 3.5. The data collected at the Utah State University are referenced for computing the difference and percent difference. The difference between the two datasets is primarily due to the following two factors: 1) Through a number of iterations in the model study conducted at the Utah State University, the geometry of the control structure inlet was modified to eliminate the vortices formed in the approach channel. The SAFL model of the control structure, however, was never modified and the original geometry was maintained throughout the model study. 2) The Utah State University model of the control structure was operated by a series of taintor gates, while SAFL s was 23

43 operated by a single sluice gate extended through all bays. These differences impacted water depths downstream of the gates (vena contracta), primarily when the gates were throttled and because the flow regime along the 2% chute was supercritical. The impact was evident at station 14+. The largest difference between the two models was under the 22,625 cfs flow condition (Table 3.5). The data given in Table 3.5 are plotted in Figure 3.7 Rooster tails downstream of the control structure due to abrupt expansion in supercritical flows were evident in both models (Figure 3.8). Table 3.3. Prototype water depths measured in the Utah State model at station 14+ Utah State Model Reservoir Prototype Prototype Depth Measurements (ft) Elevation Discharge (ft) 1 (cfs) L 25% Center 25% R , , , , , , Table 3.4. Prototype water depths measured in the SAFL model at station 14+ SAFL Model Prototype Reservoir Prototype Depth Measurements (ft) Discharge Elevation (ft) (cfs) L 25% Center 25% R , , , , , , The reservoir elevation-discharge relationship may slightly change after the tests are completed for the Utah State model. 24

44 Table 3.5. Difference between measured water depths obtained from the Utah State and SAFL models at Station 14+ Reservoir Elevation Difference (ft) Flow Rate Difference (cfs) Prototype Depth Measurements Difference (ft) L 25% Center 25% R Average % Different % % % % % % 2 2% 1 1% Depth Difference (ft) % -1% -2% -3% -4% Discharge Difference (%) -5-5% 8, 16, 24, 32, Discharge (cfs) Depth Left Depth 25% Left Depth Center Depth 25% Right Depth Right Average Depth Discharge Figure 3.7. Difference between measured water depths obtained from the Utah State and SAFL models at station 14+ and the associated differences in flow rates. 25

45 Figure 3.8. Typical exit condition from the control structure under the design flow, 135, cfs. 26

46 3.3. Third Test Series After the second test series, minimum tailwater levels between the SAFL model and the Bureau of Reclamation model were found to be different. The difference was due to the channel expansion on the right bank (looking downstream), which was not modeled at SAFL 2 but it was correctly modeled at the Bureau of Reclamation Laboratory in Denver, CO. For this reason, the third test series was proposed where the tailwater levels were set equal to the minimum tailwater levels obtained from the SAFL model study. The hydraulic conditions are summarized in Table 3.6. Return Period Total Discharge Table 3.6. Main Spillway Discharge Summary of the hydraulic conditions in the third test series Target Actual Target Actual Auxiliary Auxiliary Head Head Spillway Spillway water water Discharge Discharge Target Tailwater Actual Tailwater cfs cfs cfs cfs ft ft ft ft 2-yr 22,625 22,625 23, yr 115, 115, 112, yr 115, 25, 9, 89, yr 16, 16, 158, yr 16, 25, 135, 137, PMF 562, 25, 312, 31, A number of pressure measurement locations were also added for the third test series to obtain a better picture of the pressure distribution along the steps and the stilling basin. They included six pressure taps on the faces of steps 35, 4, 45, 5, 55, and 6 (Figure 3.9). These were located.27 feet (for the prototype) below the outer vertex of the steps, to locate maximum negative pressures along the steps as estimated by the numerical model developed at the Bureau of Reclamation to simulate the flow over the stepped spillway. Three pressure taps were also installed on the end sill of the model as shown in Figure 3.1. Two were installed in the upstream side; one was centered behind a baffle block while the other was aligned with the gap between two baffle blocks. The last pressure tap was installed in the center of the end sill on the back side. All of these taps were located half way up the height of the end sill. Five dynamic pressure transducers were installed on the floor of the stilling basin. Another pressure transducer was temporarily installed at the mid point between the upstream face of two 2 The SAFL model was built inside of its 9-ft wide Main Channel and due to width limitation, the downstream geometry could not be modeled correctly. 27

47 baffle blocks (Figure 3.11). Its readings were only available for the design flow of 135, cfs. That transducer was later moved and installed between two baffle blocks in alignment with the downstream end of the baffle blocks. For the third test series, the pressure taps B' and B 3 were relocated to more relevant locations (Figure 3.9). The pressure tap B' was moved to along the north wall at the face of the new blocks and located 3.9 feet (for the prototype) above the stilling basin floor. The pressure tap B was moved along the north wall 3.9 feet above the upstream slope of the new end sill. It was located 17.3 feet before the downstream side of the end sill. During the third test series, the following data were collected. Water surface elevations at the locations outlined in Table 3.7. Velocity measurements at station 32+ using a Prandtl tube Velocity measurements taken at station using ADV Hydrostatic and averaged dynamic pressure measurements were collected at a total of 66 locations throughout the model, of which 44 were located on the first 1 steps, 13 throughout the remaining steps, three on the north wall of the stilling basin, three in the end sill, two on the right wall downstream of the basin, and one on the wall just upstream of the start of the stepped spillway. Dynamic pressures were measured on the four sides of a single baffle block as well as five on the floor of the stilling basin. Three were placed in the vicinity of the baffle blocks with the other two at the front of the basin where the jet of the spillway impacts the floor. In the following subsections, the results of this test series will be presented and discussed. 3 The initial location of pressure taps B' and B was based on the initial design of the stilling basin, next to the baffle blocks and at the end of the stilling basin. 28

48 Table 3.7. Third test series: water surface measurement stations. Where depths were recorded sonar angle was perpendicular, where water surface elevations were recorded, sonar angle was vertical. Station Type Depth 16+6 Depth Depth Depth Depth 33+2 Water Surface Elevation 34+ Water Surface Elevation 35+1 Water Surface Elevation 36+7 Water Surface Elevation Depth Water Surface Elevation Water Surface Elevation Water Surface Elevation Reservoir Water Surface Elevation 29

49 (2) Pressure taps on the floor A B C D Figure 3.9. Locations of pressure taps along the stepped spillway and the stilling basin at the model scale during the third test series. The pressure taps on the side wall (group #1 and #5) were for measuring hydrostatic pressures, and the pressure taps on the floor (groups #2, 3,4 and 6), were for measuring time averaged dynamic pressures. 3

50 Figure 3.1. The pressure taps installed on the end sill Figure The pressure transducers installed on the floor of the stilling basin to determine the locations where the pressure drops below vapor pressure, i.e. potential locations for cavitation 31

51 Water Surface Elevations The mean water surface elevation for the 135, cfs discharge is shown in Figure 3.12 and the mean, minimum and maximum elevations are tabulated in Table 3.8. To determine the stations where water surface elevations were recorded, water depths were measured perpendicular to the bed along the 2% chute and perpendicular to the outer vertex of the steps along the steps. The sonar sensor located at station 38+98, at the toe of the steps, did not give reliable results because of poor echo returns and was left out of the following tables and figures. The sampling was performed at 1 Hz and averaged over one minute of model time. This is equivalent to sampling at about 2 Hz for a little over 5 minutes for the prototype. The minimum and maximum deviations from the mean values under the 135, cfs flow condition are shown in Figure Deviations along the chute are consistently within the range of about two ft along the entire chute. The exceptions are the large deviations found at station due to the first standing waves interacting with each other, which were caused by the expansion downstream of the control structure. As expected, water surface elevation deviations from the mean are more intense once the standing waves interact over the steps and become chaotic in the stilling basin. The histograms of the data were used to obtain a better idea of how the water surface profile changed over time. Figures 3.14 and 3.15 show the skewness and kurtosis calculated from the histograms. Both are used to compare the distribution of the data to a normal distribution. In this case, positive skewness indicates that the majority of the elevations read by the sonar were smaller than the mean. A positive kurtosis indicates an acute peak and fat tails. The kurtosis given in Figure 3.15 varies primarily from -1 to about zero, so the data are relatively normally distributed with frequent smaller deviations from the mean. Along the stepped spillway, both skewness and kurtosis show a rise in infrequent spikes with a maximum at station 37+39, the last measurement location on the stepped spillway. This is probably caused by the aeration seen in Figure The results of water surface elevations measured under other discharges are given in Appendix A. 32

52 Elevation Right 3. Elevation Right 25% Elevation (ft) Elevation Center Elevation Left 25% Elevation Left Spillway Floor 15. Basin Floor Station Figure Mean water surface elevations at a discharge of 135, cfs 33

53 Table 3.8. Summary of Mean, Minimum, and Maximum Water Surface Elevations at 135, cfs Elevation Right Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average Elevation Right 25% Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average Elevation Center Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average

54 Elevation Left 25% Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average Elevation Left Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average

55 14 12 Maximum Differences from Mean Elevation (ft) Right Min - Mean Right 25% Min - Mean Center Min - Mean Left 25% Min - Mean Left Min - Mean Right Max - Mean Right 25% Max - Mean Center Max - Mean Left 25% Max - Mean Station Figure Maximum and minimum deviations from mean water surface elevations at a discharge of 135, cfs Skewness Right Right 25% Center Left 25% Left Station Figure Skewness of water surface elevation data at a discharge of 135, cfs 36

56 Kurtosis 2 1 Right Right 25% Center Left 25% Left Station Figure Kurtosis of water surface elevation data at a discharge of 135, cfs Figure Location of the sonar at station and the flow conditions at 135, cfs. This is the station where the kurtosis and skewness of the water surface elevation data were large probably due to air entrainment. 37

