Andritz (Canada)

In hydraulic turbines, cavitation has unwanted consequences such as vibrations, noise, or material degradation. Thus, developping a method which can anticipate this phenomenon with good accuracy is vital from the designer’s perspective.This work aims at predicting two aspects of cavitation erosion: determining areas most endangered, and quantifying cavitation erosion in a relative way.

A robust multi-fidelity optimization methodology has been developed, focusing on efficiently handling industrial runner design of hydraulic Francis turbines. The computational task is split between low- and high-fidelity phases in order to properly balance the CFD cost and required accuracy in different design stages. In the low-fidelity phase, a physics-based surrogate optimization loop manages a large number of iterative optimization evaluations. Two derivative-free optimization methods use an inviscid flow solver as a physics-based surrogate to obtain the main characteristics of a good design in a relatively fast iterative process. The case study of a runner design for a low-head Francis turbine indicates advantages of integrating two derivative-free optimization algorithms with different local- and global search capabilities.

No-load speed is an important performance factor for the safe operation of hydropower systems. In turbine design, the manufacturers must conduct several model tests to calculate the accurate value of no-load speed for the complete range of operating conditions, which are expensive and time-consuming. The present study presents steady and unsteady methods for calculating no-load speed of a Francis turbine. The steady simulations are implemented using a commercial flow solver and an iterative algorithm that relies on a smooth relation between turbine torque and speed factor. The unsteady method uses unsteady RANS simulations that have been integrated with a user subroutine to compute and return the value of runner speed, time step and friction torque. The main goal of this research is to evaluate and compare the two methods by calculating turbine dynamic parameters for three test cases consisting of high and medium head Francis turbines. Overall, the numerical results agreed well with experimental data. The unsteady method provided more accurate results in the opening angle range from 20 to 26 degrees. Nevertheless, the steady results showed more consistency than unsteady results for the three different test cases at different operating conditions.

Compared to actual strains, the values obtained with strain gauges during experimental measurements contain biases and uncertainties. In this article, we propose a methodology using Monte Carlo simulations to estimate the effects of biases and uncertainties from the following: location uncertainty, integration effect and transverse sensitivity errors in unidirectional strain gauges. Moreover, the specific behaviour of welded gauges is also considered. The approach simulates strain gauges on the displacement fields obtained from the structure’s finite element analyses to predict the expected biases and uncertainties. With the use of experimental measurements designed to highlight the biases between gauge measurements and finite element analyses strain results, we verify the methodology. In our experimental verification, we observe that biases are adequately predicted by the proposed method. It is worth mentioning that such an approach can be used not only for validations between finite element analyses and experimental measurements but also for optimizations of strain gauge positioning during measurement campaigns.

A robust multi-fidelity design optimization methodology has been developed to integrate advantages of high- and low-fidelity analyses and alleviate their weaknesses. The aim of this methodology is to reach more efficient turbine runners with respect to different constraints, in reasonable computational time and cost. In such a framework, an inexpensive low-fidelity (inviscid) solver handles most of the computational burden by providing data for the optimizer to evaluate objective functions and constraint values in the low-fidelity phase. An open-source derivative-free optimizer, NOMAD, explores the search space. Promising candidates are selected among all feasible solutions using a filtering process. The proposed filtering process accounts for Pareto optimal solutions and considers solutions which are different in the design variable space and are dominant in their local territories. A high-fidelity (viscous) solver is used outside the optimization loop to accurately evaluate filtered solutions. Accurate information achieved by high-fidelity analyses is also employed to recalibrate the low-fidelity optimization. The developed methodology demonstrated its ability to redesign a Francis turbine blade for a given best efficiency operating condition. The original and optimized cases were evaluated and compared for a complete range of operating conditions by calculating the efficiency curves and losses of different components. The optimal blade has provided an efficient runner for the given operating conditions considering the design constraints.

This chapter presents a number of common oscillation phenomena which are not due to a direct external force but due to a feedback mechanism which may depend on the response of a larger system. Accordingly, the frequency of this kind of fluctuation is dictated by a natural frequency rather than a forcing frequency. For example, if a small displacement in a turbine runner creates a labyrinth force that tends to increase the displacement, then this may suddenly start a whirling motion at a natural bending frequency of the shaft line.