HYDROTURBO 2004, ON HYDRO-POWER ENGINEERING
INTERNATIONAL CONFERENCE,
OCTOBER 18-22 2004, M YSLIVNA HOTEL - BRNO
Water Column Separation in Long
Tailrace Tunnel
Stanislav Pejovic1, Bryan Karney2, Qinfen Zhang3
Annotation
In hydropower plants with long tailrace tunnels, the minimum pressure downstream
the turbine runner caused by load rejection or any other transient may cause water
column separation and subsequent rejoinder; these phenomena have the potential to
cause serious if damage to the machine and to the tailwater conveyance system. In
this paper, based on a series of measurements during site transient tests at a large
hydropower plant, a numerical model of transient analysis for hydro unit system is
calibrated and then the calculated and measured results of those tests with obvious
water column separation phenomena are summarized. In particular, a useful void
index is calculated and discussed; it is argued that such an index could and should
be referenced in the operation and re-designed of such hydraulic systems. Overall
the paper argues that hydraulic waterways must be correctly designed and protec ted,
since water column separation could well result in serious damage to the system.
Key words
Hydroelectric; Transient; Waterhammer; Tailrace tunnel; Water column separation;
Reverse waterhammr Turbine; Pump-turbine; Draft tube; Runaway; Load rejection;
Air injection; Surges
Introduction
With the development of the underground engineering techniques, more and more
underground hydroelectric projects are being used and designed worldwide; some
hydroelectric plants have been in operation for decades without trouble while other have
chronically experienced trouble. In underground systems, long pressured tunnels are
becoming a more popular design. However, this creates a challenge as well, for waterhammer
is always a potential issue in such long tunnels; to decide whether various surge protection
devices are necessary in a project, it is compulsory to analyze transient flow including
conditions of water column separation (Murray, 1980).
The minimum pressure during transient operations of hydroelectric turbines may induce water
column separation; the subsequent rejoinder of the water column is capable of creating forces
that could damage both turbine runners and non-rotating parts. This condition occurs when a
local pressure drops below the vapor pressure or partial pressure of gases (air). The sometimes
rapid and dramatic pressure rises following the collapse of the voids can crack internal linings
1
Prof., Dept. of Civil Engineering, University of Toronto, Canada, [email protected]
Prof., Dept. of Civil Engineering, University of Toronto, Canada
3
PhD student, Dept. of Civil Engineering, University of Toronto, Canada,01-416-978-5972,[email protected]
2
of the conduit, can damage hydraulic connections and the turbo machines themselves, as well
as their associated devices. The damage may not be evident immediately but is often observed
after repetitive transients, creating a ticking bomb of future hydraulic and structural problems.
To control transient flows in water courses, the wicket gates of a turbine are the primary flow
regulators; and upstream (penstock valves) and/or downstream valves (tailrace tunnel gates)
are the auxiliary flow control devices. Such valves can be closed under emergency conditions
or if the wicket gates malfunction, thus preventing the plant from eventual damage and water
losses, should a failure ultimately occur.
The minimum pressure in any conduit (tunnel, penstock, pipeline) should not fall bellow 0.05
MPa (0.5 bar) even temporarily, in order to avoid the danger of water column separation and
consequent reverse waterhammer (ASME, Pejovic S. co-author; 1996; Murray H., 1980;
Pejovic at al. 1992; Pejovic at al. 1987). This minimum pressure must be the instantaneous
cross-sectional “average” value of minimum pressure during the transient event at the highest
position, which is typically at runner outlet or at the upper limit of draft tube lining. However,
the pressure distribution at a cross-section is uneven under both steady and or transient state
operation. However, since a pressure transducer only can be attached on the wall of draft tube
or pipe (site tests), the measured pressure at any section of the draft tube cone is invariable at
the maximum value for a given cross-section; the pressure in the vortex core, by contrast, is
likely at absolute vapor pressure or at air release pressure of the dissolved air in water, or
perhaps slightly above this if air injected (Ohashi, H., 1991; Krivchenko et al. 1975; Pejovic at
al. 1980). Therefore, the criterion of minimum pressure above 0.05 MP is inappropriate for
measured pressures; overall, the interpretation must take into account the pressure and
velocity distribution over the cross-section. Some manufacturers have empirical data for their
turbines (Murray H., 1980), and some have measured the distribution of pressure and velocity
for their model turbine draft tubes (Krivchenko, et al. 1975). All data must be carefully
evaluated because there is no similarity between any two-phase steady and transient flows
(Lee et al 1996; Pejovic S., 1989).
