# Analysis of Bulb Turbine Hydrofoil Cavitation
## 1 Introduction  
Historically, hydropower was used as a source of baseload generation for electric power, but now it is increasingly used for grid balancing. Among dispatchable renewable energy sources, hydropower plants are the most often used [1], achieving up to 15 s response times [2] for 90% of the total power response. The future potential of hydropower is shifting towards grid regulation tasks. Including nondispatchable renewable energy sources, e.g., inter alia wind and photovoltaics, and market deregulation, creates the requirement for rapid power generation fluctuations and power increase in the afternoon [3, 4, 5]. Any new hydraulic turbine design should therefore enable this type of operation and reach high efficiency and stable operation outside its optimal operating interval. Besides stable continuous turbine operation away from the best efficiency point, new designs will also need to function sufficiently in transient operation. Bulb turbines face challenges for such operation; designers will have to overcome the detrimental effects that flow fluctuations and cavitation have on turbine operation, while still ensuring adequate performance over a broad interval of operating points and in transient operation [3]. At the best efficiency point, an optimal combination of the runner frequency of the rotation, head, and discharge is available. At such an operating point, flow separation is usually low, and no cavitation is observed. For operation away from the optimum efficiency point, bulb turbines, as compared e.g., to Francis turbines [4], feature double regulation and may operate in a wide interval of operating conditions with reasonably high efficiency. Although all hydraulic turbine types are constantly improved, the gains in efficiency are in the per mille range and the cavitation in hydraulic turbines remains anissue. The cavitation in the hydraulic turbines [4; 6; 7] decreases efficiency and increases vibrations and erosion, thereby reducing the service life. The procedures optimizing the performance of turbine hydraulics are most often based on the use of so-called inverse design methods [8] and computational fluid dynamics (CFD) [9]. Inverse design methods have been in use for decades, with the first 3D methods emerging around 30 years ago. These methods are based on the a priori specification of the pressure or blade loading distribution. Such distribution along the runner blade in the radial and meridional directions facilitates the calculation of the runner blade's angle. This reduces the computational CFD work required when insufficient information on the runner geometry is known in advance. [PERSON] [10] proposed a three-dimensional design method for radial and mixed turbines for the compressible case. Today his method is still often used for designing radial turbine machinery. [PERSON] et al. performed inverse design optimization of the reversible pump-turbine [11], while also considering cavitation characteristics. [PERSON] and [PERSON] [12] very recently provided an open-source implementation of an inverse Francis turbine design, together with a validation study confirming the approach's appropriateness. Cavitation is not often studied using inverse design methods; among the available studies, [PERSON] and [PERSON] [13] linked the blade loading and blade stacking to the efficiency and cavitation characteristics of a Francis runner, providing a valuable physical understanding and useful design guidelines. The 3D design of the runners and the guide apparatus may be determined by performing consecutive CFD calculations, while constantly varying 3D geometry and design parameters [9; 14]. Unfortunately, CFD alone is unable to establish an optimized 3D design. A 3D design study using CFD was performed by [PERSON] et al. [15], considering the efficiency, stability of design, and cavitation of a pump turbine during pumping mode. A comprehensive hydraulic and parametric analysis of a Francis turbine runner was performed by [PERSON] et al. [16].