Increasing the life of supporting structures was a top priority for engineers involved in the planning of Iran’s biggest hydro project, the Masjed-E-Soleiman dam. SA Sadrnezhad and N Saadat describe modelling of the effects of pressure fluctuation on the stability of the big flap gate, and its consideration in the design of servomotors for the project
In the power station section of this project, there are big flap gates at the end of the draft tube bend, 9m downstream of the turbine axis. The function of these gates are to stop the tailrace water flowing back to the turbine space during repair and maintenance. In order to avoid vibration of these gates when they are in an open position, the top parts are vacuumed.
In addition to hydrostatic internal and external pressures to which flap gates and their steel linings are exposed, the forces induced by vibration of the gate due to pressure fluctuation in draft tube flow, are typical unknown hydrodynamic forces. The intention of present work is to define these forces as cyclic loading which causes the gate, as well as the servomotor (hydraulic cylinders for opening/closure of the gate) forces to oscillate while the gate is open. These oscillating forces must be considered in the design of servomotors.
The structure of the steel lining and flap gate under different conditions is investigated in this paper. Of particular interest and importance is the performance of the lining while the gate is in an open position under the normal tailrace head with applied top vacuum, especially while keeping forces by servomotors and being supported by two pivots and top supports oscillated due to pressure fluctuation.
According to the results obtained from a hydraulic model test scaled 1:30, the worse condition of oscillation is quoted at a frequency of 3.75cycles/sec (maximum and minimum measured pressure fluctuation ?H/H equal to 10% and 3.5% respectively). A normalised time function representing time variation of pressure multiplied by hydraulic unbalanced head was considered for the existing pressure fluctuation. The effect of this dynamic load is added to the result of stability of the gate including its weight.
The results indicate that further to hydrostatic proof, the overall effects of pressure fluctuation on the gate provides a pushing action. This creates some compressive forces on the two existing servomotors and top support lines. However, this compression may not cause any change in the design of servomotors, ie to increase the pushing force. Consequently, under the existing conditions and pressure fluctuation, no change needs to be considered for the system.
The Masjed-E-Soleiman (MIS) hydroelectric project is located in Iran’s province of Khuzestan, about 160km from the capital city, Ahwaz. The dam is situated in the Zagros mountains on the Karun river, about 26km downstream from the Shahid Abbaspour hydro power scheme (see IWP&DC, July 1999, p18).
The dam will be operated essentially as a run-of-river plant with a daily poundage capacity generating peak and base load energy. This is due to the regulated river flow and the small reservoir live storage volume (around 48x106m3 ).
Based on regional historic stream flow and rainfall records, which date back to 1890, a long-term stream flow series was generated for the purpose of energy generation simulations, using the HEC-4 multi-site, multi-variant regression model and a variable transfer function (VTF) type rainfall run-off model. For the large catchment area of 27550km, the long-term mean discharge at the MIS site was calculated as 365m3/sec, equivalent to a net run-off of 418mm per year. The reconstituted stream flow series for 45 years shows a variation from the average monthly stream flows between 186m3/sec in September and 710m3/sec in March. Since 1976, the Karun river flow has been regulated by the large reservoir of the Shahid Abbaspour scheme.
To dimension the river diversion works, the flood hydrograph with a return period of 100 years was routed through the Shahid Abbaspour reservoir, resulting in a peak discharge of Q100=2900m3/sec.
For the design of flap gates, the natural probable maximum flood (PMF) for a peak flow of 25200m3/sec was routed through the future Karun III and existing Shahid Abbaspour reservoirs, resulting finally in 60.8m of head above the sill beam elevation of the flap gate downstream.
As regards seismicity, large and destructive earthquakes have occurred during this century within 300km of the project site. Earthquakes in the region result from the tectonic forces exerted by the Arabian plate on the Iranian plate. As a result of numerous analyses, a design base earthquake with a magnitude of MS=7.5 was adopted, resulting in a peak ground acceleration of ah=0.30g (horizontal) and av=0.20g (vertical). The maximum credible earthquake was defined as having a magnitude of MS=7.7, resulting in a horizontal peak ground acceleration of ah=0.46g.
The power house cavern, 154.5m long, 30m wide and 47.5m high, is split into an erection bay, four unit bays and a service bay. It houses all electro-mechanical equipment such as the butterfly valves, turbine, governors, generators, all associated auxiliary equipment and flap gates. Each turbine will have a digital electro-hydraulic governor for speed regulation and power control. The governors will be equipped for both local and remote control, and for manual and fully automatic start up and operation. They are capable of isolated operation and operation in parallel with other power stations in the system. Under automatic operation, the time between startup of turbines, synchronising, and switching on line will be less than 45sec. However, the closure time for turbine stop under normal conditions is 22sec and in emergency conditions this time is reduced to 13sec.
