Circular-crested Weir Research Articles

Experimental investigation of flow characteristics over asymmetric Joukowsky hydrofoil weirs for free and submerged flow

Weirs are one of the most common hydraulic structures used to regulate the upstream approach flow depth and measure the flow discharge. The hydrofoil weirs are a type of short-crested weirs that are designed based on the airfoil theory. These weirs have some merits compared to other types, such as a higher discharge coefficient, more stability, better submergence limiting condition, and lower fluctuations of the pressure and the free-surface profile. In the present study, experimental models of hydrofoil weirs with different relative eccentricities, cambers, angles of attack, and upstream slope angles are applied to investigate their hydraulic characteristics under free and submerged flow conditions. The longitudinal profiles of static pressure over different hydrofoil weirs are compared to circular-crested and ogee weirs. The results indicate that the maximum bed negative pressure belongs to the circular-crested weir, and the lowest bed pressure over the hydrofoil and ogee weirs are approximately the same. Applying a hydrofoil weir with an appropriate curvature and angle of attack instead of a circular-crested weir not only increases the structural weir height as well as the upstream water depth but also results in the lowest values of bed negative pressure, thereby reduces the potential of cavitation over the weir body, being safer hydraulic structures. The results also show that the discharge coefficient of hydrofoil weirs is greater than that of the broad- and short-crested weirs for the upstream approach flow depth relative to the weir crest to weir length h1/L > 0.12 and is greater than that of the ogee weirs for 0.35 < h1/L < 0.45. Furthermore, the derived relationships for the discharge coefficient, threshold submergence, and the discharge reduction factor due to submergence accurately predict the hydraulic characteristics of hydrofoil weirs compared to the available developed empirical relationships for these weirs and can be used efficiently for design purposes.

Uncertainty analysis of discharge coefficient of circular crested weirs

The circular crested weir (CCW) has been introduced as weirs having a high discharge coefficient (Cd). The ratio of flow head to the radius of the crest (H/R) is the most important parameter affecting the Cd, that the {text{Cd}} approx aleft( {H/R} right)^{b} can mathematical model their relation. In this study, the parameters of the Cd formula (i.e., a and b) were uncertainty analyzed using Monte Carlo (MC) and Bootstrap methods (BM). To perform these methods, some of the built-in functions of Excel software were utilized. The results declared that the average values of a and b were 1.187 and 0.140. The outcome of the MC method showed that the range of a and b at 95% confidence interval changed between 1.179 to 1.194 and 0.134 to 0.146, respectively, while at the same confidence interval the BM ranged from 1.187 to 1.200 and 0.133 to 0.147.

Simulation of free surface flow over the streamlined weirs

The streamlined weirs are a special type of weirs, designed on the basis of airfoil theory. Because of their particular design, they have some merits compared to the other types of weirs, such as; high discharge coefficient, more stability of overflow and less fluctuations of water free surface. In the present study, a numerical simulation performed using an open source software namely, OpenFOAM, to give details about the flow structure over, up- and downstream of these weirs. Also, an experimentation setup was devised to evaluate the numerical results and determine the best numerical model. Analyzing the results of different turbulence models including; standard k-ε, realizable k-ε, RNG k-ε, k-ω SST, and Reynolds stress LRR, indicated that all the aforementioned models accurately estimate the flow field and hydraulic parameters. However, the k-ω SST model gives more accurate results, very close to the experimental data especially for the Reynolds stresses. Accordingly, the k-ω SST turbulence model was chosen as the best turbulence model for analyzing the flow over the streamlined weirs. Numerical results for different relative eccentricities show that, by increasing the relative eccentricity, the flow velocity over the crest of the weirs increases and accordingly the pressure in such section decreases. For a constant flow discharge upstream of different types of the streamlined weirs, the lowest bed pressure and the most probable potential of cavitation belongs to a circular-crested weir (a streamlined weir with a relative eccentricity of unity). Furthermore, the greatest bed shear stresses and the compressive forces occur downstream of the circular-crested weir. Thus, downstream of a circular-crested weir is responsible for larger potential of bed erosion. This is partly due to the formation of shock waves, reduction of the flow depth, and enhancement of the flow velocity downstream of a circular-crested weir. Moreover, the lowest bed shear stresses were observed upstream of the circular-crested weir. Therefore, upstream of a circular-crested weir shows the greatest potential of sedimentation. Finally, applying the streamlined weirs with an appropriate curvature, diminishes the unfavorable flow conditions, as observed for the circular-crested weir, being the safer and economic hydraulic structures.

Analysis of Overflow Characteristics around a Circular-Crested Weir by Using Numerical Model

The present study used the hydrodynamic numerical model, with the Reynolds-averaged Navier-Stokes equations (RANS) as its governing equations, to analyze overflow characteristics such as the discharge coefficient of circular-crested weir and the flow velocity and pressure distribution of weir crest. The simulation results well reproduced the overflow characteristics of the overfall of circular-crested weir both qualitatively and quantitatively. As for the discharge coefficient, rational results were yielded by the discharge coefficient equation proposed by Hager(1985) in the and by the discharge coefficient equation proposed by Samani and Bagheri(2014) in the >, respectively. Because most existing discharge coefficient equations were developed by disregarding the effects of the approach velocity, when they are applied, it is necessary to evaluate the effects of the approach velocity on the overflow head beforehand.

