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The influence
of a Vortex-flow Throttle on Transmission and reflection of Pressure Wave
BORIS HUBER and REINHARD
PRENNER
Institute of Hydraulic
Engineering, University of Technology, Vienna, Austria
A-1040 Vienna, Karlsplatz 13
Tel. 43-1-58801-22244, Fax.
43-1-58801-22299
boris.huber@kw.tuwien.ac.at,
reinhard.prenner@kw.tuwien.ac.at
ABSTRACT
In order to reduce watermass oscillations, special
vortex-flow throttles have been installed in some Austrian high-head power
plants. They are situated at the end of the lower surge chamber, at the
beginning of the rising shaft of the surge tank. The asymmetrical shape of this
throttle element - similar to a Francis-turbine with its spiral case and
straight axial suction diffusor - causes significantly different head-losses
between up- and downsurging water levels for reasons of varied streamflow. Pressure
waves induced by valves, turbines, pumps and regulation processes may damage
the concrete tunnel lining under certain circumstances. This paper attempts to
investigate the behavior of this special vortex throttle under transmission of
single pressure waves combined with various steady-flow conditions. To
ascertain quickly the influence of this throttle element on the pressure wave
transmission, the measurement results are depicted as transmission coefficients
depending on the gradient of the pressure wave. Furthermore, the experimental
results were compared with a mathematical model based on a standard method of
characteristics (MOC), in order to obtain the unsteady differences from the
assumptions of the quasi-steady calculation.
INTRODUCTION AND AIM OF THE
INVESTIGATION
In large electricity systems such as the European
Electricity Network, strict requirements for the operation of high-head and
pump-waterpower plants are essential. To cover consumption peaks, to provide an
immediate reserve in the case of a breakdown of a thermal power plant block and
to stabilize the network frequency, quick closing, opening and regulation
procedures are necessary. Pressure and velocity waves pass through the entire
duct system with the local wave propagation velocity and are partly
transmitted, reflected and superpositioned at changes of pipe cross sections,
branches, throttle elements, etc. Such processes can lead to considerable
stresses and watermass oscillations in the pressure duct system. In a high-head
plant, therefore, a surge tank is usually installed between the pressure tunnel
and penstock. Its damping effects on the mass oscillations can be improved by a
throttle element. Though the influence of most common throttles regarding the
mass oscillation is well known, there is still uncertainty concerning their
behavior during pressure wave transmission. Within the scope of a major
research work at the Institute of Hydraulic Engineering, University of
Technology Vienna, the influence of pressure waves on various circular orifice
plates in pressure pipe systems were investigated [1]. This paper presents an
extension of the investigation regarding the vortex-flow throttle.
THE
VORTEX-FLOW THROTTLE
The
vortex-flow throttle was first mentioned in 1930 by D. THOMA [2]. It consists
essentially of a spiral case with a tangential and an axial junction. The flux
at the tangential connection (flow direction is backward - downsurging) results
in a vortex flow which has a considerably larger hydraulic resistance than the
rotation-free in-flow at the axial junction (flow direction is forward -
upsurging).
Fig.1: flow conditions in a vortex-flow throttle [3]
Because
of the different flow configurations in the two flow directions, the vortex
throttle can be compared to a swing check valve with a central orifice. This
throttle is far more reliable than such a valve, however, because it has no
movable construction elements. The first practical application of a vortex flow
throttle in a high-head plant was realized in the Kaunertal power plant
(Austria). There, the original shape of the vortex-flow throttle was adjusted
to the conditions of high-head plants and tested for suitability. Additional
vortex-flow throttles were later used at the Zemm and Malta powerplants, where
they are still successfully in operation [4,5].
Fig. 2: Vortex-flow throttle at the surge tank of the
Kaunertal waterpower plant [3]
Lately,
the vortex throttle with a more simple geometry (a cylindrical chamber section)
has also been used for discharge control in flood retention reservoirs and
sewage treatment plants. In this field it is usually called a "Vortex
Chamber Diode".
The
hydraulic behavior of the vortex-flow throttle was the subject of several
investi-gations [6], [7], [8] covering high-head conditions, low-head ranges
and the initial phases of the flow development. Nevertheless, until recently,
there have been no experimental results on the throttle behavior during
pressure wave transmission, not least because of the lack of appropriate
measuring equipment. Yet such behavior is particularly important in the context
of high-head plants because of the question whether a vortex-flow throttle can
have a negative influence on the water conduit sys-tem. Numerous hydraulic
experiments were carried out to investigate this question. The experimental
results were also verified with a computer program based on a common,
one-dimensional, explicit method of characteristics [9], in order to show possible
unsteady differences to the quasi-steady assumption of control calculations.
