- Email: [email protected]
Effect of blade thickness on the hydraulic performance of a Francis hydro turbine model
Renewable Energy 134 (2019) 807e817
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Effect of blade thickness on the hydraulic performance of a Francis hydro turbine model Seung-Jun Kim a, b, Young-Seok Choi a, b, Yong Cho c, Jong-Woong Choi c, Jin-Hyuk Kim a, b, * a
Green Process and Energy System Engineering, Korea University of Science & Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon, 34113, Republic of Korea Thermal & Fluid System R&D Group, Korea Institute of Industrial Technology, 89 Yangdaegiro-gil, Ipjang-myeon, Seobuk-gu, Cheonan-si, Chungcheongnam-do, 31056, Republic of Korea c K-water Convergence Institute, Korea Water Resources Corporation, 125, Yuseong-daero 1689beon-gil, Yuseong-gu, Daejeon, 34045, Republic of Korea b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 June 2018 Received in revised form 5 November 2018 Accepted 15 November 2018 Available online 20 November 2018
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 NaviereStokes 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. © 2018 Elsevier Ltd. All rights reserved.
Keywords: Francis hydro turbine Blockage effect Blade thickness Hydraulic performance Internal flow characteristics
1. 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
* Corresponding author. Thermal & Fluid System R&D Group, Korea Institute of Industrial Technology, 89 Yangdaegiro-gil, Ipjang-myeon, Seobuk-gu, Cheonan-si, Chungcheongnam-do, 31056, Republic of Korea E-mail address: [email protected] (J.-H. Kim). https://doi.org/10.1016/j.renene.2018.11.066 0960-1481/© 2018 Elsevier Ltd. All rights reserved.
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,
808
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
Nomenclature N n P H g D2 Q Δt r1
b p
r T
u ƞ
Rotational speed for a specific speed Rotational speed Power Head Gravitational acceleration Runner outlet diameter Discharge Blade thickness on the inlet section Runner inlet radius Blade relative flow angle Pressure Density Torques Angular speed Efficiency
this standard is relevant for manufacturing runner blades of smallscale 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 offdesign 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 Reynoldsaveraged Navier-Stokes (RANS) calculations were conducted with a keu 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. 2. 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
Fig. 1. Schematic diagram showing the 3D model of the Francis hydro turbine, where the main components are defined.
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
809
rotational speed at the BEP of the actual-scale Francis hydro turbine are represented by Eqs. (2)e(4), which yield the head coefficient, discharge coefficient, and speed factor according to IEC 60193 [1]. The Francis hydro turbine model was scaled down from the actualscale so that the speed factor, head, and discharge coefficients would have the same values, as given in Table 1. Main specifications are listed in Table 1. The performance and internal characteristics were investigated at the BEP and the off-design conditions of the Francis hydro turbine model.
Ns ¼
pffiffiffi N P
(1)
5
H4
HnD ¼
gH n2 D2
(2)
QnD ¼
Q nD3
(3)
nD nED ¼ pffiffiffiffiffiffi gH
(4)
3. 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 r1, as described below [13]:
r1 ¼
Dt1 t1
Dt ¼ 2pr1 z1
(5)
1
Fig. 2 shows a schematic diagram defining the blockage, where all the relevant variables are defined. Here, t1 is the circumference of the runner divided by the number of runner blades, r1 is the inlet radius of the runner blade, and Δt1 is the blade thickness in the inlet section. The reference thickness s1, which is based on the hydrodynamic flow through the runner, is the thickness measured in the direction normal to the blade contour from the stream surface. If b1 is the relative flow angle of the inlet, then Δt1 can be written as follows [13]:
Dt1 ¼
s1 sinb1
(6)
In this study, a Francis hydro turbine model was numerically analyzed with various blockage ratios from 2.5% to 12.5%. The reference blockage ratio was 5%, and five cases were analyzed to compare the overall performance and internal flow characteristics. Table 1 Specification of the Francis hydro turbine. Specifications
Real size
Model
Specific speed, Ns (m, kW, min1) Runner outlet diameter, D2 (m) Head coefficient, HnD () Discharge coefficient, QED () Speed factor, nED () Runner blade number (ea) Stay vane number (ea) Guide vane number (ea)
310 4.34 3.16 0.59 0.56 12 20 20
310 0.32 3.16 0.59 0.56 12 20 20
Fig. 2. Definition of blockage at the inlet.
To compare the effect of various blockage ratios, the thickness of the runner blade was varied by increasing or decreasing the thickness ratio according to the camber line of the runner. Fig. 3 shows blade cross-sections at the mid-span for the reference blockage ratio of 5% and one of 7.5%. The flow passage decreased as the blockage ratio increased. Fig. 4 shows the flow passage area normalized using the maximum flow passage area of the runner blade through the meridional length. The flow passage areas along the line from the leading edge (LE) to the trailing edge (TE) by the meridional length were different for the various blockage ratios as the different thickness was applied to the same camber line of the runner blade as shown in Fig. 3. 4. 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 analysis were discretized using the finite volume method. The working fluid of the Francis hydro turbine model was water at 25 C. The area-averaged total pressure and static pressure were set at the inlet and outlet of the turbine, respectively. The same head condition and various blockage ratios were applied for the numerical analysis of the Francis hydro turbine model. Additionally, for numerical analysis of the off-design conditions, different guide vane openings were applied to investigate the off-design conditions at constant head and various discharge conditions for various blockage ratios. When modeling fluid machinery, in order to decrease the computational time and improve convergence, numerical analysis usually applies
810
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
turbulence model to accurately predict the flow separation under an adverse pressure gradient [15,16]. This model uses the keu and keε models in the near-wall region and freestream area, respectively, and a blending function ensures smooth transitions between these two models [17]. Fig. 5 shows the numerical grid construction of the Francis hydro turbine model. A structured grid system was constructed in the computational domain with O-type grids near the surfaces of the runner blade, stay vanes, and guide vanes and H-type girds in other regions, such as the spiral casing and draft tube. In order to apply the low-Reynolds shear transport model near the wall of the Francis hydro turbine model runner during numerical analysis, the first grid point was kept at yþ 2. The numerical grid dependency test was performed, and the results were expressed as the normalized efficiency values along the node numbers, which were in the range of 3.7e14.3 106. The optimum node number of 8.17 106 was selected, as shown in Fig. 6. 5. Results and discussion 5.1. Validation of the numerical analysis results
Fig. 3. Schematic diagrams of mid-span cross-sections of blades of the Francis hydro turbine model with different blockage ratios.
