Subcritical Flow Conditions Research Articles

Prediction of boundary shear stress in circular and trapezoidal channels with entropy concept

Relying on the power law to develop new relationships, the present study developed the Shannon entropy concept to predict shear stress distribution. The presented method was evaluated and compared with valid laboratory results and the shear stress distribution surveyed through this concept in circular, circular with flat bed and trapezoidal channels. By increasing the flow depth in circular channels, the model presented herein gives an improved prediction of shear stress distribution, while in circular channels with flat bed it is better in predicting shear stress both at lower flow depth and subcritical flow conditions. In comparison, in trapezoidal channels the model is much better in predicting the shear stress distribution at lower flow depths. Accordingly, with a mean error percentage of 1.99% in circular channels, 3.69% in circular channels with flat bed and 4.1% in trapezoidal channels, this novel model shows good ability in predicting shear stress distribution.

Computational investigation of baffle configuration on impedance of channelized debris flow

Channelized debris flows surge downslope in mountainous regions and have large impact forces. Arrays of debris flow baffles are frequently positioned in front of rigid barriers to engage torrents and attenuate flow energy. They are regularly designed on empirical and prescriptive basis because their interaction mechanism is not well understood. Numerical back-analysis of flume experiments using the discrete element method (DEM) is conducted to provide insight on flow interaction with an array of baffles. Varying configurations of baffle height, a second staggered row, and spacing between successive rows are examined. Upstream and downstream kinematics are monitored to capture and compare the Froude number, kinetic energy, and discharge resulting from each baffle configuration. Results from this study reveal that the height of baffles can be categorized relative to the initial approach flow depth (h), namely tall baffles (1.5h) and short baffles (0.75h). Tall baffles are characterized by the development of upstream subcritical flow conditions, whereas short baffles exhibit supercritical upstream conditions. Furthermore, tall baffles facilitate the suppression of overflow, and short baffles lead to excessive overflow that is supercritical in nature. Less flow attenuation occurs as the distance increases both upstream and downstream from each array of baffles. A second staggered row of short staggered baffles is ineffective in reducing debris kinetic energy, whereas tall baffles should be positioned as close as possible.

Choke Performance in High-rate Gas Condensate Wells Under Subcritical Flow Condition

Flow through a surface choke can be described as either critical or subcritical. Most of the correlations available to petroleum engineers are for critical flow but in a lot of high rate gas/condensate wells subcritical flow occurs in large choke sizes. Field data of 15 high rate wells producing from 10 gas condensate reservoirs located in Iran were used to extend two main approaches for high rate wells: a plotting technique proposed by Al-Attar to describe the subcritical flow behavior of gas condensates through wellhead chokes and a general Gilbert-type formula obtained by nonlinear regression of data points for high rate gas condensate wells. The present study extends the work of Al-Attar for high rate gas condensate wells flowing through different large choke sizes between 40/64 and 192/64 in. under subcritical flow conditions, in order to develop individual empirical correlations to be applied to predict gas flow rates under a wide range of flow conditions usually encountered during the flow of gas condensates through wellhead chokes in high rate wells .Also, a new Gilbert-type correlation was generated for high rate Iranian gas condensate wells using nonlinear regression based on the same data points. A comparison between these two approaches is done with five different errors parameters. According to five different errors analysis, the results of gas flow rates calculated by the general formula were compared with those calculated by the individual choke size formulae, and the latter were found to be more accurate. The results of this study could be considered in the design and implementation of deliverability tests, pressure transient tests, well control, and long-term well production of high rate gas condensates wells.

