A Numerical Study of the Flow and Sediment Interaction in the Middle Reach of the Huai River

: In recent years, the incoming sediments from upstream of the Huai River have continuously decreased. The relationship between ﬂow and sediment has signiﬁcantly changed. Therefore, the erosion and deposition characteristics of the river could be affected. To investigate this interaction between ﬂow and sediment, the present study was conducted using the Wanglin section in the middle reach of the Huai River as the study site. A 1D hydrodynamic model was developed and validated using ﬁeld data. Data from 1985–2014 were used as a continuous series while data from 2004–2014 were used as a repetitive series. The sediment variation and distribution processes at different locations were discussed. It was found that the river channel displayed several notable characteristics. In the ﬂow direction, the channel had frontal erosion and backward deposition. The variation rate was relatively slow. With reduced sediment, the overall deposition at the Wanglin section was signiﬁcantly mitigated. Future recommendations are provided based on the present simulation for ﬂood mitigation along the Huai River.


Introduction
Predicting the response of natural or man-made channels to imposed supplies of flow and sediment is one of the most difficult practical problems faced by hydraulic engineers. The flow of the river moves the sediment and the channel bed is altered by erosion and the deposition of sediment. The shape of the river channel further modifies the flow. The interaction between flow and sediment is one of the primary dynamic factors in shaping riverbed channels. This complex interaction has been a continuous interest for river researchers and engineers. It plays an important role in determining erosion and deposition characteristics in natural river channels [1]. Much work has been conducted globally in the past to study the interaction between vegetation, flow and sediment [2][3][4], over grassed areas [5], and through numerical simulations [6,7]. However, few studies can be found which investigate the interaction of flow and sediment in China. A research gap was noted. In recent years, significant changes have been noted in flow and sediment interaction due to the combined effects of climate change and human activities. Some changes are noted along the middle reach of Yangtze River and the estuary of the Yellow River. The riverine ecosystems have been affected by the changes in the flow and sediment relationship. Additionally, as a major river in China, the Huai River is also notoriously vulnerable to flooding. The interaction between flow and sediment along the Huai River has been significantly changed. A significant reduction in sediment has been noted in the middle reach of the Huai River [8]. The main reasons for the reduction in sediment include: the construction of hydraulics structures, such as dams and sluices; soil conservation practice; and high-intensity sand mining. As shown in Figure 1, the average annual sediment runoff in the mainstream station of Lutaizi has decreased from 18 million tons in the 1950s to 3 million tons in 2000. However, the flow rate has remained relatively constant over the years. The decrease in sediment can have a significant impact to river channel development in the Huai River, which has received wide attention. Yu and Yu et al. [9][10][11] analyzed the erosion and deposition characteristics of the mainstream channel based on field data. It was noted that the deposition from Wangjiaba to Lutaizi was reduced, while from Lutaizi to Bengbu, the sediment movement changed from deposition to erosion. Between Bengbu and Fushan, further erosion was noted. Liu and Yang et al. [12,13], used topographic data of river cross-sections in the mainstream of the Huai River gathered over the past 70 years. It was found that the river channel erosion had been significantly increased due to sediment mining activities, which caused an uneven channel cutting in many sections of the Huai River. Moreover, with a deep cut and steep slope, river banks have a high potential of collapse, which poses a significant threat to flood control, navigation and shoreline utilizations. The behavior of sediment transport could potentially increase the flooding risk and pose a significant threat to public safety [14]. From the 1990s onwards, flood disasters in the Huai River have shown an increasing trend [15]. Investigation into the flow and water interaction in the Huai River is thus urgently needed. gathered over the past 70 years. It was found that the river channel erosion had been sig-nificantly increased due to sediment mining activities, which caused an uneven channel cutting in many sections of the Huai River. Moreover, with a deep cut and steep slope, river banks have a high potential of collapse, which poses a significant threat to flood control, navigation and shoreline utilizations. The behavior of sediment transport could potentially increase the flooding risk and pose a significant threat to public safety [14]. From the 1990s onwards, flood disasters in the Huai River have shown an increasing trend [15] . Investigation into the flow and water interaction in the Huai River is thus urgently needed.
Previous studies focused on the relationship between flow and sediment along the Huai River are mainly based on field data analysis or the temporal evolution of sediment movement. It is difficult to predict the long-term equilibrium sediment variation considering the many influencing parameters. The detailed characteristics of the river channel variation are not well understood. To date, many numerical models of river sedimentation have been developed. Some of the models, such as Deflt3D and EFDC, have been well applied to rivers. However, none of these models have been applied to the middle reach of the Huai River. It is also noted that in many cases, it is not reasonable to apply a 3D model to a river with a width of several hundred channels and very limited cross-sections. A 1D flow model is more appropriate [16]. In the present study, a 1D hydrodynamic model was used to investigate the interaction of flow and sediment along the Huai River using scenario analysis. The impacts of flow variation on sediment were numerical simulated, which could provide a direct insight to allow decision makers to better manage the Huai River.

