(1)
Tang Chunling
Beijing Lili New Technology Development Corporation,
Beijing,
100055, China, 86-10-63455836
Chen Dong
China Institute of Water Resources and Hydropower Research,
Beijing, 100044, China, 86-10-68415522-6633
Sun Ying Chen Zhaohe
Beijing Postgraduates School, North China Inst. of Water Resources & Hydropower,
Beijing,
100044, China, 86-10-63286960
Abstract:
Numerical simulation of unsteady flow in
long-distance water-transfer project with multi-structures is illustrated in
this paper. Variable steps in time/space and continuous computation involving
the inner boundary conditions are used to simulate the step-type flow and
long-distance waterway with multi-structures. Utilizing the function of
man-machine interaction and the automatical state-identification of sub-system,
the operator of projects can give the model a set of instructions, which can
automatically identify the flow state of sub-systems and quickly feed back the
simulation result. Different operation schemes can be compared each other with
little time and cost consumption. The model is verified with the field data of
the Luanhe-Tianjin water-transfer Project with a distance of more than 100km
from Yu-Qiao reservoir located in Luanhe River to Da-Zhang-Zhuang pump station
in Tianjin, China, along with many hydraulic structures such as pump stations,
inverted siphons, flumes, sluices and etc. The relative error between numerical
computation and field measurement varies within 1~3% which shows an excellent
agreement.
Keywords: unsteady flow, water-transfer project, numerical simulation, multi-structures
The purpose of water-transfer project is to transfer water from one watershed or location to another. The boundary conditions of incoming water at the entrance of the water passageway may be classified into two categories. The first deals with the gradually varied flow shown in Fig. 1-a, whereas the second the rapidly varied flow with longtime steady stages or so-called “step-type flow”(Fig. 1-b). For the purpose of better adaptation to the users’ water demand and better utilization of water resources, the second category is more popular under the operation of water turbine. On the other hand, the water-transfer project often has to have a long-distance waterway, along with many hydraulic structures such as pump station, inverted siphon, flume, sluice and etc. In addition, the operation schemes of the project often run into extreme complexity in order to meet either the natural conditions or better serve to the user’s demand.
Numerical simulation of rapidly varied flow in long-distance water-transfer project with multi-structures is illustrated in this paper. The computed water surface profile and discharge are successfully verified with the field data of the Luanhe-Tianjin water-transfer Project.
Basic equations used for the numerical simulation are the complete Saint Venant Equations along with the corresponding boundary conditions and initial conditions.
Continuity equation:
|
|
(1) |
Momentum equation:
|
|
(2) |
Where, T is independent variable of time; X is independent variable of distance; q is lateral inflow; K is the coefficient of local head loss; n is the coefficient of roughness; Q(X,T) is discharge; A(X,T) is cross sectional area; R(X,T) is hydraulic radius; Z(X,T) is water level.
In order to ensure the accuracy, the complete equations of Saint Venant should be employed in such a model for water-transfer project. Furthermore, due to the long distance of waterway, the proper selection of the roughness coefficients for each cannel reach is very important. It is better to calibrate them by field measurements under different flow discharges.
To fit the special conditions of water-transfer project such as various operation scheme, long distance water conveyance, many hydraulic structures along the transfer route and etc., efforts have been made to divide the whole waterway into several sub-systems which are connected in series. For instance, the sub-systems divided by the author for Luanhe-Tianjin water-transfer Project are shown in Fig. 2. Continuous computation along these sub-systems involves the inner boundary conditions, which consider the structures as a short reach ΔX and substitute the Saint Venant Equations with the following ones:
Qi=Qi+1 (3)
Qi=Qs (4)
Where, Qi and Qi+1 are the
flow discharge upstream and downstream respectively; Qs is the
controlled discharge through the related structure. Coordination among Qi,Qi+1,Zi
and Zi+1 can be obtained within the implicit sheme solution.
Theoretically speaking, there are no limit to the amount of inner boundary.
The operating state of subsystems may vary with the inflow discharge. When the flow discharge is smaller than certain value, the pumping pattern of Chao-Bai-He and Er-Wang-Zhuang pump stations are changed into free drainage pattern by using of the by-pass open-channel for each pumping station. The change of flow pattern may also occur in sluice discharge, i.e. orifice flow (Fig.3-a) changed to weir flow (Fig.3-b), or vice versa.
