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IIT Jodhpur

Department of Civil & Infrastructure Engineering

Journal of Engineering Mechanics

Erratum: "Characteristics of turbulent flow in submerged jumps on rough beds" (Journal of Engineering Mechanics (2008) vol. 134 (1) (49-59))

This paper reports an experimental investigation on the velocity and turbulence characteristics in an evolving scour hole downstream of an apron due to submerged jets issuing from a sluice opening detected by an acoustic Doppler velocimeter. Experiments were carried out for the conditions of submerged jets, having submergence factors from 0.96 to 1.85 and jet Froude numbers from 2.58 to 4.87, over sediment beds downstream of a rigid apron. The distributions of time-averaged velocity vectors, turbulence intensities, and Reynolds stress at different streamwise distances are plotted for the conditions of initial flat bed, intermediate scour holes, and equilibrium scour hole downstream of an apron. Vector plots of the flow field show that the rate of decay of the submerged jet velocity increases with an increase in scour hole dimension. The bed-shear stresses are determined from the Reynolds stress distributions. The flow characteristics in evolving scour holes are analyzed in the context of self-preservation, growth of the length scale, and decay of the velocity and turbulence characteristics scales. The most significant observation is that the flow in the scour holes (intermediate and equilibrium) is found to be plausibly self-preserving. © 2008 ASCE.

World University root node

Characteristics of submerged jets in evolving scour hole downstream of an Apron

This paper presents an experimental investigation on the characteristics of a horseshoe vortex system near the juncture of a square cylinder and a horizontal base plate, using particle image velocimetry and flow visualization technique. Experiments were conducted for Reynolds numbers (based on the free stream velocity and the width of square cylinder) ranging from 2.0 × 102 to 6.0 × 103. The flow patterns are first classified into four major regimes: Steady horseshoe vortex system, periodic oscillation vortex system with small displacement, periodic breakaway vortex system, and irregular vortex system. The classifications can be demonstrated as a figure of Reynolds number versus the ratio of the height of square cylinder to undisturbed boundary layer thickness. The study then mainly focused on the characteristics of steady horseshoe vortex system (corresponding to Reynolds numbers ranging from 2.0 × 102 to 2.5 × 103). The nondimensional characteristics, including the horizontal and vertical distances from the primary vortex core to frontal face of the vertical square cylinder and bottom boundary of the base plate, respectively, the height of stagnation point at frontal face of the square cylinder, and the down-flow discharge as well as circulation of the primary vortex, all increase with increase of the ratio of the height of square cylinder to undisturbed boundary layer thickness. However, they all decrease with the increase of the aspect ratio (i.e., the height-to-width ratio) of the square cylinder. The study provides essential properties of a steady horseshoe vortex system and gives an insight for related engineering applications. It can be served as a basis for more complicated horseshoe vortex systems occurring at high Reynolds numbers. © 2008 ASCE.

Characteristics of steady horseshoe vortex system near junction of square cylinder and base plate

The results of an experimental investigation on the flow field in submerged jumps on horizontal rough beds, detected by an acoustic Doppler velocimeter, are presented. Experiments were conducted for the conditions of submerged jumps, having submergence factors from 0.96 to 1.85 and jet Froude numbers from 2.58 to 4.87, over rough beds of Nikuradse's equivalent sand roughness equaling 0.49, 0.8, 1.86, and 3mm. The vertical distributions of time-averaged velocity components, turbulence intensity components, and Reynolds stress at different streamwise distances from the sluice opening and the horizontal distribution of bed-shear stress are plotted. Vector plots of the flow field show that the rate of decay of jet velocity in a submerged jump increases with increase in bed roughness. The flow characteristics on rough beds, being different from those on smooth bed, are discussed from the point of view of similarity, growth of the length scale, and decay of the velocity and turbulence characteristics scales. The most important observation is that the flow in the fully developed zone is found to be self-preserving. © 2008 ASCE.

