Zhang Junhua, Li Shuxia, Ma Huaibao, Chen Shukui, Shi Biaoqin and Hu Tian

Yellow River Institute of Hydraulic Research, Zhengzhou, 450003,China

Abstract: The paper is intended to investigate the laws governing the density current and show the application of the laws in the Xiaolangdi reservoir on the stem Yellow River. Sediment brought by the feeding flow to the reservoir, which is on the early stage of impoundment, can be only released out of it through density current. Using the data of density current measured in the Xiaolangdi reservoir, and referring to the research results obtained in physical models, the authors investigated the basic laws for genesis, movement and sediment releasing of density current, and obtained the critical conditions for sediment release by density current, and formulas for resistance, sediment carrying capacity, travel time, and sediment release of density current. Prior to the field experiments of flow-sediment regulation, which were conducted in 2002-2004, the authors applied the results to design regulation schemes for operating the Xiaolangdi dam and other dams. Following the schemes, the field experiments were implemented smoothly. The field experiments not only regulated the formed-naturally density current in a proper way, but created density current as wanted and released the sediment by the density current successfully as well, therefore realizing the objectives like sedimentation reduction, optimizing the rebalance between flow and sediment released.

Key words: Xiaolangdi Reservoir, density current, flow-sediment regulation field experiment

1         Introduction

The Xiaolangdi reservoir, which is in water impoundment in the period of trapping sediment, especially in its early stage, has impounded a great amount of water. When rainfall in the middle Yellow River in flood season or the flow discharge by Sanmenxia Reservoir before flood season brings a great quantity of sediment to Xiaolangdi, the only way to remove it is by forming density current and turbid water and taking sediment out of the reservoir with the current. In line with the law that density current can carry out enormous sediment and doesn’t interblend with clear water, we could expect that by maintaining a certain hydraulic head and operating the Xiaolangdi dam in a proper way, we may reduce sedimentation in the Xiaolangdi reservoir and extend its life. 

Proper operation is the precondition of realizing sediment release by density current with high efficiency. It, nevertheless, must depend on the understanding of physical phenomena and laws. For instance, in accordance with the conditions for density current generation and continuous movement to the dam, a judge can be made on whether density current can occur or move to a dam. With the understanding of the conditions, several reservoirs may be operated jointly to create flow and sediment conditions for density current. With the understanding, one can calculate the travel time of density current, which can help to seize the right time for sluice gate controlling and raise the efficiency in sediment discharge, which is especially important at the period of severe water shortage. With the calculation of the sediment transport, one can find out sediment concentration of density current when released out of the reservoir. With the understanding, one can operate the dam (m) to optimize the combination of flow discharge and sediment concentration, both which even are from different origins . 

2         Law of density current movement

Study on basic theories and laws is not only the process of get insight into natural phenomena and its evolution laws, but also lays a foundation for utilizing those laws. With the analysis of the data of density current measured at the Xiaolangdi reservoir and the physical scale model for it, and a flume, and by verification of the equations developed by predecessors, an equation was put forward, which can quantitatively describe the conditions for continuous moving of density current under the conditions of natural incoming flow and sediment and present boundary of Xiaolangdi, and moving speed of density current and its sediment discharge efficiency under the different flow and sediment combinations. The equation has played an appropriate role in the flow and sediment regulation experiment.  

2.1  Composite resistance

Average resistance factor of density current is calculated by the equation by Mr. Fan Jiahua:

                             （1）

in which, is river bottom gradient; is change in thickness of density current;  and  is thickness and velocity of density current, respectively; is gravity correction factor. With equation (1), the composite resistance of density currentmeasured several times at Xiaolangdi were estimated , which ranges 0.022～0.029 in average.

2.2  Sediment carrying capacity

Equation (2) for sediment carrying capacity is established on the basis of energy consumption theory. It represents the law for sediment transportation of density current, i.e. the more sediment to come, the more sediment to be discharged. The equation is verified with the data in the field and the models for the Sanmenxia and Xiaolangdi reservoirs.

