IAHR AIIH INTERNATIONAL SYMPOSIUM ON HYDRAULIC STRUCTURES

CIUDAD GUAYANA, VENEZUELA, OCTOBER 2006

SIMULATION OF FAST PUMPED-STORAGE SCHEMES WITH THE PHYSICAL EXPERIMENT

ROMAN KLASINC*,MARKUS LARCHER*, ANDREJ PREDIN**, MITJA KASTREVC** *Institute of Hydraulic Engineering and Water Resources Management, Graz University of Technology ,Stremayrgasse

10, A-8010 Graz, AUSTRIA, E-mail: roman.klasinc@tugraz.at ** Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, SLOVENIA,

E-mail: Andrej.Predin@uni-mb.si

ABSTRACT

Changing conditions in the European energy market have brought about a rising demand for peak energy. In the light of the general energy shortage and the problems faced in meeting peak loads there is a constant need for the construction of new pumped-storage schemes. Pumped storage has come to be the environmentally most compatible method of balancing sudden drops in demand or unexpected production increase from wind power stations. Present-day electricity generating plant is characterized by optimal utilization of hydrostatic head and turbine efficiency. As the available numerical simulations of the complex hydraulic processes involved tend to be limited to one-dimensional analyses whose results are not sufficiently reliable, unsteady processes are studied in physical models.

The particular case discussed in this article is a pumped-storage station equipped with three pressure surge tanks, for which the dynamic processes in the tailwater portion were studied. A pressure above atmospheric of 2 or 3 bar lowers the water level in order to ensure sufficient clearance for the Pelton turbine. Another problem is the surge waves caused by the increasing rapidity of the mode changes between the pumping and generation modes. The sophisticated design of the hydraulic scale model (equipped with process control) presented in this article has provided valuable general information on the complex behavior of surge waves.

KEY WORDS: pump storage, hydraulic scale model, process control INTRODUCTION

Following the liberalization of the European electricity market, power has become a commodity traded on the stock exchange, and this has fundamentally changed the setting for the generation of electrical energy. Many different power station types cooperate to provide the clients with electricity of the desired quality and availability. Thermal power stations – the dominant power station type in Europe – supply their energy “blindly” to the system. Their purpose is primarily to generate energy in abundance, so as to make optimal use of the fuel, producing a maximum amount of energy with a minimum of pollutant emission. Any change in output from large-scale thermal power plant is slow. As forecasts of power demand can never be a hundred percent precise, there may often be too many or too few power stations working, without the “blind” power stations being aware. Moreover, the rapidly increasing development of wind energy has added to the flexibility problem, because unforeseen variations may now occur on the production side as well. Thus,

energy suppliers need rapid and flexible means to balance variations in power demand at short notice. Pumped-storage stations help to make efficient use – in terms of both energy and ecology – of extra capacities in the system by pumping water to a high-level reservoir and using it when the demand arises. The total capacity of such plant is available at very short notice, that is, nowadays within not more than a minute. The same applies to shut-down or change-over to the pumping mode.

Figure 1.- Powerhouse cavern with the pressure surge tank That means, however, that the hydraulic equipment – water conveyance structures and

mechanical equipment – of present-day power stations must satisfy extremely high demands. This new situation is being met by improvements in surge-tank strategy and especially in the tailwater portion of power plants.

Where ground conditions make access difficult or exhibit insufficient imperviousness to resist the planned pressures, pressure surge tanks may offer substantial advantages over the conventional designs. They are also much in use in drinking-water supply systems for damping water hammer effects.

The design of pressure surge tanks provides for a low-level underground chamber to ensure sufficient inlet pressure for the main pump. This, however, places the rotor of the Pelton turbine below the drawdown level of the tailwater basin, which implies the need to apply air pressure to keep the wheel clear of the water surface. As Pelton turbines can work under pressure above atmospheric, the additional head so created can be used for power generation.