During calculations, similar considerations of pressures variations must be taken into account.
For example, the minimum pressure drop at a point of draft tube can be calculated, based on
one-dimensional waterhammer theory; this value represents the “average” value of minimum
pressure across the section, which is usually lower than the measured minimum pressure on
the cone but is still higher than the pressure in the vortex core.
Figure 1 depicts the pressure distribution across a draft tube cross-section and several
frequently used terminologies (values) such as: the average pressure calculated by onedimensional waterhammer or mass oscillation theory, the maximum pressure on the draft tube
wall measured by the pressure transducers and the minimum pressure in the vortex core. This
draft tube surge phenomenon is widely elaborated in the literature (Murray, 1980; Ohashi,
1991; ASME, Pejovic co-author, 1996; Pejovic 2000; Pejovic, 2002; Raabe J, 1989).
Pressure distribution across A - A
Measured draft tube pressure at wall
Local pressure
Average / Calculated pressure
A
Minimum pressure at core
A
Figure 1 Pressure distribution at a cross-section of the draft tube
This paper presents an analysis method of water column separation based on the measured
pressures at draft tube cone hDT and the calculated/simulated pressures based on one
dimensional transient theory hWH. These head values are in tern used to estimate two empirical
coefficients, kDT and kWH, respectively, that then become an aid and index to be used in design
and operational work.
Draft Tube Coefficient
Several approaches are adopted to develop a suitable index of destructive cavitation for the
draft tube that would avoid dangerous water column separation and that could be used to
assess whether the issue is likely to be severe or not. The one summarized here has been
developed for certain time period and commonly used in hydro engineering (Murray, 1980).
(i) Coefficient based on measured pressures - KDT
Field test data show that the partial water column separation takes place even if the measured
pressure at the draft tube cone is above the vapor pressure. The minimum pressure hDT, and
the reverse waterhammer pressure rise hmax at draft tube cone can be measured; however, the
pressure distribution in the draft tube cannot be measured conveniently on site or predicted
numerically.
In order to obtain the required submergence of a turbine installation, the draft tube coefficient
KDT is defined as follows:
K DT = hDT
u e2
2g
(1)
where g = gravity acceleration; hDT = the minimum value among the measured pressures at
the draft tube cone during the transient event; ue = the corresponding peripheral velocity of
the runner measured under the corresponding over-speed condition. This minimum pressure
point refers to that pressure drop occurred right before a sudden pressure rise caused by
collapse of void downstream of the turbine runner. The idea is that the velocity head in the
denominator is a convenient indicator of the potential magnitude of the radial or
circumferential flow in the draft tube; although it would be desirable to use the tangential
velocity itself, this term is almost never directly available.
The critical value of the draft tube coefficient is calculated based on the measured pressure
fluctuations in the draft tube (see Figure 2). This figure presents two typical transient events
caused by load rejection of the turbine with medium specific speed. Submergence hs (see
Figure 1) applied in this plant was based on the critical cavitation coefficient σ with
minimum safety, that is,
σplant≅σcriticaland σ plant ≥ σ critical
The definition of cavitation coefficient is σ ≈ (10 + hs ) / H where H is the turbine net head.