급변류에 의한 하상변동 예측을 위한 수심적분 수치모형

천이류와 같은 급변류에 의한 하상변동을 예측하기 위한 이차정확도의 유한체적법 모형을 제시하였다. 부정류 조건하에서의 유사이송과 하상변동문제에 적용하기 위하여 유사이송모형을 천수방정식과 연계하였다. 지배방정식은 MUSCL 기반의 유한체적법을 이용하였고, 계산요소간 흐름률은 HLLC approximate Riemann solver를 이용하여 계산하였다. 일차원과 이차원 수로에서의 댐붕괴파에 의한 하상변동문제와 월류로 인한 하류부 댐사면의 침식문제에 적용한 결과, 적정한 매개변수를 이용하는 경우에 전반적으로 정확한 수치모의 결과를 얻을 수 있었다. 또한 전반적인 계산결과는 수치적으로 안정적이고 물리적으로 타당한 결과를 나타내었고, 이로부터 제시된 수치모의 기법이 상류와 사류조건하에서의 하상변동 문제에 적용이 가능할 것으로 판단된다. A stable second-order finite volume method was proposed to predict sediment transport under rapidly varied flow conditions such as transcritical flow. For the use under unsteady flow conditions, a sediment transport model was coupled with shallow water equations. HLLC approximate Riemann solver based on a monotone upstream-centered schemes for conservation laws (MUSCL) reconstruction was used for the computation of the flux terms. From the comparisons of dam break flow experiments on erodible beds in one- and two-dimensional channels, good agreements were obtained when proper parameters were provided. Lastly, dam surface erosion problem by overtopped water was simulated. Overall, the numerical solutions showed reasonable results, which demonstrated that the proposed numerical scheme could provide stable and physical results in the cases of subcritical and supercritical flow conditions.

Determination of Shape Co-efficient and Drag Co-efficient of Triangular Piers under Sub-Critical Flow Conditions

Determination of Shape Co-efficient and Drag Co-efficient of Triangular Piers under Sub-Critical Flow Conditions

Free surface and velocity field in a circular channel along the side weir in supercritical flow conditions

A side weir is a kind of flow regulator hydraulic structure which is used in drainage systems, irrigation and sewage disposal network. The passing flow over side weir is a spatial variability flow with discharge reduction. Circular channels with side weir have been used widely for regulating runoff and flood. In this research the flow free surface and the passing flow field through a circular channel with side weir is simulated by commercial software. In this CFD analysis, the RNG k–ε turbulence model is used for simulating the turbulence of the flow field and the free surface changes are modeled using VOF model. Comparison between changes in the free surface, the passing discharge over the weir, the discharge coefficient and the specific energy at the beginning section of side weir obtained from the numerical simulation and experimental results indicates acceptable accuracy of the CFD model in the supercritical regime. Given that most previous numerical studies have been focused on the rectangular channel with side weir and in the subcritical flow condition, the main purpose of this simulation is study of the free surface changes and the velocity field along a side weir located on a circular channel in the supercritical regime.

DISCHARGE COEFFICIENT OF SHARP‐CRESTED SIDE WEIR IN TRAPEZOIDAL CHANNEL WITH DIFFERENT SIDE‐WALL SLOPES UNDER SUBCRITICAL FLOW CONDITIONS

ABSTRACTIn this study, a comprehensive experimental study was performed to find an equation for the estimation of flow discharge over a sharp‐crested side weir in a trapezoidal channel. A physical model with side slopes of 1.5, 1, 0.5 and 0 was used and sharp‐crested side weirs with different lengths and heights were tested under different flow conditions. In this study, 212 laboratory tests were performed with different side‐wall slopes under subcritical flow conditions since the Froude number = 0.08–0.80. As a result, using statistical analysis, a linear relationship is proposed here for estimation of the side‐weir discharge coefficient in a trapezoidal channel. The new equation is a function of the upstream Froude number, weir height and side‐wall slope. The new equation enables estimation of flow discharge over the side weir with consideration of different side slopes. Furthermore, previously proposed discharge relationships for estimation of the discharge coefficient over sharp‐crested side weirs were compared with the new equation and experimental data from this study and this comparison is also reported in this paper. Copyright © 2014 John Wiley & Sons, Ltd.

Wellhead Choke Performance in Oil Well Pipeline Systems Based on Genetic Programming

AbstractThe accurate determination of choke performance in oil pipelines is considered a main challenge for petroleum engineers. This study introduces a new correlation based on genetic programming (GP) to describe choke performance in both critical and subcritical flow conditions in pipeline flow regimes. The GP model is developed using field data collected from various Iranian oil well pipelines. Statistical error parameters are used to compare the accuracy of results obtained from the new correlation with other empirical models. The GP model predicted the choke performance for critical flow condition with relatively lower error (normalized mean square error = 0.006) and higher accuracy (R=0.993%). In addition, the results of the model in a subcritical flow regime showed that the GP model could be applied effectively and yield high accuracy for choke performance pipeline forecasting.

