The Pennsylvania State University The Graduate School College of Engineering THE HISTORY AND DESIGN OF A RAPIDLY DEPLOYABLE

Transcription

1 The Pennsylvania State University The Graduate School College of Engineering THE HISTORY AND DESIGN OF A RAPIDLY DEPLOYABLE ADVANCED HUBLESS LOW HEAD HYDROPOWER TURBINE A Thesis in Mechanical Engineering by Erik J Brown 2017 Erik J Brown Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2017

2 The thesis of Erik J Brown was reviewed and approved by the following: John M. Cimbala Professor of Mechanical Engineering Thesis Adviser Savas Yavuzkurt Professor of Mechanical Engineering Karen A. Thole Distinguished Professor of Mechanical Engineering Head of Mechanical and Nuclear Engineering Department Signatures are on file in the Graduate School. ii

3 Abstract The hydroturbines currently in industry and literature have a high levelized cost of energy (LCoE) in low head and low power environments, are not able to operate over a wide range of changing flow conditions, and are not self-cleaning. A turbine has been designed that and can offer all of the advantages stated above, with the added benefit of being rapidly deployable. It is shown that the designed hubless turbine prototype turbine can operate at 90.6 percent peak efficiency, producing 41.2 kw of power. The turbine design can be scaled to fit various waterways, and can respond to a range of inlet flow conditions via an integrated variable speed drive (the range for the present design is from 108 to 225 RPM). The history and design of this new turbine is examined, and future work for advancement of the understanding of the flow physics is recommended. iii

4 Table of Contents List of Figures Acknowledgments vi viii Chapter 1 INTRODUCTION Legacy of Low-Head Hydropower Variable Speed Operation Development of Low Head, Low Power Hydropower Rim-Drive Technology Hubless Technology Transition to Energy-Generation Industry Chapter 2 OBJECTIVES 9 Chapter 3 DESIGN METHODOLOGY Preliminary Design Other Design Considerations Mechanical Factor of Safety Cavitation Consideration Uncertainty Detailed Design Streamline Curvature Computational Fluid Dynamics (CFD) Analysis Design Modifications and Off-Design Analysis Flow Rate Modification Study Blade Count Modification Study Comparison of Designs with Fielded Turbine Types iv

5 Chapter 4 SELECTION AND OPERATION OF TURBINE Selection of Turbine Size Selection of Turbine Speed Chapter 5 MODIFIED STREAMLINE CURVATURE METHOD Routine Drivers Routine Method Routine Issues Chapter 6 CONCLUSION 32 Chapter 7 RECOMMENDATIONS FOR FUTURE WORK 34 Bibliography 35 v

6 List of Figures 1.1 Diagram of a Pelton Wheel and Francis and Kaplan Hydroturbines, Adapted from [1] Diagram of Adjustable Speed Hydro [2] Summary of Power Potential in the United States [3] Map of Power Potential in the United States [4] Rolls Royce Hub-Type Thruster [5] Brunvoll Hubless Thruster [6] a) Hub-Type Thruster and b) Hubless Type Thruster [7] Performance of Hub versus Hubless type Thrusters [7] Classification of Hydroturbines based on Power, Flow Rate, and Head Drop, Adapted from [3] Design Space of Low Head, Low Power Hydroturbine prototype Typical Operating Ranges based on Specific Speed, Adapted from [8] Comparison of Various Rotor Types from left to right: (17) Kaplan Turbine, Ω = 2.41 (18) Axial Compressor, Ω = 2.41 (19) Axial Compressor, Ω = 3.21 (20) Propeller Pump, Ω = 3.21 (21) Axial Blower, Ω = 4.82 (22) Propeller Pump, Ω = 5.36 (23) Kaplan Turbine, Ω = 5.36, Adapted from [8] Comparison of Kaplan and Propeller Turbines, Correlation from [9] Mechanical Factor of Safety Approximation Cavitation Coefficient over a Range of Specific Speeds, Adapted from [1] Estimated Uncertainty over a Range of Efficiencies, Correlation from [10] Simplified Example 1D Turbine Domain, Flow from Left to Right Example Streamline Curvature Domain Result Endwall View of Mesh of one Rotor Blade and one Inlet Guide Vane Simplified Domain Boundary Conditions CFD Results for an IGV, Suction and Pressure Sides Visualizations 21 vi

7 3.14 CFD Results for a Rotor, Pressure and Suction Sides Visualizations Visualization of Four Different Inlet Guide Vane and Rotor Designs Plot of Hydrodynamic Efficiency vs Rotor Power Specific Speed Plot of Hydrodynamic Efficiency vs Rotor Tip Speed Ratio (TSR), Design Variable Inlet Flow Rate CFD Results Variable Rotor Blade Count CFD Results Variable IGV Count CFD Results Comparison of Designs with Fielded Turbine Types, adapted from [11] Size and Speed Performance charts for Design 1 Turbine for 90% Hydrodynamic Efficiency Performance chart for Design 1 for Constant 0.45 meter Turbine Radius vii