Pressure surge tanks usually consist of horizontal horseshoe-section tunnels with impervious linings designed as necessitated by the surrounding geology. MODEL SETUP AND MEASURING EQUIPMENT

The model covered the whole tailwater portion over a length of about 350m and was mainly

built in plexiglass. The water levels in the lower reservoir were adjusted by a flap to suit the water level data (figure 2). In order to maintain a constant water level, an additional device was provided

Pump Inlet

Turbine Inlet Pressure Surge Tank

which fed about 100 litres per second to the container. This helped to avoid the falsifying effect of a varying water level.

P1Fb

TreppePumpenraum

Unit for PumpSimulation

b

a

b

6.99

°

A

1C

2

1A

1D

1D

Plan of Site

1

2

3

4

1E Air Pressure Surge TankF Turbine 1-3B

BB

1E

1C

Level Measurement Flow Measurement: Pressure Measurement:

1G Tailrace Tunnel

1H Pump 1-3

1G1F

1H

Pressure Surge Tank

Chamber Surge Tank

Lower Basin

Tailrace Tunnel System

Video Recording:

Water Inlet Turbine 1 -3

Figure 2.- Model layout showing measuring equipment

Water was supplied separately to each of the three turbine controls in the model through a

pipe line system, equipped with a separate inductive flow meter of 100mm diameter for each control. Another inductive flow meter, 250mm in diameter, was provided in the tailrace tunnel of the system to measure the total flow.

Each surge tank chamber was provided with the following measuring equipment: • 1 potentiometric probe for measuring the water level at the end of the chamber, • 1 ultrasonic probe for measuring the water level at the beginning of the chamber, • 1 pressure transducer for measuring the pressure above atmospheric in the chamber. For determining the friction losses and local head losses, the internal pressure was measured

by a total of 15 closed circular pipelines in the tailwater portion. The velocity curves were measured at seven cross sections arranged along the surge

chamber. The degassing was studied by taking digital photographs along the two chamber walls.

MODEL LAWS – SCALE EFFECTS A hydraulic scale model is run according to Froude’s criterion of similitude. Froude’s

similitude means that the same relationship between inertia forces and gravity applies both in the model and in the prototype.

As the studied surge-tank model answered Froude’s law, the Reynolds number had to be allowed for in the sections with flow under pressure, as this has a substantial influence on the transferability of friction losses between model and prototype. As the Reynolds numbers tend to be lower on scale models, and due to the materials used, the model conditions had on principle to be considered as being “too rough” as compared with the prototype. So the tunnel cross sections in this model were increased in order to account for this influence on friction and local head losses in the

system. The resulting influence on surge-tank oscillation within the system, in turn, was balanced by adjusting the lengths of certain tunnel sections.

PRESSURE SURGE TANK – DYNAMIC PROCESS

The relationships among the quantities involved in a dynamic process are best described by

the continuity equation, the motion equation, and the equation of the changes of state in the surge tank. In fact, the surge tank acts like a spring. The spring becomes stiffer as the available air space in the pressure-resistant chamber decreases. This may be allowed for by assuming isothermal behaviour to be replaced by adiabatic behaviour. The considerations which followed were based on the gas law as written below:

constVp =⋅ κ [1]

p stands for the pressure in the pressure surge tank, V is the air volume present, and κ the polytropic exponent.

The numerical value of the constant on the right side of the equation [2] is dependent on the temperature, the mass, and the type of gas. For a given mass of a given gas, the constant increases as the temperature increases. In the pressure-volume diagram, the equation takes the shape of a hyperbola.

Pressure / Volume - Relationship

05

101520253035404550556065707580859095

100105110115

0 1000 2000 3000 4000 5000 6000 7000 8000

Air Volume V [m³]

Inte

rnal

Pre

ssur

e hi

ght p

[m]

Polytropic exponent = 1,0 Polytropic exponent =1,2 Polytropic exponent =1,4

∆P

P2

K

P1

V2

V1 ∆V

Figure 3.- Pressure plotted against volume for the prototype

The best-known methods of analysis are based on a constant polytrophic exponent κ for the

change of state in the air component of the pressure surge tank. Assuming the same exponent of whatever quantity for both model and prototype would, however, be contradictory to the theory of thermodynamics. For simplification, the equations used for a general isothermal change of state (κ = 1) in the pressure surge tank were