57 Velocity Measurement Station 32+ Prandtl Tube Sampling Measuring velocity using a Prandtl tube (pitot tube) was conducted at station 32+ where high velocities could not be measured using ADV. The results of velocity measurements under the 135, cfs flow condition are shown in Figure The velocities were measured at five locations along the channel width and 9 depths at each location. The locations along the channel width were 1.8, 42.6, 84.9, 127 and ft away from the channel wall and relatively symmetrical with respect to the channel centerline. Due to the presence of standing waves and unsteadiness of water surface elevations, the top of each profile was determined visually by recording the point at which the tube was half in the water and half out of the water as waves passed the tube. Since the velocity recorded at this point was subject to significant errors, the water surface velocity was assumed to be the final velocity in the profile. The maximum (point) velocity measured was 77.5 fps and velocities as high as 6.5 fps were observed at.9 ft from the channel bed at a discharge of 135, cfs (Figure 3.17). The two profiles closest to the sidewalls of the chute reached their maximum velocities at about a depth of 6 feet and then slowed as the free surface was reached. Under the 22,6 flow condition, the maximum velocity measured was about 37 fps (Figure B.1) and increased to approximately 67 fps under the 9, cfs flow condition (Figure B.4) and about 85 fps under the 312, cfs flow condition (Figure B.13). Velocity profiles under all flow conditions are given in appendix B Station ADV Sampling A two-dimensional ADV was used to measure the water velocities at the downstream extent of the model, station The lateral locations were the same as those used at station 32+ and are given with respect to the channel centerline in Figure The maximum streamwise velocities under the 135, cfs flow condition were recorded to be 2.4 fps and occurred slightly below the surface, i.e. at a depth of about 37 ft above the bed. The low velocities near the surface are due to rollers leaving the basin and indicate that the flow is not fully developed at 38

58 station at a discharge of 135, cfs. The maximum velocity under the 22,6 cfs flow condition was measured to be approximately 9 fps and the velocities near the surface did not indicate the presence of any rollers at station However, at a discharge of 115, cfs and larger flows, velocities near the surface were measured to be about 2 fps and lower. Lateral velocities are given in Figure The lateral velocities did not exceed 3 fps anywhere within the downstream outlet of the model. The slope of these velocities with lateral distance from positive to negative and vice-versa indicate the presence of one large streamwise vortex (roller) with a peak velocity of 3 fps. Velocity profiles under other flow conditions are given in appendix B Distance from Floor (ft) Distance from Right Wall (ft) Velocity (ft/sec) Figure Velocity profiles at station 32+ at a discharge of 135, cfs. 39

59 Distance from Floor (ft) Lateral Location (ft) Downstream Velocity (ft/s) Figure Velocity profiles at Station at a discharge of 135, cfs 4 3 Lateral Velocity (ft/s) Distance from Floor (ft) Lateral Location (ft) Figure Lateral Velocity at Station at a discharge of 135, cfs 4

60 Energy Loss over the Stepped Spillway Energy loss over the stepped spillway was primarily investigated to determine any significant difference between the SAFL and USBR models since the two models were built at two different scales, i.e. 1:26 and 1:48, respectively. To determine energy loss over the stepped spillway, velocity measurements were taken at steps, 32, and either 61 or 63 for each test. A total of four tests were done; two sets of both 135, and 312, cfs discharges. Steps and 32 were chosen because they bound the curvilinear portion of the stepped spillway, i.e. the constant slope started from step 32. To measure the energy loss along the remainder of the stepped spillway, the last step where velocity measurement was possible was chosen. The steps in this linear portion of the spillway were assumed to have the same roughness per step so that the energy loss along the downstream steps could be estimated from the linear portion from steps 32 to 63 and the loss per step was applied to the remaining steps to estimate the total energy loss along the linear portion. Energy loss had to be estimated along five steps in the first set of tests and along seven steps in the second set. The Prandtl tube was visually aligned with the flow direction. Small misorientation was found to have negligible affects on the results. The location of the water surface was determined as discussed in section The outer vertex of the steps was used as the bed level for referencing the depth along the steps. The results of the tests are shown in Tables 3.9 through 3.12 for two flow conditions with target values of 135, and 312, cfs, and two repeat tests. Two methods were employed to estimate the energy loss along the steps. In the first method, the stilling basin was taken as the datum and the sum of potential and kinetic energies was estimated from the water surface at three locations. The pressure head was estimated as ycosθ, where y was the perpendicular depth measured from the surface to the line passing through the outer vertex of the steps. The relative energy loss along the stepped spillway with a constant slope, i.e. from step 32 to e.g. step 61 (Table 3.1), was then estimated and subsequently average energy loss per step along that section of the steps was calculated. By assuming that the remaining steps would have the same energy loss, the energy loss was extrapolated and finally total energy loss along the steps was estimated. Using this method, the energy loss along the entire stepped spillway was estimated to vary from 48% to 56% at a discharge of roughly 135, cfs, and from 27% to 31% 41

61 at a discharge of approximately 314, cfs. In the second method, Chanson s (1994) proposed equation for a stepped spillway was utilized. The difficulty in using this method is in assigning value to the friction factor which varies significantly with the step rise and run, and the effects of aeration. Herein, the friction factor was back calculated from the measured data. The equation is given below. H H C = 1 1/ 3 f cos θ +. 5C H y dam c 2 / 3 f (3.1) In equation 3.1, the left hand side is the energy loss as a fraction of total energy in the reservoir, H dam is the height of the spillway crest above the toe, y c is the critical depth, θ = tan -1 (h/l), h and l are the rise and run of the steps, respectively, and C f = f/(8 sinθ) where f is the friction factor. By utilizing equation 3.1 over the section of the steps with a constant slope, and assuming that H dam is the elevation difference between step 32 and either 61 or 63, and H is the total energy at step 32, the friction factor was calculated. By using the calculated friction factor, the total head loss was estimated in ft along the entire section of the steps with a constant slope and then added to the head loss measured from the first step to step 32. The total energy loss was then estimated and recorded on the last rows of Tables 3.9 to The percent energy loss then varied from 53% to 58% at a discharge of approximately 135, cfs and from 33% to 35% at a discharge of approximately 314, cfs. The variability is partly due to change in the flow from one test to another and partly due to difficulties in measuring the velocities at station 32+ due to the presence of standing waves. The average friction factors along the constant slope of the steps are also given in Tables 3.9 to 3.12, which varied from.22 to.29. The average friction factor along the curvilinear section of the steps was also back calculated and determined to vary from.13 to.17. The slope of the curvilinear section of the steps was set equal to 12. o in these calculations. Estimated discharge values from the Prandtl tube velocity readings were checked against the flow as recorded by the downstream weir. The estimated flows were routinely about 96% of the measured flow rate. The exceptions are the predicted flow rates from those taken at Step of 135, cfs runs. These were both about 91%. For this reason, the energy loss from step to 42

62 step 32 for these flows are speculated to be an underestimate. Table 3.9. Energy loss over the stepped spillway for the target 135, cfs flow condition (Test 1). Elevations given in the table are from the stilling basin invert. 2/28/28 Data Q (cfs) 134,86 HW (ft) Prototype Elevation, Step Vertex (ft): Prototype Elevation, Step 32 Vertex (ft): Prototype Elevation, Step 63 Vertex (ft): Basin Floor Model Elevation (ft): Velocity Head Depth Elevation Total Total energy, Step (ft) Total energy, Step 32 (ft) Total energy, Step 63 (ft) Energy Dissipation (%) 51% Energy Dissipation from Step to Step 32 (%) 22% Energy Dissipation from Step 32 to 63 (%) 29% Energy Dissipation per Linear Step (%).94% Estimated Energy Loss for Last 5 Steps (%) 4.7% Total Estimated Energy Loss (%) 55.6% Total Estimated Energy Loss (%) Using Chanson s equation, f=.25, y c =26.9 ft 58% Table 3.1. Energy loss over the stepped spillway for the target 135, cfs flow condition (Test 2). Elevations given in the table are from the stilling basin invert. 3/14/28 Data Q (cfs) 136,498 HW (ft) Prototype Elevation, Step Vertex (ft): Prototype Elevation, Step 32 Vertex (ft): Prototype Elevation, Step 61 Vertex (ft): Basin Floor Model Elevation (ft): Velocity Head Depth Elevation Total Total energy, Step (ft) Total energy, Step 32 (ft) Total energy, Step 61 (ft) Energy Dissipation (%) 43% Energy Dissipation from Step to Step 32 (%) 2% Energy Dissipation from Step 32 to 61 (%) 23% Energy Dissipation per Linear Step (%).8% Estimated Energy Loss for Last Seven Steps (%) 5.6% Total Estimated Energy Loss (%) 48.2% Total Estimated Energy Loss (%) Using Chanson s equation, f=.22, y c = 27.3 ft 53% 43

63 Table 3.11 Energy loss over the stepped spillway for the target 312, cfs flow condition (Test 3). Elevations given in the table are from the stilling basin invert. 2/29/28 Data Q (cfs) 316,773 HW (ft) Prototype Elevation, Step Vertex (ft): Prototype Elevation, Step 32 Vertex (ft): Prototype Elevation, Step 63 Vertex (ft): Basin Floor Model Elevation (ft): Velocity Head Depth Elevation Total Total energy, Step (ft) Total energy, Step 32 (ft) Total energy, Step 63 (ft) Energy Dissipation (%) 28% Energy Dissipation from Step to Step 32 (%) 12% Energy Dissipation from Step 32 to 63 (%) 16% Energy Dissipation per Linear Step (%).51% Estimated Energy Loss for Last Five Steps (%) 2.54% Total Estimated Energy Loss (%) 3.5% Total Estimated Energy Loss (%) Using Chanson s equation, f=.29, y c = 47.8 ft 35% Table Energy loss over the stepped spillway for the target 312, cfs flow condition (Test 4). Elevations given in the table are from the stilling basin invert. 3/16/28 Data Q (cfs) 31,844 HW (ft) Prototype Elevation, Step Vertex (ft): Prototype Elevation, Step 32 Vertex (ft): Prototype Elevation, Step 61 Vertex ft): Basin Floor Model Elevation (ft): Velocity Head Depth Elevation Total Total energy, Step (ft) Total energy, Step 32 (ft) Total energy, Step 61 (ft) Energy Dissipation (%) 24% Energy Dissipation from Step to Step 32 (%) 12% Energy Dissipation from Step 32 to 61 (%) 12% Energy Dissipation per Linear Step (%).41% Estimated Energy Loss for Last Seven Steps (%) 2.9% Total Estimated Energy Loss (%) 26.6% Total Estimated Energy Loss (%) Using Chanson s equation, f=.27, y c = 47.2 ft 33% 44

