Elsevier

Renewable Energy

Volume 134, April 2019, Pages 807-817
Renewable Energy

Effect of blade thickness on the hydraulic performance of a Francis hydro turbine model

https://doi.org/10.1016/j.renene.2018.11.066Get rights and content

Highlights

  • Effect of blade thickness on the performance of a Francis turbine was presented.

  • The definition of the blockage ratio for runner was applied with numerical analysis.

  • The blockage effects were investigated at best efficiency and off-design conditions.

  • The power and efficiency gradually decreased as the blockage ratio increased.

  • The efficiency of about 3.4% decreased as the blockage ratio increased with 12.5%.

Abstract

Francis turbines are the most commonly used turbines for hydroelectric power generation. Preliminary studies to verify turbine designs are often performed with small-scale models; however, when the runner blade of a full-size turbine is geometrically scaled down to prepare a model for evaluating the design variables and performance characteristics, the blades become very thin and difficult to manufacture. Hence, the blockage effect of the runner blade should be considered to find a suitable blade thickness that satisfies the required hydraulic performance. Furthermore, a clear understanding of the blockage ratio at the highest efficiency point and off-design condition is required to investigate different blade thicknesses and performance characteristics. Here, the blockage effect of the runner blade on the hydraulic performance and internal flow characteristics of a 300-class Francis hydro turbine was investigated. Three-dimensional Reynolds-averaged Navier–Stokes calculations were performed with a shear stress transport turbulence model to analyze the internal flow characteristics near the runner blade and compare the blockage effect with various blade thicknesses on major performance parameters such as the hydraulic efficiency. Flow analyses for the off-design conditions were also performed with various blade thicknesses. The obtained results indicated that the power and efficiency gradually decreased with increasing blockage ratio. The runner head loss increased due to the mismatches between the flow angle and blade angle with changing the inlet velocity triangle components according to blockage ratio. Especially the efficiency of approximate 3.4% decreased as the blockage ratio increased with 12.5%, compared to the reference model. It was verified that the blockage effect significantly affects the design of Francis turbine models.

Introduction

Francis turbines are extensively studied as they are the most common turbine technology used in hydroelectric power generation. Preliminary tests to verify the design variables and performance characteristics of large-scale Francis hydro turbines are required before installation. However, tests using full-scale turbines are prohibitively expensive and time consuming. Therefore, usually scaled-down models with the same geometric, kinematic, and dynamic similarities as actual Francis hydro turbines are used to evaluate the design variables and performance characteristics. When the runner blade of a Francis hydro turbine is scaled down to a model with geometric similarity, the runner blades become very thin, which makes manufacturing of the model blades difficult. The blockage ratio, defined as the ratio of the blocked area by the runner blade thickness to and flow passage area, is used to describe the flow around the runner blade. To find a suitable runner thickness while satisfying the requirements of hydraulic performance and structural strength, the blockage effect as a function of runner blade thickness should be considered. The IEC 60193 standard [1] suggests a permissible maximum blade thickness deviation for the Francis hydro turbine runner as acceptable ratio of an individual value to an average value at the actual scale and a model. However, this standard is relevant for manufacturing runner blades of small-scale model and indicates the extent to which the thickness affects performance. In addition to the issue of geometric similarity, the minimum thickness of the runner blade can depend on the material used for manufacturing the model. Therefore, understanding the influence of variations in the thickness is necessary to investigate the hydrodynamic performance and characteristics of models with various blockage ratios.

In a related study of blade thickness, Samad and Kim [2] applied surrogate modeling to compressor blade shape optimization for modifying the blade stacking line and airfoil thickness to simultaneously enhance the adiabatic efficiency and total pressure ratio. Mu et al. [3] studied numerically the effect of blade thickness on hydraulic performance with six types of impellers, which had different blade thickness and were assembled in the same pump for comparing head and efficiency under design condition. Shigemitsu et al. [4] investigated the effect of blade outlet angle and blade thickness on the performance and internal flow condition of a mini centrifugal pump with experimental and numerical analysis. They obtained the results that the head of the mini centrifugal pump increased according to the decrease of the blade thickness. Tao et al. [5] investigated the influence of blade thickness on the transient flow characteristics of a centrifugal slurry pump with a semi-open impeller. They also manufactured a specimen and conducted experimental tests of the hydraulic performance to verify the simulation results. Yang et al. [6] performed experimental and numerical studies of the influence of the blade thickness on a pump as turbine system, which had three different specific speeds with different blade thicknesses. Sarraf et al. [7] studied two fans that differed only in the thickness of their blades to highlight the effects of blade thickness on the overall performance and pressure and velocity fluctuations. In this way, studies of the effect of the blade thickness on the fluid mechanics were performed. However, studies considering the performance characteristics at both the off-design and best efficiency point (BEP) conditions as a function of blade thickness are lacking.

