Luo Lin¹, Deng Yun², Zhao Wenqian¹ and Li Jia¹

1Professors; ²Ph.D. Candidate

State Key Hydraulics Lab of High Speed Flows, Sichuan University

Chengdu, Sichuan 610065, China

Tel: +86-28-5401551 Fax: +86-28-5405148 E-mail: lluo1@mail.sc.cninfo.net

Abstract: The Sichuan province, southwestern China, has plentiful hydropower resources. The assessment of environmental impact for development of this type of projects is very important. For a large-scale deep reservoir, one of the planning projects, the temperature field or stratified behavior and/or outflow temperature is a key issue for ecosystem concern, especially during the spawning season for aquatic animals. Hence, the prediction of the outflow temperature is a pronounced task to assess the environment impact for this hydropower project. Based on the 2-D computation of the temperature field, which is described in a separate paper, the detailed 3-D temperature distribution near the dam and the outflow temperature were studied. The results showed that strong 3-D effect caused by power station intakes, and the different temperature distribution with the 2-D results under some circumstances. The 3-D effect is weaker with the water depth. When the reservoir operates in high-depth period, the 3-D and 2-D results were nearly agreed with each other. However, in low-depth operation, the quite difference of the temperature field was observed. The reasons for the above behavior have been discussed, and applicability of 2-D or 3-D numerical modeling for deep reservoir is investigated.

 

Keywords: deep reservoir, 3-D temperature field, 2-D/3D numerical modeling applicability

The environmental concern plays increasingly important role in developing hydropower projects today. Generally speaking, construction of dam will result in stratified flow, especially for deep reservoir, say, over 100m in depth. The planning project investigated here is a typical large-scale deep reservoir, located in Sichuan province, southwestern China. Its depth will be 220m high during October to January next year period, 160m high at May, and variations between these two depths in other durations. In this case, the temperature distribution right up to the dam, near the power station intakes, and the resulted outflow temperature would have very important effect on the downstream ecosystem.

Usually the power intakes would position at height of epilimnion or thermocline area in such reservoir. That means the sharp temperature variation would happen. Due to the 3-D effect of the power station intakes, which are arranged at both banks of the river for this project, and 290m up from the dam, the commonly used 2-D temperature calculation would not provide detail enough modeling information for the outflow temperature. Therefore, the 3-D modeling was introduced here to pinpoint the temperature distribution near the power intakes, and predict the outflow temperature to assess the impact of the dam built. The computational domain, which covers 10km long up the dam, coordinate system, and power station intakes arrangement are shown in Figure 1. [1][2][3]

Fig. 1 Calculation domain diagram

 

2    GOVERNING EQUATIONS AND COMPUTATION BOUNDARY CONDITIONS

The RANS solver adopted the k-ε model as the numerical turbulence closure model. The body fitted curvilinear coordinate system was used under the Cartesian axes. The uniform equation system is as follows:

                                   (1)

when q= 1, refer to continuity equation,

= u, v, w, momentum equations,

= h, energy equation,

= k, turbulence kinetic energy, and

= ε, turbulence dissipation rate.

J, U_i, and G_ij are the Jacobian transformation matrix, contravariant velocities, and diffusion metrics respectively. They are defined as

                                            (2)

is the effective turbulence diffusion coefficient, where, and σ_q stands for Prandtl number, their values shown on Table 1.

The source terms of the equation (1) are

represented continuity, momentum, energy, turbulence kinetic energy, and turbulence dissipation rate equation respectively.

Where P_r is the production rate for turbulence kinetic energy:

The constants of the k-ε model are shown in Table 2.

The computational boundary conditions were set as follows:

bed, banks and dam-no slip, adiabatic walls,

upstream inlet-uniform velocity profile, vertical temperature distribution adopted 2-D results,

power station intakes-mass conservative outflows,

water surface-symmetric surface.

Considering relative short distance of the computational domain, the surface heat exchange was neglected. According to an on-site measuring datum [4], the surface temperature raised about 1.5oC along 100km distance. Then ignorance of the surface heat flux should have no significant effect on the numerical solution. The numerical test confirmed that.

In order to calibrate the RANS solver, a similar deep reservoir, which operates for two years, was simulated first. The computational domain of the reservoir is shown in Figure 2. It is very similar to the project studied, except that it has only one side of power station intakes on left bank. The operation water depth of the reservoir varied from 150m to 170m during the simulation period. The same boundary conditions and modeling parameters were adopted for the calibration case. The results show that the simulated outflow temperature through power station intakes agreed with the measured data quite well, see Table 3.

