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Standard module hydraulic technology: A novel geometrical design methodology and analysis for a low-head hydraulic turbine system, Part I: General design methodology and basic geometry considerations
Energy 196 (2020) 117151
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Standard module hydraulic technology: A novel geometrical design methodology and analysis for a low-head hydraulic turbine system, Part I: General design methodology and basic geometry considerations Jinbo Chen a, *, Abraham Engeda b a b
Ph.D. Candidate in the Department of Mechanical Engineering, Michigan State University, United States Professor in the Department of Mechanical Engineering, Michigan State University, United States
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 October 2019 Received in revised form 6 February 2020 Accepted 13 February 2020 Available online 14 February 2020
Low-head hydropower has the potential to generate a significant amount of electricity from rivers that traditionally were unsuitable for developing hydraulic power plants and supporting the resiliency of the U.S electricity system. Based on the 2016 Hydropower Vision Report, across the U.S, approximately 65.5GW of new stream-reach hydropower capacities are available. The development of those resources could be possible only if the technologies for low-head hydropower that balance efficiency, economics, and environmental sustainability were developed. The traditional hydropower design method was limited to the new challenges of the Low-head application. Therefore, a Standard Modular Hydropower Technology (SMH) was proposed by the U.S. Department of Energy (DOE) in 2017. This new concept offers a new paradigm for small hydropower technology development based on the premise that standardization, modularity, and preservation of stream functionality must become essential and fully realized features of next-generation hydropower technologies and project designs. This technology has three major modules: Generation Module, Passage Modules, Foundation Modules. This paper is the first of this series of papers that propose and develop a new design methodology for the Generation Module that is a low impact, damless Kaplan turbine system for the low-head new stream-reach sites SMH application. © 2020 Elsevier Ltd. All rights reserved.
1. Introduction Hydropower has been a major source of renewable energy for more than 100 years. With a significant amount of electricity being produced and initial capital being invested, the design philosophies of the large hydropower system focus on the long-term reliability of energy production and safety. However, recently, as the science of the effect of large hydraulic powerplant on the local ecosystem has been revealed [1,2], small hydraulic systems regain a great deal of research attention. Compared to the large hydraulic system, the small hydropower system is both economically and environmentally friendly to the developer. Additionally, most of the technical hydropower resource
* Corresponding author. 2500 Engineering Building, 428 S.Shaw Lane, East Lansing. MI 48824, United States. E-mail address: [email protected] (J. Chen). https://doi.org/10.1016/j.energy.2020.117151 0360-5442/© 2020 Elsevier Ltd. All rights reserved.
potentials in the U.S are comprised in new stream-reach development sites [3]. These sites are characterized by low-head, varying flows, and highly valued river functions, including fish preservation, sediment transport, and recreational usage, etc. Based on the 2016 Hydropower Vision Report, across the U.S, approximately 65.5 GW of new stream-reach hydropower capacities are available [3]. However, this potential energy resource can only be utilized if the innovative design methods that balance efficiency, economics, and environmental sustainability are developed. Therefore, the U.S. Department of Energy (DOE) proposed a new Standard Modular Hydropower Technology (SMH) concept that can enable hydropower technology to deploy and operate in a new stream-reach site with minimal environmental impacts and greater public acceptance at a reduced cost.
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Nomenclature A Turbine Cross-sectional Area a0 ; a1 ; a2 ; a3 ; a4 Blade thickness distribution coefficients B(t) Bezier curve function C Absolute Velocity [m/s] Cssa Stator Stagger angle setting constant Crsa Runner Stagger angle setting constant C1 ; C2 Bezier Curve Control points D Turbine Diameter [m] g Standard Gravity Constant [m/s2] H Design Head [m] K Vortex Constant m_ Mass Flow rate [kg/s] ns Specific Rotation Speed P1 ; P2 ; P3 ; P4 Bezier Curve set of points Q11 Unite Flow Rate [m1/2/s] R Runner blade r Radius location [m] S Stator blade T Relative Blade Thickness U Radial rotational velocity [m/s] W Relative Velocity [m/s] WT Turbine Work [J] DWT Turbine Specific Work [J/kg] x x coordinate y y coordinate yt Blade thickness distribution function
1.1. Standard Modular Hydropower Technology (SMH) SMH technology is a new design paradigm that places the functionalities of a stream that must be preserved at the forefront of the design process, while also utilizing standardization and modularity principles to reduce site-specificity and project costs [4]. The first concept of modularity refers to the use of different module types to assemble an entire SMH facility. The SMH has three major modules, and some modules have serval sub-modules for different sites’ application, Table 1 summarizes the basic function of each module [4]. All those modules can be assembled to form an SMH facility that matches the scale, environmental attributes, and watershed context of the site selected for development [4]. The second concept of modularity refers to the scalability at many sites through multiple modules of the same type. For example, an upstream fish passage module may be applicable at many sites with a watershed region; a cost-optimized, compact generation module designed with wide operational flexibility could be applied at multiple sites throughout the country [4]. Based on
Greek Symbol Specific Rotation Speed Absolute Velocity Angle [degree] Relative Velocity Angle [degree] Stagger angle Turbine Overall Hydraulic Efficiency General Inclined Angle [Degree] w Camberline tangential angle r Fluid Density [kg/m3] f1c ; f2c Auxiliary angle U Rotational Speed [RPM] u Rotational Speed [rad]
Us a b g ht q
Subscript c Hub L LC p r s s Tm Tip u 1/2/3
Points on the camberline Hub Location Leading-edge Chord length Points on the blade pressure surface Runner Stator Points on the blade suction surface Maximum thickness Tip Location Circumferential direction Stator Inlet/Runner Inlet/Runner Outlet,
the initial investigation, a successful SMH facility should have six features [4]: 1. Predictable and somewhat regular production of electricity; 2. Minimal alteration of the inflow hydrograph and minimal impoundment of inflow water; 3. Environmental mitigation technology (functionality) inherent within and integral to the facility design (including fish passage, water quality, and sediment management design); 4. Minimal disruption to the aesthetics of the natural stream and stream-scape; and do not occupy the full width of the river; 5. Minimal fluctuations of water surface elevation; 6. Enabling of safe recreational passage through and activity around the project;
1.2. Description of the generation module As the most critical module for SMH technology, the Generation Module is envisioned as an integrated water-to-wire module that contains a hydraulic water turbine, generator, controls, and
Table 1 The basic function for each SMH modules (Adapted from Ref. [4]). Major Modules
Basic Function
Generation Module including, Turbine Rotor Module; Generator Module Passage Module including, Fish Passage Module, Sediment Passage Module, Recreation Passage Module, Water Passage Module Foundation Module
Encompasses all hydraulic and electric machines, equipment, and systems necessary for hydroelectric power generation. Allow fish, sediment, water, and recreational craft to pass the facility safely.
Provides structural resistance and reliably interface with the streambed to support generation and passage modules
J. Chen, A. Engeda / Energy 196 (2020) 117151
electrical equipment within a single unit [4]. The overall design goal of the generation module is to balance the performance, economic, and environmental sustainability, so it is appealing for developers. 1.2.1. Performance considerations The traditional hydraulic system often equips with a large reservoir that helps the system maintain the optimum operating condition.; however, the SMH system for new stream-reach sites requires minimal water impoundment. Moreover, one major characteristic of the new stream-reach development sites is various flow features, and Fig. 1 shows an example of a daily flow rate of one selected new stream-reach development site. Additionally, at most low-head new stream-reach sites, the tailwater elevation generally rises twice as fast as headwater elevation when river flow increases, leading to a significant reduction in the available gross head [5]. As a result, the low-head new stream-reach sites with high variability in flow and head often result in operating beyond the acceptable performance and efficiency limits for the traditional turbine. This variability requires a different deployment of regulation methods and presents a significant design challenge for generation module design. 1.2.2. Economics considerations The immediate installed cost target for an SMH project is under $6000/kW that including all necessary modules [4]. Over time, this number should be reduced as the module deployment increase. Conventionally, there are six main cost sectors for developing a small hydro project: 1. Installation Cost. 2. Planning Cost. 3. Civil work. 4. Infrastructure and Logistic.5. Electrical connection/Construction. 6. Equipment Cost. And, among those sectors, the civil work normally represents 40%e50% of the total project cost for a hydro-power project [6]. This civil work cost normally is because of the construction of the dam for creating a necessary head, and the water channel for diverting the river to the turbine. However, for low head new stream-reach sites, which feature the minimal water impoundment and run-of-river type operation, the traditional dam structure is not a necessity. Therefore, a damless concept for the generation module which means the size of the generation module can be large enough for creating enough low head conditions,
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which will significantly reduce the overall cost, but at the same time create new design challenges for turbine designs. 1.2.3. Environmental sustainability considerations The preservation of stream functionality is one of the most instrumental premises for SMH technology, and there are three major environmental considerations for the new stream-reach sites: 1. Fish Preservation. 2. Sediment Preservation. 3. Recreation Activities Preservation. Among all those three, there is one major consideration that is critical for the generation module design, which is fish preservation. The new stream-reach sites’ river often has high-valued native fish species (anadromous, catadromous, and amphidromous), and hydropower facilities can work as barriers for them. Therefore, the low head hydro-system needs to have maximum protection for fish migrations. To achieve this fish protection, there are two ways: Introducing advanced fish passage design for overall facility construction and introducing the fishfriendly turbine design concept that allows fish to pass the generation module safely. For a fish-friendly generation module, the DOE’s criteria for design and evaluation of the new fish-friendly turbine runner [7] is a useful guideline for the initial design consideration. Among all those criteria, there are two critical requirements for the initial design: Large turbine area for fish migration, low peripheral runner speed for minimizing fish strike injury. Those two criteria limit the size and operating conditions (namely overall diameter, and rotational speed) for the SMH generation module. 1.2.4. Design Specifications for SMH generation module Because of the above performance, economics, and environmental considerations, the DOE has five specific design specifications for SMH generation module [4]: 1. Must be fully immersed in water, which necessitates the use of the reaction-type of the turbine. 2. Must encompass all equipment and systems for safe and reliable operation. 3. The design flow rate should be less than 113 m3/s and design head less than 9 m per unit. 4. Run-of-river type operation is preferred meaning the sum of inflows into the upstream region of the facility must equal the sum of outflows into the downstream reach of the facility. 5. Minimal environmental disturbance, including low fish mortality rate, and low noise level, etc. 1.3. Current status of the low-head hydropower development
Fig. 1. Daily flow rate for a selected new stream-reach site. (Data extrapolated from Oak Ridge National Laboratory SMH Explorer website: https://smh.ornl.gov/explorer/).