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) was relatively accurate at a guide vane opening of 75%; hence, this condition was chosen as the BEP for this model. Thus, the numerical analysis of the Francis hydro turbine model is considered valid. In the performance curves, the power (P), efficiency (h), and mass flowrate were normalized by the maximum value in order to express dimensionless values. The power and efficiency were calculated using Eqs. (7) and (8), respectively.
P ¼ Tu
h¼
P
rgHQ
(7) (8)
Fig. 4. Normalized flow passage area in runner blade with various blockage ratios along the meridional length from the leading edge (LE) to the trailing edge (TE).
periodic conditions to one passage, where the flow field between two adjacent blades forms regularly with respect to the direction of rotation. However, the flow field in a Francis hydro turbine cannot be assumed to be regular due to interactions between the internal flow generated at the stay vanes, guide vanes, and expanded spiral casing. Therefore, the analysis was conducted for the entire area, including all runner blades, stay vanes, and guide vanes. The frozen-rotor method was applied to connect the rotating runner and stationary domains such as guide vanes and draft tubes for steady-state analysis. The keu-based SST model was used as a
Fig. 5. Schematic diagram defining the numerical grids of the Francis hydro turbine model.
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
811
Fig. 6. Efficiency curve from the grid dependency test. Fig. 8. Performance curves with various blockage ratios of Francis hydro turbine model at BEP condition.
hydraulic performance, especially the power, as shown in Fig. 8. Dptotal T u
Hloss
Fig. 7. Performance curves of modeled (CFD) and experimental (EXP) results for a realscale Francis hydro turbine [18,19].
5.2. Influence of the blockage effect at the BEP condition To investigate the blockage effect on the performance and internal flow characteristics of a Francis hydro turbine model, steadystate 3D analyses were performed at the BEP condition. Fig. 8 shows the numerical results (normalized P and h) for the Francis hydro turbine model at the BEP condition with various blockage ratios; the same effective head condition and guide vane opening was used for all cases. The P and h values decreased as the blockage ratio increased. In addition, the power at a blockage ratio of 2.5% (thin blade) was slightly higher than of the reference model (blockage ratio of 5%), while the efficiency was lower slightly. Although the power was the highest at a blockage ratio of 2.5%, it can be seen that the efficiency decreased due to the higher flowrate with the thinner runner blade. For blockage ratios higher than the reference, the power decreased with increasing blockage ratio due to a narrower flow passage. Hence, both the output torque and input flowrate decreased with increasing blockage ratio, where the output torque was more sensitive to the blockage ratio. Head loss calculations of the runner blade were performed at the BEP condition for different blockage ratios (runner blade thicknesses), as calculated using Eq. (9) [11]. The normalized head losses are shown in Fig. 9. The loss distribution confirmed that the runner head loss increased with increasing blockage ratio. Consequently the runner head loss had an adverse effect on the entire
runner
¼
Q
rg
(9)
Fig. 10 shows the velocity vector distributions on the blade surface at the mid-span of the runner blade under the BEP condition. The analyzed runner blades were located near the tongue of the spiral casing, which demonstrated complex flows, as shown in Fig. 10(a). As shown in Fig. 10(b) and (c), the flow passage area between runner blades more decreased with a blockage ratio of 12.5% than the blockage ratio of 5%. Even though the same boundary condition for both blockage ratios of 5% and 12.5% is given for the analysis, the flow characteristics and flow angle are changed totally because of different annulus flow passage area. Thus, the detailed comparison for the flow characteristic analyses can be observed clearly with velocity triangle distributions as shown in Fig. 11. Vector triangles of the velocity are indicated near the leading edge at the mid-span of runner for both blockage ratios (5% and 12.5%) for investigating the internal flow characteristics at the runner inlet. Here, U is the runner peripheral velocity, W is the relative velocity, and Cm is the meridional velocity, which indicates
Fig. 9. Normalized head loss of the runner blades with various blockage ratios at the BEP condition.
812
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
(a) Locations on the studied runner blade where vector distributions were analyzed (A, B, and C).
(b) Vector distributions for 5% blockage ratio (reference thickness)
(c) Vector distributions for 12.5% blockage ratio Fig. 10. (a) Locations on the studied runner blade where vector distributions were analyzed (A, B, and C). Vector distributions for (b) 5% blockage ratio (reference thickness) and (c) 12.5% blockage ratio showing blade views of the Francis hydro turbine model at mid-span at BEP conditions.
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
the flow rate at the runner inlet position. The reference model with a blockage ratio of 5% showed that the angle of the relative velocity component matched the blade angle in the velocity triangle well, as shown in Fig. 11(a). While the blockage ratio of 12.5% narrowed the flow passage area between blades, the Cm component decreased with decreasing flow rate. Thus, the relative velocity component depended on Cm. Consequently, the incidence angle between the flow angle and blade angle did not match, as shown in Fig. 11(b). This flow phenomenon explains the considerable increase in the runner head loss with increasing blockage ratio, as shown in Fig. 9. The values of the normalized pressure surrounding the blade pressure and suction sides along the streamwise direction were compared quantitatively at the BEP condition, as shown in Fig. 12, at the hub-, mid- and shroud-span of the runners with blockage ratios of 5% and 12.5%. Position A was analyzed, as defined in Fig. 10(a).