64 Energy Loss through the Stepped Spillway and Stilling Basin Using the data obtained from velocity measurements at stations 32+ and 43+52, as described in section 3.3.2, total energy at the upstream end of the stepped spillway and at the downstream end of the stilling basin (at the downstream of the model), as well as the total energy loss across the stepped spillway and the stilling basin were estimated. The results are summarized in Table The total energy loss is given in Table 3.13 and is calculated using equation 3.2. Total Energy Loss H H 1 2 = (3.2) H1 Ele2 In equation 3.2, H 1 and H 2 are the total energy at stations 32+ and 43+52, respectively. The parameter Ele 2 is the bed elevation at station 43+52, i.e ft. Under low flow conditions, the system dissipates about 93% of the total head and under the design flow, i.e. 135, cfs, approximately 8% of the energy is dissipated. Incorporating the energy losses obtained from Chanson s equation in Section 3.3.3, as shown in the seventh column of Table 3.13, it is evident that most of the energy is dissipated over the stepped spillway. It is only under the PMF, when there is a greater depth of skimming flow over the steps, that the energy loss in the stilling basin is comparable to the energy loss over the steps. From Table 3.13, it is evident that for discharges less than 22,5 cfs, more than 93% of energy will be dissipated along the stepped spillway and the stilling basin. In order to determine the energy for other flows between 22,5 and the PMF, the total energy losses summarized in Table 3.13 were plotted versus the Froude number at station 32+. Because the flow under the 22,5 cfs condition is in transition from the nappe flow to skimming flow, energy loss could not be explained using the Froude number. Therefore, the total energy losses shown in Table 3.13 have been plotted versus a dimensionless discharge in Figure B.16. Using a quadratic function, one can determine the energy loss for other discharges within the range tested. In this model study, air entrainment was evident along the downstream section of the stepped spillway. Since it is likely that more air would be entrained for the prototype, bulking of the flow is more likely to occur. Therefore, it is believed that the energy loss over the steps for the prototype will be slightly more than the results shown in Table 3.13 up to and including a discharge of 135, cfs. 45

65 Table Total energy loss along the stepped spillway and the stilling basin under different flow conditions. Total energy, H, given in column 5 has been calculated from the stilling basin invert Discharge 22,58 89, , ,49 158,249 31,71 Location Velocity Head (ft) Depth (ft) H, Total Energy (ft) Total Energy Loss Stepped Spillway Energy Loss (ft) Stilling Basin Energy Loss (ft) 93% % % - - 8% 55% 25% 78% % 34% 33% Hydrostatic and Average Dynamic Pressure Measurements Hydrostatic and dynamic pressures were collected using pressure taps throughout the stepped spillway and stilling basin. For each flow tested, two sets of pressure data were collected. Since these pressure measurements were conducted via pressure taps and plastic tubes, the fluctuations were damped and the measurements represent hydrostatic and quasi-average dynamic pressures at those locations. It is quasi-average dynamic pressure, because dynamic pressures were averaged over an unspecified period of time, which was more or less dependent on the damping effects of plastic tubes. Due to the unsteady characteristics of dynamic pressures over short periods, the recorded pressures may not be the true average dynamic pressures. The measurements were repeated twice to determine if the readings were steady. There was a good agreement between the repeated measurements except for one reading under the 9, cfs flow condition, where the second reading at the tap located on top of step 63 had to be discarded because of poor results. The most noticeable results under the 135, cfs flow condition are presented in Table Wherever hydrostatic pressure was collected, i.e. wherever the pressure taps were installed on the side wall, e.g. tap A and A', the tap height from the channel floor was 46

66 added to the readings. In Table 3.14, the hydrostatic pressure at tap A gives the water depth near the wall at station 32+. This depth is about one foot less than the depth recorded during the velocity measurement under the 135, cfs flow condition (Figure 3.17). The difference is believed to be due to the presence of standing waves where velocities were measured. None of the averaged dynamic pressures listed in Table 3.14 are near vapor pressure. Therefore, based on these measurements cavitation is unlikely to occur over the steps where dynamic pressures were measured. At a discharge of 312, cfs, no negative pressure was recorded. Under some lower flow conditions, negative pressures on the face of the steps were evident (Appendix C); however, none of the pressure heads were less than -3 ft. All of the results for the third test series along with tap locations can be found in Appendix C. Negative pressures are highlighted and poor data are struck through. The measured pressure distributions along the steps are given in Figures 3.2 and 3.21 under six flow conditions. Pressure fluctuations in the first ten steps could be captured because there were 44 pressure taps installed on the first 1 steps, and pressure fluctuations disappear along the rest of the steps because there were only 13 pressure taps installed along the remaining 58 steps. Nevertheless, the overall trend in the pressure distribution can be observed along the steps, which indicates a pressure fluctuation between slightly below zero gauge pressure and approximately 7 psi gauge at a discharge of 135, cfs with a decreasing trend. The decreasing trend does not show large negative gauge pressures, which could be due to the position of the taps on the face of the steps. 47

67 Table Pressure heads recorded at the pressure taps at a discharge of 135, cfs Tap Location Description Pressure Pressure Difference between Dataset 1 (ft) Dataset 2 (ft) two sets (ft) 3e Face step e Face step e Face step e Face step e Face step Top step Top step A Before first step rise A' After last step rise B Before d/s end of end sill C After d/s end of end sill D At tailwater location E Halfway up u/s end sill E' Halfway up u/s end sill E'' Halfway up d/s end sill Figure 3.2. Measured pressure distributions along the steps at 22,6 cfs and 9, cfs. 48

68 Figure Measured pressure distributions along the steps at 115, cfs, 135, cfs, 16, cfs and 312, cfs Unsteady Dynamic Pressure Measurements Unsteady dynamic pressure measurements were collected on all four sides of the center baffle block and at five locations on the floor of the stilling basin, as shown in Figure The initial data collected from the third test series were unusable because of calibration errors. The dynamic sampling was then repeated on March 18, 28. The transducers were recalibrated as described in the instrumentation section of the report. The dynamic pressures measured in the model did not drop below the water vapor pressure. The model pressure heads were linearly scaled up to determine the prototype pressure heads and signals, with some of the reported pressures below the water vapor pressure which could not occur because a cavitation bubble would form. Nevertheless, to be accurate with respect to the data collected at the model scale, the entire range of recorded pressures has been plotted in the figures. A solid red line, however, has been added to the plots which represent where cavitation could potentially occur for the prototype. The solid line represents gage water vapor pressure and 49

69 was estimated to be ft of water based on the standard atmospheric pressure and a water temperature of 68 F. The power spectra were calculated and plotted using the entire range of the pressure data, i.e. the pressure heads below the vapor pressure, ft, were not excluded. The results of the tests under all other flow conditions are given in Appendix D Baffle Blocks All of the transducers in the baffle block were mounted at half the height of the block (Figure 3.22a). The transducers mounted on the front and back faces of the baffle block were centered with respect to the width of the baffle block and the side transducers were mounted 5.42 feet away from the front face of the block. Table 3.15 gives the mean values of the dynamic pressure head readings. Table Mean dynamic pressure heads measured on the baffle block at 135, cfs Block Location Mean Pressure Standard Deviation (ft of water) (ft of water) Face Right Left Back Pressure difference between Right and Left The pressure signals and power spectra are illustrated in Figures 3.23 through To plot the power spectra of the data, the mean of the data was subtracted from the dynamic pressure data. For each flow rate tested, three sets of data were collected. The results of the pressure measurements show that the face of the baffle blocks are subject to positive pressures as high as 86 psi (2 ft of water) at 135, cfs (Figure 3.23). Pressure on the back of the baffle block drops below zero gage pressure due to flow separation, however, the location where the tap was mounted does not exhibit cavitation at a discharge of 135, cfs (Figure 3.29), i.e. the pressure does not drop below the water vapor pressure. There were no prevalent frequencies evident at the back of the baffle block and the only prevalent frequencies on the face of the baffle block were at.4,.5 and 1. Hz, which are characterized by pressure head fluctuations of 7 ft, 26 ft, and 33 ft, respectively. 5

70 At a discharge of 135, cfs, the sides of the baffle block consistently exhibited pressures below vapor pressure. Thus, the maximum cavitation damage is most likely downstream of those taps, because the lowest pressure is located close to the start of the separation zone, i.e. the upstream edge of the block, and the location on the side of the baffle block where cavitation damage is worst is characterized by an average pressure slightly above the vapor pressure. This can also be seen under the 16, (Figure D.32) and 312, cfs (Figure D.42) flow conditions. The average pressure heads at 16, and 312, cfs were about and -17 ft of water, respectively. Under the 22,6 cfs flow condition, cavitation on the sides of the baffle block does not seem to be likely (Figure D.5), but under the 9, cfs flow condition it could occur frequently enough to cause significant damage (Figure D.12). The power spectrum for the lateral pressures (Figure 3.32) was obtained by analyzing the difference between the pressures on both sides. If at a given time step, the pressure on one side of the baffle block dropped below the water vapor pressure, the water vapor pressure was assigned for that side at that time step. By referring to Figure 3.32, it is evident that there was a prevalent frequency in the lateral pressures on the baffle block at a discharge of 135, cfs. The frequency had a value of.94 Hz and is characterized by a pressure of about 38 ft of water, which was obtained by subtracting the right pressures from the left pressures. 51

71 Figure Locations of pressure measurement (a) on the faces of the baffle block, and (b) on the stilling basin floor. 52

72 Pressure Signal Face Block 25 2 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Figure Pressure signal from the face of the baffle block at a discharge of 135, cfs Pressure Spectrum Face Block PSD (h 2 /HZ) Hertz Figure Pressure spectrum from the face of the baffle block at a discharge of 135, cfs 53

73 Pressure Signal Right Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Figure Pressure signal from right side of the baffle block at a discharge of 135, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. Pressure Spectrum Right Block 12 1 PSD (h 2 /HZ) Hertz Figure Pressure spectrum from right side of the baffle block at a discharge of 135, cfs 54

