Experimental study of effect of creating an additional cycle along the lateral crest of the labyrinth weirs

One of the practical and economical ways to enhance the discharge capacity is to use labyrinth weirs. The longer crest length in labyrinth weirs than in linear weirs has caused these weirs to have both a higher discharge coefficient and water discharge capacity than a linear weir. In the present study, the discharge coefficient of trapezoidal and triangular labyrinth weirs was investigated by creating an additional cycle along the lateral crest of the weir. By constructing 10 physical models of labyrinth weirs, tests were performed in the hydraulic and sediment laboratory of the Khuzestan Water and Power Authority (KWPA). Dimensional analysis by the Buckingham method revealed the discharge coefficient (Cd) as a function of variable parameters such as the total hydraulic head to weir height ratio (Ht/P) and weir shape factor (Sf). The results of experimental tests showed that at the hydraulic head ratio (Ht/P) of 0.1, the TP weir had a higher discharge coefficient of 3.5% than the TPTPO weir and 2.5% than the TPTRO weir. However, at a hydraulic head ratio of 0.12, the TR weir had a lower discharge coefficient of 4.6% than the TRTPO weir and 6.9% compared to the TRTRO weir. For the hydraulic head ratio of 0.14, the TRTPI weir was 5.8% and the TRTRI weir was 9.4% higher than the TR weir. Statistical analysis using SPSS indicated that TRTPO and TPTRO weirs had the highest correlation with the cubic model.     

Flow characteristics over asymmetric triangular labyrinth side weirs

Side weir is placed at the channel bank as a head regulator or a diversion device. Flow over a side weir has been the subject of many research studies considering its three dimensional and complicated characteristics. However, the labyrinth side weirs warrant further research due to their higher efficiency compared to linear side weirs. In this paper, subcritical flow characteristics and discharge coefficient for both symmetric and asymmetric triangular labyrinth side weirs were studied experimentally. The results show that asymmetric labyrinth side weirs have higher discharge coefficient compared to symmetric labyrinth side weirs; since a larger portion of the crest is orthogonal to the flow. Using the present laboratory data, general equations were proposed for the estimation of discharge coefficient of both symmetric and asymmetric triangular labyrinth side weirs. The results of this study can be useful to design side weirs with high hydraulic performance.     

Evaluation of flow characteristics in labyrinth weirs using response surface methodology

Labyrinth weirs can increase the flow discharge capacity for a specific head and width by increasing the weir length. This paper studies the flow behavior of labyrinth weirs using Flow-3D® software. The main goal is to evaluate the capability of the response surface methodology (RSM), especially central composite design (CCD), to describe the performance of labyrinth weirs. Traditional and RSM-CCD methodologies are applied using experimental data of previous researchers and numerical data of the present study, respectively. Results show that RSM-CCD can produce an acceptably accurate model for the discharge coefficient of labyrinth weirs with only a small fraction of the data required for the traditional model. In addition, the discharge coefficient of a labyrinth weir decreases by increasing head and decreasing sidewall angle due to the inflow contraction and nappe interference in inlet and outlet cycles, respectively. The discharge efficiency can be up to 4.5 times higher for a labyrinth weir compared to a linear weir. Finally, a new method is introduced for designing labyrinth weirs.     

Reliability-based design optimization of slider air bearings

This paper presents a design methodology for determining configurations of slider air bearings considering the randomness of the air-bearing surface (ABS) geometry by using the iSIGHT. A reliability-based design optimization (RBDO) problem is formulated to minimize the variations in the mean values of the flying heights from a target value while satisfying the desired probabilistic constraints keeping the pitch and roll angles within a suitable range. The reliability analysis is employed to estimate how the fabrication tolerances of individual slider parameters affect the final flying attitude tolerances. The proposed approach first solves the deterministic optimization problem. Then, beginning with this solution, the RBDO is continued with the reliability constraints affected by the random variables. Reliability constraints overriding the constraints of the deterministic optimization attempt to drive the design to a reliability solution with minimum increase in the objective. The simulation results of the RBDO are listed in comparison with the values of the initial design and the results of the deterministic optimization, respectively. To show the effectiveness of the proposed approach, the reliability analyses are simply carried out by using the mean value first-order second-moment (MVFO) method. The Monte Carlo simulation of the RBDO’s results is also performed to estimate the efficiency of the proposed approach. Those results are demonstrated to satisfy all the desired probabilistic constraints, where the target reliability level for constraints is defined as 0.8.     

