Pål-Tore Storli

Transient Friction in Pressurized Pipes. II: Two-Coefficient Instantaneous Acceleration–Based Model

The goal in the field of modeling of hydraulic transients is a comprehensive model for pipe networks that is computationally fast and accurate. The fastest models are the one-dimensional (1D) models that use instantaneous acceleration–based (IAB) properties, but unfortunately these models are not as accurate as the more demanding 1D convolution-based (CB) models or quasi two-dimensional models. Focusing on a single pipe, this paper investigates the fundamental behavior of the much more accurate 1D CB model to find two coefficients for use with the two-coefficient formulation of the much-used modified IAB (MIAB) model for complete closing of a downstream valve. Two coefficients are found based on the weighting function used in the CB model, and these coefficients vary along the pipe length. Simulations are compared with two experimental results from tests performed at University of Adelaide in Australia in 1995. The experimental results are for different initial Reynolds numbers of approximately 2,000 and ...

Transient Friction in Pressurized Pipes. III: Investigation of the EIT Model Based on Position-Dependent Coefficient Approach in MIAB Model

Recently, the modified instantaneous acceleration-based (MIAB) model has been improved by the authors by using position-dependent coefficients found from investigation of the convolution-based (CB) model. Although this improvement is not proven general by any means, the fit with experimental results is very good. The three existing classes of one-dimensional models for the water-hammer transient that are applicable from an engineering point of view are the two models mentioned previously and the extended irreversible thermodynamics (EIT) model, which uses a coefficient found from thermodynamical considerations. This paper seeks the equivalent coefficients for the EIT model corresponding to the position-dependent coefficient the MIAB model to investigate the implications to the EIT model by using these coefficients. This is interesting because the EIT model is based on physical considerations using irreversible thermodynamics, and conclusions can possibly be drawn from this approach. The EIT coefficients f...

Transient Friction in Pressurized Pipes. I: Investigation of Zielke's Model

This paper investigates the well-known model for unsteady friction developed by Zielke in 1968. The model is based on weights of past local bulk accelerations and is analytically correct for laminar flow, but computationally demanding. Different models have been proposed using dynamic properties, typically based on instantaneous accelerations (IAB) that are more rapid in computational schemes. Unfortunately, they are not as accurate as Zielkes model and fail to model certain types of transients. This paper points out that the water hammer transient is dominated by a periodicity varying along the pipe. Because of this, the unsteady friction calculated by the Zielke model is distributed nonuniformly along the pipe, and changes in the pipe length change the local unsteady friction. This phenomenon may explain why IAB models using calibrated coefficients to match experimental results have a large span in value for the reported coefficients. This paper will hopefully contribute to further work to find highly accurate and rapid models. The subject deserves to be brought up for discussion as a part of a total understanding of the problem.

Simulations of the dynamic load in a francis runner based on measurements of grid frequency variations

In the Nordic grid, a trend observed the recent years is the increase in grid frequency variations, which means the frequency is outside the normal range (49.9-50.1 Hz) more often. Variations in the grid frequency leads to changes in the speed of rotation of all the turbines connected to the grid, since the speed of rotation is closely related to the grid frequency for synchronous generators. When the speed of rotation changes, this implies that the net torque acting on the rotating masses are changed, and the material of the turbine runners must withstand these changes in torque. Frequency variations thus leads to torque oscillations in the turbine, which become dynamical loads that the runner must be able to withstand. Several new Francis runners have recently experienced cracks in the runner blades due to fatigue, obviously due to the runner design not taking into account the actual loads on the runner. In this paper, the torque oscillations and dynamic loads due to the variations in grid frequency are simulated in a 1D MATLAB program, and measured grid frequency is used as input to the simulation program. The maximum increase and decrease in the grid frequency over a 440 seconds interval have been investigated, in addition to an extreme event where the frequency decreased far below the normal range within a few seconds. The dynamic loading originating from grid frequency variations is qualitatively found by a constructed variable , and for the simulations presented here the variations in are found to be around 3 % of the mean value, which is a relatively small dynamic load. The important thing to remember is that these dynamic loads come in addition to all other dynamic loads, like rotor-stator interaction and draft tube surges, and should be included in the design process, if not found to be negligible.

Measurements and simulations of turbines on common grid

Speed droop control is of basic importance for the primary governing in the Nordic grid. The speed droop control. a mandatory and build-in regulatory loop on all larger units. is automatically changing the produced power on synchronous units as the grid frequency changes. This part of the governor allows a certain deviance from the nominal 50 Hz grid frequency. If the grid frequency is decreasing this means that the load on the grid is greater than the power delivered into the grid. and the local speed droop regulatory loop on each unit then autonomously increases the production to obtain a new balance between load and production. which will be at a lower frequency than 50 Hz. If the power delivered into the grid is greater than the load. the rotating masses will be accelerated (thus increasing the grid frequency) and the speed droop operation will act to reduce the power produced to obtain a new balance. this time at a higher frequency than 50 Hz. The frequency in the Nordic power grid has in recent years for increasing duration been outside the allowed steady state frequency band of 50 ± 0.1 Hz. In order to study the behaviour of a turbine operating on a common grid, measurements have been done at site. The measurements performed are the generator power, main servo motor position, the rotational speed of the unit and the grid frequency. The purpose of the measurements was to see if it is possible to observe the behaviour of the machine as it is linked together with all the other machines on a synchronous grid. It is interesting to observe the response to deviations in the frequency due to the speed droop operation. In order to better understand the behaviour, a simulation model of two power plants, complete with individual conduit system, turbine and generator, connected to the same grid was used.

Optimization procedure for variable speed turbine design

ABSTRACT This article outlines a design procedure for variable speed Francis turbines using optimization software. A fully parameterized turbine design procedure is implemented in MATLAB. ANSYS CFX is used to create hill diagrams for each turbine design. An operation mode of no incidence losses is chosen, and the mean efficiency in the range of the best efficiency point is used as optimization criterion. This characteristic is extracted for each design, and optiSLang is used for system coupling and optimization. In the global optimization loop, the downhill simplex method is used to maximize the turbine performance. For this article, the bounding geometry of the runner is kept as in the original configuration. This way, the performance of the different variable speed turbines can be compared directly. Two optimization parameters describing the blade leading-edge geometry have been used in the optimization procedure. The resulting design was an almost circular leading edge, and shows an increase in mean efficiency of 0.25% compared to the reference case. There was a significant change in the turbine performance, with close to no change at the best efficiency point, and an increase in efficiency of almost 1% at low rotational speed. The outlined procedure is parallelizable and can be performed within an industrial timeframe.