Currently, there are two paths for utilizing the potential energy of the low head or new stream-reach sites: 1. Low-head Hydropower Application. 2. River Current Application. For the low-head hydropower application, there are five major types of turbines that currently used: 1. Open-flume Francis turbines. 2. Kaplan turbine. 3. Tubular turbines. 4. Crossflow turbine. 5. Archimedes screw turbines. Table 2 summaries some advantages and disadvantages of those types of turbines [8]. For the River-current application, the hydro-kinetic turbine is commonly used. This type of turbine uses ultra-low or zero head conditions and driven by the free-flow stream. This technology has two advantages: 1. Multi-unit arrays can be deployed for maximum power production like the wind farm. 2. The structural requirements are low; thus, the civil cost will be limited. However, this technology still suffers from some significant drawbacks, including 1. Relatively low efficiency. 2. High installation cost. 3. High maintenance difficulties. Based on the DOE’s design specification, only the reaction type
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Table 2 Five major types of the turbine for low-head applications (Adapted from Ref. [8]). Turbine Type
Advantages
Disadvantages
Open-flume Francis Turbine Kaplan Turbine Tubular Turbine
High efficiency on the design condition High efficiency over a wide range. High efficiency, and various configurations for a low hydraulic loss. Wide operation range (head and flow). Wide operation range, high tolerance for debris, and fish friendly.
Narrow operation range, expensive to manufacture The regulation method can be complex Need straight passage through the turbine, can increase the civil cost. Relatively low efficiency Relatively large for transportation, technology still immature.
Crossflow Turbine Archimedes Screw Turbine
of turbine is suitable for SMH technology, and the high variability mentioning above limits the turbine selections; therefore, among all turbine types, the Kaplan turbine (or its variants) is the best option for the SMH technology. However, the new design method and considerations need to be developed for the challenges associated with the new SMH technology.
2.1. Generation module initial size and operation condition design 2.1.1. Generation module overall size and positioning Initial size design is the first challenge for developing a lowhead hydraulic turbine. Traditionally, a specification map is used
1.4. Objectives Based on the need for a new and innovate design method for SMH technology that is suitable for potential new stream-reach sites, this first paper presents the basic concept and design specification of SMH technology, detailed design methodology development, some fundamental geometrical considerations, and basic performance prediction from advanced numerical simulation results. 2. Design methodology development The proposed generation module is an open flume and damless Kaplan turbine system and has eight major components. Fig. 2 shows an example of this generation module. This Generation Module has a fixed stator, and an adjustable runner, the geometry of the stator and runner can be optimized for better performance. This first paper focuses on two major geometrical design tasks, Generation Module’s initial size and operation condition design, and Generation Module blade profile design.
Fig. 3. A typical specification map for different hydraulic turbine types [9].
Fig. 2. The overall generation module configurations. (Left: Total Assembly Model. Right: Close-up for each component).
J. Chen, A. Engeda / Energy 196 (2020) 117151
for determining the basic turbine characteristics, including head, rating power, and rotational speed for optimum performance. Fig. 3 [9] shows a typical specification map of the specific speed and specific diameter for various turbine types, and Fig. 4 [10] shows a Kaplan turbine specification map of the specific speed and head. Those charts come from years of surveys from the major hydro stations and often provide an accurate initial size design for the traditional hydro-system. For a low head condition, those charts can result in a smaller size and higher rotational speed for better performance. Those features are contradicted with the concept of SMH, which requires a large turbine area and less fish damage. This proposed turbine uses its turbine structure (Part-A in Fig. 2) to provide the low head condition; therefore, the initial turbine size is related to the designed head and the positioning of the turbine structure. For a low head application turbine, the turbine structure is often positioned in water with a general-inclined angle (refer as q in Fig. 2), and this angle is generally from 15 45 [11]. A larger inclined angle requires a more extended turbine structure and is more subject to the tailwater elevation; and a smaller inclined angel can have a shorter turbine structure, which means a smaller turbine area. Turbine structure minimum length can be calculated as
Turbine structure minimum structure lengthz
H cosq
(1)
This minimum length gives a guideline for the initial size of the turbine (Turbine Overall Diameter), and addition head-gate (Part-H in Fig. 2) can be equipped for more headspace for the off-design condition.
2.1.2. Generation module hub diameter After determining the overall diameter, the turbine hub diameter is the next parameter that is needed to be considered with cares. For an SMH generation module, the hub volume must contain the generator and control components; this means the hub diameter and its impact on turbine performance must be studied thoroughly for future generator selections and designs. Additionally, depending on which 1-D design method was used for the turbine runner, the hub diameter can have a significant impact on the turbine runner shape, which was covered in section 2.2.1. For a
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traditional Kaplan turbine, two empirical equations can be used for determining the hub-tip ratio for optimum performance [9,10].
Dhub ¼ 0:8 0:1Us Dtip
(2)
Dhub 94:64 ¼ 0:25 þ ns Dtip
(3)
Those equations can only be used for the initial guess, and the different hub-tip ratio must be studied for low-head application. For this paper, five different hub-tip ratios between 0.68 and 0.8 were studied, and the results are shown in section 4.1.
2.1.3. Generation module operation condition For the initial design stage, the rotational speed is the only operation condition that needs to be considered. The criteria for determining rotational speed comes from environmental considerations. The high rotational speed is typically required for a low head application that can have a high risk for fish damaging. In 1999, DOE developed ten criteria for designing a fish-friendly hydraulic turbine system [7]. This criteria state that a fish-friendly turbine should have a less than 12.24 m/s (preferably 6.12 m/s) peripheral runner speed and limits the maximum rotational speed for the SMH generation module.
2.2. Generation module blade profile design 2.2.1. 1-D turbine design All turbine design starts with a 1-D velocity calculation, so it is crucial to define the velocity component. Fig. 5 shows a typical velocity triangle for a Kaplan turbine. For the initial 1-D Kaplan turbine design, there are two steps to calculate the velocity at each radial span location: 1. Determining the mean velocity value, 2. Determining other spans’ velocities with an appropriate velocity assumption. Determining mean velocity value is simplified by using three fundamental conservation equations as 1. Conservation of Mass:
ð ð ð m_ ¼ rCx1 dA1 ¼ rCx2 dA2 ¼ rCx3 dA3
(4)
2. Conservation of Energy
Fig. 4. A Kaplan Turbine specification map [10].
Fig. 5. A typical velocity triangle for a Kaplan turbine with three-stages. (1: Stator Inlet. 2. Runner Inlet [Stator Outlet]. 3. Runner Outlet).
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_ WT ¼ ht mgH
(5)
3. Conservation of Momentum
W
DWT ¼ _ T ¼ UðCu2 Cu3 Þ m
(6)
The next step is determining the velocity component at each radial span location, which is the most crucial part of the design. Conventionally, the free-vortex assumption is widely used for initial velocity calculation. Free vortex assumption, which is an inviscid and ideal case, has two major parts: 1. Flow upstream of the runner is assumed to be free-vortex which means: rCu ¼ constant, r is the radial location; 2. Flow has uniform velocity distribution in the axial direction, which means: Cx ¼ constant. There are two other assumptions that could also be used for initial velocity calculation: Force vortex assumption, Constant vortex. The forcevortex means Cu ¼ Kr, where K is vortex constant. The constant vortex means Cu ¼ constant. Fig. 6 shows examples of runner blade geometries designed with three different vortex assumptions. Previous research [12] has shown that different vortex assumptions trend to have similar hydraulic performance, and the only difference was the pressure distribution pattern across the blade, which may result in different deformation behavior of the blades. This paper mainly uses the free vortex assumption for initial velocity calculations. When utilizing the free vortex assumption for designing the runner blade because of the relatively low rotational speed, a small hub diameter can result in large Cu2 velocity and small U velocity. This can cause a negative b2 value. This negative b2 value at specific radial span locations can cause a larger twist angle of the blade and Fig. 7 shows three blade geometries with three hub diameters. A large twist angle blade can increase the complexity and the manufacturing cost of the blade. Therefore, it is crucial to define a minimum hub-tip ratio for preventing a large blade twist angle. When using the free vortex assumption, the minimum hub-tip ratio is defined when b2 ¼ 0, and can be calculated as
D2hub 4ht g cos q ¼ Dtip u2
(7)
Where ht is the initial guessed turbine efficiency, gis standard gravity constant, q is turbine general inclined angle, u is the
Fig. 7. Three example runner blades configurations with different hub diameter settings. (From left to right: hub-to-tip ratios [Dhub /Dtip ¼ 0.685, 0.743, 0.8.)
designed rotational speed in rad. This equation can provide the initial guide for the turbine hub diameter design. 2.2.2. 1-D blade profile design By using the calculated velocity values from the vortex assumption, blade geometry can be constructed by two steps: 1. Blade camberline construction, 2. Blade thickness distribution. The proposed generation module has two blade profiles: one is the stator blade, and another one is the runner blade. Those two blades profiles share the same design process. Here shows a general process for designing a runner blade geometry (for stator blade geometry, replace the runner blade angle values with stator angle values). Based on Equation-(6), the power delivered by the turbine runner blade is only extremely on blade inlet and outlet velocity conditions. Therefore, for general 1-D considerations, the blade camberline can be any curve shape as long as the blade inlet and outlet match the velocity condition (namely velocity direction). However, the blade geometry has a significant effect on overall hydraulic performance. Therefore, the blade camberline construction method needs to meet two main requirements: 1. Must match the inlet and outlet velocity conditions. 2. Must have the flexibility to control the general curve shape for further optimization. To achieve those two requirements, the fourth-order Bezier Curve is used to construct the blade camberline geometry. The Bezier curve is a parametric curve constructed by a set of points. The first point (P0 ) and last point (P4 ) are always at the beginning and endpoint of the camberline, and the other points are used for constraining the curve. The general nth order Bezier curve state as
BðtÞ ¼
n X n i¼0
i
ð1 tÞni t i Pi
(8)
n Where is the binomial coefficient, Pi is the set of points. i So, for the fourth-order Bezier curve
BðtÞ ¼ ð1 tÞ4 P0 þ 4ð1 tÞ3 tP1 þ 6ð1 tÞ2 t 2 P2 þ 4ð1 tÞt 3 P3 þ t 4 P4 (9) Fig. 6. Three example runner blades with different vortex assumptions. (From Left to right: Free Vortex, Force Vortex, Constant Vortex).
For a standard unit runner blade camberline shown in Fig. 8, P0 is the inlet point, P4 is the outlet point: P0 ¼ ð0; 0Þ; P4 ¼ ð1; 0Þ.
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Fig. 8. A standard-unit runner-blade camber line configuration.
