PREDICTION OF SCOUR FORMATION DUE TO A TURBULENT WALL JET ALONG A NON-COHESIVE SEDIMENT BED

Transcription

1 The Pennsylvania State University The Graduate School Department of Civil Engineering PREDICTION OF SCOUR FORMATION DUE TO A TURBULENT WALL JET ALONG A NON-COHESIVE SEDIMENT BED A Thesis in Civil Engineering by Brian D. Younkin c 2008 Brian D. Younkin Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2008

2 The thesis of Brian D. Younkin was read and approved 1 by the following: David F. Hill Associate Professor of Civil and Environmental Engineering Adviser Chair of Committee Michael N. Gooseff Assistant Professor of Civil and Environmental Engineering Kendra V. Sharp Assistant Professor of Mechanical Engineering Peggy A. Johnson Professor of Civil and Environmental Engineering Head of the Department of Civil and Environmental Engineering 1 Signatures on file in the Graduate School.

3 iii Abstract Scour in non-cohesive sediment beds is a concern in engineering projects such as dam spillways and shallow maritime navigation locations. Significant scour can lead to undermining of hydraulic structures and altered boundary flow along the bed. Research has been undertaken to advance the current state of knowledge regarding scour due to planar wall jets. Experiments presented here also investigate the flexibility and suitability of Particle Image Velocimetry (PIV) for other sediment transport applications. Improved scour prediction methods are developed by utilizing state-of-the-art experimental techniques. Experiments are carried out over a range of particle sizes ( mm) and Reynolds numbers (2,222-7,777). Incremental scour data is collected by profile plotting and centerline scour measurements. Measurements reveal a bedform that is nearly self-similar. From the dimensionless self-similar scour profiles, rigid boundary sediment beds are constructed so that the flow along the scour profile could be analyzed. Flow characteristics including velocity fields and boundary layers along the scour profile are obtained with PIV. Research indicates a strong correlation of the measured velocity fields with results from previous researchers. From the PIV acquired data, the boundary shear stress is calculated using a quadratic friction law. Predictions of scour profile equilibrium are performed by equating the jet induced boundary shear to the slope corrected critical shear. A scour evolution model is developed based on established sediment transport formulae. Scour prediction models are validated with data collected

4 iv from laboratory experiments. Results indicate that existing sediment transport equations over-predict scouring rates. In addition to long term scouring, PIV technology is implemented to study the rapidly evolving early stages of scour. PIV provides a non-intrusive, near-instantaneous technique for data collection. Results from early stage live-bed scour experiments indicate scour growth is linearly related to the logarithm of time. This is in agreement with the long-term scour profile data collection. In addition, cyclic digging and filling cycles are observed during the early stages of scour.

5 v Table of Contents List of Tables viii List of Figures x Acknowledgments xviii Chapter 1. Introduction Motivation Hypothesis Objectives and Goals Uniqueness of the Research Chapter 2. Literature Review Introduction Two-dimensional Turbulent Jets Scour in Non-Cohesive Sediment Beds Measurement Techniques in Scour Experiments Scour Prediction and Sediment Transport Equations Chapter 3. Live-Bed Scour Experiments Introduction Laboratory Facilities Long Term Scour

6 vi Scour Profile Tracing Equilibrium Scour Profiles Early Stage PIV Boundary Detection Facilities Procedures Experimental Uncertainty and Limitations Results and Discussion Chapter 4. Velocity Field PIV Measurements Introduction Fixed-Bed Models of Scour Profiles Particle Image Velocimetry Data Collection Data Processing Chapter 5. Validation of Flow Characteristics Introduction Velocity Profiles Boundary Layer Thickness Shear Stress Quadratic Friction Law Reynolds Shear Stress Measurements Chapter 6. Prediction of Equilibrium Scour Profiles

7 vii 6.1 Introduction Procedure Results and Discussion Chapter 7. Scour Evolution Predictions Introduction Procedure Results and discussion Chapter 8. Conclusions Live-Bed Scour Experiments Velocity Field PIV Measurements Scour Equilibrium Model Scour Evolution Predictions Future Research Appendix. List of Variables Bibliography

8 viii List of Tables 2.1 Overview of past research regarding scour due to two-dimensional wall jets Experimental conditions for live-bed trials Summary of dimensional and non-dimensional parameters for the early stage boundary detection experiments Comparison of measured maximum velocities to calculated maximum velocities from Rajaratnam (1976), Wu and Rajaratnam (1995) and Hogg et al. (1997) for a 140 LPM jet along a flat profile Comparison of measured maximum velocities to maximum velocities computed from equations provided by Rajaratnam (1976) and Hogg et al. (1997) for several locations along the sloping scour profile models Boundary layer thickness at several locations along the flat-bed model. Data are extracted from velocity fields obtained in the PIV experiments Jet half-widths (y 1/2 ) as measured from experimental velocity data on sloping model bedforms Critical shear stress parameters for the 3 sediment classes Measured angles of repose for experimental data Summary of experimental conditions for equilibrium comparisons (continued on next page... )

9 ix 6.3 (continued on next page... ) (continued from previous page) Measured angles of repose for sand and gravel. Reproduced from Dey and Sarkar (2006) Summary of scour profile elements and their relationship to the horizontal distance to crest (x c ) Summary of RMSE values calculated for the six sediment transport methods performed on each experimental run

10 x List of Figures 1.1 Sketch of the vertical velocity distribution of a wall jet Comparison of the theoretical velocity profile of the turbulent wall jet versus the experimental data (redrawn from Bakke (1957)) Linear relationship of turbulent shear stress (g 12 ) to height above wall (η). The vertical axis is the non-dimensional shear stress, and the horizontal axis is the height non-dimensionalized to the half width of the jet. The figure is limited to the boundary layer. (redrawn from Schwarz and Cosart (1961)) Self-similarity of vertical profiles of streamwise velocity profiles along the centerline of a circular wall jet. Data are non-dimensionalized with respect to vertical location of half maximum velocity, Z m/2 (vertical axis) and maximum velocity, U mo (horizontal axis). (From Law and Herlina (2002)) Data from Rajaratnam (1981) that suggest the similarity of scour profiles at various time intervals. The top plot (a) shows a longitudinal profile of scour at different times (data divided between three horizontal axes for clarity). The lower plot (b) shows that for the majority of the scour evolution, the maximum depth of scour increases linearly relative to the logarithm of time

11 xi 2.5 Application of Meyer-Peter and Müller equation to non-horizontal slopes. Equation (17) is the MPM sediment transport equation. (Redrawn from Damgaard et al. (1997)) Total sediment transport under steady flows over flat beds. θ denotes the available shear parameter, referred to as θ in the present thesis. (Redrawn from Nielsen 1992) Schematic of experimental flume Photograph of the two-dimensional nozzle Size gradations of sediment used in scour experiments Measured scour profiles for trial B Non-dimensional scour profiles for the B class sediment. Also shown, by the thick black line, is the average of the profiles Comparison of average scour profiles Dimensionless bedforms for the A100 trial. Scour bedform shapes are obtained with a point-gage at the centerline and sidewall profile sketches Plot of scour growth (distance to dune crest) vs. time as the profile approaches equilibrium. Bed sediment is 1 mm sand Schematic of experimental flume with boundary detection set-up Image of laser light reflection along a scour profile. The image is taken approximately two minutes after start-up of the A60 trial. The original image has been imported into MATLAB so that the pixel intensities are represented by a color spectrum

12 xii 3.11 Plan (a) and perspective (b) views of the scour hole evolution with time for the A60 trial. The black line highlights the dune crest at each time step Plan (a) and perspective (b) views of the scour hole evolution with time for the A100 trial Plan (a) and perspective (b) views of the scour hole evolution with time for the AC60 trial Temporal evolution of the distance to the dune crest and the per-unitwidth scour hole volume for the A60 trial. The data from the early-stage boundary detection method are shown with closed symbols and the longterm data profile sketches are shown with open symbols Comparison of the average scour profiles to the model bed profile Comparison between the linear scour profile approximation and the nondimensional centerline profile obtained from point-gage measurements Photograph of polycarbonate scour profile models Elevation view of the camera fields of view for a sample model bed profile Illustration of an interrogation window with particle movement. Open circles symbolize initial particle location, and filled circles show particle placement after a time interval. The resultant velocity vector is shown in red