The flap gates
To prevent tailwater entering the turbine space during repair, four flap gates are used and positioned after the draft tube bend. The clear gate width is 7750mm, though the gate leaf width is 8070mm. This leaves an offset of 160mm for each side seal and supports. The clear gate height is 4891mm, which is increased to 6500mm to account for the top casing of the gate. The ceiling and bottom of the gate frame are inclined, while the gate sill elevation is at approximately 195.5m asl. The gate frame length is 9.5m. The flap gate position and interface with the draft tube liner are shown in the diagram The gate leaf has a closed box structure with skin plates on both sides. Rubber seals are located on the upstream side of the gate leaf.
A mechanical locking device holds the gate leaf in an open position during maintenance. During turbine operation or during an idled period when no maintenance is being carried out, the flap gate remains open, held by servomotors. To ensure the gate leaf is held firmly and with no vibration the servomotor slots will be evacuated by two vacuum pumps, one pump in service and the second on standby. The vacuum pumps will be located on the turbine floor at an elevation of 204m asl.
There are two servomotors to open and close the gate. The distance between the turbine centreline and the servomotors is 12406mm and the servomotors are separated by 4776mm. The pressurised oil required to operate the servomotors is supplied from the turbine governor’s oil accumulator and they are furnished with an additional chevron seal at the piston rod.
The bypass line, with two isolating valves has one control valve (a manually operated needle valve and a differential pressure gauge with bleeder valve) to fill the draft tube from the downstream tailrace tunnel before opening the flap gate. The draft tube should not therefore be filled through the butterfly valve bypass or the pressure shaft dewatering line.
The control panel protection is classified as IP54 (IEC529), and it includes: an electrohydraulic control valve; motor starters for the vacuum pumps; control switches; signal lamps; fuses; and internal wiring to a terminal strip. The panel allows local control and supervision of the flap gate. A summery alarm signal for transmission to the unit control board will also be provided. This alarm signal will be released by the interlocking device in case the vacuum pump is tripped. A trip signal for transmission to the unit control board will also be initiated if the gate leaf closes inadvertently. The control panel will be located on the turbine floor at an elevation of 212.25m asl.
The flap gate operates under the conditions of hydrostatic pressure specified in DIN 19704 for the NB, BB, and AL conditions. Other technical specifications for the operation of the flap gate are:
•The gate will serve as an emergency shut-off device against the tailrace system.
•Under normal operating conditions, the gate will remain open, pre-stressed against stop blocks by its oil-hydraulic servomotor, to stop the flap gate from vibrating during turbine operation.
•On the downstream side of the gate, a second seal will be provided. In the open gate position the seal will serve to close the housing of the gate operating mechanism against tailwater pressure. Thus, maintenance or repair of the operating mechanism and gate servomotor will be possible without dewatering the tailrace system.
•An extra mechanical locking device has been provided to hold the gate in an open position, preventing accidental gate movement during maintenance works. The locking device will not be used to hold the gate in an open position during turbine operation.
The following circumstances must also be considered for flap gate load conditions:
Elevation of the sill is 195.5m asl.
•Maximum pressure over the sill should be 60.8m, because DIN 19704 specifies the following tailwater elevation pressure
230.33m asl (normal elevation) 34.83m (normal).
247.50m asl (at 10,000 years flood) 52.00m (special).
256.30m asl (at PMF) 60.80m (exceptional).
•Permissible stresses according to DIN 19704, are:
Normal case 40% of yield strength
Special case 50% of yield strength
Exceptional case 80% of yield strength
However, the remote possibility of an exceptional case of PMF allows the acceptance of 90-95% of yield strength to avoid an extremely heavy flap gate design.
•The permissible deflections for the normal case must satisfy the following:
Deflection at top line
< l/1000Deflection at bottom line < l/800.
•The closing time of the gate is limited as follows:
Normal closing time 7-12 min.
Normal opening time 7-12 min.
Due to the lack of access to the gate bearing sleeves, these bearings are self-lubricating bushing.
The numerical model of the flap gate included the steel lining and gate leaf.
The steel lining part comprises the following: gate casing at the top; top support line; side support lines; sill beam; and pivot bases. All support lines are provided with stainless sealing paths at their sides.