Then, to match the velocity direction, two lines are drawn that are both tangential to the curve at inlet and outlet. The intersection point of two lines is the P2 ,
1
0 B P2 ¼ B @
1 1þ
cotf1c cotf2c
;
cotf1c C C 1 þ cotf1c A
(10)
cotf2c
f1c ¼ gr þ b2 f2c ¼ 180 gr b3
(11)
where, gr is the stagger angle of the runner blade (gs is for the stator). For a continuous curve
90 b3 < gr < 90 b2 ; gr ¼ ð90 b3 Þ þ Crsa ðb3 b2 Þ
Fig. 9 shows three runner blade profiles with Crsa ¼ 0.1; 0.5; 0.9. The main function of a runner is turning the flow from b2 to b3 . When Crsa is small, the stagger angle (gr ) and the camberline leading-edge tangential angle (wL ) are close to the inlet flow angle. As a result, the location of the blade turning action happens close to the leading edge. This location, Lw , can be indicated by the location when the camberline tangential angle equal to zero (wc ¼ 0). For example, when Crsa ¼ 0:1, Lw ¼ 13:8% of the chord length; when Crsa ¼ 0:9, Lw ¼ 74% of the chord length. Small Crsa value can result in a blade profile with a long tail region (Shown in Fig. 9) which improve the flow attachment; however, extremely small Crsa value can result in irregular blade leading edge shape which causes inlet flow mismatch. Therefore, this stagger angle setting constant is critical for the turbine blade design and has a significant influence on the turbine’s overall hydraulic performance. Fig. 10 shows examples of runners and stators geometry with different stagger angle setting constants, and detailed numerical results were shown in section 4.2. Conventionally, three points (P0 ; P2 ; P4 Þ are enough for constructing a blade camberline for the right velocity condition. However, a three-point Bezier curve (second-order Bezier curve) has one disadvantage: for a given velocity condition (which means b2 and b3 are given), the blade profile is only related to the stagger angle. This means, for a fixed stagger angle, the blade profile cannot be changed, which can cause less fixable control for further optimization. So instead of a second-order Bezier curve, the fourthorder Bezier curve is used by adding two more points to construct the blade camberline. One point (P1 Þ is on the straight line P0 P2
P1 ¼ c1 P2x ; c1 P2y
(12)
where, Crsa is the runner blade stagger angle setting constant, and Crsa is between 0 and 1 (For stator blade, the stator blade stagger angle setting constant is referred to Cssa and can be defined the same way with stator blade angle b1 and b2 ).
(14)
C1 and C2 are two Bezier curve control points. By adding those two points, this method not only meets the velocity conditions but also increases the flexibility for further optimization. Therefore, the general fourth-order Bezier curve point coordinate for the runner blade camberline is
BðxÞ ¼ ½4c2 3 þ P2x ð6 c1 4c2 Þx4 þ ½4 4c2 þ P2x ð12c1 þ 4c2 12Þx3 þ P2x ð6 12c1 Þx2 þ 4P2x c1 x
(15)
BðyÞ ¼ P2y ð24 16c1 16c2 Þx4 þ 4 4c2 þ P2y ð12c1 þ 4c2 12Þ x3 þ P2y ð6 12c1 Þx2 þ 4P2y c1 x
(16)
After choosing the correct value for the stagger angle setting constant and the Bezier curve control point, the camberline can be designed. The last step for constructing a blade profile is to have a thickness distribution function for the camberline. For this paper, the NACA-4 series profile is used and can be written as
RLc
Fig. 9. Three runner blade profiles with different runner blade stagger angle setting constant (Crsa ¼ 0:1; 0:5; 0:9).
(13)
another point (P3 ) is on the straight line P2 P4
P3 ¼ ð1 ð1 P2x Þc2 ; c2 P2y
where, f1c and f2c are auxiliary angles, that come from the velocity triangle
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yt R or ST a0 x0:5 þ a1 x þ a2 x2 þ a3 x3 þ a4 x4 ¼ T or SLc 0:2
(17)
where, RLC and SLC are the runner and stator blade chord length; and RT and ST are the runner and stator blade relative maximum thickness as:
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Fig. 10. (a). Runner Blade and (b). Stator Blade, with three different stagger angle setting constants.
RT ¼
RTm S ; ST ¼ Tm RLc SLc
(18)
where, RTM and STM are the runner and stator blade maximum thickness, and the a0 to a4 are prescribed coefficients:
a0 ¼ 0:2969; a1 ¼ 0:126; a2 ¼ 0:3516; a3 ¼ 0:2843 a4 ¼ 0:1015 or 0:1036 for a closed trailing edge
3. Numerical analysis method and conditions
(19) To utilize this thickness distribution function, a superposition method which superimposes the thickness onto the camberline is needed. This superimposes method calculates the blade’s suction and pressure side surface point coordination using points located at the camberline. Assuming the point on the camberline has coordinations (xc yc ), the blade suction surface point coordination (xs ys ) can be calculated as:
xs ¼ xc ðyt ðxc ÞÞsinwc ys ¼ yc þ ðyt ðxc ÞÞcoswc
(20)
the blade pressure surface point coordination (xp yp ) can be calculated as:
xp ¼ xc þ ðyt ðxc ÞÞsinwc yp ¼ yp ðyt ðxc ÞÞcoswc
The above method has great flexibility for designing an SMH generation module, for example, by using 11 radial span locations, the runner blade has a total of 33 parameters for modifying runner blade geometry, which is good for future pressure distribution, stress, and performance optimization.
(21)
where wc is the camberline tangential angle at each chosen point. By using the above method, the blade profile for each span location can be determined; then by using standard CAE software that connects each span’s blade profile, the final blade geometry can be constructed.
CFD (computational fluid dynamic) has played an important role in the general water turbine design and performance prediction. As shown in Ref. [13], a detailed comparison between experimental results and different CFD models prediction results for a Kaplan turbine system. The transient simulation model has advantages over steady-state simulation [13]. However, the computational costs are too expensive for developing a design methodology that required numerous CFD simulations. A steady-state k u SST CFD model was used in this paper, which has acceptable accuracy for predicting the discharge rate, torque, and efficiency [13]. The general CFD software ANSYS FLUENT 17.2 (ANSYS.Inc) was used to perform the 3-D steady-state flow analysis [14]. The overall hydraulic performance of the turbines is measured by the calculated hydraulic turbine efficiency ht . This efficiency value indicates what percentage of the total available hydraulic power is converted into the turbine work. The hydraulic efficiency is calculated as
ht ¼
Tu _ mgH
(22)
where T is the torque on the runner blade, u is the runner blade rotational speed, g is the standard gravity constant, m_ is the mass flow rate, and H is the available head.
J. Chen, A. Engeda / Energy 196 (2020) 117151
3.1. Computational domains The mesh represents the geometric domain for the numerical simulation, which has a significant impact on the accuracy and the computational cost of the simulation. For this method, the computational domains include three parts: inlet water channel, stator, and runner. Fig. 11 shows an example of this mesh. The runner is the rotating part, and the rest are the stationary parts. The multiple reference frame model is used to solve the stationary and rotating parts. Generally, more grids mean more accurate results but with a higher computational cost. Therefore, it is necessary to demonstrate how the mesh size would influence the overall prediction of the performance. Five different mesh schemes were selected for one example model, and Table 3 shows the detailed mesh information for each scheme. Fig. 12 shows the mesh quality and performance relation. All values in Fig. 12 were normalized to the mesh scheme-2 values. The results show that with a finer mesh, the efficiency increases by around 0.68%, the mass flow rate decreases around 0.57%, and the power increases by around 0.12%. Scheme-5 would provide more accurate results; however, the computational cost was too substantial. By using the same computing power, scheme-5 required 45 times more computational time than scheme-2. This methodology needs hundreds of simulations to verify the geometry settings and other parameters; therefore, Mesh scheme-2 was considered sufficiently reliable for predicting the overall hydraulic performance and was mainly used
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Table 3 Detailed mesh information for five different mesh schemes. Mesh Scheme 1 Mesh size [m] Mesh Type Total grid Number [million]
2
3
4
5
0.015 0.01 0.0075 0.006 0.005 Tetrahedrons Mesh þ 10 layer near the wall ~13.6 ~33.3 ~70.8 ~178.4 ~304.5
Fig. 12. Mesh quality and normalized performance relation for five different mesh schemes.
in this paper. Table 4 summarizes the design conditions and numerical simulation conditions for this paper. 4. Numerical results and discussion The first paper focuses on three major geometrical design parameters, including Hub Size, Stator stagger angle setting constant, and Runner stagger angle setting constant. Each setting was investigated by numerical simulations to find its impact on the overall hydraulic performance. 4.1. Hub size consideration
Fig. 11. The numerical grids for the three computational fluid domains.
As shown in Fig. 7, the hub size has a massive impact on the turbine blade design, which can have a significant influence on the overall hydraulic performance. Moreover, for the SMH generation module, the hub should have enough space for generator and control components. So, it is essential to thoroughly investigate the hub size and its impact on overall hydraulic performance. Five different hub-to-tip ratios (Dhub/Dtip) were chosen and thoroughly investigated, and Fig. 13 shows the results. The results show that for low flow rate conditions (when Q11 < 0:2), the largest hub diameter (Dhub/Dtip ¼ 0.8) model has the best performance, and the performance decrease with decreasing hub diameter and the maximum performance difference between different hub sizes is around 3.2%. When the flow rate increases, the smallest hub model (Dhub/Dtip ¼ 0.685) has the best overall hydraulic performance, and the maximum performance difference for different hub sizes is around 10.1%. Also, the results indicate that the smaller hub diameter has a flatter performance curve than a larger hub diameter, and the hub size has a larger impact on overall hydraulic performance at a large flow rate condition.
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J. Chen, A. Engeda / Energy 196 (2020) 117151 Table 4 Design and Numerical simulation conditions. Design Condition
Design Head (H)
2
6 Unit Flow Rate (Q11) 6 4Q11
Numerical simulation Condition
3 m3 Q s 7 ¼ 2 pffiffiffiffi 7 5 Dtip H
Overall Diameter (Dtip) Rotational Speed (U) Inlet/Outlet Boundary Condition Turbulence Model Simulation Type Mesh Size
2.5m 0.103~0.52m1/2/s
3.5m 40rpm Total Pressure k u SST Steady State ~33 Million
At a larger flow rate condition (Fig. 14-b), the smaller hub configuration has a larger circumferential velocity difference across all span locations (Blue Arrow). This massive difference causes the smaller hub configuration to have a significantly better overall performance at a larger flow rate condition. In general, choosing the right hub size is about balancing the design flow rate and the required hub volume. At a high flow rate, the smaller hub can provide an excellent overall hydraulic performance but with limited hub volume that can have high overheating possibilities for the generator, which can further affect the overall electrical performance. Balancing the hub size and performance is the key for the initial sizing of the turbine unite. Fig. 13. The relation between overall hydraulic efficiency and design flow rate (Q11) for five selected Hub-to-Tip ratio configurations.
4.2. Stator stagger angle setting constant considerations
According to Equation (6), the runner blade power is determined by the magnitude of the runner blade circumferential velocity difference. Therefore, Fig. 14 shows the circumferential velocity difference (Cu2eCu3) distribution plots from hub to tip at two Q11 conditions for all five different hub-size configurations. At a lower flow rate condition (Fig. 14-a), on the close to hub region (less 25% Span Location), smaller hub configuration has a significantly larger circumferential velocity difference (Red Arrow). However, this circumferential velocity difference drops steeply and remains at a very low value (Black Arrow) on the close to tip region (between 60% and 100% Span Location). In general, at a low flow rate conditions, the smaller hub configuration tends to have a worse performance on the close to tip region, which leads to poor overall performance.