74 Pressure Signal Left Block 15 1 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Figure Pressure signal from left side of the baffle block at a discharge of 135, cfs 14 Pressure Spectrum Left Block 12 1 PSD (h 2 /HZ) Hertz Figure Pressure spectrum from left side of the baffle block at a discharge of 135, cfs 55

75 Pressure Signal Back Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Figure Pressure signal from back of the baffle block at a discharge of 135, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. Pressure Spectrum Back Block PSD (h 2 /HZ) Hertz Figure 3.3. Pressure spectrum from back of the baffle block at a discharge of 135, cfs 56

76 Pressure Signal Lateral Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Figure Pressure signal from sum of the lateral pressures exerted on the baffle block at a discharge of 135, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. Pressure Spectrum Lateral Block PSD (h 2 /HZ) Hertz Figure Pressure spectrum from sum of the lateral pressures exerted on the baffle block at a discharge of 135, cfs 57

77 Stilling Basin Floor The locations of the transducers in the stilling basin were positioned as follows (Figure 3.22b) feet downstream of the last step rise of the stepped spillway feet downstream of the last step rise of the stepped spillway. 3a..54 feet upstream of the middle baffle block. 3b. Centered in the gap between the fourth and fifth baffle blocks at the upstream edge of the blocks 4. In the separation zone created by the edge of the block. The exact location was 1.5 ft downstream of the upstream face of the baffle block and.4 feet from the right side of the fifth block from the right, looking downstream. 5. Centered in the gap between the fourth and fifth baffle blocks at the down stream edge of the blocks The transducer at location 3b was installed for only one run at a discharge of 135, cfs. For all the other runs, the same transducer was placed at 3a. Mean dynamic pressure heads under the 135, cfs flow condition are summarized in Table Table Mean dynamic pressure heads measured on the stilling basin floor at a discharge of 135, cfs Floor Location Mean Pressure Heads (ft) Standard Deviation (ft) a b The pressure signals and power spectra under the 135, cfs flow condition are illustrated in Figures 3.33 through For all other flows they are given in Appendix D. The results of the pressure measurements show an impact and rebound from the jet entering the stilling basin under all flow conditions. At 135, cfs, on average the most upstream dynamic pressure head signal is approximately 15 feet greater than the next location 13 feet downstream (Table 3.16). There are no prevalent frequencies in the data collected except for in the separation zone along 58

78 the baffle block (location 4) and.54 ft upstream of the baffle block (location 3a). The latter exhibits prevalent frequencies of.26, 1. and 1.42 Hz with amplitudes of 28, 39, and 37 ft of water, respectively. The signals at the location 3a show no negative gage pressure (Figure 3.37) with an average pressure head of 145 ft (Table 3.16), while signals at the location 3b show pressure heads as low as vapor pressure (Figure 3.39). It is believed that at.54 ft upstream of the baffle blocks, a cavity flow (closed streamlines) in front of the baffle block could occur and cause high positive pressure heads. The floor of the stilling basin in the vicinity of the separation zone coming off the blocks is consistently below vapor pressure at 135, cfs and also contains a few prevalent frequencies which are all less than 1.5 Hz and have amplitudes of about 59 feet of water. Based on the data collected, the stilling basin floor will be subject to cavitation at all flows tested except 22,6 cfs. The transducer located on the floor at the downstream edge of the baffle blocks (location 5) recorded pressures above vapor pressure at all times. Thus, it is suspected that the cavitation damage on the floor should occur somewhere between the baffle blocks. 59

79 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Figure Pressure signal from the floor, 17.9 ft away from steps at a discharge of 135, cfs Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure Pressure spectrum from the floor, 17.9 ft away from steps at a discharge of 135, cfs 6

80 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Figure Pressure signal from the floor, 31.7 ft away from steps at a discharge of 135, cfs Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure Pressure spectrum from the floor, 31.7 ft away from steps at a discharge of 135, cfs 61

81 Pressure Signal Floor 3a 35 3 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Figure Pressure signals from the floor,.54 ft downstream of the face of the baffle block at a discharge of 135, cfs Pressure Spectrum Floor 3a PSD (h 2 /HZ) Hertz Figure Pressure spectrum from the floor,.54 ft downstream of the face of the baffle block at a discharge of 135, cfs 62

82 Pressure Signal Floor 3b Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Figure Pressure signals from the basin floor, at the upstream edge of the baffle blocks and centered in the gap between the baffle blocks at a discharge of 135, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 35 Pressure Spectrum Floor 3b 3 25 PSD (h 2 /HZ) Hertz Figure 3.4. Pressure spectrum from the basin floor, at the upstream edge of the baffle blocks and centered in the gap between two baffle blocks at a discharge of 135, cfs. 63

83 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Figure Pressure signal from the basin floor inside the separation zone of the baffle block at a discharge of 135, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. Pressure Spectrum Floor 4 PSD (h 2 /HZ) Hertz Figure Pressure spectrum from the basin floor inside the separation zone of the baffle block at a discharge of 135, cfs 64

84 Pressure Signal Floor 5 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Figure Pressure signal from the basin floor at the downstream edge of the baffle blocks and centered in the gap between two baffle blocks at a discharge of 135, cfs. The solid red line represents gauge water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure Pressure spectrum from the basin floor at the downstream edge of the baffle blocks and centered in the gap between two baffle blocks at a discharge of 135, cfs 65

85 66

86 4. Maximum Water Surface Elevations at 322, cfs Water surface elevations for the chute and spillway were measured under 322, cfs to determine the maximum wall height required for the construction of the chute and the stepped spillway. A cart and rails were constructed and leveled such that water surface could be measured every 26 ft (one ft for the model) along the chute (Figure 4.1). Initially, the floor elevations were surveyed at all locations and then subtracted from the measured water surface elevations to minimize the errors. In addition, five cross sections were selected along the stepped spillway to determine the water depths along the spillway. Under the 322, cfs flow condition, a skimming flow occurs and according to the empirical equation proposed by Wood et al. (1983) the point of inception of air entrainment is beyond the length of the Folsom Dam Stepped Spillway, therefore, the measured depths at the model scale could give a realistic depth for the prototype at a discharge of 322, cfs. For all measurements, the water surface elevations were sampled at 1 Hz for 6 seconds in model time. Mean, minimum, and maximum water surface elevations along with histograms were documented. The maximum recorded values are illustrated in Figure 4.2 and tabulated in Tables 4.1 and 4.2. The maximum depth was recorded to be 35.5 ft at station Discharge was recorded over the period of testing and is shown in Figure 4.3. During the test, the debris in the Mississippi River partially clogged the SAFL Main Channel intake and the flow rate dropped from 323, cfs to 319,. Two anomalies were evident in the data: one was the extreme asymmetry at station 12+7, and the other one was the high water surface elevations near the walls at station over the steps. The asymmetry at station 12+7 was due to the presence of a vortex in the head tank causing instabilities downstream of the left bay looking downstream. Upon exiting of vortices from the left bay, a significant change in water surface elevation would occur at station The problem was documented using a digital video camera. The high water surface elevations at station were due to return flows over the stilling basin walls, which were discharged back into the downstream end of the stepped spillway. Figure 4.4 illustrates the return flow. Thus, water surface elevations recorded on right side of the channel at station 12+7 are correct for that station, and water surface elevations on the left side of the channel should be ignored. 67

87 Figure 4.1. Sonar cart and rails used to measure water surface elevations at a discharge of 322, cfs 68

88 42 Maximum Water Surface Elevations over the Chute and Stepped Spillway under 322, cfs (Looking Downstream) Elevation (feet) Station Right LDS Right 25% LDS Center LDS Left 25% LDS Left LDS Floor Figure 4.2. Maximum water surface elevations along the chute and spillway at a discharge of 322, cfs 69

89 Discharge over Duration of 322, cfs WSE Test 335 Discharge ( prototype CFS) y = x R 2 = Time ( model seconds ) Figure 4.3. Change in discharge over the period of the test at a discharge of 322, cfs Figure 4.4. Water flowing upstream over the stilling basin walls back into the stepped spillway at a discharge of 322, cfs 7

90 Table 4.1. Maximum water surface elevations measured along the 2% chute and the stepped spillway at a discharge of 322, cfs. LDS stands for looking downstream. Station (ft) Water Surface (feet) Local Floor Elevation Right Right 25% Center Left 25% Left LDS LDS LDS LDS LDS

91 Station (ft) Local Floor Right Right 25% Center Left 25% Left Elevation LDS LDS LDS LDS LDS

92 Table 4.2. Maximum water surface elevations measured at a discharge of 322, cfs at the last station over the stepped spillway. Because of the steep angle of flow and the observed variability in the water surface elevation, the sonar was slightly adjusted at each location, thus the correct station associated with each reading along the width of the stepped spillway is tabulated below. Local Floor Right Right 25% Center Left 25% Left Station (ft) Elevation LDS LDS LDS LDS LDS

93 74

94 5. Summary A 1:26 model of the Folsom Dam Auxiliary Spillway System was constructed over the Main Channel of the St. Anthony Falls Laboratory (SAFL). The objectives of the model study were to assess the performance of the stilling basin under six flow conditions, from 22,6 cfs to 312, cfs (PMF), to determine the maximum water surface elevations under the PMF along the 2% chute and the stepped spillway, to measure the head loss over the stepped spillway and the stilling basin under the 135, and 312, cfs flow conditions, to determine if the stepped spillway or the stilling basin is subject to cavitation damages at discharges equal or less than the design flow (135, cfs) and to investigate the addition of roughness elements to increase self aeration on the spillway. The extent of the 1:26 model built at SAFL was from upstream of the control structure, station , to 222 ft downstream of the final design of the stilling basin, station During the initial test series, the design of the stilling basin seemed to be inadequate in confining the hydraulic jump inside the basin under the design flow, therefore, the basin length was extended by 8 ft and the two rows of 9-ft high baffles were replaced with one row of 16-ft high baffle blocks. In addition, the 4.5 ft high solid end sill was replaced with a 15-ft high solid end sill. Subsequently, three series of tests were conducted to assess the performance of the system. In the first test series the minimum tailwater levels to confine the jump inside the stilling basin were determined. The results of this test series showed that a linear relationship exists between the minimum tailwater levels and flow rates. In the second test series, water surface elevations, velocities and pressures were measured for tailwater levels specified by the USCOE. The third test series was a repeat of the second test series under the minimum tailwater levels determined in the first test series. Prior to the third test series, five pressure transducers were installed on the floor of the stilling basin, six more pressure taps were installed along the steps and three pressure taps were installed on the end sill. The maximum pressure was measured on the face of the baffle block to be 86 psi at 135, cfs. The results of the third test series showed that some steps along the vertical face exhibit negative 75

