Nappe Flow Research Articles

Plunge pool dynamic pressures: a temporal analysis in the nappe flow case

ABSTRACTRectangular jet, or nappe flow, constitutes one of the energy dissipation methods used in the overtopping of dams. This paper reports new laboratory data on pressures, velocities and air entrainment and analyses the degree of break-up of a rectangular jet before entering the basin and the pressure fluctuations on the bottom of the pool. It is found that the maximum mean dynamic pressure coefficient of 0.86, which is valid for circular jets, is reduced to 0.83 for a rectangular jet. The study has also led to a relationship between the fluctuating pressure coefficient and the degree of the jet break-up. The peak pressure coefficient occurred for break-up length ratios (i.e. falling height/length) in the range of 1.00–1.20. The scaling effects are negligible for scales less than 1:10. The new set of characteristics given in the paper fills the current knowledge gap related to rectangular jets.

A Study on Imposing Exact Solutions as Internal Boundary Conditions in Simulating Shallow-water Flows over a Step

이 연구에서는 계단과 같이 불연속 횡단 구조물을 지나는 천수 흐름에 대해 내부 경계조건으로서 정확해를 부여하는 기법을 제안하였다. 제안된 기법의 검토를 위해 MUSCL이 적용된 HLLL 근사 Riemann 해법을 이용하였다. 계단을 지나는 천수 흐름에 대한 다양한 문제에서 모의 결과는 정확해와 잘 일치하였다. 또한, 계단에서 댐 붕괴 실험 및 급경사 수로 실험의 결과와 부합되었다. 개발된 모형으로 낙차공과 같이 불연속 바닥을 지나는 천수 흐름에 대해 별도의 수위-유량 관계나 지형의 완화 없이 모의가 가능하다. 향후, 계단에 의한 흐름 저항과 수맥에 의한 에너지 손실에 대해 적절한 평가가 이루어진다면, 보나 옹벽(강변 도로)과 같은 불연속 지형을 넘나드는 천수 흐름에 대한 수치모의가 가능할 것으로 기대된다. In this study, was proposed a numerical scheme imposing exact solutions as the internal boundary conditions for the shallow-water flows over a discontinuous transverse structure such as a step. The HLLL approximate Riemann solver with the MUSCL was used for the test of the proposed scheme. Very good agreement was obtained between simulations and exact solutions for various problems of the shallow-water flows over a step. In addition, results by the numerical model showed good agreement with those of dam-break experiments over a step and stepped chute one. Developed model can simulate the shallow-water flows over discontinuous bottom such as a drop structure without additional rating curve or topography smoothing. Given the proper evaluations for the flow resistance by a step and the energy loss by the nappe flow in the future, could be simulated flooding and drying of the shallow-water flows over discontinuous topography such as a weir or the river road with retaining wall.

Improving the hydraulic performance of single step broad-crested weirs

In this study the hydraulic performance of single step broad-crested weir was improved. Through analyzing the parameters that have effect on the shape of the step and its influence on the flow characteristics, and energy dissipation percent (E%) downstream (D/S) of the weir. The differential equation of gradually varied flow for the water surface profile over the weir was solved analytically .Furthermore, empirical relations for E% and discharge coefficient (Cd) due to the affecting factors were derived .The results showed that the weir model when the ratio of the length of D/S step to the length of the weir L2/L1=0.5 gives a higher E% in comparison with other weir models. Three types of flow regimes were observed, nappe flow below 350 cm3 /s/cm, transition flow 350-700 cm3/s/cm and skimming flow upper than 700 cm3/s/cm . The comparison between calculated values by the differential equation of gradually varied flow and experimental values gives a good agreement, the maximum difference is about 7%.Two empirical relations were obtained, the first to estimate Cd in terms of the ratio for upstream U/S water head to U/S weir height H/P1 and L2/L1. While the second relation to estimate E% in terms of the ratio for D/S water head to U/S weir height h/P1, L2/L1 and the Froude number Fr2 with a high correlation coefficient . Key words: Hydraulics; weirs ; performance ; dissipation energy.