1

1

112

=

∆±⋅=

κ

VVVPP [2]

The pressure within a pressure surge tank falls into two parts. One component is a hydrostatic portion composed of a basic atmospheric pressure and a pressure above atmospheric resulting from the difference in geodetic levels, while the other component consists of superimposed hydrodynamic pressure variations from unsteady motions. As the basic atmospheric pressure during unsteady processes can be considered as constant, it is the hydrodynamic pressure variations that are responsible for changes in internal air pressure.

( )DPGPPP PPPP ,,0, ∆±+= [3]

where: PP ...... initial air pressure in the prototype PP,0 ...... atmospheric air pressure in the prototype PP,G ...... differential head in the prototype PP,D ...... dynamic change in internal air pressure in the prototype On a model of a certain scale, the internal pressure within the pressure surge tank also falls

into a constant basic pressure and a variable hydrodynamic pressure. However, the percentage of basic atmospheric pressure cannot be reduced at the model scale, as it is actually larger in relation to the variable pressure component than on the prototype. In dynamic terms, this means that the process of air compression and decompression in the model is too much damped or not sufficiently relieved as compared with the prototype. The internal air pressure in the model is composed as follows:

∆±+=

MP

MP

PP DPGPMM

,,0,

[4] where: PM ...... initial pressure in the model PM,0 ...... atmospheric pressure in the model M ...... scaling factor in the model Figure 4 is a graph showing the different stiffness K=dp/dV of the prototype and the model.

The stiffness behavior of the model should be adjusted to prototype conditions to allow the model results to be transferred to the prototype.

Stiffness Gradient - Model -and Prototyp

-1,1

-0,6

-0,1

0,4

0,9

1,4

1,9

0,94 0,95 0,96 0,97 0,98 0,99 1 1,01 1,02 1,03 1,04

V/V0 [-]

dp P

roto

typ

[m]

-0,49

-0,29

-0,09

0,11

0,31

0,51

0,71

dp M

odel

[dm

]

Gradient K Prototyp Gradient K Model

Figure 4.- Comparing stiffness dp/dV in the model and in the prototype In the model the excessive stiffness of the system can be reduced by enlarging the air

volume in the pressure surge tank, using the fundamental physical equation [1], that is, by deliberately building a model with an air volume enlarged by a factor C. For determining the required additional volume, it is necessary first to use equation [5] to make allowance for Froude’s law of similitude, and solve it towards VM.

PPMM VPMVP ⋅=⋅⋅ 4 [5]

where: VM ...... initial air volume in the model VP ...... initial air volume in the prototype

3314 MVC

MV

MPP

PMVPV PP

M

P

M

PPM ⋅=⋅

⋅=

⋅⋅

= [6]

C ...... enlargement factor The amount of required volume enlargement is composed of a constant C-fold volume

enlargement characteristic of the initial condition, and a varying component for the dynamic water level variations.

( )

4342143421iably

M

DP

const

M

GPPDG PM

PPMPP

CCC

var

1,

1,0,

⋅

∆±

⋅

+=±= [7]

where : CG ..... enlargement factor for the initial condition CD .... dynamic enlargement factor

The C-fold volume enlargement of a steady or static water level was carried out prior to starting the test run, by providing an additional container. This is written as:

( )

331,0,

3 MV

MV

PMPP

MVCV PP

M

GPPPGM −⋅

⋅

+=⋅=∆ [8]

For transferring the measured quantities, formula [6] above is transformed, and the change in water level is in turn calculated from VP.

C

MVV MP

3⋅= [9]

PELTON TURBINES – VALVE SOLUTION

A turbine built to model scale 1:22.5 would have a diameter of 0.19m. The project under study provides for a six-jet Pelton turbines. As building a turbine true to scale would be very high in cost, this was replaced by a simple valve (figure 5).

