(
=1,2)
(1)
Yang Ming1, Zhang Hongwu2,
Zhang Junhua3 and Li Dongfeng4
1 Engineer, Institute of Hydraulic Research ,YRCC, Zhengzhou, 450003,China
2 Ph.D,Professor. Tsinghua University. Beijing. 100084,China
3 Ph.D.Professor. Institute of Hydraulic Research, YRCC. Zhengzhou 450003,China
4 Senior Engineer. Institute of Hydraulic Research, YRCC. Zhengzhou 450003,China
Abstract: The theoretical frame of a new two-dimensional sediment mathematical model is established on the basis of the resent research achievements about the sediment transport law of the Yellow River. The formulas of sediment carrying capacity of flow, which reflect the features of the Yellow River, are applied to it. The finite element scheme is employed to deduce the discretized equations of the model .Verifications of the model are carried out with the flood occurring on Jinan reach of the Yellow Rive during the flood season in 1976.The calculation results with the model are in good agreement with the measured data. The programs calculating indicates that the Jinanyan's constructing will be of great benefit to Jinan city's flood protecting and water supply.
Keywords:
two-dimensional sediment numerical modeling, the Yellow River, Jinanyan project
The Yellow River is famous for its
heavy sediment load and complex fluvial processes. Obvious advances have been
made in the two-dimensional sediment mathematical model for the rive .Among the
models created before the mechanism of sediment transport and related physical
parameters, such as sediment velocity, sediment carrying capacity and river
friction etc. are not yet understood very well. The synchronous observed data of
the flow with sediment, especially at hyperconcentration, are not enough for the
model calibration. Therefore the development of two-dimensional sediment
mathematical model and the improvement of calculation accuracy are limited and
furthermore these models created are restricted in their application. In view of
existing problems, some equations are improved and some new expressions are set
up based on the experimental and measured data. It leads to the establishment of
a new two-dimensional sediment mathematical model. The new model has been tested
and verified with the synchronous data of flow and sediment. The verification results indicate its
reliability the correct understanding of mechanism of sediment transport in the
Yellow River.
Jinanyan project is planned by Jinan
city government to utilize parts of Beizhan
area which has been built for releasing flood as intake river. 30% discharge can
be diverted into the intake river once the flood threaten the Jinan city. In
other way, it can be impounded 200 millions cubic meters water(300 times volume
to Daming Lake) for irrigating and city construction.
The mathematical model for numerical simulation of the river bed degradation and aggradation phenomena contents mainly two types of the basic relationship, namely: the water movement equations and sediment motion equations. Obviously the known equations are less than the unknown parameters. Additional equations are required if the problem is to be completely solved.
The continuity and momentum equations for depth-integrated flow are as follows.
(
=1,2)
(1)
(
,
=1,2)
(2)
In which:
Z is water stage; H is water depth;
is velocity component in
direction;
is water density; g is gravity acceleration;
is coefficient of turbulent viscosity; f is Coriolic parameter(=2
);
is the angular velocity of rotation of the earth;
is the latitude of the side; C is Chezy,s
resistance coefficient(C=
);n is Manningˊs Roughness coefficient; R is hydraulic radius(R=H),
is coefficient matrix defined by
The sediment
movement equations and the river bed deformation equation are modified (Xie,1990),considering the interaction
between different phase particles and turbulent flow field as follows.
(
=1,2) (3)
(4)
In which:
is water velocity component in
direction;
is settling velocity of sediment
particles, calculated with Equation(12);S is sediment concentration;
is sediment carrying capacity;
is the unsaturation coefficient, calculated
with Equation(9);K1 is the correction coefficient, i.e.
additional coefficient reflecting the attached effect of sediment and the
horizontal diffusion caused by the turbulent fluctuation, calculated with
Equation(8);
is the coefficient of balance sediment distribution and represents the
ratio between the bottom and average concentration in the balance condition. It
can be deduced from the formula of concentration distribution along water depth by the author (Zhang et al, 1993) and has the
expression as follows
(5)
in which
(6)
where:
is von Kármán’s constant;
is the vortex coefficient(=0.375
);
is friction velocity; C is Chezy,s resistance coefficient.