The effect of flow patterns and energy dissipation over stepped chutes on aeration efficiency

Stepped chutes that are commonly used for gabion weirs, river training, irrigation channels, and storm waterways have become popular in recent years mainly due to the intrinsic low-cost and the speed of construction. Stepped chutes are used also for in-stream re-aeration and in water treatment plants to enhance the air-water transfer of atmospheric gases and of volatile organic components. In a stepped chute, the provision of steps can produce significant energy dissipation. This paper seeks the effect of energy dissipation over stepped chutes on aeration efficiency. It is observed from the results that aeration efficiency increases with increasing energyloss ratio. There is higher energy dissipation in nappe flows than skimming flow situations and nappe flow regime lead to greater aeration efficiency than skimming flow regime. Moreover, regression equations are obtained relating aeration efficiency to stepped chute slope and energy-loss ratio. For this aim, genetic expression programming, a recently developed artificial intelligence technique, is used. The model equations obtained have high correlation coefficients and low minimum square error values.

Reply to comment by Keith Richardson on “Flow regimes, bed morphology, and flow resistance in self‐formed step‐pool channels”

Reply to comment by Keith Richardson on “Flow regimes, bed morphology, and flow resistance in self‐formed step‐pool channels”

Nappe flow over horizontal stepped chutes

Stepped chutes have been frequently used since the 1980s in order to take advantage of their dissipation efficiency, aeration characteristics and relative ease of construction. Two basic flow regimes exist for stepped chutes: nappe flow and skimming flow, with the nappe flow having received less attention in comparison to the skimming flow regime. This work suggests a simple iterative method, valid for sub-to-supercritical approach flow conditions, for predicting the basic nappe flow features on a horizontal multi-step structure. The proposed calculation procedure, if applied along the stepped chute, allows us to calculate the flow depth at each step brink and at each nappe impact point, the thickness of the water cushion beneath the nappe, the jet impact length and the energy dissipation rate. For validating the proposed analytical approach, a comparison between experimental and calculated data is also presented.

Aeration characteristics of a rectangular stepped cascade system

Aeration experiments, maintaining nappe flow conditions, were carried out on a rectangular stepped cascade of total height 3.0 m to determine the total number of steps, slope of the entire cascade and hydraulic loading rate at which maximum overall aeration efficiency occurs, keeping the surface area of individual steps constant. Based on dimensional analysis, the overall aeration efficiency at standard conditions (E(20)) was expressed as a function of square of total number of steps (N(2)) and dimensionless discharge (d(c)/h), where d(c) and h represent critical depth in a rectangular prismatic channel and individual step height respectively. An empirical equation with E(20) as the response and N(2) and d(c)/h as the independent parameters was developed based on the experimental results subject to 36<or=N(2)<or =196 and 0.009<or=d(c)/h< or=0.144. The experimental results showed that the overall aeration efficiency (E(20)) for a particular step height of stepped cascade increases with increase in d(c)/h up to a certain value and then decreases. This may be due to at higher d(c)/h, i.e., at higher hydraulic loading rate, the flow approaches the transition zone and thereby aeration efficiency decreases. E(20) was also found to increase with number of steps at any hydraulic loading rate, because of the increased surface area of fall. The optimum number of steps, slope of the entire stepped cascade and hydraulic loading rate were found to be 14, 0.351 and 0.009 m(2)/s respectively producing the maximum value of overall aeration efficiency of 0.90.

Discussion of “Verification and validation of a computational fluid dynamics (CFD) model for air entrainment at spillway aerators” Appears in the Canadian Journal of Civil Engineering 36(5): 826-838.

The Authors presented the outputs of some numerical modelling of a spillway aerator conducted using a commercial package (Aydin and Ozturk 2009). A spillway aeration device is located on the spillway bottom and sometimes on the sidewalls. It is designed to deflect high-velocity flow away from the chute surface (and walls) to artificially introduce air into the flow and protect the spillway invert from cavitation erosion. The main flow regions are: (a) the approach flow region, which characterizes the initial nappe flow conditions; (b) the transition region, which coincides with the length of the deflector; (c) the aeration region; (d) the impact point region; and (e) the downstream flow region (Chanson 1989a, 1989b; Kramer et al. 2006). A key feature of the flow abovestream and downstream of an aerator is the strong mixing of air and water yielding a complicated high-velocity airnwater flow. Herein, it is argued that the validation and certification of the commercial CFD package were ill-performed and that the physical modelling technique based upon a proper dimensional analysis remains the basic design tool.In summary, we believe that the validation and certification of the Authorsr numerical results were improper. These should be conducted on the detailed airnwater flow properties of the flow abovestream and downstream of the spillway aerators, and several extensive datasets are freely accessible (e.g., Chanson 1988; Kramer 2004; Toombes 2002). The physical modelling and theoretical calculations remain the basic tools of the design engineers to size the spillway aeration devices on a large spillway, although the physical model dimensions must be carefully selected to address the potential scale effects (e.g., Kramer 2004; Chanson 2009).