8 Acknowledgments Special thanks to my thesis advisor, John Cimbala, for all of his continued support throughout my undergraduate and graduate career. Thanks to ARL for the wonderful opportunity to be able to further my career with graduate school; particular thanks to Arnie Fontaine and Nick Jaffa for their time and wisdom, and for selecting me for the amazing opportunity to learn and grow as a student and a scholar on our project. Thanks to the US Department of Energy s Energy Efficiency and Renewable Energy (EERE) office for funding the project that set me on an incredible journey in renewable energy. I am thrilled to be a part of the energy research industry, and I cannot wait to see what the future holds. viii

9 Dedication To my wife, for all of your love and support, thank you. ix

10 Chapter 1 INTRODUCTION 1.1 Legacy of Low-Head Hydropower The history of water wheels and hydroturbines has been reviewed by various authors, and multiple historical compilations have been released into the literature. Lewis and Cimbala, in particular, review the lineage of the ancient Greek undershot water wheel up to the development of the modern Francis turbine, during the boom of the Industrial Revolution [12]. These designs perform well under high heads and low flow rates; however, as the need for higher power and efficiency escalated, the required increase in runner size and decrease in runner rotation rate started to become cumbersome. This industry need led to the development of the propeller-like turbines (Kaplan in Europe, and Nagler in America) that offered lower wetted areas than their Francis turbine predecessors to reduce friction and also allowed for higher wheel speeds and lower head drops [13]. Figure 1.1: Diagram of a Pelton Wheel and Francis and Kaplan Hydroturbines, Adapted from [1] While the modern Pelton water wheels and Francis hydroturbine lineages trace back to English and American roots in the 1800s, the Kaplan turbine arose out of 1

11 Austria in 1913, out of the mind of Viktor Kaplan. Kaplan received his doctorate in the design of the Francis hydroturbine in 1909, however, his continued work on making changes to the Francis turbine in the lab quickly led to the development of the propeller-like design that is known as the Kaplan turbine. Kaplan s designs found a home in Europe around the First World War, and eventually leaked into America about a decade later due to Kaplan s addition of automated variable angle blades and wicket gates that allow for a broad range of high-efficiency performance. At the same time as Kaplan s development, the Nagler turbine was developed in America, however, it vanished from use before long because it could not offer the same performance as the Kaplan turbine due to its fixed blades and gates [13]. The Kaplan turbine survives today, like that shown in Figure 1.1, with everincreasing size and energy-extraction ability with the development of modern design methodologies that allow for cavitation control at the large scales and speeds. 1.2 Variable Speed Operation With the rise of complex engineering possibilities, in the form of electronic motors, controllers, and converters, the need to utilize the tools to enhance the performance of existing machines can be seen as a natural extension. Similar to Kaplan s feedback loops that controlled the blade and wicket gate angles starting at the end of the 20th century, the concept of variable speed hydro machines and motors controlled by their environmental conditions came into light. These machines would be capable of higher efficiencies over wider ranges of operation than their constant speed counterparts, and would be able to respond to the changes in load. Adjustable speed hydro machines could also avoid the onset of cavitation, and reduce the noise and vibration levels by adjusting to the flow loading [2]. Figure 1.2 shows a simple diagram of an adjustable speed hydro machine. The schematic portrays the interaction of the turbine generator system with the incoming and outgoing power grid through a series of transformers and a general forced commutated converter (a high voltage DC converter, HVDC) that together allow for the proper current and voltage type and level for both the power grid and the generator. 2

12 Figure 1.2: Diagram of Adjustable Speed Hydro [2] 1.3 Development of Low Head, Low Power Hydropower Up until the early 2000s, it became apparent that while much of the hydro industry was focusing its effort on developing the most efficient, largest hydroturbines as possible, the applications for those designs benefit only geographical areas near major water sources [14]. For other areas, where only minor rivers and streams are present, the large machines being designed would not fit or be able to perform efficiently with such low head drops. The solution for these smaller energy sources would have to come from specialized hydroturbine systems. The machine power curves, when plotted on a head drop-flow rate plot, have been used to categorize the types of low-head designs [3]. Some of the few categories of operating conditions are: small hydro (<2500 kw), mini-hydro (<500 kw), micro-hydro (<100 kw), and pico-hydro (<5 kw) [3], [15]. Each of these categories can be further sub-divided into low, conventional, and high-head groups. Figure 1.3 shows that the United States Department of Energy (DOE) estimates that 57% of the United States total energy potential is available to be developed [3]. It can be seen from Table 1 that approximately 71% of that available power potential is in the form of high power (< 1 MW), 16% is the high head, low power type, and the low head, low power type accounts for the remaining 13% of the total potential. Although the low head, low power slice of the available power pie is the smallest 3

13 Figure 1.3: Summary of Power Potential in the United States [3] of the three categories, it has the greatest potential for a positive impact. With 87% available energy, the low head, low power is the most undeveloped category of hydropower, and as such has the most capacity for improvement and impact. One of the reasons that the low head, low power category is the least developed is that they tend to be regions farther away from the large power potential locations. These sites often have access to low head, low power sources of water flow, and would benefit the most from the technologies. Another benefit from developing methods and technologies for the low head, low power environments is that they could serve as an effective model for what most small villages, tribes, or families around the world could use as a power source in their daily lives. Figure 1.4 shows the distribution of the available power sites in the United States for the small hydro and low power categories of hydroturbines. This map shows that energy generation on some of the major rivers, such as the Mississippi River and the Columbia River, and certain sections of other ones, such as the Missouri River and the Colorado River, would benefit greatly from the use of low power hydro. 4