95 pressures but not sufficiently low enough to cause cavitation along the steps. However, the low pressures measured on the side of the baffle blocks and on the floor of the stilling basin indicate cavitation at flows equal to and larger than 9, cfs. The velocity measurements indicated maximum velocities of 77 and 21 fps under the 135, cfs flow condition at stations 32+ and 43+52, respectively. The energy losses along the steps and stilling basin were estimated from the velocity measurements. It was found that 8% of the energy at station 32+ would be dissipated under the 135, cfs flow condition, of which 55% would be dissipated along the stepped spillway. The water surface elevations were measured at five locations across the width along the 2% chute and the stepped spillway. The maximum water depth was measured to be 35.5 ft at station at 322, cfs. 76

96 6. Reference Boes, R.M. and Hager, W.H. (23). Two-phase Flow Characteristics of Stepped Spillways. Journal of Hydraulic Engineering, ASCE, Vol. 129, pp Chanson, H., Hydraulic Design of Stepped Cascades, Channels, Weirs and Spillways. Elsevier Science, Oxford, England. Knight, Donald W. and J. Alasdair Macdonald,: 1979, Hydraulic Resistance to Artificial Strip Roughness. Journal of the Hydraulics Division, Vol. 15, No. 6, June 1979, pp Pfister, M., Hager, W.H. and Minor, H.E. (26). Stepped Chutes: Pre-aeration and Spray Reduction. International Journal of Multiphase Flow, Vol. 32, pp Wood, I. R., Ackers, P/\., and Loveles, J General Method for Critical Point on Spillways. Journal of Hydraulic Engineering, ASCE, Vol. 19:2, pp

97 78

98 Appendix A. Third Test Series: Water Surface Elevation Data A.1. Discharge of 22,625 cfs 4 35 Elevation Right 3 Elevation Right 25% Elevation (ft) 25 2 Elevation Center Elevation Left 25% Elevation Left Spillway Floor 15 Basin Floor Station Figure A.1. Mean water surface elevations at a discharge of 22,625 cfs 79

99 Table A.1. Summery of mean, minimum, and maximum water surface elevations at 22,625 cfs Elevation Right Station Average Elevation Min Elevation Min -Average Max Elevation Max -Elevation Elevation Right 25% Station Average Elevation Min Elevation Min -Average Max Elevation Max -Elevation Elevation Center Station Average Elevation Min Elevation Min -Average Max Elevation Max -Elevation

100 Elevation Left 25% Station Average Elevation Min Elevation Min -Average Max Elevation Max -Elevation Elevation Left Station Average Elevation Min Elevation Min -Average Max Elevation Max -Elevation

101 14 12 Maximum Differences from Mean Elevation (ft) Right Min - Mean Right 25% Min - Mean Center Min - Mean Left 25% Min - Mean Left Min - Mean Right Max - Mean Right 25% Max - Mean Center Max - Mean Left 25% Max - Mean Station Figure A.2. Maximum and minimum deviations from mean water surface elevations at a discharge of 22,625 cfs Skewness 1. Right Right 25% Center Left 25% Left Station Figure A.3. Skewness of water surface elevations measured at a discharge of 22,625 cfs 82

102 Kurtosis 3 2 Right Right 25% Center Left 25% Left Station Figure A.4. Kurtosis of water surface elevations measured at a discharge of 22,625 cfs 83

103 A.2. Discharge of 9, cfs 4 35 Elevation Right 3 Elevation Right 25% Elevation (ft) 25 2 Elevation Center Elevation Left 25% Elevation Left Spillway Floor 15 Basin Floor Station Figure A.5. Mean water surface elevations at a discharge of 9, cfs 84

104 Table A.2. Summery of mean, minimum, and maximum water surface elevations at 9, cfs Elevation Right Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average Elevation Right 25% Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average Elevation Center Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average

105 Elevation Left 25% Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average Elevation Left Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average

106 14 12 Maximum Differences from Mean Elevation (ft) Right Min - Mean Right 25% Min - Mean Center Min - Mean Left 25% Min - Mean Left Min - Mean Right Max - Mean Right 25% Max - Mean Center Max - Mean Left 25% Max - Mean Station Figure A.6. Maximum and minimum deviations from mean water surface elevations at a discharge of 9, cfs Skewness Right Right 25% Center Left 25% Left Station Figure A.7. Skewness of water surface elevation measured at a discharge of 9, cfs 87

107 4 3 2 Kurtosis 1 Right Right 25% Center Left 25% Left Station Figure A.8. Kurtosis of water surface elevation measured at a discharge of 9, cfs 88

108 A.3. Discharge of 115, cfs 4 35 Elevation Right 3 Elevation Right 25% Elevation (ft) 25 2 Elevation Center Elevation Left 25% Elevation Left Spillway Floor 15 Basin Floor Station Figure A.9. Mean water surface elevations measured at a discharge of 115, cfs 89

109 Table A.3. Summery of mean, minimum, and maximum water surface elevations at 115, cfs Elevation Right Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average Elevation Right 25% Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average Elevation Center Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average

110 Elevation Left 25% Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average Elevation Left Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average

111 15 Maximum Differences from Mean Elevation (ft) Right Min - Mean Right 25% Min - Mean Center Min - Mean Left 25% Min - Mean Left Min - Mean Right Max - Mean Right 25% Max - Mean Center Max - Mean Left 25% Max - Mean Station Figure A.1. Maximum and minimum deviations from mean water surface elevations at 115, cfs Skewness Right Right 25% Center Left 25% Left Station Figure A.11. Skewness of water surface elevations measured at 115, cfs 92

112 Right Kurtosis 1 t Right 25% Center Left 25% Left Station Figure A.12. Kurtosis of water surface elevations measured at 115, cfs 93

113 A.4. Discharge of 16, cfs 4 35 Elevation Right Elevation (ft) Elevation Right 25% Elevation Center Elevation Left 25% Elevation Left Spillway Floor 15 Basin Floor Station Figure A.13. Mean water surface elevations at 16, cfs 94

114 Table A.4. Summery of mean, minimum, and maximum water surface elevations at 16, cfs Elevation Right Station Average Elevation Min Elevation Min - Average Max Elevation Max -Average Elevation Right 25% Station Average Elevation Min Elevation Min - Average Max Elevation Max -Average Elevation Center Station Average Elevation Min Elevation Min - Average Max Elevation Max -Average

115 Elevation Left 25% Station Average Elevation Min Elevation Min - Average Max Elevation Max -Average Elevation Left Station Average Elevation Min Elevation Min - Average Max Elevation Max -Average

116 12 1 Maximum Differences from Mean Elevation (ft) Right Min - Mean Right 25% Min - Mean Center Min - Mean Left 25% Min - Mean Left Min - Mean Right Max - Mean Right 25% Max - Mean Center Max - Mean Left 25% Max - Mean Station Figure A.14. Maximum and minimum deviations from mean water surface elevations at 16, cfs Skewness Right Right 25% Center Left 25% Left Station Figure A.15. Skewness of water surface elevations measured at 16, cfs 97

117 4 3 2 Kurtosis 1 Right Right 25% Center Left 25% Left Station Figure A.16. Kurtosis of water surface elevations measured at 16, cfs 98

118 A.5. Discharge of 312, cfs 45 4 Elevation Right 35 Elevation Right 25% Elevation (ft) 3 25 Elevation Center Elevation Left 25% Elevation Left 2 Spillway Floor 15 Basin Floor Station Figure A.17. Mean water surface elevations at 312, cfs 99

119 Table A.5. Summery of mean, minimum, and maximum water surface elevations at 312, cfs Elevation Right Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average Elevation Right 25% Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average Elevation Center Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average

120 Elevation Left 25% Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average Elevation Left Station Average Elevation Min Elevation Min -Average Max Elevation Max -Average

121 3 25 Maximum Differences from Mean Elevation (ft) Right Min - Mean Right 25% Min - Mean Center Min - Mean Left 25% Min - Mean Left Min - Mean Right Max - Mean Right 25% Max - Mean Center Max - Mean Left 25% Max - Mean Station Figure A.18. Maximum and minimum deviations from mean water surface elevations at 312, cfs Skewness Right Right 25% Center Left 25% Left Station Figure A.19. Skewness of water surface elevations measured at 312, cfs 12

122 3 2 1 Kurtosis Right Right 25% Center Left 25% Left Station Figure A.2. Kurtosis of water surface elevations measured at 312, cfs 13

123 14

124 Appendix B. Third Test Series: Velocity Profiles B.1. Discharge of 22,625 cfs Distance from Floor (ft) Distance From Right Wall (ft) Velocity (ft/sec) Figure B.1. Velocity profiles at 22,625 cfs at station Distance from Floor (ft) Lateral Location (ft) Downstream Velocity (ft/s) Figure B.2. Velocity profiles at 22,625 cfs at station

125 Lateral Velocity (ft/s) Distance from Floor (ft) Lateral Location (ft) Figure B.3. Lateral velocities at 22,625 cfs at station

126 B.2. Discharge of 9, cfs 9 8 Distance from Floor (ft) Distance From Right Wall (ft) Velocity (ft/sec) Figure B.4. Velocity profiles at a discharge of 9, cfs at station Distance from Floor (ft) Lateral Location (ft) Downstream Velocity (ft/s) Figure B.5. Velocity profiles at a discharge of 9, cfs at station

127 Lateral Velocity (ft/s) Distance from Floor (ft) Lateral Location (ft) Figure B.6. Lateral velocities at a discharge of 9, cfs at station