BASIC ASPECTS
To
achieve a quick and easy assessment of the influences of local discontinuities
on pressure wave transmission, dimensionless coefficients can be used. Here, if
one disregards unsteady flow effects, the ratio between the reflected (DHrefl) or transmitted (DHtrans) wave
and the incident (DHinc)
wave is given by a reflection factor 
and a transmission
factor 
.
THE EFFECT OF A VORTEX FLOW THROTTLE ON A WATERHAMMER
The
investigation of the throttle was carried out using a model of the Malta Power
Plant throttle, which has a scale of 1:26, a torus-shaped chamber with a
diameter of 312 mm, a height of 80 mm and an axial suction diameter of 120 mm.
The diameters of the tangential and the axial junctions increase slightly.
Fig.3: Investigated model of the vortex flow throttle
[10]
Some
variations of the geometry can be achieved by using different lids and bottom
inserts at the suction diffusor outlet. Furthermore, there is a ventilation
aperture in the center of the lid, which is necessary to avoid the development
of cavitation zones in the vortex center. When a air or cavitation core has
developed in the vortex center, the transmission factor becomes
indefinitely. Due to the limited pump
pressure head available, this investigation covered only flow configurations
with a water-filled vortex core.
Because
of the expansion space in the vortex chamber, the vortex-flow throttle under
pressure wave transmission can be compared to a resonator.
THEORETICAL CONSIDERATIONS FOR A PIPE EXPANSION
In
a long, straight pipe with a sudden short expansion space in the middle, the
propagation of a steep pressure wave spreading out with the local pressure wave
propagation velocity a1 (t=t1) - disregarding steady and
unsteady hydraulic losses through expansion, contraction, pipe friction etc. -
is as follows:
At
the location of the expansion, a pressure reduction occurs which spreads out up
- and downstream from the place of the discontinuity. When the transmitted wave
arrives at the normal pipe cross-section, a renewed reflection upstream and
transmission downstream (t=t3) takes place. Thus, the pressure wave
oscillates in the expansion space, with the transmitted and reflected
components constantly decreasing. Finally, the oscillations settle to a
constant pressure level equivalent to the pressure height of the incident wave,
or in the case of a short pressure impulse, to the stationary hydraulic
pressure.
In
the case of a sudden pipe expansion, the transmission factor s is simplified [11] as:
and the reflection
factor as 
.
This
yields 
.
A1,
A2 ... cross-section area in the individual pipe section
a1,
a2 ... pressure wave velocity in the individual pipe sections
a) pressure wave with constant level b) short pressure wave
impulse
Fig. 4: Passing of a pressure wave through a short
pipe expansion section
ADDITIONAL INFLUENCES
Pressure
wave transmission through the vortex throttle is a complex, three-dimensional
process. To simplify the problem for the mathematical approach it was necessary
to clarify which parameters or influences were important. In addition to the
geometric parameters, the transmission and reflection factors are also
dependent on the gradient of the pressure wave (steeper pressure wave gradients
lead to smaller transmission factors). Other influences such as various spiral
case bottoms, different suction diffusors, ventilation of the throttle chamber
and also different basic flow conditions did not influence the transmission
behavior significantly in the investigated range.
EXPERIMENTAL INVESTIGATIONS
The
numerous tests were carried out at the new Hydraulic Laboratory of the
Institute of Hydraulic Engineering, University of Technology Vienna within the
scope of a doctoral study.
DESCRIPTION OF THE HYDRAULIC MODEL
A
100-mm-diameter steel pipe system was rigidly fixed to the foundation plate of
the laboratory with two special steel constructions (fixpoints). The throttle
was installed horizontally and fastend
to the second fixpoint to prevent shifting. Since pressure waves are reflected
at each point of discontinuity, the lengths of the pipe sections were chosen to
prevent any influence of the reflection waves from the pipe ends on the
measurement of the incident and transmitted single pressure waves. The single
pressure waves were generated by a falling weight on a rubber-damped piston and
introduced into the pipe system near fixpoint 1. The various steep single
pressure waves (with pressure levels from 30 to 70 m) were recorded by 5 high
resolution inductive pressure gauges (0-100 meters) and transferred to a PC
measuring program via an A/D converter. Measurements of the flow discharges
were carried out via a magnetic inductive flow meter. The available pump
allowed a maximum pressure height of 12 m, which corresponds to a pipe-flow
velocity of 1.50 m/s in the downsurge direction. Further investigations with a
stronger pump are currently being conducted to achieve higher flow-velocities
and to investigate influences of cavitation.