813
The areas of the pressure distribution denote the pressure difference between the pressure and suction sides. As shown in Fig. 12, the streamwise direction along the abscissa represents the length from the leading edge (0) to the trailing edge (1) of the runner blade. Examining the normalized pressure distribution, Fig. 12(a)e(c) show that the pressure curves for a blade with a blockage ratio of 5% showed a smooth curve between the pressure and suction sides for the three observed spans. However, the pressure curves for a blade with a blockage ratio of 12.5% showed that the areas between the pressure and suction sides were not clear, and irregular pressure distribution curves were observed for all three spans. In particular, comparing the pressure distribution at mid-span for blockage ratios of 5% and 12.5% (Fig. 12(b)), the suction side was reversed to the pressure side at the near leading edge and the pressure distribution at the suction side with a blockage ratio of 12.5% showed a pressure pulsation. This is because the angle of the flow matched the blade angle at a blockage ratio of 5%, as confirmed by the vector distribution at the mid-span. Smooth flow along the pressure and suction surfaces was observed, resulting in a clear pressure difference between the pressure and suction sides of the blade. On the other hand, at a blockage ratio of 12.5%, the flow angle did not match the blade angle, and irregular flow occurred at the near leading edge of the runner and the suction pressure surface, which affected the pressure distribution on the suction side surface. 5.3. Influence of the blockage effect at off-design conditions
(a) Velocity triangle for 5% blockage ratio (reference thickness)
(b) Velocity triangle for 12.5% blockage ratio Fig. 11. Velocity triangle for (a) 5% blockage ratio (reference thickness) and (b) 12.5% blockage ratio showing blade views of the Francis hydro turbine model at mid-span at BEP conditions.
To investigate the blockage effect on the performance and internal flow characteristics of a Francis hydro turbine model at offdesign conditions, steady-state 3D analysis was performed. Fig. 13(a) shows the numerical results of the efficiency as a function of the normalized mass flowrate for each blockage ratio at guide vane opening values of 35%, 53%, 67%, 75%, and 84% for a Francis hydro turbine model with off-design conditions. The efficiency and mass flowrate were normalized by the respective values at the BEP condition (guide vane opening of 75%). For the same guide vane opening, when the blockage ratio increased, the flowrate decreased, and the efficiency increased clearly at guide vane openings of 35% and 53%, as shown in Fig. 13(a). In addition, the MEP for each blockage ratio changed significantly compared to the flow rate of the model with the reference blockage ratio of 5%. It was confirmed that the flowrate characteristics depended on the blockage ratio and hence, flow passage between the blades. Furthermore, the hydraulic characteristics and suitable operating conditions (hence, overall performance of the turbine) depended on the blockage ratio. Fig. 13(b) shows an expanded view of the efficiency curves shown in Fig. 13(a) (as indicated by the dashed rectangle) to investigate changes in MEP. Among the five blockage ratios, values of 2.5%, 5%, and 7.5% showed MEPs at a guide vane opening of 75%, i.e., the BEP condition. Compared to the efficiency curve of the reference blockage ratio, the general efficiency curve trends for blockage ratios of 2.5% and 7.5% were generally similar. Hence, the blockage effects were not large enough to significantly change the MEP for different guide vane openings. On the other hand, when the blockage ratio increased further to 10% and 12.5%, the flow rate decreased further due to the narrower flow passage, resulting in the maximum efficiency being observed at a guide vane opening of 67%. Compared with the reference blockage ratio, the guide vane opening condition resulting in the MEP changed from 75% to 67% with a higher blockage ratio. This efficiency difference can be understood considering the blockage effects; when the blockage ratio changed with the thickness of the runner blade, the performance of the Francis hydro turbine changed remarkably.
814
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
(a) Hub span
(b) Mid span
(c) Shroud span Fig. 12. Pressure distributions along the streamwise direction of the runner with a blockage ratio of 5% at the (a) hub span, (b) mid span, and (c) shroud span for runner An under BEP conditions.
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
815
(a) Overall view of Efficiency curves with various blockage ratios
(a) At guide vane openings of 75%
(b) Expanded view of the efficiency curves in (a) Fig. 13. Efficiency curves with various blockage ratios of (a) overall view and (b) Expanded view for Francis hydro turbine models at off-design conditions.
To qualitatively confirm the performance characteristics, the streamline distributions were compared on the pressure side of runner at guide vane openings of 75% and 67%, corresponding to the BEP condition for the reference model and MEP for a blockage ratio of 10%, respectively, as shown in Fig. 14. The observed location of the runner was that labelled A in Fig. 10(a). The streamline distribution on the pressure side at a guide vane opening of 75% showed relatively more irregular and secondary flows than the pressure side at a guide vane opening of 67%, where this irregular flow contributed to a lower hydraulic performance. For the blockage ratio of 10% of runner as relatively thick runner, the flow characteristics for good performance conditions were changed to lower flowrate condition, from guide vane opening of 75% to 67%. Hence, the hydraulic characteristics of the runner blade with a blockage ratio of 10% changed to lower flowrate conditions, resulting in improved performance. Fig. 15 shows the pressure distribution on the meridional surface of a runner under the same conditions as shown in Fig. 14. The pressure values were normalized by the maximum pressure. Fig. 15(a) shows data for the guide vane opening of 75%, where it can be seen that the pressure passing through the runner from the leading edge to trailing edge showed irregular distribution at the near trailing edge of the hub and shroud. However, the pressure
(b) At guide vane openings of 67% Fig. 14. Streamline distributions on the pressure surface of a runner blade with a blockage ratio of 10% at guide vane openings of (a) 75% and (b) 67% under conditions of BEP and MEP, respectively, at location A.
contour changed gradually and smoothly at the near trailing edge for a guide vane opening of 67% (MEP condition), as shown in Fig. 15(b). This showed that the qualitative characteristics depended on the blockage ratio, along with the streamline distributions on the surface of runner blade in Fig. 14. In order to investigate the performance characteristics at the MEP, Fig. 16 compares the specific speed (which is an index of the performance characteristics and specifications of the Francis hydro turbine model) as a function of the blockage ratio. This figure shows that the specific speed at MEP conditions decreased as the blockage ratio increased as the flowrate and output power decreased. Therefore, the specific speed change of the Francis hydro turbine model at MEP depended on the blockage ratio, i.e., the thickness of the runner blade. Hence, these factors should be considered as
816
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
important design criteria for the manufacture and design of Francis hydro turbines. 6. Conclusions
(a) At guide vane openings of 75%
(b) At guide vane openings of 67%
Fig. 15. Pressure distributions on the meridional surface of a runner with blockage ratio of 10% at guide vane openings of (a) 75% and (b) 67%, corresponding to BEP and MEP conditions, respectively, at location A.