As shown in Fig. 10-b and Equation (12), the Stator Blade Stagger Angle Setting Constant (Cssa ) is a critical parameter for designing the stator blade profile. Fig. 15 shows how this parameter affects the overall performance at four flow rate conditions. The results show that for small flow rate condition, the overall hydraulic efficiency increases with the increase of Cssa and reaches the maximum efficiency when Cssa is around 0.7e0.8, then decrease with the increase of Cssa . For large flow rate conditions, the overall hydraulic efficiency increases with the increase of Cssa and reaches the maximum efficiency when Cssa is around 0.5e0.7, then remains relatively constant, then decreases when Cssa is larger than 0.8. For all flow rate conditions, the initial increase of efficiency with the increase of Cssa is universal, and the maximum efficiency occurs when Cssa is around 0.5e0.8. Four models under one flow rate condition (Red Square in Fig. 15) were selected for further
Fig. 14. The circumferential velocity difference (Cu2eCu3) distribution plots from hub to tip at two Q11 conditions for all five different hub-size configurations, (a) Low Flow Rate Condition. (b) High Flow Rate Condition.
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Fig. 15. The Relation between overall hydraulic efficiency and stator blade stagger angle setting constant Cssa for four flow rate conditions.
investigations. The primary function of the stator is to redirect the inflow to the runner blade with the desired angle, so for the four selected models, two angles were studied: b2 and a2 . 4.2.1. -Considerations The b2 is the runner blade inlet relative flow angle (see in Fig. 5), and ideally, the b2 flow angle should be the same as the b2 blade angle. A large difference between b2 blade and b2 flow can increase the runner blade incidence loss, which can affect the overall performance. Fig. 16 shows the comparison between the b2 blade and b2 flow for the four selected models. The results show that near the hub region because of the boundary flow and low runner circumferential velocity (velocity U in Fig. 5), the b2 flow is larger than the b2 blade for all four selected models and the maximum angle difference is around 12 . And near the tip region because of the boundary flow and larger runner circumferential velocity, all b2 flow value is larger than the b2 blade for the four selected models, and the maximum angle difference is around 9 . However, results are different in the center of the span region. - The smaller Cssa models (Cssa ¼0.1,0.3) trends to have a larger b2 flow than the b2 blade ; the maximum angle difference is ~þ3 . - The medium Cssa models (Cssa ¼0.5) trends to have a very similar b2 flow than the b2 blade ; the maximum angle difference is only ~þ0.4 . - The larger Cssa models (Cssa ¼0.8) trends to have a smaller b2 flow than the b2 blade ; the maximum angle difference is ~ -4 . As shown above, the difference between b2 flow and b2 blade can undoubtedly affect the overall performance, but the results in Fig. 16 cannot fully explain the trend shown in Fig. 15. Therefore, another angle a2 has been studied. 4.2.2. a2 -Considerations The a2 is the runner blade inlet absolute flow angle (see in Fig. 5), and this angle determines the magnitude of the runner blade inlet circumferential velocity (Cu2). Larger a2 means larger Cu2These which results in more substantial potential work done on
11
Fig. 16. The runner blade inlet b2 flow angle distribution plots for four selected models in comparison with the designed b2 blade value.
the runner blade (based on Equation. (6)). Fig. 17-(a) shows the a2 distribution plot across all span location for the four selected models with the comparison with the 1-D designeda2 values. The smaller Cssa (Cssa ¼0.1) model shows significant lower a2 values in the majority center span region (expect the hub and tip boundary region), the difference is around 60 . The larger Cssa (Cssa ¼0.8) model also shows lower a2 values in the majority span center region, but the difference is only around 10 . This huge difference in the a2 value explains why Model-4 (Cssa ¼0.8) has significantly better performance than the Model-1 (Cssa ¼0.1). For better visualization, Fig. 17-(b) shows the stator blade stream-line pattern for the Model-1(Cssa ¼0.1) and Model-4 (Cssa ¼0.8) at 50% span location, and Fig. 18 shows the corresponding runner blade stream-line pattern (Absolute velocity) at the same span location. When Cssa is small, as shown in Fig. 17-(bBottom), the stator blade camberline has a flat profile in the font region, and the diversion of the flow only happens near the trailing edge. This profile results in poor flow redirection and leads to very small a2 value. When Cssa is large, as shown in Fig. 17-(b-Top), the stator blade camberline has a flat profile in the rear region; the diversion of the flow happens near the leading edge. This profile results in good flow redirection and leads to a larger a2 values. In general, the Cssa value has a larger impact on a2 values than b2 values and has a profound influence on stator outlet flow behaviors, which can further affect the overall performance.
4.3. Runner blade stagger angle setting constant Just like the stator blade stagger angle setting constant, the runner blade stagger angle setting constant (Crsa ) is a critical geometrical parameter for the runner blade profile. Fig. 19 shows how this parameter affects the overall performance under four different flow rate conditions. For all flow rate conditions, the efficiency first increases with the increase of Crsa , then reaches the maximum efficiency when Crsa is between 0.3 and 0.5, then the efficiency decreases significantly with the increase of the Crsa .
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J. Chen, A. Engeda / Energy 196 (2020) 117151
Fig. 17. (a). The runner blade inlet absolute flow angle (a2 ) distribution plots for four selected models in comparison with the designed a2 value; (b). The stator stream-line pattern for the Model-4 (Top) and Model-1 (Bottom), at 50% span location.
Fig. 18. The runner stream-line pattern for the Model-4 (a) and Model-1 (b), at 50% span location.
Four models were selected (Red Square in Fig. 19) for further investigation. As described in section 4.1, the magnitude of the circumferential velocity difference (Cu2eCu3) represents how effective a runner blade is converting the hydraulic power to mechanical power. So, Fig. 20-(a) shows the circumferential velocity difference distribution plots for the four selected models. Model-2 has a higher (Cu2eCu3) value than the other three models, which is reasonable for its highest efficiency. Model-1 has a very similar
trend as Model-2 but with a small decrease in value near the tip region (Red Arrow), which cause a small efficiency drop compared to the Model-2. Model-3 and Model-4 have significantly lower (Cu2eCu3) values, especially in the 40%e80% span location (Blue Arrow), which cause them to have lower efficiency. For better visualization, Fig. 20-(b) shows the stream-line pattern for the Model-2 (Crsa ¼0.3) and Model-4 (Crsa ¼0.8) at 80% span location. Model-2 shows a great flow attachment, which gives
J. Chen, A. Engeda / Energy 196 (2020) 117151
Fig. 19. The Relation between overall hydraulic efficiency and runner blade stagger angle setting constant Crsa for four flow rate conditions.
it a better performance, and the Model-4 shows some flow distortion near the leading edge on the pressure side of the blade, which causes the drawback of the efficiency. In comparison with Cssa in which has a 12% maximum efficiency difference, the Crsa with a 9% maximum efficiency difference has less impact on the performance. However, this impact is still significant enough and needs to be carefully considered. Based on the comprehensive results, initially, the suggested range for Cssa is between 0.7 and 0.8, and for Crsa is between 0.2 and 0.3. 5. Conclusions Low-head hydropower has the potential to generate a significant amount of electricity from rivers that traditionally were unsuitable for developing hydraulic power plants and supporting the
13
resiliency of the U.S electricity system. The development of those resources could be possible only if the technologies for low-head hydropower that balance efficiency, economics, and environmental sustainability were developed. The traditional hydropower design method was limited to the new challenges of the Low-head application. Therefore, a Standard Modular Hydropower Technology (SMH) was proposed by the U.S. Department of Energy (DOE) in 2017. This paper proposed a new design methodology for SMH technology generation modules. This methodology consists of a new method for constructing the blade profiles with great flexibility and novel considerations for several critical geometrical setting parameters. Three of them were covered in this first part of the paper: Hub size, Stator stagger angle setting constant, and Runner stagger angle setting constant. With numerous numerical simulation results, the relation between each geometrical setting parameter and the overall hydraulic efficiency was presented. There are two major findings: (1) The hub size has a critical impact on performance, especially at large flow rate conditions. Smaller hub size has better performance at larger flow rate conditions, and larger hub size models have better performance at low flow rate conditions. The different circumferential velocity distributions patterns cause this performance difference. At a high flow rate, the smaller hub can provide an excellent overall hydraulic performance but with limited hub volume that can have high over-heating possibilities for the generator, which can further affect the overall electrical performance. Balancing the hub size and performance is the key for the initial sizing of the turbine unite. (2) The stator and runner blade stagger angle setting constant are critical for the stator and runner blade profile. A smaller stator blade stagger angle setting constant can cause poor flow redirection at the stator outlet, which causes low efficiency. A larger runner blade stagger angle setting constant
Fig. 20. (a). The circumferential velocity difference (Cu2eCu3) distribution plots from hub to tip for four selected models. (b). The stream-line pattern for the Model-2 (Top) and Model-4 (Bottom), at 80% span location.
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can cause flow distortion near the runner blade leading edge, which causes low efficiency. References [1] Tullos Desiree. Assessing the influence of environmental impact assessments on science and policy: an analysis of the Three Gorges Project. J Environ Manag 2009;90:S208e23. [2] Botelho Anabela, et al. Assessment of the environmental impacts associated with hydropower. Renew Sustain Energy Rev 2017;70:896e904. [3] O’connor Patrick, et al. Hydropower vision A new chapter for America’s 1st renewable electricity source. 2016. No. ORNL/TM-2016/688. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). [4] Witt Adam, et al. Exemplary design envelope specification for standard modular hydropower technology: draft for public comment. 2016. [5] Brown Kinloch David. Demonstration of variable speed permanent magnet generator at small, low-head hydro site. Midway, KY (United States): Weisenberger Mills, Inc.; 2015. No. Final Report: DOE-WEISENBERGEREE0005429-1.
[6] Johnson Megan, Uria-Martinez Rocio, O’Connor Patrick. Hydropower market report update metadata. Oak Ridge, TN (United States): Oak Ridge National Lab.(ORNL); 2016. 2017. [7] Odeh Mufeed. A summary of environmentally friendly turbine design concepts. US Department of Energy Idaho Operations Office; 1999. [8] Zhou Daqing, Deng Zhiqun Daniel. Ultra-low-head hydroelectric technology: a review. Renew Sustain Energy Rev 2017;78:23e30. [9] Korpela Seppo A. Principles of turbomachinery. Hoboken, NJ: Wiley; 2011. [10] De Siervo F, De Leva F. Modern trends in selecting and designing Kaplan turbines. Water power and dam construction 1978;30(1):28e35. [11] Gordon JL, Eng P. Turbine selection for small low-head hydro developments. Buffalo: Proc. Waterpower XII; 2003. [12] Muis Abdul, Sutikno Priyono. Design and simulation of very low head axial hydraulic turbine with variation of swirl velocity criterion. International Journal of Fluid Machinery and Systems 2014;7(2):68e79. [13] Jost Dragica, Skerlavaj Alja z, Lipej Andrej. Improvement of efficiency prediction for a Kaplan turbine with advanced turbulence models. Strojniski vestnik-Journal of Mechanical Engineering 2014;60(2):124e34. [14] Guide, ANSYS FLUENT user’S. Ansys Inc; 2016. Release 17.0.