Function
has following expression
(7)
,the additional coefficient appearing is Equations(3) and (4),is treated as a
comprehensive correction coefficient at present. Based on the similarity theory
and the experimental data of moveable bed models, the expression of
is derived with dimensional
analysis as follows
(8)
The unsaturation coefficient
is induced from numerous
experimental data and has following expression
(9)
The mathematical models created before are not suitable to the flow at hyperconcentration in the Yellow River . Their conduct is a problem even to the ordinary flow . After calibration and adjustment, the so-called“coefficient of sediment recovery saturation" in these models still is far less than 1.The reasons for the contradictory between theory and practice are mainly the simplification adverse to the practice and the unsuitable formula of the sediment carrying capacity. The sediment carrying capacity resulted from the formula employed in the model is on the low side, but it is the key to the calculation of bed deformation. To ensure that the model is suitable to the flow of the Yellow River, especially the flood at hyperconctration, following equation of sediment carrying capacity is introduced(Zhang et al.,1992)
(10)
in which:
is sediment concentration in volume;
is median diameter of bed materials;
is von Kármán’s constant,
calculated with Equation(11);
is settling velocity of sediment
particles in muddy water, calculated with Equation(12);
is specific weight of muddy water.
Following equations represent
,
,and
in turn
(11)
(12)
(13)
in Equation(10)-Equation(13):
is specific of water;
is specific weight of sediment; S is sediment concentration;
is median diameter of suspended sediment, mm;
is settling velocity of sediment particles in clear water, as for uneven
sediment, take the weight mean of the settling velocities of sediment particles
with different size.
The boundary forms appearing in the
flow simulation usually are entrance, outlet, solid and free surface boundaries.
The time courses of flow velocity or specific discharge are given in entrance
boundary and the discharge stage relation or the time courses of stage in outlet
boundary. On solid boundaries normal velocity component equals 0 and tangent is
not 0,i.e.
.
As to the boundary conditions of sediment movement, the concentrations at nodes of the entrance section are give and normal sediment flux on solid boundary should be null.
Some initial values of physical parameters, such as flow velocity, stage and sediment concentration, and topographic features are given as initial conditions. They can be considered as constants approximately at selected moment. The error resulted from the approximation can quickly disappear under the control of correct boundary conditions.
Calibration and verification of the model has been carried out using the data from field and physical model tests. The typical flow during the flood season in 1976 and typical Jinan reach of the Yellow River are selected.
The reach in the lower Yellow River from Zhangchun to Huojialiu, about 48 km long, is controlled by the engineering forming meandering stream. The longitudinal slope is about 1‰0 and the distance between two dikes is 0.7-2.5km.
The domain calculated of the model is selected considering available data of flow, sediment and topography etc. The geometry of land boundaries bas a great influence on the pattern of erosion of deposition in a river reach, so accurate simulation of the geometry of land boundaries is of great importance. Therefore Zhangchun section and a section nearby Huojialiu are selected as entrance and outlet section respectively. Solid boundaries consist of the stable engineerings such as dykes, controlling and guiding works built along the edges of floodplains and vulnerable sports, where spur dykes, groins, and revetments are laid along the dykes for protection.
The mesh used for the finite analytic method is consist of 5924 triangle elements and 3199 nodes. The element density can be readjusted to satisfy the calculation meet, In dealing with elements located in channel, their side length in river width direction are generally about 20-50m but on floodplains about 80m-120m. The topography data measured in early June,1976 are adopted as initial condition of topography and in middle October,1976 as verification target. The preparation tests for the steady flow are carried out and the calculated stage, velocity and concentration are initial values for the formal calculation.
The verification period selected is from Aug.2,1976.According to measured data at Luokou station,the peak discharge is 8 000m3/s.During the period total 7 flood peaks occurred at Huayuankou station. The floods presented with a high level profile and bed degradation took place over Shandong reach in the lower Yellow River.