In respect of the Bulkhead gates in open channel of the Luanhe-Tianjin water-transfer Project, the criteria for orifice and weir flow can generally be described as follows:
E/H ≤ 0.65 sluice flow
E/H > 0.65 weir flow (5)
Where, E is the gate opening and H is the water head.
The number of gates and their opening are important features effect the operation scheme, whereas the number of working pumps is another equally important feature. Utilizing the function of man-machine interaction and the automatical state-identification of sub-system, the operator of Projects can give the model a set of instructions, which can automatically identify the flow state of sub-systems and quickly feed back the simulation result. Different operation schemes can be compared each other with little time and cost consumption.
Considering the long distance and the step-type suddenly varied unsteady flow mentioned above, variable steps in both time and space should be used in the model. A dilemma of choosing the time step may often be faced for the step-type flow. A large time step should be used for the long steady flow stage due to economy. However, non-negligible errors and convergence or stability problems may occur at the rapidly varied inflow stage of the step-type flow. This problem was solved by halving the time step when the computed area of a certain cross section runs into negative value or when the iteration process fall into an endless loop. If the same problem still exists, the model will halve the new time step again. The final adapted time step will be restored and, if necessary, may be printed out.
The example for Luanhe-Tianjin water-transfer project will be illustrated as follows.
The Luanhe-Tianjin water-transfer project has a waterway more than 100km long, beginning from Yu-Qiao reservoir through Zhou river channel, Jiu-Wang-Zhuang sluice, Chao-Bai-He pump station (including a free drainage way), Er-Wang-Zhuang pump station (including a free drainage way, pumps in open channel), Da-Zhang-Zhuang pump and five inverted siphons. The flow state contains open channel flow, pressure flow and sluice flow.
Two important factors influence the result of numerical simulation. One is the division of system, and the other is the selection of the roughness coefficients for each reach. The proper division of system is based on the special characteristics of the project. The rational selection of the roughness coefficients should be made in accordance with local conditions. In the river channel, the coefficients may vary from season to season. However, they may mainly depend on the situation of lining on the open channel. Experience and engineering judgment will be necessary to decide these coefficients, although it is better to calibrate them with field measurements under different flow discharges.
Several schemes have been simulated with the model presented herein. Table 1 shows the comparison between computed and measured results on Sept.12, 1992. The error within 3% shows an excellent simulation.
Table1 Comparison between computed and measured results of water surface profile
|
Water Level (m) |
YuQiao |
Jiu-Wang- Zhuang Sluice |
Chao-Bai-He pump station |
Er-Wang- Zhuang pump station |
Da-Zhang- Zhuang pump stataion |
|
Measured |
8.31 |
3.61 |
3.42 |
1.52 |
0.214 |
|
Computed |
8.35 |
3.54 |
3.33 |
1.56 |
0.214 |
|
Error (%) |
0.40 |
1.90 |
2.60 |
2.60 |
0.000 |
A mathematical model developed by the author for the unsteady flow in a long-distance water-transfer projects with multi-structures was described in this paper. Associated with initial condition and boundary conditions internal and external, the model can make a numerical solution by finite difference method of implicit scheme. Several distinguishing characteristics of the model are as follow:
(1) The problem of multi-structures and long distance of waterway can be successfully solved by means of continuous computation of sub-systems.
(2) Function of man-machine interaction and automatical identification of sub-system is used in the model to better serve the operator’s need.
(3) Considering the long distance and the step-type suddenly varied flow mentioned above, variable steps in both space and time should be used in the model.
The example shown for the Luanhe-Tianjin water-transfer Project successfully substantiates the rationality and accuracy of the numerical model. With its spread, a good economic and social benefits can be expected in the future.
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(a) Graduated varied flow (b) Step-type flow
Fig. 1 Sketch of gradually varied flow and step-type flow
Fig. 2 Sub-systems divided by the author for Luanhe-Tianjin Water-transfer project
Fig. 3 Flow pattern varied from orifice flow into weir flow
Fig. 4 Survey on Luanhe-Tianjin water-transfer project