14 Figure 1.4: Map of Power Potential in the United States [4] 1.4 Rim-Drive Technology In 2005, both Rolls-Royce and Brunvoll revealed their rim-driven technologies for marine thrusters [6], [5]. Figures 4 and 5 show the designs released by Rolls-Royce and Brunvoll at that time, respectively. Although the concept for a mechanically rim-driven thruster was suggested in 1957 [16], the advancements in electronic and induction motors would not come about until at least the 1980s, and would not come into production until the early 2000s. The rim-driven technology was a natural advancement for the seafaring industries, due to issues such as ropes and sea debris getting caught on and wrapped around the shaft that drives the propeller, and decreased efficiency and increased vibration from shafts and gears that pass through the hulls of the vessels. Building the driving mechanism into the moving ring inside of the duct around the propeller protects the motor from the environment, and also removes the need to have a gearbox and supporting mechanical systems that can cause extra drag and vibration. Due to size constraints, the motor driving the propeller could not easily be an ordinary mechanical system like what was originally suggested, but would instead need to be an electric or 5

15 magnetic induction motor, as it is with the designs shown in Figures 1.5 and 1.6. An induction motor system works by generating a magnetic flux in a set of stator windings via a sinusoidal electronic current signal, which then acts on a set of permanent magnets (or poles) in a rotor section. The magnetic field created within the stator windings creates a net force on the rotor magnets, causing rotation of the rotor section. As the rotor poles pass by the stator elements, electronic devices control the stator current timing so that the torque on and rotational speed of the rotor section can be regulated. Figure 1.5: Rolls Royce Hub-Type Thruster [5] Figure 1.6: Brunvoll Hubless Thruster [6] 6

16 1.5 Hubless Technology Hubless marine thruster designs were first introduced and patented by 1994 [17], numerical and experimental renditions on the design did not surface until the early 2000s [18]. Although the rim-driven technology eliminated the likelihood of ropes or debris getting caught around the driving shaft, in many instances there was initially still a mandrel or hub designed in the center of the blades that could allow debris to become trapped within the duct itself, such as in the Rolls-Royce design shown in Figure 1.5, or Figure 1.7a below. The natural answer to this issue was to remove the hub or mandrel from the duct, and leave an open annulus in the center of the blades, such as in Figure 1.6 and Figure 1.7b. This would allow, with proper blade design, most debris to pass through the propeller or thruster and not become tangled and cause damage. Although initial prototypes such as in Hsieh et al. s work did not perform as well as anticipated, other researchers performed computational analyses to demonstrate the performance of hubless designs. Song et al. s work, summarized in Figure 1.8, showed that the hubless designs for marine thrusters operated at equivalent or higher efficiency (up to 2.2% greater at the design point, J = 0.7), higher thrust, and higher torque than their hub counterparts in open water simulations, particularly at large advance ratios and large hub to tip ratios. Figure 1.7: a) Hub-Type Thruster and b) Hubless Type Thruster [7] 7

17 Figure 1.8: Performance of Hub versus Hubless type Thrusters [7] 1.6 Transition to Energy-Generation Industry After the aforementioned technologies had been established in the nautical industry, the energy-generation industry began to see the benefit of these advances [19]. In many rivers and streams across the world, there is not an enormous head drop or flow rate for the advanced large scale turbines, and debris and wildlife pose an environmental issue to a hydroturbine. However, with the compact protected motor design of the rim-driven hubless thrusters, a hydroturbine could be designed rapidly to fit within the operation condition of most flowing bodies of water, and would be able to operate with minimal effect on the surrounding environment. The rapidly designable and deployable nature of the hydroturbines would come alongside the advancement in design tools and in additive manufacturing techniques. 8

18 Chapter 2 OBJECTIVES The goal for this document is to utilize the findings from a literature search into and the design process for an advanced hubless hydroturbine. The Department of Energy (DoE) sponsored project had the following goals in designing the turbine: Design a compact, variable speed turbine Design a turbine that accepts a wide range of flow conditions with high efficiency Design a corrosion resistant turbine with advanced materials manufacturing Reduce levelized cost of energy (LCoE) via Additive Manufacturing Reduce operation and maintenance costs via Condition Based Maintenance This report covers the design items above, from the preliminary considerations to the detailed design. After the full design process has been covered, the consideration of deliverables is shown in the form of several contour plots that act as a "catalog" of turbines and turbine operating points. Lastly, recommendations for future work are made. 9

19 Chapter 3 DESIGN METHODOLOGY 3.1 Preliminary Design Design Region Scaled Region Figure 3.1: Classification of Hydroturbines based on Power, Flow Rate, and Head Drop, Adapted from [3] The preliminary design stage begins with choosing the estimated operating point for the intended design that will deliver the required outputs at a high efficiency. The decision to make a full-scale or down-scaled prototype also is necessary, based on the availability of computational and/or experimental validation resources. Figure 3.1 shows two different views of the design space, the first viewing the space from a power perspective, and the second includes a conventionality limit, based on the head drop for a given type of turbine. The region for design was chosen to be in the conventional region (between 8 and 30 feet of head drop) which corresponds to a low power hydroturbine (between 100 kw and 1 MW). For this project, a scaled down version of the full-size turbine was chosen, as denoted in Figure 3.1, that would operate in the microhydro region. The scaled-down prototype would allow 10

