Computational analysis of flow over a cascade of S-shaped hydrofoil of fully reversible pump-turbine used in extracting tidal energy
Introduction
Energy requirement is on the rise and this ever-increasing demand together with growing consciousness of the adverse environmental effects posed by fossil-based energy sources have generated a renewed interest in looking for alternative means of producing sustainable energy. Like solar, geothermal and wind energy, tidal energy also contributes to pollution free energy to the long term solution for the energy crisis. Tidal power plants do not exert a large-scale harmful influence on the flora and fauna and human health and favors the production of fish mass [1]. The major reason that restricts the tapping of energy from the tidal power plant is large construction cost. In future depletion of fossil fuel may make tidal power economically viable for global energy production [2]. In India, for example, the Gulf of Cambay and the Gulf of Kutch in Gujarat, and the Gangetic delta in West Bengal are the potential sites for tidal power extraction [3].
In order to extract the tidal energy effectively and economically, it is necessary to design a hydraulic machine suitable for a tidal power plant. In a typical tidal power plant there are two directions of flow namely, during high tide flow sea water enters the basin from the sea and during low tide the reverse direction of flow takes place. Thus, a hydraulic turbine should ideally be able to perform equally well for flow of water into the basin and for that owing out of the basin. This can be achieved by a cross flow turbine and there has been a recent surge in activities relating to the design and development of cross flow turbine capable of handling bi-directional flow ([4], [5], [6], [7], [8], [9]). However, these turbines usually suffer from low efficiency, low starting torque and high torque ripple. Attempts are made to reduce torque ripple and increase efficiency and improve starting torque. For example, Malipeddi and Chatterjee [9] tried to design a duct which will improve the efficiency and reduce the torque ripple.
There is another approach in which the problem of tackling bi-directional flow can be achieved without the use of low-efficiency cross flow turbines. This is done through novel blade modification and details of the performance of this type of blade are the content of the present paper. Such a turbine design should be capable of producing power output for both directions of flow. Additionally, in order to increase the head available to the turbine, a pump may be used to drive additional water from the sea to the basin during end of high tide period. Further, the water is evacuated from basin to sea during end of low tide period in order to accommodate more water during next cycle [10]. In this novel approach, the same hydraulic machine will be able to perform both as a pump and as a turbine for both directions of flow. This idea is, in principle, similar to a pump storage unit but a major difference lies in the fact that here the same hydraulic machine has to work alternately as a turbine and as a pump for both directions of flow. The direction of flow is to be considering from basin to sea for direct turbining and direct pumping operations. On the contrary, the direction of flow is from sea to basin for reversed turbining and reversed pumping operations. Thus in a tidal power plant the hydraulic machine has to perform four modes of operations namely, 1) direct turbining, 2) reverse turbining, 3) direct pumping, and 4) reverse pumping. Such a machine which performs the above mentioned cycle of operation is referred to as a ‘fully reversible pump-turbine’.
If a Kaplan turbine with conventional hydrofoil is used in fully reversible mode for power generation, the blade setting has to be rotated by as high as 180° to switch from one mode of operation to another. However, a hydraulic machine with S-shaped profile will require only about 30° of rotation without stopping the operation of the machine [10]. As shown in Fig. 1, S- shaped hydrofoil has successive concave and convex curvatures on the lower surface, further, it has successive convex and concave surface on the upper surface. It is represented as S followed by a four digit number [11]. First digit represents maximum camber; second digit represents maximum thickness as percentage of chord length and last two digits together represents the location of maximum camber as percentage of chord from either end of the blade. Madhusudan et al. [12] studied the boundary layer characteristics over the S-shaped aerofoil at 0° angle of incidence. Flow separations, variation of mean and turbulence quantities over upper and lower surfaces of the S-shaped aerofoil were also elaborately studied. In the present work S3525 has been used as this particular profile has a better operational range and it is best suited as the runner blade in fully reversible pump-turbine of tidal power plant [13].
Flow over a single and a cascade of hydrofoils are of major interest for the hydrodynamic design of turbomachinery like pump and turbine. A review of literature revealed that numerous papers exist on aerodynamic characteristics for a cascade of gas turbine blades. However, information available for a cascade in case of water turbine, in general, and fully reversible pump turbine, in particular, is very restricted. Ravindran [14] investigated a fully reversible pump turbine. The blade profile of runner of this hydraulic machine has S-shaped camber with thickness distribution corresponding to the first half of the NACA 0010-35, symmetrically distributed from the either end to mid chord. In these experiments, it was observed that a runner with an S-shaped hydrofoil profile gave an approximately equal efficiency of about 78% in all the four modes of operation. However, runner with conventional hydrofoil gave very low efficiency in the reversed flow operations. Ramachandran [15] investigated aerodynamic study of S-blade in both isolated and cascade modes for various cambered profiles. It was concluded from this study that a low-cambered S-blade had a better operational range than the highly cambered profile. However, the effect of stagger angle (βs) was not systematically studied in this work. Ramachandran et al. [13] found that the angle of incidence corresponding to the best performance increased with an increase in the maximum camber. The results indicated that the S-blade with camber less than 5% of the chord would be suitable for the design of the axial flow fully reversible pump-turbine.