After the calibration, the solver was used to simulate the studied case during a whole year period. The simulation results showed in Figure 3. The 2-D and 3-D computed outflow temperature, the related water depths were plotted in Figure 3 to compare with each other.

Fig. 2    Calibration Case Domain

Fig. 3     Simulation results and comparison with the water depth

From the results above, one can see that the 2-D and 3-D outflow temperatures were close during high-depth months, or 2-D model only can predict the temperature well. Nevertheless, during the low water depth months, the 2-D and 3-D predicted temperatures were quite different with each other. Especially on the lowest water depth month – May, the temperature difference reached 3.9oC. In order to provide further confidence for the 3-D results, two more commercial RANS solvers, CFX-5 and Fluent 5, were used to calculate the same case too. All of the three 3-D solvers gave the same result on the most different month, May. It should be said that the 3-D results were acceptable.

Now the problem is why there is so much different between 2-D and 3-D results during the low depth months. The authors believe the reason is that the strong 3-D effect dominated the flow near the power intakes at low-depth condition under such arrangement of the power intakes in this project. During the high depth operation of the reservoir, the 3-D effect of the power station intakes played some role on the flow field, but not the domination factor. Then the difference of temperature is not that big. Figure 4 plotted the 2-D and 3-D vertical temperature profiles of the mid-cross section at the position of power intakes for the months May and December. It can be seen that the 3-D mixing effect existed in both months, but the month May stronger than the month December. In other words, the water depth took a great impact factor on the 3-D effect, that’s because 1. the power station intakes located very near the surface in this project (only about 20m at May), and 2. the vertical 2-D assumption was no longer true under low-depth operation conditions.

Temperature( ℃ ) in May Temperature ( ℃ ) in December

Fig. 4     The vertical temperature profiles for May and December

Furthermore, considering the arrangement pattern of the power station intakes of this project, it is found that it was too complicated to make the 2-D assumption in this case. In 2-D simplified case, the outlet of reservoir can only be positioned at far end of the computation domain. Moreover, the whole width outlet has to be assumed, but usually the area of power station intakes took only a small part of a dam. On the other hand, low water depth pronounced this mismatch between 2-D model and 3-D realm. Then, it was not strange that big difference occurred between 2-D and 3-D computations.

One thing should be remembered, at high water depth and/or power station intakes far from the surface, 2-D model can did a very well work too. In short, water depth and the arrangement pattern of power station intakes should be taken into the first consideration for choosing 2-D or 3-D model to simulate the stratified flow problem near the dam.

From the above work, the following conclusion can be addressed:

(1) A 3-D numerical model was applied to simulate a planning hydropower project stratified flow problem near the dam, in order to assess the environmental impact of this project. Different results between 2-D and 3-D simulation were encountered.

(2) It was found that the water depth of the reservoir played a very important role in the 2-D and 3-D mismatch story. High water depth implied the good agreement of 2-D and 3-D simulation, and low water depth enhanced the difference of the results.

(3) It is believed that the depth of power station intakes under the surface contributed the disparity of the 2-D and 3-D computation. The shallower the depth, the bigger the discrepancy.

(4) Three RANS solvers provided the same 3-D results for this project. It should be considered that the 3-D simulation in this study was acceptable. Therefore, the 2-D results near the dam could not reflect the strong 3-D effect realm that dominated the flow under this circumstance.

(5) The criteria for choosing 2-D or 3-D model to simulate the stratified flow problem near the dam of a deep reservoir, therefore, should depend on operation water depth and power station intakes arrangement pattern.

[1]  Rodi, W., Prediction Methods for Turbulent Flows, McGraw-Hill International Book Company, New York, USA, 1980

[2]  Csanady, G.T., Hydrodynamics of large lakes, Annual Review of Fluid Mechanics, 7, pp357-385, 1975.

[3]  Johnson, B. H., A review of multidimensional reservoir hydrodynamics modeling, Proc. Of the Symp. on Surface Water Impoundments, H. F. Stefan, editor, ASCE, 1, pp497-507, 1980.

[4]  Report of the on-site temperature measurement of Ertan reservoir, Chengdu hydroelectric investigation and design institute of SPC, 2000 (in Chinese)

[5]  Using CFX-5, AEA Technology, 1999.

[6]  FLUENT 5 User’s Guide, FLUENT Inc., 1998.