Fig.5: General layout of the experimental arrangement TEST RESULTS For
determining the transmission factor, it is necessary to know the incident
pressure before the throttle without reflection influences, so this was
recalculated by subtracting the unsteady fluid friction from the data at
measurement point "2" (the function of unsteady fluid friction
depending on the maximum pressure wave was taken from the study of PRENNER [1],
because the same pipes were used as in that study). The transmission factors
under various basic flow conditions also depend, as said before, on the
pressure wave gradient which can be seen in Fig. 6. No influence of basic flow
conditions on the transmission factor can be recognized in the velocity range
investigated. Fig. 6 Transmission factors of a vortex-flow throttle a) upsurging basic flow direction (inflow
into the surge chamber) b) downsurging basic flow direction (outflow from the surge chamber) NUMERICAL MODEL For
mathematical modelling of unsteady pipe flow, the momentum and continuity
equations [9] were solved under inclusion of boundary conditions with an
explicit characteristics method (MOC). For the one-dimensional method of
characteristics there is, basically, the problem of considering a
three-dimensional structure within one-dimensional conditions of the calculated
grid. The throttle expansion was simulated by 3 grid distances whith a
cross-section area of about 10 times the pipe cross-section. The conical
junctions were represented by linear interpolation between throttle chamber
cross-section areas and pipe cross-section areas. Fig. 7: Computed measurement for a single wave in the
vortex-flow throttle - steep incident pressure wave Fig. 8: Computed measurement for a single wave in the
vortex-flow throttle -moderately inclined incident pressure wave The
unsteady fluid friction was measured and subtracted from the incident pressure
wave before the numerical calculations. Thus only the quasi-steady throttle
headloss was considered in the calculation. The average throttle headloss
coefficient (related to the average pipe flow velocity) in the investigated
low-head range was found to be xthrottle,outflow
» 12 and xthrottle,inflow » 0,8. The calculated headlosses
were negligible in contrast to the headlosses caused by the expansion of the
vortex chamber. Numerous
tests with various gradients of the incident pressure waves were numerically
calculated. A comparison between measurements and calculations for a steep and
a moderately inclined pressure wave is depicted in Fig. 7 and 8. In
all cases, the transmitted wave was simulated fairly accurately. The pressure
decrease in the measuring sections before the throttle was also reproduced very
well by the calculation. Because of the dispersion of the wave in the throttle
chamber, there is a delayed increase of the pressure wave after the relaxation
wave has passed. This could not be calculated exactly, especially for steeper
inclined pressure waves, as the unsteady effects are higher. CONCLUSIONS AND PRACTICAL IMPLICATIONS The
behavior of the vortex-flow throttle during pressure wave transmission is
simple to describe with transmission and reflection factors and can also, in
spite of the complicated geometric structure, be calculated well with a
one-dimensional method of characteristics. Slightly inclined pressure waves,
which commonly occur in water power plants, are not appreciably hindered by the
vortex-flow throttle; they are transmitted with little or no influence. In
addition to the advantageous hydraulic characteristics and the safe operating
structure of the throttle, there is a damping effect on waterhammers in pipe
systems. This effect is caused by the expansion space of the vortex chamber
torus and is reduced for slightly inclined pressure waves, but in contrast to
throttle elements with cross-section contractions such as throttle plates or
nozzles, there is at least no positive reflection, which could endanger the
pressure tunnel in the case of higher pressure loads. Although
the advantages of the vortex-flow throttle over conventional throttle types are
obvious, the vortex throttle is very rarely realized in water conduit systems
of high-head plants. In many cases, it may make sense to install such a
throttle when extending an existing power plant, because an expensive
enlargement of the surge chamber could then be avoided. REFERENCES [2] THOMA,
D.: Die Rückstromdrossel; VDI-Zeitschrift BD. 74, 1930 [3] SEEBER, G.: Das Wasserschloß des Kaunertalkraftwerkes der TIWAG; Schweizerische
Bauzeitung 88 (1970), Heft 1 [9] WYLIE, E.B. ; STREETER, V.L.: Fluid
Transients in Systems, Prentice Hall Publications, 1993 [11] PARMAKIAN, J.:Waterhammer Analysis, Dover
Publications, New York, 1963
