Application of a Depth-Integrated Two-Dimensional Numerical Model to the Lauffen Reservoir on the Neckar River

Yichun Xu¹, Sam S.Y. Wang² and Yafei Jia³

1 Res. Sci., National Ctr. for Computational Hydrosci. and Engrg., Univ. of Mississippi, University, MS 38677. E-mail: xu@ncche.olemiss.edu

2 PF.A.P. Barnard Distinguished Prof. And Dir., E-mail: wang@ncche.olemiss.edu. The same address.

3 Assoc. Prof., E-mail: jia@ncche.olemiss.edu. The same address 

Abstract: The numerical model CCHE2D has been applied to simulate flow field for the Lauffen Reservoir on the Neckar River, Germany. The model predicted water surfaces and velocity fields under unsteady states. Manning’s coefficient was identified in the model calibration using measured field data. The calibrated model was then validated using more filed data measured during several flood events. The results showed that predicted water surface elevations were in a good agreement with the field measurements and imply that the CCHE2D model can simulate a unsteady natural river channel flow with a complicated geometry with sharp bends and wider flood plains. 

Keywords: numerical modeling, unsteady flow

1    INTRODUCTION

Open channel flow simulation present challenges. A cross-section geometry and morphology of natural river channels are complicated and change along the channel course resulting in a complex flow field characterized by turbulence, secondary currents and vortices. Successful flow simulation in a natural river channel requires numerical methods to be capable of taking into account sharp bends, irregular channel topography, bed roughness in different scales, vegetation on the flood plains. Many efforts have been given to compute such complicated flow field using CFD method in last decades.

CCHE2D model is a depth-integrated two-dimensional numerical model, which can be used to simulate unsteady flow in natural river channels with complicated arbitrary cross sections. This paper presents a validation of CCHE2D model using field measurements through applying it to the Lauffen Reservoir, on the Neckar River, Germany. Realistic simulation of over bank flow is an important task for flood control and river management in the Lauffen Reservoir, since overbank flow frequently occurs in this reach. Calculation reproduced the temporal and spatial variation of the flow and results agree with the measured data well. The validation shows that the numerical model, CCHE2D, is a useful tool to simulate unsteady flows in natural river channels with very complicated geometry.

Unsteady depth-integrated Reynold’s equations and continuity equation are solved in CCHE2D model using mixed finite element and finite volume method. Three turbulence closure schemes, the depth integrated parabolic eddy viscosity, the depth integrated mixing length eddy viscosity and the k-e model, are available for computing Reynold’s stress. A detail description of the model CCHE2D is beyond the scope of this paper, it can be found in the publications Jia and Wang [1,3].

2    DESCRIPTION OF STUDY REACH

The Lauffen Reservoir on the Neckar River is a channel reservoir, built in 1938 - 1970. The Lauffen Reservoir was located near the Stuttgart, Germany (Fig. 1). It stretches 12 km long from the upstream Bitigheim to the downstream Lauffen with two 180° sharp bends and wide large floodplains in the reach between 129.0 km and 132.3 km. Since 1950 the suspended sediment inflow of the reservoir decreased considerably due to the construction of a cascade of 13 dams in the upstream channel. According to channel profiles in the Lauffen Reservoir surveyed by Wasser- und Schiffahrtsverwaetung, Germany, in different years, the channel bed elevations have been changed considerably, especially in the lower reach between 125.2 and 126.0 km. Over the period of 1950 to 1973, sediments of about 2 m in the depth were deposited in the area near the weir structure between 125.2 km and 130.0 km. The discharge at the gauge station of Lauffen varies from 14.1 m³/s to 1650 m³/s. The mean discharge is 88.5 m³/s. The Enz River discharge into the Neckar River, downstream of the Bitigheim Station. The mean discharge of the Enz River is 20 m³/s.

Fig. 1    Description of study reach, the Lauffen Reservoir on the Neckar River in Germany

the bend areas is finer than those in the straight channel reaches. Most cross section profiles were surveyed by Wasser- und Schiffahrtsverwartung. Interpolation was used for sections between surveyed sections. Moving boundary with wet and dry node technique was used to handle dynamically the water surface boundary which varies with water stages.

Model calibration was performed to identify the roughness coefficients. The data used for the calibration were the free surface elevation measured along the channel at the peak flow discharge of a flood event in 1990. The hydrograph of the flood event was used as boundary condition. A fixed water stage of 169.7m at the downstream boundary was applied. Bed material in the study reach is non-uniform and varies from coarse gravel to sand and fine clay from upstream to downstream. The Manning’s coefficient calibrated varies from 0.017 to 0.031 in the main channel from downstream to upstream and from 0.04 to 0.06 on the flood plains. Field data were measured along the river course near the left and right banks at the peak discharge of 1644 m³/s of flood 1990. Figure 2 shows the reproduced water surface elevation compared with measured data. From this figure one can see that the general agreement between the computation and measurements is good. The average difference between observed and predicted water surface elevation, , along the channel is less than 0.17 m, and the relative error, , is smaller than 4.6 %, where d is the water depths at the measured position, and i is a number of measured data. There exist larger differences in water surfaces near the inner and outer banks in the sharp bend reaches. The difference of water surface elevation at the left and right banks at the station 130.2 km is 8 cm, 171.95-171.87 m (compared with measured data, 3 cm, 171.73-171.76) and at the station of 130.8 km, 26 cm, 172.52-172.26 m (compared with measured data, 26 cm, 172.61-172.35m).