13 xiii 4.6 Mean velocity fields for a jet (Re = 7,777) flowing over the flat scour bed model. Horizontal velocities are shown in the color contours, and only a percentage of the vectors are shown for visual clarity Mean velocity fields for a jet (Re = 7,777) flowing over scour profile 1 (dune crest at 20 cm). Horizontal velocities are shown in the color contours, and only a percentage of the vectors are shown for visual clarity Mean velocity fields for a jet (Re = 7,777) flowing over scour profile 3 (dune crest at 31.6 cm). Horizontal velocities are shown in the color contours, and only a percentage of the vectors are shown for visual clarity Mean velocity fields for a jet (Re = 7,777) flowing over scour profile 5 (dune crest at 50 cm). Horizontal velocities are shown in the color contours, and only a percentage of the vectors are shown for visual clarity Non-dimensional velocity profiles normal to the sediment bed at various locations along several different scour profiles. Nozzle discharge is 140 LPM for all runs Measured maximum velocities along a non-horizontal scour profile compared to computed velocities from the flat-bed equations of Rajaratnam (1976) and Hogg et al. (1997) Calculated boundary shear stresses along the face of the scour hole. The x-axis is normalized to the distance along the slope. Note: increasing profile numbers correspond to increasing scour profile size

14 xiv 5.4 Illustration of total shear stress relative to the velocity profile in a turbulent boundary layer. Also shown are the laminar and turbulent components of the total shear stress Contour map of Reynolds shear stresses along a portion of Profile 5. The flow rate is 140 LPM Comparison between shear stresses calculated by the quadratic friction law and the Reynolds stress method along the scour face of Profile 5 for a 140 LPM flow rate Comparison between measured and calculated values of x c at equilibrium. A line of perfect agreement is included in the plot as a black line Comparison between the measured and calculated evolution of the scour profile for the AC40 trial (F 0 = 6.18). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line Comparison between the measured and calculated evolution of the scour profile for the AC60 trial (F 0 = 9.26). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line Comparison between the measured and calculated evolution of the scour profile for the AC80 trial (F 0 = 12.35). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line

15 xv 7.4 Comparison between the measured and calculated evolution of the scour profile for the AC100 trial (F 0 = 15.44). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line Comparison between the measured and calculated evolution of the scour profile for the B40 trial (F 0 = 2.56). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line Comparison between the measured and calculated evolution of the scour profile for the B60 trial (F 0 = 3.84). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line Comparison between the measured and calculated evolution of the scour profile for the B80 trial (F 0 = 5.12). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line Comparison between the measured and calculated evolution of the scour profile for the B100 trial (F 0 = 6.39). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line

16 xvi 7.9 Comparison between the measured and calculated evolution of the scour profile for the B120 trial (F 0 = 7.67). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line Comparison between the measured and calculated evolution of the scour profile for the A60 trial (F 0 = 3.23). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line Comparison between the measured and calculated evolution of the scour profile for the A80 trial (F 0 = 4.30). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line Comparison between the measured and calculated evolution of the scour profile for the A100 trial (F 0 = 5.38). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line Comparison between the measured and calculated evolution of the scour profile for the A120 trial (F 0 = 6.45). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line

17 xvii 7.14 Comparison between the measured and calculated evolution of the scour profile for the A140 trial (F 0 = 7.53). Measured values are obtained from laboratory experiments. The calculated equilibrium size is included as a horizontal dashed line Comparison between the Einstein-Brown method and the modification presented by Gill (1968). The data used for the comparison is from the A140 trial and the experimental data are included for reference Comparisons of the calculated RMSE values versus F o. Plots are for each sediment class, a) AC, b) B, and c) A class sediment

18 xviii Acknowledgments I wish to thank my adviser, Professor David Hill for his hard work and tireless guidance in the completion of this dissertation. Thank you to Professors Peggy Johnson and Arthur Miller for cultivating my interest in water resources. I am also grateful to Dave Faulds and Matt Hassinger for their help with the laboratory facilities. My colleagues Justin Lennon, Geoffery Walters, Sue Niezgoda, Scott Sheeder and countless other graduate students deserve a special thanks for their help through my graduate experience. A very special thank you to my parents. I am truly grateful for the help and support that they have provided on my academic journey. Finally, I would also like to thank the many friends and colleagues for all of the motivation they have given me throughout my college career.

19 1 Chapter 1 Introduction 1.1 Motivation The purpose of this research is to further the current knowledge of scour processes caused by a turbulent wall jet along a non-cohesive sediment bed. The scope of this research combines two areas of fluid mechanics research: turbulent wall jets and sediment transport. Scour due to turbulent jets impacts numerous hydraulic engineering projects. Turbulent jets are typically associated with engineered hydraulic features, including stationary structures such as spillways, outlet works, and grade control structures, and with mobile sources such as propeller wash and nozzle discharges. Natural occurrences of turbulent jets are more limited, but can be found where water flows over and around natural stream obstructions such as boulders and submerged rock shelves. Sediment is transported when the combination of lift and drag forces acting on it overcome the gravitational forces and surrounding particle interactions. While lower pressures in a scour hole promote sediment transport, the primary mechanism of sediment transport is the high shear stress created as a wall jet flows along the sediment bed. Significant localized bed degradation may occur when shear stresses along the bed are abnormally high, such as in a high flow event. However, the scouring process is not limited to occasional flow events. Steady high velocity discharges from in-stream hydraulic

20 2 structures also can lead to scour. Reservoir spillways and grade-control structures can alter the natural flow regime of a stream, leading to increased scouring of the streambed material. Discharge pipes from sources such as factories and water treatment facilities also create scour potential, especially if they are located near the channel bed. Forces leading to scour do not need to be stationary. As shown by research conducted on the effects of propeller wash on scour (Hamill et al., 1999; Dargahi, 2003), turbulent propeller wash from ship thrusters poses a concern for pier and harbor construction. Scour due to propeller wash is also a concern in shallow waterways. Propellers operating in shallow water generate increased water velocities near the channel bed, potentially forcing sediment into suspension. The advances in scour knowledge gained from the present research are applicable to both mobile water jets and stationary jets near hydraulic structures. While much has been written regarding the negative aspects of scour, the scour process also poses benefits. Removing channel bed sediment with a high velocity water jet can have advantages. In 1996, 2004, and 2008, the United States Geological Survey (USGS) conducted scour and sediment transport studies on the Colorado River flowing through the Grand Canyon (Collier et al., 1997; Patten et al., 2001; Topping et al., 2005). The studies involve increasing outflow from the Glen Canyon Dam to mimic the historic floods of the pre-dam era. Since the completion of the dam in 1961, flow fluctuations have been muted by the water storage available in Lake Powell. Gone are the large seasonal floods that provided the catalyst for sediment transport. Tributaries continue to discharge sediment into the Colorado River below Glen Canyon Dam, but the river does not have the capacity to move all of the sediment. River aggradations and incising

21 3 have led to reduced floodplains and changes in the river bed composition. This process has allowed non-native vegetative and aquatic species to push out the native species. Flood releases by the Bureau of Reclamation are an attempt to remove sediment by scour processes. A release in November 2004 produced a peak flow of 1,160 cms for a period of 60 hours. During this man-made flood, an estimated 800,000 metric tons of river sediment were transported downstream. Studies have reported that the controlled floods successfully limited the rate of debris fan aggradation in the Grand Canyon (Yanites et al., 2006). Additional studies are currently being conducted to determine the effect of these floods on the native species populations. On a smaller scale, dredging navigational channels with scouring water jets is another beneficial application of scour. A dredging system on the tidal Bromborough Dock in the United Kingdom used water jets to dislodge bed material from lock entrances (Ali and Halliwell, 1980). The scouring process commonly occurs due to the shearing stress between moving water and stationary bed sediment. Turbulent wall jets flow along the boundary between the water and sediment bed, as shown in Figure 1.1, potentially creating large velocities near the boundary. Knowledge of wall jets has advanced over the last 50 years as newer technology and research methods have become available. To date, a considerable amount of knowledge is available about the effects of a wall jet flowing over a flat boundary. A goal of this research was to expand the understanding of how wall jets behave along non-planar scoured sediment beds. The experimental conditions for this research were intentionally designed to be simple, allowing for precise measurements and isolating the physical processes at work.