Study Site
The middle reach of the Huai River, from Wangjiaba to Linhuagang (Wanglin section), was used as the study site for this simulation. This section is located at the transition Previous studies focused on the relationship between flow and sediment along the Huai River are mainly based on field data analysis or the temporal evolution of sediment movement. It is difficult to predict the long-term equilibrium sediment variation considering the many influencing parameters. The detailed characteristics of the river channel variation are not well understood. To date, many numerical models of river sedimentation have been developed. Some of the models, such as Deflt3D and EFDC, have been well applied to rivers. However, none of these models have been applied to the middle reach of the Huai River. It is also noted that in many cases, it is not reasonable to apply a 3D model to a river with a width of several hundred channels and very limited cross-sections. A 1D flow model is more appropriate [16]. In the present study, a 1D hydrodynamic model was used to investigate the interaction of flow and sediment along the Huai River using scenario analysis. The impacts of flow variation on sediment were numerical simulated, which could provide a direct insight to allow decision makers to better manage the Huai River.

Study Site
The middle reach of the Huai River, from Wangjiaba to Linhuagang (Wanglin section), was used as the study site for this simulation. This section is located at the transition zone between the upstream and middle reach of the river, in a region comprising mountains and plains. A higher concentration of sediment was noted in this region due to the changes in the river channel slope and velocity [13]. Additionally, a basin-wide flood occurred in this Water 2021, 13, 2041 3 of 11 section in July 2020, with overland flooding reaching heights of 0.22-0.46 m. The flooding had a significant impact on the local economy and communities. The current flow capacity from Wangjiaba to Nanzhaoji is around 6000 m 3 /s, which is below the designed flow rate of 7400 m 3 /s. Urgent action is required to investigate the relationship between flow and sediment in order to mitigate flooding risk.
The location of the study site can be found in Figure 2. In total, the Wanglin section is 110.98 km in length, with high elevations on both sides and low elevations in the middle. The tributaries include the Hong River, the Hong River Flood Diversion Channel, the Gu River, the Run River, the Bailu River and the Shiguan River. Most of these branches are relatively short in length, but high in velocities. Both the Hong River and the Shiguan River have large watersheds compared to the other branches. In the study area, the section between Wangjiaba to Nanzhaoji is treated as a flooding basin, as shown in Figure 2. From Nanzhaoji to Linhuagang, the river channel is relatively straight. Linhuagang station is the largest water control station along the middle reach of the Huai River.  To understand the relationship between flow and incoming sediment, data from between 1985 and 2014 were collected from the following stations: Wangjiaba, Shangang, Dili and Jiangjiaji. It was found that the multiyear average flow rate at Wangjiaba is 318 m 3 /s, with 2.99 million tons of sediment. The flood season is from June to September, which accounts for 61% of the annual flow and 75% of the annual sediment [17,18]. To further present the relationship between flow rate and sediment yield in the study site, the K-mean method was used, which can be seen in Table 1. A relationship between flow rate and sediment can be observed. The rich/medium/poor vs. rich/medium/poor is used to indicate the relationship between flow rate and sediment. A high flow rate normally has a higher sediment yield. The numerical study was conducted in order to understand the relationship between flow rate and sediment in the study site.

Governing Equations
Many branches have been noted at the Wanglin section, as seen in Figure 2. The unsteady flow model was selected, as it achieved better accuracy in the flooding simulation and sediment calculation. Additionally, the flow in this section was dominated by suspended sediment transport. Therefore, the unsteady flow and sediment model was applied. The governing equations can be found below.

Continuity equation:
∂Q ∂x Momentum equation: ∂Q ∂t Suspended sediment advection equation: Sediment transport equilibrium equation: where Q is the flow rate (m 3 /s); Z is the water level (m); B is the water surface width (m); x is the flow path (m); t is the time (s); q is the side inflow flow rate, positive for inflow and negative for outflow (m 3 /s); A is the cross-sectional area (m 2 ); n is roughness factor; α is the coefficient of momentum correction; V x is the component of side inlet velocity on the mainstream (m/s); S k and S * k are the sediment concentration and sediment holding capacity of the group k particle size (kg/m 3 ); ω k is settling velocity of the group k particle size(m/s); k s and m are calibration parameters of sediment transport formula-gain and exponent; a s . is coefficient of saturation recovery; γ is the dry capacity of sediment (kg/m 3 ); A d . is the area of deposition (m 2 ); L(n) and M(n) are the total numbers of inlet and outlet reaches connected with branching point; and n. S i,k . and S j,k are the sediment concentration of the group k sediment grain size (kg/m 3 ).
The model uses Visual C#2013 as the platform. The SQL Server 2012 is used as the database. The two modules used are a flow calculation module and sediment transport module. The two modules are connected using a non-coupling approach. The flow is calculated first to provide hydraulic parameters for the sediment module. The discrete solution of each module can be found in the references [19][20][21][22][23].