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 increasing blockage ratio due to the narrowed flow passage. The blockage effect on the hydraulic performance was confirmed by analyzing the loss distribution at various blockage ratios and comparing internal flow characteristics as velocity vectors, velocity triangle and pressure distribution on the blade surface at the mid-span of the runner. The results indicated that considerable enhancement of the runner head loss with increasing blockage ratio was due to mismatches between the flow angle and blade angle. Hence, we concluded that increasing the blockage ratio had adverse effects on the hydraulic performance and internal flow characteristics of a Francis hydro turbine model. Secondly, when analyzing the off-design conditions, the MEP for each blockage ratio depended on the flow rate accompanying the blockage ratio. The flow rate decreased as the blockage ratio increased, resulting in changes in the performance characteristics of the turbine. In addition, by comparing the efficiency at the BEP and MEP conditions for various blockage ratios, it was confirmed that the flow characteristics as flow rate condition for higher performance were changed according to blockage ratio. Qualitative comparisons were conducted for confirming flow characteristics changing with streamline and pressure distributions. Finally, it confirmed that the specific speed of the MEP (an indicator of the general turbine performance) depended on the blockage ratio. Therefore, when the runner blade design is scaled down from the actual scale to a model, the effect of the blockage ratio (runner blade thickness) on the hydraulic performance characteristics should be considered as an important factor when manufacturing and designing the runner blades. 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. References
Fig. 16. Specific speed of MEP with each blockage ratio.
[1] International Electrotechnical Commission, Hydraulic Turbines, Storage Pumps and Pump-turbines e Model Acceptance Tests, Standard No. IEC 60193, 1999. [2] A. Samad, K.Y. Kim, Application of surrogate modeling to design of a compressor blade to optimize stacking and thickness, Int J Fluid Mach Syst 2 (1) (2009) 1e12. [3] J.G. Mu, B. Zhu, S.H. Zheng, J.J. Gan, Response of blade thickness to hydraulic performance of stamping and welding multistage centrifugal pump, Appl. Mech. Mater. 299 (2012) 351e356. [4] T. Shigemitsu, J. Fukutomi, K. Kaji, Influence of blade outlet angle and blade thickness on performance and internal flow conditions of mini centrifugal pump, Int J Fluid Mach Syst 4 (3) (2011) 317e323. [5] Y. Tao, S. Yuan, J. Liu, F. Zhang, J. Tao, Influence of blade thickness on transient flow characteristics of centrifugal slurry pump with semi-open impeller, Chin. J. Mech. Eng. 29 (6) (2016) 1209e1217. [6] S. S. Yang, C. Wang, K. Chen, X. Yuan, Research on blade thickness influencing pump as turbine, Adv. Mech. Eng., 6 (2014) 190530, 8 pages.
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817 [7] C. Sarraf, H. Nouri, F. Ravelet, F. Bakir, Experimental study of blade thickness effects on the overall and local performances of a controlled vortex designed axial-flow fan, 35(4) (2011) 684-693. [8] Z. Chen, P.M. Singh, Y.D. Choi, The effect of runner blade loading on the performance and internal flow of a Francis hydro turbine model, J. Mech. Sci. Technol. 30 (4) (2016) 1617e1623. [9] E. Kocak, S. Karaaslan, N. Yucel, F. Arundas, A numerical case study: Bovet approach to design a Francis turbine runner, Energy Procedia 111 (2017) 885e894. [10] I. Kassanos, J. Anagnostopoulos, D. Papantonis, Numerical investigation of draft tube pressure pulsations in a Francis turbine with splitter blades, J. Phys. Conf. 813 (1) (2017) 012049. [11] Z. Chen, P.M. Singh, Y.D. Choi, Francis turbine blade design on the basis of port area and loss analysis, Energies 9 (3) (2016) 164. [12] D.V. Chirkov, A.S. Ankudinova, A.E. Kryukov, S.G. Cherny, V.A. Skorospelov, Multi-objective Shape Optimization of a Hydraulic Turbine Runner Using Efficiency, Strength and Weight Criteria, Structural and Multidisciplinary
817
Optimization, 2018, pp. 1e14. [13] M. Teodor, Impeller design using CAD techniques and conformal mapping method, in: D. Papantonis (Ed.), Centrifugal Pumps, InTech, 2012. [14] ANSYS CFX-17.1, ANSYS CFX-solver Theory Guide, ANSYS Inc, 2017. [15] F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering application, AIAA J. 32 (8) (1994) 1598e1605. [16] J.E. Bardina, P.G. Huang, T. Coakley, Turbulence modeling validation, in: Proc. 28th Fluid Dynamics Conference, Snowmass Village, CO, 1997, p. 2121. [17] M.W. Heo, J.H. Kim, T.W. Seo, K.Y. Kim, Aerodynamic and aeroacoustic optimization for design of a forward-curved blades centrifugal fan, Proc. Inst. Mech. Eng. Part A: J Power Energy 230 (2) (2016) 154e174. [18] S.J. Kim, Y.I. Kim, Y.S. Choi, K.Y. Lee, I.S. Ahn, J. Cho, J.H. Kim, Effect of a leakage wall on hydraulic performance of spiral casing tongue in a Francis hydro turbine, KSFM J. Fluid Mach. 21 (2018) 5-11 (in Korean). [19] Korea Agency for Infrastructure Technology Advancement. reportDevelopment of Construction Technology for Medium Sized Hydropower Plant (1st Year Report) (2017), Report No. 17IFIP-B128598-01.
