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DIGITAL ASSIGNMENT – 2
Review on Numerical research of cavitation on Francis turbine runners
Rahul Radhakrishnan | 16BME0032 | Turbomachines (MEE2026) | Faculty: Dr. Nithin Battula
Credits: Google Images
Introduction
Hydropower is produced in 150 countries, with the Asia-Pacific region generating 33 per cent of the global hydropower in 2013. The cost of hydroelectricity is low compared to the electricity generated by other power plants, making it a competitive source of renewable electricity. Most hydroelectric power comes from the mechanical energy of dammed water driving a water turbines and generator. Hydraulic turbines are classified based on the amount of head consumed, flow rate and its direction of flow. Francis turbine is a type of water turbine which is a combination of radial and axial flow water turbine concept and they are one of the most common water turbines in use today.

Cavitation is a common phenomenon in hydraulic machinery which is subjected to low-pressure conditions. It occurs if the liquid pressure drops below the vapour pressure and the resulting negative pressures are relieved by forming gas-filled or gas- and vapour-filled cavities. It is undesirable as it decreases the performance of the device, generates noise and damages the setup costing us a fortune. Also, the turbine does not always operate under the design conditions. Due to fluctuations in the flow rate and energy available in the fluid, there is a necessity to address the problem of cavitation in the off-design conditions. Understanding and resolving the problem of cavitation is a great challenge and opportunity in various fields such as propulsion.

There are four types of cavitation in Francis turbines. Leading edge cavitation is due to flow separation at suction or pressure side of the runner because of the incidence angle of the flow. Travelling bubble cavitation occurs at the suction side of runner near the trailing edge at overload conditions. Draft tube swirl cavitation occurs beneath the runner at tube’s centre. Inter-blade vortex cavitation occurs at high heads due to flow separation along leading edge. Thoma number is a dimensionless number which measures the cavitation in hydraulic turbine installation, relating vapour pressure, barometric pressure, runner setting, tail water and head. For a turbine to avoid cavitation from happening, its Thoma number should be less than the Plant Thoma number. Changes made in the design of runner blades and draft tube geometry can have little, but significant reduction in cavitation phenomenon and prevent damage of the device and increase in its performance. For such an efficient design process, we plot a hill chart comprising of the head coefficient and discharge coefficient.

? = patm- ?gH(s)-p(v)?gHHere, ? is the Plant Thoma number
H(s) is the suction head of the turbine
H is the net head
P(v) is the vapor pressure of the fluid
Technological advancement in computation has led to the development of various models which can model these problems and help us solve them to some extent. Over the years these models have become more accurate which helps engineers to modify the current designs of hydraulic machineries and make them more efficient using computational fluid dynamics (CFD) tools. In this paper, we are going to see how a numerical research to design a cavitation-free operating Francis turbine is carried out and how it can be made to operate effectively even in off-design conditions.

Literature Review
Celebioglu K, et al., Numerical research of cavitation on Francis turbine runners, International Journal of Hydrogen Energy (2017)
Celebioglu and Altintas (2017) took the runner geometry of a Francis turbine which belongs to an actual hydroelectric power plant that was designed and implemented in 1960s and identified the causes of different types of cavitation which were affecting the overall efficiency of the machinery. Since, Thoma number tells whether the turbine will operate in cavitation free, for every design they made, they made sure that the Thoma number at any location on the runner was less than the Plant Thoma number. They redesigned with the help of the state of the art computational fluid dynamics techniques for cavitation free operation and in order to match with the above condition, they had to perform numerous simulations at 33 different operating points. They also calculated the cavitation limits for the off-design conditions in order to increase the overall efficiency of the turbine in real-time by plotting numerical hill charts. It was observed that increasing the ellipse ratio of the leading edge and trailing edge prevented sudden drop in pressure in the runner, hence making it more free from cavitation process. They also concluded that on-design cavitation free operation led to minimization at off-design conditions as well. By doing so, they increased the power output of the turbine by 0.1 MW and its efficiency by 2%.

Critical Review
In the current study, the geometry of the runner of a Francis turbine which was designed in the 1960s was determined using laser scanning. It was observed that the blade geometry was very irregular in nature due to cavitation erosion. Study of the numerical hill chart revealed that the cavitation free operating region was very narrow for the blade and it did not even include the design point of the turbine. They realized that there is a strong necessity to design a new runner blade with a wider range of cavitation free operating region and which includes the design point. This new design would also ensure that the cavitation is minimized even in off-design conditions.