Yilbas et al. [16] carried out numerical analysis on attached and separated flows over the isolated and cascade of NACA 0012 aerofoil using k − ε turbulence model. It was found that the angle of incidence at which maximum lift occurs would increase with solidity. Moreover, in this case, a slight increase in drag is observed. Premkumar, and Chatterjee [17] brought out the difficulties of modeling turbulent flow over S-blade and compared predictions based on four different turbulence models, namely, k − ε Realizable, k − ω SST, and Reynolds Stress Model (RSM). They compared the predictions of mean and turbulent quantities on upper and lower surfaces of S3525 with experimental results available. It was observed that the predictive capabilities of k − ω SST were better than the model for mean quantities like the lift and drag coefficients.
The computational tool can ease the designer to rapidly evaluate new reversible pump turbine blade geometries and this can significantly reduce overall design cycle time. In many of the turbomachinery applications, the flow over the blades may have Reynolds number which falls in the transition range. Hence, the successful prediction of the results depends on the turbulence and transitional modeling employed during the simulation.
The transitional turbulence model developed by Walters and co-workers [18], [19] seems to be a very good option for modeling this type of flows. Walters and Cokljat [19] applied k − kL − ω 3 equation model to a number of aerofoil test cases for different flow conditions and wide range of geometry, including freestream turbulence conditions, Reynolds number, and angle of incidence. The transitional behavior for each of these cases was well reproduced by the new transitional model. In one of the earlier works (Premkumar et al. [20]), shows the usefulness of this modeling approach for predicting flow features over an individual S-shaped hydrofoil.
It is seen from the study of the existing literature that numerical simulation of flow over concave and convex surfaces is not very easy and hence the modeling of turbulent flow over S-shaped aerofoil is even more difficult as the geometry involves both concave and convex surfaces. But a better understanding of the flow physics is a pre-requisite for a better design of fully reversible pump-turbine. Experimental results are valuable but experiments conducted so far on S-blade indicates the lack in complete information and most of the results concerning the flow over a cascade of S-blades are heavily dependent on the measurements carried out at the ends of the cascade. Thus the main objective of this work is to understand and predict flow features for S-shaped cascade geometry that helps in designing an S-blade runner for fully reversible pump-turbine. This objective is achieved by conducting careful simulations of flow over single and multiple (a cascade of) blades and validating some of these results with the experimental result available. The specific steps involve simulation of both pump and turbine cascades and determines if the S-blade geometry is useful for both cascades or not. Design data of a cascade of blades for a fully reversible pump-turbine is reported in the next section. Numerical methods and turbulence models with appropriate equations are presented in Section 3. Simulation procedure, including grid sensitivity study and validation, is also covered in Section 3 while results and discussions are given in Section 4 and major conclusions are outlined in Section 5.
Section snippets
Cascade details for fully reversible pump-turbine
These types of hydraulic machines normally have higher specific speeds and Ravindran [14] had mentioned that typical specific speed of this type of hydraulic machine is around 850 rpm. In a tidal power plant the head difference for turbining and pumping operations is small. For example, the mean value of the tidal head in the Gulf of Cambay in India is around 7 m [14]. Hence axial flow pump-turbine is best suited for tidal power application. Actual design calculation for the fully reversible
Numerical analysis
The governing equations for the present analysis are:
Moreover, the flow is assumed to be the steady and incompressible. k − kL − ω transition model is used to take care of the Reynolds number of the flow. Transport equations for the k − kL − ω model are explained in Ref. [21] and are not given here for brevity.
Results and discussion
At the very outset of presentation of results, the effect of angles of incidence on the performance of cascade is examined at the design value of stagger angle and pitch-chord ratio.
Fig. 4 shows the variation of static pressure over the over upper and lower blade surfaces along the streamline for different angles of incidence. These curves intersect each other due to negative camber of S-blade after the mid chord. The enclosed area of Cp curve at ahead of point of intersection contribute to
Conclusions
Numerical methodology has been established with the help of strict validation and grid sensitivity studies. Computational work has been carried out at the design stagger angle of βs = 27° and blade spacing of S/C = 1. Sensitivity of the dependence of cascade performance on these parameters were tested. This brings out flow physics and helps to find a useful range of angle of incidence. It is found that pressure loss in the turbine cascade is generally lower than that in the pump cascade.
Acknowledgments
Micha Premkumar, T. would like to acknowledge Council of Scientific Industrial Research (CSIR), New Delhi, India for providing fellowship to carry out a part of this work. The authors would like to thank High Performance Computing Facilities of Computer Center at IIT Madras for enabling them to carry out the simulation work.
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