                     (2)

The variables are in kg, m and s, and the settling velocity can be expressed as follows:

                           (3)

where,is karman constant of turbid water; density of turbid water;mass settling velocity of sediment in turbidity water; falling velocity of sediment in clear water;  medium size of bed materials； medium size of the suspended load；sediment content of density current in volume by percentage, and the other symbols have the same meaning as the above.

2.3  Propagation time

The propagation (travel) period of density current is mainly subject to incoming flood peak, sediment concentration, backwater length, reservoir bottom gradient, etc. Although the movement of density current front shows a feature of unsteady flow, it can be calculated approximately with equation (4).

                                                （4）

in which, is mileage of immersing (or say, diving) point of density current from the dam; is flow discharge per unit width;is sediment content at the cross section of the immersing point；is reservoir bottom gradient（）；is coefficient.

2.4 Sediment release by density current

Sediment discharged by density current is calculated by using the formulas for sediment concentration and particle size grading developed by Han Qiwei and validated with the data from the Sanmenxia, Guanting and Hongshan reservoirs.

                                         （5）

                                       （6）

where, is grading percentage at immersing cross section；is saturation coefficient, to be calibrated with observed data；is grain size grading group number； is grain size settling velocity of group ； is grading percentage at outlet cross section；is effective falling velocity；is sedimentation percentage；is taken as 0.5.

2.5 Critical flow and sediment conditions for density current continuously moving to the dam

The conditions for density current generation and moving to a dam include not only flood duration, but also flow and sediment content. Namely, the energy provided with density current by flow and sediment processes must be much enough to compensate its loss.

Velocity and sediment carrying capacity of density current is proportional to its sediment concentration. Velocity and sediment concentration are complemented with each other. With the data of flow and sediment coming to the Xiaolangdi reservoir in 2001～2004 when density current was found to happen, the relationship between flow and sediment concentration was plotted in Fig.1, in which the numbers marked beside points refer to percentage of fine sediment weight. With Fig.1 analysis is done for the critical conditions for creating density current and making it move continuously to the dam. Three areas, A, B and C , can be divided according to point distribution.

In Area A, density current can move to the dam continuously, i.e. in the conditions that a flood to the Xiaolangdi reservoir lasts a certain period and that the weight of the suspended particles with ＜0.025mm is about 50%, and further 

If  500 m³/s ≤＜2000m³/s，and，then＞0；

If ＞2000m³/s，and ＞40 kg/m³，then＞0.

Area B covers two cases: one is that density current can move to the dam continuously and other is that it cannot.

The former case often has one of the following three conditions: 1) the flood is on the receding stage. On the stage the resistance to be overcome by density current during its approaching to the dam is smaller than that by its front; 2) although the sediment concentration coming to the reservoir is quite low, erosion takes place in the reach between its inlet to the reservoir and the end of the backwater reach, resulting in increase in sediment content at immersing cross section of density current; 3) the weight of fine sand entering the reservoir is over 75% of the total. 

In Area C ＜500 m³/s or ＜40 kg/m³，density current is usually unable to reach the dam .

When the inflow to the reservoir,  , and sediment concentration,  , are large,  the percentage () of the suspended sediment particles ( ≤0.025mm) is quite small, and the relationship between  the three variables is given as  .

It is necessary to note that the conditions for density current movement are influenced not only by flow and sediment conditions, but also boundary conditions. If there is a significant change in boundary conditions, the critical flow and sediment conditions, which are given above, would change accordingly.

3         Utilization and formation of density current

In the case of the Xiaolangdi reservoir, sediment, which is one of the conditions creating density current, comes from the upper reach, or from the reservoir reach itself. There are two sources for the sediment from the upper reach. One is from the floods which take place in the middle Yellow River. With optimum operation of the dam, ratios of sediment release from the dam can be increased, consequently extending the life of the Xiaolangdi reservoir. The other is the sediment which is deposited in the Sanmenxia Reservoir during non-flood season. With proper operating the dam, it is possible to make suitable flow and sediment processes, with which density current can carry sediment out of the reservoir, consequently reducing the deposition in the reservoir. The sediment, which originates from its own replenishment in the reservoir reach, refers to the deposits which are accumulated in the upper part of the reservoir reach. The sediment can be flushed by large flow and get into suspension. The fine part can be carried out of the reservoir in the form of density current.            