20 for experimental testing in a 48-inch diameter water tunnel, and would also allow for possible in-situ deployment. The full scale on-design operating condition is 7.5m 3 /s, under 5.95 meters of head drop. The 1.39 meter diameter machine could deliver 353 kw (assuming an overall machine efficiency of 80%), which scales down to 39 kw of power for a 0.9 meter diameter prototype under 2m 3 /s of flow rate and 2.5 meters of head drop. 15 Head vs. Flow Rate, Changing Specific Speed sp = 1.53 sp = 2.16 sp = kw Power 39.2 kw Power 19.6 kw Power Low Power Limit (100 kw) High Power Limit (1 MW) Upper Convention Limit Lower Convention Limit Constant Constant Diameter Bellefonte Site Condition Possible Testing Condition Possible Scaled Condition Head (m) Flow Rate (m 3 /s) Figure 3.2: Design Space of Low Head, Low Power Hydroturbine prototype Figure 3.2 shows a windowed section of the design space of figure 3.1. Figure 3.2 shows the investigation into the design space, based on the range of possible specific speeds of the proposed turbine prototype, where specific speed is defined as: Ω sp = Ω Ẇ mech ρ (g dht) 5/4 Where Ω is the rotational speed of the rotor, Ẇ mech is the mechanical power extracted by the turbine, and dht is the total head drop across the turbine. Similarly used is the tip speed ratio: T SR = Ω R Q π R 2 Dimensionless quantities such as the power specific speed and the tip speed ratio 11

21 are very powerful tools to show the scaling of a turbomachine, because similarity of the dimensionless variable will ensure that with a scaled turbomachine size or rotor rotation rate, efficiency can be kept at a high level. For example, at a specific speed of 2.65, if the turbine diameter is doubled, then the rotation rate would have to be decreased to approximately 60% of its original speed, assuming that the turbine original torque and flow conditions were kept nearly constant. These curves of specific speed are very important in that the curves are the scaling laws between the design and prototype regions (curves of constant rotor speed), and also show the in-situ operation of the turbine with a variable speed drive (curves of constant diameter). Possible Design Possible Design Possible Design Figure 3.3: Typical Operating Ranges based on Specific Speed, Adapted from [8] Figure 3.4: Comparison of Various Rotor Types from left to right: (17) Kaplan Turbine, Ω = 2.41 (18) Axial Compressor, Ω = 2.41 (19) Axial Compressor, Ω = 3.21 (20) Propeller Pump, Ω = 3.21 (21) Axial Blower, Ω = 4.82 (22) Propeller Pump, Ω = 5.36 (23) Kaplan Turbine, Ω = 5.36, Adapted from [8] One of the implications of the specific speed dimensionless quantity is that it shows which type or "look" of turbine that can operate in the required range of 12

22 operation with acceptable efficiency. Figures 3.3 and 3.4 show common fielded turbine and compressor types that are selected for their performance over ranges of operating specific speeds. Based on the head drop, power, and rotational speed of the targeted turbine, a propeller or Kaplan type turbine could have been chosen for this project. For this application, constraints in the rotor design were considered due to the fact that additive manufacturing (AM) was used to create the blades. To fit within a build envelope of the AM techniques, a higher blade count and lower blade heights were favored when comparing to commonly used designs. Figure 3.5: Comparison of Kaplan and Propeller Turbines, Correlation from [9] To validate the proposed designs against fielded turbines, an empirical sizing relation was employed, the results of which are shown in Figure 3.5. The comparison shown in Figure 3.5 shows that either type of turbine would be a valid choice. For this project, a propeller-type turbine was chosen, resembling the precursor thrusters that utilized technology similar to this turbine. After the turbine type has been chosen, the number of blade rows and size of each row should be chosen. In this case, one constant-radius stage (comprised of one inlet guide vane row and one rotor row) was chosen to reduce manufacturing costs, but to keep overall machine efficiency high. 13

23 3.1.1 Other Design Considerations After the machine has been preliminarily chosen and sized, other considerations that should be investigated to check the design are: the blade mechanical factor of safety, the cavitation coefficient, and the uncertainty levels associated with the machine. Depending on the depth of the preliminary design performed, specifically if loading and pressure distribution information is known or assumed, these analyses may have to be taken into consideration after the detailed design, which is discussed in Section II Mechanical Factor of Safety Figure 3.6 shows the approximation used to estimate the mechanical factor of safety. Each blade was assumed to be a cantilevered beam with a uniform rectangular cross-sectional area. The induced stress due to the primary forcing, the bending load, was calculated to be approximately 9 MPa. For stainless steel, the yield strength was approximated to be 215 MPa, which yielded a factor of safety of approximately 20. This shows that the design will safely withstand the loading due to the bending force of the water. Other components of loading were neglected compared to the bending moment due to the low flow rate and low rotational speed of the machine. Similarly, the maximum stress was estimated in the full-scale design. For a full-scale flow rate of 11m 3 /s and 5.95 meters of head drop, a new rotational speed of 245 RPM would be required to operate at peak efficiency. Under these scaled conditions, a full-scale mechanical safety factor of approximately 14 can be calculated from the bending moment. This shows that both the prototype and the full-scale design should be able to safely operate without the risk of cracking or breaking from the hydrodynamic loading Cavitation Consideration Cavitation in turbomachines is a crucial issue to examine due to the possibility of mild to severe performance loss and blade damage due to rapid expansion and explosive compression of bubbles. The criterion for cavitation is presented in the form of the Thoma cavitation coefficient, which is effectively a factor of safety measure of the minimum pressure from the vapor pressure of the working fluid. Figure 3.7 shows a plot of the Thoma cavitation coefficient versus power 14