Characteristics of turbulent flow in submerged? Jumps on rough beds

This paper presents an experimental investigation on the characteristics of the development of turbulent horseshoe vortex flow in an evolving (intermediate stages and equilibrium) scour hole at square cylinder measured by an acoustic Doppler velocimeter (ADV). As the primary objective was to study the turbulent flow characteristics of horseshoe vortex in an evolving scour hole, the flow zone downstream the cylinder was not considered. Experiments were conducted with a square cylinder of width 12 cm embedded in the bed of uniform sand of median diameter 0.81 mm under the approaching flow having undisturbed flow depth (= 25 cm) greater than twice the width of the cylinder and the depth-averaged approaching flow velocity (= 35.7 cm/s) equaling approximately 0.95 times the critical velocity for the uniform bed sand. The ADV flow measurements were taken inside the intermediate scour holes (having depths of 0.25, 0.5 and 0.75 times the equilibrium scour depth) and the equilibrium scour hole (frozen by spraying glue). The contours of the time-averaged velocities, turbulence intensities and Reynolds stresses at different azimuthal planes (0°, 45° and 90°) are presented. The change of the characteristics of horseshoe vortex flow associated with a downflow from intermediate stages to equilibrium condition of scour hole is revealed through the vector plots of the flow field at different azimuthal planes. Also, the flow characteristics of the horseshoe vortex are analyzed from the point of view of similarity with the velocity and turbulence characteristic scales. The important observation is that the flow and the turbulence intensities in horseshoe vortex flow in a developing scour hole are reasonably similar. © 2008 International Association of Hydraulic Engineering and Research.

Journal of Hydraulic Research

Kinematics of horseshoe vortex development in an evolving scour hole at a square cylinder

The paper reports on an experimental investigation concerning two important issues: (1) local scour and (2) riprap stability at a 45° wing-wall abutment in a degrading river bed of noncohesive sediment. The abutment considered was short (that is abutment length/flow depth <1). From the experimental observations, no influence of abutment inclusion on bed degradation was evident, as bed profiles with and without abutment were quite identical apart from the immediate vicinity of the abutment. Total scour depth at an abutment is found to be the maximum abutment scour depth in addition to the reduction of bed elevation due to bed degradation. The maximum abutment scour depth can be estimated from the equation given by Kandasamy and Melville in their 1998 paper. For scouring time beyond 24h, the local abutment scour depth remains independent of time. In a degrading bed, the bed forms cause edge failure of the riprap at an abutment when the dunes propagate over the riprap layer. Initially, the dune height is significant causing the maximum damage of riprap layer. As the flow velocity reduces, the resulting bed-shear stress diminishes with the degrading bed and gradually the formation of dunes ceases. An additional experiment reveals that the damaged riprap layer is significantly vulnerable against a subsequent flood accompanied by large dunes. © 2008 ASCE.

Journal of Hydraulic Engineering

Local scour and riprap stability at an abutment in a degrading bed

Laboratory experimental results on the turbulent flow characteristics, measured by an acoustic Doppler velocimeter, over loose rough boundaries at the near-threshold of motion are reported. The primary endeavor was to investigate the response of the turbulent flow field, having zero-pressure gradient, to the uniform gravel beds at the near-threshold of motion with reasonably wide range of relative roughness ε/h (0.02 < ψ/h < 0.15; where ε=Nikuradse's equivalent roughness and h=flow depth). Five uniform gravel sizes, ranging from 4.1to14.25 mm, were used in the experiments. The vertical distributions of time-averaged velocity, turbulence intensities and the Reynolds stress were measured and analyzed. The variation of the mixing-length is considerably linear with the depth within the inner layer, whose thickness is 0.23 times the boundary layer thickness δ, and the von Kármán constant is obtained as 0.35. The boundary shear stresses were determined by three independent methods, such as using the logarithmic law (the Clauser method), Reynolds stress profiles and bed slope. It is observed that in the inner layer, the logarithmic law of wall for the time-averaged streamwise velocity holds with the von Kármán constant 0.35 and a constant of integration 7.8; whereas in the outer layer, the law of the wake defines the velocity profiles with average value of the Coles' wake parameter 0.11. Alternatively, velocity profiles based on 1/nth power law are also put forward, where n is expressed as a function of ε/δ. The equation of the friction factor f is obtained from the depth averaging of the velocity profile; and the collapse of the estimated f and the measured data (experimental and field) is reasonable. The turbulence intensities being non-isotropic can be defined by an exponential law; whereas the Reynolds stress varies almost linearly with the depth. The values of the Shields parameter for the threshold of gravel motion obtained experimentally correspond closely with the curve obtained from the modified model of Dey considering the present logarithmic law of velocity. For all the aforementioned parameters, thorough statistical and error analyses of the experimental data are done to ascertain the adequacy of the proposed equations. © 2007 ASCE.

