Zhang Zhong-Qing
Guangxi University,Nanning,China
Abstract: In connection with the model test for flow condition of Longtan Hydroelectric Project (LHP) power house intake, this paper discusses the cause of vortex flow near the intake , its affecting factors and measures to eliminate it. Some modifications to the existing empirical formula and extension to its scope of calculation in order to replace model test with an empirical formula are suggested to provide basis for the design of intake .
Keywords: intake, vortex
The vortex, which shapes like a hopper, is a kind of air absorbing one. It is required in the design of intake that the top of intake should be located under DWL with certain submergence to assure no negative pressure at the top thus avoiding negative pressure and vortex. This kind of vortex is very harmful to the power plant operation, because it will carry air into the intake ,the intake conduit and the turbine chamber, resulting in vibration and noise in the conduit and unit ,forming aerated flow affecting the flow quantity and reducing the unit output. The badly contaminated trash－rack by debris will reduce the flow and increase head loss. Therefore the designer will at any account try to prevent occurrence of vortex.
In
the design of hydropower plant when condition allows, it is usually to locate
the power house on banks or underground to simplify the configuration, for
convenience of rcc construction, reducing interference caused by the
construction of power house intake system both within and without the dam body.
Sometimes, due to restriction of topography, for rather better geological
condition , the power house is located on the bank either open or underground .
For such configuration the intake is located on the bank or dam abutment and
water flow from upstream will be turned by 90°to the intake
thus forming reverse flow . For different water level and different combination
of unit operation, the scope of reverse flow and circulating velocity are
different . This reverse flow produces bigger effect on vortex, i.e. on critical
submergence depth. Our main consideration is to suggest modifications to the
existing empirical formula .
1: 40 normal model is adopted for researching the flow condition near intake to simulate the intake of 9 units and 7 bays of spillway. The scope of simulation for the reservoir is 1200m .Two-year flow released Q=10500m3. Max. flow for a single unit is Q=566m3/s. Diameter of penstock D=10m. Unit capacity N=600MW. Dimensions of intake gate outlet b×h=8×12m. NPL 375m . DWL 340m.Invert level of intake 290m for 1#--3＃,305m for 4#－7#,315m for 8#－9# units. The conditions for forming vortex and measures to eliminate it will be determined by means of flow test (fig.1)
Fig.1 Typical layout of intake of a power plant
In engineering practice , when liquid bypasses a convex object , many vortexes will be formed behind it. This phenomenon can be illustrated by means of the theory of boundary laminar flow.
As shown
in Fig. 2. The pressure at A is max. Under higher pressure , liquid will flow
forward. Due to obstruction by the object’s surface, the boundary layer
is formed . The special oharacter within boundary layer is the energy loss in
motion. Due to curved surface , the compacted flow velocity continuously
increases along its way .Therefore , the outer surface of boundary layer
=positive, and
=negative, i. e. along the outer surface the pressure is decreasing . The
boundary is in the condition of accelerated depressurization. In
this section of boundary layer ,the depressurization will compensate the
energy loss, and the residual will be turned
to kinetic . At C the pressure reduces to min. and flow velocity
increases to max. After C, if the pressure keeps increasing,
no kinetic energy can be changed to pressure energy and the main
stream will be separated from the curved surface to alleviate the stream
expansion and the surrounding liquid will immediately comes up to fill up the
empty space left by main
stream, thus forming vortex. This phenomenon is
called the separation
of surface from surface layer ,and CD
is then called the separation surface .
Fig.2 Separation of surface layer
The position of C relates closely to the surface form and roughness of the object as well as the flow condition . When acute angle protruding on the surface ,the point of separation usually takes place at the tip of such angle , and the formed vortex behind this object will be carried away by the stream Due to fluid viscosity ,the vortex will gradually attenuate or even disappear in a certain distance.In the process of formation and attenuation of vortex , the lost energy will be turned into heat. This energy loss is called vortex loss, and its corresponding resistance is called vortex resistance. Magnitude of vortex resistance closely relates to the position of separation point on the object’s surface while liquid bypasses it The closer to the end of object ,the smaller the size of vortex and the smaller the vortex resistance. Otherwise ,bigger resistance can be observed. Therefore in general engineering practice, the structure is designed elliptic- shaped or streamlined in order that boundary separation cannot take place or be enabled close to the end when the flow velocity is large.
As known from the theory of boundary layer, the resistance of liquid which bypasses object is composed of surface friction on the object’s surface and the vortex resistance. From the view of mechanics, the force applied on the bypassed object can be decomposed into tangential and normal components to the object’s surface. The later is the dynamic water pressure.
The projection of liquid friction on the object’s surface in stream direction is friction resistance Ff , which can be expressed as
where Af——specific area of bypassed object. It is the projected area of tangential force.
Cf——coefficient of surface resistance
——density of liquid
U0——flow velocity .
Vortex at the tail of object causes unsymmetrical distribution of pressure on the object’s surface. The pressure difference is vortex resistance and takes the name pressure resistance. Because it relates to the shape and position of bypassed object, it is also called form resistance. Pressure resistance can be expressed as follows.
where : CP——coefficient of pressure resistance.