24 Figure 3.6: Mechanical Factor of Safety Approximation specific speed. For this design, referencing the inlet conditions (atmospheric ambient pressure and 2m 3 /s flow rate), the minimum pressure was calculated to be approximately 65 kpa. A safety factor of 4 was then calculated for the design at the chosen operating point, which is conservatively within the safe no-cavitation region shown in Figure 3.7. This means that there is a large buffer between the minimum pressure and the vapor pressure of the fluid, so it is unlikely that bubbles will form on the blade surface, and any bubbles that might pass through the regions of lowest pressure have a low risk of expanding and rapidly collapsing, which is typically the main source of cavitation damage Uncertainty Another key issue to examine during the design process is the uncertainty of the analysis, experiment, or any associated processes. Figure 3.8 shows a plot of scaling efficiency uncertainty over a range of Reynold number ratios. At a one-to-one ratio of Reynolds numbers from the prototype to the scaled model, the uncertainty is zero. As the Reynolds number ratio decreases towards zero, the uncertainty becomes greater, up to approximately twenty points difference in expected efficiency for a very low efficiency design (70% efficiency). The uncertainty in efficiency for the current design due to scaling the prototype design is relatively small due to the model efficiency being at or above 90%, ensuring a high degree of accuracy when the prototype is increased to full-scale. Equally important, this plot shows the need to closely match the design conditions for experimental verification and validation, in that the losses associated with various design points will scale with the Reynolds number. For future work on this project, a 48-inch water tunnel 15

25 Cavitation Coefficient Figure 3.7: Cavitation Coefficient over a Range of Specific Speeds, Adapted from [1] will be used for experimental testing and validation of the design, which allows for the 65% of full-scale prototype to be tested near the matched operating point. In order to fit in with the torque, rotational rate, and power constraints of the motor and supporting electronics for the test, the flow rate has to be reduced to 75% of the designed operating condition and the rotation rate also has to be decreased to 75% to maintain the desired range of tip speed ratio (and to maintain the torque coefficient by reducing the torque by the square of the rotation rate). This means that for an expected nominal efficiency greater than 90%, there is less than 1% uncertainty in the efficiency scaling concept. Additionally, the Reynolds number, even at the reduced flow rate condition, does not globally drop below a value of approximately a million, and thus is assumed to remain turbulent, allowing any drag crisis or other low or transitional Reynolds effects to be neglected. 3.2 Detailed Design Once the preliminary design is completed, the detailed design then fills in more of the system information, and provides extended insight into the performance and properties of the system. The detailed design involves utilizing one or more 16

26 Figure 3.8: Estimated Uncertainty over a Range of Efficiencies, Correlation from [10] tools to analyze the flow field and the system s interaction with that field. Two of the possible tools that could be used are Streamline Curvature Method (SCM) tools or Computational Fluid Dynamics (CFD) tools. The detailed design will often include multiple design revisions, and off-design analyses to examine the performance curves for each potential revision Streamline Curvature The Streamline Curvature Method is a quasi-1d potential flow routine in which an Euler solution is coupled with a Bernoulli solution, solving for the velocity and pressure fields of a turbomachinery system. SCM is quasi-1d because it views the 3D flow field in a simplified 1D domain, but allows the streamlines to curve in the transverse flow direction, thus having some 2D qualities to the routine. Figures 3.15 and 3.9 show one blade passage of the 3D and simplified 1D domains, respectively. The flow occurs from left to right through the domain, where the inlet guide vane (IGV) section is encountered first, and then the rotor section. Figure 3.10 shows an example of the result from a SCM routine, where each horizontal black line on the left side of the figure is one streamline, and the flow is from left to right. SCM provides valuable insight into the flow character within the domain, and also 17

27 the equally valuable approximate pressure field from the Euler equation. For this design, it can be seen that the streamlines in the rotor section diverge from the endwall area (the top) towards the centerline (the bottom). This knowledge allowed for a modification to the initial design that included a converging endwall in the rotor section that forced the fluid to remain attached to the wall. Figure 3.9: Simplified Example 1D Turbine Domain, Flow from Left to Right Figure 3.10: Example Streamline Curvature Domain Result Computational Fluid Dynamics (CFD) Analysis Another useful tool for evaluating system behavior and performance is fully threedimensional CFD. Solving the governing equations in a less simplified form than 18