In the course of three field experiments of flow-sediment regulation, several modes for the regulation were established in view of different flow and sediment sources, the reservoir’s storage and boundary conditions. And the so-called flow and sediment regulation with the Xiaolangdi dam is, in essence, the regulation especially for both forming density current and making its movement through the reservoir reach and out of it. By proper operating the dam, density current can be produced and take the sediment out of the reservoir, so realizing multiple objectives like reducing sedimentation in reservoir, making a sediment blanket behind the dam, and adjusting deposition forms.   

3.1 Natural flood-caused density current regulation and utilization

High-concentrated floods often occur in the middle Yellow River during flood season. For the Xiaolangdi reservoir, which is in impoundment stage, removing the sediment through density current is an effective way for sedimentation reduction. The multi-objective regulation done in the first two field experiments on the YR has been successfully realized by taking full advantage of characteristics and laws of density current.

(1)    Operate the dams to regulate flow and sediment required

The first flow and sediment regulating field experiment on the YR takes no sedimentation or even erosion in the lower YR as one of major goals. In the operating scheme of the experiment, the average sediment concentration is suggested to be less than 20kg/m³ at Huayuankou Gauging Station. Therefore, how to control the outlet tunnels to produce sediment concentration as expected is the hard nut to crack in the experiment. In accordance with the known characteristics and laws of density current transport in Xiaolangdi, monitoring of the generation, propagation time, movement, sediment release, flow and sediment distribution and other parameters was done in the process of the experiment. With the monitored data, and by lifting and closing the flow release tunnels in the Sanmenxia dam, natural flow and sediment processes from the middle Yellow River was regulated effectively and the released flow and sediment successfully formed density current in the downstream Xiaolangdi reservoir, which went continuously to the dam. Flow release tunnels in the Xiaolangdi dam at different elevations were operated to release flow and sediment processes as expected.     

（2）Turbid reservoir generated by density current is utilized for spatial joint of flow and sediment

When the density current reaches the dam, it will accumulate behind the dam and form into a turbidity reservoir if it has not been released out of the reservoir in time. As its particles are extremely small, the suspended sediment often falls in a turbidity body slowly. That feature enables the flow and sediment regulation more flexible, which has been applied in 2003’ field experiment to match well flow and sediment from different places.  

In the early August of 2003 a turbid reservoir was shaped in the Xiaolangdi reservoir and the elevation of the interface between clear and turbidity water changed little until August 28. When the second density current moved to the dam at the end of that month, the interface rose rapidly, even reached 204.16 m in elevation on 3^rd Sep. And it had a thickness of 22.2 m then. The turbid reservoir was as large as about 0.9 billion m³ containing suspended load as large as 0.1 billion t.

In the second field experiment, by operating the flow release tunnels at different elevations in the Xiaolangdi dam, temporally-varying flow discharge and sediment concentration processes, the former having a certain duration, were created such that the flow and sediment, which have been joined with “clear water” coming from the Yi river and the Luo river and the Qin river downstream of Xiaolangdi, had a harmonious relationship at Huayuankou station, which is so called spatial flow and sediment joint. In the filed experiment, the sediment released from the Xiaolangdi reservoir amounted to 0.0815 billion t. Meanwhile, other goals like discharging more sediment from the Xiaolangdi reservoir and erosion of the whole lower YR course were realized.

（3）Elongate sediment release time by joint operation of dams

Under a certain boundary condition of a reservoir, continuous movement of density current and significant sediment release need adequate energy and lasting time of density current. The energy of density current depends on the flow and sediment conditions for its formation. Large inflow and high sediment concentration with more fine particles provide the density current with high energy and big starting speed. Its lasting time depends on how long the flood lasts. The shorter duration the flood has, the shorter the time for sediment release by density current from the reservoir is. When the flood flow from the upper reach decreases so that it cannot provide density current with enough energy, the density current will soon cease and disappear.          

The operating of the Sanmenxia dam can have a big effect on the sediment discharge by density current through the Xiaolangdi. When a flood comes from the middle Yellow River, the Sanmenxia empties its water for flushing, which can increase the duration and sediment concentration of the flood entering the Xiaolangdi reservoir. That is quite favorable for the sediment discharge by the density current.