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Standard module hydraulic technology: A novel geometrical design methodology and analysis for a low-head hydraulic turbine system, Part I: General design methodology and basic geometry considerations Jinbo Chen a, *, Abraham Engeda b a b
Ph.D. Candidate in the Department of Mechanical Engineering, Michigan State University, United States Professor in the Department of Mechanical Engineering, Michigan State University, United States
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 October 2019 Received in revised form 6 February 2020 Accepted 13 February 2020 Available online 14 February 2020
Low-head hydropower has the potential to generate a significant amount of electricity from rivers that traditionally were unsuitable for developing hydraulic power plants and supporting the resiliency of the U.S electricity system. Based on the 2016 Hydropower Vision Report, across the U.S, approximately 65.5GW of new stream-reach hydropower capacities are available. The development of those resources could be possible only if the technologies for low-head hydropower that balance efficiency, economics, and environmental sustainability were developed. The traditional hydropower design method was limited to the new challenges of the Low-head application. Therefore, a Standard Modular Hydropower Technology (SMH) was proposed by the U.S. Department of Energy (DOE) in 2017. This new concept offers a new paradigm for small hydropower technology development based on the premise that standardization, modularity, and preservation of stream functionality must become essential and fully realized features of next-generation hydropower technologies and project designs. This technology has three major modules: Generation Module, Passage Modules, Foundation Modules. This paper is the first of this series of papers that propose and develop a new design methodology for the Generation Module that is a low impact, damless Kaplan turbine system for the low-head new stream-reach sites SMH application. © 2020 Elsevier Ltd. All rights reserved.
1. Introduction Hydropower has been a major source of renewable energy for more than 100 years. With a significant amount of electricity being produced and initial capital being invested, the design philosophies of the large hydropower system focus on the long-term reliability of energy production and safety. However, recently, as the science of the effect of large hydraulic powerplant on the local ecosystem has been revealed [1,2], small hydraulic systems regain a great deal of research attention. Compared to the large hydraulic system, the small hydropower system is both economically and environmentally friendly to the developer. Additionally, most of the technical hydropower resource
* Corresponding author. 2500 Engineering Building, 428 S.Shaw Lane, East Lansing. MI 48824, United States. E-mail address: [email protected] (J. Chen). https://doi.org/10.1016/j.energy.2020.117151 0360-5442/© 2020 Elsevier Ltd. All rights reserved.
potentials in the U.S are comprised in new stream-reach development sites [3]. These sites are characterized by low-head, varying flows, and highly valued river functions, including fish preservation, sediment transport, and recreational usage, etc. Based on the 2016 Hydropower Vision Report, across the U.S, approximately 65.5 GW of new stream-reach hydropower capacities are available [3]. However, this potential energy resource can only be utilized if the innovative design methods that balance efficiency, economics, and environmental sustainability are developed. Therefore, the U.S. Department of Energy (DOE) proposed a new Standard Modular Hydropower Technology (SMH) concept that can enable hydropower technology to deploy and operate in a new stream-reach site with minimal environmental impacts and greater public acceptance at a reduced cost.
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Nomenclature A Turbine Cross-sectional Area a0 ; a1 ; a2 ; a3 ; a4 Blade thickness distribution coefficients B(t) Bezier curve function C Absolute Velocity [m/s] Cssa Stator Stagger angle setting constant Crsa Runner Stagger angle setting constant C1 ; C2 Bezier Curve Control points D Turbine Diameter [m] g Standard Gravity Constant [m/s2] H Design Head [m] K Vortex Constant m_ Mass Flow rate [kg/s] ns Specific Rotation Speed P1 ; P2 ; P3 ; P4 Bezier Curve set of points Q11 Unite Flow Rate [m1/2/s] R Runner blade r Radius location [m] S Stator blade T Relative Blade Thickness U Radial rotational velocity [m/s] W Relative Velocity [m/s] WT Turbine Work [J] DWT Turbine Specific Work [J/kg] x x coordinate y y coordinate yt Blade thickness distribution function
1.1. Standard Modular Hydropower Technology (SMH) SMH technology is a new design paradigm that places the functionalities of a stream that must be preserved at the forefront of the design process, while also utilizing standardization and modularity principles to reduce site-specificity and project costs [4]. The first concept of modularity refers to the use of different module types to assemble an entire SMH facility. The SMH has three major modules, and some modules have serval sub-modules for different sites’ application, Table 1 summarizes the basic function of each module [4]. All those modules can be assembled to form an SMH facility that matches the scale, environmental attributes, and watershed context of the site selected for development [4]. The second concept of modularity refers to the scalability at many sites through multiple modules of the same type. For example, an upstream fish passage module may be applicable at many sites with a watershed region; a cost-optimized, compact generation module designed with wide operational flexibility could be applied at multiple sites throughout the country [4]. Based on
Greek Symbol Specific Rotation Speed Absolute Velocity Angle [degree] Relative Velocity Angle [degree] Stagger angle Turbine Overall Hydraulic Efficiency General Inclined Angle [Degree] w Camberline tangential angle r Fluid Density [kg/m3] f1c ; f2c Auxiliary angle U Rotational Speed [RPM] u Rotational Speed [rad]
Us a b g ht q
Subscript c Hub L LC p r s s Tm Tip u 1/2/3
Points on the camberline Hub Location Leading-edge Chord length Points on the blade pressure surface Runner Stator Points on the blade suction surface Maximum thickness Tip Location Circumferential direction Stator Inlet/Runner Inlet/Runner Outlet,
the initial investigation, a successful SMH facility should have six features [4]: 1. Predictable and somewhat regular production of electricity; 2. Minimal alteration of the inflow hydrograph and minimal impoundment of inflow water; 3. Environmental mitigation technology (functionality) inherent within and integral to the facility design (including fish passage, water quality, and sediment management design); 4. Minimal disruption to the aesthetics of the natural stream and stream-scape; and do not occupy the full width of the river; 5. Minimal fluctuations of water surface elevation; 6. Enabling of safe recreational passage through and activity around the project;
1.2. Description of the generation module As the most critical module for SMH technology, the Generation Module is envisioned as an integrated water-to-wire module that contains a hydraulic water turbine, generator, controls, and
Table 1 The basic function for each SMH modules (Adapted from Ref. [4]). Major Modules
Basic Function
Generation Module including, Turbine Rotor Module; Generator Module Passage Module including, Fish Passage Module, Sediment Passage Module, Recreation Passage Module, Water Passage Module Foundation Module
Encompasses all hydraulic and electric machines, equipment, and systems necessary for hydroelectric power generation. Allow fish, sediment, water, and recreational craft to pass the facility safely.
Provides structural resistance and reliably interface with the streambed to support generation and passage modules
J. Chen, A. Engeda / Energy 196 (2020) 117151
electrical equipment within a single unit [4]. The overall design goal of the generation module is to balance the performance, economic, and environmental sustainability, so it is appealing for developers. 1.2.1. Performance considerations The traditional hydraulic system often equips with a large reservoir that helps the system maintain the optimum operating condition.; however, the SMH system for new stream-reach sites requires minimal water impoundment. Moreover, one major characteristic of the new stream-reach development sites is various flow features, and Fig. 1 shows an example of a daily flow rate of one selected new stream-reach development site. Additionally, at most low-head new stream-reach sites, the tailwater elevation generally rises twice as fast as headwater elevation when river flow increases, leading to a significant reduction in the available gross head [5]. As a result, the low-head new stream-reach sites with high variability in flow and head often result in operating beyond the acceptable performance and efficiency limits for the traditional turbine. This variability requires a different deployment of regulation methods and presents a significant design challenge for generation module design. 1.2.2. Economics considerations The immediate installed cost target for an SMH project is under $6000/kW that including all necessary modules [4]. Over time, this number should be reduced as the module deployment increase. Conventionally, there are six main cost sectors for developing a small hydro project: 1. Installation Cost. 2. Planning Cost. 3. Civil work. 4. Infrastructure and Logistic.5. Electrical connection/Construction. 6. Equipment Cost. And, among those sectors, the civil work normally represents 40%e50% of the total project cost for a hydro-power project [6]. This civil work cost normally is because of the construction of the dam for creating a necessary head, and the water channel for diverting the river to the turbine. However, for low head new stream-reach sites, which feature the minimal water impoundment and run-of-river type operation, the traditional dam structure is not a necessity. Therefore, a damless concept for the generation module which means the size of the generation module can be large enough for creating enough low head conditions,
3
which will significantly reduce the overall cost, but at the same time create new design challenges for turbine designs. 1.2.3. Environmental sustainability considerations The preservation of stream functionality is one of the most instrumental premises for SMH technology, and there are three major environmental considerations for the new stream-reach sites: 1. Fish Preservation. 2. Sediment Preservation. 3. Recreation Activities Preservation. Among all those three, there is one major consideration that is critical for the generation module design, which is fish preservation. The new stream-reach sites’ river often has high-valued native fish species (anadromous, catadromous, and amphidromous), and hydropower facilities can work as barriers for them. Therefore, the low head hydro-system needs to have maximum protection for fish migrations. To achieve this fish protection, there are two ways: Introducing advanced fish passage design for overall facility construction and introducing the fishfriendly turbine design concept that allows fish to pass the generation module safely. For a fish-friendly generation module, the DOE’s criteria for design and evaluation of the new fish-friendly turbine runner [7] is a useful guideline for the initial design consideration. Among all those criteria, there are two critical requirements for the initial design: Large turbine area for fish migration, low peripheral runner speed for minimizing fish strike injury. Those two criteria limit the size and operating conditions (namely overall diameter, and rotational speed) for the SMH generation module. 1.2.4. Design Specifications for SMH generation module Because of the above performance, economics, and environmental considerations, the DOE has five specific design specifications for SMH generation module [4]: 1. Must be fully immersed in water, which necessitates the use of the reaction-type of the turbine. 2. Must encompass all equipment and systems for safe and reliable operation. 3. The design flow rate should be less than 113 m3/s and design head less than 9 m per unit. 4. Run-of-river type operation is preferred meaning the sum of inflows into the upstream region of the facility must equal the sum of outflows into the downstream reach of the facility. 5. Minimal environmental disturbance, including low fish mortality rate, and low noise level, etc. 1.3. Current status of the low-head hydropower development
Fig. 1. Daily flow rate for a selected new stream-reach site. (Data extrapolated from Oak Ridge National Laboratory SMH Explorer website: https://smh.ornl.gov/explorer/).