Exponential stability of shallow water equations with arbitrary time dependent action

In this paper, we examine an exponential stability result in \(L^2-\)norm of the classical solution of shallow water equations. By using Riemann analysis with sub-critical flow condition, we show that only one boundary control law suffices to achieve the exponential stability. For that, we provide a sufficient dissipative condition as second order polynomial inequality with respect to the boundary control law which relies on the setting of a non-increasing arbitrary action.

Flow resistance of vegetated oblique weir-like obstacles during high water stages

Abstract. At high water stages, obstacles (submerged and particularly emerged vegetation) in the flood plains of a river contribute to the flow resistance and hamper the conveyance capacity. In particular the elevated vegetated parts are expected to play an important role. The objective of this research work is to determine the form drag due to vegetated oblique weir-like obstacles. Experiments have been performed to measure the energy head losses for a range of subcritical flow conditions, varying discharges and downstream water levels. The energy head loss caused by the submerged vegetated weir-like obstacle has been modeled using an expansion loss form drag model that has been derived from the one-dimensional momentum conservation equation and accounts for the energy loss associated with a deceleration of the flow downstream of a sudden expansion. The results have been compared with the experimental data and showed an overall good agreement.

Discharge coefficient of rectangular sharp-crested side weirs Part II: Domínguez's method

The hydraulic design of a side weir is complicated because the flow conditions vary with distance along the weir, resulting in the 3-D nature of flow over side weirs. Accordingly, by considering the criticism on De Marchi's discharge coefficient formula (Part I), the present study examines a method proposed by Domínguez for estimating the discharge over the side weirs under a subcritical flow condition. Further, on the basis of a comprehensive analysis of the available experimental data, the merits of the practical application of the Domínguez's method were evaluated. The results reveal that the fundamental assumptions of Domínguez, e.g., constant specific energy and linear free surface profile along the side weir in the main channel centerline, are appropriately satisfied. Finally, on the basis of the dimensional analysis, novel correlations were derived for calculating the Domínguez's discharge coefficient with respect to the most significant dimensionless parameters. The estimated results compare well with the results of the model experimentation.

Dune bedforms produced by dilute pyroclastic density currents from the August 2006 eruption of Tungurahua volcano, Ecuador

A series of pyroclastic density currents were generated at Tungurahua volcano (Ecuador) during a period of heightened activity in August 2006. Dense pyroclastic flows were confined to valleys of the drainage network, while dilute pyroclastic density currents overflowed on interfluves where they deposited isolated bodies comprising dune bedforms of cross-stratified ash exposed on the surface. Here, the description, measurement, and classification of more than 300 dune bedforms are presented. Four types of dune bedforms are identified with respect to their shape, internal structure, and geometry (length, width, thickness, stoss and lee face angles, and stoss face length). (1) “Elongate dune bedforms” have smooth shapes and are longer (in the flow direction) than wide or thick. Internal stratification consists of stoss-constructional, thick lensoidal layers of massive and coarse-grained material, alternating with bedsets of fine laminae that deposit continuously on both stoss and lee sides forming aggrading structures with upstream migration of the crests. (2) “Transverse dune bedforms” show linear crests perpendicular to the flow direction, with equivalent lengths and widths. Internally, these bedforms exhibit finely stratified bedsets of aggrading ash laminae with upstream crest migration. Steep truncations of the bedsets are visible on the stoss side only. (3) “Lunate dune bedforms” display a barchanoidal shape and have stratification patterns similar to those of the transverse ones. Finally, (4) “two-dimensional dune bedforms” are much wider than long, exhibit linear crests and are organized into trains. Elongate dune bedforms are found exclusively in proximal deposition zones. Transverse, lunate, and two-dimensional dune bedforms are found in distal ash bodies. The type of dune bedform developed varies spatially within an ash body, transverse dune bedforms occurring primarily at the onset of deposition zones, transitioning to lunate dune bedforms in intermediate zones, and two-dimensional dune bedforms exclusively on the lateral and distal edges of the deposits. The latter are also found where flows moved upslope. Elongate dune bedforms were deposited from flows with both granular-based and tractional flow boundaries that possessed high capacity and competence. They may have formed in a subcritical context by the blocking of material on the stoss side. We do not interpret them as antidune or “chute-and-pool” structures. The dimensions and cross-stratification patterns of transverse dune bedforms are interpreted as resulting from low competence currents with a significant deposition rate, but we rule out their interpretation as “antidunes”. A similar conclusion holds for lunate dune bedforms, whose curved shape results from a sedimentation rate dependent on the thickness of the bedform. Finally, two-dimensional dune bedforms were formed where lateral transport exceeds longitudinal transport; i.e., in areas where currents were able to spread laterally in low velocity zones. We suggest that the aggrading ash bedsets with upstream crest migration were formed under subcritical flow conditions where the tractional bedload transport was less important than the simultaneous fallout from suspension. This produced differential draping with no further reworking. We propose the name “regressive climbing dunes” for structures produced by this process. A rapid decrease in current velocity, possibly triggered by hydraulic jumps affecting the entire parent flows, is inferred to explain their deposition. This process can in principle hold for any kind of particulate density current.Electronic supplementary materialThe online version of this article (doi:10.1007/s00445-013-0762-x) contains supplementary material, which is available to authorized users.