3.2 Man-made density current formation and utilization

The third field experiment in the YR was carried out at the time of no flood occurring in the middle reach. In the experiment, by exact operating the Wanjiazhai dam, the Sanmenxia dam and the Xiaolangdi dam and releasing the water impounded above the flood control level in the reservoirs of Wangjiazhai and Sanmenxia, the sediment deposited both in the Sanmenxia reservoir and in the upper part of the Xiaolangdi reservoir reach was washed out and created the density current that then took sediment out of the Xiaolangdi reservoir. Objectives like sedimentation reduction and adjusting deposition form in the reservoirs have been successfully achieved. 

（1）Work out a scheme for regulation following law for density current transport

To create density current and make it move to a dam requires that flow and sediment process which have created the density current remain able to sustain its movement continuously. This means that the flood running into a reservoir shall supply energy enough to density current to cover energy loss along the course and at the local places, otherwise, the density current may vanish halfway.  

The key point in the 2004’field experiment is how to determine flow discharge and its timing from the Sanmenxia and Wanjiazhai dams. Prior to and during the experiment, many scenarios were compared about scouring process and sediment release effect by density current through the Sanmenxia and Xiaolangdi reservoirs under different flow discharge timing and flow process from the Sanmenxia and Wanjiazhai reservoirs, which are based on the knowledge of the laws for immersing , continuous movement and sediment release capacity of density current at the Xiaolangdi reservoir, as well as flow and sediment movement in the Sanmenxia reservoir and open channel flow. Some key technical issues were also extensively studied.    

① Magnitude order of outflow from the Sanmenxia dam. Releasing water from the Sanmenxia dam aims at adjusting sedimentation pattern in the Xiaolangdi Reservoir and generating density current there. Thus, determination of the outflow from the Sanmenxia reservoir needs consideration of two factors: a) the outflow should be sufficient to change the deposition delta in the Xiaolangdi reservoir , i.e. to fully adjust its upper part of the XLD reservoir in both transverse and longitudinal directions; b) the outflow should provide large energy to wash away the silted in the delta so that the sediment floated in water can shape density current, which then can move continuously to the dam. The study results indicate that the flow released from the Sanmenxia reservoir shall not be less than 2000 m³/s.

② Matching flow with sediment content. Content of sediment carried by flow, especially the content of fine particles is a critical factor in sediment discharge by density current. Insight to the formation of deposition delta in the Xiaolangdi reservoir indicates that percentage of fine particles is quite low. So, density current can be generated by two sediment sources, one is the deposition delta in the Xiaolangdi reservoir, which can be suspended mainly by large flow released from the Sanmenxia dam. The other is fine sediment deposited in the channel of the Sanmenxia reservoir, which can be stirred up by the flow released from the Wanjiazhai dam when the water in the Sanmenxia Reservoir is at low level or the reservoir empties its storage .

③ matching flow released from the Wanjiazhai dam with the flow the Sanmenxia dam (i.e., spatial joint). To form density current and discharge sediment through it, some kind of flow (in term of magnitude and duration) and adequate fine sediment in water are needed. Therefore, the needed magnitude of flow discharge from the Wanjiazhai and Sanmenxia dams should be such that they not only make sure the flow from the two sources match well, but also the flow can erode and carry a certain amount of sediment during the flow going ahead. The analysis of different regulation schemes shows that the peak of sediment process out of the Sanmenxia dam usually appear when it is close to the empty state meanwhile the flow coming from the Wanjiazhai dam is flushing the sediment in the Sanmenxia reservoir. The flow released from the Wanjiazhai dam should be such that when it reaches the Sanmenxia reservoir, the water level in the latter has been lowered to lower than 310m. The flow released from the Sanmenxia dam should increase to empty its storage as soon as possible so that the flow discharged from the Wanjiazhai dam can cause progressive and retrogressive erosion in the Sanmenxia reservoir, consequently to flush as much the deposits in the reservoir out of the reservoir as possible. The flow and sediment will serve as power for generating the density current in the XLD reservoir.     