Model Calibration and Validation
The model was calibrated using field data from Honghekou to Lutaizi in the mainstream of the Huai River, which covers the study area of the Wanglin section. The flow rate, water level and sediment concentration data from 1999 to 2008 were used. In the present study, the aerial survey map of 1999 was adopted for model calculation.
The application of erosion and deposition in the reach of the mainstream of the Huai River below Bengbu showed that the values of some parameters in the model were relatively stable. The sediment carrying capacity index m had a value of around 0.92; the average value of a s is between 0.5 and 0.6. Empirical values were used for such parameters to reduce uncertainty. From the debugging and calculation, the roughness of the main channel was 0.0215 and the roughness of the bank regions was 0.034. The sediment carrying capacity coefficient ks changed with the erosion and deposition of the river channel. When sand content S was near the sand carrying capacity S*, a value of ks = 0.025 was used. Under other conditions, k s = 0.025∆k, in which ∆k is the adjustment coefficient, which can be expressed as follows: The perpendicular method was used to allocate the erosion and deposition area, which can be seen below [20].
In which δZ i ∆B i are the thickness and width of erosion and deposition in the perpendicular direction; δA is the calculated erosion and deposition are of the cross-section; η i is the perpendicular flow depth; and c is the adjustment index, which equals to 1.5 for scouring and 0.5 for deposition.
The comparison between the field data and simulation can be found in Table 2. It should be noted that for both calibration and validation, the difference between the field data and simulation is below 15%, with the exception of 2001. The 2005 data are used in Figure 3 to demonstrate the simulation results. A good agreement was reached between the simulation and field data regarding both water level and flow rate. The present model was then applied to the Wanglin section for erosion and deposition simulation.

Boundary Conditions
The computational boundary conditions were determined using a typical flow and sediment relationship for the analysis of long-term river channel variation. It was noted that the incoming sediment to the Huai River continuously decreased from 1950 onwards. After 2000, this decreasing trend stabilized. It was further analyzed, using statistical analysis, that the incoming sediment to the Huai River would be low in the next few years [24] .
In the present study, the following two scenarios of flow and sediment transport rate were conducted, as shown in Table 3. Scenario 1 was a continuous series considering the flow-sediment interaction from 1985 to 2014. In this scenario, 30 years of data were used to investigate the impacts of flow-sediment interaction to river channel morphology. Scenario 1 can be used as a baseline study. Scenario 2 was a repetitive series using field data from 2000 to 2014. The collected data were repeated once to form a 30-year flow-sediment interaction. This set of data were based on the field data which showed a good indication of current situations in the Huai River, with a 17% reduction in the incoming sediment. Using this scenario, the future river channel morphology can be further predicted. The modeling region from Wangjiaba to Linhuaigang is shown in Figure 1. From Wangji to the Meng River station, the initial topography was constructed based on the most recent measurement from 2018 with cross-sections 500 m apart. From Wangji to the

Boundary Conditions
The computational boundary conditions were determined using a typical flow and sediment relationship for the analysis of long-term river channel variation. It was noted that the incoming sediment to the Huai River continuously decreased from 1950 onwards. After 2000, this decreasing trend stabilized. It was further analyzed, using statistical analysis, that the incoming sediment to the Huai River would be low in the next few years [24].
In the present study, the following two scenarios of flow and sediment transport rate were conducted, as shown in Table 3. Scenario 1 was a continuous series considering the flow-sediment interaction from 1985 to 2014. In this scenario, 30 years of data were used to investigate the impacts of flow-sediment interaction to river channel morphology. Scenario 1 can be used as a baseline study. Scenario 2 was a repetitive series using field data from 2000 to 2014. The collected data were repeated once to form a 30-year flow-sediment interaction. This set of data were based on the field data which showed a good indication of current situations in the Huai River, with a 17% reduction in the incoming sediment. Using this scenario, the future river channel morphology can be further predicted. The modeling region from Wangjiaba to Linhuaigang is shown in Figure 1. From Wangji to the Meng River station, the initial topography was constructed based on the most recent measurement from 2018 with cross-sections 500 m apart. From Wangji to the Linhuagang station, the cross-section measurements from 2011 300 m apart were used. The proposed two scenarios were used regarding upstream boundary conditions, while downstream boundary condition can be analyzed using the stage-discharge relation curve at Linhuaigang station. The sediment diameter was selected from a field measurement in 2008, with d 50 equal to 0.04 mm.
To ensure the stability of calculation, 300 s was used as time step. For each time step, daily data were used to calculate the flow and sediment boundary. It is noted that using the time period of 30 years was very time consuming in regard to the calculation. A threshold was used for erosion and deposition. The file was only updated when the cumulative elevation change exceeded the threshold. In the present research, a threshold of 0.05 m was used.