22 4 Fig Sketch of the vertical velocity distribution of a wall jet. First, the wall jet discharged into a deep water condition. A deep water condition contributed to a near constant water surface elevation above the study area, thus eliminating hydrostatic pressure fluctuations. It was shown in scour research performed by Ali and Lim (1986) that the effects of depth were insignificant when the ratio of water depth to nozzle width was greater than 16. In addition, a deeply submerged jet prevented air entrainment. Second, the jet discharged into a still body of water. Therefore, the only water velocities experienced were those initiated by the jet. Third, this research was limited to non-cohesive sand beds. Finally, the experiments were performed with a twodimensional nozzle, thus reducing cross-channel variations. These limitations defined the applicability of the research. This research related theoretical relationships in fluid mechanics to experimental observations. Using state-of-the-art data collection techniques, this research increases the knowledge of the scour process for the scientific community. While the application of the

23 5 data collection methods utilized in this research was limited to a controlled laboratory setting, this research developed physically-based relationships that advanced the current state of knowledge. The results from this research apply to several engineering scenarios. Hydraulic structures such as bottom-release radial and vertical sluice gates produce wall jets and their behavior correlates to this research. Submerged culverts discharging onto sand beds exhibit similar behavior. Also, bridges under high flood condition, ice/debris dams, and bottom-release hydraulic structures can all produce accelerated flow along the channel bed, therefore, the foundations of these structures are susceptible to bed scour due to wall jets. 1.2 Hypothesis The hypothesis of this research was that state-of-the-art data collection methods and established fluid dynamic and sediment transport formulas can advance the abilities of water resources professionals to predict scour development. To date water resource professionals were limited to conservative equilibrium scour profile design criteria. Currently, these design parameters could lead to over-built protection and excessive cost (Abt et al., 1987). In addition, there was little understanding of transient or short duration scour events and the potential non-equilibrium scour profile predictions. As discussed in the previous section there are numerous motivations for enhancing scour predictions. For example, predicting the evolution of scour is beneficial when considering the impact of hydraulic structures on natural channels. In addition, predictions of short term scouring events can benefit sediment removal operations such as dredging and outlet cleaning. This research intends to prove there are more precise methods for

24 6 understanding scour development; therefore, improving the ability to predict results in certain flow phenomenon. While difficult to quantify, the level of improvement will be evidenced in refined prediction methods; thus, lowering adverse environmental impacts, reducing stream protection expenses, and increasing the beneficial use of water jets on sediment transport. 1.3 Objectives and Goals The primary objective of this research was to develop a physically-based model for the formation of scour due to turbulent wall jets along a non-cohesive sediment bed. This model predicts the rate of growth of the scour hole as well as the ultimate (equilibrium) size of the scour. Much of the previous research regarding scour is empirically based and often relied on intrusive data collection methods. These empirical studies were often limited to parameters that have been directly investigated. A purely computational approach can treat a wide range of parameters, but may be too complex to be accessible to general users. To provide tools accessible to a wide range of users, this model offers a simplified approach utilizing existing jet velocity profiles, boundary layer thickness and shear stress knowledge. This low-order approach isolated the key processes at work and helped to create a straightforward scour prediction model. Live-bed experiments were used to validate the prediction model. The goal was to generate non-dimensional scour relationships for non-cohesive sand that can be extrapolated beyond the specific live-bed experiments conducted in the laboratory. Several steps were undertaken to complete the scour model. The first was to conduct experiments with live sediment beds, with the goal of determining the shape of

25 7 scour profiles for different flow rates and sediment sizes. The second step involved the construction of fixed-bed profiles resembling the observed live-bed scour profiles. The next step uses particle image velocimetry (PIV) to study the flow along the fixed-beds. Used with this state-of-the-art data collection method, a more complete understanding of the relationship between wall jets and sediment transport during scour hole formations was derived. From the PIV data, information such as velocity profiles, maximum velocity relative to distance from the jet nozzle, boundary layer thickness and velocity fluctuations was extracted. The bed shear stresses were then determined from the measured velocity fluctuations and the velocity profile. Using an established sediment transport equation, which is a function of shear stress, the time dependent rate of sediment transport was determined. Finally, the sediment transport equations coupled with the conservation of mass equation predicted the rate of growth of the bedform. A secondary objective was to research the very early stages of scour. Previous studies examined equilibrium profiles and similarities of scour profiles throughout the period of scour development. Only limited research analyzed the growth of scour holes during the initial stages. Previous researchers (Faraci et al., 2000; Voropayev et al., 2003) showed that the boundary between the water and the sediment bed can be distinguished from PIV images. The present research analyzed these images to produce the scour profile at the time the image was taken. With the aid of PIV, non-invasive profile measurements with high time resolution were taken during the initial start-up phase of scouring. In addition, unlike previous research, data collection using PIV was possible without turning off the flow. These early stage profiles were then compared to profiles measured at later stages as well as to results from previous research. This research

26 investigated the flexibility and suitability of PIV measurements in sediment transport predictions Uniqueness of the Research An important consideration when researching scour and applying the results is the issue of scaling. To address this issue the work within this research utilized nondimensional relationships of the experimental variables. The advantage to using dimensionless variables was that the application of the results from this research can be applied to situations beyond those tested in the controlled laboratory setting. It should be noted that the research was limited to non-cohesive bed sediment and that the laboratory experiments were limited to sand size bed sediment ( mm).

27 9 Chapter 2 Literature Review 2.1 Introduction The literature reviewed for this research focused on turbulent wall jets and scour hole formations in non-cohesive bed sediments. While this research project focused on sediment transport within a scour hole, several summaries of studies on turbulent jets have been included and are intended to support the present research on scour, not to treat comprehensively the great amount of research on turbulent jets. The summaries of research on scour include the measurement methods and numerical modeling techniques to predict scouring rates and equilibrium dimensions. The literature review is separated into two sections: the analysis of two-dimensional turbulent jets, and the analysis of scour in non-cohesive sediment. 2.2 Two-dimensional Turbulent Jets Glauert (1956) was perhaps the first to publish research on wall jets, and supporting experiments were developed by Bakke (1957). Glauert defined a wall jet as the phenomenon of a high velocity flow moving along a boundary. By using a vertically positioned jet striking a horizontal plate, Glauert was able to produce a wall jet radiating out from the point of impact. Theories by Bakke (1957) hypothesized that the vertical velocity distributions at any distance from the point of impact are similar. Glauert

28 10 considered a turbulent wall jet to be composed of two regions: an inner region from the boundary up to the maximum velocity location, and an outer region located above the height of the maximum velocity. Glauert determined that the inner region, which was valuable for shear stress calculations, could be described by the Blasius formula, τ = ρu 2 max ( ) ν 1/4, (2.1) u max r where τ was the boundary shear stress, ρ the density of the fluid, u max the maximum velocity at a given distance from the nozzle exit, ν the kinematic viscosity of the fluid, and r the radius of the nozzle. Through wall jet experiments, Glauert discovered a relationship between shear stress and jet velocity. Comparisons between Glauert s theoretical velocity profile and Bakke s experimental profiles are shown in Figure 2.1. Fig Comparison of the theoretical velocity profile of the turbulent wall jet versus the experimental data (redrawn from Bakke (1957)).