128 B.3. Discharge of 115, cfs Distance from Floor (ft) Distance From Right Wall (ft) Velocity (ft/sec) Figure B.7. Velocity profiles at a discharge of 115, cfs at station Distance from Floor (ft) Lateral Location (ft) Downstream Velocity (ft/s) Figure B.8. Velocity profiles at a discharge of 115, cfs at station

129 4 3 Lateral Velocity (ft/s) Distance from Floor (ft) Lateral Location (ft) Figure B.9. Lateral velocities at a discharge of 115, cfs at station

130 B.4. Discharge of 16, cfs Distance from Floor (ft) Distance From Right Wall (ft) Velocity (ft/sec) Figure B.1. Velocity profiles at a discharge of 16, cfs at station Distance from Floor (ft) Lateral Location (ft) Downstream Velocity (ft/s) Figure B.11. Velocity profiles at a discharge of 16, cfs at station

131 4 3 Lateral Velocity (ft/s) Distance from Floor (ft) Lateral Location (ft) Figure B.12. Lateral velocities at a discharge of 16, cfs at station

132 B.5. Discharge of 312, cfs 25 2 Distance from Floor (ft) 15 1 Distance From Right Wall (ft) Velocity (ft/sec) Figure B.13. Velocity profiles at a discharge of 312, cfs at station Distance from Floor (ft) Lateral Distance (ft) Downstream Velocity (ft/s) Figure B.14. Velocity profiles at a discharge of 312, cfs at station

133 6 4 Lateral Velocity (ft/s) Distance from Floor (ft) Lateral Location (ft) Figure B.15. Lateral velocities at a discharge of 312, cfs at station % 9% 8% Energy Loss (%) 7% 6% 5% 4% 3% y = x x R 2 = % 1% % Q/g.5 b 2.5 Figure B.16. Energy loss over the Folsom Dam stepped spillway and the stilling basin as a function of a dimensionless discharge. 114

134 Appendix C. Third Test Series: Pressure Heads along the Steps and inside the Stilling Basin Table C.1. Locations of pressure taps throughout the model during the third test series Position Tap Rough Location Distance (ft) Lateral Location (ft) Step Length (ft) Step Run Elevation (ft) Tap Station (ft) Tap Elevation (ft) Low Cal Calibration Point N/A N/A N/A N/A N/A N/A 1 2nd Cal Calibration Point N/A N/A N/A N/A N/A N/A 2 3rd Cal Calibration Point N/A N/A N/A N/A N/A N/A 3 4th Cal Calibration Point N/A N/A N/A N/A N/A N/A 4 High Cal Calibration Point N/A N/A N/A N/A N/A N/A 5 2a Top Step b Top Step c Top Step d Top Step e Face Step a Top Step b Top Step c Top Step d Top Step e Face Step a Top Step b Top Step c Top Step d Top Step e Face Step a Top Step b Top Step c Top Step d Top Step

135 Position Tap Rough Location Distance (ft) Lateral Location (ft) Step Length (ft) Step Run Elevation (ft) Tap Station (ft) Tap Elevation (ft) 24 5e Face Step a Top Step b Top Step c Top Step d Top Step e Face Step a Top Step b Top Step c Top Step d Top Step e Face Step a Top Step b Top Step c Top Step d Top Step e Face Step a Top Step b Top Step c Top Step d Top Step e Face Step a Top Step b Top Step c Top Step d Top Step Top Step Top Step e Face Step Top Step e Face Step e Face Step e Face Step

136 Position Tap Rough Location Distance (ft) Lateral Step Step Run Tap Tap Location (ft) Length (ft) Elevation (ft) Station (ft) Elevation (ft) Top Step e Face Step e Face Step Top Step Top Step Top Step A Before First Step Rise A' After Last Step Rise B' At Face of Baffle Block B Before D/S end of End Sill C After DS end of End Sill D At TW Location E 69 E' 7 E'' Halfway Up U/S End sill Halfway Up U/S End sill Halfway Up D/S End Sill.. Directly Between Baffles (72.5) Directly Behind Baffle (84.5)

137 Table C.2. Results of the pressure head measurements during the third test series Position Tap Tap Elevation (P ft) 22,625 9, 115, 135, 16, 312, Low Cal nd Cal rd Cal th Cal High Cal a b c d e a b c d e a b c d e a b c d e a b c d e a

138 Position Tap Tap Elevation (P ft) 22,625 9, 115, 135, 16, 312, 31 7b c d e a b c d e a b c d e a b c d e e e e e e

139 Position Tap Tap Elevation (P ft) 22,625 9, 115, 135, 16, 312, 62 A A' B' B C D E E' E''

140 Appendix D. Third Test Series: Unsteady Dynamic Pressure Measurements D.1. Discharge of 22,625 cfs Table D.1. Average dynamic pressure heads on the baffle block at 22,625 cfs Block Average Pressure Heads Standard Deviation (ft) Location (ft) Face Right Left Back Right - Left

141 Pressure Signal Face Block 25 2 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Block Face 25 2 PSD (h 2 /HZ) Hertz Figure D.1. Pressure on the face of the baffle block at 22,625 cfs 122

142 Pressure Signal Right Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Block Right PSD (h 2 /HZ) Hertz Figure D.2. Pressure on right side of the baffle block at 22,625 cfs 123

143 Pressure Signal Left Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Block Left PSD (h 2 /HZ) Hertz Figure D.3. Pressure on left side of the baffle block at 22,625 cfs 124

144 Pressure Signal Back Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Block Back PSD (h 2 /HZ) Hertz Figure D.4 Pressure on the back side of the baffle block at 22,625 cfs 125

145 Pressure Signal Lateral Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Block Lateral PSD (h 2 /HZ) Hertz Figure D.5. Lateral pressure on the baffle block at 22,625 cfs (limited by vapor pressure) 126

146 Table D.2. Average dynamic pressure heads on the basin floor at 22,625 cfs Floor Location Average Pressure Head (ft) Standard Deviation (ft) a

147 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor 1 PSD (h 2 /HZ) Hertz Figure D.6. Pressures on the basin floor, 17.9 ft from steps at 22,635 cfs 128

148 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.7. Pressures on the basin floor, 31.7 ft from steps at 22,625 cfs 129

149 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.8. Pressure on the basin floor,.54 ft upstream of the baffle block at 22,625 cfs 13

150 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.9. Pressure on the basin floor inside the separation zone at 22,625 cfs 131

151 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.1. Pressure on the basin floor along the downstream edge of the baffle blocks at 22,625 cfs 132

152 D.2. Discharge of 9, cfs Table D.3. Average dynamic pressure heads on the baffle block at 9,cfs Block Location Average Pressure Head (ft) Standard Deviation (ft) Face Right Left Back Right - Left

153 Pressure Signal Face Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Face Block PSD (h 2 /HZ) Hertz Figure D.11. Pressure on the face of the baffle block at 9, cfs 134

154 Pressure Signal Right Block 15 1 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Right Block PSD (h 2 /HZ) Hertz Figure D.12. Pressure on the right side of the baffle block at 9, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 135

155 Pressure Signal Left Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Left Block PSD (h 2 /HZ) Hertz Figure D.13. Pressure on the left side of the baffle block at 9, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 136

156 Pressure Signal Back Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Back Block 12 1 PSD (h 2 /HZ) Hertz Figure D.14. Pressure on the back side of the baffle block at 9, cfs 137

157 Pressure Signal Lateral Block 1 5 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Lateral Block 25 2 PSD (h 2 /HZ) Hertz Figure D.15. Lateral pressure on the baffle block at 9, cfs (limited by vapor pressure) 138

158 Table D.4. Average dynamic pressure heads on the basin floor at 9, cfs Floor Location Mean Pressure (ft of water) St Dev Pressure (ft of water) a

159 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.16. Pressure on the basin floor, 17.9 ft from steps at 9, cfs 14

160 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.17. Pressure on the basin floor, 31.7 ft from steps at 9, cfs 141

161 Pressure Signal Floor 3a 25 2 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor 3a PSD (h 2 /HZ) Hertz Figure D.18. Pressure on the basin floor,.54 ft upstream of the baffle block at 9, cfs 142

162 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.19. Pressure on the basin floor, inside the separation zone at 9, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 143

163 Pressure Signal Floor 5 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.2. Pressure on the basin floor along the downstream edge of the baffle blocks at 9, cfs 144

164 D.3. Discharge of 115, cfs Table D.5. Average dynamic pressure heads on the baffle block at 115, cfs Block Location Average Pressure Head (ft) Standard Deviation (ft) Face Right Left Back Right - Left

165 Pressure Signal Face Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Face Block PSD (h 2 /HZ) Hertz Figure D.21. Pressure on the face of the baffle block at 115, cfs 146

166 Pressure Signal Right Block 15 1 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Right Block PSD (h 2 /HZ) Hertz Figure D.22. Pressure on the right side of the baffle block at 115, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 147

167 Pressure Signal Left Block 15 1 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Left Block PSD (h 2 /HZ) Hertz Figure D.23. Pressure on the left side of the baffle block at 115, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 148

168 Pressure Signal Back Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Back Block 6 5 PSD (h 2 /HZ) Hertz Figure D.24. Pressure on the back side of baffle block at 115, cfs 149

169 Pressure Signal Lateral Block 15 1 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Lateral Block PSD (h 2 /HZ) Hertz Figure D.25. Lateral pressure on the baffle block at 115, cfs (limited by vapor pressure) 15

170 Table D.6. Average dynamic pressure heads on the basin floor at 115, cfs Floor Location Average Pressure Head (ft) Standard Deviation (ft) a

171 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.26. Pressure on the basin floor, 17.9 ft from steps at 115, cfs 152

172 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.27. Pressure on the basin floor, 31.7 Feet from steps at 115, cfs 153

173 Pressure Signal Floor 3a 3 25 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor 3a 3 25 PSD (h 2 /HZ) Hertz Figure D.28. Pressure on the basin floor,.54 ft upstream of the baffle block at 115, cfs 154

174 Pressure Signal Floor 4 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.29. Pressure on the basin floor inside the separation zone at 115, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 155

175 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.3. Pressure on the basin floor along the downstream edge of the baffle blocks at 115, cfs 156