Ap——projection area normal to the flow direction.
Total fluid resistance on bypassed object is
where : Cd——coefficient of bypass flow
Ad——projection area normal to flow direction .
The coefficient of bypass flow resistance is determined mainly by experiments. The bypass resistance coefficient C of cylindrical object relates to Reynold’s no. Re=U0d/v. For small Re the boundary layer is laminar flow , and there is only friction resistance without vortex. Cd is reversely proportional to Re Vortex takes place when Re increases. When Re increases to 104 , pressure resistance prevails and friction resistance becomes relatively small . Therefore bypass resistance nealy does not relate to Re. When Re increase to 3×105, the boundary layer of laminar flow starts to be turbulent and Cd of boundary layer drops abruptly . In turbulent flow , the flow velocity of boundary layer is larger and the position of separation point is more close to the tail than in laminar flow.
Trash-rack is necessary for power house intake . Piers are installed for trash－rack (spacing for this project is 3.05m).When water flow into the funnel and gate chamber from front , piers have no remarkable influence on flow. When water enters inclinedly , piers have immense effect. If there are grate bars in the gate slot (fig.3),sidewise ( or inclined ) flow bypasses the piers. When water flow from right side, the max. pressure is at A and min. pressure at c. The min, velocity at A increases gradually to C . Velocity reaches max. at C. After C water diffuses and the empty space left by main stream comes to be filled up by water body thus forming vortex. After assembling grate bars, water flows between bars after passing through C and forms parallel flow filaments due to restriction by grate bars. Therefore ,grate bars are good for elimination of vortex.
Fig.3 Trash－rack piers
Results of experiment proves the above-mentioned reasoning.
Dimensions of funnel W=b×h=22×18.3=402.6m2.
Velocity before trash－rack
V=Q/W=566/402.6=1.41m/s. Kinetic Coefficient of water flow at 10℃
. Clear spacing between piers
b=3.05m.
Reynold’s no . of fluid between parallel walls of solid body Re.
Without grate bars:
With grate
bars:
Calculation shows that Reynold’s no . without grate bars is larger than that with grate bars. It is concluded that vortex is apt to takes place while without grate bars.
At DWL
340m, all 1#--9# are in full load operation, the
max. intake flow is Q=566 X
9=5094
, and water flows into intake sidewisely or inclinedly .There is only one
counterclockwise vortex before 9# unit on the left side with max
circular velocity 0.13m/s . The rest filaments are basically parallel without
reverse flow or vortex. At level 350m with all
1#--9#unit in operation , the flow condition is
basically the same as before ,and the position and rotation direction of vortex
are the same. The max . circular
flow is 0.38m/s without any vortex .
At level 340m, with 5#--9#units in operation , there are two vortexes . The reverse flow before 7# unit is rather small in counterclockwise direction ,with max circular velocity 0.31m/s . The reverse flow before 9# unit is larger with max . circular velocity 0.37m/s. No vortex is observed for both . At level 340m, 3#,5#,7#,9# units are in simultaneous operation , there is only one counterclockwise reverse flow on the left side of 9# unit, with max ,circular velocity o.18m/s . No vortex is observed . A t level 340m , 2#,4#,6#,8# units are in simultaneous operation, there are two reverse flows . The first one takes place before 7# unit , counterclockwise ,max circular velocity o.28m/s, and the second one takes place at the left side of 9# unit, counterclockwise,max. circular velocity 0.12m/s . No vortex.
The result shows, either all or part of units are in operation , at level 340m, no vortex can be observed except for 7#---9# in operation.
In conclusion of the above mentioned , under level 350m ,vortex takes place only under level 350m with 7#---9# units in operation. There are two reverse flows on the surface .Now , the plane distribution and cause for vortex can be analyzed as follows .
At level 340m , with 7#---9# units in operation water flows to the front of 6#, 7# units from right side (fig.4). From A to C , the pressure at A is max. Under higher pressure , fluid flows onward . Due to resistance on the object’s surface , the boundary layer is formed. Character within the boundary layer is energy loss while the fluid is in motion. Its velocity increases along its way , and pressure intensity decreases accordingly . The boundary layer is in the state of accelerated depressurization .The energy loss is thus compensated by pressure decease in this section of boundary layer . Part of energy changes to kinetic. The pressure increase reduces to min. at C ,and velocity increase to max. Below C, if the pressure intensity keeps increasing, no kinetic energy can then be converted to pressure energy, and the main stream will depart the object’s surface to retard stream diffusion. In this case fluid will subsequently fill up the empty space left by main stream, thus forming vortex. After passing through D, flow proceeds onward and comes to the bank slope at D, then turns to the upstream . Meeting flow from upstream then forms counterclockwise reverse flow.
The first reverse flow varies from larger to smaller from water surface (level 340m)down to the invert (level 315m). The max flow. reverse flow and circular velocity take place at the surface. Close to the invert, the reverse flow disappears. Vortex takes place on the surface layer. The distribution is quite coincident with theoretical analysis (Fig.4) .The second reverse flow takes place at the left side of 9# unit away from the trash－rack, The reverse flow distributes from water surface to the bottom ranging: small—large—vanishing.