Hydraulic Structures in Water Aeration Processes

The primary purpose of water aeration is to increase the oxygen saturation of the water. This can be achieved by using hydraulic structures because of substantial air bubble entrainment at these structures. This paper reviewed the literature on hydraulic structures used in water aeration processes. The hydraulic structures were divided into two groups as the high-head flow systems and the free-surface flow systems. The high-head flow systems were circular and venturi nozzles, pipe with venturi tube, and high-head conduit, and the free-surface flow systems were weir, stepped cascade, and free-surface conduit. Air/water flow ratio and aeration efficiency in circular nozzles with air holes and venturi nozzles were significantly high. Pipes with venturi tubes showed high aeration efficiency although they had low air/water flow ratio. In high-head and free-surface conduits, almost full oxygen transfer, up to the saturation value, occurred. Forty-five degrees triangular sharp-crested weir had significantly better air/water flow ratio and aeration efficiency than other sharp-crested weir shapes. Stepped cascades, in particular nappe flow regime, were very efficient means of aeration.

Impact force on downstream bed of weir by free overfall flow

According to previous experimental studies on free overfall, the main influencing factors of the local scour downstream of a drop structure were found to be the impact position of the nappe flow and the force striking on the channel bed. In this study, the pressure transducers and strain amplifiers, which did not disturb the flow field, were set up to measure the pressure distributions along the streamwise direction downstream of the weir. The data were recorded through an A‐D converter and compared with the data collected by Moore (1943) and Rand (1955). Expressions for the impact position and impact force of the flow nappe derived from the experimental results and the theoretical analysis. The relationship among weir height h, impact position of free overfall Lp , and drop number D were put into the following equation: Lp/h = 1.82D 0.17.

Physical and Numerical Modeling of the Nappe Flow in the Stepped Spillways

Physical and Numerical Modeling of the Nappe Flow in the Stepped Spillways

Flow patterns in nappe flow regime down low gradient stepped chutes

Although modern gravity dam spillways include often steep chutes operating in skimming flow regime, succession of free-falling nappes (i.e. nappe flow regime) are more common on low gradient chutes and cascades, and this flow situation received little attention to date. New experiments were conducted in nappe flows without hydraulic jump in two large-size facilities with flat slopes. The flow on the stepped cascade displayed complex, three-dimensional patterns. Detailed air–water flow measurements were performed in the jet, at nappe impact and in the downstream flow region. Key results demonstrated that the flow on each step was rapidly varied, highly three-dimensional and strongly aerated.

Reduction of Low-frequency Noise Induced by Nappe Flow over Head Work Gates

Reduction of Low-frequency Noise Induced by Nappe Flow over Head Work Gates

Prediction of oxygen content of nappe, transition, and skimming flow regimes in stepped-channel chutes

In a stepped-channel chute, the chute face is provided with a series of steps, from near the crest to the toe. Like many other high-speed flow configurations in hydraulic engineering, stepped-channel chute flows are characterized by the large amount of self-entrained air. Air entrainment on stepped-channel chutes is also recognized for its contribution to the oxygen transfer. The flow conditions in stepped-channel chutes have been classified into nappe flows, transition flows, and skimming flows. In this study, the aeration efficiency of stepped-channel chutes was investigated, and in particular, the effect of varying flow regimes. The results indicated that the nappe flow regime led to the larger aeration efficiency than the other flow regimes. Moreover, the mass transfer equations were developed to predict the aeration efficiency of the stepped-channel chutes in terms of dissolved oxygen. There is good agreement between the measured aeration efficiency values and the values computed from the predictive equations.Key words: aeration efficiency, oxygen transfer, stepped-channel chute, skimming flow, transition flow, nappe flow.

Aeration efficiency with nappe flow over stepped cascades

Hydraulic structures can increase dissolved oxygen levels by creating turbulent conditions where small air bubbles are carried into the bulk of the flow. Chute aeration is a particular instance of this. A chute is characterised by a steep bed slope associated with torrential flow. This chute flow may be either smooth or stepped. This paper investigates stepped chutes and how they affect the aeration efficiency. It is demonstrated that stepped chutes are very efficient at oxygen transfer because of the strong turbulent mixing associated with substantial air bubble entrainment and that this advantage becomes more pronounced in the nappe flow regime. In a nappe flow regime, the oxygen transfer on each step results from the flow aeration and mixing in the free-falling nappe, at the plunge point and possibly at the downstream hydraulic jump. An empirical correlation predicting aeration efficiency of one individual step for nappe flow regime was developed. A stepped chute design in terms of aeration efficiency can be optimised using this empirical correlation.