176 D.4. Discharge of 16, cfs Table D.7. Average dynamic pressure heads on the baffle block at 16, cfs Block Location Average Pressure Head (ft) Standard Deviation (ft) Face Right Left Back Right - Left

177 Pressure Signal Face Block 3 25 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Face Block PSD (h 2 /HZ) Hertz Figure D.31. Pressure on the face of the baffle block at 16, cfs 158

178 Pressure Signal Right Block 2 1 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Right Block 3 25 PSD (h 2 /HZ) Hertz Figure D.32. Pressure on the right side of the baffle block at 16, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 159

179 Pressure Signal Left Block 2 1 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Left Block 3 25 PSD (h 2 /HZ) Hertz Figure D.33. Pressure on the left side of the baffle block at 16, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 16

180 Pressure Signal Back Block 6 4 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Back Block PSD (h 2 /HZ) Hertz Figure D.34. Pressure on the back side of the baffle block at 16, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 161

181 Pressure Signal Lateral Block 15 1 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Lateral Block 12 1 PSD (h 2 /HZ) Hertz Figure D.35. Lateral Pressure on the baffle block at 16, cfs (limited by vapor pressure) 162

182 Table D.8. Average dynamic pressure heads on the basin floor at 16, cfs Floor Location Average Pressure Head (ft) Standard Deviation (ft) a

183 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor 1 PSD (h 2 /HZ) Hertz Figure D.36. Pressure on the basin floor, 17.9 ft from steps at 16, cfs 164

184 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.37. Pressure on the basin floor, 31.7 ft from steps at 16, cfs 165

185 Pressure Signal Floor 3a 35 3 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor 3a 25 2 PSD (h 2 /HZ) Hertz Figure D.38. Pressure on the basin floor,.54 ft upstream of the baffle block at 16, cfs 166

186 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.39. Pressure on the basin floor inside the separation zone at 16, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 167

187 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor 5 PSD (h 2 /HZ) Hertz Figure D.4. Pressure on the basin floor along the downstream edge of the baffle blocks at 16, cfs 168

188 D.5. Discharge of 312, cfs Table D.9. Average dynamic pressure heads on the baffle block at 312, cfs Block Location Average Pressure Head (ft) Standard Deviation (ft) Face Right Left Back Right - Left

189 Pressure Signal Face Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Face Block 6 5 PSD (h 2 /HZ) Hertz Figure D.41. Pressure on the face of the baffle block at 312, cfs 17

190 Pressure Signal Right Block 2 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Right Block PSD (h 2 /HZ) Hertz Figure D.42. Pressure on the right side of the baffle block at 312, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 171

191 Pressure Signal Left Block 4 2 Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Left Block PSD (h 2 /HZ) Hertz Figure D.43. Pressure on the left side of the baffle block at 312, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 172

192 Pressure Signal Back Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Back Block PSD (h 2 /HZ) Hertz Figure D.44. Pressure on the back side of the baffle block at 312, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 173

193 Pressure Signal Lateral Block Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Lateral Block PSD (h 2 /HZ) Hertz Figure D.45. Lateral pressure on the baffle block at 312, cfs (limited by vapor pressure) 174

194 Table D.1. Average dynamic pressure heads on the basin floor at 312, cfs Floor Location Average Pressure Head (ft) Standard Deviation (ft) a

195 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.46. Pressure on the basin floor, 17.9 ft from steps at 312, cfs 176

196 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.47. Pressure on the basin floor, 31.7 ft from steps at 312, cfs 177

197 Pressure Signal Floor 3a Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor 3a PSD (h 2 /HZ) Hertz Figure D.48. Pressure on the basin floor,.54 ft upstream of the baffle block at 312, cfs 178

198 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.49. Pressure on the basin floor inside the separation zone at 312, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 179

199 Pressure Signal Floor Pressure Head (ft) :37 59:54 :12 :29 :46 1:3 1:21 1:38 1:55 2:12 2:3 2:47 Time (s) Pressure Spectrum Floor PSD (h 2 /HZ) Hertz Figure D.5. Pressure on the basin floor along the downstream edge of the baffle blocks at 312, cfs. The solid red line represents gage water vapor pressure based on the standard atmospheric pressure and a water temperature of 68 F. 18

200 Appendix E: Estimating the Air Uptake over the Stepped Spillway The pressures measured along the stepped spillway did not indicate potential for cavitation along the steps. However, pressures were measured at only one location on the vertical steps. Cavitation potential along the stepped spillway is currently the subject of a CFD numerical model and a physical model in the low ambient pressure chamber facility at the Bureau of Reclamation's Hydraulic Laboratory in Denver, CO. The USACE will review technical literature and the results of all of the numerical and physical modeling performed for the Folsom Dam project before deciding if any means of adding air at the upstream end of the stepped chute is needed. The literature review will include actual experiences at existing stepped spillways. This appendix would be useful if it is found that air needs to be supplied, and describes a sequence of steps followed to analytically estimate the air discharge that could be supplied in a bottom aerator of the auxiliary stepped spillway at Folsom Dam. E.1. Description of the Problem In a stepped spillway, the edges and vertical walls of the steps can be subject to low pressures which may cause cavitation of the flowing water. If there is potential for cavitation erosion on the spillway surface, one means of protecting the spillway is to add air through a duct onto the spillway face. If the air quantity is sufficient (approximately 2% by volume), the compressibility of the mixed media will reduce the severity of pressure pulses on the spillway surface. In order to add air, a low pressure location must be found. In addition, the following questions need to be answered: How to aerate. How to determine the region of highest risk. How to estimate air supply. E.2. Application to the Folsom Dam Auxiliary Spillway Pfister et al. (26) provided equations for the aeration of a stepped spillway, and applied them to a case study with a water discharge per unit width q w =1 m 3 /s/m and a step height s =1.2 m. At the Folsom Dam Auxiliary Spillway, the design parameters are q w = 181

201 8 m 3 /s/m (86 ft 2 /s) and s =.91 m (3 ft). E.3. How to Aerate The aerator considered by Pfister et al. (26) is sketched in Fig. E.1. A metal plate separates the eddy in the steps from the skimming flow over the steps. This will result in a more uniform low pressure region for the various flows that the spillway encounters. Air is supplied through a slot just above the metal plate. The aerator is positioned in the first step of the spillway, and the spillway is sloped upstream of the first step. The current design of the Folsom Dam Auxiliary Spillway has close to horizontal flow off of the channel flowing into the steps. Figure E.1. Geometrical arrangement of the bottom aerator considered here. E.4. Region of Highest Risk The cavitation index, σ bi, is used to determine if the hydraulic structure is under cavitation risk. The cavitation index is defined as: where: hpi hv + ha σ bi = (E.1) 2 V / 2g wi 182

202 h pi = bottom gauge pressure head, h v = absolute vapor pressure head, h a = atmospheric pressure head, V wi = blackwater velocity = q w /h wi, q w = specific discharge, or discharge per unit width, and h wi = depth without air entrainment or water surface roughness. For stepped spillways, there is little information on the critical value of the cavitation index, σ c that would cause cavitation damage. In fact, cavitation damage on a stepped spillway has never been reported to our knowledge (Boes and Hager, 23). The following equations (Pfitser et al., 26)) can be used to obtain the parameters V wi and h pi for equation E.1. h wi mi ( C ) = h 1 C =. 228 = air content in water (E.2) ia ia.6 h mi =.4 s F * (E.3) In equation E.3, h mi is the water depth with air entrainment and water surface roughness F* = qw (E.4) 3 g sinφ s h = / cosφ (E.5) pi h wi where q w is the water discharge per unit width, s is the step height and φ is the angle between the pseudo-bottom of the spillway and the horizontal plane. Table E.1 furnishes vapor pressures for different temperatures, which permits calculation of the vapor pressure head h v of equation E.1. Following Pfitser et al. (26), the bottom air inception point is the most critical location for cavitation damage along the spillway. The position L i of this region is obtained from (Boes and Hager, 23) 183

203 L i 6 / hc = (E.6) 5 1/ 5 ( sinφ) 7 / s where 1/ 3 2 q w hc = (E.7) g g = acceleration of the gravity L i = the distance with origin at the crest of the spillway. Table E.1. Temperature ( o C) Vapor pressure as a function of temperature Vapor Pressure (kn/m 2 ) Temperature ( o F) Vapor Pressure (psi) E.4.1. Position of the Bottom Air Inception Point on the Folsom Dam Stepped Spillway For the Folsom Dam, s =.91m (3 ft), φ = 21.8 o, and temperature can be assumed to be 25 o C (77 o F). Then, equations E.6 and E.7 are used to furnish the graph of Figure E.2, where L i becomes 32 m (993 ft) for q w =74 m 3 /s/m (8 ft 2 /s). 184

204 Applying equations E.1 through E.5 to the Folsom Dam Auxiliary Spillway results in Figure E.3, which shows that the spillway would not need any aerators for q 19 m 3 /s/m (25 ft 2 /s). For q w = 74m 3 /s/m (8 ft 2 /s) the cavitation index is.34, showing risk of cavitation and the need of aeration. w Figure E.2. Variation of L i in terms of the discharge per unit width, q w Figure E.3. Critical cavitation index σ bi versus discharge per unit width q w. Assuming s=.91m (3 ft), φ = 21.8 o, and temperature of 25 o C (77 o F), then σ bi =.33 for q w =8 m 3 /s/m (86 ft 2 /s). 185

205 E.4.2. Estimating Air Supply Following Pfitser et al. (26), the air supply for the employed aerator is given by: β =.77 ( Fo 3.2) 3.2 <F <6. (E.8) In equation E.8, β is the ratio between air and water discharges, and V F =, (E.9) g h where V is the flow velocity at the edge of the first step and h is the water depth at the same location. E.4.3. Air supply at the Folsom Dam Auxiliary Spillway. For this case, V and h were measured for q w =74 m 3 /s/m (8 ft 2 /s). Considering an aerator with the same characteristics of that used by Pfitser et al. (26), and the values h = 3.3 m (1.8 ft) and V = 22.7 m/s (74.4 fps), equations E.8 and E.9 furnish: F = 3.99 β = The air discharge per unit width for q w =74 m 3 /s/m is q a =.488 m 3 /s/m. For the actual design, measurements indicated that there would be a sub-atmospheric pressure only at step 3, 5, 6 and 55 at 135, cfs. This indicates that only those steps would be able to vent air. Reported experimental results on air discharges in bottom aerators of stepped spillways are rare, so that experiments and simulations are recommended to estimate the air that can be vented at a given location. E.5. Summary of Findings 1. The study described in this appendix indicates that if air needs to be supplied to the Folsom Dam stepped spillway to reduce cavitation damage, it could be a 186