Currently, there are two paths for utilizing the potential energy of the low head or new stream-reach sites: 1. Low-head Hydropower Application. 2. River Current Application. For the low-head hydropower application, there are five major types of turbines that currently used: 1. Open-flume Francis turbines. 2. Kaplan turbine. 3. Tubular turbines. 4. Crossflow turbine. 5. Archimedes screw turbines. Table 2 summaries some advantages and disadvantages of those types of turbines [8]. For the River-current application, the hydro-kinetic turbine is commonly used. This type of turbine uses ultra-low or zero head conditions and driven by the free-flow stream. This technology has two advantages: 1. Multi-unit arrays can be deployed for maximum power production like the wind farm. 2. The structural requirements are low; thus, the civil cost will be limited. However, this technology still suffers from some significant drawbacks, including 1. Relatively low efficiency. 2. High installation cost. 3. High maintenance difficulties. Based on the DOE’s design specification, only the reaction type
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Table 2 Five major types of the turbine for low-head applications (Adapted from Ref. [8]). Turbine Type
Advantages
Disadvantages
Open-flume Francis Turbine Kaplan Turbine Tubular Turbine
High efficiency on the design condition High efficiency over a wide range. High efficiency, and various configurations for a low hydraulic loss. Wide operation range (head and flow). Wide operation range, high tolerance for debris, and fish friendly.
Narrow operation range, expensive to manufacture The regulation method can be complex Need straight passage through the turbine, can increase the civil cost. Relatively low efficiency Relatively large for transportation, technology still immature.
Crossflow Turbine Archimedes Screw Turbine
of turbine is suitable for SMH technology, and the high variability mentioning above limits the turbine selections; therefore, among all turbine types, the Kaplan turbine (or its variants) is the best option for the SMH technology. However, the new design method and considerations need to be developed for the challenges associated with the new SMH technology.
2.1. Generation module initial size and operation condition design 2.1.1. Generation module overall size and positioning Initial size design is the first challenge for developing a lowhead hydraulic turbine. Traditionally, a specification map is used
1.4. Objectives Based on the need for a new and innovate design method for SMH technology that is suitable for potential new stream-reach sites, this first paper presents the basic concept and design specification of SMH technology, detailed design methodology development, some fundamental geometrical considerations, and basic performance prediction from advanced numerical simulation results. 2. Design methodology development The proposed generation module is an open flume and damless Kaplan turbine system and has eight major components. Fig. 2 shows an example of this generation module. This Generation Module has a fixed stator, and an adjustable runner, the geometry of the stator and runner can be optimized for better performance. This first paper focuses on two major geometrical design tasks, Generation Module’s initial size and operation condition design, and Generation Module blade profile design.
Fig. 3. A typical specification map for different hydraulic turbine types [9].
Fig. 2. The overall generation module configurations. (Left: Total Assembly Model. Right: Close-up for each component).
J. Chen, A. Engeda / Energy 196 (2020) 117151
for determining the basic turbine characteristics, including head, rating power, and rotational speed for optimum performance. Fig. 3 [9] shows a typical specification map of the specific speed and specific diameter for various turbine types, and Fig. 4 [10] shows a Kaplan turbine specification map of the specific speed and head. Those charts come from years of surveys from the major hydro stations and often provide an accurate initial size design for the traditional hydro-system. For a low head condition, those charts can result in a smaller size and higher rotational speed for better performance. Those features are contradicted with the concept of SMH, which requires a large turbine area and less fish damage. This proposed turbine uses its turbine structure (Part-A in Fig. 2) to provide the low head condition; therefore, the initial turbine size is related to the designed head and the positioning of the turbine structure. For a low head application turbine, the turbine structure is often positioned in water with a general-inclined angle (refer as q in Fig. 2), and this angle is generally from 15 45 [11]. A larger inclined angle requires a more extended turbine structure and is more subject to the tailwater elevation; and a smaller inclined angel can have a shorter turbine structure, which means a smaller turbine area. Turbine structure minimum length can be calculated as
Turbine structure minimum structure lengthz
H cosq
(1)
This minimum length gives a guideline for the initial size of the turbine (Turbine Overall Diameter), and addition head-gate (Part-H in Fig. 2) can be equipped for more headspace for the off-design condition.
2.1.2. Generation module hub diameter After determining the overall diameter, the turbine hub diameter is the next parameter that is needed to be considered with cares. For an SMH generation module, the hub volume must contain the generator and control components; this means the hub diameter and its impact on turbine performance must be studied thoroughly for future generator selections and designs. Additionally, depending on which 1-D design method was used for the turbine runner, the hub diameter can have a significant impact on the turbine runner shape, which was covered in section 2.2.1. For a
5
traditional Kaplan turbine, two empirical equations can be used for determining the hub-tip ratio for optimum performance [9,10].
Dhub ¼ 0:8 0:1Us Dtip
(2)
Dhub 94:64 ¼ 0:25 þ ns Dtip
(3)
Those equations can only be used for the initial guess, and the different hub-tip ratio must be studied for low-head application. For this paper, five different hub-tip ratios between 0.68 and 0.8 were studied, and the results are shown in section 4.1.
2.1.3. Generation module operation condition For the initial design stage, the rotational speed is the only operation condition that needs to be considered. The criteria for determining rotational speed comes from environmental considerations. The high rotational speed is typically required for a low head application that can have a high risk for fish damaging. In 1999, DOE developed ten criteria for designing a fish-friendly hydraulic turbine system [7]. This criteria state that a fish-friendly turbine should have a less than 12.24 m/s (preferably 6.12 m/s) peripheral runner speed and limits the maximum rotational speed for the SMH generation module.
2.2. Generation module blade profile design 2.2.1. 1-D turbine design All turbine design starts with a 1-D velocity calculation, so it is crucial to define the velocity component. Fig. 5 shows a typical velocity triangle for a Kaplan turbine. For the initial 1-D Kaplan turbine design, there are two steps to calculate the velocity at each radial span location: 1. Determining the mean velocity value, 2. Determining other spans’ velocities with an appropriate velocity assumption. Determining mean velocity value is simplified by using three fundamental conservation equations as 1. Conservation of Mass:
ð ð ð m_ ¼ rCx1 dA1 ¼ rCx2 dA2 ¼ rCx3 dA3
(4)
2. Conservation of Energy
Fig. 4. A Kaplan Turbine specification map [10].
Fig. 5. A typical velocity triangle for a Kaplan turbine with three-stages. (1: Stator Inlet. 2. Runner Inlet [Stator Outlet]. 3. Runner Outlet).
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_ WT ¼ ht mgH
(5)
3. Conservation of Momentum
W
DWT ¼ _ T ¼ UðCu2 Cu3 Þ m
(6)
The next step is determining the velocity component at each radial span location, which is the most crucial part of the design. Conventionally, the free-vortex assumption is widely used for initial velocity calculation. Free vortex assumption, which is an inviscid and ideal case, has two major parts: 1. Flow upstream of the runner is assumed to be free-vortex which means: rCu ¼ constant, r is the radial location; 2. Flow has uniform velocity distribution in the axial direction, which means: Cx ¼ constant. There are two other assumptions that could also be used for initial velocity calculation: Force vortex assumption, Constant vortex. The forcevortex means Cu ¼ Kr, where K is vortex constant. The constant vortex means Cu ¼ constant. Fig. 6 shows examples of runner blade geometries designed with three different vortex assumptions. Previous research [12] has shown that different vortex assumptions trend to have similar hydraulic performance, and the only difference was the pressure distribution pattern across the blade, which may result in different deformation behavior of the blades. This paper mainly uses the free vortex assumption for initial velocity calculations. When utilizing the free vortex assumption for designing the runner blade because of the relatively low rotational speed, a small hub diameter can result in large Cu2 velocity and small U velocity. This can cause a negative b2 value. This negative b2 value at specific radial span locations can cause a larger twist angle of the blade and Fig. 7 shows three blade geometries with three hub diameters. A large twist angle blade can increase the complexity and the manufacturing cost of the blade. Therefore, it is crucial to define a minimum hub-tip ratio for preventing a large blade twist angle. When using the free vortex assumption, the minimum hub-tip ratio is defined when b2 ¼ 0, and can be calculated as
D2hub 4ht g cos q ¼ Dtip u2
(7)
Where ht is the initial guessed turbine efficiency, gis standard gravity constant, q is turbine general inclined angle, u is the
Fig. 7. Three example runner blades configurations with different hub diameter settings. (From left to right: hub-to-tip ratios [Dhub /Dtip ¼ 0.685, 0.743, 0.8.)
designed rotational speed in rad. This equation can provide the initial guide for the turbine hub diameter design. 2.2.2. 1-D blade profile design By using the calculated velocity values from the vortex assumption, blade geometry can be constructed by two steps: 1. Blade camberline construction, 2. Blade thickness distribution. The proposed generation module has two blade profiles: one is the stator blade, and another one is the runner blade. Those two blades profiles share the same design process. Here shows a general process for designing a runner blade geometry (for stator blade geometry, replace the runner blade angle values with stator angle values). Based on Equation-(6), the power delivered by the turbine runner blade is only extremely on blade inlet and outlet velocity conditions. Therefore, for general 1-D considerations, the blade camberline can be any curve shape as long as the blade inlet and outlet match the velocity condition (namely velocity direction). However, the blade geometry has a significant effect on overall hydraulic performance. Therefore, the blade camberline construction method needs to meet two main requirements: 1. Must match the inlet and outlet velocity conditions. 2. Must have the flexibility to control the general curve shape for further optimization. To achieve those two requirements, the fourth-order Bezier Curve is used to construct the blade camberline geometry. The Bezier curve is a parametric curve constructed by a set of points. The first point (P0 ) and last point (P4 ) are always at the beginning and endpoint of the camberline, and the other points are used for constraining the curve. The general nth order Bezier curve state as
BðtÞ ¼
n X n i¼0
i
ð1 tÞni t i Pi
(8)
n Where is the binomial coefficient, Pi is the set of points. i So, for the fourth-order Bezier curve
BðtÞ ¼ ð1 tÞ4 P0 þ 4ð1 tÞ3 tP1 þ 6ð1 tÞ2 t 2 P2 þ 4ð1 tÞt 3 P3 þ t 4 P4 (9) Fig. 6. Three example runner blades with different vortex assumptions. (From Left to right: Free Vortex, Force Vortex, Constant Vortex).
For a standard unit runner blade camberline shown in Fig. 8, P0 is the inlet point, P4 is the outlet point: P0 ¼ ð0; 0Þ; P4 ¼ ð1; 0Þ.
J. Chen, A. Engeda / Energy 196 (2020) 117151
Fig. 8. A standard-unit runner-blade camber line configuration.