The main shell of the steel lining must sustain water pressure under different conditions. Among them are applying pressure at the downstream face of the closed gate, and maintaining water flow while the gate is positioned at the top casing (kept in place by hydraulic servomotors and the suction arising from the area of vacuum). The main shell should be able to react against gate leaf support action along support lines and pivot bases. Further to these forces, the steel lining should remain stable against external pressures, such as fresh concrete during construction, and seepage and grouting pressure. Therefore, the stability of the steel lining must be ensured by adding enough stiffeners circumfrentially outside the plates. The stability of segments must also be checked for lifting, storing and transportation. A proper bracing system must be used to prevent the system from deformation against the stated loading conditions.
It has been assumed that approximately 50% of reaction against the internal pressure is provided by backing reinforced concrete. Therefore, the steel lining will sustain only the next 50% of internal pressure effects individually.
A finite element mesh was composed using shell elements with five stiffness components at each node, conformed with axial membrane and plate bending effects. This system was employed for all plate members such as liner, stiffeners, back flanges, and sitting base plates. The diagram shows the symmetrically meshed half steel lining. The supporting effect of reinforced concrete was considered by using three axial linear elastic springs to support the nodes in contact with the concrete. A trial and error method was used to find proper stiffness values for the springs. To make sure that there would not be any disconnection and sliding between steel shell elements and the surrounding steel lining, lots of steel reinforcing end anchored bars were welded by the other end to shells spaced such as to make the of steel shells compatible with reinforced concrete. These bars will avoid any discontinuity between steel plates and concrete if there is a sudden change in temperature at the start of water flow through the draft tube.
The same type of shell elements were adopted for meshing the gate leaf. The leaf consists of a main skin plate, horizontal and vertical stiffeners, back flanges, pivot plates and side supporting end plates.
To arrange proper boundary conditions, two inclined side support lines at the sides, and one support line at the top are restrained in a perpendicular direction to the gate leaf surface. The pivot centres are also restrained in three axial directions. To consider the friction effects of side line supports, some tangential springs with low stiffness values are adopted. The diagram shows the gate leaf mesh, including the restrained points.
Under loading conditions, it is easily concluded that the stress calculation is dominated by the AL loading case. The diagram shows the combined stress distribution and deformed mesh due to internal pressures. The maximum deformation values are less than the permitted values.
The draft tube may pulsate not only at off load working points in normally steady operations, but also during transients (ie under time-varying rotational speed).
The frequency of pulsatory phenomena and the time variance should be kept in mind. Amplification under steady-state operation is undoubtedly worrying. If manoeuvres are frequent then the amplification under transient conditions could eventually lead to harmful effects. To control hydrodynamic stability and induced vibration of the flap gate, pressure fluctuation in the passing flow must somehow be recognised.
The specification of pressure change can normally be measured in a properly designed hydraulic test. The location of transducers around the submerged gate in water can provide the applied pressure changes to the gate. The oscillations are simulated as a time function F(t) multiplied by amplitudes P(x,y,z), which are pressure potentials normal to the surfaces of the gate body simulated as shell elements. The pressure oscillation on the frequency of pressure fluctuation which is presented in time function F(t) makes the gate vibrate, though the sustaining forces of servomotors have to oscillate at the same frequency.
In this study, the pressure fluctuation relates to transducers located in the draft tube cone of the model turbine. This condition may dictate the results as an upper limit and a more severe oscillation of the gate, but leads to a more problematic change of servomotor forces. Therefore, the analysis of the draft tube flap gate forces was based on the pressure fluctuation measured in the draft tube cone of the model turbine. Also, as a more severe condition, this oscillation is considered to exist for the water over and at the sides of the casing in the open gate condition.
Maximum measured pressure fluctuation and correlated frequencies are ?H/H= 10.9% (H=head and ?H= pressure fluctuation), while in the model:
•Qa= 2.8×10-4 m3/sec
•Guide vane opening of model turbine, A0 =9
•Unit speed, N11 =68.8
•Cavitation coefficient of the plant, op= 0.163
•Frequency of pressure fluctuation, f =3.66
The pressure fluctuation affects the gate when it is open, particularly in the area of the top casing which is held by a vacuum of 0.8Atm. This sucking force, and the pull from the servomotor, act against gate gravity and pressure pulsation applied — they act around the gate, but not on the top surface which is sucked up. When there is a compressive effect, pressure fluctuation acts towards the top side seal line supports. In order to retain the side seal, this cannot be moved by more than 3mm.