The circular velocity ranges: small—large—vanishing. Because it is far away from the trash－rack, its small vortex has no evident influence on flow.
Reverse flow will help to bring about vortex. Cancellation or diminishing reverse flow will reduce factors affecting vortex formation. Now ,the following measures are analyzed .
(1) A guide wall is designed between 7# and 8# units. Extending horizontally the mid pier between 7#and 8# units. Top level of wall 350m. Bottom level 315m.Height of wall 35m. Counting from the trash rack along the axis of intake, the bottom width is 12m ,top width 24m ,wall thickness 1.7m .Water will flow from the right side(Fig. 4) to the wall. Extending AC by 1/2 length of AC . It is evident that vorter becomes larger and flow condition is worsening. It is not recommendable.
Fig. 4 Flow condition while 7#-9# units are in operation
(2) Design of a fixed cover
On the top of funnel of 8# and 9# units at level 340m, a 13.6× 54.0m fixed cover is designed to cover the front part of 8# and 9# units. When water level is over 340m, open 7#--9#, a constantly moving vortex takes place in the upstream district of cover with small depth. The vortex sometimes appears and sometimes disappears. This alternative for eliminating vortex is feasible, but complicated with regards to structural layout. The height and span of cover is larger and is not idealistic. Moreover, whether the vortex before intake will extend into the funnel needs more elaboration.
(3) Change the shape of funnel
The top of funnel of 8#, 9# units are designed as 1/4
circular arc with radius R=13.00m. It is suggested to change into elliptic curve
. Under level 350m open 7#—9# , the position and
elevation of vortex are basically the same as original design. It is understood
that the change of 1/4arc or elliptic curve remains the
same flow condition. Then
the change of funnel shape has no
evident effect.
(4) Change the left bank slope (Fig.4)
According to the original design, the left bank slope is nearly perpendicular to the front of intake, therefore the stream is not smooth. If the angle is changed from 90°to 110°,open 7#—9# units under level 340m, the position and scope of reverse flow is basically the same as before , and open 7#—9# under level 350m, no big difference is observed. It is concluded that the slope angle has no meaningful effect on flow condition.
Chang the front side of 7#—9# into vertical
According to the original design , the front side of 7#—9# units is inclined with slope angle 65°,the upstream side of 1#—6# units is vertical. There is an abrupt change between 6# and 7# units (Fig.4) .By changing the upstream side of 7#—9# units into vertical, thus smoothing it with 1#—6# units (Fig.5). In this case , water flows parallel to the spillway dam axis into intake, then part of water keeps flowing on ,and the other part flows into funnels. Due to simplification of boundary condition, in opening 7#—9# units under level 340m, reverse how appears only on the left front side of 9# unit. No other reverse flow and vortex are observed . The flow condition is good .
The test result shows that complicated boundary condition is apt to cause reverse flow thus forming vortex and more submergence depth is required to eliminate it. By symplifying the boundary condition and reducing reverse flow, the required submergence depth will be reduced correspondingly.
Fig. 5 Flow condition while changing the upsteam face of 7#-9# units into vertical
In literature [1] ,it is synthesized that in order to eliminate negative pressure on top of the intake. Y.R Reddy and his partners considered that the formation of vortex is dependent on Fraude no (Fe),critical submergence depth (h/d) and wave parameters, where d is the diameter of circular funnel . J.L. Gordon took inflow both from front and side into account and introduced five methods into consideration. At last he recommended J.L.Gordon formula to calculate the sidewise inflow condition, which asks for critical submergence depth as follows.
Where, height of gate opening a= 12m ,flow through each opening Q=566m3/s, velocity V=566/(12×8)=5.89m/s , coefficient c for symmetrical inflow c= 0.55, for sidewise inflow c=0.73. For this project ,the inflow is sidewise , the required water depth hkp=0.73×5.89×121/2＝14.89m. Water level which will not induce vortex is 341.89m.Result of integral model test requires level 350m which does not induce vortex, then the converted c=1.13, It is understood that this formula cannot be used to calculate the flow condition prior to modification ,and the complicated condition for sidewise infow should be considered with c=1.13.
As shown in Fig.4 , reverse flow will be induced due to complicated boundary condition thus producing vortex . By modifying J.L Gordon formula as above, it is considered that this formula can be applied to calculate the critical submergence depth for various conditions, for symmetrical infow c=0.55, for sidewise inflow c=0.78 , and for sidewise inflow with complicated boundary condition c= 1.13.
The intake level of power house should be located below min. operation level with certain submergence depth to ensure no negative pressure on its top to avoid vortex . Flow condition in front of the opening has evident effect on submergence depth. The reverse flow will increase submergence depth, then the intake level showld be lowered or DWL should be raised. This paper through investigation on model test suggests a modified J.L.Gordon formula and may be used to take the place of expensive and time wasting model test . The calculated values may be used as design parameters .
[1] Handbook of Hydraulics –Hydropower station structures. East China Institute of Hydraulics engineering. Water and power publishing House 1989.5.
[2] WU Chi-gong. Hydraulics (Vol. II) Senior Education Publishing House. 1985.5.