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Effect of blade thickness on the hydraulic performance of a Francis hydro turbine model Seung-Jun Kim a, b, Young-Seok Choi a, b, Yong Cho c, Jong-Woong Choi c, Jin-Hyuk Kim a, b, * a
Green Process and Energy System Engineering, Korea University of Science & Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon, 34113, Republic of Korea Thermal & Fluid System R&D Group, Korea Institute of Industrial Technology, 89 Yangdaegiro-gil, Ipjang-myeon, Seobuk-gu, Cheonan-si, Chungcheongnam-do, 31056, Republic of Korea c K-water Convergence Institute, Korea Water Resources Corporation, 125, Yuseong-daero 1689beon-gil, Yuseong-gu, Daejeon, 34045, Republic of Korea b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 June 2018 Received in revised form 5 November 2018 Accepted 15 November 2018 Available online 20 November 2018
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 NaviereStokes 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. © 2018 Elsevier Ltd. All rights reserved.
Keywords: Francis hydro turbine Blockage effect Blade thickness Hydraulic performance Internal flow characteristics
1. 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
* Corresponding author. Thermal & Fluid System R&D Group, Korea Institute of Industrial Technology, 89 Yangdaegiro-gil, Ipjang-myeon, Seobuk-gu, Cheonan-si, Chungcheongnam-do, 31056, Republic of Korea E-mail address: [email protected] (J.-H. Kim). https://doi.org/10.1016/j.renene.2018.11.066 0960-1481/© 2018 Elsevier Ltd. All rights reserved.
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,
808
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
Nomenclature N n P H g D2 Q Δt r1
b p
r T
u ƞ
Rotational speed for a specific speed Rotational speed Power Head Gravitational acceleration Runner outlet diameter Discharge Blade thickness on the inlet section Runner inlet radius Blade relative flow angle Pressure Density Torques Angular speed Efficiency
this standard is relevant for manufacturing runner blades of smallscale 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 offdesign 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 Reynoldsaveraged Navier-Stokes (RANS) calculations were conducted with a keu 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. 2. 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
Fig. 1. Schematic diagram showing the 3D model of the Francis hydro turbine, where the main components are defined.
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
809
rotational speed at the BEP of the actual-scale Francis hydro turbine are represented by Eqs. (2)e(4), which yield the head coefficient, discharge coefficient, and speed factor according to IEC 60193 [1]. The Francis hydro turbine model was scaled down from the actualscale so that the speed factor, head, and discharge coefficients would have the same values, as given in Table 1. Main specifications are listed in Table 1. The performance and internal characteristics were investigated at the BEP and the off-design conditions of the Francis hydro turbine model.
Ns ¼
pffiffiffi N P
(1)
5
H4
HnD ¼
gH n2 D2
(2)
QnD ¼
Q nD3
(3)
nD nED ¼ pffiffiffiffiffiffi gH
(4)
3. 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 r1, as described below [13]:
r1 ¼
Dt1 t1
Dt ¼ 2pr1 z1
(5)
1
Fig. 2 shows a schematic diagram defining the blockage, where all the relevant variables are defined. Here, t1 is the circumference of the runner divided by the number of runner blades, r1 is the inlet radius of the runner blade, and Δt1 is the blade thickness in the inlet section. The reference thickness s1, which is based on the hydrodynamic flow through the runner, is the thickness measured in the direction normal to the blade contour from the stream surface. If b1 is the relative flow angle of the inlet, then Δt1 can be written as follows [13]:
Dt1 ¼
s1 sinb1
(6)
In this study, a Francis hydro turbine model was numerically analyzed with various blockage ratios from 2.5% to 12.5%. The reference blockage ratio was 5%, and five cases were analyzed to compare the overall performance and internal flow characteristics. Table 1 Specification of the Francis hydro turbine. Specifications
Real size
Model
Specific speed, Ns (m, kW, min1) Runner outlet diameter, D2 (m) Head coefficient, HnD () Discharge coefficient, QED () Speed factor, nED () Runner blade number (ea) Stay vane number (ea) Guide vane number (ea)
310 4.34 3.16 0.59 0.56 12 20 20
310 0.32 3.16 0.59 0.56 12 20 20
Fig. 2. Definition of blockage at the inlet.
To compare the effect of various blockage ratios, the thickness of the runner blade was varied by increasing or decreasing the thickness ratio according to the camber line of the runner. Fig. 3 shows blade cross-sections at the mid-span for the reference blockage ratio of 5% and one of 7.5%. The flow passage decreased as the blockage ratio increased. Fig. 4 shows the flow passage area normalized using the maximum flow passage area of the runner blade through the meridional length. The flow passage areas along the line from the leading edge (LE) to the trailing edge (TE) by the meridional length were different for the various blockage ratios as the different thickness was applied to the same camber line of the runner blade as shown in Fig. 3. 4. 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 analysis were discretized using the finite volume method. The working fluid of the Francis hydro turbine model was water at 25 C. The area-averaged total pressure and static pressure were set at the inlet and outlet of the turbine, respectively. The same head condition and various blockage ratios were applied for the numerical analysis of the Francis hydro turbine model. Additionally, for numerical analysis of the off-design conditions, different guide vane openings were applied to investigate the off-design conditions at constant head and various discharge conditions for various blockage ratios. When modeling fluid machinery, in order to decrease the computational time and improve convergence, numerical analysis usually applies
810
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
turbulence model to accurately predict the flow separation under an adverse pressure gradient [15,16]. This model uses the keu and keε models in the near-wall region and freestream area, respectively, and a blending function ensures smooth transitions between these two models [17]. Fig. 5 shows the numerical grid construction of the Francis hydro turbine model. A structured grid system was constructed in the computational domain with O-type grids near the surfaces of the runner blade, stay vanes, and guide vanes and H-type girds in other regions, such as the spiral casing and draft tube. In order to apply the low-Reynolds shear transport model near the wall of the Francis hydro turbine model runner during numerical analysis, the first grid point was kept at yþ 2. The numerical grid dependency test was performed, and the results were expressed as the normalized efficiency values along the node numbers, which were in the range of 3.7e14.3 106. The optimum node number of 8.17 106 was selected, as shown in Fig. 6. 5. Results and discussion 5.1. Validation of the numerical analysis results
Fig. 3. Schematic diagrams of mid-span cross-sections of blades of the Francis hydro turbine model with different blockage ratios.