206 challenge to supply sufficient air. The need for adding air will be further evaluated by the USACE, who will be conducting CFD numerical modeling and low ambient pressure chamber testing to evaluate cavitation potential at the Bureau of Reclamation's Hydraulic Laboratory. If it is determined that air needs to be supplied to the stepped spillway to prevent cavitation, a detailed design effort would be needed due to the potential cost of supplying a sufficient air duct and auxiliary facilities. 2. It may be possible to initiate self-aeration earlier on the spillway, therefore reducing L i. If this distance can be reduced such that air reaches the spillway face before the location where cavitation may begin, then aerators would not be required. 3. The results of the present study reflect the conditions in which the design equations (based on empirical results) were obtained. Deviations may occur for different operation situations and geometrical arrangements. 187

207 188

208 Appendix F: Enhancing Self Aeration Using Artificial Roughness In an investigation of mitigation for potential cavitation resulting from subatmospheric pressures on the steps, it was decided to test the impact of artificial roughness at the downstream end of the 2% chute in the 1:26 model of the Folsom Dam auxiliary spillway system. The scope of this task was to design and install some artificial roughness at the model scale (1:26) and to visually assess the changes in the point of inception of surface air entrainment. In order to design the artificial roughness, the boundary layer development due to change in roughness and the change in bed slope over the steps were taken into account. In addition, the impact forces of the high velocity chute flow on the roughness elements will be reduced through a gradual implementation of the full roughness height. As a third test, the roughness was extended to the first few steps of the stepped spillway, because it was believed that this would help in the development of an aerated boundary layer. These experimental investigations relate to boundary layer development on the spillway, and will be used to provide a relative indication of the change of aeration inception location with different roughness elements. In addition, the results can be used to calibrate an analysis of boundary layer development on the prototype spillway. Boundary layer development is not a gravity driven process, and thus Froude scaling to prototype would not be appropriate. F.1. Theoretical Boundary Layer Development The most common equation for estimating the internal boundary layer growth due to change in surface roughness was given by Elliot in 1958 (Savelyev, 26). δ z D z =.75.3ln z D U x z D.8 (F.1) where δ is the boundary layer depth from floor, z D is the downstream roughness length, z U is the upstream roughness length and x is the distance downstream from the roughness 189

209 transition. Roughness height is the average height of the physical elements in the flow while the roughness length, i.e. the dynamic roughness, is the height above the floor at which the velocity becomes zero according to the logarithmic profile of velocity in the water column. The roughness length for sufficiently spaced roughness elements is commonly about 1/4 of the roughness element height (Kondo, 1986). Values of z D and z U To find z U, the roughness length of the chute, the logarithmic velocity distribution was used. u U * 1 = ln κ z z. (F.2) In equation F.2, u is velocity, U * is shear velocity, z is depth and z is the roughness length. By integrating equation F.2 from z to h, i.e. from the roughness length to the flow depth, and dividing it by the flow depth, the mean velocity can be calculated from U U* 1 h hln h + z hκ z = (F.3) Using the values given in Table F.1, which were obtained from the SAFL 1:26 model, z can be estimated using an iterative method. Table F.1. Model and prototype parameters at the downstream end of the 2% chute (no roughness elements added) at a discharge of 135, cfs 1:26 Model h =.48 ft S e =.231 R h =.419 ft κ =.41 U * = gr H S e =.563 ft/s U = ft/s z chute =.121 ft Prototype h = ft S e =.231 R h = ft κ =.41 U * = gr H S e = ft/s U = ft/s z chute =.29 ft 19

210 It is difficult to estimate z D, the downstream roughness length, along the steps because the roughness element sizes are constantly changing along the first few steps of the stepped spillway, where the steps follow a quadratic function. However, by assuming that z is proportional to the roughness element height, or the tangential step height (Figure F.1), one can provide an estimate of z for all steps. To find the relationship between roughness length and the roughness element height, the velocity profile near the toe of the stepped spillway at 135, cfs was plotted on a semi-log graph (Figure F.2). The entire range of the velocity profile does not necessarily follow a logarithmic relationship, especially near the surface where air entrainment is likely. At the toe of the stepped spillway, the roughness associated with the constant slope part of the steps was assumed to be fully controlling the velocity profile. The intercept of the logarithmic portion of the velocity profile was determined to estimate the roughness length z. From Figure F.2, the intercept of the trend line is determined to be Since the y-axis is the natural logarithm of the depth, the exponential of the offset was calculated to find z, i.e. the depth at which the velocity becomes zero. The value was found to be.75 ft above the inner vertex of the steps for the prototype, which is approximately in agreement with the 1/4 of the roughness element height (Kondo, 1986) The depths in Figure F.2 are calculated from the inner vertex of the steps (Figure F.1), and not the outer steps which are sometimes referred to as the pseudo-bottom of a stepped spillway. F.2. Roughness Strip Design Criteria All ribs installed followed the relation for placement, L = 8, d where d is the height of the roughness element and L is the length to the face of the next rib downstream. This 8:1 length to height ratio has been found to maximize friction factor as well as placing the downstream element in the turbulent wake of the previous element (Knight and MacDonald, 1979). Also, element heights equal to the tangential step heights were used to make the upstream roughness equal to the roughness of the steps. F.3. Roughness Elements Three configurations of rectangular ribs were tested and photographed. All of the configurations 191

211 can be explained by referring to Figure F.3. The roughness elements of the three configurations tested are as follows. Configuration 1: Five ribs were placed at the end of the chute at station 32+. The roughness elements started at a height of. 7 ft (.27 ft for the model) with each downstream element increased in height to be 4/3 of the height of the previous element. The fifth and last element was placed just upstream of the first step and was 2.21 ft tall (.85 ft tall in the model). The downstream side of this element was 3 ft (.115 ft model) including the step drop. Configuration 2: Four additional elements were added to the end of the next four steps. The height of these elements were made such that the height of the roughness elements, including the local step rises, was equal to the height of the element at station 32+ including the step drops. Thus, the elements continually grew smaller until the steps themselves were 3 ft tall (Figures F.4 and F.5). Configuration 3: Ribs on the steps were removed and three additional ribs were placed between the fourth and fifth ribs while still applying the 8:1 ratio for maximum friction. The first rib in the added series was the same size as the original fifth rib. The other two added ribs were 3 feet tall (.115 ft model). The intended effect was to have a greater distance of constant roughness before the downstream steps (Figure F.6). The ribs of configurations 1 and 2 were of the following dimensions at the prototype scale: 1).7 ft at (Configurations 1 & 2) 2).93 ft at (Configurations 1 & 2) 3) 1.24 ft at (Configurations 1 & 2) 4) 1.66 ft at (Configurations 1 & 2) 5) 2.21 ft at (Configurations 1 & 2) 6) 1.79 ft at (end step 1) (Configuration 2) 7) 1.53 ft at (end step 2) (Configuration 2) 8) 1.3 ft at (end step 3) (Configuration 2) 9).52 ft at (end step 4) (Configuration 2) Ribs 1 through 5 are designated as rough chute in the pictures at the end of this document and ribs 1 through 9 are designated as rough chute and spillway in the pictures. The ribs of configuration 3 were of the following dimensions: 192

212 1).7 ft at ).93 ft at ) 1.24 ft at ) 1.6 ft at ) 2.21 ft at ) 3. ft at ) 3. ft at ) 2.21 ft at F.4. Results Configurations 1 and 2 are designated as rough chute and rough chute and spillway, respectively in Figures F.7 and F.8 and F.9. They show the changes in the point of inception of surface air entrainment. For a discharge of 26 cfs model (89, cfs prototype), the point of inception was at 35+, 33+ and 33+ for the original, rough chute and rough chute and spillway, respectively (Figure F.7). Under the 39 cfs (133, cfs prototype) flow condition, the point of inception was at 36+, 35+ and 33+5 for the original, rough chute and rough chute and spillway, respectively (Figure F.8). Under the 88 cfs (33, cfs prototype) flow condition, there was no air entrainment on the model stepped spillway. Configuration 3 at a discharge of 39 cfs (135, cfs prototype) is shown in Figure F.1. Again the inception point is found to be at about A qualitative assessment of results indicates that configurations 2 and 3 yield relatively the same results under the design flow. Both configurations cause air inception as early as station The disadvantage of configuration 2 is that elements must be placed on the first five steps whereas in configuration 3, taller elements must be installed at the end of the chute to induce the same effects. None of the tested configurations resulted in aeration at the higher flow rate of 88 cfs (33, cfs prototype). 193

213 Tangential step height Figure F.1. Inner vertex datum, outer vertex datum and the tangential step height Prototype Log Velocity Profile at Step Log Depth from Inner Vertex of Steps (P ft) y =.231x R 2 = Velocity (P ft/s) Upper Portion Bottom Portion Log Portion Linear (Log Portion) Figure F.2. Semi-log plot of the prototype velocity profile at step

214 STA 32+ Figure F.3. Positions of rectangular ribs in the second configuration tested Figure F.4. Second configuration of roughness ribs looking downstream 195

215 Figure F.5. Second configuration of roughness ribs looking upstream Figure F.6. Third configuration of roughness ribs, side view 196

216 Figure F.7. Visual assessment of the air entrainment point of inception at Q = 89,62 cfs, HW = ft 197

217 Figure F.8. Visual assessment of the air entrainment point of inception at Q = 133,43 cfs, HW = ft 198

218 Figure F.9. Visual assessment of the air entrainment point of inception at Q = 33,329 cfs, HW = 481 ft 199

219 Figure F.1. Visual assessment of the air entrainment point of inception using configuration 3, i.e. an extended rough chute at Q = 135, cfs, HW = 466 ft. 2