In addition, many studies related to Francis hydro turbine models have been performed considering various issues. Chen et al. [8] conducted computational fluid dynamics (CFD) analyses to predict the effect of runner blade loading on the performance and internal flow of a Francis turbine model with three different blade loadings. Kocak et al. [9] performed both analytical calculations and numerical simulations to design a Francis turbine runner blade. The single blade was designed using the Bovet method which uses empirical equations to obtain the parameters of the turbine runner. Kassanos et al. [10] numerically studied the effect of the splitter blade geometry on the draft tube vortex rope. Two different splitter blade designs were compared to the case of the initial runner without splitter blades at two different operating conditions. Chen et al. [11] developed a new method on basis of the port area and loss analysis to design a Francis turbine runner. The port area was defined as the minimum blade passage area at the exit of the blade passage and adjusted to correct the outflow angle at the runner exit. Chirkov et al. [12] presented the multi-discipline optimization of the hydraulic turbine runner shape with a new parameterization of the blade thickness function. They suggested an objective function as the weighted sum of maximal stress and the blade volume to account for both the strength and weight of the runner. However, studies considering the effect of the blade thickness on the performance and internal flow characteristics at wide operating conditions of a Francis hydro turbine model have not been undertaken. Among the design components of runner, the blade thickness is an important and sensitive geometrical factor and then it is determined the performance characteristics of runner with flow channel. The satisfied design and manufacturing of runner blade for safe and sustainable generation of turbine are required and should be studied. Therefore, the effect of the blockage ratio as a function of runner blade thickness is needed to observe the hydraulic characteristics at wide operating conditions as BEP and off-design conditions.

This study focused on the blockage effect of a runner blade on the hydraulic performance and internal flow characteristics of a Francis hydro turbine model with a specific speed of 300-class [rpm, kW, m]. Three-dimensional (3D) steady-state Reynolds-averaged Navier-Stokes (RANS) calculations were conducted with a k–ω based shear stress transport (SST) turbulence model to analyze the hydraulic performance of the Francis hydro turbine model. Major performance parameters, such as the efficiency and power, were investigated to determine the internal flow characteristics near the runner blade and compare the blockage effect using various blade thicknesses. In addition, in order to investigate the flow behavior in the Francis hydro turbine model with various blade thicknesses at the off-design conditions, steady flow analyses of the off-designs were performed.

Section snippets

Specification of the Francis hydro turbine model

In this study, a 3D numerical analysis was conducted on a Francis hydro turbine with a specific speed of 300-class [rpm, kW, m]. The specific speed of the Francis hydro turbine was calculated with Eq. (1). Fig. 1 shows the 3D modeling and overall geometry with respect to the main flow region, such as the spiral casing, stay vane, guide vane, runner and draft tube. The head, discharge and rotational speed at the BEP of the actual-scale Francis hydro turbine are represented by Eqs. (2)–(4), which

Definition of the blockage ratio

In the Francis hydro turbine, the blades made blocked by the stacked spans in the runner channel and their thickness decreases the annulus passage area over the entire blade zone. This decrease in area can be accurately quantified by the blockage ratio, which is defined as the ratio of the blocked to the unobstructed sections. The blade thickness s1 has a blockage ratio ρ1, as described below [13]:ρ1=Δt1t1=Δt12πr1z1

Fig. 2 shows a schematic diagram defining the blockage, where all the relevant

Numerical analysis

In this study, the internal flow field of the Francis hydro turbine model was analyzed in the steady state using the ANSYS CFX-17.1 commercial software [14]. The numerical grids for the blade and other parts were generated using the Turbo-Grid and ICEM-CFD packages, respectively. ANSYS CFX-Pre, CFX-Solver, and CFX-Post were used to define the boundary conditions, solve governing equations, and post-process the results, respectively. The governing equations used for the steady-state numerical

Validation of the numerical analysis results

In order to evaluate the accuracy of the numerical analysis, the results of the flow analysis should be validated with experimental results. The steady-state numerical results for an actual Francis hydro turbine were validated by comparison with experimental results from a previous study, as shown in Fig. 7 [18,19]. The performance curves show that the trends of the numerical and experimental results were generally consistent. In particular, the performance at the maximum efficiency point (MEP)

Conclusions

Steady-state 3D RANS analysis was conducted to investigate the influence of the blockage effect resulting from runner blades with different thicknesses on the hydraulic performance of a Francis hydro turbine model at the BEP and off-design conditions. The main conclusions from this work are summarized as follows.

Firstly, when analyzing the BEP condition, the power and efficiency gradually decreased with increasing blockage ratio. Both the output torque and input flowrate decreased with

Acknowledgments

This research was funded by the Korea Agency for Infrastructure Technology Advancement under the Ministry of Land, Infrastructure and Transport grant number 18IFIP-B128598-02; and partly the Korea Institute of Industrial Technology under the Ministry of Science and ICT grant number UR180019.

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