Minimizing the hydraulic side effects of weirs construction by using labyrinth weirs

It is no doubt that weirs are one of the most important hydraulic structures that play a vital role in irrigation project. So, it is necessary to minimize the hydraulic side effects of weirs. Throughout this paper, experiments were conducted to investigate the suitable dimensions and shape of weir's crest to increase head loss, decrease upstream bank level upstream weir and get the most economic structure. Various crest angles of labyrinth weir were tested under different flow conditions. Also back water curve upstream weir was studied according to different weir crest angles. A case of linear weir crest was also included in the test program. The experimental results indicated that labyrinth weirs have lower operating heads and longer crest length compared with a linear weir having the same lateral space and the same discharge. Results showed that the crest weir angle of 60° is the best angle of weir crest. It reduces water level above crested level and the relative jump depth by 18% and 20%, respectively. In addition, it increase the average values of the dissipated energy and the discharge coefficient by 15% and 14%, respectively. It also gave maximum reduction in backwater curve profile by about 17%. Furthermore, the model was verified using CFD numerical model. The numerical results agreed with the experimental results.     

Discharge characteristics of a modified oblique side weir in subcritical flow

Side weirs are frequently used in many water projects. Due to their position with respect to the flow direction, side weirs are categorized as plain, oblique and labyrinth. One of the advantages of an oblique side weir is the increase in the effective length of the weir for overflowing and, therefore, diverting more discharge with the same channel opening, weir height and flow properties (i.e., upstream discharge, upstream Froude number and so on). In this paper, an experimental set-up of a new design of an oblique side weir with asymmetric geometry has been studied. The hydraulic behavior of this kind of oblique side weir, with a constant opening length, different weir heights and asymmetric oblique angle, has been investigated in a subcritical situation. The results from over 200 test measurements show that this kind of weir is up to 2.33 times more efficient with respect to the conventional side weir in a rectangular channel among the tested conditions. Finally, the discharge coefficient as a function of geometrical and flow variables are presented for design engineers. In addition, a more precise relation has been obtained for flow with Froude numbers less than 0.4.     

Discharge characteristics and structure of flow in labyrinth weirs with a downstream pool

A new design of a labyrinth weir is introduced in this study by adding a square pool to the vertex of a one-cycle triangular labyrinth weir with a sidewall angle of 45°. The addition of the square pool increased weir length without causing an excessive nappe interaction, and as a result, reduced the head water over the weir with the same discharge. Laboratory experiments were carried out to investigate the hydraulic performance of the new design with a potential application in pool-weir fishways. Mean and turbulence characteristics of flow for different weir geometries and in both free and submerged flow regimes were measured to be used for prediction of fish behaviour in the upstream of the proposed weir models. Discharge coefficients based on channel width and weir length were calculated. It was found that the new design can significantly increase the capacity of triangular labyrinth weirs and provide financial advantages in construction over triangular labyrinth weirs without pools in low discharges. In submerged flow conditions, the proposed model performed better than sharp-crested linear weirs in low discharges. Contour plots of the three-dimensional velocity components showed a region of strong mean flow around the neck of the new weir model. Turbulent characteristics such as turbulent kinetic energy, power spectra, exuberance ratio, and joint probability distribution functions of velocity fluctuations were extracted from instantaneous three dimensional velocities for different weir depths and flow regimes. Two vertical planes were identified based on the highest turbulent mixing in free and submerged flow regimes. The depths contributing the most to turbulent mixing were identified; active depths decreased as the flow regime changed from free to submerge flow regime.     