Erosion and Deposition Process
The sediment deposition under the simulated scenarios was numerically simulated. From the simulation, it was found that the deposition at the Wanglin station could be significantly reduced at Scenario 2, as shown in Figure 4. At the end of 10 years, the sediment deposition under Scenario 2 was 2.01 million m 3 , which is 63.7% less compared to that of Scenario 1. At the end of the 30-year calculation period, the sediment deposited at the Wanglin station was calculated to be 6.19 million m 3 under Scenario 2, which is 34.6% less compared to that of Scenario 1. The main difference between the two scenarios is in the first 15 years. Due to the increased incoming sediment from 1987 to 1991, the sediment concentration was accumulated rapidly in Scenario 1. The largest difference was regarding the value at the end of 12 years, with an amount of 4.23 million m 3 .
ing the value at the end of 12 years, with an amount of 4.23 million m .
From the simulation, Wanglin station shows a continuous accumulation of sediment under both scenarios. After 30 years, no equilibrium state was reached. It is extremely hard to transform the river channel to stabilized conditions considering the many human activities undertaken in this section. Sediment mining should be prohibited at this section. It may take hundreds of years for the river channel to reach an equilibrium state under natural flow conditions. From the simulation, Wanglin station shows a continuous accumulation of sediment under both scenarios. After 30 years, no equilibrium state was reached. It is extremely hard to transform the river channel to stabilized conditions considering the many human activities undertaken in this section. Sediment mining should be prohibited at this section. It may take hundreds of years for the river channel to reach an equilibrium state under natural flow conditions. Table 4 is used to show the relationship between flow rate and sediment concentration in the past 30 years. The relationships between deposition and erosion at different years are presented using the maximum value and average value. It is found that a higher flow rate can result in a relative larger deposition value. Overall, the erosion is more favorable at a larger flow rate and lower incoming sediment, which can avoid deposition. From the table, the average ratio of incoming sediment to transported sediment is around 0.97 for Data Number 2, which indicates a state of relative equilibrium. In certain years-for example, Data Number 5 in Table 4-with limited flow and large amounts of incoming sediment, the sediment deposition could become more obvious. In the repetitive series, it may take a shorter period of time to reach a state of equilibrium.

Deposition Distribution
The simulated deposition at the end of the 30 years is presented in Table 5. From the numerical modeling, it can be found that the section from Wangjiaba to Sanhejian is dominated by erosion, with an amount of 1.05 million m 3 . The section from Runheji to Wangji shows an equilibrium state. The other sections in the middle reach of the Huai River have a major deposition with an amount of 7.01 million m 3 of sediment, which accounts for 74% of the total deposition. In the transverse direction, all the sections have erosion in the main channel and deposition along the bank. The average erosion depth is around 30 cm, while the deposition height is 15 cm. In Scenario 2, with repetitive series, the main reach of the Huai River shows erosion in the upper reach and deposition in the downstream of Sanhejian station. Further analysis indicates that the upstream has a larger reduction in deposition, especially from Wangjiaba station to Sanhejian station. The middle reach of the Huai River shows dominated erosion behavior in the main channel under the continuous series of Scenario 1. Although the changes are not significant, the impacts of incoming sediment are very clear. Overall, the main reach of the Huai River shows increasing erosion and decreasing deposition from the simulation. Table 5. Distribution of river erosion and deposition at the end of the simulated scenarios (unit: 10,000 m 3 ).

Recommendations
The recommendations for flooding mitigation in the middle reach of the Huai River are presented. The Wanglin section is used as the test site. For flooding mitigation, it is important to maintain stabilization of the bank. From the simulation, it is found that the overall trend of the Huai River is erosion. Some recommendations are provided, as follows: (1) Main channel dredging The simulation indicates that the Wanglin section will be dominated by erosion. However, the main channel in this section is around 250 m in width. The flow capacity in the main channel is around 1500 m 3 /s, which is less than 1/5 of the bankfull value. The main channel is relatively small, which presents a larger threat to overland flooding. Dredging the main channel is thus recommended. The present study indicates that dredging the channel is preferable to widening the main channel.
(2) Floodplain protection The beach bank along this section is close to 1500 m in length and has many functions, including water drainage, water storage, and sediment deposition. From the simulation, less incoming sediment results in a reduction in sediment deposition, which may impact