（2）The experiment results achieved the objectives expected

The objectives of the experiments were realized in the third experiment:

① The deposition pattern at the tail (end) of the Xiaolangdi reservoir was successfully adjusted. By way of man-made disturbance at its end and natural flow flushing, the apex of the deposition delta moved downstream from the 70km from the dam to the 47km and 0.1329 billion m³ of sediment in the delta was washed away.

② Density current was formed and it took the sediment out of the reservoir successfully. The formation of sensity current was made through two stages. The first one started at 15:00 of July 7 when the Sanmenxia dam released clear water and it caused heavy scouring at the deposition delta of the Xiaolangdi reservoir and the resultant density current immersed at No. 34 cross section, about 57km upstream from the dam, and marched towards the dam without stop. The second took place at 8:00 of July 7, at that time the flow released from Wanjiazhai met with that from the Sanmenxia. Then the flow discharged from the latter was increased to wash away its deposits there. The density current started to carry sediment out of the Xiaolangdi reservoir at 13:50 of July 8.

③ More in-depth knowledge of density current movement law was obtained. The third experiment experiences a process from practice to knowledge to practice. The more in-depth understanding would be of importance for the filed experiment of the kind in future.

4         Conclusions

（1）At the early stage of the Xiaolangdi dam operation, which is for sediment impoundment, the sediment, which flowed into it,  cannot have been released from it without density current formed. It is clear that following density current law, proper operation of the dam(s) can lengthen their lives.

（2）Analysis of all the data, which were measured in the field, in an experimental flume and a physical scale model, and verification by the equations developed by predecessors leads to establishment of a new equation, which can quantitatively describe moving speed of density current and its sediment discharge efficiency under the conditions of natural incoming flow and sediment and present boundary of the Xiaolangdi reservoir, continuous moving conditions of density current and different flow and sediment combinations. The equation has played an appropriate role in the experiments.

（3）In the first two field  experiments, such targets as sedimentation reduction in the reservoirs, sediment blanket formation behind the dam, spatial junction (matching) of flow and sediment for the regulation in the first two experiments on the YR have been successfully realized by taking full advantage of characteristics and laws of density current for sediment discharge, and by rational regulation of the high-concentrated floods. 

(4)The third experiment on the YR washed out the sediment both in the Sanmenxia reservoir in the non-flood season and in the upper part of the Xiaolangdi Reservoir area and furthermore, created the density current that dragged sediment out of he Reservoir by joint operating the Wanjiazhai, Sanmenxia and Xiaolangdi reservoirs, and by making the most of the water above flood control limit level in the Wanjiazhai and Sanmenxia reservoirs, so that the targets like sedimentation reduction and adjusting deposition pattern have been successfully achieved.

References

Qian Ning, Fan Jiahua , et al. Density current, Water Press, 1957.

Han Qiwei, Reservoir Deposition , Science Press, 2003.

Zhang Junhua, “Method for Simulating Density Current in the Sediment-laden River and Application ” (dissertation for Doctor degree), Beijing University of Aeronautics & Astronautics, 2002. 

Li Shuxia, Zhang Junhua, Liang Guoting, Qu Shaojun, et al. Special Report for Design of Creating Density current for Sediment Discharge through the Xiaolangdi Reservoir in Yellow River Flow -Sediment Regulation Field Experiment in 2004, YRIHR, 2004.

Li Shuxia, Ma Huaibao, Zhang Junhua, Chen Shukui, et al. Annual Special Report 3 for Consultation and Tracking Research of YRIHR: Xiaolangdi Reservoir Operation and Flow and Sediment Movement Characteristics in 2002, YRIHR, 2004.

Li Shuxia, Zhang Junhua, Chen Shukui, Ma Huaibao et al. Annual Special Report 5 for Consultation and Tracking Research of YRIHR: Xiaolangdi Reservoir Operation and Flow and Sediment Movement Characteristics in 2002, YRIHR, 2003.

Zhang Junhua, Chen Shukui, Li Shuxia, Ma Huaibao, et al. Verification of the Model Experiment  on Density Current through the Xiaolangdi Reservoir, YRIHR, 2002.

Source:  www.yellowriver.gov.cn   Editor:HuangFeng