Hydraulic performance of multiple and single LOPAC gates

In this study, the authors investigate effective soil hydraulic parameter averaging schemes for steady-state flow in heterogeneous shallow subsurfaces useful to land–atmosphere interaction modeling. “Effective” soil hydraulic parameters of the heterogeneous shallow subsurface are obtained by conceptualizing the soil as an equivalent homogeneous medium. It requires that the effective homogeneous soil discharges the same mean surface moisture flux (evaporation or infiltration) as the heterogeneous media. Using the simple Gardner unsaturated hydraulic conductivity function, the authors derive the effective value for the saturated hydraulic conductivity Ks or the shape factor α under various hydrologic scenarios and input hydraulic parameter statistics. Assuming one-dimensional vertical moisture movement in the shallow unsaturated soils, both scenarios of horizontal (across the surface landscape) and vertical (across the soil profile) heterogeneities are investigated. The effects of hydraulic parameter statistics, surface boundary conditions, domain scales, and fractal dimensions in case of nested soil hydraulic property structure are addressed. Results show that the effective parameters are dictated more by the α heterogeneity for the evaporation scenario and mainly by Ks variability for the infiltration scenario. Also, heterogeneity orientation (horizontal or vertical) of soil hydraulic parameters impacts the effective parameters. In general, an increase in both the fractal dimension and the domain scale enhances the heterogeneous effects of the parameter fields on the effective parameters. The impact of the domain scale on the effective hydraulic parameters is more significant as the fractal dimension increases.

Regulators and other hydraulic structures are essential for managing flow in open channels. However, improper operation of these structures' gates can lead to unpredictable and potentially damaging scour patterns. This study investigates the optimal operation of the Kalat Saleh Regulator's gates in Iraq, focusing on sediment movement and sedimentation issues. Using Flow-3D software and the RNG turbulent model, sediment movement was simulated under various flow conditions and gate opening scenarios. The study found that the number of open gates and their operational sequence significantly affect scour development downstream of the regulator. Specifically, the maximum scour depth was observed when a single gate was opened, resulting in an eight-fold increase compared to the scenario where all gates were opened at a flow rate of 125 m³/s. Additionally, a direct correlation between flow rate and scour depth was established, with the maximum scour depth recorded at -2.6 m for a flow rate of 75 m³/s, and -4.41 m for a flow rate of 125 m³/s, representing a 1.7-fold increase. These findings suggest that careful management of gate operations can mitigate the risk of excessive scouring, which has practical implications for the design and operation of similar hydraulic structures. By optimizing gate operations, it may be possible to reduce sediment-related issues, enhance structural integrity, and improve the efficiency of water flow management in open channels.

Guidelines of effective soil hydraulic parameters were developed to be applicable in simulating average infiltration and subsequent moisture redistribution over a large-scale heterogeneous field. Average large-scale infiltration and redistribution in heterogeneous soils were quantified through multiple simulations of local-scale processes. The effective hydraulic parameters were derived to simulate the average amount of infiltrating water, and to capture the subsequent surface soil moisture redistribution averaged over the large heterogeneous landscape. The results demonstrated that the effective hydraulic parameters typically exhibited a step change from infiltration to redistribution, with the size of the step change being related to the degree of hydraulic parameter heterogeneity and the correlations among the hydraulic parameters. However, the effective hydraulic parameters did not change significantly over time for the moisture redistribution. It was further demonstrated that the size of the step change was smallest for effective saturated hydraulic conductivity. Editor Z.W. Kundzewicz; Associate editor Y. Guttman Citation Zhu, J.T. and Sun, D.M., 2012. Soil hydraulic properties for moisture redistribution in a large-scale heterogeneous landscape. Hydrological Sciences Journal, 57 (6), 1196–1206.

This study investigated the use of effective soil hydraulic properties (expressed in terms of hydraulic parameters) applicable to large‐scale transient infiltration problems in a landscape with horizontally heterogeneous soil hydraulic properties. The heterogeneous landscape was conceptualized as an equivalent homogeneous medium with effective hydraulic properties. The main objectives were to investigate: (i) which effective soil hydraulic property schemes are suitable to represent average behavior of large‐scale infiltration processes, (ii) how the effective hydraulic parameters are sensitive to the process time frame, and (iii) how hydraulic parameter variability and correlation impact the effective hydraulic parameters. The heterogeneous landscape was represented by a series of vertically homogeneous stream tubes or parallel columns. Large‐scale average infiltration behavior in the heterogeneous soils was quantified through Monte Carlo simulations of multiple realizations (stream tubes) of local‐scale infiltration. The optimal effective hydraulic parameters were then calculated with an inverse procedure that minimized the difference between average cumulative infiltration and cumulative infiltration based on a single set of effective parameters. Three scenarios were used to optimize either two hydraulic parameters simultaneously or only one hydraulic parameter while using the arithmetic mean for the other parameter. Results indicate that while the effective hydraulic parameters could simulate average infiltration more closely when multiple parameters were optimized together, the effective parameter values were more variable as time evolved. Optimizing only one hydraulic parameter while keeping the arithmetic mean for the other parameter produced more uniform effective hydraulic parameters with time, but this approach did not represent average infiltration behavior of the heterogeneous soils as well as when multiple hydraulic parameters were optimized simultaneously.

