According to the IEC 60041 standard, the pressure-time method (1D PTM) can be employed to determine the flow rate in hydraulic turbines. This method assumes a one-dimensional flow and applies to straight pipes with uniform cross-sections, with specific restrictions on the pipe length, fluid velocity, and distance between the measurement sections from any irregularities in the pipeline. However, challenges arise when applying this method in low-head hydropower plants due to the short lengths, irregularities like bends and developing flows in the intake. The present paper aims to improve the performance of the method in the presence of a bend. To this end, a test rig has been developed and measurements performed, including such geometry. The data are evaluated using the development of a newly proposed approach combining the 1D PTM based on an energy balance formulation and three-dimensional computational fluid dynamics (3D CFD) developed for axis-symmetrical accelerating flows. The updated methodology includes a correction of the experimental pressure measurements used in the 1D PTM to account for the effects of the Dean vortices present after the bend as well as the kinetic energy correction factors which deviate from known values in transient conditions. The results obtained under conditions involving the presence of bends either between or in close proximity to one show a significant improvement compared to the standard one-dimensional pressure-time method.

Water hammer is a transient phenomenon that occurs when a flowing fluid is rapidly decelerated, which can be harmful and damaging to a piping system. Three-dimensional computational fluid dynamics (CFD) with three-dimensional geometry is a common tool for studying water hammer, which is more accurate than numerical simulation with one-dimension approximation of the geometry. There are different methods with different accuracy and computational costs for valve closure modelling. This paper presents the result of water hammer 3D simulation with three main technics for modelling an axial valve closure: dynamic mesh, sliding mesh, and immersed solid methods. The variation of the differential pressure variation and the wall shear stress are compared with experimental results. Additionally, the 3D effects of the flow after the valve closure and the computational cost are addressed. The sliding mesh method presents the most physical results compared to the other two methods. The immersed solid method predicts a smaller pressure rise which may be the result of using a source term in the momentum equation instead of modelling the valve movement. The dynamic mesh method adds fluctuations to the primary phenomenon. Moreover, the sliding mesh is less expensive than the dynamic mesh method in terms of computational cost (approximately one-third), which was the primary method for axial valve closure modelling in the literature.

The flow rate is a challenging hydrodynamic parameter to measure in order to determine turbine efficiency. The pressure-time method is a cost-effective alternative to estimate the flow rate. Its principle is based on the transformation of momentum into pressure during the deceleration of the liquid mass. Numerical simulations give valuable information to develop the method. One of the challenges in the numerical study of the pressure-time method is modelling the valve movement. In previous numerical studies, the dynamic mesh has been used for valve closure modelling. The dynamic mesh may lead to divergence, and re-meshing makes this method more time-consuming. 

In this paper, the valve closure is modelled considering immersed solid method. The results' sensitivity is studied by different time-step, grid, and boundary conditions at the inlet. It is shown that the result is independent of the time-step size smaller than 0.1 ms. Furthermore, it is observed that only the opening boundary condition at the inlet can predict the oscillation of variables during water hammer phenomenon. Then, the numerical results are validated with experimental data. Finally, the pressure-time method is applied to the data, and the flow rate is estimated

The Gibson method is commonly used for discharge measurements at hydropower plants to estimate turbine efficiency. This paper presents a detailed numerical study of this method in order to estimate the physical quantities of importance in the method. Additionally, a modification of the Gibson method is proposed that adds temporal acceleration to the calculation procedure. The modification is numerically and experimentally validated for Reynolds numbers ranging from ≈0.6×106 to 1.7×106. Using both simulations and experimental data, it is shown that the modified method, the unsteady Gibson method, can reduce the flow estimation error by as much as 0.4% compared to the standard Gibson method. Depending on the conditions, the unsteady Gibson method corrects, or partly corrects, both under- and overestimations of the flow rate that are calculated when using the standard Gibson method.

Hydropower, originally designed as a base electrical power, is now used to balance grid fluctuations that are primarily produced by market deregulation and the introduction of other renewable energy resources. New turbine designs must account for such constraints while also achieving high efficiency. Computational fluid dynamics, now an integrated tool in the hydraulic industry, requires accurate and detailed experimental data for validation purposes.The present work presents the investigation of a modern Kaplan turbine model combined with laser Doppler anemometry and flush-mounted pressure sensors, with a focus on the draft tube at the best turbine efficiency. Mean and phase-resolved quantities are presented for the velocity and pressure at several locations. The results demonstrate the strong influence of the swirl leaving the runner for a well-functioning draft tube as well as the negative impact of the draft tube cone. The blade-hub clearance is also found to have an impact on the flow beneath the runner cone.

Off-design conditions of hydropower turbines are becoming more frequent with the deregulation of electricity markets and the introduction of renewable energy resources. Originally, turbines were not built to operate under such conditions. It is evident that there is a need to develop turbines that can operate under off-design conditions while attaining high efficiency. This may be achieved with computational fluid dynamics (CFD). However, the complexity of Kaplan turbine flows is challenging to treat using CFD. Therefore, detailed experimental investigations are necessary to validate and develop CFD. This paper presents an investigation of a modern design Kaplan turbine model. The measurements were performed in the draft tube with laser Doppler anemometry and flush-mounted pressure sensors, with a focus on the part load and high load operation of the turbine. Mean and phase-averaged quantities are presented for the velocity and pressure along several sections. A contra-rotating flow region was observed under high load operation. Under part load operation, a rotating vortex rope (RVR) develops due to vortex breakdown. The presence of the RVR significantly reduces the draft tube performance.

Hydropower is a clean and sustainable energy resource that has been developed and used since the late 19th century. In Sweden, power plants have been constructed over the entire 20th century, with a peak in the period of 1950-1970. Currently, many of the older plants are in need of refurbishment. A modern hydropower turbine can have efficiency up to 95%. By upgrading older turbines, substantial gain can be achieved.As part of this thesis, a detailed experimental investigation of the flow in a Kaplan turbine model has been performed with a main focus on the draft tube. Besides the goal of describing the flow, the result will serve as validation data for CFD simulations and for scale-up studies (corresponding prototype is available for similar measurements). The investigation is performed with time-resolved pressure measurements in which different periodic flow phenomena are captured. The turbine is investigated at three different loads: part load, best efficiency point and near full load.During the refurbishment of a turbine, site efficiency tests are common practice to verify the improvements. A key feature of many methods regarding efficiency tests is flow rate measurements. Several commonly used methods exist for this task, such as current meter, Gibson's and ultrasonic (acoustic) methods. These methods can provide trustworthy results, but the difficulty to obtain satisfactory accuracy for low-head machines, below 50 m, is common to most of them. Gibson's method is rather economical and is easily performed on site. However, it has some limitations that make it difficult to apply to low-head turbines, such as short and non-uniform water passages. This thesis also aims to extend Gibson's method for use on low-head machines, i.e., outside the criteria stated in the IEC 41 standard. The investigation is performed with both numerical and experimental methods. In the numerical investigation, the physical quantities in rapidly decelerated flows are studied in detail. Unsteady friction terms are implemented in Gibson's method to enhance the accuracy under non-preferred conditions. A test rig was developed at the Norwegian University of Science and Technology in Norway for investigation with Gibson's method outside the criteria stated in the standard, as well as the validation of the numerical model and the updated Gibson method.