29 11 Further research supporting Glauert was published by Rajaratnam (1965). One important difference was that, in Rajaratnam s research, the wall jet was created by a vertical sluice gate. Rajaratnam referred to this as a submerged hydraulic jump, but the flow characteristics were similar to a wall jet. The data collected from Rajaratnam s experiment supported the conclusion that the velocity profiles along the jet are selfsimilar. In addition, Rajaratnam concluded that the local boundary shear stresses were inversely related to both the boundary thickness and to the maximum velocity at that location. Studies of two-dimensional turbulent wall jets were also conducted by Schwarz and Cosart (1961). They discovered that a jet s velocity profile is controlled by its proximity to a boundary. The interface between a jet and the surrounding water has a free boundary, while the jet-wall interface by definition has a solid boundary. The close proximity of the boundary to the location of maximum horizontal velocity creates a large velocity gradient (high shear stress). Both the wall and the surrounding fluid have a velocity of zero relative to the water jet. Their research examined the shear stresses along the wall boundary using experiments conducted in a wind-tunnel. Mean velocity measurements were acquired using a hotwire anemometer. Data were collected to within 0.2 mm of the wall and at various distances downstream of the nozzle exit. The results suggested that the boundary layer thickness was a function of a number of factors: the nozzle velocity, the downstream distance from the nozzle, the viscosity and density of the fluid, and the width of the nozzle. Furthermore, using measured velocity fluctuations, Schwarz and Cosart (1961) calculated turbulent shear stresses from the Reynolds shear

30 12 stress equation, τ r = ρu v, (2.2) where τ r denoted the Reynolds shear stress, ū and v denoted the time averaged velocity fluctuations parallel and perpendicular to the boundary. The researchers noted that laminar flow near the wall could render the shear stress calculations by the Reynolds method inaccurate. However, for the majority of the boundary layer, the shear stress was calculated by the Reynolds stress equation. Figure 2.2 illustrates the linear relationship of the turbulent shear function to a non-dimensionalized distance above the bed. In the figure g 12 is the non-dimensional turbulent shear stress. In addition, the wall shear stress calculated by the quadratic friction factor is denoted by the datum point labeled C f. A linear relationship suggests that the boundary shear stress could be determined by extrapolation if several Reynolds stress values are known within the boundary layer. Schwarz and Cosart (1961) found that the Reynolds stresses could be used to calculate shear stresses produced by wall jets. Wygnanski et al. (1992) conducted experiments on turbulent wall jets in a wind tunnel. Their results suggested that the jet velocity profiles were self-similar when scaled by the kinematic momentum flux at the nozzle and the kinematic viscosity of the fluid. The flow was also independent of the Reynolds number when the Reynolds number was greater than about The Reynolds number was given by Re = U 0b 0 ν, (2.3)

31 13 Fig Linear relationship of turbulent shear stress (g 12 ) to height above wall (η). The vertical axis is the non-dimensional shear stress, and the horizontal axis is the height non-dimensionalized to the half width of the jet. The figure is limited to the boundary layer. (redrawn from Schwarz and Cosart (1961)) where U 0 was the nozzle exit velocity, b 0 the nozzle thickness, and ν the kinematic viscosity of air. Their research estimated the shear stress at the wall by measuring the mean velocity gradient with a Preston tube. Their experimental results also demonstrated that the normalized velocity gradient near the wall was not self-similar; however, between the viscous sub-layer and the maximum velocity height within the vertical velocity profile, the velocity could be related to a turbulent boundary layer.

32 14 Eriksson et al. (1998) studied two-dimensional turbulent jets with laser doppler velocimetry (LDV). The (LDV) provided a non-intrusive technique that allowed the researchers to measure the velocities in the near-wall region. From the measured mean velocity gradients, the wall shear stresses could be determined. In addition, data obtained from the outer region were compared to earlier hot-wire anemometer measurements. Large differences were found, suggesting that the hot-wire anemometers could not capture the high turbulence intensities. The experiment was limited to a nozzle exit Reynolds number of The measurements obtained very close to the wall suggested that velocity increases linearly moving away from the wall, out to approximately 3 mm. The skin friction calculated in this research was much higher than in previous data (Wygnanski et al., 1992) due to the additional information available closer to the wall. This was due to the finer data collection resolution provided by the LDV method as opposed to the coarser Preston tube instrumentation. This research also illustrated that the non-dimensionalized vertical velocity profiles were self-similar over the range of data collection (to a streamwise distance of 200 nozzle widths), thus supporting the work of Bakke (1957). More recently, research was published by Law and Herlina (2002) detailing the use of PIV in studying turbulent jets. While these researchers studied a circular jet, which is beyond the scope of work for this research, their experimental methods are worth noting. PIV was incorporated in order to determine the velocity profiles of the water jet. The PIV data illustrated the self-similarity of the streamwise velocity along the centerline of the jet. Figure 2.3 illustrates the self-similarity of the vertical velocity profiles along the centerline of a circular jet.

33 15 Fig Self-similarity of vertical profiles of streamwise velocity profiles along the centerline of a circular wall jet. Data are non-dimensionalized with respect to vertical location of half maximum velocity, Z m/2 (vertical axis) and maximum velocity, U mo (horizontal axis). (From Law and Herlina (2002))

34 Scour in Non-Cohesive Sediment Beds Scour due to jets can be classified into several different categories. First, a jet can be two-dimensional or three-dimensional. Second, the angle at which the jet impinges on the sediment bed is a factor in the scouring process. A third classification is the composition of the bed itself. Beds made of cohesive sediment exhibit different scouring characteristics than a sediment bed without cohesion. This research focused on the twodimensional scour of a non-cohesive sediment bed due to a turbulent wall jet. Therefore, the summary of literature in this section is limited to these characteristics. Studies of erosion due to two-dimensional or plane jets can be dated to Chatterjee and Ghosh (1980), who studied the characteristics of a water jet over an erodible sediment bed. They tried to measure shear stresses and to relate critical shear stresses to the equilibrium scour state. They determined that the jet s local maximum velocity and the growth of the boundary layer were functions of flow depth, length of a rigid apron, grain size, and distance from the nozzle. However, the study s attempts at shear stress calculations produced unsatisfactory results. The calculated critical shear, developed from a solution of von Karman s integral equation, did not agree with the critical shear derived from the Shield s parameter. Further attempts at measuring the shear through a pressure-shear relationship were unsuccessful due to data collection limitations. Specifically, the pressure measurements near the sand bed were restricted due to suspended sand particles choking the Preston tube. Rajaratnam (1981) found that the scour profile geometry (such as maximum depth of scour or length of scour) initially increases linearly with the logarithm of time.

35 17 Rajaratnam further found that a characteristic length scale will eventually reach an equilibrium state. Figure 2.4 illustrates Rajaratnam s data as collected with a pointgage, and displays the similarities of the scour profiles at different time intervals. Rajaratnam adopted a dimensionless number to characterize jets over erodible beds. Referred to as the densimetric Froude number, it is now widely used to characterize the jet/sediment bed relationship, and was given by F o = U 0, (2.4) g ρ ρ d where U 0 was the initial jet velocity, ρ the fluid density, ρ the density difference between the fluid and the sediment, and d the grain diameter. Experiments carried out by Rajaratnam exhibited similar scour profiles for both sand and small gravel sediment beds. Rajaratnam determined that the characteristic length scales of the scour hole were mainly functions of this densimetric Froude number. Several studies were subsequently undertaken to find equilibrium profiles and the variables controlling their characteristics. Ali and Lim (1986), Johnston (1990), and Balachandar et al. (2000b) all researched the effect of tailwater depth on the scour profile. Their results suggested that tailwater depth was important when the tailwater depth was less than approximately 16 times the nozzle width. For the purposes of the present research, the tailwater depth in the laboratory experiments was sufficient to ensure that the tailwater depth did not effect the scour profile. Further equilibrium research was published by Chatterjee et al. (1994) who found that the maximum scour depth can be expressed in terms of a Froude number (based on the nozzle thickness, b 0 )

36 18 given by F c = U 0. (2.5) gb0 Additionally, Chatterjee et al. (1994) found that the scour profiles were similar in shape, but the overall profile sizes were dependent on the sediment bed grain size. Kells et al. (2001) supported this, finding that initial jet velocity and sediment size both effect scour size. Aderibigbe and Rajaratnam (1998) further developed the relationship of discharge velocity and sediment size by using the previously mentioned densimetric Froude number (Equation 2.4). Table 2.1 summarizes the scour research relevant to the present research. The relevant parameters and the data collection methods used are included. Select data from these studies were used for comparison and validation purposes in the present research.