A delayed feedback control for network of open canals

This paper proposes an algebraic method to design time-delay boundary feedback controllers to regulate the water flow and level in a network of open canals. The network is modeled as $$n$$ canals with one junction where all canals come together. The Saint-Venant equations are linearized around a prescribed steady state. We consider steady subcritical flow condition and an energy estimate, to build feedback boundary conditions. These boundary conditions depend on data at earlier times and ensure the exponential decrease in $$L^2$$ -norm of the solution of the linearized model. A single canal is first treated and afterward the analysis is extended to the network. Finally, the controllers are applied numerically to the nonlinear Saint-Venant equations.

Simulation of the ice regime in a Norwegian regulated river

River ice models are commonly used to study ice conditions in wide and low-gradient rivers in cold regions. However, examples of applications of these tools in shallow and fast-flowing rivers are rarely reported. In this study, the one-dimensional model MIKE-Ice was applied to study the ice regime of the regulated river Orkla in Norway. The river Orkla is characterized as a steep and shallow river with sequences of pools and riffles throughout its length. The model was calibrated and validated for the winters, 2010–2011 and 2011–2012 respectively. The study shows that the model is applicable in a steep river with transects of both subcritical and supercritical flow conditions, which is a different environment than most previously reported applications of river ice models. The simulated hydrodynamics and water temperature show good agreement with observations. The model was further tested on its ability to simulate the presence/absence of frazil ice and the development of an ice cover at observation points in the river using continuous monitoring with cameras. The ability to correctly simulate the ice cover extent of the entire model domain was also tested based on a number of field campaigns. The ice simulation results correspond well with observations both spatially and temporally. Further, two discharge scenarios were simulated: a) No hydropower regulation, and b) reduced hydropower operation: to assess the impact of the regulation and to explore the sensitivity of the model. The simulation results demonstrate how hydropower regulation has altered the thermal and ice regimes. The study concludes that Mike-Ice is a useful tool for predicting the river regime in the river Orkla, where dynamic ice formation is a dominant process.

LIVE BED SCOUR AT A SIDE‐WEIR INTERSECTION LOCATED ON AN ALLUVIAL CHANNEL

ABSTRACTThis study aims to obtain both the depth of clear water and live bed scour around side‐weirs located on an alluvial channel for sharp‐crested side‐weirs under subcritical flow conditions. At the downstream end of the side‐weir, a longitudinal bar in the middle of the channel and a scour hole close to the outer bank are formed because of changes in shear stress field and velocities. Dimensionless depth of scour increases with an increase of the dimensionless parameters of flow depth, side‐weir length and sediment size. The dimensionless depth of scour increases almost linearly with the dimensionless parameter of flow velocity for clear water scour, and it decreases for live bed conditions at the straight channel due to the decreasing deviation angle and kinetic energy toward the side‐weirs and bed material coming from upstream of the main channel. Because of the effect of the helicoidal flow created by bends, the dimensionless depth of scour fluctuated with the dimensionless parameter of flow velocity at the maximum value of clear water scour for movable bed conditions at a bend. At the 30° section of a bend, the equilibrium depth of scour is achieved as maximum values due to the deviation on the path of maximum velocity towards the outer bank. Copyright © 2013 John Wiley & Sons, Ltd.