Such a submergence, hs, cannot prevent the water column separation in the draft tube and the
huge pressure rise in the penstock, if tailrace tunnel is longer than 10 to 50 m, depending on
the water deceleration, the diameter of tailrace system and the inertia of rotating parts of the
turbine and generator. The graphs in Figure 2 are for a plant having 400 m long tailrace
tunnel.
(b) Severe load rejection
(a) Mild load rejection
140
4
200
120
Penstock pressure
Speed
3
100
150
2
80
Speed
Draft tube
100
1
60
Guide vanes
opening
Draft tube
pressure
50
0
0
50 1
Min
40
20
100
Min
2
150
200
250
300
Time
0
450000
0
Guide vanes
opening
470000
-1
-2
Time
490000
Figure 2 Two typical turbine load rejections
In Fig. 2(a), the large cavity in the draft tube occurs after the second minimum in the
measured pressure at the cone; at this time the vortex component of water flow is forming
larger voids due to the associated greater runaway speed. The high runner speed at the second
minimum of the pressure measured in the draft tube leads directly to the huge pressure
variation in the draft tube cone, thus causing large water column separation and high collision
pressure. By contrast, the speed at first minimum is not great enough to cause large voids, so
it has little impact on water column separation. In Fig.2 (b), a severe water column separation
took place at smaller runner speed because of the higher deceleration of the water in the
tunnel, followed up by the severe, more dangerous pressure rise accompanied by a
correspondingly brutal axial thrust.
Among the great number of site tests of load rejection, 18 cases with sharp pressure rises,
caused by the collapse of void in the turbine draft tube, were selected to calculate the draft
tube coefficient KDT for each case. The black points and trend line in Figure 4 are constructed
in order to determine the critical coefficient. A dangerous value of draft tube coefficient
becomes a useful index of hazardous water column separation, which is used to determine the
required submergence of turbine installation hs. In Figure 4, the abscissa is the draft tube
coefficient calculated based on measured or numerically modeled minimum draft tube
pressure and its corresponding runner speed (see the arrows in Figure 2). The ordinate is the
measured peak pressure (see the stars in Figure 2) following the minimum pressure point.
Measurements of pressure and runner speed fluctuate with different frequencies, and it is very
difficult to read the mean value and amplitudes of fluctuation. The maximum pressure
fluctuation at steady state can be as high as 10 m and thus the measurement error is
unavoidable.
(ii) Coefficient based on numerically modeled pressures - KWH
A numerically modeled minimum pressure at the draft tube, based on one-dimensional
waterhammer theory represents an “average” value at the cross section which should be
somewhere in the middle of the indicated zone (Figure 1); therefore the variation of pressure
distribution at a cross section of the draft tube must be considered as well when the
numerically modeled minimum pressures are used to calculate the draft tube coefficient KWH.
Water column separation takes place even if the calculated minimum pressure below the
turbine runner or at the inlet of the draft tube, hWH, is above the vapor pressure.
To verify the numerical model of transient analysis applied in this paper, simulation results
(the dashed lines) and measurements from a site test (the solid lines) are compared in Figure 3.
In this numerical model, the pressures at the inlet of spiral case (that is, upstream node of the
turbine unit) and the outlet of draft tube (that is, downstream node of the turbine unit) are
calibrated to agree initially. The pressure at the measured section of the draft tube cone
(somewhere below the runner outlet) is retrieved/calculated from the simulated draft tube
outlet pressure by considering the elevation and diameter variations along the draft tube,
based on the head balance equation for the turbine system.
There is no obvious phenomenon of water column separation in this study case, which
demonstrates the numerical simulation agrees generally well with the measurement. As
expected, the simulated minimum pressures at draft tube are lower than the measured values.
