Hydro acoustic resonance

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Method and sources

Air injection

A literacy study and discussions with adepts at Alstom and Andritz Hydro will act as the fundament for the theoretical understanding of the air injection system.
H. Lindsjö at Andritz Hydro is consulted to make an economic estimate of the installation costs of an atmospheric air injection system at the case study.

Water injection

The theoretical understanding will be built from literacy research, meetings with adepts at NTNU and FDB. Also a visit is made to Skibotn, a 72MW facility owned and operated by Statkraft, utilizing the water injection system. At FDB H. Francke provides with results from the systems and M. Kjeldsen is consulted for an estimate of the installation costs at the case study.

Structure

The report starts with a theoretical introduction of turbine equipment, its related problems and a description of countermeasures to these problems as well as a description of a certain case study. Following the theory is a results chapter which consists of technical and economic summaries of the air and water injection systems separately, referring to results from several documented scenarios. The results chapter ends with the case study findings. The report is finished with an analytical discussion about attained results and further research.

Theory

This section concerns some basic theory surrounding the investigated phenomena’s and techniques. It is presented to give a general understanding of the key factors.

Francis turbine

The Francis turbine is the most commonly used turbine in hydropower plants globally and can be designed to utilize a large range of water heads with high efficiency. Most Francis turbines suffer a common problem related to pressure surges in the draft tube occurring around half load and operating at these loads is therefore avoided. To explain the Francis turbine makeup, a short review of its parts is presented below. They are presented in the same order as water is passing through the turbine. A cut through picture is seen in Figure 5-1 Penstock – Provides pressure potential and flow of water to the spiral casing. Pressure is exerted by the weight of the above water head.
• Spiral Casing – Surrounding the runner with spiral geometry of area decreasing with its length, this is to maintain uniform velocity to the stay vanes. This structure is housing the stay and guide vanes that are spatially distributed around the runner in the center.
• Stay vanes – Fixed fins that convert pressure potential to kinetic energy and are reducing swirl of the inlet flow by aligning the direction of the flow towards the runner section.
• Guide vanes – Movable fins that are used to regulate flow rate and the angle of attack to the runner. These are connected in a circular structure called a wicket gate, which can be moved hydraulically to change their position simultaneously.
• Runner – Converts kinetic energy and pressure potential energy in the water to torque transferred by the shaft. Water enters radially and leaves axially exerting both impulse and lift force to the runner blades.
• Draft tube – Connects to the runner outlet and converts kinetic energy to pressure potential due to a diffusing geometry meaning an area increasing along its length.
• Shaft – Connecting the turbine runner and generator rotor and is transferring the torque extracted by the runner from the water. This part is not characteristic for the Francis turbine but can due to its sometimes hollow structure be used as an air path when injecting air and is due to the nature of this report mentioned here.
When water is leaving the turbine operating at BEP and enters the draft tube, its velocity profile should ideally consist only of an axial and no angular component. When the turbine is operated in part or over load modes the swirl generated by the wicket gate in the spiral casing is not matching the angular momentum extracted by the runner, hence leaving a residual rotational velocity component at the runner outlet. Direction of water flow leaving the runner is depicted by the red vector in Figure 5-2.
Figure 5-2 – Velocity distribution for water leaving Francis runner at BEP, Part load and Overload The residual swirling velocity is thought to be the cause of severe pressure surges in the draft tube and it is noted that at part loads the swirling flow is rotating in the same direction as the runner and at over load the swirl is rotating in the opposite direction of the runner.
Difference in pressure at runner and guide vanes varies with the difference in water head over the turbine. Power plants with large head variation may suffer operational problems due to the difficulties in designing a turbine runner that can handle the different operating regimes sufficiently.

General flow characteristics

A general understanding of the relation between pressure, elevation and velocity in a fluid flow can be achieved by studying a simple one dimensional version of Bernoulli’s principle as presented below
is relative velocity in a control region [ ]
is gravitational acceleration [ ]
is elevation [ ]
is pressure in the control region[ ]
is density [ ]
The equation is expressing continuity of enthalpy in the flow where the effect from changing each variable easily can be mirrored into the others. The inverse relation between pressure and velocity is of most importance when studying flow behavior since it can give a simple understanding of effects such as cavitation and pressure pulsations.
It should be noted that the Bernoulli expression above is valid for laminar flows and the flows discussed in this report is turbulent patterns and breakdown of these into less structured turbulent flows.
Using Darcy-Weisbach equation for turbulent flow the only addition is a decrease in the relation between pressure loss and velocity relative to the decreased in wall friction as velocity and Reynolds number increases.
A dimensionless number used to describe the amount of swirl present in the flow is the so called swirl number S, which is defined as the ratio between angular and axial momentum in the studied boundary as depicted below. The axial velocity profile of the draft tube flow at runner exit for different swirl numbers is depicted in Figure 5-3 below.
An increase in the swirling velocity component will result in increased axial velocity around the draft tube edges and a reduction in axial velocity at the center of the tube.
In swirling flows the velocity relative to the surrounding fluid can become very high and if recirculation starts to occur in the central region of the flow, the water at the boundaries of this region experiences very large differences in relative velocity which results in a drastic decrease in pressure.

