Master equation, design equations and runaway speed of the Kaplan turbine

Zhang, Zh.

doi:10.1007/s42241-021-0020-1

Cited by 3 publications

(9 citation statements)

References 10 publications

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“…Experiments had confirmed the function and practical effect of the calculation method, which could accurately calculate the runaway velocity of the axial-flow turbine and its relationship with the guide vane setting. 15 Wang et al used a fluid dynamics model and a coupled population balance model to calculate the enterprise flow power of a turbine. Localized bubble size was captured by particle image velocimetry (PIV) measurements.…”

Section: Literature Reviewmentioning

confidence: 99%

Research on energy‐saving technology of loader hydraulic torque converter based on MATLAB dynamic characteristic simulation

Sun

Luo

2023

Adv Control Appl

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At present, hydraulic transmission loaders have high automatic adaptability and convenient operation, but their transmission efficiency is low, and the intelligent degree of energy consumption regulation is limited. Strengthening the research of locking device in torque converter is an important measure to effectively reduce energy consumption. Therefore, the research uses MATLAB software and torque converter parameters to build the external characteristic curves of the engine and torque converter, and builds the dynamic model based on the working principle and locking process of the lockup clutch. The research and experimental analysis are carried out from three aspects of the lockup dynamic process of the torque converter, the lock‐up and unlocking conditions, and the change of the lockup oil pressure of the clutch. The results show that the speed difference range between pump wheel and turbine (233.08–365.44 rpm) is much lower than that of other cases (409.68–616.23 rpm) when the engine and torque converter are matched. And the fuel rate is the highest when the throttle opening of the loader is 70%, about 38%. The above results show that the locking structure of the hydraulic torque converter of the loader can effectively reduce the working vibration and improve the service life and fuel rate. And its energy‐saving application effect has an important enlightening effect on the performance optimization and resource utilization of construction machinery, and provides new ideas for improvement.

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Section: Literature Reviewmentioning

confidence: 99%

Research on energy‐saving technology of loader hydraulic torque converter based on MATLAB dynamic characteristic simulation

Sun

Luo

2023

Adv Control Appl

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“…It goes back to and interprets the design equations which have been established for Francis and Kaplan turbines. 12,13 For preliminary information, it not only represents the impeller size in a manner similar to the diameter number in equation (8). In particular, it also gives the shape of each turbine unit, that is, the ratio of the height of the wicket gate to the impeller diameter (thickness of the impeller) and is even related to the nominal guide-vane angle.…”

Section: Design Parameters and Relationsmentioning

confidence: 99%

“…As with Francis turbines, the physical background of using the turbine shape factor for Kaplan turbines is found in the derived design equation in. 13 This is given by the following relation…”

Section: Cordier Diagram and Extensionmentioning

confidence: 99%

“…At this moment, the design rule for the hub size of the impeller should be given. According to, 13 the radius of the hub of the impeller in connection with the height of the wicket gate and the nominal setting of the guide-vane angle should satisfy the following condition…”

Section: Cordier Diagram and Extensionmentioning

confidence: 99%

“…This is possible after deriving the design equations for Francis and Kaplan turbines in conjunction with the corresponding master equations. 12,13 The turbine shape factor is introduced. Because the best available data are used for both the improved and extended Cordier diagrams, as can be expected, the diagrams are capable to accurately specify the geometric design of turbines, including turbine type, size, and shape.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improvement and extension of Cordier diagram for hydraulic turbines

Zhang

2022

Proceedings of the Institution of Mechanical Engineers, Part A:

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The Cordier diagram for hydraulic turbines has been accurately improved and extended. The first part of this work completes the Cordier diagram by adding the effect of the number of injector nozzles in Pelton turbines. The Cordier lines (or bands) for Francis and Kaplan turbines have been recalculated based on the use of most available empirical relations without artificial smoothing of the boundaries between the different types of hydraulic turbines. Both turbine type and impeller diameter can be more accurately determined. The part of extending the Cordier diagram is based on the application of design equations for hydraulic turbines and the introduction of the turbine shape factor. This shape factor has a clear physical meaning in contrast to the diameter number in the conventional Cordier diagram. For Pelton turbines, it is representative of the ratio between runner diameter and jet diameter; for Francis and Kaplan turbines, it is representative of the ratio between the height of the wicket gate and the diameter of the impeller. The Cordier diagram for the diameter number can be replaced by the new diagram for the turbine shape factors. Exclusively for Francis turbines, the impeller shape factor also combines the blade profile (angle) at the impeller inlet with design parameters. The method presented in this paper can be well applied to create the extended Cordier diagram for the use of shape factors for pumps and compressors.

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Influence of Blade Number on the Hydrodynamic Performance of a Propeller-Type Axial Turbine for In-Pipe Installation

Oscar Monsalve,

Sebastián Velez-Garcia,

Josept David Revuelta-Acosta

2024

CFDL

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In-pipe hydraulic turbines are a promising energy-harvesting technology. Recent studies have demonstrated a strong influence of the turbine blade number on the performance of an axial propeller-type turbine. However, limited research has been dedicated to turbine diameters less than 100 mm. Therefore, this research aimed to determine the effect of the number of blades on the hydrodynamic performance of a 75.3 mm diameter axial propeller turbine for in-pipe installation. A parametric numerical study was performed by varying the angular velocity from 1600 to 3800 rpm and the number of blades from 2 to 6. Results identified an inverse correlation between the hydraulic efficiency of the turbine and its blade number and a direct correlation between the pressure head and the turbine torque. Furthermore, the performance showed hydraulic behavior comparable to those found in literature, confirming a similar hydraulic behavior as turbines with diameters exceeding 100 mm. Additionally, the turbine’s internal flow behavior was analyzed by visualizing the vortex structure using the Q-criterion. Lastly, this study provides a deeper understanding of the effect of the number of blades on the hydrodynamic performance of an axial turbine for in-pipe installation.

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Master equation, design equations and runaway speed of the Kaplan turbine

Cited by 3 publications

References 10 publications

Research on energy‐saving technology of loader hydraulic torque converter based on MATLAB dynamic characteristic simulation

Research on energy‐saving technology of loader hydraulic torque converter based on MATLAB dynamic characteristic simulation

Improvement and extension of Cordier diagram for hydraulic turbines

Influence of Blade Number on the Hydrodynamic Performance of a Propeller-Type Axial Turbine for In-Pipe Installation

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