A review of studies on estimating the discharge coefficient of flow control structures based on the soft computing models

The discharge coefficient (Cd) plays a vital role in the accurate design and safety of weirs, spillways, and dams. In the last decade, Soft Computing(SC) models, which showed excellent capabilities for non-linear mapping between parameters, were widely used to estimate the discharge coefficient of flow control structures. This study provides a comprehensive review of the application of SC models for estimating Cd of different flow control structures such as ogee spillways, orifices, side weirs, etc. In addition, the most common empirical relations which are obtained from laboratory experiments are discussed briefly. The findings revealed that weir length/flow depth ratio, weir length/channel width ratio, weir height/flow depth, and Froude number are widely used to estimate Cd in the side weirs. Besides, the ratio of orifice crest height to height of side orifice, the ratio of main channel width to length of side orifice, ratio of main channel width to height of side orifice, and ratio of the height of side orifice to upstream flow depth were extensively employed to calculate Cd of orifice structures. The common parameters for measuring Cd of labyrinth weirs are, discharge over a labyrinth cycle, weir height, channel width, apex constant, upstream head, discharge over the weir, effective length, convergence constant, sidewall angle, and Froude number. In the weir-gate structure, some factors such as contraction coefficient of the gate, head loss, and weir height are key parameters for the accurate evaluation of Cd. The trends of SC models, features of popular models, and the background of models are discussed briefly in this paper. Also, research gaps and possible directions for new studies are suggested.     

Experimental and numerical simulation of arced trapezoidal piano key weirs

Piano key weirs are high performance labyrinth weirs particularly at lower heads (water height over the weir). These weirs are considered a recent development in terms of application and research. This study was conducted to numerically and experimentally investigate the hydraulic performance of arced trapezoidal piano key weirs ATPKW under different hydraulic and geometric conditions. The main purpose was to investigate the effect of the planform arc angle on the weir's hydraulic performance. To this end, four LRPKW models as well as four ATPKW models were studied. Due to the complexities associated with flow over piano key weirs, numerical models were used to simulate the flow pattern over the weir. Comparison of the results obtained for the ATPKW and LRPKW models indicated that, at upper heads, the ATPKW models offered a higher hydraulic performance than the LRPKW models. On the other hand, LRPKW model indicated better performance at lower heads. In addition, it was found that reducing the planform arc angle from 90° to 45° caused an initial reduction in the discharge coefficient, after which it dramatically increased. Also, LRPKW models indicated a more effective length and a more appropriate performance.     

Design optimization of a wind turbine gear transmission based on fatigue reliability sensitivity

Fatigue failure of gear transmission is one of the key factors that restrict the performance and service life of wind turbines. One of the major concerns in gear transmission under random loading conditions is the disregard of dynamic fatigue reliability in conventional design methods. Various issues, such as overweight structure or insufficient fatigue reliability, require continuous improvements in the reliability-based design optimization (RBDO) methodology. In this work, a novel gear transmission optimization model based on dynamic fatigue reliability sensitivity is developed to predict the optimal structural parameters of a wind turbine gear transmission. In the model, the dynamic fatigue reliability of the gear transmission is evaluated based on stress–strength interference theory. Design variables are determined based on the reliability sensitivity and correlation coefficient of the initial design parameters. The optimal structural parameters with the minimum volume are identified using the genetic algorithm in consideration of the dynamic fatigue reliability constraints. Comparison of the initial and optimized structures shows that the volume decreases by 3.58% while ensuring fatigue reliability. This work provides new insights into the RBDO of transmission systems from the perspective of reliability sensitivity.     

Effect of anti-vortex structures installed on stepped labyrinth side weirs on discharge capacity

Side weirs are essential structural elements commonly used to control water levels in rivers and canals. If the length of the opening is limited, a labyrinth side weir can be used to increase the amount of water diverted out of the channel and the effective length. This research studied the influence of installing an antivortex structure in stepped labyrinth side weirs on discharge capacity. It has four types of antivortex installed in different hydraulic conditions at different Froude numbers, dimensionless crest height, dimensionless weir opening length, step number, and head angle. Using data from 168 experimental runs without antivortex to allow comparison and 672 experimental runs to determine the best performance of antivortex structures that improved discharge capacity, and 528 runs measured velocity to investigate the intensity of secondary currents generated by lateral flow and other hydraulic conditions, including water surface profiles. According to the research results, installing antivortices regulated the flow, significantly improved the efficiency of the single-cycle stepped labyrinth side weir, and lowered secondary flows caused by interaction with the vertical axis. Finally, the discharge coefficient improves to 18% after analyzing the best type of antivortex, considering shape and height.     