Characteristics of loose rough boundary streams at near-threshold

Experiments were conducted to investigate the effect of upward seepage on the characteristics of scour hole due to horizontal submerged jets and the resulting flow field within the scour hole. In the experiments, the submerged jets had a range of submergence factors from 3.22 to 26.5 and jet Froude numbers from 0.82 to 1.48 over beds of sediments (median sizes = 0.8 mm, 1.86 mm and 3 mm) downstream of a sluice gate under different upward seepage velocities. The characteristic lengths of the scour hole determined from the equilibrium scour profiles are: The maximum equilibrium scour depth, the horizontal distance of maximum scour depth from the sluice gate, the horizontal extension of scour hole from the sluice gate, the dune height and the horizontal distance of dune crest from the sluice gate. The experimental results show that all the characteristic lengths decrease with increase in seepage velocity, as a result of jet deflection by the upward seepage velocity. Using the experimental data, the time-variation of scour depth is scaled by an exponential law, where the time scale decreases linearly with increase in the ratio of seepage velocity to issuing jet velocity. The flow field within scour hole under different upward seepage velocities was detected by the acoustic Doppler velocimeter. Vector plots of the flow field show that the decay rate of submerged jet increases with increase in seepage velocity. The vertical profiles of turbulent kinetic energy and Reynolds stress at different streamwise distances and the horizontal distributions of bed shear stress acting on the scoured beds are plotted for different (with and without) upward seepage velocities. © 2007 International Association of Hydraulic Engineering and Research.

Effect of seepage on scour due to submerged jets and resulting flow field

The upward seepage through the bed sediment downstream of an apron of a sluice gate structure is a common occurrence due to afflux of the flow level between the upstream and downstream reaches of a sluice gate. The result of an experimental investigation on the characteristics of the scour hole and the flow-field downstream of an apron due to submerged jets under the influence of upward seepage through the bed sediment is presented. Experiments were run for the conditions of submerged jets, having submergence factors from 0.99 to 1.72 and jet Froude numbers from 3.15 to 4.87, over beds of sediments (median sizes=0.8, 1.86, and 3 mm) downstream of an apron under upward seepage velocities. The characteristic lengths of the scour hole determined from the scour profiles are: the maximum equilibrium scour depth, the horizontal distance of the location of maximum scour depth from the edge of the apron, the horizontal extent of the scour hole from the edge of the apron, the dune height, and the horizontal distance of the dune crest from the edge of the apron, all of which were found to increase with an increase in the seepage velocity. Using experimental results, the time variation of the scour depth is scaled by an exponential law, where the nondimensional time scale decreases linearly with an increase in the ratio of the seepage velocity to the issuing jet velocity. The flow field in the submerged jets over both the apron and within the scour hole was detected using an acoustic Doppler velocimeter. The vertical distributions of time-averaged velocities, turbulence intensities and Reynolds stress at different streamwise distances, and the horizontal distribution of bed-shear stress are plotted for the conditions of scour holes with and without upward seepage. Vector plots of the flow field show that the rate of decay of the submerged jet decreases with an increase in the seepage velocity. The flow characteristics in the scour holes are analyzed in the context of the influence of upward seepage velocity on the decay of the velocity and turbulence intensities and the growth of the boundary layer. © 2007 ASCE.