Fig: Meridional view of the Francis turbine runner geometry

Fig: Numerical hill chart and cavitation free operating range in the existing runner
In general, the runner geometry is made using ANSYS Bladegen and an unstructured hexahedral mesh is generated using ANSYS TurboGrid. It had 3.5 million elements overall in the flow passage and y+ values over the blade were kept below 2.5. ANSYS CFX was used for performing the numerical simulation. The governing equations are mass conservation and Navier-Stokes equation. Shear Stress Transport turbulence model was used to solve Reynolds Averaged Navier-Stokes (RANS) equations which combines two turbulence models, K-epsilon and K-omega, to give accurate near wall results. Cavitation simulations are done using homogeneous multiphase model as it allows the modelling of the mixture as a pseudo-fluid. Rayleigh Plesset model is used for the detection of cavitation. The boundary conditions used were mass flow rate inlet and pressure outlet with periodic interface. The results from design point were used as initial conditions for off-design point simulations.
It was observed that, for the existing blade, the Thuma number exceed the Plant Thuma number (about 0.052) in the suction side of the runner near the trailing edge. This was checked for each operating point to plot the narrow cavitation region that we discussed before on the hill chart.
In order to rectify the above issues a new runner blade geometry was designed. The camber length was 0.2 m shorter than the current blade and had a symmetrical airfoil profile (NACA0050). It was observed that increasing the leading edge and trailing edge ellipse ratio made a significant reduction in cavitation. A smaller ellipse ratio generally makes the fluid to flow from a larger area to a smaller area. From Bernoulli’s principle, there would be a sudden change in the static pressure of the fluid. So, in the new design the leading edge ellipse ratio was increased from 2 to 5 and that of the trailing edge was increased to 16 which resulted in a much smoother transition of pressure along the runner. Flow separation and irregularities at the leading edge were eliminated by setting ? equal to ?. Here ? is the angle between the relative velocity and the tangent vector at the leading edge and ? is the angle between the tangent of the leading edge and the tangent of the chamber.

Fig: Effect of change in pressure along the runner with increase in ellipse ratio
The design had the following figures:
Design Flow rate – 6.1 m3/s
Design Head – 151 m (Slightly lesser than the existing blade which had about 153 m)
Efficiency – 98 % (95% for the old design)
Incidence angle – 16.5 deg (17.5 deg for old design)
Now, all these changes widened the cavitation free operating region for the turbine and it was time to find out the limits of cavitation in the off-design points.

Operating Points 1 2 3 4
Net head (m) 197 145.1 87.3 195.4
Flow rate (m3/s) 6.7703 6.7703 5.11 3.72
Shaft power (MW) 12.68 9.37 3.96 6.8
Efficiency (%) 97.24 97.55 90.6 95.6
Incidence angle (Deg) 15 15 21 7
Operating point 1 resulted in a leading edge cavitation because of the net head and flow rate being greater than the values for which the blades were designed for. Operating point 2 resulted in a travelling bubble cavitation in the suction side of the runner near the trailing edge. Even though operating point 3 operated at a head much lower than the design head, it resulted in leading edge cavitation in the pressure side of the runner. Operating point 4 is a partial load operating condition in which there is a possibility of inter-blade vortex cavitation. But the simulations showed no signs of cavitation as the Thoma number was lesser than 0.052 giving us an important conclusion.
At the end, a hill chart was made for the new design showing the cavitation and non-cavitation operating point.

Fig: Numerical hill chart and cavitation free operating region for the new design of runner
Design and Development
The new design of the runner blade consists of a NACA0050 profile, which is a symmetrical airfoil. Attempt must be made to implement complex airfoil shapes which can provide superior flow quality in the runner passage than the new design. Manufacture of complex profile for runner blades should not be considered as a limitation. With advanced techniques under development in Additive manufacturing industry, it is very much possible to implement this and reduce the overall cost and time of manufacturing a turbine.

Another important future study should be to observe the effect of changing the ellipse ratio of the leading edge. In the present study, ellipse ratio has been increased only up to 5 along with making the ? and ? values same. If one wishes to continue with the current new runner design, then the effect of changing solely this value on the cavitation phenomenon would be really useful while designing the future runner blades of similar specification. A separate study should involve the effect the change of these angles.
Newer designs should be tested comparing the performance of the turbine with the camber length of the blades. In the present study, fixed camber length is used and it was kept lesser than the existing blade. Effect of changing the camber length of the blades will also be an important study and will give important results which can be implemented in future designs.

Not much information has been given on the paper regarding how the new design is performing overall compared to all the other Francis turbines present today. Doing the above suggested studies would actually give us an idea of how cavitation is affected by changing certain parameters and will help us to arrive at an optimized design.

It is seen from the new hill chart that cavitation can be avoided at greater than design head values by decreasing the flow rate. Suitable design modifications must be made to decrease the flow rate in such cases so that we can still avoid cavitation from happening. In such conditions, operating the Francis turbine under the same flow rate would not be advisable and it would further decrease its performance.

The paper also tells that there are no identical experimental cases present with the cavitation. So, it is suggested that once optimized design of the Francis turbine is obtained for cavitation free operation, it should be manufactured and tested for cavitation so that we can validate our results.

Conclusion
Operating a turbomachine cavitation free is one of the major challenges in the aerospace industry and hydropower plants. In the paper reviewed, a runner designed in the 1960s in redesigned to give better performance characteristics in terms of cavitation free operation. As per the new design it appears as if we need to compromise on the operating net head of the turbine slightly to avoid the phenomenon. But, not enough statements are given to support the fact that it is the best design that one could come up with. Future studies should focus on the effect of changing different parameters like ? and ?, ellipse ratio and camber length of the blade on the phenomena of cavitation. Only then one would be able to tell whether we can come up with better designs or it is the best design, hence providing future designers with enough data for them to design. Experimental cases need to be set up to validate computational results and a shift towards additive manufacturing for such experiments which can save time and money. The present study is not only specific to Francis turbines, but can also be applied to other classes of turbines.

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