Flow velocity pattern around trapezoidal piano key side weirs

In general, the side weirs are the structures installed along a channel or river. When the flow depth rises above the weir crest, the overflow passes through these weirs and enters the lateral canal. Nowadays, piano key weirs are considered as an important alternative to labyrinth weirs to modify the weirs encountering with difficulty to pass the maximum flow discharges. The present study investigates the hydrodynamic performance and the effect of the uniformity of velocity field on the resultant kinetic energy in the trapezoidal piano key side weirs with 90° installed laterally in the main channel wall. These weirs are classified as A-Type piano key weirs and two approaches (main: Mode 1 and adverse: Mode 2) were used to investigate the effect of the weirs' placement on their performance. The results showed that for velocity vectors in both modes, on average, the maximum flow discharge through the side weir occurred in the x and y directions (V_x and V_y) at Z*<0.2 and 0.2<Y*<0.7. The results also showed that at the control surface of X* = 1, the maximum values of α occur due to existing the inverse flow and increasing the deflection angle of the velocity vectors. The performance of the weir in Mode 2 was more appropriate Mode 1 due to the lack of weir base at the flow inlet, which is an obstacle for the deflection angle of the velocity vectors.     

Experimental study of discharge coefficient of trapezoidal arced labyrinth weirs of widened middle cycle

Arced labyrinth weir is a certain type of nonlinear weirs with a very high discharge capacity. Thanks to the increased effective length and the ensuing increased discharge capacity of these weirs, they can be used in dam spillways and water regulating structures. This study focused on trapezoidal Arced labyrinth weirs (TALW) of widened middle cycle. Various experiments were performed to evaluate the effect on discharge coefficient of various geometric parameters, including the ratio of inside apex width of the end cycles to that of the middle cycle (w₂/w₁) and the ratio of the length of labyrinth weir (Apron) in flow direction to the width of the middle cycle (B/w₁). Results of this study showed that with a decrease in w₂/w₁ from 0.42 to 0.30, discharge coefficient (C_d) would increase by 13–33%.     

Design for a Crane Metallic Structure Based on Imperialist Competitive Algorithm and Inverse Reliability Strategy

Uncertainties in parameters such as materials, loading, and geometry are inevitable in designing metallic structures for cranes. When considering these uncertainty factors, reliability-based design optimization (RBDO) offers a more reasonable design approach. However, existing RBDO methods for crane metallic structures are prone to low convergence speed and high computational cost. A unilevel RBDO method, combining a discrete imperialist competitive algorithm with an inverse reliability strategy based on the performance measure approach, is developed. Application of the imperialist competitive algorithm at the optimization level significantly improves the convergence speed of this RBDO method. At the reliability analysis level, the inverse reliability strategy is used to determine the feasibility of each probabilistic constraint at each design point by calculating its α-percentile performance, thereby avoiding convergence failure, calculation error, and disproportionate computational effort encountered using conventional moment and simulation methods. Application of the RBDO method to an actual crane structure shows that the developed RBDO realizes a design with the best tradeoff between economy and safety together with about one-third of the convergence speed and the computational cost of the existing method. This paper provides a scientific and effective design approach for the design of metallic structures of cranes.     

Reliability-based design optimization via high order response surface method

To reduce the computational effort of reliability-based design optimization (RBDO), the response surface method (RSM) has been widely used to evaluate reliability constraints. We propose an efficient methodology for solving RBDO problems based on an improved high order response surface method (HORSM) that takes advantage of an efficient sampling method, Hermite polynomials and uncertainty contribution concept to construct a high order response surface function with cross terms for reliability analysis. The sampling method generates supporting points from Gauss-Hermite quadrature points, which can be used to approximate response surface function without cross terms, to identify the highest order of each random variable and to determine the significant variables connected with point estimate method. The cross terms between two significant random variables are added to the response surface function to improve the approximation accuracy. Integrating the nested strategy, the improved HORSM is explored in solving RBDO problems. Additionally, a sampling based reliability sensitivity analysis method is employed to reduce the computational effort further when design variables are distributional parameters of input random variables. The proposed methodology is applied on two test problems to validate its accuracy and efficiency. The proposed methodology is more efficient than first order reliability method based RBDO and Monte Carlo simulation based RBDO, and enables the use of RBDO as a practical design tool.     