37 Author(s) Year Fo b 0 Data Collection Key Research Findings (mm) Method Bey et al Laser Doppler Research measured flow structures and their effect on the anemometer scouring process. Dey and , 12.5 Profile sketching Researched the effects of rigid apron lengths on scour profiles. Sarkar and 15 Kurniawan Acoustic Doppler Velocity and turbulence measurements were made within and Altinakar velocity profiler a scour hole. Kells et al Video imaging Study effect of grain size on scour dimensions (shallow tailwater condition). Balachandar Video imaging and Researched the effects of tailwater depth on scour hole growth et al. laser-doppler anemometer and dimensions. Aderibigbe and Point gage Studied equilibrium profile dimension relationships. Rajaratnam measurements Balachandar Video imaging Research found a cyclic scour profile phenomenom and Kells (digging and filling). Chatterjee Point gages and Researched time to obtain equilibrium (maximum) profile size. et al. preston tube Ali and Profile photographing Studied scour due to offset jets. Research is included for limited Neyshaboury and current meter wall jet data. Johnston and 25.4 Point gage Study of the effects of tailwater depth on scour hole development measurements Ali and Lim Point gage Experiments measured max depth of scour and scour volume during measurements the scour process. Found tailwater depth effected the scour process Rajaratnam , Point gage Experiments to research equilibrium scour profile dimensions. and 25 Chatterjee Preston tube Studied time variations of boundary layer thickness and velocity and Ghosh decay. Research included rigid aprons. Table 2.1. Overview of past research regarding scour due to two-dimensional wall jets. 19

38 20 Fig Data from Rajaratnam (1981) that suggest the similarity of scour profiles at various time intervals. The top plot (a) shows a longitudinal profile of scour at different times (data divided between three horizontal axes for clarity). The lower plot (b) shows that for the majority of the scour evolution, the maximum depth of scour increases linearly relative to the logarithm of time.

39 Measurement Techniques in Scour Experiments The present research introduces PIV, a state-of-the-art data collection technique, to scour prediction research. To date, no previous study has applied this technology to study scour due to wall jets. PIV data complement the important findings of previous researchers. Early research used point-gage measurements and profile sketching (Rajaratnam, 1981; Ali and Lim, 1986; Johnston, 1990; Chatterjee et al., 1994; Aderibigbe and Rajaratnam, 1998; Dey and Sarkar, 2006) to get information about bedform shapes and growth. Information including velocity profiles and boundary layer thickness was obtained with Preston tubes and current meters (Chatterjee and Ghosh, 1980; Ali and Neyshaboury, 1991; Chatterjee et al., 1994). While data collected using these methods have been valuable in the advancement of scour research, these data collection methods have limitations. Due to the intrusive nature of point-gages, Pitot tubes, and current meters, the velocity data obtained with these instruments may be inaccurate. These time-intensive methods also limited the possible resolution of data collection. For example, Ali and Neyshaboury (1991) only measured velocities at one elevation at several streamwise locations along the flume centerline. Regarding bedform evolution, many early studies limited data collection to the equilibrium scour profile. Most researchers of scour profile evolution rely on side-wall profile sketches (Rajaratnam, 1981) or on point-gage measurements (Ali and Lim, 1986), both of which also halted the flow during data collection. As a result, very limited data were collected during the early, rapidly evolving stage of scour.

40 22 The last ten years have seen significant advancement in data collection techniques. Advancements in video imaging and processing have allowed more detailed side-profile data collection. Balachandar and Kells (1997), Balachandar et al. (2000a), and Kells et al. (2001) employed video imaging to quantify evolving scour profile dimensions. Not only did these researchers provide profile information at earlier time steps, they also discovered cyclical scour processes (Balachandar and Kells, 1997). These studies report that the scour face cycled between a digging phase and a filling phase ( sec. cycles). In addition to video imaging, non-intrusive data collection methods have become available for measuring scouring jet velocities. Both acoustic and laser Doppler anemometers were used to research the flow structures within a scour hole (Balachandar et al., 2000b; Kurniawan and Altinakar, 2002; Bey et al., 2007). Since these experimental methods were still point measurement methods, the data were limited to a rather coarse grid along the centerline of the flume. Kurniawan and Altinakar (2002) used an acoustic profiling instrument to measure the vertical profile, from which they deduced stresses along the sediment bed. The results from Kurniawan and Altinakar (2002) illustrated higher shear stress along the scour face. To date, however, no PIV research has been published regarding the evolution of a scour hole due to a 2-D wall jet, which is the focus of this study. Refer to Table 2.1 for a summary of the measurement techniques employed by previous researchers. 2.5 Scour Prediction and Sediment Transport Equations Attempts to make scour profile predictions by using mathematical models were performed by Hogg et al. (1997). To predict scour, the authors incorporated the theory of

41 23 critical shear stress. The critical shear stress is the shear stress at which sediment begins to move, also known as incipient motion. Within the authors mathematical models, the shear stress was determined from the integral of the conservation of momentum equation. The model relied on a hypothesis that the shear created by the water jet flowing along a rough bed is similar to a turbulent boundary layer which can be modeled with the momentum and continuity equations. Hogg et al. (1997) incorporated the Meyer-Peter and Müller (MPM) equation to predict sediment transport, Φ = 8(θ θ c ) 1.5, (2.6) where Φ is the dimensionless sediment discharge, θ the dimensionless available shear, and θ c the dimensionless critical shear for movement. Their predictions from the mathematical model showed a qualitative agreement with the experimental results by Rajaratnam (1981). several assumptions were made by Hogg et al. (1997). For the mathematical model, The first assumption was a modification of the Shields critical parameter for incipient motion. Shields experimented with the incipient motion of particles along a flat bed. Hogg et al. (1997) noted the need to modify Shields shear stress parameters once the sediment bed was strongly nonhorizontal, as in the case of scour faces. Hogg et al. (1997) modified the boundary shear stress equation to account for sloping beds, θ c = θ c sin (α + β), (2.7) sin α

42 24 where θ c was the slope-modified Shields parameter, α the angle of repose and β the sediment bed inclination (positive for adverse slopes). The second assumption made by Hogg et al. (1997) was that the water jet flow paralleled the sediment bed. Assuming that flow was parallel to the sediment bed was reasonable for conditions along much of the dune face. However, an area of considerable scour occurred at the location where the jet impinged, at some angle, on the sediment bed. At this location, where the jet attached to the sediment bed, a component of the velocity was perpendicular to the bed. Previous research had not studied the potential variation of the shear stress due to impinging jets. Hogg et al. (1997) alluded to the fact that there was no available model or data to describe the variations of shear stress when the sediment bed was nonhorizontal. They hypothesized that with further research related to shear stresses and scour rates, improved models could be developed. The excess shear sediment transport equation used by Hogg et al. (1997) was based on work by Meyer-Peter and Müller (Meyer-Peter and Müller, 1948). Meyer- Peter and Müller originally developed the excess shear equation based on studies of bed load transport along river reaches. In its original form, the MPM equation applied to gravel channels on non-adverse slopes. However, contemporary researchers successfully applied this same equation to sand movement along adverse slopes: most notably were Damgaard et al. (1997), McLean et al. (1999), Dey and Debnath (2001), and Nielsen (1992). Research by Damgaard et al. (1997) suggested that the MPM sediment transport model was valid for use on adverse slopes (Figure 2.5). Note that the Equation (17) referred to in Figure 2.5 is Equation 2.6 in the present thesis. The lines in the plot refer to MPM predictions based on a critical shear parameter modified with Equation 2.7,