Effect of upward seepage on scour and flow downstream of an apron due to submerged jets

Experimental results on scour below a high vertical drop (drop height/ critical depth >1) in uniform sands and gravels are presented. The experimental results are used to describe the effects of important parameters, identified from the dimensional analysis, on equilibrium scour depth. The important observations are that the equilibrium scour depth increases with increase in densimetric Froude number, whereas the scour depth decreases with increase in sediment size and tailwater depth. The time scale of scour depth that follows an exponential law is determined. The nondimensional time scale decreases with increase in densimetric Froude number. © 2007 ASCE.

Scour below a high vertical drop

The outcome of an experimental study on the turbulent horseshoe vortex flow within the developing (intermediate stages and equilibrium) scour holes at cylindrical piers measured by an acoustic Doppler velocimeter (ADV) are presented. Since the primary objective was to analyze the evolution of the turbulent flow characteristics of a horseshoe vortex within a developing scour hole, the flow zone downstream of the pier was beyond the scope of the investigation. Experiments were conducted for the approaching flow having undisturbed flow depth (=0.25m) greater than twice the pier diameter and the depth-averaged approaching flow velocity (=0.357m/s) about 95% of the critical velocity of the uniform bed sand that had a median diameter of 0.81mm. The flow measurements by the ADV were taken within the intermediate (having depths of 0.25, 0.5, and 0.75 times the equilibrium scour depth) and equilibrium scour holes (frozen by spraying glue) at a circular pier of diameter 0.12m. In order to have a comparative study, the ADV measurements within an equilibrium scour hole at a square pier (side facing the approaching flow) of sides equaling the diameter of the circular pier were also taken. The contours of the time-averaged velocities, turbulence intensities, and Reynolds stresses at different azimuthal planes (0, 45, and 90°) are presented. Vector plots of the flow field at azimuthal planes reveal the evolution of the characteristics of the horseshoe vortex flow associated with a downflow from intermediate stages to equilibrium condition of scour holes. The bed-shear stresses are determined from the Reynolds stress distributions. The flow characteristics of the horseshoe vortex are discussed from the point of view of the similarity with the velocity and turbulence characteristic scales. The imperative observation is that the flow and turbulence intensities in the horseshoe vortex flow in a developing scour hole are reasonably similar. © 2007 ASCE.

Characteristics of horseshoe vortex in developing scour holes at piers

An experimental study on incipient motion of gravel-bed streams under steady-decelerating flow is presented. Experiments were carried out in a flume with two median grain sizes, d 50 = 16·7 mm for a fixed-bed case and d 50 = 8 mm for a mobile bed case. In addition, an effort is made to determine a simplified method for the estimation of bed shear stress in decelerating flow over fixed and mobile beds for use in field situations. From the observation of eleven fixed-bed and nine mobile-bed velocity profiles, it is revealed that the parabolic law method (PLM) and the Reynolds stress method are comparable for estimation of shear velocity in general. Also, the results show that the shear stress distribution adopts a convex form over fixed and mobile beds. Due to this form the critical Shields parameter value for decelerating flow is less than the reported values in literature. This paper supports Buffington &amp; Montgomery (1997) statement that less emphasis should be given on choosing a universal shields parameter, and more emphasis should be given on choosing defendable values based on flow structure. © Printed in India.