Water surface profile along a side weir in a parabolic channel

A side weir is an overflow structure set into the side of a channel. This structure is used for water level control in channels, diverting excess water from a main channel into a side channel and as storm overflows from urban sewage systems. Computation of water surface profile over the side weirs is essential to determine the flow rate of the side weir. Discharge estimation of the side weir is still an important research subject. Most previous research works for the side weir were carried out in main channels with rectangular, triangular, trapezoidal and circular cross sections. Analytical solutions for water surface profile along a rectangular side weir are available only for the special cases of rectangular and trapezoidal main channels on the basis of a constant specific energy. No analytical solution is available for a rectangular side weir located in a parabolic channel. This research presents an elegant analytical solution for establishing the water surface profile along a side weir located in a parabolic channel which involves the use of incomplete elliptic integrals. The solution, which yields a direct computation, should be a useful computational tool for evaluation and design of rectangular side weirs in parabolic channels.     

基于改进LHS模式的可靠性设计优化

在设计优化中,确定性优化由于没有考虑输入量的不确定性,其优化结果可能不可靠(不安全),因此基于可靠性的设计优化(reliability-based design optimization,RBDO)得到关注.然而可靠性设计优化计算量大,尤其对于高维问题.基于此,提出一种新方法--改进拉丁超立方体取样(Latin hyp...     

Multidisciplinary wing design optimization considering global sensitivity and uncertainty of approximation models

In recent years, high-fidelity analysis tools, such as computational fluid dynamics and finite element method, have been widely used in multidisciplinary design optimization (MDO) to enhance the accuracy of design results. However, complex MDO problems have many design variables and require long computation times. Global sensitivity analysis (GSA) is proposed to assuage the complexity of design problems by reducing dimensionality where variables that have low impact on the objective function are neglected. This avoids wasting computational effort and time on low-priority variables. Additionally, uncertainty introduced by the fidelity of the analysis tools is considered in design optimization to increase the reliability of design results. Reliability-based design optimization (RBDO) and possibility-based design optimization (PBDO) methods are proposed to handle uncertainty in design optimization. In this paper, the extended Fourier amplitude sensitivity test was used for GSA, whereas a collaborative optimization-based framework with RBDO and PBDO was used to consider uncertainty introduced by approximation models. The proposed method was applied to an aero-structural design optimization of an aircraft wing to demonstrate the feasibility and efficiency of the developed method. The objective function was to maximize the lift-to-drag ratio. The proposed process reduced calculation efforts by reducing the number of design variables and achieved the target probability of failure when it considered uncertainty. Moreover, this work evaluated previous research in RBDO with MDO for the wing design by comparing it with the PBDO result.     

Prediction of the discharge of side weir in the converge channels using artificial neural networks

Considering the common use of side weirs in irrigation and drainage networks, estimation of the discharge of the side weirs has always given a consideration by water engineering researchers. Another issue about side weirs is the change in flow conditions in the weir and downstream channel. To optimize the flow conditions in the side weir, this structure is established in a converging channel to reduce the channel width and compensate the reduced discharge. The geometrical parameters assumed as variables in this study are: weir length, weir height, convergence angle and downstream channel width. About 248 experiments were performed. Three neural network models were used to estimate the discharge from the side weir. The model was constructed using MATLAB, and the dimensionless variables that were the geometrical and hydraulic ratios of the model were selected as input parameters. Four ratios were selected as inputs to the model to estimate the discharge coefficient and the discharge from the weir. Considering the outputs of the model, the neural-fuzzy networks have the least error compared to the other models, and this model estimates the discharge of side weir overflowing with 99.8% accuracy.