Estimation of effective hydraulic parameters in heterogeneous soils at field scale

The study investigated the simulation of flow characteristics over an Ogee-type spillway surface. This research utilizes a Flow-3D numerical model that builds upon the findings from prior experimental data and numerical models simulated by Ansys with a Flow-3D k-epsilon turbulence model. It utilizes Flow-3D methods with RNG and LES turbulence models to analyze flow rate, water profile, pressure, shear stress, and velocity at seven points along the spillway. The study reports strong agreement between the RNG turbulence model's numerical results and experimental data, demonstrating that the numerical model accurately reflects the physical flow behavior. As the discharge increases, the pressure distribution decreases, demonstrating a clear relationship between flow rate and pressure distribution along the spillway. This analysis highlights two negative pressure regions: one at the Ogee curve and the other at the end of the sloping straight section beyond the curve. Error analysis reveals closely aligned results, comparing experimental data with Ansys simulations across various turbulence models for seven sensors. The mean absolute error (MAE) values for Ansys, k-epsilon, RNG, and LES are 0.0261, 0.0252, 0.0268, and 0.0278, respectively, while root mean squared error (RMSE) values are 0.0269, 0.0279, 0.0283, and 0.0299, respectively, indicating good consistency with experimental findings. Additionally, comparisons of velocity distribution within Flow-3D, utilizing models such as k-epsilon, RNG, and LES, reveal MAE values of 0.0846 for RNG and 0.1382 for LES, alongside RMSE values of 0.0984 for RNG and 0.1552 for LES, highlighting the precision of the data. This study highlights the flow dynamics of Ogee spillways, demonstrating Flow 3D's accuracy in modeling discharge, design effects on pressure distribution, and cavitation risk.

Overflow structures are among the most important hydraulic structures used for measuring flow, controlling floods in reservoirs, and regulating water levels in open channels. Alternative options, such as combined structures like spillway-gates, are preferred due to their compatibility with natural and ecological needs. This study investigates the impact of different soil gradations downstream on the scouring profile of combined spillway-gate structures. Scouring and sedimentation downstream of the spillway-gate were examined under various particle sizes of 0.0008, 0.001, and 0.0014 m, with a constant density in both free and submerged flow conditions using the FLOW-3D software. In this study, the k-ε, k-ω, LES, and RNG turbulence models were evaluated, and the RNG turbulence model was selected among that group. In free flow conditions, the highest sediment deposition occurred with the smallest particle diameter. For larger particle diameters, the void spaces between the particles reduce friction and increase the movement threshold, leading to increased scouring and decreased sediment height. In submerged flow conditions, the changes in scouring for different particle sizes were minor, with results being closely aligned. In submerged flow conditions, increasing the particle diameter resulted in a decrease in sediment deposition in the post-scouring area.

In this study we investigate effective soil hydraulic parameter averaging schemes for steady‐state flow with plant root water uptake in heterogeneous soils. “Effective” soil hydraulic parameters of a heterogeneous soil formation are obtained by conceptualizing the soil as an equivalent homogeneous medium. The “effective” homogeneous medium is only required to discharge the same ensemble‐mean flux across the soil surface. One‐dimensional flow at the local scale has been used as an approximation for various simplified problems under investigation (e.g., a shallow subsurface dominated by vertical flows). The domain is assumed to be composed of homogeneous one‐dimensional soil columns without mutual interactions. Using Gardner's unsaturated hydraulic conductivity model, we derive the effective value for the parameter α. While root water uptake influences the overall water budget, its impact on the effective hydraulic parameter averaging scheme was found to be secondary. Results show that the arithmetic mean of Gardner's α is usually too large to serve as an effective parameter. Deviations of the effective parameter from the arithmetic mean become larger as the surface suction increases; that is, the flow scenario switches from infiltration to evaporation. The results consistently show a smaller effective parameter for evaporation scenarios than for infiltration scenarios. The effective parameter α eff decreases with an increase in the mean value of α. Spatial variability in α also decreases the effective value of α eff Alternative root water uptake distributions do not produce significant differences in both the water budget and the averaging scheme as long as total water loss to the plant roots remains the same.