43 25 and for this illustration, positive slope refers to uphill flow direction. Nielsen (1992) also worked with Equation 2.6, presenting a slightly modified version of the MPM formula for the transport of fine coastal sands along a flat bed (Figure 2.6). While not applied to an adverse slope, Nielsen s work illustrated that this sediment transport model was not limited to downhill slopes. In addition, Nielsen extended the work of MPM to include finer bed material. Successful validation of his modified equation against data indicates that the MPM equation was applicable for the motion of a sand-sized bed material. New modeling techniques were developed to gather additional information on shear stress and scour evolution. Karim and Ali (2000) modeled scour with the FLUENT computational fluid dynamics (CFD) computer package. Within FLUENT, the scour process was modeled using the governing equations of the classic wall jet and related the incipient motion of particles with the boundary shear stress. Some questions arose from their work, since a detailed explanation for calculating shear stress was not provided. However, reasonable model results were generated when calibrated with previous research on wall jets and scour due to wall jets (Wu and Rajaratnam, 1995; Ali and Lim, 1986). Another approach to scour prediction was to collect more detailed data of the velocity fields within the scour hole. New technology is increasing the quality and quantity of data that can be gathered. As discussed previously, Kurniawan and Altinakar (2002) implemented an Acoustic Doppler Velocity Profiler (ADVP) to measure velocities within a scour hole. The ADVP measured the instantaneous velocity vector at a number of layers within the water column. Experimental data were collected for a sand bed (d = 2 mm) after five to six days of clear-water scouring. This period of time suggested that the scour hole was in an equilibrium state. Calculations of the Reynolds stress near

44 26 the bed indicated that there was insufficient shear stress to initiate further movement of sediment. The limitations of this research were that no data were collected during the period of active scour, and that ADVP measurements were only taken at coarse streamwise intervals along the centerline of the jet.

45 27 Fig Application of Meyer-Peter and Müller equation to non-horizontal slopes. Equation (17) is the MPM sediment transport equation. (Redrawn from Damgaard et al. (1997)).

46 28 Fig Total sediment transport under steady flows over flat beds. θ denotes the available shear parameter, referred to as θ in the present thesis. (Redrawn from Nielsen 1992)

47 29 Chapter 3 Live-Bed Scour Experiments 3.1 Introduction The first task in this research was to collect data to validate theoretical equations utilized in this research s scour prediction model. Data of interest included scour profile geometries and scour growth rates. The data collected in these experiments were supplemented with published data from previous studies. The combination of these data sets provided a large foundation for validating the scour prediction model validation. This chapter presents the live-bed scour experiments. This chapter is divided into three experimental sections. Section 3.3 discusses data collection through the long term (hours) of scour evolution. Long term scour evolution experiments involved profile sketching at various time steps. Due to the rapidly evolving scour profile at scour initiation, a different data collection method was required during this early stage. Data collection for early stage scour profiles is presented in Section 3.4. Finally, for equilibrium scour information, experiments were conducted to characterize the maximum scour profiles (Section 3.3.2). The combination of these three experiment groups provided a data set that encompassed the entire evolution of the scour profile.

48 Laboratory Facilities A simplified drawing of the experiment flume is presented in Figure 3.1. Experiments are conducted in a rectangular recirculating flume 183 cm long, 30.5 cm wide, and 45.7 cm high. The flume was constructed of 0.95 cm thick glass for strength and optical clarity. The flume was connected to the suction side of the pump via a 3.18 cm inside diameter hose. A drain was located within this hose to facilitate draining the flume. Water returned to the flume through 2.54 cm PVC tubing. Within the PVC tubing were two ball valves to regulate flow because coupled valves provided a finer degree of adjustment than the bulky movements of a single ball valve. In addition, it was discovered while running the experiments that the partial closure of two valves produced less cavitation than only one valve closed at the same desired flow rate. A turbine flow meter developed by Great Plains Industries was located along the pipe from the pump discharge to the flume. The flow meter read continuous flow rates in increments of 0.1 liters over a range of 18.9 to liters. Calibration experiments confirmed that the flow meter accuracy was within 1.5%. Within the flume, cm high polycarbonate walls were attached to create a sediment containment area measuring 91.4 cm long. Downstream of the sediment bed was an area that collected suspended sediment before it could be sucked into the pump. The sediment bed was isolated from the suction vortices at the downstream end of the flume by a polycarbonate partition wall, perforated at 20 cm above the flume bed. A crucial component to the experiment was the nozzle that created the water jet. The experiment design criteria required the nozzle to discharge water in a steady uniform

49 31 Fig Schematic of experimental flume. jet across the width of the flume. The nozzle was constructed of polycarbonate, with a 3 cm opening height tapering to a 1 cm exit height. The first step to creating a uniform flow jet was to divide the flow from the 2.54 cm PVC pipe through a manifold that discharged through four 1.27 cm PVC pipes. This manifold attached to the upstream end of the nozzle. Upon entering the nozzle, the water flowed through nylon mesh before moving through a flow straightener. The flow straightener consisted of quarter-inch diameter honeycomb cells produced by Plascore, Inc. During early experiment runs, the polycarbonate nozzle exit expanded in height under higher flows. This was remedied by gluing 1/8 inch thick glass to the exterior surfaces around the nozzle to increase its rigidity. A photograph of the nozzle and pipe manifold is shown in Figure 3.2. A support was constructed with four leveling screws to position the nozzle in the proper location.

50 32 Fig Photograph of the two-dimensional nozzle.

51 Long Term Scour Scour Profile Tracing The first task in the experiment was to determine the natural shape of scour profiles throughout the long term evolution of the scour process. This was accomplished by tracing the actual sediment scour profiles. Sediment was placed in the sediment containment area of the flume to a depth of cm. The sediment was a solid glass spherical particle produced by Omni Finishing Systems. These particles were used for their likeness to sand (specific gravity of ) and their uniform sizing. Experiments were conducted to develop scour profiles for each of three sediment sizes. The three sediment sizes, according to Omni Finishing Systems specifications, have grain size ranges of microns (AC), microns (B), and microns (A). The AC, B, and A are the size designations used by the vendor. Figure 3.3 illustrates the size distribution (in terms of percent passing a given sieve opening size) of the three sediments. Note the relatively uniform size distribution for each sediment type. The scour profiles were observed by first creating a wall jet of known exit velocity across the sediment bed. Table 3.1 outlines the conditions for each of the experimental trials. The Reynolds number was given in Equation 2.3 and the densimetric Froude number in Equation 2.4. Each scour profile started with a horizontal sediment bed at time zero. At time zero, the pump was turned on and the profiles of the scour were manually sketched at various time intervals. The scour profiles were sketched on tracing paper (with a x cm grid pattern) attached to the outside wall of the flume. The profiles were projected onto the paper by backlighting the flume with a 100 watt

52 AC sediment B sediment A sediment Percent passing (%) Sediment size (mm) Fig Size gradations of sediment used in scour experiments. lamp. An initial bed profile was sketched before the pump was turned on, which provided a base line reference for later profiles. The profiles were sketched at time intervals that increased roughly geometrically (see Figure 3.4 for an example). At each time step, the pump was turned off during sketching to ensure consistent profiles. The sediment bed was re-leveled to a horizontal plane between each flow rate experiment. After the sketches were completed, the scour profiles were converted to computer data for processing. Converting the profiles from the grid paper sketches to the computer database was accurate to within one millimeter in both the horizontal and vertical axes. Once the raw scour profile data were entered, they were non-dimensionalized. As found by experimentation, the best results were obtained by non-dimensionalizing the profiles by the horizontal distance to crest, x c. Other non-dimensional factors such as distance to trough, height of crest and depth of trough produced less satisfactory results. Nondimensionalizing the profiles by x c produced highly self-similar profiles across all time

