Design of a small hydro Kaplan turbine with a self-sealing rotor Sebastiaan Annerel Supervisors: Erik Dick, Jan Vierendeels Abstract This paper describes the design of a small Kaplan turbine with movable rotor blades with a form so that the rotor can be turned into a fully closed position. So, the turbine also functions as a valve. To reach such a rotor, quite unconventional design options have to be taken. The resulting design method is widely tested using CFD. Keywords Kaplan turbine, self-sealingness, streamtube method, CFD analysis, diffuser
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I. INTRODUCTION Civil engineering structures, like a dam or weir, are common practice on navigable rivers to locally raise the water level and to create a water reservoir. River ships pass these differences in height by locks. The wastage is usually diverted by a spillway. Alternatively, a small hydropower plant can be installed on the weir. A minimum water level needs to be guaranteed for navigability. For this reason the axial Kaplan turbine has to cope with a big variety of flow rates, in particular with zero flow. Therefore, for very flexible use of the turbine, it would be a big advantage if the rotor blading would allow to be turned in a position that is fully sealing. The paper describes the design of such a turbine for a location on the river Sambre in Belgium. The available head is 3.60 m. The design flow rate is 16 m³/s. This gives a power of about 400 kW. The design of the machine is quite unconventional as described hereafter. II. MULTIPLE STREAMTUBE DESIGN The initial design of the rotor blades is done using the multiple streamtube method with the simple radial equilibrium assumption. This well-known design method is implemented in a computer algorithm. It calculates the optimal blade profile for specified values of inner and outer diameter, flow rate, head, rotational speed, number of blades and recovery factor of the diffuser. This is done for nine blade sections. The program also delivers an estimation of the shaft power and the total efficiency of the turbine. From the resulting profiles a 3D volume is generated using CAD software. The design program has been successfully successfully used a number number of times times in the past for small turbines for very low head that all were installed in Belgium. The design of the turbine has first been done in the conventional way. The number of blades has been chosen a priori very high, 16 blades, in order to assure that the blades in design position would not have a big clearance at the cylindrical casing. This number was determined by the turbine manufacturer who has realised all previous designs. Also, the
S. Annerel is with the Department of Flow, Heat and Combustion Mechanics, Ghent University (UGent), Gent, Belgium. E-mail:
[email protected] Sebastiaan.Annerel@U Gent.be .
suggestion to study the design of a Kaplan turbine with a rotor that can completely be closed came from the same manufacturer manufacturer who has interest in such a design for a number of small head installations on the river Sambre in Belgium. To obtain the self-sealingness, the normal design concept of a hydraulic turbine rotor has to be changed. For optimal efficiency, i.e. normal design, it is preferred to have the largest camber at the hub with with decreasing camber camber towards the tip. In order to obtain a self-sealing rotor, the opposite is necessary: small camber at the hub and increasing camber towards the tip. For that reason we began by setting to zero the camber at the hub and imposing positive camber towards the casing. We rotate the blades until contact at the hub using CAD software. Subsequently we force sealingness towards the tip by changing the stagger angle on the different radial positions. Of course, in order to maintain good efficiency, these angle changes should be small. A large solidity at the hub is chosen to increase overlap, which helps to reach the self-sealingness. Also large blade thickness at the hub is beneficial. The streamtube design program learns that this only implies a small loss in power against the optimal (non-sealable) design. Because losses in the rotor form only a small fraction of the total losses in a hydraulic turbine, this result was expected. It took about 10 manual adjustments of chord, thickness and camber distributions to obtain a rotor that closes perfectly at the hub, the mid radius and the casing. To reach closeness at the other radii, the stagger angle of the blades was slightly changed with a maximum change of 1.7 degree. The outer and inner diameters of the rotor are 2 m and 0.8 m. The rotational speed is 130 rpm. Figure 1 shows cylindrical cuts of the blades in closed position.
Figure 1. Cylindrical cuts of the blades in closed position, from hub (left) to casing (right). The red dot marks the pivot point
Figure 2 shows the obtained rotor, in nominal position and in closed position. The difficulty with the obtained design is that due to the zero camber at the hub, the angle of attack becomes locally very high. It reaches 10.8 degrees at the hub. This large angle is allowed in the streamtube design method, but in reality it may cause separated flow.
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IV. DIFFUSER DESIGN AND ANALYSIS
Figure 2. Design of the rotor in nominal position (left) and closed position (right)
III. CFD ANALYSIS OF THE ROTOR The obtained rotor was analysed with the CFD package FLUENT. The k-ε turbulence model is used with enhanced wall treatment. The design is conventional, which implies that the work is constant over the radius and that swirl is minimised in the flow leaving the rotor. Also, radial equilibrium is respected at the outlet. As a consequence, pressure is almost constant in a section immediately downstream of the rotor. So, the rotor was analysed on its own, by imposing upstream the flow distribution as obtained from the multiple streamtube program, and imposing downstream a constant pressure. Figure 3 and 4 shows the obtained pressure distribution and relative velocity magnitude at the mid section. No separation at the hub is visible. The separation at the hub is prevented by using a combination of big solidity and big thickness. A big solidity at the hub gives it a forced nature, there where the flow at the tip streams more freely. The bigger thickness realizes an obstruction at the hub, which results in a redistribution of the flow towards the tip. Also, the flow does not follow the negative incidence at the tip, which is necessary to reach a constant work distribution in the design program. This means an increase of the flow rate and work towards the tip. The combined effects relieves the hub and creates a bigger load at the tip section. This implies a change in the work distribution. At the casing, 30 % more work is transferred. Therefore, the flow at the hub receives a stagger angle that is less extreme then predicted in het design program. So separation is not present.
Figure 3. Static Pressure Contour (Pa) at radius 475mm near hub
A diffuser was placed downstream of the rotor to recuperate the rotor outlet kinetic energy. It consists of a truncated cone with a length of 4 m, an inlet radius of 1 m and an outlet radius of 1.370 m. The diffuser was designed to have a high theoretical pressure recovery factor (of approximately 0.7). This means that it transforms 70 percent of the dynamic rotor outlet pressure into useable static pressure. The diffuser was then analysed with the use of CFD. The k- ω SST turbulence model is used because it gives accurate predictions involving flow separation under adverse pressure gradients. The resulting resulting static pressure pressure contour and and absolute velocity magnitude field are shown in Figure 5 and 6. It shows no (stationary) separation. Because of the constant pressure at the diffuser entry, the theoretical pressure recovery of 70% is reached. It results in an increase of the efficiency with 14%.
Figure 5. Static Pressure of the diffuser (in Pa)
Figure 6. Absolute Velocity Magnitude of the diffuser (in m/s)
V. OPTIMIZATION OF THE GUIDE VANES By imposing the flow rate, the net head in the previous CFD simulations becomes larger than 3.6m. The desired value can be found by decreasing the guide vane angle. An initial guide vane angle of 26.5° is determined with the design program. Because adjusting the guide vane angle affects the efficiency, a trade-off has to be made. Alternatively, the net head can be reduced by lowering the stagger angle of the rotor blades. A combination of both options (i.e. lowering the stagger angle and decreasing the guide vane angle) leaded to an optimal guide vane angle of 20° for a net head of 3.6m. This final design was simulated. It has a total efficiency of around 70% with a power output of nearly 400kW. VI. OFF-DESIGN PERFORMANCE The performance of the turbine is simulated for an increased flow rate. The rotor stagger angle is set to the average between optimal value and fully sealed. The sliding meshes method is used. No separated flow is visible in the result. This indicates