In this study we investigate effective soil hydraulic parameter averaging schemes for steady-state flow with plant root water uptake in heterogeneous soils. “Effective” soil hydraulic parameters of a heterogeneous soil formation are obtained by conceptualizing the soil as an equivalent homogeneous medium. The “effective” homogeneous medium is only required to discharge the same ensemble-mean flux across the soil surface. One-dimensional flow at the local scale has been used as an approximation for various simplified problems under investigation (e.g., a shallow subsurface dominated by vertical flows). The domain is assumed to be composed of homogeneous one-dimensional soil columns without mutual interactions. Using Gardner9s unsaturated hydraulic conductivity model, we derive the effective value for the parameter α. While root water uptake influences the overall water budget, its impact on the effective hydraulic parameter averaging scheme was found to be secondary. Results show that the arithmetic mean of Gardner9s α is usually too large to serve as an effective parameter. Deviations of the effective parameter from the arithmetic mean become larger as the surface suction increases; that is, the flow scenario switches from infiltration to evaporation. The results consistently show a smaller effective parameter for evaporation scenarios than for infiltration scenarios. The effective parameter α eff decreases with an increase in the mean value of α. Spatial variability in α also decreases the effective value of α eff . Alternative root water uptake distributions do not produce significant differences in both the water budget and the averaging scheme as long as total water loss to the plant roots remains the same.

The turbine flow meter is widely used in the flow rate measuring for its high accuracy and good repeatability. The flow rate will be calculated based on its meter factor, which is the most important factor of the turbine flow meter. The meter factor means pulses or revolution of the impeller per unit volume, and it can only be got from the calibration experiment. At the given flow rate, the driving torque on the impeller is equal to the drag torque, as many paper have pointed out. Based on the torque balancing equations, unsteady numerical simulation is carried out with RNG turbulence model and UDFs (User Defined Functions) in Fluent Code. The meter factor under different flow rate is calculated with the unsteady simulation. The prediction results based on the numerical simulation showed the same trends as the calibration experiment. At the most flow rate, the meter factor keeps constant, but at the lower flow rate, the meter factor higher than the constant. Because of neglecting the bearing friction drag in the process, the meter factor by numerical simulation is larger than experiment.

In hydroclimate and land‐atmospheric interaction models, effective hydraulic properties are needed at large grid scales. In this study, the effective soil hydraulic parameters of the areally heterogeneous soil formation are derived by conceptualizing the heterogeneous soil formation as an equivalent homogeneous medium and assuming that the equivalent homogeneous soil will approximately discharge the same total amount of flux and produce same average pressure head profile in the formation. As compared to previous effective hydraulic property studies, a specific feature of this study is that the derived effective hydraulic parameters are mean‐gradient‐dependent (i.e., vary across depth). Although areal soil heterogeneity was formulated as parallel homogeneous stream tubes in this study, our results appear to be consistent with the previous findings of mean‐gradient unsaturated hydraulic conductivity [Yeh et al., 1985a, 1985b]. Three widely used hydraulic conductivity models were employed in this study, i.e., the Gardner model, the Brooks and Corey model, and the van Genuchten model. We examined the impact of parameter correlation, boundary condition (surface pressure head), and elevation above the water table on the effective saturated hydraulic conductivity and shape parameter. The correlation between the saturated hydraulic conductivity Ks and the shape parameter α increases the effective saturated hydraulic conductivity, while it does not affect the effective α. The effective α is usually smaller than the mean value of α, while the effective Ks can be smaller or larger than the mean value depending on no correlation or full correlation between Ks and α fields, respectively. An important observation of this study is that Gardner and van Genuchten functions resulted in effective parameters, whereas it is difficult to define effective parameters for the Brooks Corey model since this model uses a piecewise‐continuous profile for hydraulic conductivity.

Upscaled soil hydraulic properties are needed for many large‐scale hydrologic applications such as regional and global climate studies and investigations of land–atmosphere interactions. Many larger scale subsurface flow and contaminant transport studies also require upscaled hydraulic property estimates. The objectives of this study were to develop a methodology for upscaling hydraulic property functions using a p‐norm approach, to examine how p‐norm values differ for two commonly used soil hydraulic property models (the Gardner and van Genuchten functions), and to investigate the relative sensitivities of p‐norms and the effective hydraulic parameters to the degree of soil heterogeneity (expressed in terms of variances and auto‐correlation lengths of the hydraulic parameters) and other environmental conditions. The p‐norm approach expresses upscaling schemes such that it reduces their sensitivity to uncertainties (heterogeneities) in site conditions. The upscaling schemes are obtained as the result of two new criteria proposed to upscale soil hydraulic properties in this study—one preserving the ensemble vertical moisture flux across the land–atmosphere boundary, and a second preserving the ensemble soil surface moisture content. The effective soil hydraulic parameters of a heterogeneous soil formation are then derived by conceptualizing the formation as an equivalent homogeneous medium that satisfies the upscaling criteria. Upscaling relationships between the Gardner and van Genuchten models can then also be established for steady‐state vertical flow using the statistical structures of the hydraulic parameters of these two models as estimated from field measurements. The upscaling scheme is demonstrated using hydraulic property data collected at 84 locations across a site in the Mojave Desert. Our results show that the p‐norms generally vary less in magnitude than the effective parameters when the variances of the hydraulic parameters increase. We also show that, in general, p‐norm values are better defined for the van Genuchten model than the Gardner model. Hydraulic parameter auto correlations, as defined by correlation lengths, were found to have little impact in relating the upscaling schemes (p‐norm values) for the two hydraulic property models, but correlation between the hydraulic parameters within the hydraulic property models can significantly affect p‐norm relationships.