Then, to match the velocity direction, two lines are drawn that are both tangential to the curve at inlet and outlet. The intersection point of two lines is the P2 ,
1
0 B P2 ¼ B @
1 1þ
cotf1c cotf2c
;
cotf1c C C 1 þ cotf1c A
(10)
cotf2c
f1c ¼ gr þ b2 f2c ¼ 180 gr b3
(11)
where, gr is the stagger angle of the runner blade (gs is for the stator). For a continuous curve
90 b3 < gr < 90 b2 ; gr ¼ ð90 b3 Þ þ Crsa ðb3 b2 Þ
Fig. 9 shows three runner blade profiles with Crsa ¼ 0.1; 0.5; 0.9. The main function of a runner is turning the flow from b2 to b3 . When Crsa is small, the stagger angle (gr ) and the camberline leading-edge tangential angle (wL ) are close to the inlet flow angle. As a result, the location of the blade turning action happens close to the leading edge. This location, Lw , can be indicated by the location when the camberline tangential angle equal to zero (wc ¼ 0). For example, when Crsa ¼ 0:1, Lw ¼ 13:8% of the chord length; when Crsa ¼ 0:9, Lw ¼ 74% of the chord length. Small Crsa value can result in a blade profile with a long tail region (Shown in Fig. 9) which improve the flow attachment; however, extremely small Crsa value can result in irregular blade leading edge shape which causes inlet flow mismatch. Therefore, this stagger angle setting constant is critical for the turbine blade design and has a significant influence on the turbine’s overall hydraulic performance. Fig. 10 shows examples of runners and stators geometry with different stagger angle setting constants, and detailed numerical results were shown in section 4.2. Conventionally, three points (P0 ; P2 ; P4 Þ are enough for constructing a blade camberline for the right velocity condition. However, a three-point Bezier curve (second-order Bezier curve) has one disadvantage: for a given velocity condition (which means b2 and b3 are given), the blade profile is only related to the stagger angle. This means, for a fixed stagger angle, the blade profile cannot be changed, which can cause less fixable control for further optimization. So instead of a second-order Bezier curve, the fourthorder Bezier curve is used by adding two more points to construct the blade camberline. One point (P1 Þ is on the straight line P0 P2
P1 ¼ c1 P2x ; c1 P2y
(12)
where, Crsa is the runner blade stagger angle setting constant, and Crsa is between 0 and 1 (For stator blade, the stator blade stagger angle setting constant is referred to Cssa and can be defined the same way with stator blade angle b1 and b2 ).
(14)
C1 and C2 are two Bezier curve control points. By adding those two points, this method not only meets the velocity conditions but also increases the flexibility for further optimization. Therefore, the general fourth-order Bezier curve point coordinate for the runner blade camberline is
BðxÞ ¼ ½4c2 3 þ P2x ð6 c1 4c2 Þx4 þ ½4 4c2 þ P2x ð12c1 þ 4c2 12Þx3 þ P2x ð6 12c1 Þx2 þ 4P2x c1 x
(15)
BðyÞ ¼ P2y ð24 16c1 16c2 Þx4 þ 4 4c2 þ P2y ð12c1 þ 4c2 12Þ x3 þ P2y ð6 12c1 Þx2 þ 4P2y c1 x
(16)
After choosing the correct value for the stagger angle setting constant and the Bezier curve control point, the camberline can be designed. The last step for constructing a blade profile is to have a thickness distribution function for the camberline. For this paper, the NACA-4 series profile is used and can be written as
RLc
Fig. 9. Three runner blade profiles with different runner blade stagger angle setting constant (Crsa ¼ 0:1; 0:5; 0:9).
(13)
another point (P3 ) is on the straight line P2 P4
P3 ¼ ð1 ð1 P2x Þc2 ; c2 P2y
where, f1c and f2c are auxiliary angles, that come from the velocity triangle
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yt R or ST a0 x0:5 þ a1 x þ a2 x2 þ a3 x3 þ a4 x4 ¼ T or SLc 0:2
(17)
where, RLC and SLC are the runner and stator blade chord length; and RT and ST are the runner and stator blade relative maximum thickness as:
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Fig. 10. (a). Runner Blade and (b). Stator Blade, with three different stagger angle setting constants.
RT ¼
RTm S ; ST ¼ Tm RLc SLc
(18)
where, RTM and STM are the runner and stator blade maximum thickness, and the a0 to a4 are prescribed coefficients:
a0 ¼ 0:2969; a1 ¼ 0:126; a2 ¼ 0:3516; a3 ¼ 0:2843 a4 ¼ 0:1015 or 0:1036 for a closed trailing edge
3. Numerical analysis method and conditions
(19) To utilize this thickness distribution function, a superposition method which superimposes the thickness onto the camberline is needed. This superimposes method calculates the blade’s suction and pressure side surface point coordination using points located at the camberline. Assuming the point on the camberline has coordinations (xc yc ), the blade suction surface point coordination (xs ys ) can be calculated as:
xs ¼ xc ðyt ðxc ÞÞsinwc ys ¼ yc þ ðyt ðxc ÞÞcoswc
(20)
the blade pressure surface point coordination (xp yp ) can be calculated as:
xp ¼ xc þ ðyt ðxc ÞÞsinwc yp ¼ yp ðyt ðxc ÞÞcoswc
The above method has great flexibility for designing an SMH generation module, for example, by using 11 radial span locations, the runner blade has a total of 33 parameters for modifying runner blade geometry, which is good for future pressure distribution, stress, and performance optimization.
(21)
where wc is the camberline tangential angle at each chosen point. By using the above method, the blade profile for each span location can be determined; then by using standard CAE software that connects each span’s blade profile, the final blade geometry can be constructed.
CFD (computational fluid dynamic) has played an important role in the general water turbine design and performance prediction. As shown in Ref. [13], a detailed comparison between experimental results and different CFD models prediction results for a Kaplan turbine system. The transient simulation model has advantages over steady-state simulation [13]. However, the computational costs are too expensive for developing a design methodology that required numerous CFD simulations. A steady-state k u SST CFD model was used in this paper, which has acceptable accuracy for predicting the discharge rate, torque, and efficiency [13]. The general CFD software ANSYS FLUENT 17.2 (ANSYS.Inc) was used to perform the 3-D steady-state flow analysis [14]. The overall hydraulic performance of the turbines is measured by the calculated hydraulic turbine efficiency ht . This efficiency value indicates what percentage of the total available hydraulic power is converted into the turbine work. The hydraulic efficiency is calculated as
ht ¼
Tu _ mgH
(22)
where T is the torque on the runner blade, u is the runner blade rotational speed, g is the standard gravity constant, m_ is the mass flow rate, and H is the available head.
J. Chen, A. Engeda / Energy 196 (2020) 117151
3.1. Computational domains The mesh represents the geometric domain for the numerical simulation, which has a significant impact on the accuracy and the computational cost of the simulation. For this method, the computational domains include three parts: inlet water channel, stator, and runner. Fig. 11 shows an example of this mesh. The runner is the rotating part, and the rest are the stationary parts. The multiple reference frame model is used to solve the stationary and rotating parts. Generally, more grids mean more accurate results but with a higher computational cost. Therefore, it is necessary to demonstrate how the mesh size would influence the overall prediction of the performance. Five different mesh schemes were selected for one example model, and Table 3 shows the detailed mesh information for each scheme. Fig. 12 shows the mesh quality and performance relation. All values in Fig. 12 were normalized to the mesh scheme-2 values. The results show that with a finer mesh, the efficiency increases by around 0.68%, the mass flow rate decreases around 0.57%, and the power increases by around 0.12%. Scheme-5 would provide more accurate results; however, the computational cost was too substantial. By using the same computing power, scheme-5 required 45 times more computational time than scheme-2. This methodology needs hundreds of simulations to verify the geometry settings and other parameters; therefore, Mesh scheme-2 was considered sufficiently reliable for predicting the overall hydraulic performance and was mainly used
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Table 3 Detailed mesh information for five different mesh schemes. Mesh Scheme 1 Mesh size [m] Mesh Type Total grid Number [million]
2
3
4
5
0.015 0.01 0.0075 0.006 0.005 Tetrahedrons Mesh þ 10 layer near the wall ~13.6 ~33.3 ~70.8 ~178.4 ~304.5
Fig. 12. Mesh quality and normalized performance relation for five different mesh schemes.
in this paper. Table 4 summarizes the design conditions and numerical simulation conditions for this paper. 4. Numerical results and discussion The first paper focuses on three major geometrical design parameters, including Hub Size, Stator stagger angle setting constant, and Runner stagger angle setting constant. Each setting was investigated by numerical simulations to find its impact on the overall hydraulic performance. 4.1. Hub size consideration
Fig. 11. The numerical grids for the three computational fluid domains.
As shown in Fig. 7, the hub size has a massive impact on the turbine blade design, which can have a significant influence on the overall hydraulic performance. Moreover, for the SMH generation module, the hub should have enough space for generator and control components. So, it is essential to thoroughly investigate the hub size and its impact on overall hydraulic performance. Five different hub-to-tip ratios (Dhub/Dtip) were chosen and thoroughly investigated, and Fig. 13 shows the results. The results show that for low flow rate conditions (when Q11 < 0:2), the largest hub diameter (Dhub/Dtip ¼ 0.8) model has the best performance, and the performance decrease with decreasing hub diameter and the maximum performance difference between different hub sizes is around 3.2%. When the flow rate increases, the smallest hub model (Dhub/Dtip ¼ 0.685) has the best overall hydraulic performance, and the maximum performance difference for different hub sizes is around 10.1%. Also, the results indicate that the smaller hub diameter has a flatter performance curve than a larger hub diameter, and the hub size has a larger impact on overall hydraulic performance at a large flow rate condition.
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J. Chen, A. Engeda / Energy 196 (2020) 117151 Table 4 Design and Numerical simulation conditions. Design Condition
Design Head (H)
2
6 Unit Flow Rate (Q11) 6 4Q11
Numerical simulation Condition
3 m3 Q s 7 ¼ 2 pffiffiffiffi 7 5 Dtip H
Overall Diameter (Dtip) Rotational Speed (U) Inlet/Outlet Boundary Condition Turbulence Model Simulation Type Mesh Size
2.5m 0.103~0.52m1/2/s
3.5m 40rpm Total Pressure k u SST Steady State ~33 Million
At a larger flow rate condition (Fig. 14-b), the smaller hub configuration has a larger circumferential velocity difference across all span locations (Blue Arrow). This massive difference causes the smaller hub configuration to have a significantly better overall performance at a larger flow rate condition. In general, choosing the right hub size is about balancing the design flow rate and the required hub volume. At a high flow rate, the smaller hub can provide an excellent overall hydraulic performance but with limited hub volume that can have high overheating possibilities for the generator, which can further affect the overall electrical performance. Balancing the hub size and performance is the key for the initial sizing of the turbine unite. Fig. 13. The relation between overall hydraulic efficiency and design flow rate (Q11) for five selected Hub-to-Tip ratio configurations.
4.2. Stator stagger angle setting constant considerations
According to Equation (6), the runner blade power is determined by the magnitude of the runner blade circumferential velocity difference. Therefore, Fig. 14 shows the circumferential velocity difference (Cu2eCu3) distribution plots from hub to tip at two Q11 conditions for all five different hub-size configurations. At a lower flow rate condition (Fig. 14-a), on the close to hub region (less 25% Span Location), smaller hub configuration has a significantly larger circumferential velocity difference (Red Arrow). However, this circumferential velocity difference drops steeply and remains at a very low value (Black Arrow) on the close to tip region (between 60% and 100% Span Location). In general, at a low flow rate conditions, the smaller hub configuration tends to have a worse performance on the close to tip region, which leads to poor overall performance.