53 35 Table 3.1. Experimental conditions for live-bed trials. Trial Number Median Sediment Flow Rate, Q Re F o Size, d (mm) (liters per minute) AC , AC , AC , AC , B , B , B , B , B , A , A , A , A , A , steps for each sediment type. In this thesis, the non-dimensional horizontal and vertical axes were referred to as x and y. A composite scour profile for each experimental trial was then produced by averaging the non-dimensional scour profiles from all time steps. Figure 3.5 illustrates the non-dimensional scour profiles, one for each flow rate, for the B sediment class. These average profiles for each flow rate were then averaged to generate an overall composite dimensionless profile for each sediment size. As an example, this overall average profile is included in Figure 3.5. Figure 3.6 illustrates the overall average profile for each of the three sediment classes. Inspection of the results showed that the overall

54 36 4 y (cm) minutes 10 minutes 20 minutes 40 minutes 80 minutes 160 minutes 320 minutes 640 minutes x (cm) Fig Measured scour profiles for trial B120. profile shape was generally similar between all sediment classes. It should be noted that the AC profile differed slightly from the other sediment classes. This was due to the finer particles becoming suspended in the jet and depositing further downstream from the dune. To check the two-dimensionality of the scour profile, limited profile data were collected along the centerline with a point-gage and were compared to the profile sketches taken at the sidewall. Figure 3.7 presents this comparison for the A class sediment. The plot shows that the centerline profile exhibits higher overall elevations. This was most likely due to boundary layer effects at the flume sidewall. It should be noted that while the elevations varied between the two profiles, the horizontal scale was quite similar. Since the profile sketching method and the point gage method yield similar profiles, it was decided to use profile sketching over the more time-intensive point-gage method.

55 y* lpm 60 lpm 80 lpm 100 lpm 120 lpm Average x* Fig Non-dimensional scour profiles for the B class sediment. Also shown, by the thick black line, is the average of the profiles. 0.1 y* AC Sediment B Sediment A Sediment x* Fig Comparison of average scour profiles.

56 y* Centerline Profile x* Fig Dimensionless bedforms for the A100 trial. Scour bedform shapes are obtained with a point-gage at the centerline and sidewall profile sketches.

57 Equilibrium Scour Profiles An objective of this research was to predict the equilibrium scour profile for a given condition. In this research, the equilibrium profile was defined as the maximum scour size that can form for a given condition. Relating to sediment transport, an equilibrium profile was reached when sediment could no longer be transported beyond the dune crest. Long term scour profile trials discussed in the previous section concluded when minimal sediment was observed to move over the dune crest. The final profile sketch in each trial was considered to be the equilibrium profile. To further study equilibrium profiles several very long term scour experiments were run. The sediment used in these experiments was 1 mm sand. Data collection involved centerline point-gage measurements at the crest. A plot of the experimental results is provided in Figure 3.8. Results indicated a linear growth of the distance to crest relative to the logarithm of time. This finding was in accordance with previous research (Rajaratnam, 1981; Chatterjee et al., 1994; Aderibigbe and Rajaratnam, 1998). The experiments were terminated before a true equilibrium was reached. However, visual observations detected very little sediment movement over the dune crest. Occasionally a sediment grain was seen to roll over the dune crest. Also, sediment was transported when eddies in the scour hole lifted particles into the jet. Over long periods of time this minor movement will produce a measurable growth in the profile. However, for the purposes of this research, equilibrium was considered to have been reached when only the occasional sediment grain was transported beyond the crest.

58 40 60 x c (cm) lpm 100 lpm Time (minutes) Fig Plot of scour growth (distance to dune crest) vs. time as the profile approaches equilibrium. Bed sediment is 1 mm sand.

59 Early Stage PIV Boundary Detection Previous researchers often relied on intrusive and time consuming data collection methods to measure scour profiles. While these methods were valid for longer time steps, they failed to capture the rapidly changing profile during the early stages of scour. In addition, previous research using bed surveys often interrupted the flow in order to retrieve data. Observations during the current experiment suggested that the sediment bed profiles were quite different depending on whether the flow is on or not. The force of the jet had the ability to steepen the scour slope beyond the angle of repose, then once the jet was turned off the sediment returned to near the angle of repose. In order to better understand the shape of a dynamic bed, the present research utilized non-intrusive PIV images. These near-instantaneous snapshots, taken at known time steps, recorded the scour profile during the initial rapid scouring process Facilities The experiments were carried out in the horizontal flume illustrated in Fig In addition to the experimental setup used in the long term experiments, a laser was incorporated for illumination purposes. The laser was mounted on a stand beyond the downstream end of the flume. The stand allowed the laser to be positioned so the light beam was aligned with the centerline of the flume and the laser was above the free water surface. Exiting the laser housing, the light beam was focused through a spherical lens then spread into a sheet via a cylindrical lens. The curvature selection for the two corrective lens was chosen to produce a thin (approximately 1-2 mm) light

60 sheet spanning 20 cm. To illuminate the bed surface, the laser sheet was redirected from horizontal to vertical by a polished stainless steel plate (see Figure 3.9). After reflecting 42 off the steel, the laser sheet passed through the water free surface. To minimize the laser refraction from the free surface, a clear glass plate was floated on the water surface, allowing the light to pass through the interface at a right angle. In all experiments, the free surface was 25 cm above the nozzle exit. The sediment bed was 1 m long, 10 cm high, and spanned the full width of the flume. The same glass beads used in the previous scour profile experiments were used in order to obtain a nearly uniform grain size distribution and to ensure a strong laser light reflection. The two sediment classes AC and A (0.200 mm and mm) were studied. Fig Schematic of experimental flume with boundary detection set-up. Imaging of the sediment bed was accomplished using a four megapixel, 12 bit digital camera (PowerView G) and a 120 mj pulse 1 Nd:Yag laser. A synchronizer

61 43 facilitated the timing of the laser pulse and image acquisition, and images were acquired and stored using Insight software (TSI, Inc., v.3.53). The camera field of view (FOV) covered a region about 20 cm x 20 cm, yielding a resolution of 0.1 mm pixel 1. The FOV was aligned to capture the region immediately downstream of the nozzle, and the vertical centerline of the FOV was elevated slightly above the initial bed surface in order to allow a clear line of sight to the middle of the flume. Before beginning an experiment, a calibration image was taken to relate the raw images to physical space Procedures For a given trial, the pump was turned on and images were obtained at a rate of 0.67 Hz for approximately the first five minutes of the scouring process. The data from the first five minutes yielded approximately 200 images per trial. Figure 3.10 illustrates a raw image. Post-processing included mapping the images into physical space and then using edge detection methods to identify the intersection of the laser sheet with the sediment bed. A 1 cm boxcar filter was then applied along the x-axis in order to smooth the raw profile image. In addition, a second boxcar filter was applied through time, comparing bed elevations at the same location through five adjacent time profiles. Image mapping and the application of the filters were performed in a MATLAB program.

62 Fig Image of laser light reflection along a scour profile. The image is taken approximately two minutes after start-up of the A60 trial. The original image has been imported into MATLAB so that the pixel intensities are represented by a color spectrum. 44

63 45 Experiments were carried out for two sediment sizes, and for several flow rates. A summary of the experimental matrix, including calculated values of the nozzle Reynolds number and the densimetric Froude number (F o ) is presented in Table 3.2. Table 3.2. Summary of dimensional and non-dimensional parameters for the early stage boundary detection experiments. Trial Number Median Sediment Flow Rate, Q Re F o Size, d (mm) (liters per minute) AC , AC , AC , A , A , A , A , Experimental Uncertainty and Limitations For most of the experimental trials, the uncertainty of the measurements was comparable to other recent studies. The scattering of the laser light from the rough bed yielded a relatively thick line on the order of 1 to 2 mm in width. Similar values were reported by Faraci et al. (2000) and by Baglio and Foti (2003). Trials with high values of F o were characterized by significant amounts of suspended sediment. In these trials, the suspended sediment reflected the laser sheet and obscured the true sediment bed boundary. This in turn led to unsatisfactory imaging of the bed, highlighting the suitability of the present experimental method to predominantly bedload transport applications.