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) was relatively accurate at a guide vane opening of 75%; hence, this condition was chosen as the BEP for this model. Thus, the numerical analysis of the Francis hydro turbine model is considered valid. In the performance curves, the power (P), efficiency (h), and mass flowrate were normalized by the maximum value in order to express dimensionless values. The power and efficiency were calculated using Eqs. (7) and (8), respectively.
P ¼ Tu
h¼
P
rgHQ
(7) (8)
Fig. 4. Normalized flow passage area in runner blade with various blockage ratios along the meridional length from the leading edge (LE) to the trailing edge (TE).
periodic conditions to one passage, where the flow field between two adjacent blades forms regularly with respect to the direction of rotation. However, the flow field in a Francis hydro turbine cannot be assumed to be regular due to interactions between the internal flow generated at the stay vanes, guide vanes, and expanded spiral casing. Therefore, the analysis was conducted for the entire area, including all runner blades, stay vanes, and guide vanes. The frozen-rotor method was applied to connect the rotating runner and stationary domains such as guide vanes and draft tubes for steady-state analysis. The keu-based SST model was used as a
Fig. 5. Schematic diagram defining the numerical grids of the Francis hydro turbine model.
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
811
Fig. 6. Efficiency curve from the grid dependency test. Fig. 8. Performance curves with various blockage ratios of Francis hydro turbine model at BEP condition.
hydraulic performance, especially the power, as shown in Fig. 8. Dptotal T u
Hloss
Fig. 7. Performance curves of modeled (CFD) and experimental (EXP) results for a realscale Francis hydro turbine [18,19].
5.2. Influence of the blockage effect at the BEP condition To investigate the blockage effect on the performance and internal flow characteristics of a Francis hydro turbine model, steadystate 3D analyses were performed at the BEP condition. Fig. 8 shows the numerical results (normalized P and h) for the Francis hydro turbine model at the BEP condition with various blockage ratios; the same effective head condition and guide vane opening was used for all cases. The P and h values decreased as the blockage ratio increased. In addition, the power at a blockage ratio of 2.5% (thin blade) was slightly higher than of the reference model (blockage ratio of 5%), while the efficiency was lower slightly. Although the power was the highest at a blockage ratio of 2.5%, it can be seen that the efficiency decreased due to the higher flowrate with the thinner runner blade. For blockage ratios higher than the reference, the power decreased with increasing blockage ratio due to a narrower flow passage. Hence, both the output torque and input flowrate decreased with increasing blockage ratio, where the output torque was more sensitive to the blockage ratio. Head loss calculations of the runner blade were performed at the BEP condition for different blockage ratios (runner blade thicknesses), as calculated using Eq. (9) [11]. The normalized head losses are shown in Fig. 9. The loss distribution confirmed that the runner head loss increased with increasing blockage ratio. Consequently the runner head loss had an adverse effect on the entire
runner
¼
Q
rg
(9)
Fig. 10 shows the velocity vector distributions on the blade surface at the mid-span of the runner blade under the BEP condition. The analyzed runner blades were located near the tongue of the spiral casing, which demonstrated complex flows, as shown in Fig. 10(a). As shown in Fig. 10(b) and (c), the flow passage area between runner blades more decreased with a blockage ratio of 12.5% than the blockage ratio of 5%. Even though the same boundary condition for both blockage ratios of 5% and 12.5% is given for the analysis, the flow characteristics and flow angle are changed totally because of different annulus flow passage area. Thus, the detailed comparison for the flow characteristic analyses can be observed clearly with velocity triangle distributions as shown in Fig. 11. Vector triangles of the velocity are indicated near the leading edge at the mid-span of runner for both blockage ratios (5% and 12.5%) for investigating the internal flow characteristics at the runner inlet. Here, U is the runner peripheral velocity, W is the relative velocity, and Cm is the meridional velocity, which indicates
Fig. 9. Normalized head loss of the runner blades with various blockage ratios at the BEP condition.
812
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
(a) Locations on the studied runner blade where vector distributions were analyzed (A, B, and C).
(b) Vector distributions for 5% blockage ratio (reference thickness)
(c) Vector distributions for 12.5% blockage ratio Fig. 10. (a) Locations on the studied runner blade where vector distributions were analyzed (A, B, and C). Vector distributions for (b) 5% blockage ratio (reference thickness) and (c) 12.5% blockage ratio showing blade views of the Francis hydro turbine model at mid-span at BEP conditions.
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
the flow rate at the runner inlet position. The reference model with a blockage ratio of 5% showed that the angle of the relative velocity component matched the blade angle in the velocity triangle well, as shown in Fig. 11(a). While the blockage ratio of 12.5% narrowed the flow passage area between blades, the Cm component decreased with decreasing flow rate. Thus, the relative velocity component depended on Cm. Consequently, the incidence angle between the flow angle and blade angle did not match, as shown in Fig. 11(b). This flow phenomenon explains the considerable increase in the runner head loss with increasing blockage ratio, as shown in Fig. 9. The values of the normalized pressure surrounding the blade pressure and suction sides along the streamwise direction were compared quantitatively at the BEP condition, as shown in Fig. 12, at the hub-, mid- and shroud-span of the runners with blockage ratios of 5% and 12.5%. Position A was analyzed, as defined in Fig. 10(a).