Fulltext

Sadhana - Academy Proceedings in Engineering Sciences

Influence of decelerating flow on incipient motion of a gravel-bed stream

A new theory is developed for the steady free surface flow over a horizontal rough bed with uniform upward seepage normal to the bed. The theory is based on the Reynolds averaged Navier-Stokes (RANS) equations applied to the flow domain that is divided into a fully turbulent outer layer and an inner layer (viscous sublayer plus buffer layer), which is a transition zone from viscous to turbulent regime. In the outer layer, the Reynolds stress far exceeds viscous shear stress, varying gradually with vertical distance. Near the free surface, the velocity gradient in vertical direction becomes lesser giving rise to wake flow. On the other hand, in the composite inner layer close to the bed, the viscous shear stress exists together with the turbulent stress. Thus, for the outer layer, a logarithmic law having modified coefficients from the traditional logarithmic law is obtained for the streamwise velocity, whereas for the inner layer, a fifth-degree polynomial including effective height of protrusions holds. The exact velocity expressions for inner and outer layer, which contain principal terms in addition to infinitesimally small terms, are in agreement with the experimental data obtained from laboratory measurements through an acoustic Doppler velocimeter. The experiments were run on two conditions of no seepage and a low upward seepage. Expressions for the Reynolds stress are also derived and computed for validation by the experimental data. © 2006 The Royal Society.

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Theory of free surface flow over rough seeping beds

The paper presents (1) a semi-theoretical model for the computation of maximum clear-water scour depth below underwater pipelines in uniform sediments under steady flow and (2) an experimental investigation on the influence of upward seepage on clear-water scour depth below underwater pipelines. Based on the "image method" of the potential flow theory for the flow through the gap between a circular pipeline and the scoured bed, a theoretical model is presented for the computation of maximum scour depth below underwater pipelines in clear-water condition considering the wall correction. Also, a simple theoretical calculation, that involves Chiew's (1991) [Chiew, Y.M., 1991. "Prediction of maximum scour depth at submarine pipelines." J Hydraul Eng 117(4), 452-466] gap flow curve, is proposed to estimate the maximum scour depth considering the wall correction. The computed results agree satisfactorily with the experimental data. In addition, the potential predictors of the maximum scour depth given by different researchers are compared with the experimental data. The result of an experimental investigation on the scour depth below pipelines under the influence of upward seepage through the bed sediment is presented. In general, the scour depth below pipelines with upward seepage is smaller than that without seepage. There exists a critical value of the ratio of seepage velocity to main flow velocity that corresponds to a minimum scour depth. © 2007 International Association for Hydraulic Engineering and Research, Asia Pacific Division.

Journal of Hydro-Environment Research

Clear-water scour depth below underwater pipelines

The results of a theoretical investigation on the Reynolds and boundary shear stresses in submerged jets on horizontal rough boundaries are presented. The decay of submerged jet and the growth of the boundary layer are formulated empirically. Then, the Reynolds and boundary shear stresses are theoretically determined integrating the Navier-Stokes equations aided by the functional relationships of the longitudinal velocity and the turbulence stresses within the boundary layer. Experiments were carried out to detect the velocity by an acoustic Doppler velocimeter (ADV) in submerged jets of different submergence ratios over rough boundaries. The theoretical results correspond reasonably with the experimental data. The Reynolds stress near the boundary is positive and diminishes sharply changing its sign to negative and forming protuberance that increases with increase in boundary roughness. However, the boundary shear stress diminishes with increase in longitudinal distance and increases with increase in boundary roughness. © 2007 International Association for Hydraulic Engineering and Research, Asia Pacific Division.

Computation of Reynolds and boundary shear stress in submerged jets on rough boundaries

A new theoretical approach is presented for the derivation of free surface profiles of two-dimensional steady and unsteady flows by solving the Reynolds-averaged Navier-Stokes equations applied to the turbulent flow regime. This approach enables us to compute the steady and unsteady curvilinear flows having small curvatures, such as free overfall and constant velocity surge. In addition, the applications of the theory to the second-order waves are illustrated through the problems of small height bore and second-order tide. © 2007 ASCE.