As shown in Fig. 10-b and Equation (12), the Stator Blade Stagger Angle Setting Constant (Cssa ) is a critical parameter for designing the stator blade profile. Fig. 15 shows how this parameter affects the overall performance at four flow rate conditions. The results show that for small flow rate condition, the overall hydraulic efficiency increases with the increase of Cssa and reaches the maximum efficiency when Cssa is around 0.7e0.8, then decrease with the increase of Cssa . For large flow rate conditions, the overall hydraulic efficiency increases with the increase of Cssa and reaches the maximum efficiency when Cssa is around 0.5e0.7, then remains relatively constant, then decreases when Cssa is larger than 0.8. For all flow rate conditions, the initial increase of efficiency with the increase of Cssa is universal, and the maximum efficiency occurs when Cssa is around 0.5e0.8. Four models under one flow rate condition (Red Square in Fig. 15) were selected for further
Fig. 14. The circumferential velocity difference (Cu2eCu3) distribution plots from hub to tip at two Q11 conditions for all five different hub-size configurations, (a) Low Flow Rate Condition. (b) High Flow Rate Condition.
J. Chen, A. Engeda / Energy 196 (2020) 117151
Fig. 15. The Relation between overall hydraulic efficiency and stator blade stagger angle setting constant Cssa for four flow rate conditions.
investigations. The primary function of the stator is to redirect the inflow to the runner blade with the desired angle, so for the four selected models, two angles were studied: b2 and a2 . 4.2.1. -Considerations The b2 is the runner blade inlet relative flow angle (see in Fig. 5), and ideally, the b2 flow angle should be the same as the b2 blade angle. A large difference between b2 blade and b2 flow can increase the runner blade incidence loss, which can affect the overall performance. Fig. 16 shows the comparison between the b2 blade and b2 flow for the four selected models. The results show that near the hub region because of the boundary flow and low runner circumferential velocity (velocity U in Fig. 5), the b2 flow is larger than the b2 blade for all four selected models and the maximum angle difference is around 12 . And near the tip region because of the boundary flow and larger runner circumferential velocity, all b2 flow value is larger than the b2 blade for the four selected models, and the maximum angle difference is around 9 . However, results are different in the center of the span region. - The smaller Cssa models (Cssa ¼0.1,0.3) trends to have a larger b2 flow than the b2 blade ; the maximum angle difference is ~þ3 . - The medium Cssa models (Cssa ¼0.5) trends to have a very similar b2 flow than the b2 blade ; the maximum angle difference is only ~þ0.4 . - The larger Cssa models (Cssa ¼0.8) trends to have a smaller b2 flow than the b2 blade ; the maximum angle difference is ~ -4 . As shown above, the difference between b2 flow and b2 blade can undoubtedly affect the overall performance, but the results in Fig. 16 cannot fully explain the trend shown in Fig. 15. Therefore, another angle a2 has been studied. 4.2.2. a2 -Considerations The a2 is the runner blade inlet absolute flow angle (see in Fig. 5), and this angle determines the magnitude of the runner blade inlet circumferential velocity (Cu2). Larger a2 means larger Cu2These which results in more substantial potential work done on
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Fig. 16. The runner blade inlet b2 flow angle distribution plots for four selected models in comparison with the designed b2 blade value.
the runner blade (based on Equation. (6)). Fig. 17-(a) shows the a2 distribution plot across all span location for the four selected models with the comparison with the 1-D designeda2 values. The smaller Cssa (Cssa ¼0.1) model shows significant lower a2 values in the majority center span region (expect the hub and tip boundary region), the difference is around 60 . The larger Cssa (Cssa ¼0.8) model also shows lower a2 values in the majority span center region, but the difference is only around 10 . This huge difference in the a2 value explains why Model-4 (Cssa ¼0.8) has significantly better performance than the Model-1 (Cssa ¼0.1). For better visualization, Fig. 17-(b) shows the stator blade stream-line pattern for the Model-1(Cssa ¼0.1) and Model-4 (Cssa ¼0.8) at 50% span location, and Fig. 18 shows the corresponding runner blade stream-line pattern (Absolute velocity) at the same span location. When Cssa is small, as shown in Fig. 17-(bBottom), the stator blade camberline has a flat profile in the font region, and the diversion of the flow only happens near the trailing edge. This profile results in poor flow redirection and leads to very small a2 value. When Cssa is large, as shown in Fig. 17-(b-Top), the stator blade camberline has a flat profile in the rear region; the diversion of the flow happens near the leading edge. This profile results in good flow redirection and leads to a larger a2 values. In general, the Cssa value has a larger impact on a2 values than b2 values and has a profound influence on stator outlet flow behaviors, which can further affect the overall performance.
4.3. Runner blade stagger angle setting constant Just like the stator blade stagger angle setting constant, the runner blade stagger angle setting constant (Crsa ) is a critical geometrical parameter for the runner blade profile. Fig. 19 shows how this parameter affects the overall performance under four different flow rate conditions. For all flow rate conditions, the efficiency first increases with the increase of Crsa , then reaches the maximum efficiency when Crsa is between 0.3 and 0.5, then the efficiency decreases significantly with the increase of the Crsa .
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Fig. 17. (a). The runner blade inlet absolute flow angle (a2 ) distribution plots for four selected models in comparison with the designed a2 value; (b). The stator stream-line pattern for the Model-4 (Top) and Model-1 (Bottom), at 50% span location.
Fig. 18. The runner stream-line pattern for the Model-4 (a) and Model-1 (b), at 50% span location.
Four models were selected (Red Square in Fig. 19) for further investigation. As described in section 4.1, the magnitude of the circumferential velocity difference (Cu2eCu3) represents how effective a runner blade is converting the hydraulic power to mechanical power. So, Fig. 20-(a) shows the circumferential velocity difference distribution plots for the four selected models. Model-2 has a higher (Cu2eCu3) value than the other three models, which is reasonable for its highest efficiency. Model-1 has a very similar
trend as Model-2 but with a small decrease in value near the tip region (Red Arrow), which cause a small efficiency drop compared to the Model-2. Model-3 and Model-4 have significantly lower (Cu2eCu3) values, especially in the 40%e80% span location (Blue Arrow), which cause them to have lower efficiency. For better visualization, Fig. 20-(b) shows the stream-line pattern for the Model-2 (Crsa ¼0.3) and Model-4 (Crsa ¼0.8) at 80% span location. Model-2 shows a great flow attachment, which gives
J. Chen, A. Engeda / Energy 196 (2020) 117151
Fig. 19. The Relation between overall hydraulic efficiency and runner blade stagger angle setting constant Crsa for four flow rate conditions.
it a better performance, and the Model-4 shows some flow distortion near the leading edge on the pressure side of the blade, which causes the drawback of the efficiency. In comparison with Cssa in which has a 12% maximum efficiency difference, the Crsa with a 9% maximum efficiency difference has less impact on the performance. However, this impact is still significant enough and needs to be carefully considered. Based on the comprehensive results, initially, the suggested range for Cssa is between 0.7 and 0.8, and for Crsa is between 0.2 and 0.3. 5. Conclusions Low-head hydropower has the potential to generate a significant amount of electricity from rivers that traditionally were unsuitable for developing hydraulic power plants and supporting the
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resiliency of the U.S electricity system. The development of those resources could be possible only if the technologies for low-head hydropower that balance efficiency, economics, and environmental sustainability were developed. The traditional hydropower design method was limited to the new challenges of the Low-head application. Therefore, a Standard Modular Hydropower Technology (SMH) was proposed by the U.S. Department of Energy (DOE) in 2017. This paper proposed a new design methodology for SMH technology generation modules. This methodology consists of a new method for constructing the blade profiles with great flexibility and novel considerations for several critical geometrical setting parameters. Three of them were covered in this first part of the paper: Hub size, Stator stagger angle setting constant, and Runner stagger angle setting constant. With numerous numerical simulation results, the relation between each geometrical setting parameter and the overall hydraulic efficiency was presented. There are two major findings: (1) The hub size has a critical impact on performance, especially at large flow rate conditions. Smaller hub size has better performance at larger flow rate conditions, and larger hub size models have better performance at low flow rate conditions. The different circumferential velocity distributions patterns cause this performance difference. At a high flow rate, the smaller hub can provide an excellent overall hydraulic performance but with limited hub volume that can have high over-heating possibilities for the generator, which can further affect the overall electrical performance. Balancing the hub size and performance is the key for the initial sizing of the turbine unite. (2) The stator and runner blade stagger angle setting constant are critical for the stator and runner blade profile. A smaller stator blade stagger angle setting constant can cause poor flow redirection at the stator outlet, which causes low efficiency. A larger runner blade stagger angle setting constant
Fig. 20. (a). The circumferential velocity difference (Cu2eCu3) distribution plots from hub to tip for four selected models. (b). The stream-line pattern for the Model-2 (Top) and Model-4 (Bottom), at 80% span location.
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can cause flow distortion near the runner blade leading edge, which causes low efficiency. References [1] Tullos Desiree. Assessing the influence of environmental impact assessments on science and policy: an analysis of the Three Gorges Project. J Environ Manag 2009;90:S208e23. [2] Botelho Anabela, et al. Assessment of the environmental impacts associated with hydropower. Renew Sustain Energy Rev 2017;70:896e904. [3] O’connor Patrick, et al. Hydropower vision A new chapter for America’s 1st renewable electricity source. 2016. No. ORNL/TM-2016/688. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). [4] Witt Adam, et al. Exemplary design envelope specification for standard modular hydropower technology: draft for public comment. 2016. [5] Brown Kinloch David. Demonstration of variable speed permanent magnet generator at small, low-head hydro site. Midway, KY (United States): Weisenberger Mills, Inc.; 2015. No. Final Report: DOE-WEISENBERGEREE0005429-1.
[6] Johnson Megan, Uria-Martinez Rocio, O’Connor Patrick. Hydropower market report update metadata. Oak Ridge, TN (United States): Oak Ridge National Lab.(ORNL); 2016. 2017. [7] Odeh Mufeed. A summary of environmentally friendly turbine design concepts. US Department of Energy Idaho Operations Office; 1999. [8] Zhou Daqing, Deng Zhiqun Daniel. Ultra-low-head hydroelectric technology: a review. Renew Sustain Energy Rev 2017;78:23e30. [9] Korpela Seppo A. Principles of turbomachinery. Hoboken, NJ: Wiley; 2011. [10] De Siervo F, De Leva F. Modern trends in selecting and designing Kaplan turbines. Water power and dam construction 1978;30(1):28e35. [11] Gordon JL, Eng P. Turbine selection for small low-head hydro developments. Buffalo: Proc. Waterpower XII; 2003. [12] Muis Abdul, Sutikno Priyono. Design and simulation of very low head axial hydraulic turbine with variation of swirl velocity criterion. International Journal of Fluid Machinery and Systems 2014;7(2):68e79. [13] Jost Dragica, Skerlavaj Alja z, Lipej Andrej. Improvement of efficiency prediction for a Kaplan turbine with advanced turbulence models. Strojniski vestnik-Journal of Mechanical Engineering 2014;60(2):124e34. [14] Guide, ANSYS FLUENT user’S. Ansys Inc; 2016. Release 17.0.