813
The areas of the pressure distribution denote the pressure difference between the pressure and suction sides. As shown in Fig. 12, the streamwise direction along the abscissa represents the length from the leading edge (0) to the trailing edge (1) of the runner blade. Examining the normalized pressure distribution, Fig. 12(a)e(c) show that the pressure curves for a blade with a blockage ratio of 5% showed a smooth curve between the pressure and suction sides for the three observed spans. However, the pressure curves for a blade with a blockage ratio of 12.5% showed that the areas between the pressure and suction sides were not clear, and irregular pressure distribution curves were observed for all three spans. In particular, comparing the pressure distribution at mid-span for blockage ratios of 5% and 12.5% (Fig. 12(b)), the suction side was reversed to the pressure side at the near leading edge and the pressure distribution at the suction side with a blockage ratio of 12.5% showed a pressure pulsation. This is because the angle of the flow matched the blade angle at a blockage ratio of 5%, as confirmed by the vector distribution at the mid-span. Smooth flow along the pressure and suction surfaces was observed, resulting in a clear pressure difference between the pressure and suction sides of the blade. On the other hand, at a blockage ratio of 12.5%, the flow angle did not match the blade angle, and irregular flow occurred at the near leading edge of the runner and the suction pressure surface, which affected the pressure distribution on the suction side surface. 5.3. Influence of the blockage effect at off-design conditions
(a) Velocity triangle for 5% blockage ratio (reference thickness)
(b) Velocity triangle for 12.5% blockage ratio Fig. 11. Velocity triangle for (a) 5% blockage ratio (reference thickness) and (b) 12.5% blockage ratio showing blade views of the Francis hydro turbine model at mid-span at BEP conditions.
To investigate the blockage effect on the performance and internal flow characteristics of a Francis hydro turbine model at offdesign conditions, steady-state 3D analysis was performed. Fig. 13(a) shows the numerical results of the efficiency as a function of the normalized mass flowrate for each blockage ratio at guide vane opening values of 35%, 53%, 67%, 75%, and 84% for a Francis hydro turbine model with off-design conditions. The efficiency and mass flowrate were normalized by the respective values at the BEP condition (guide vane opening of 75%). For the same guide vane opening, when the blockage ratio increased, the flowrate decreased, and the efficiency increased clearly at guide vane openings of 35% and 53%, as shown in Fig. 13(a). In addition, the MEP for each blockage ratio changed significantly compared to the flow rate of the model with the reference blockage ratio of 5%. It was confirmed that the flowrate characteristics depended on the blockage ratio and hence, flow passage between the blades. Furthermore, the hydraulic characteristics and suitable operating conditions (hence, overall performance of the turbine) depended on the blockage ratio. Fig. 13(b) shows an expanded view of the efficiency curves shown in Fig. 13(a) (as indicated by the dashed rectangle) to investigate changes in MEP. Among the five blockage ratios, values of 2.5%, 5%, and 7.5% showed MEPs at a guide vane opening of 75%, i.e., the BEP condition. Compared to the efficiency curve of the reference blockage ratio, the general efficiency curve trends for blockage ratios of 2.5% and 7.5% were generally similar. Hence, the blockage effects were not large enough to significantly change the MEP for different guide vane openings. On the other hand, when the blockage ratio increased further to 10% and 12.5%, the flow rate decreased further due to the narrower flow passage, resulting in the maximum efficiency being observed at a guide vane opening of 67%. Compared with the reference blockage ratio, the guide vane opening condition resulting in the MEP changed from 75% to 67% with a higher blockage ratio. This efficiency difference can be understood considering the blockage effects; when the blockage ratio changed with the thickness of the runner blade, the performance of the Francis hydro turbine changed remarkably.
814
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
(a) Hub span
(b) Mid span
(c) Shroud span Fig. 12. Pressure distributions along the streamwise direction of the runner with a blockage ratio of 5% at the (a) hub span, (b) mid span, and (c) shroud span for runner An under BEP conditions.
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
815
(a) Overall view of Efficiency curves with various blockage ratios
(a) At guide vane openings of 75%
(b) Expanded view of the efficiency curves in (a) Fig. 13. Efficiency curves with various blockage ratios of (a) overall view and (b) Expanded view for Francis hydro turbine models at off-design conditions.
To qualitatively confirm the performance characteristics, the streamline distributions were compared on the pressure side of runner at guide vane openings of 75% and 67%, corresponding to the BEP condition for the reference model and MEP for a blockage ratio of 10%, respectively, as shown in Fig. 14. The observed location of the runner was that labelled A in Fig. 10(a). The streamline distribution on the pressure side at a guide vane opening of 75% showed relatively more irregular and secondary flows than the pressure side at a guide vane opening of 67%, where this irregular flow contributed to a lower hydraulic performance. For the blockage ratio of 10% of runner as relatively thick runner, the flow characteristics for good performance conditions were changed to lower flowrate condition, from guide vane opening of 75% to 67%. Hence, the hydraulic characteristics of the runner blade with a blockage ratio of 10% changed to lower flowrate conditions, resulting in improved performance. Fig. 15 shows the pressure distribution on the meridional surface of a runner under the same conditions as shown in Fig. 14. The pressure values were normalized by the maximum pressure. Fig. 15(a) shows data for the guide vane opening of 75%, where it can be seen that the pressure passing through the runner from the leading edge to trailing edge showed irregular distribution at the near trailing edge of the hub and shroud. However, the pressure
(b) At guide vane openings of 67% Fig. 14. Streamline distributions on the pressure surface of a runner blade with a blockage ratio of 10% at guide vane openings of (a) 75% and (b) 67% under conditions of BEP and MEP, respectively, at location A.
contour changed gradually and smoothly at the near trailing edge for a guide vane opening of 67% (MEP condition), as shown in Fig. 15(b). This showed that the qualitative characteristics depended on the blockage ratio, along with the streamline distributions on the surface of runner blade in Fig. 14. In order to investigate the performance characteristics at the MEP, Fig. 16 compares the specific speed (which is an index of the performance characteristics and specifications of the Francis hydro turbine model) as a function of the blockage ratio. This figure shows that the specific speed at MEP conditions decreased as the blockage ratio increased as the flowrate and output power decreased. Therefore, the specific speed change of the Francis hydro turbine model at MEP depended on the blockage ratio, i.e., the thickness of the runner blade. Hence, these factors should be considered as
816
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817
important design criteria for the manufacture and design of Francis hydro turbines. 6. Conclusions
(a) At guide vane openings of 75%
(b) At guide vane openings of 67%
Fig. 15. Pressure distributions on the meridional surface of a runner with blockage ratio of 10% at guide vane openings of (a) 75% and (b) 67%, corresponding to BEP and MEP conditions, respectively, at location A.
