Influence of wall roughness on discharge coefficient of sonic nozzles

To research the influence of roughness on discharge coefficient of axisymmetric sonic nozzles systematically, a turbulence model was established, and standard k–ε model was used in the turbulent core region while Wall Functions was carried out in the boundary layer region. A series of numerical simulations were conducted to research discharge coefficients of 6 critical flow Venturi nozzles with throat diameter ranging from 0.5 to 100 mm when Reynolds numbers ranges from 10⁴ to 10⁹ and relative roughness from 10⁻² to 10⁻⁶. The validity of the simulation model was confirmed by both the experimental data of Stewart and ISO 9300 empirical equation. According to the simulation results and theoretical analysis, the relations between discharge coefficient and relative roughness were obtained. It is recommended that the dimensionless parameter relative roughness should be used in ISO 9300 rather than absolute roughness. Additionally, when the machining of nozzle cannot satisfy the ISO 9300 requirement or the Reynolds numbers exceed the upper limits of the ISO 9300 equation, the effect of roughness should be considered, and the relative roughness of sonic nozzle should be provided clearly in the further experiment of discharge coefficient.     

Influence of divergent section on flow fields and discharge coefficient of ISO 9300 toroidal-throat sonic nozzle

The effect of divergent section of ISO 9300 toroidal-throat nozzle on discharge coefficient was analyzed based on the inviscid transonic flow model and laminar boundary layer theory. A series of numerical simulations were conducted to verify the results of theory, and investigate the effect of divergent section length L and diffuser angle θ operated at different Reynolds numbers. Combined with the numerical results in this study and the experimental data reported by Nakao, it showed the discharge coefficient increases with the rise of diffuser angle θ or the drop of divergent section length L. A lot of new results about the effect of divergent section were obtained. It indicated that the effect of divergent section on discharge coefficient of ISO 9300 toroidal-throat nozzle should be considered when Re<1.1×10⁴. At last, a concept of effective critical flow was proposed to discuss the effect of divergent section on discharge coefficient.     

Theoretical discharge coefficient of a critical circular-arc nozzle with laminar boundary layer and its verification by measurements using super-accurate nozzles

The discharge coefficient of a circular-arc critical Venturi nozzle is derived theoretically by combining theories to calculate mass flow defects caused by the core flow distribution and the laminar boundary layer. The equation obtained is verified by measurements using a constant volume tank system and nozzles of similar shape machined by super accurate lathes, which achieved mirror finish without polishing thus resulting in a machining error of less than 1 μm. The agreement of the theoretical and measured discharge coefficients is better than 0.04% at Reynolds numbers larger than 8×10⁴, the minimum used. The equation derived is in an analytical form, which enables an estimation of the effects of specific heat ratio as well as nozzle shape.     

The effects of various upstream arches of crest of the circular crested weir on hydraulic parameters

Weirs are one of the oldest hydraulic structures ever built by mankind. Weirs are used to measure and regulate the flow. In this paper by using obtained experimental data from physical model, the effects of the various upstream crests on some hydraulic parameters were investigated. The experiments were carried out in the arch angles of 0°, 30°, 45°, 60°, and 90° from the upstream crest in the hydraulics laboratory of Kermanshah Islamic Azad University. The results indicated that effects of the upstream crested arch on the discharge coefficient and energy loss had been negligible, and except for the arch angle of 0°, such effects upon the velocity distribution and the depth of the flow upon the crest of weir are not effective.     

Potential of particle swarm optimization based radial basis function network to predict the discharge coefficient of a modified triangular side weir

Estimating the discharge coefficient is one of the most important steps in the process of side weir design. In this paper, the particle swarm optimization algorithm and radial basis neural network are combined (RBFN-PSO) and employed to model the discharge coefficient of a modified triangular side weir. The developed RBF network has five neurons in the input layer and one neuron in the output layer. The inputs include a wide range of non-dimensional geometrical and hydraulic parameters of a modified triangular side weir, and the output is the discharge coefficient. The RBFN-PSO performance is evaluated using published experimental results and compared with the backpropagation radial basis function network (RBFN-BP) by using the statistical indexes Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and average absolute deviation (%δ). According to the results, the PSO algorithm successfully improved the RBFN while the RBFN-PSO model’s generalization capacity enhanced, with RMSE of 0.071 compared to the RBFN-BP model with RMSE of 0.114 in the testing dataset.     