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Deleterious flow effects

Pressure surges are normally divided into synchronous and asynchronous types, both of these types can cause effects in the flow which might show harmful to the plant infrastructure. The effect believed to be most harmful and mainly responsible for the draft tube pressure surges are named vortex breakdown and vortex rope, these are discussed in this section and are depicted in Figure 5-4 below.
Pressure surges can propagate through the whole hydraulic system and even cause pressure and head variations in the penstock. Some problems associated with draft tube surges include severe vibrations, noise, power swings, bearing and shaft run-out, and increased stress on the runner. Although it should be noted that statistical investigation covering 34 low head Francis runners manufactured the years 1928-1967 with heads between 20m to 80m shows that the number of yearly starts and stops together with the height of water head has the strongest negative correlation to the turbine lifetime. [3]
This suggests that the start stop problem is more prominent and that it is not only desirable to decrease pressure pulsations at part loads in order to increase the permissible operating range. But it can also be interesting in cases where it is possible to decrease the number of yearly start and stop cycles as a result of the extended operating range.

Vortex breakdown

As the swirl increases to a critical level, a sudden change of the flow characteristics can be observed. Namely a reverse flow starts in the stalled center region, see Figure 5-3. A helical vortex will form at edges of this reverse flow region. In this boundary the pressure can decrease to vapor pressure, causing evaporation. The water gas bubbles will make the vortex visible and when such a flow structure occur the phenomena is called vortex breakdown. See Figure 5-4
It should also be mentioned that the axial velocity of the water flow usually is depicted as a steady profile with non-changing vector sizes. When recirculating flow occurs there is a discontinuous break in the velocity profile, called boundary layer separation.
As the flow continues along the positive pressure gradient in the draft tube, the vortex is gradually loosing kinetic energy until the cavitated core condenses and the vortex dissolves into turbulent flow in almost all cases. When the cavitated bubbles collapse to liquid there is a resulting pressure pulse.
Some flow patterns can be termed regular and some irregular. Laminar flow and synchronous flow patterns can then be seen as regular. As turbulent and unstable flow patterns can be seen as irregular. A depicted test setup using dye injection to picture a helical vortex flow pattern is seen in Figure 5-5.

Vortex rope

This flow pattern is the most severe cause of efficiency reduction and pressure fluctuations experienced by most Francis turbines at part load. These fluctuations can in extreme cases even propagate to the electrical grid due to the oscillating pressure experienced by the runner. This is more prominent in facilities that have a considerably small amount of rotational mass.
The residual swirling component left in the flow due to off design operation of Francis turbines is entering the expanding and often non-conical geometry of the draft tube. This is causing uneven pressure increase as well as velocity decrease in the flow, resulting in a change in the rotational axis of the swirl. This gives as a result a helically precessing vortex rope, such as depicted in Figure 5-6.
This vortex rope is rotating at the so called Rheingans frequency, which is found to be in the region of about ¼- ½ of the runner frequency but is empirically found to be of the runner frequency. [4] Any stationary point in this region of the draft tube will experience uneven mass transfer and pressure pulsations as the vortex rope rotates, see Figure 5-7.
This flow pattern is quite robust and is rotating uniformly and regularly. At the limits of the range of its occurrence it can however become intermittent as neighboring flow patterns become prevalent. [5]
The length of the cavitated core is related to flow speed and when the cavitated vortex core or parts of it implodes, sharp pressure shocks are produced. This happens in flow regions between two different flow patterns which can occur at different loads in the draft tube as the velocity and pressure changes along its length.
This vortex has received many names such as helical vortex, Figure 5-6 – Draft tube vortex rope at part load spiral vortex, corkscrew vortex and the term vortex rope which is used in this report. The rotating motion around its axis has been termed the precession of the vortex. [6]

All structures in nature resonate at a certain frequency and can be associated with springs whose resonant frequency is depending on its mass and stiffness/rigidity. Just as potential energy and kinetic energy is exchanged between each other in the oscillating motion of a spring is the potential and kinetic energy within a material structure is exchanged between each other in a periodic manner as it oscillates. This exchange will result in positive interference if oscillating forces are in phase with each other in the systems characteristic frequency. This causes amplification of the oscillation amplitudes and something that becomes highly undesirable in the maintenance and reliability point of view.
The resonance frequencies of the water way system is usually quite low, somewhere between a few Hertz to a few tens of Hertz and in most cases lower then 200Hz. The frequency of the so called water hammer phenomena is related to the length between two free water surfaces and the propagation speed of acoustic waves in the water

Table of contents :

Abstract
1 Introduction
2 Aim
3 Method and sources
3.1 Air injection
3.2 Water injection
4 Structure
5 Theory
5.1 Francis turbine
5.2 General flow characteristics
5.3 Deleterious flow effects
5.3.1 Vortex breakdown
5.3.2 Vortex rope
5.3.3 Hydro acoustic resonance
5.4 Countermeasures
5.4.1 Air injection
5.4.2 Water injection
5.4.3 Other countermeasures
5.5 Case study Lövhöjden power plant
6 Results
6.1 Technical summary
6.1.1 Air injection
6.1.2 Water injection
6.2 Economic summary
6.2.1 Air injection
6.2.2 Water injection
6.3 Case study
7 Analysis, discussion and conclusions
8 Proceeding work/Research/Recommendations
9 Appendix