( b) Dr af t t ube out l et pr essur e ( %)
( a) Spi r al case i nl et pr essur e
120
115
Pr essur e ( %)
Pr essur e ( %)
100
110
105
100
80
60
40
20
95
0
66
70
74
78
82
86
66
70
Ti me ( s)
80
130
60
120
40
110
20
100
90
0
78
Ti me ( s)
82
86
86
200
Pr essur e ( %)
140
Gat e Openi ng ( %)
Runner Speed ( %)
100
74
82
( d) Pr essur e at dr af t t ube cone
( %)
150
70
78
Ti me ( s)
( c) Runner speed
66
74
160
120
80
40
0
- 40
66
70
74
78
82
86
Ti me ( s)
Measurment ▬▬; Waterhammer Calculation ----Figure 3 Comparison of measurement and numerical model of transient. Bigger
wavelength of measured pressure is caused by the air chamber effects of the void in the
draft tube. The bigger the void the bigger the wave length.
For the same 18 measured cases with sharp pressure rises, numerically simulation of the
transient conditions is used to determine the minimum pressures, hWH, and the corresponding
runner speeds. In this way, the draft tube coefficient KWH for each case was calculated
respectively based on each numerical simulation result. In Figure 4, the red points and red
trend line are constructed in order to determine the critical coefficient:
KWH =
hWH
(2)
u e2
2g
where hWH = the minimum modeled pressures, ue = the corresponding modeled peripheral
velocity of the runner, after which a sudden pressure rise caused by collapse of void
downstream of the turbine runner has occurred.
Max. Measured Draft Tube Pressure (m)
60
50
Safety Area
40
30
20
Measur ed Dat a
Cal cul at ed Dat a
Measur ed Tr end Li ne
10
Cal cul at ed Tr end Li ne
Saf et y Li mi t
Kcr
0
0
0. 02
0. 04
0. 06
0. 08
0. 1
0. 12
0. 14
0. 16
0. 18
Draft tube coefficient KDT and KWH
Figure 4 Draft tube pressure coefficient
The numerical simulated minimum pressures are generally lower than the measurements;
however the corresponding speed may be also slightly smaller than measured speed as well in
some cases. Overall, though, the calculated draft tube coefficients are quite close to the
measured ones. Furthermore, the difference between simulation and measurement are usually
practically insignificant; in other words, the difference between simulation and measurement
is within the range of the fluctuation and measurement error. Therefore, in this case, there is
no significant difference between critical draft tube coefficient either based on the
measurement data or the numerical simulated data. In Figure 4, the measured black points and
the simulated red points could have a common conservative safety limit (the thick line), which
includes inaccuracy of measurement and the safety factor. If the 10 to 30 m (water column) is
the permitted maximum pressure rise in the draft tube, then the critical draft tube coefficient
can be taken as Kcr (the thick line in Fig. 4). This criterion is built on both measured and
simulated draft tube minimum pressures. With this critical coefficient, the draft tube system is
safe if the minimum pressure h measured or simulated at draft tube cone is larger than the
critical minimum pressure hcr.
h ≥ hcr = K cr
u e2
2g
(3)
The only published data in the literature, available to the authors (Murray H., 1980) for high head
pump-turbines is Kcr = 0.11.
Full Runway and water Column Separation
A full runaway condition, as simulated in Figure 5 (which has the same initial steady state
condition as the case in Figure 3), occurs when guide vanes fail to close during load rejection
event. Here, we can see the accelerated runner speed reduces the flow passing through the
turbine, and thus causes an initial pressure drop at the draft tube and pressure rise at the
penstock; the runner speed at full runaway condition is the highest one which can occur.
Compared with the case of load rejection with a normal closure of guide vanes, though the
pressure drop at the draft tube cone is less severe,, water column separation could still occur
at this condition, because the full runaway speed is much greater than that with normal guide
vane closure. In this state, the higher rotation speed increases the volume of air voids inside
draft tube, which will collapse even if the calculated or measured pressures at the draft tube
cone are not as low as they were formerly.