Curvilinear flow profiles based on reynolds averaging

Clear-water scour at circular and square piers, embedded in a sand bed overlain by a thin armor layer of gravels, was experimentally studied. Depending on the pier width, flow depth, armor gravel, and bed-sand sizes, three cases of scour holes at piers in armored beds were recognized. A comparison of the experimental data shows that the scour depth at a pier with an armor layer under limiting stability of the surface particles is greater than that without an armor layer for the same bed sediments, if the secondary armoring formed within the scour hole is scattered. The equations of maximum equilibrium scour depths at piers in armored beds for these cases are proposed. On the other hand, the scour depth with an armor layer is less than that without an armor layer for the same bed sediments, when the scour hole is shielded by the compact secondary armor layer. © 2007 ASCE.

Clear-water scour at piers in sand beds with an armor layer of gravels

Experiment was conducted in a laboratory flume to measure the 3D turbulent flow field by an acoustic Doppler velocimeter in a scour hole at a 45° win-wall abutment under a clear water regime. The profiles of time-averaged velocity components, turbulence intensity components, turbulent kinetic energy and Reynolds stresses at different azimuthal planes are presented. In the upstream, vector plots of flow field at azimuthal and horizontal planes show the presence of a large primary vortex associated with a downflow within the scour hole. In the downstream, the flow is upward. The bed shear stresses within the scour hole are estimated from the Reynolds stresses and the velocity gradients. The data presented in this study, would be useful to the researchers for the future development and validation of theoretical models of flow field in a scour hole at bridge abutments. © 2006 International Association of Hydraulic Engineering and Research.

3D flow field in a scour hole at a wing-wall abutment

The paper presents an experimental investigation of (i) scour at a pier within a long contraction and (ii) scour of a thin layered bed within a long contraction. The scour depth at piers within long contractions increases with an increase in sediment size and a decrease in channel opening ratio. A theoretical calculation proposed to estimate the maximum equilibrium scour depth suggests that it is the summation of the individual equilibrium scour depth within a long contraction and the equilibrium scour depth at a pier under critical flow conditions in the upstream bed. The scour depth (relative to the approaching flow depth) within long contractions with thin gravel layers increases with an increase in the ratio of the diameter of the surface gravel to that of the bed sand and a decrease in the channel opening ratio. The scour depth within a channel contraction with a gravel layer, however, is greater than that with a unlayered bed of uniform sediment. Further, the maximum equilibrium scour depths within long contractions with gravel layers calculated theoretically using the energy and continuity equations are in agreement with the experimental data. © 2006 NRC Canada.

Canadian Journal of Civil Engineering

Pier scour and thin layered bed scour within a long contraction

An experimental study on the control of scour at vertical circular piles under monochromatic waves and a steady current is presented. The experiments on wave and steady currents were carried out under live-bed and clear-water regimes, respectively. In waves, splitter plate attached to the pile along the vertical plane of symmetry and threaded pile (helical wires or cables wrapped spirally on the pile to form threads) were found to be effective to reduce the scour depth. For the Keulegan-Carpenter numbers 6-100, the vortex shedding is the main mechanism of scour under waves. The splitter plate and threaded pile disrupt the vortex shedding. The average reduction of the scour depth by the splitter plate was 61.6%. For threaded piles, different combinations of cable and pile sizes were tested, and the best combination was found for a cable-pile diameter ratio equaling 0.75, in which average scour depth reduction was 51.1%. The average reductions of scour depths for other cable-pile diameter ratios of 0.33 and 0.5 were 43.2 and 48.1%, respectively. On the other hand, in a steady current, the threaded pile proved to be effective to control scour depth to a great extent. Cables wrapped spirally forming threads on the pile help to weaken the downflow and horseshoe vortex, which are the principal agents of scour under a steady current. The experimental results showed that the scour depth consistently decreases with an increase in cable diameter and the number of threads, and with a decrease in thread angle. The maximum reduction of scour depth observed was 46.3% by using a triple threaded pile having a thread angle of 15° and a cable-pile diameter ratio of 0.1. The proposed methods of controlling scour are easy to install and are economical. © 2006 ASCE.