Application of convex streamline theory to circular-crested weir

Circular-crested weirs are overflow structures that can be used for flow measurement, water level control in open channels and flood control in reservoirs. Combining Newton's second law for a rectangular fluid particle on a convex streamline with Bernoulli's equation, the differential equation of velocity profile at crest section of circular-crested weir is obtained. This equation was used to derive the discharge coefficient, crest velocity profile and crest pressure profile of the weir. A wide range (0.44 ≤ H/R ≤ 7.56) of existing experimental data of circular-crested weir is used to evaluate the obtained equations. Results of the study indicated that obtained equations have good agreement with experimental data. Also, in comparison with Dressler and potential flow theories, proposed theory predicts the crest velocity profile with the better precision.

Effect of Weir Face Angles on Circular-Crested Weir Flow

The standard circular-crested weir is often found in engineering applications and is used as a discharge measurement device or as an overflow structure. This research determines the discharge coefficients for ten circular-crested weir configurations with various combinations of up- and downstream angles. Two different weir heights and four different overflow depths are considered for each weir shape. For free overflow, the discharge coefficient is determined experimentally by using the total head of the approach flow. The results indicate that the upstream weir face angle has only a small effect on the discharge coefficient. In contrast, increasing the downstream weir face angle increases the discharge coefficient notably. A new formula for the discharge coefficient is presented, including both the up- and downstream weir face angles. Further, the hydraulic performance of the circular-crested weir, the resulting discharge reduction from tailwater submergence, and transition flow are discussed.

Overflow characteristics of circular-crested weirs

Circular-crested weirs are one of simplest types of hydraulic structures used for discharge measurement and regulation of open channel flow. In the present study, the flow over a circular-crested weir was simulated with an irrotational vortex to determine the weir discharge coefficient and velocity values over the crest. Two dimensionless parameters including circulation and curvature coefficient were defined and determined experimentally. The results show that these parameters could be presented by power equations. To develop and evaluate the proposed method, physical models of circular-crested weirs, containing various radii, heights and slopes, were investigated. It was found that this method produces the main features of weir flow reasonably well.

Higher order critical flow condition in curved streamline flow

A new extended Bernoulli energy equation, which is valid for moderately curved channel flows, is presented. From this generalized energy equation, a higher order critical flow condition valid for curved streamline flow was developed. As a practical application, the flow over a circular-crested weir was studied. The proposed new critical flow theory improves the results of a previous lower order theory up to a dimensionless specific energy of 2, thus obtaining accurate results in situations in which the velocity is non-uniform, the pressure non-hydrostatic, and the conventional critical flow theory not valid.

Overflow Characteristics of Circular Weirs: Effects of Inflow Conditions

The most common types of weirs are the broad-crested weir, the sharp-crested weir, the circular-crested weir and nowadays the ogee crest weir. Advantages of the cylindrical weir shape include the stable overflow pattern, the ease to pass floating debris, the simplicity of design compared to ogee crest design and the associated lower costs. In this study, the authors describe new experiments of circular weir overflows, with eight cylinder sizes, for several weir heights and for five types of inflow conditions : partially-developed inflow, fully-developed inflow, upstream ramp, upstream undular hydraulic jump and upstream (breaking) hydraulic jump. Within the range of the experiments, the cylinder size, the weir height D/R and the presence of an upstream ramp had no effect on the discharge coefficient, flow depth at crest and energy dissipation. But the inflow conditions had substantial effects on the discharge characteristics and flow properties at the crest. Practically the results indicate that discharge measurements with circular weirs are significantly affected by the upstream flow conditions.

Characteristics of Circular‐Crested Weir

The circular-crested weir is used for flow measurement and has wide applications in hydraulic engineering, where it serves as an overflow structure. It can be used to control the water level in farm ponds and reservoirs. The discharge coefficient of such a weir is obtained experimentally as a function of the dimensionless total head of the approaching flow. It is shown that changing the upstream slope does not alter the weir-discharge coefficient. However, increasing the downstream weir slope appears to increase the discharge coefficient. The weir crest pressure is determined as a function of the dimensionless head and its variation is related to the weir-discharge coefficient. The experimental data indicate that the circular-crested weir behaves like a sharp-crested weir, when the dimensionless total head is extremely large.

Application of Dressler Theory to Weir Flow

The curvilinear flow past a circular-crested weir is analyzed with the help of Dressier equations. Specifically, the lower range of the depth over the weir crest is considered in the analysis, so that the shallow depth model could be adopted. The weir discharge coefficient is determined as a function of the total head of the approach flow and the crest radius. The weir discharge coefficient obtained on the basis of Dressier theory is verified with the help of present and previous experimental data.