在役起重机金属结构载荷统计分析及分项系数的确定

通过在起重机上安装远程在线实时动态监测系统,得到实际工作载荷数据,对载荷数据作统计分析,用工程结构设计中提出的完全可靠性法确定分项系数.由可靠指标的几何意义构造虚拟极限状态曲面得到分离系数,利用分离函数从可靠指标公式中分离出各分项系数,建立分项系数与载荷、抗力统计值和目标可靠指标的关系式,明确指出影响分项系数取值的各因...     

Radial Basis Neural Network and Particle Swarm Optimization-based equations for predicting the discharge capacity of triangular labyrinth weirs

Conventional weirs are utilized for controlling, measuring and adjusting the flow depth in hydraulic structures, such as those found in irrigation and drainage networks. Various weirs with modified shapes are utilized to increase the discharge capacity. The main goal of this study is to investigate the discharge coefficient (C_d) of triangular labyrinth weirs using soft computing methods. The performance of the Radial Basis Neural Network (RBNN) is compared with that of Multiple Nonlinear and Multiple Linear Particle Swarm Optimization (MNLPSO and MLPSO). Models developments are conducted using published experimental data from the literature. Comparing the RBNN, MLPSO and MNLPSO results obtained through these soft computing techniques with experimental data shows that all models perform well in predicting the discharge coefficient of a triangular labyrinth weir. Performance of the proposed approaches which demonstrated explicit equation given by MNLPSO model provided the discharge capacity with lower error (RMSE=0.0223) is compared with the MLPSO (RMSE=0.0346) and RBNN (RMSE=0.045) approaches.     

Performance evaluation of two different neural network and particle swarm optimization methods for prediction of discharge capacity of modified triangular side weirs

Technical design of side weirs needs high accuracy in predicting discharge coefficient. In this study, discharge coefficient prediction performance of multi-layer perceptron neural network (MLPNN) and radial basis neural network (RBNN) were compared with linear and nonlinear particle swarm optimization (PSO) based equations. Performance evaluation of the model was done by using root mean squared error (RMSE), coefficient of determination (R²), mean absolute error (MAE), average absolute deviation (δ) and mean absolute relative error (MARE). Comparison of the results showed that both neural networks and PSO based equations could determine discharge coefficient of modified triangular side weirs with high accuracy. The RBNN with RMSE of 0.037 in test data was found to be better than MLPNN with RMSE of 0.044 and multiple linear and nonlinear PSO based equations (ML-PSO and MNL-PSO) with RMSE of 0.043 and 0.041, respectively. However, due to their simplicity, PSO based equations can be sufficient for use in practical cases.     

Measurement of mass flow rate and evaluation of heat transfer coefficient for high-pressure pneumatic components during charge and discharge processes

Both the mass flow rate and heat transfer characteristics are significant factors to the flow behavior of the high-pressure air; however, they are not easy to be obtained by analytical model during discharge and charge processes. In this paper, the mass flow rate characteristics of high-pressure pneumatic components (HPPC) are measured by a compounding approach; two components under test with the same geometry and dimension are needed to be connected in series. Both the effective cross-section area and critical pressure ratio of HPPC are determined accurately, and only the pressure variation and the steady-state temperature of air in the chamber are utilized. The compared results between experimental and simulation data show that the accuracy of the measured effective cross-section area and critical pressure ratio of the HPPC is high when the sonic and adiabatic releasing time is less than 2 s. And then, a new combined method of calculating the heat transfer coefficient during discharging and charging processes for the high-pressure air is proposed. The computational fluid dynamics (CFD) method is used to illustrate the intensity of heat exchange between the high-pressure air inside the chamber and outer atmosphere. The dynamic flow behavior is analyzed based on the tested flow rate characteristics of HPPC, mixed heat transfer theory and numerical results. The results show that the heat-transfer coefficient during charge process is much greater than discharge process, and the forced convection heat exchange happened owing to the strong “air agitation” during the charge process. The experimental results also validate that the proposed method of calculating the transient heat transfer coefficient is more reasonable to describe the heat transfer behavior. The findings may also have general implication in the development of the design and analysis of the high-pressure pneumatic system.