An experimental study of turbulence in a heterogeneous channel

This paper examines the velocity field in an idealised heterogeneous open channel during normal flow conditions, corresponding to two different subcritical flow conditions (discharges of 0·040 m3/s and 0·056 m3/s, with corresponding Froude numbers 0·51 and 0·57). The bed of the channel is formed of two full-length, longitudinal strips of equal width, a smooth section constructed from polyvinyl chloride and a rough section constructed from gravel (d72 = 10 mm). The results indicate that the turbulence appears to propagate vertically from the rough bed and horizontally over the rough–smooth boundary. There is also evidence to suggest that the turbulent momentum transfer is maximised at the rough–smooth boundary. Secondary flow structures are seen to exist due to the rough–smooth boundary and provide another mechanism for momentum transfer. These transfer mechanisms are important in understanding the effect of a heterogeneous channel bed on open-channel flow.

Discharge coefficient for compound sharp crested side weirs in subcritical flow conditions

Summary Side weirs are one of the most common diversion structures used for flow control, irrigation, drainage networks, and waste-water channels. Side weirs are generally rectangular sharp crested in form and hence, have some limitations in precise flow measurement. For accurate flow measurement and management in wide range of discharges, use of compound side weirs are suggested in this study. Experiments have been carried out in a rectangular compound side weir with variable heights and widths. It was determined that discharge coefficient of a compound side weir is a function of upstream Froude number (Fr1), ratio of weighted crest height of weir to upstream water depth w ¯ / y 1 and ratio of weir length to upstream water depth (L/y1). Based on the experimental data and regression modeling, a dimensionless equation has been developed for prediction of the discharge coefficient and an equation has been proposed for estimation of flow discharge in compound rectangular sharp crested side weirs. Through comparison of results of these equations and experimental data, good agreement was achieved. The mean and maximum relative errors of the discharge equation were −2.3% and 10.7%, respectively.

Flow Resistance of Vegetated Weirlike Obstacles during High Water Stages

The objective of this study is to estimate, model, and parameterize the form drag due to vegetated weirlike obstacles. An experimental study has been carried out for validation purposes. The prototype weirlike structure (in the form of a dike or groyne) has been modeled as a weir with various downstream slopes (1:4, 1:7, 1:15), and vegetation has been represented in various shapes placed on top of the crest of the weir with 25% blockage area inside the vegetated region. Measurements for energy head losses are carried out for a range of discharges and downstream water levels covering submerged and subcritical flow conditions. The energy head loss attributable to submerged vegetated dikes and groynes can be modeled well by an expansion loss form drag model, which is based on a one-dimensional energy and momentum conservation equations.

Reverse flow routing in open channels: A Bayesian Geostatistical Approach

Summary Reverse flow routing in open channels is a procedure of practical interest: it allows to obtain hydrographs in upstream ungauged stations by means of information available at downstream monitored sites. In this paper a Bayesian Geostatistical Approach for reverse flow routing in open channels is presented. The capabilities of the methodology are shown by means of synthetic test cases. Input hydrographs of different shape were routed downstream using a numerical flow model that solves the one dimensional De Saint Venant equations; the resulting outflow hydrographs were, in almost all the cases, corrupted with random errors and then used for the inversion. Both prismatic and non-prismatic irregular channels, under subcritical flow conditions, were analyzed as well. The considered non-prismatic channel with irregular cross sections and variable friction coefficients represents a very practical situation that can be encountered in the field. The results show that the proposed methodology is able to properly reproduce the input inflows even in presence of errors affecting the downstream discharges up to 10%.

A discharge coefficient for a trapezoidal broad-crested side weir in subcritical flow

An experimental investigation of the flow over trapezoidal broad-crested side weir in rectangular channels under subcritical flow conditions is reported. It was found that the discharge coefficient of a trapezoidal broad-crested side weir is related to the Froude number at the upstream of the weir, ratios of weir height to depth of flow, weir length to width of main channel and length of broad-crested weir to width of main channel for different side slopes. Additionally, a reliable equation for calculating the discharge coefficient of trapezoidal broad-crested side weirs is presented.