Numerical simulation of skimming flow over mild stepped channel *

Numerical simulation of stepped channel flow was conducted using turbulence models based on the VOF technique. Stepped channel flow is a complicated air-water two-phase flow with free surface, which can be divided into three flow regimes: skimming flow, nappe flow and transition flow. The characteristics of skimming flow over mild stepped channel was investigated, including friction factors, air concentration profiles velocity field, clear-water and bulked depths, static pressure, etc. Smooth channel flow was also simulated to compare the hydraulic characteristics of the stepped channel flow with the smooth one. Comparisons between the computed and the measured were made. Furthermore, comparison of the computed air concentration with Straub and Anderson's data was also performed. The Fluent 6.1 software was employed to conduct this numerical simulation work.

하천 보의 형태에 따른 공기 유입의 수리학적 검토

This paper presents the hydraulic analysis of the air entrainment by the weir types. For the weir types, the stepped weir, the labyrinth weir and the gate underflow weir were selected, and the oxygen transfer efficiency was estimated by the site investigation and the hydraulic model tests. The most effective type for the oxygen transfer was stepped weir The more steps the stepped weir had, the higher efficiency it revealed. Oxygen transfer was proportional to the flow velocity, the Froude number, and the flow discharge in order. Hydraulic model tests showed that a nappe flow occurred at small flow rates. The concurrent condition of a nappe flow and a skimming flow occurred as flow rate increases, nappe flow at the upper part and skimming flow at the lower part. In the region of nappe flow, air inception occurred from the step edges due to flow separation, and air entrainment was made through a free-falling nappe, an air pocket, a nappe impact and a subsequent hydraulic jump. In the region of skimming flow, air entrainment occurred by the variation of water surface over the steps, but it was relatively small compared with nappe flow.

Hydraulics of Stepped Chutes and Spillways

Hydraulics of Stepped Chutes and Spillways

Energy Dissipation and Air Entrainment in Stepped Storm Waterway: Experimental Study

For the last three decades, research focused on steep stepped chutes. Few studies considered flat-slope stepped geometries such as stepped storm waterways or culverts. In this study, experiments were conducted in a large, flat stepped chute (θ=3.4°) based upon a Froude similitude. Three basic flow regimes were observed: nappe flow without hydraulic jump, transition flow, and skimming flow. Detailed air–water flow measurements were conducted. The results allow a complete characterization of the air concentration and bubble count rate distributions, as well as an accurate estimate of the rate of energy dissipation. The flow resistance, expressed in terms of a modified friction slope, was found to be about 2.5 times greater than in smooth-chute flow. A comparison between smooth- and stepped-invert flows shows that greater aeration and larger residence times take place in the latter geometry. The result confirms the air–water mass transfer potential of stepped cascades, even for flat slopes (θ<5°).

Review of The hydraulics of stepped chutes and spillways by Hubert Chanson

‘‘Some may think another book on stepped spillways,’’ while others will welcome this new book of Hubert Chanson as a valuable addition to hydraulic engineering. Chanson worked for more than a decade on free surface air-water flows; first on air entrainment of chute flow, then mainly on stepped spillways ~Figs. 1 and 2!. He has largely published his results and when you discuss these professional matters with him, you can feel his involvement and his advance knowledge relating to these hydraulic structures. This new book of Chanson’s is, in a way, a reflection of this background, and it is certainly not a usual hydraulic text. The work is subdivided into 10 chapters, which are briefly considered here for the interested reader: ~1! introduction; ~2! historical development; ~3! nappe flow regime; ~4! transition flow regime; ~5! skimming flow; ~6! mass transfer; ~7! design; ~8! accidents and failures; ~9! wave phenomena; and ~10! summary. In addition, there is a rather long glossary including a historical background, and nine appendices. Two or three years ago, nobody would have thought that a relatively large book might be published on the single topic of stepped spillways. Having contributed a lot to those structures not only on the hydraulics but also on the history starting thousands of years B.C., Chanson is obviously the person to render evidence of our professional ancestors that would already use steps to dissipate hydraulic energy along drops. Chapters 3 to 5 contain the real hydraulics of stepped spillways, with an introduction to the phenomena termed by now the nappe, the transition, and the skimming flow regimes, followed with detailed lists of sources on specific items, and finally the proposals for designing stepped spillways. Let us consider Chapter 5, for example, which opens with a presentation of flow features, continues with the inception of air entrainment, and closes