104
Speed
Speed, dr af t t ube pr essur e,
f l ow and gat e openi ng
( %, %, %, %)
170
102
160
Penstock Pressure
150
100
140
98
130
120
96
Draft Tube Pressure
110
94
100
Gate opening
90
92
80
Spi r al case i nl et Pr essur e ( %)
180
Flow
70
90
70
75
80
85
90
95
100
Ti me ( s)
Figure 5 Simulated full runaway. The first minimum draft tube pressure at 125% speed
of the runner is expected to result (this must be confirmed) in water column separation,
but at full runaway at 175% speed dangerous water column separation will quite likely
ruin the runner and waterways if they were not protected.
Minimum calculated draft tube pressures, corresponding over speeds and evaluated safety
void coefficient (blue line in Figure 4) deliver the critical permitted minimum pressure of
hcr = k Cr
u e2
= 38m
2g
which is higher them calculated pressure h = 11 + 10 = 21m. Therefore
h = 21 < hDT = k DT
u e2
= 38m
2g
and if there is no protection accident will occur.
A unit’s submergence calculated to prevent cavitation in a normal steady operation, is
insufficient to save a power plant from harm if it has a long tailrace tunnel, without other
protective devices. In this state, it will be very vulnerable in transients during operation and
all transient must be analysed if the system is to be protected properly from water column
separation.
The following photo shows a water column separation in the draft tube at high runner speed
and insufficient submergence.
Figure 6 Void in a draft tube cone. Model test of cavitation and vortex core
Conclusion
Since the waterhammer calculation is usually one-dimensional and the results represent an
“average” values of pressure heads; the variations in pressure distribution must be added to
the calculated pressure in the draft tube. A required minimum submergence of turbine
installation as a function of rotational speed of runner is shown in Figure 7; such a limit is
established to control the water hammer pressure drop under a negligible level which does not
lead to an excessive pressure rise to cause the damage of the unit and waterways; the runner
overspeed must also be taken into consideration, since a very small pressure drop could
further increase a void (a water column separation) under higher speed and the following
rejoining creates forces that would damage turbine runners and non-rotating parts. Even more,
if submergence near the limit, a void formed by centrifugal force of rotating water is great
enough and the pressure rise caused by very slow acceleration/deceleration of water in the
tailrace tunnel could still be dangerous. Under this situation, additional transient analysis must
be performed theoretically and confirmed experimentally. In addition, the full runaway
condition must be simulated and analyzed as an Abnormal Conditions (ASME, Pejovic, coauthor, 1996; Pejovic et al., 1987).
Submergence (m)
30
25
20
15
10
1
1. 2
1. 4
Dimensionless Speed
1. 6
Figure 7 Required minimum submergence versus runner speed
References
Gajic A., Pejovic S., Waterhammer and Hydraulic Vibrations (in Serbo-Croatian), JUGEL,
Ljubljana, 1980, pp. 59-70.
Gajic A., Pejovic S., Arnautovic D., Ignjatovic B., 1992, Reverse Waterhammer Analysis in
Kaplan Turbines, IAHR Symposium, São Paulo, Brazil, pp. 161-171.
Krivchenko, G. I., Arshenevsky, N. N., Kvyatkovskaya, E. V., Klabukov, V. M., 1975,
Hydraulic Transients in Hydroelectric Power Plants, (in Russian), Moskva.
Lee T. S., Pejovic S., 1996, Air Influence on Similarity of Hydraulic Transients and
Vibrations, Transaction of the ASME, Journal of Fluids Engineering, Vol. 118, December
1996, pp. 706-709.
Murray H., 1980, Hydraulic Topics in Development of High Head Pump-Turbine and
Investigation on Related Problems in Japan, General Lecture, 9th IAHR Symposium on
Hydraulic Machines and cavitation, Tokyo, Japan, pp. 1 - 14.
Nonoshita T., Matsumoto Y., Ohashi H., Kubota T, 1992, Water Column Separation in an
Elbow Draft Tube, 16th IAHR Symposium on Hydraulic Machines and Cavitation, Sao
Paulo, Brazil. 141 - 149.
Ohashi, H., 1991, Editor, Vibration and Oscillation of Hydraulic Machinery, Avebury
Technical.