This paper proposes an improved gating system design for casting process using experimental and simulation studies. The principle motivation behind optimization of gating system is to overcome the defects like shrinkage, gas porosity, slag, inclusion, cold shuts and misruns etc. Four different designs having different sprue location and runner cross-sectional area are taken into considerations for study. Discharge through multiple gates which are connected to horizontal runner has been evaluated as a performance parameter for comparing the designs. Experiments are conducted by tap and collect method using water and the volume of flow through each gate is observed for all designs. A simulation-based study is carried out for all four designs on finite-volume commercial code FLUENT. Boundary and initial conditions, such as velocity, pressure, temperature, etc., was reasonably set. It is found that the flow rate, as well as average velocity through the farthest gate, is higher for the parallel runner while this difference gets reduced with a tapered runner. Furthermore, design with a central position of sprue also minimizes the difference in flow rates as well as velocity. Finally, a design with a tapered cross-sectional area and justified position, as well as orientation of different gates, is finding out to be optimum having balance flow rate through the four gates with less filling time.

In the present study, an artificial neural network and its combination with wavelet theory are used as the computational tool to predict the depth of local scouring from the bridge pier. The five variables measured are the pier diameter of the bridge, the critical and the average velocities, the average diameter of the bed aggregates, and the flow depth. In this study, the neural wavelet method is used as a preprocessor. The data was passed through the wavelet filter and then passed to the artificial neural network. Among the various wavelet functions used for preprocessing, the dmey function results in the highest correlation coefficient and the lowest RMSE and is more efficient than other functions. In the wavelet-neural network compilation method, the neural network activator function was replaced by different wavelet functions. The results show that the neural network method with the Polywog4 wavelet activator function with a correlation coefficient of 87% is an improvement of 8.75% compared to the normal neural network model. By performing data filtering by wavelet and using the resulting coefficients in the neural network, the resulting correlation coefficient is 82%, only a 2.5% improvement compared to the normal neural network. By analyzing the results obtained from neural network methods, the wavelet-neural network predicted errors compared to experimental observations were 8.26, 1.56, and 1.24%, respectively. According to the evaluation criteria, combination of the best effective hydraulic parameters, the combination of wavelet function and neural network, and the number of neural network neurons achieved the best results.

In this paper we give reconstruction algorithms for depth-3 arithmetic circuits with $k$ multiplication gates (also known as $\Sigma\Pi\Sigma(k)$ circuits), where $k=O(1)$. Namely, we give an algorithm that when given a black box holding a $\Sigma\Pi\Sigma(k)$ circuit $C$ over a field $\F$ as input, makes queries to the black box (possibly over a polynomial sized extension field of $\F$) and outputs a circuit $C'$ computing the same polynomial as $C$. In particular we obtain the following results. 1) When $C$ is a multilinear $\Sigma\Pi\Sigma(k)$ circuit (i.e. each of its multiplication gates computes a multilinear polynomial) then our algorithm runs in polynomial time (when $k$ is a constant) and outputs a multilinear $\Sigma\Pi\Sigma(k)$ circuits computing the same polynomial. 2) In the general case, our algorithm runs in quasi-polynomial time and outputs a generalized depth-3 circuit (as defined in \cite{KarninShpilka08}) with $k$ multiplication gates. For example, the polynomials computed by generalized depth-3 circuits can be computed by quasi-polynomial sized depth-3 circuits. In fact, our algorithm works in the slightly more general case where the black box holds a generalized depth-3 circuits. Prior to this work there were reconstruction algorithms for several different models of bounded depth circuits: the well studied class of depth-2 arithmetic circuits (that compute sparse polynomials) and its close by model of depth-3 set-multilinear circuits. For the class of depth-3 circuits only the case of $k=2$ (i.e. $\Sigma\Pi\Sigma(2)$ circuits) was known. Our proof technique combines ideas from [Shpilka09] and [KarninShpilka08] with some new ideas. Our most notable new ideas are: We prove the existence of a unique canonical representation of depth-3 circuits. This enables us to work with a specific representation in mind. Another technical contribution is an isolation lemma for depth-3 circuits that enables us to reconstruct a single multiplication gate of the circuit.