It is complex to obtain the relationship between the pressure oscillation under the gate skin plate and the corresponding effects around it in the casing, due to wave transformation. The difference between pressure beneath the gate, at the side and at the top depends, among other things, on the distances and the geometry of the gate, casing, steel lining and the existing gap width.
To consider the worst case, one may neglect the conditions of wave transformation and assume the same pressure fluctuation all around the gate, where the surfaces are affected by pressure pulsation.
The normalised time function F(t) was carried out within ±1 from the measured data. Neglecting the effects of those pressures applied on both sides of the steel plates, the amplitude of potential applied to the gate was obtained. To apply the pressure oscillation it multiplied by a time function F(t).
The real variation of pressure may be considered as a time function which varies in a domain between ± 1. The distributed pressure around the gate, perpendicular to the gate element surfaces is :
P(x,y,z,t) = P(x,y,z) F(t) (1)
where, t corresponds to time and P(x,y,z) is the applied pressure amplitude on the gate surfaces.
The flap gate which must stand the pressure fluctuation weighs 40t, and in the open position is supported by two yokes and a rectangular top seal support. The effect of pressure fluctuation will be felt at the rectangular seal supports. If suction pulls the gate down it must be countered by the two servo-motors.
To model the gate conditions, the gate body is mapped by shell elements. To avoid any divergency from the natural frequency of the gate body submerged in the flow, pivot points act as a restraint avoiding displacements in three directions and the servomotor eyes are constrained by suitable stiffness springs. To provide fair boundary conditions for top seal base supports, some nodal forces obtained by trial and error are applied in the Z direction. These forces represent the effects of supports plus rubber seal pre-stressing by 3mm to stop leakage into the servomotor space.
The gate should not oscillate so severely that the amplitude of displacement is more than 3mm over the domain of pre-stressed gate seals. Furthermore, increasing the amplitude adds hoist keeping and supporting reactions. These boundary conditions are in agreement with any separation of the rubber seals from the top seal supports of the gate.
To consider the submerged condition of the gate body in water, element masses must be increased by a factor of 6. This coefficient was obtained by comparing the natural frequency of a similar plate in water with experimental results (I Rasolan, Numerical investigation of trashrack vibration against hydro-dynamics effects, MSc Thesis, University of Tehran, 1998).
To present the results of the dynamic analysis of the gate under applied pressure fluctuation, the obtained normalised F(t) should be multiplied by existing pressure amplitudes on the gate surfaces.
The axial force time history of the corresponding frame element, joining servomotor eye nodes to a support in the Z direction was obtained. The maximum and minimum values of forces applied to the servomotor eye points can then be deduced. Each servomotor force due to the pressure fluctuation, is in the range +22570 <= Fs - <=19940kg.
These two values show the minimum (compressive) and maximum (tensile) forces due to vibration effects. If the hydrostatic constant water pressure is within the obtained values, the maximum value of servomotor force will be -3430 <= Fs <= 45940kg.
The tensile force due to the weight of the gate leaf is calculated for each hoist as 32000kg. Consequently, the maximum force due to vibration, weight of the gate, and hydraulic pressure is-13940 <= Fs <= +28570kg.
The displacement time history of hoisting eye points was calculated. The minimum and maximum gate movement in the Z direction is -0.2645e-1 <= Ds <= 0.2337e-1mm.
The displacement time history of one point on the end plate was also calculated. The minimum and maximum gate movement in the Z direction is -0.1528e-0 <= De <= 0.1343e-0mm
In this range the rubber seals remain pressed against the seal bases within 3mm, which guarantees no leakage.
The weight of the gate is considered as submerged in water. If the pressure somehow increases, the servomotors undergo only part of the reaction based on the ratio of the gate deformation at eye points, and the rest of the reactions are supported by top sealing supports. But it is clear that if the gate leaf is going to separate from the top sealing supports, the corresponding compressive reactions will be made up by the more compressive forces in servomotors. Therefore there is no need to be concerned about any sudden increase in servomotor tensile force.
If the vibration displacement amplitude in the Z direction is within the obtained range, the applied force to each servomotor is less than its maximum capacity, which is 51t. So during the severest vibration of the gate, when the maximum displacement at the gate tip is within 1mm, a displacement of the top seal base may be caused which is less than these values but creates a force in the servomotors which can be safely sustained.
To check the possibility of any case resonance taking place by pressure fluctuation while the gate is forced to vibrate, the frequencies of the first five nodes are calculated (see table). Using the procedures outlined above, we can predict the most probable frequency of the gate, and check the effects of fatigue on any critical part in supporting facilities and the gate leaf.