Pejovic S., 2002, Troubleshooting of turbine vortex core resonance and air introduction into
the draft tube, IAHR Symposium, Lausanne, Switzerland, CD.
Pejovic S., 2000, Understanding the Effects of Draft Tube Vortex Core Resonance, Hydro
Review Worldwide, HCI Publications, September 2000, pp. 28.
Pejovic S., 1990, Guidelines to Hydraulic Transient Analysis and Measurement on Pumping
Auxiliary Systems of Hydro- and Thermal Powerplants (in Serbo-Croatian), Faculty of
Mechanical Engineering, Belgrade, pp. 88.
Pejovic S., 1989, Similarity in Hydraulic Vibrations of Power Plants, Joint ASCE/ASME
Mechanics, Fluids Engineering, and Biomechanics Conference, San Diego, USA 1989,
American Society of Mechanical Engineers, Paper 89-FE-4, pp. 5.
Pejovic S., 1984, Guidelines to Hydraulic Transient Analysis (in Serbo-Croatian), Belgrade,
pp. 119.
Pejovic S., 1977, Waterhammer and Transient Operations of Hydraulic Systems (in SerboCroatian), Masinski Fakultet, Beograd, pp. 122.
Pejovic S., 1977, Hydraulic Transients and Reverse Waterhammer (in Serbo-Croatian),
Masinski Fakultet, Beograd, pp. 84
Pejovic S., co-author, 1996, ASME (American Society of Mechanical Engineers) Hydro
Power Technical Committee, The Guide to Hydropower Mechanical Design, HCI
Publication, pp. 374.
Pejovic S., Boldy A.P., 1992, Guidelines to Hydraulic Transient Analysis of Pumping
Systems, P & B Press, Belgrade - Coventry, pp. 181
Pejovic S., Boldy A.P., 1987, Obradovic D., Guidelines to Hydraulic Transient Analysis,
Technical Press, England, pp. 144.
Pejovic S., Gajic A., 1989, Cases and Incidents Due to Hydraulic Transients - Yugoslav
Experiences, International Congress on Cases and Accidents in Fluid Systems, São Paulo,
Brazil, pp. 181-223.
Pejovic S., Gajic A., Obradovic D., 1980, Reverse Water Hammer in Kaplan Turbines, IAHR
Symposium, Tokyo, pp. 489-499.
Pejovic S., Krsmanovic Lj., Gajic A., Obradovic D., 1980, Kaplan Turbine Incidents and
Reverse Waterhammer, Water Power and Dam Construction, pp. 36-40.
Pejovic S., Krsmanovic Lj., Gajic A., Obradovic D., 1980, Kaplan turbine Accidents and
Reverse Water Hammer, Third International Conference on Pressure Surges, Canterbury,
pp. 391-399.
Pejovic S., Krsmanovic Lj., Gajic A., 1978, Reverse Waterhammer and Accident in Hydro
Power Plant "Zvornik" (in Serbo-Croatian), Masinski Fakultet, Belgrade, pp. 90.
Pejovic S., Krsmanovic Lj., Gajic A., Obradovic D., 1981, Kaplan Turbine Incidents and
Methods of Reverse Waterhammer Calculations (in Serbo-Croatian), JUGEL, Mostar, pp.
67-85.
Pejovic S., Krsmanovic Lj., Gajic A., Obradovic D., 1980, Kaplan Turbine Incidents and
Reverse Waterhammer, ( in Serbo-Croatian), Elektroprivreda, pp. 359-365.
Raabe J., 1989. Hydraulische Maschinen und Anlagen, VDI-Verlag GmbH, Düsseldorf.
Raabe J., 1985, Hydro Power - The Design, Use and Function of Hydromechanical, Hydraulic
and Electrical Equipment, VDI, Verlag GmbH, Düsseldorf.
Vladislavlev, L.A., 1972, Machine Vibration of Hydroelectric Plant, Moskva.