Fig.1 presents the time courses of stages at Zhengjiadian and Luokou station. The solid lines display the numerical simulation data from Aug.2,1976 to Oct. 15,1976 and black triangle dots present the field data.
Fig.2 shows the calculating flow field with discharge 2350m3/s and 7700 m3/s.
(a) Zhengjiadian Station (b) Luokou Station
Fig. 1 River stage hydrograph of calculated and measured at typical station
(a) Q=2350m3/s (b) Q=7700m3/s
Fig. 2 Flow field with different discharges
Aims to reduce the pressure of flood protecting and water supply of Jinan city ,keep the fontal city in its own way, Jinanyan project has been schemed as the "Ten-five years plan" of Shandong province. It capitalize on the theory of Dujianyan project built in 250 B.C. artfully and composed of 3 main components: Doufuwo gate, intake channel and main river. Doufuwo gate ,a diversion weir diverts flow to the intake channel which could be used for water supply to Jinan city. Once the main river flow is greater than 7000m3/s, the surplus flow directed through the Doufuwo gate to the intake channel, the Jinan city will never been flooded nor threatened by droughts. According to the designer's advice,the intake gate be located at Doufuwo, the outtake gate has two programs.Program 1 is on ahead of Houzhangzhuang cross section and program 2 is on the Fujiazhuang project nearby. How could we know the conditions after diverting flood peak discharge, and the effect on river stage of accordant junction. In addition , if the project do work, which program is better and why. Both designers and engineers are earnestly want to know all above mentioned.
As for programs calculating "82 extended" process is selected as the entrance boundary , the flood peak discharge is up to 10000m3/s. The discharge stage relation of Huojialiu section is designed in 1999 of YRCC as outlet boundary. The calculating river configuration adopt the measured field data in 1999 of YRCC too.
From 1976 to 2000, the river channel of Jinan reach was accumulately silted up average 15 cm per year, the channel shrank and the water conveying capacity of the river channel reduced greatly. With the calculating results, the Doufuwo stage is up to 38.02m once the oncoming flow is 10000m3/s,which is greatly threaten to Jinan city's safety. On the other way, if the intake river released 30% discharge, the stage of Dofuwo is low to 36.65m with program 1(36.5m with program 2).Figure 3 presents the stage changes with diverting flood and no diverting of calculating reach under the specific discharge 10000m3/s.
Fig. 3 River stage comparison of diverting and no diverting with program 1 and program 2
Some conclusions can be drawn:
(1) The Jinanyan project diverts flow can reduce the flood peak stage effectively.
(2) The accordant junction have negative effect on the river stage, program 1 is more disadvantage than program 2. As far as the incidence about the two programs, both are restricted.
(3) At the intake gate and outtake gate, should strengthen the protection of project.
(1) This paper presents authors, two-dimensional sediment mathematical model for unsteady flow. The present research results-the sediment diffusion and bed deformation equations and the improved expressions of sediment carrying capacity and roughness are applied to the model. The verifications of the model indicate that calculated results are in good agreement with the data from field and physical model tests. This model can be applied to simulating the flow and the movement of sediment as well as bed deformation in the lower Yellow River.
(2) Jinanyan project is a modern water
conservancy works, it capitalize on the theory of Dujianyan project built in 250
B.C. artfully and resolve the conflict between flood protecting and water supply
in a creative way. In this way, the Jinan reach will never been flooded nor
threatened by droughts. It will be of great benefits to peoples lived in
Shandong area and keep the fontal city in its own way.
Acknowledgements
This paper is supported by the National Foundation of Natural Science Commission of China (NO.59890200).
References
[1] Xie jianheng(ed.).River Simulation. Water Resource and Electronic Power Press. Beijing(in Chinese),1988.
[2]
Yang Ming,Zhang Hongwu,Numerical modeling of Dongzhuang Reservoir on Jing River.
Journal of Hydrodynamics,serial B.(1).2001.
[3] ZHANG Hongwu and Lv Xin, 1993. Bend Flow Hydraulics. Water Resources and Electric Power Press. Beijing (in Chinese).