28 1D or quasi-1d methods, CFD is able to provide a more detailed view of the system behavior, such as being able to measure losses via secondary flows. For this application, an in-house CFD package called OVER-REL is used. According to Richard Medvitz, "OVER-REL is a structured, overset flow solver originally based on the UNCLE code developed with an emphasis on the simulation of rotating machinery. OVER-REL provides the solution to the unsteady, incompressible, three-dimensional, single-phase RANS equations. OVER-REL takes a conservative, cell-centered, finite-volume approach applied to structured multiblock grids of hexahedral cells using a time-marching, pseudo-compressibility formulation. Inviscid fluxes are formulated from the Roe-approximate Riemann solver and extended to third-order accuracy through the MUSCL scheme. The default discretization in OVER-REL is third-order accurate upwind-biased differencing with fifth- and seventh-order accurate differencing also available. Second-order accurate central differences are utilized for the viscous fluxes. A backwards Euler implicit method is used to update the equations in pseudo-time. A symmetric Gauss-Seidel method is applied to solve the resulting linear system of equations. The code allows multiple-block-per-processor parallel processing using the message-passing interface (MPI) library for inter-processor communication. Structured overset meshes were built for OVER-REL using the commercial grid generation package Gridgen. OVER-REL allows the implementation of overset grids with the overset interpolation stencils defined using SUGGAR++. Turbulence modeling includes various two-equation turbulence models and the one-equation model of Spalart and Allmaras, which also includes a Detached Eddy Simulation (DES) capability. OVER-REL has been developed with an emphasis on the simulation of rotating machinery and has been applied and validated extensively for both turbomachinery and underwater vehicle analyses. Turbomachinery powering analyses are performed using the mixing plane model found in OVER-REL. This capability simplifies the analysis of turbomachinery by allowing the computational domain to be restricted to a single periodic blade for each blade row. Periodic boundary conditions are enforced and circumferentially averaged flow variables are passed across the mixing plane. This type of mixing plane analysis is standard practice for turbomachinery design analyses performed at ARLPSU." [20] Figures 3.11 and 3.12 show the corresponding mesh and computational domain used to simulate the turbine. As was mentioned above, the CFD analysis was 19

29 performed using a mesh that was broken up into one Rotor and one inlet guide vane (IGV) frame with different periodicities, and a mixing plane boundary condition was enforced in between to pass circumferentially-averaged flow variables between the two. The mesh was made up of between 5 and 6 million cells, and used sub-layer resolution with y + equal to approximately 1. The one-equation model of Spalart-Allmaras was used to estimate the turbulence in the simulation. At all solid boundaries, a no-slip condition was applied, and periodic boundary conditions were applied in the tangential direction. At the inlet, a slug velocity was applied to reproduce the desired unit mass flow, and a constant pressure condition was applied at the outlet of the domain. Figure 3.11: Endwall View of Mesh of one Rotor Blade and one Inlet Guide Vane Figure 3.12: Simplified Domain Boundary Conditions 20

30 Figures 3.13 and 3.14 show the computational results from the on-design conditions for one rotor blade. From the computational simulation, it was found that the peak hydrodynamic efficiency for the design was approximately 90.6% at 41.2 kw of power delivered to the rim. Figure 3.13: CFD Results for an IGV, Suction and Pressure Sides Visualizations Figure 3.14: CFD Results for a Rotor, Pressure and Suction Sides Visualizations Design Modifications and Off-Design Analysis Part of the design process is iterative, involving design revisions and modifications in order to optimize the desirable parameters. For this project, four design contenders were created that utilized various geometry and swirl velocity profiles in an attempt 21

31 to maximize the peak hydrodynamic efficiency as well as the flatness of the efficiency performance curve. The four designs are shown in Figure 3.15, in the form of the 3D rendered visualization of one turbine passage. Figure 3.16 shows the efficiency curves for each of the four designs under various rotor speed conditions, and Figure 3.17 shows the efficiency of Design 1 over the peak performance of tip speed ratio. (a) Design 1 (b) Design 2 (c) Design 3 (d) Design 4 Figure 3.15: Visualization of Four Different Inlet Guide Vane and Rotor Designs As was previously mentioned, there were two important parameters to be maximized for the designs: the peak hydrodynamic efficiency and the flatness of the efficiency curve. Examining the efficiency curves of figure 3.16, it can be seen that Design 2 fell below expectations, due to a misalignment in design of the blade to the fluid. This author attempted to create a free-vortex design with extensive flow turning at the cantilevered blade tip, which led to large velocity gradients near the tip because of the zero-work requirement in the open annulus core region. Designs 1, 3, and 4, however, performed well in both peak efficiency and broadness of operating 22

32 95 90 Efficiency (%) Power Specific Speed Design 1 Design 2 Design 3 Design 4 Poly. (Design 1) Poly. (Design 2) Poly. (Design 3) Poly. (Design 4) Figure 3.16: Plot of Hydrodynamic Efficiency vs Rotor Power Specific Speed Efficiency (%) TSR Design 1 Poly. (Design 1) Figure 3.17: Plot of Hydrodynamic Efficiency vs Rotor Tip Speed Ratio (TSR), Design 1 region, based on rotor speed. Design 1 was chosen to be further examined, on the basis of prioritizing peak efficiency. Figure 3.17 shows the efficiency curve for Design 1 again, plotted over the desired range of Tip Speed Ratio. The performance is shown in terms of tip speed ratio instead of power specific speed, due to the power specific speed being a powerful design tool for comparison, because of the fact that unlike for TSR, the extracted mechanical power is considered in the parameter. Thus, the TSR parameter creates a consistent range for comparison of the effects of one design with itself, under varying conditions, as shown in the Flow Rate Modification Study section. 23