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 increasing blockage ratio due to the narrowed flow passage. The blockage effect on the hydraulic performance was confirmed by analyzing the loss distribution at various blockage ratios and comparing internal flow characteristics as velocity vectors, velocity triangle and pressure distribution on the blade surface at the mid-span of the runner. The results indicated that considerable enhancement of the runner head loss with increasing blockage ratio was due to mismatches between the flow angle and blade angle. Hence, we concluded that increasing the blockage ratio had adverse effects on the hydraulic performance and internal flow characteristics of a Francis hydro turbine model. Secondly, when analyzing the off-design conditions, the MEP for each blockage ratio depended on the flow rate accompanying the blockage ratio. The flow rate decreased as the blockage ratio increased, resulting in changes in the performance characteristics of the turbine. In addition, by comparing the efficiency at the BEP and MEP conditions for various blockage ratios, it was confirmed that the flow characteristics as flow rate condition for higher performance were changed according to blockage ratio. Qualitative comparisons were conducted for confirming flow characteristics changing with streamline and pressure distributions. Finally, it confirmed that the specific speed of the MEP (an indicator of the general turbine performance) depended on the blockage ratio. Therefore, when the runner blade design is scaled down from the actual scale to a model, the effect of the blockage ratio (runner blade thickness) on the hydraulic performance characteristics should be considered as an important factor when manufacturing and designing the runner blades. 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. References
Fig. 16. Specific speed of MEP with each blockage ratio.
[1] International Electrotechnical Commission, Hydraulic Turbines, Storage Pumps and Pump-turbines e Model Acceptance Tests, Standard No. IEC 60193, 1999. [2] A. Samad, K.Y. Kim, Application of surrogate modeling to design of a compressor blade to optimize stacking and thickness, Int J Fluid Mach Syst 2 (1) (2009) 1e12. [3] J.G. Mu, B. Zhu, S.H. Zheng, J.J. Gan, Response of blade thickness to hydraulic performance of stamping and welding multistage centrifugal pump, Appl. Mech. Mater. 299 (2012) 351e356. [4] T. Shigemitsu, J. Fukutomi, K. Kaji, Influence of blade outlet angle and blade thickness on performance and internal flow conditions of mini centrifugal pump, Int J Fluid Mach Syst 4 (3) (2011) 317e323. [5] Y. Tao, S. Yuan, J. Liu, F. Zhang, J. Tao, Influence of blade thickness on transient flow characteristics of centrifugal slurry pump with semi-open impeller, Chin. J. Mech. Eng. 29 (6) (2016) 1209e1217. [6] S. S. Yang, C. Wang, K. Chen, X. Yuan, Research on blade thickness influencing pump as turbine, Adv. Mech. Eng., 6 (2014) 190530, 8 pages.
S.-J. Kim et al. / Renewable Energy 134 (2019) 807e817 [7] C. Sarraf, H. Nouri, F. Ravelet, F. Bakir, Experimental study of blade thickness effects on the overall and local performances of a controlled vortex designed axial-flow fan, 35(4) (2011) 684-693. [8] Z. Chen, P.M. Singh, Y.D. Choi, The effect of runner blade loading on the performance and internal flow of a Francis hydro turbine model, J. Mech. Sci. Technol. 30 (4) (2016) 1617e1623. [9] E. Kocak, S. Karaaslan, N. Yucel, F. Arundas, A numerical case study: Bovet approach to design a Francis turbine runner, Energy Procedia 111 (2017) 885e894. [10] I. Kassanos, J. Anagnostopoulos, D. Papantonis, Numerical investigation of draft tube pressure pulsations in a Francis turbine with splitter blades, J. Phys. Conf. 813 (1) (2017) 012049. [11] Z. Chen, P.M. Singh, Y.D. Choi, Francis turbine blade design on the basis of port area and loss analysis, Energies 9 (3) (2016) 164. [12] D.V. Chirkov, A.S. Ankudinova, A.E. Kryukov, S.G. Cherny, V.A. Skorospelov, Multi-objective Shape Optimization of a Hydraulic Turbine Runner Using Efficiency, Strength and Weight Criteria, Structural and Multidisciplinary
817
Optimization, 2018, pp. 1e14. [13] M. Teodor, Impeller design using CAD techniques and conformal mapping method, in: D. Papantonis (Ed.), Centrifugal Pumps, InTech, 2012. [14] ANSYS CFX-17.1, ANSYS CFX-solver Theory Guide, ANSYS Inc, 2017. [15] F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering application, AIAA J. 32 (8) (1994) 1598e1605. [16] J.E. Bardina, P.G. Huang, T. Coakley, Turbulence modeling validation, in: Proc. 28th Fluid Dynamics Conference, Snowmass Village, CO, 1997, p. 2121. [17] M.W. Heo, J.H. Kim, T.W. Seo, K.Y. Kim, Aerodynamic and aeroacoustic optimization for design of a forward-curved blades centrifugal fan, Proc. Inst. Mech. Eng. Part A: J Power Energy 230 (2) (2016) 154e174. [18] S.J. Kim, Y.I. Kim, Y.S. Choi, K.Y. Lee, I.S. Ahn, J. Cho, J.H. Kim, Effect of a leakage wall on hydraulic performance of spiral casing tongue in a Francis hydro turbine, KSFM J. Fluid Mach. 21 (2018) 5-11 (in Korean). [19] Korea Agency for Infrastructure Technology Advancement. reportDevelopment of Construction Technology for Medium Sized Hydropower Plant (1st Year Report) (2017), Report No. 17IFIP-B128598-01.