Fig. 2    Predicted water surface elevation along the channel course compared with field data.

3    MODEL VALIDATION

To evaluate the quality of calibration the CCHE2D model was then applied to simulate three flood events (1978, 1990, 1993) with the calibrated Manning’s coefficients. The water surface elevations recorded at the gauge station Bitigheim during these flood events were used for the model validation. The hydrograph of these floods have different characteristics, different flood duration, total volumes, peak discharges and discharge varying rates. The highest peak discharge was 1644 m³/s in the flood 1990, which is close to the highest historical discharge for the study reach. The validation using this data set would enhance our confidence on the model’s applicability to simulate unsteady flow in irregular natural channels.

Fig. 3    Comparison of computed and measured water surface elevation at Bitigheim station during the flood events, 1978,1990 and 1993

Figure 3 shows the comparison of the predicted unsteady water stages and measured data at Bitigheim station. The agreements of the comparison are satisfactory. The average differences between predicted and measured water stage at the Bitigheim station are 0.17, 0.13 and 0.15 m for the floods of 1978, 1990 and 1993. The maximum difference is 0.27m at the discharge of about 958 m³/s in 1993, the hydrograph near this point has steep gradient.

Additional information for validation of the model was an amount of measured data along the river course at the highest discharge stage, 1640 and 1335 m³/s during the flood events, 1978 and

1993, respectively. The average differences between observed and predicted water surface elevations, , along the river course is 0.38 m and 0.10 m, and the relative errors, , are less than 8.0% and 2.0% for the flood events of 1978 and 1993, respectively.  These error are partially attributed to the bed geometry used for the simulation, many cross section are interpolated using the relating measured sections, and to the accuracy of the calibrated roughness coefficients.

Fig. 4    Water surface elevation at the upstream during the flood events of 1978 and 1993

Fig. 5    Water surface elevation at the upstream during the flood event

To demonstrate the model’s capability of the computing unsteady flow with irregular channel morphology, simulated flow field at the peak flood discharge of 1644 m3/s (flood 1990) in the channel bends is presented in Figure 5. The area colored by blue in this figure shows the dry areas. Form it one can see clearly the flow patterns on the floodplains, secondary circulation driven by the main channel flow, near the station of 130 km and 131.2 km, and island zone, from 130.55 k to 130.8 km. The flow velocities near the inner bends are larger than that those near the outer bends. The simulated water surface near the inner bank is lower than that along the outer bank by 0.15 m at the station 130.9 km, and 0.17 m at the station 129.50 km at the peak discharge.

4    CONCLUSIONS

CCHE2D model has been applied to simulate flows in the Lauffen Reservoir on the Neckar River. The model was calibrated and validated using measured data in the field. The results can be summarized as follows:

The depth-averaged unsteady, free surface flows in a realistic river channel with complex geometry, sharp bends and wider floodplains, can be satisfactorily simulated by the CCHE2D model.

It is necessary to take into account the distribution of particle size of bed material to evaluate bed roughness coefficients for the main channel and the floodplains. The agreement of the predicted unsteady water stages and measured data indicated that the roughness coefficient is not a very sensitive parameter, if unsteady water stage prediction is concerned.  The error between the predicted measured water surface profiles are small. They could be induced by the uncertainties in the simulation, such as roughness, channel cross-sectional geometry and use of a curvilinear orthogonal coordinate as consistent with the main channel course.

The calculation results showed that the field measured and computed water surface elevation at the upstream, Bitigheim station, during flood events were in a good agreement. The average difference between predicted water surface elevation and observed data in the field, , was 0.16m and the relative error, , is less than 8.0% at the Bitigheim and was 0.19 m along the channel course for the floods of 1978, 1990 and 1993. This agreement indicates that the CCHE2D model can simulate a complicated natural river flow field with a high accuracy and under steady and unsteady flow conditions. The model is a reliable and useful tool for modeling hydrodynamics in natural river channels and promises well to give profitable guidance for engineering design.

References

[1]    Jia, Yafei and Sang, Sam S. Y., CCHE2D: A two-dimensional hydrodynamical and sediment transport model for unsteady open channel flows over loose bed. NCCHE technical report, The University of Mississippi, 1997.

[2]    Jia, Yafei and Sang, Sam S. Y., Numerical Model for Channel Flow and Morphological Change Studies. Journal Hydraulic Engineering, ASCE, 115(9), page 924-933, 1999.