33 Flow Rate Modification Study Efficiency (%) TSR Q Modification ΩΩ Modification Poly. (Q Modification) Figure 3.18: Variable Inlet Flow Rate CFD Results Figure 3.18 shows the efficiency curve of Design 1 over tip speed ratio, based on changing the inlet volume flow rate, and also based on the previously shown results of changing the rotor rotation rate. The square markers are the same points from Figure 3.17 from the variable rotor speed CFD analysis. The circle markers represent the sampled operating condition points from a variable volume flow rate CFD simulation. It can be seen from Figure 3.18 that the two sets of data lie almost exactly on top of each other, due to the dimensionless tip speed ratio parameter collapsing the conventional degrees of freedom into one variable. In other words, the tip speed ratio acts as a measure of how effective the turbomachine operates in that it captures the essential parameters that control efficiency and power production: turbine size, rotation rate, and flow rate Blade Count Modification Study To investigate the optimal blade count, CFD simulations were performed for varying IGV and Rotor blade counts. The blade count is an important parameter to investigate because it can directly affect the efficiency, and also can be a substantial driver for cost and manufacturing time. Varying the IGV and Rotor counts independently in simulation is also important, due to the possibility of the effects of both changes becoming convoluted. Figures 3.19 and 3.20 show plots of efficiency versus blade count; figure 3.19 plots against the rotor blade count for a constant 24

34 inlet guide vane count, and figure 3.20 plots against the inlet guide vane count for a constant rotor blade count. It can be seen from Figure 3.20 that any IGV count between 7 and 21 will yield efficiencies above about 89% with 13 rotor blades. However, Figure 3.19 shows that the rotor count can span only between 9 and 17 to achieve the same efficiency with 17 IGVs. This shows that, as would be expected, the system performance is more sensitive to the rotor count due to the rotors extracting the energy from the flow. To save costs and manufacture time, the rotor count could then be kept at its optimum level (13 rotor blades), and the IGV count could be reduced to the lowest count allowable in terms of mechanical stresses and hydrodynamic efficiency (11 IGVs to keep above 90% efficiency). The tradeoff, however, will be that the turbine will produce less power due to a decreased torque Constant IGV Count Efficiency (%) IGVs Poly. (17 IGVs) Number of Rotor Blades Figure 3.19: Variable Rotor Blade Count CFD Results Comparison of Designs with Fielded Turbine Types Figure 3.21 shows the comparison of the four current designs (1 through 4) with four types of fielded turbines (A through D), based on the degrees of freedom of the turbine. The plot shows the overall hydrodynamic efficiency as a function of the percent of load, or the load ratio, defined as: φ/cms, where φ is the flow coefficient and CMS is the mass flow coefficient of the best efficiency point. Design 1 through 4 are comparable in their number of degrees of freedom to turbine type C, namely, both have zero degrees of freedom in terms of their blade and gate 25

35 Constant Rotor Count Efficiency (%) Rotors Poly. (13 Rotors) Number of IGV Blades Figure 3.20: Variable IGV Count CFD Results adjustability or variability. Examining figure 3.21 though, it can be seen that the turbine designs 1 though 4 are able to operate with higher efficiency over a much larger range of load ratios, similar to the one degree of freedom designs (types B and D). This shows that the designed hubless turbine allows a zero degree of freedom turbine to perform like a one degree of freedom higher type Comparison with Existing Designs F = Fixed A = Adjustable B = Blade G = Gate A - AB, AG Efficiency, % Percent of Full Load B - AB, FG C - FB, FG D - FB, AG Design 1 Design 2 Design 3 Design 4 Figure 3.21: Comparison of Designs with Fielded Turbine Types, adapted from [11] 26

36 Chapter 4 SELECTION AND OPERATION OF TURBINE Once the turbine has been designed, it is necessary to consider how the user will select and operate the turbine. This process entails expanding the non-dimensional performance curves over the expected ranges of various conditions, and combining the results into the simplest but most meaningful diagrams possible. 4.1 Selection of Turbine Size Figure 4.1 shows the high-efficiency operation region for Design 1 expanded over a range of turbine sizes and speed conditions. These two performance maps can be used together to determine a proper turbine size and peak performance speed for a given set of flow rate and head conditions for a site. For example, knowing that the Design 1 configuration will be used in a given waterway, if the estimates of average head and flow rate are calculated to be 5 meters and 5 cubic meters per second, then a turbine of an approximate radius of 0.6 meters would be ideal while operating between 180 and 190 RPM. 4.2 Selection of Turbine Speed Once a turbine is chosen and installed at a site, it is necessary to know how to vary the speed of the rotor to maintain the highest efficiency possible for a given flow condition. Figure 4.2 shows the performance map for Design 1, with the flow 27