Figure 5.- Design of the water feeding device Figure 6.- CFD computation – flow against impact ring

The flow pattern in the valve was simulated by a standard CFD flow program. An example – with the valve wide open – is shown in figure 6.Use of the appropriate shape of impact ring allows the remaining kinetic energy to be increased or decreased.

impact ring

SIMULATION OF PUMP – TRANSIENTS

For the simulation of pump operational – steps (fig. 7); start up and suddenly net break an appropriate experimental unit was built. With this unit (fig. 8) a high flexibility for the parameter in the time diagram was achieved.

Figure 7.- Time diagram of pump discharge

Figure 8.- Experimental unit for the simulation of pump operational – steps

CONCLUSIONS

The power demand is subject to substantial variations over the day. The relatively speedy

start-up and shut-down of turbines and pumps (about 20s in the case under study) requires innovative solutions for the design of pumped-storage schemes. In the case under study, one-dimensional simulations, although relatively low in cost, were not considered to be sufficiently reliable, especially for two-phase systems. Above all, the problems involved in the unsteady processes and the air entrainment followed by the degassing process in the pressure surge tank need

Tailrace tunnel Q

V - 1

V - 2

V - 3

P

L

Control unit

Flow meter

Out

ValvesPump

Pressure vessel

Level

Pressure

Inputs Outputs

ts …. Pump start time tb … Net break time

QP

supplementary study on a physical model. Analyses conducted on a hydraulic scale model also offer the advantage of a 3D demonstration of flow processes.

For Froude’s similitude to be applicable to the model, it is necessary to adapt the volume of the pressure surge tank. Only after enlarging the air volume and making allowance for the qualitative behavior of the air/water mix does the hydraulic scale model supply realistic results that can be transferred to the prototype.

REFERENCES

Brennen C.E. (1994). Hydrodynamics of pumps, Concepts ETI, Inc. And Oxford University Press. Frank J.(1957). Nichtstationäre Vorgänge in den Zuleitungs- und Ableitungskanälen von Wasserkraftwerken, Springer-Verlag Berlin 1957. Stucky A. (1962). Druckwasserschlösser von Wasserkraftanlagen, Springer-Verlag Berlin 1962. Graze, H.R. (1968). A Rational Thermodynamic Equation for Air Chamber Design. Third Australasian Conference on Hydraulics and Fluids Mechanics, Sydney, Nov. 1968, (Paper No. 2607). Graze, H.R. (1972). The Importance of Temperature in air chamber Operations, International Conference on Pressure Surges, Canterbury, 6th - 8th September 1972. Graze, Schubert, Forrest.(1976). Analysis of Field Measurements of Air Chamber Installations, Second International Conference on Pressure Surges, Canterbury, 22nd - 24th September 1976 Klasinc, R., Logar, R., Predin, A. (2001). Hydraulic resistance at sudden pipe expansion - the influence of cavitation. V: POWER, H. (ur.), BREBBIA, C.A. (ur.). First International Conference on Computational Methods in Multiphase Flow, 14-16 March 2001, Orlando, Florida. Computational methods in multiphase flow, (International series on advances in fluid mechanics). Southampton; Boston: Wit Press, 2001, page. 197-206. Klasinc, R., Geisler, T., Predin, A. (2001). Measurement of flow velocities and interfacial wave profiles by use of the ultrasonic velocity profile monitoring. V: Instrumentation for hydraulic measurements., page. 99-105. Klasinc, R., Predin, A., BILUŠ, I. (2004). Flow patterns in symmetrical three-leg manifolds: experimental and numerical analysis. V: ICON-HERP - 2004. Rookie: Department of Civil Engineering: Indian Institute of Technology, page. 358-368. Predin, A., Bilus, I., Kastrevc, M., Klasinc, R. (2005). A driving valve for simulating the hydraulic conditions during the operation of a Pelton turbine. Ventil (Ljubl.), 11, No. 2. White M. F. (1999). Fluid Mechanics, Fourth Edition, McGraw-Hill International Editions, Mechanical Engineering Series.