64 Results and Discussion Figures show sample experimental results in the form of plan and perspective views of carpet plots of the evolving bedform. For each trial, the individual two-dimensional profiles were combined to show the temporal evolution of the bedform. The three-dimensional perspective view was useful for showing the vertical relief of the scour hole and the dune geometry.

65 y (cm) 47 (a) Time (s) 100 (b) y (cm) Time (s) x (cm) x (cm) 20 0 Fig Plan (a) and perspective (b) views of the scour hole evolution with time for the A60 trial. The black line highlights the dune crest at each time step.

66 48 (a) (b) 300 y (cm) y (cm) 0 10 x (cm) Tim e( s) Time (s) x (cm ) 20 0 Fig Plan (a) and perspective (b) views of the scour hole evolution with time for the A100 trial.

67 y (cm) 49 (a) (b) Time (s) 100 y (cm) Time (s) x (cm) x (cm) 20 0 Fig Plan (a) and perspective (b) views of the scour hole evolution with time for the AC60 trial.

68 50 Figure 3.11 shows the evolution for the lowest F o case. In addition to the bathymetry being shown, the location of the crest (point of maximum elevation) was tracked and marked by a thick black line. One item of interest was that prior to the development of the primary bedform, a short-lived transient bedform evolved in the first few seconds of the experiment. This ephemeral dune was quickly overtaken and consumed by the primary dune. Figure 3.13, showing results from one of the AC sediment experiments, also clearly shows the development of this initial and short-lived morphological feature. A second item of interest was that the main face of the bedform (the sloping region between the trough and dune) may begin to oscillate with a regular period, depending upon the experimental conditions. This phenomenon results from the alternation between digging and filling phases (Johnston, 1990; Balachandar and Kells, 1997; Bey et al., 2007). Figure 3.11 demonstrates that this oscillation began toward the end of the trial and had a relatively long period (25 s). This oscillation became more pronounced and more rapid as F o increased, as shown in Figure 3.12 and as summarized in Table 3.2. The trials with the AC sediment, which generally have higher F o values than those with the A sediment, did not demonstrate this oscillation. This difference suggested that there was some critical value of F o above which this alternation between digging and filling phases ceases. Figures 3.11, 3.12, and 3.13 represent the highly resolved information that can be collected through the boundary detection technique. The detail of scour hole growth shown in the carpet plots has not been presented in previous studies. This research

69 51 presents the contribution that boundary detection methods can have on future scour research. Figure 3.14, which corresponds to the A60 trial, shows the time history of the distance from the nozzle orifice to the dune crest, x c, and the per-unit-width volume of sand removed from the scour hole. In Figure 3.14 the present early-stage data (closed symbols) have been combined with long-stage data (open symbols) obtained with the manual tracing of profiles on the flume sidewall. As Figure 3.14 shows, the laser-derived dune crest locations match very well with the longer stage results obtained by simple profile tracing. The vertical step-down shown in the figure was due to a dune bedform migrating downstream shortly after the jet startup. The dune crest of the scour profile became the tallest bedform at approximately 100 seconds into the trial. The computed scour hole volume was more interesting, with three distinct regions (slopes) identified by the laser diagnostics. The last region (roughly 200 s < t < 300 s) appeared to have a slope consistent with the longer stage results. The discontinuity where the two data sets meet was due to variations in the measurement location. Recall that Figure 3.7 illustrated the non-uniformity of the cross-channel scour profile. The laser method, which was sampling the centerline, reported a scour volume considerably less in magnitude than the sidewall tracing method. In summary, the two components of the live-bed scour experiments (long term and early stages) provided the data to validate the scour prediction model. These experiments illustrated that scour profiles were geometrically self-similar and that the rate of growth was linearly related to the logarithm of time.

70 x c (cm) Crest Location (laser method) Crest Location (sidewall tracing) Scour Volume (laser tracing) Scour Volume (sidewall tracing) Per Unit Width Scour Hole Volume (cm 2 ) Time (sec) Fig Temporal evolution of the distance to the dune crest and the per-unit-width scour hole volume for the A60 trial. The data from the early-stage boundary detection method are shown with closed symbols and the long-term data profile sketches are shown with open symbols.

71 53 Chapter 4 Velocity Field PIV Measurements 4.1 Introduction Live-bed scour experiments, discussed in the last chapter, provided information on the scour shape. The next step of this research was to determine the flow characteristics within a scour hole. Flow characteristics of interest included mean velocity fields and turbulent velocity fluctuations. Using these characteristics, it was possible to calculate boundary layer thickness, maximum velocities, and shear stresses. Obtaining these flow characteristics allowed for the validation of the scour prediction model. This chapter focuses on the procedures needed to obtain the velocity data. Obtaining the velocity data required several steps. To obtain velocity statistics, multiple PIV image pairs had to be averaged together. During this data collection process the sediment bed had to remain stationary to ensure the captured images were similar. As discussed in the previous chapters, the sediment bed was observed to grow rapidly during early stages. Therefore, to obtain velocity statistics, it was necessary to create fixed-bed models that resembled the bed profiles observed during the livebed experiments. Models were created at several different scales in order to span the full range of bed development. The next step was to collect velocities with the PIV instrument, yielding a high resolution velocity field along the scour profile.

72 Fixed-Bed Models of Scour Profiles The fixed-bed models were based upon the average dimensionless scour profiles discussed in the previous chapter. The overall profile was divided into four sub-regions for linear approximation (Region 1, Region 2, Region 3, and Region 4). The four linear sub-sections provided a reasonable approximation of the bedform. The linear model represented the profiles with only two parameters: the initial vertical offset of the bed at the nozzle (a) and the slope of the scour faces (m). For the A (d = mm) and B (d = mm) sediments, the parameter estimates were found through least square analysis to be a = and m = Figure 4.1 illustrates the average profile for each sediment class as well as the proposed model bed profile. The linear approximation strongly agreed with the center-line data obtained from the A sediment (refer to Figure 4.2). The equations for the four regions were: Region 1 (x 0.269): y = 0.395x (4.1) Region 2 (0.269 < x 1): y = 0.395x (4.2) Region 3 (1 < x 1.362): y = 0.395x (4.3) Region 4 (x > 1.362): y = 0 (4.4) It should be noted that the profile for the AC sediment profile differed from the linear approximation. This was due to the finer particles becoming suspended in the jet. For the linear approximation, conservation of mass was observed so that the volume of the scour hole equaled the volume of the dune.

73 Region 3 Region 2 y* 0 Offset a Slope m Region Region 1 AC Sediment B Sediment A Sediment Linear approximation x* Fig Comparison of the average scour profiles to the model bed profile. In the next phase of the research, six models were constructed to represent a wide range of scour profiles. The model bed profile equations were used to create five profiles with x c of 20, 25.1, 31.6, 39.8 and 50 cm. The sixth profile was a flat bed to simulate the sediment bed at start-up. These six scour profiled provide a good representation of the range of bedform sizes observed for the three sediment classes. A photograph of the six fixed-bed models is shown as Figure 4.3. The profiles were constructed of polycarbonate sheets with a treated surface to enhance PIV imaging. The first step was to cut two vertical ribs from 1/8 inch polycarbonate sheets to the specifications of the profile. Polycarbonate sheets, 1/8 inch thick, were then glued to the ribs to create the scour bed surface. A high strength spray adhesive (3M) was then applied to the scour surface before the A class sediment (d = mm) was sprinkled onto the models. The sediment was added to represent the bed

74 y / distance to crest Centerline Linear approximation x / distance to crest Fig Comparison between the linear scour profile approximation and the nondimensional centerline profile obtained from point-gage measurements. roughness of the actual sediment bed. Finally, the scour bed surface was painted with an ultra flat black paint (Krylon) to minimize reflections of laser light into the camera during PIV operation.

75 57 Fig Photograph of polycarbonate scour profile models.