Numerical characteristics study on Delft3D for simulating the density flow caused bytemperature difference in a reservoir flume
Zijun HU, Yanbing ZHAO, and Lei ZHANG (Taiyuan University ofTechnology, China), Yun LANG* (Hohai University, China), Weiwei
GUO (Shanxi institute of water science and hydropower)

Introduction
Generally, there are two vertical coordinate type to construct a three dimensionalmodel of D3D, one is z-coordinate, the other is σ-coordinate. The existing
improvement methods of D3D such as anti-creep correction and bottom grid
redistribution cannot completely quantitatively eliminate this error. Therefore, how tochoose a suitable vertical coordinate system in the simulation of temperature
stratified density flow in reservoir bay is still need a specific study for specific problem.
Based on the physical model experiments conducted by Johnson different typesof vertical grid coordinate were employed to establish the numerical models using
D3D software. By comparing the modeling results, general suggestions on coordinate
selection for simulating reservoir bay temperature stratified density flow using D3Dmodel are given.

ModelResultsAccording to Figure 3, the time when the outlet
water temperature starts to fall is t = 15 min, and thetime when the outlet water temperature calculatedby the z is 9 minutes later than the observed value.
At the end of the z-coordinate model, the outlet
water temperature is also much higher than theobserved value.
According to Figure 4, the thickness of thesubmerged density current in cold water is 0.12 m,
while the thickness of which in the z-coordinate
model is about 0.24 m. Moreover, the reverse
velocity of the upper layer is also significantly larger
than the observed value, which indicates that thevertical velocity gradient of the z-coordinate model
is small, which causes the speed of the submerged
cold water to be small, while the reverse velocity of
the upper layer is increased.

Figure 3. Water temperature change at the outlet over time ofdifferent vertical coordinate models.

Figure 4. Vertical velocity distribution at 11.43 m upstream at t =11 min of different coordinate models.

• The vertical grid resolution is important toaccurately simulate the cold submerged flowof the reservoir, but it is not the main causeof the calculation errors of the z-coordinate
reservoirmodel.
Table 3. Simulation cases set up to study the influence of bottom slopes in different
coordinate systems on results of density flow characteristics.
• The bottom slope is larger than 4 ‰, thesimulation results of the z-coordinate model
are affected by the step approximation,
resulting in a large calculation error, and theerror also increases as the bottom slope
increases.
Table 2. Simulation cases with different numbers of vertical grids based on z-coordinates

Figure 1. Sketch of the Generalized Reservoir Hydrodynamics (GRH) water tank of the experiment

Sketch of the experiment tank is shown in Figure 1. Its length is 24.39 m, thedownstream section size is 0.91 m × 0.91 m, and the upstream section size is 0.30 m
× 0.30 m. The water tank can be divided into two sections. The upstream section is6.10 m in length, 0.30 m in depth, and the width changes linearly from 0.30 m to 0.91
m. The downstream section is 18.29 m in length, 0.91 m in width, and linearly changes
from 0.30 m to 0.91 m in depth. At the initial moment, the model reservoir is in astationary and uniform state with a water temperature of 21.44 °C. During theexperiment, cold water at 16.67 °C was introduced from 0.46 m from the upstream
section, and the baffle restricted cold water from entering 0.15 m above the bottom.
The inflow and outflow discharge are both 0.00063 m3/s. The downstream section isan orifice with a diameter of 2.54 cm, 0.15 m from the bottom and in the middle ofthe section.
Table 1. Settings of σ-coordinate and z-coordinate model.

Figure 2. Sketch of bottom grid redistribution in z-coordinate model.

Figure 6. Water temperature at the outlet ofz-coordinate model with different vertical gridnumbers

Figure 7. Vertical velocity distribution at 11.43
m upstream at t = 11 min of z-coordinate
model with different vertical grid numbers.

Figure 8. Comparison results of σ-coordinate andz-coordinate model outlet water temperature
under different bottom slope conditions

Conclusionü The selection of the vertical coordinate system has a large impact on the accuracy of thetemperature stratification flow simulation.
ü When the density currents is along the bottom of the reservoir, the model accuracy using the σcoordinate is obviously better than the model using the z-coordinateü When the slope is less than 3 ‰, the difference between the two vertical coordinate systems
becomes very small.