37 H = 5m Q = 5 m3 s Figure 4.1: Size and Speed Performance charts for Design 1 Turbine for 90% Hydrodynamic Efficiency rate and rotor speed normalized by the best efficiency point (BEP). Suppose that a turbine is operating at point 1 in Figure 4.2 (the BEP), but then a major rainstorm floods the river, increasing the normalized flow rate through the turbine by 30% (to point 2). This figure shows that the turbine efficiency would then drop to approximately 87%, which can be increased back to the full 90.5% efficiency by increasing the speed of the rotor to around 130% of the normalized BEP speed (to point 3) Figure 4.2: Performance chart for Design 1 for Constant 0.45 meter Turbine Radius 28

38 Chapter 5 MODIFIED STREAMLINE CUR- VATURE METHOD 5.1 Routine Drivers This author attempted to create a modified streamline curvature method (SCM or SCUM) routine, in order to provide a more robust and universal design method for non-typical turbines such as the one developed in this project. For the purposes of the project, this author utilized legacy SCM routines created for typical hub-type turbomachines, to begin the detailed design. However, as was shown in Figure 3.10, the legacy codes are not meant for open annulus turbines, such as for the hubless type in this project. The SCM routine implicitly creates a hub at the end of the blade surface, and does not handle flow in that section. This means that the legacy SCM routines would not be able to detect tip flow effects of the blade or any physics in the "core region" flow (the fluid flow through the region in which hub is located in a traditional turbine), where flow could be diverted to from the blade section, depending on the magnitude and distribution of the blade loading. 5.2 Routine Method The concept behind the routine is to develop a series of valves that model the flow physics of the blade and annulus, where each valve acts as a streamtube. Each valve has an associated volume flow rate, pressure drop, and set of areas (inlet and outlet), which can be combined into resistance coefficients for the inlet and 29

39 outlet of the valve. The valves can be set up in series or parallel to each other, and combined into equivalent "hydrodynamic circuits" similar to resistors in an electric circuit, where the pressure drop across the valve acts like voltage, and the flow rate through the valve acts like current. The valves, then, can model the effect of blade loading on other parts of the domain (depending on the degree of the complexity of the hydrodynamic circuit). For example, if the rotor is required to do an extensive amount of flow turning near the endwall, then the large pressure drop (and thus large resistance coefficient) across the valve that represents that area could divert flow away from that section and into lower resistance sections, such as towards the open annulus. The routine starts with setting up the valve domain, where each streamtube is modeled by at least one valve over the whole physical domain. The user provides inputs of parameters such as the distribution of swirl velocity and total pressure, and provides initial estimates for the valve area, static pressure and axial velocity distributions. The routine then solves sets of coupled, non-linear equations at axial stations on either side of each set of valves. At each station, the equations are evaluated for the flow rate, pressure drop, and areas for each valve that satisfy mass continuity coupled with Bernoulli s principle through a streamtube. This routine method has a strong advantage of being able to solve for the flow physics throughout the entire domain, even into the open core region. The disadvantage is that, compared to a traditional streamline curvature method, the user needs to input more flow information for the entire domain that involves somewhat deeper knowledge of the turbine behavior. Though the success of the routine may seem to weigh heavily on the aforementioned disadvantage, this method is not necessarily meant as a replacement for a legacy streamline curvature routine, but is meant to provide an extension from the traditional method into loss modeling and interfacing with other disciplinary routines, such as vibrations and mechanics. This would allow for a broader inter-disciplinary and deeper fluid dynamic view into the complete performance of the desired turbomachine in the initial design stages. 5.3 Routine Issues This author encountered difficulties with creating a MatLab routine for this method, due to difficulties in converging the entire domain to an expected solution. It was 30

40 found that the values of velocity and pressure for at least one valve, particularly the valve nearest the axis of rotation, did not converge to the expected values from an on-design CFD simulation. This author is unsure of the exact cause of the issue; the problem could be in the particular choice of equations, the method of splitting up the domain into valves, or in the method of simultaneously solving the equations. It is recommended that this type of streamtube analysis be further investigated, for the particular benefit of future unique and advanced turbines, such as the one in this project. 31

41 Chapter 6 CONCLUSION From the dawn of the first water wheel and turbomachine to the invention of the hubless and rim-driven marine thrusters, many advancements in technology have been culminated into a capstone of energy generation with the advanced hydroturbine described herein. This turbine has potential to tap into the country s and the world s vast reservoir of low head, low power hydro energy. Utilizing the undeveloped energy sources could be a great benefit to society, by reducing the dependence on non-renewable energy sources, but still providing flexible, environmentally-friendly energy. The design of the turbine began in the preliminary stage, which involved investigating the full design space for the desired turbine, and checking the designs for safety. The preliminary design revealed that the Kaplan- or propeller-like full scale turbine can be prototyped with a design scaled down into the microhydro operating region, as long as the specific speed or tip speed ratio is held constant. The prototype would allow for experimental testing in a 48-inch water tunnel, and would also allow for possible deployment into a local river for in-situ investigation of condition based maintenance (CBM) systems. The proposed design was then checked for mechanical and cavitation safety, and was found to have sufficient safety margins. After the preliminary stage, the next step was the detailed design. The detailed design was comprised of determining the two- and three-dimensional performance of the designed turbine over the desired range of power specific speed or tip speed ratio, accomplished by varying the rotor rotational speed, and keeping all other variables constant. Streamline curvature (SCM) and CFD simulations showed that three of the four designs perform exceptionally, operating with high efficiency over a wide 32