عنوان مقاله [English]
نویسندگان [English]چکیده [English]
Drops are hydraulic structures that are commonly used in irrigation and waste water collection networks. A vertical drop balances the elevational variation between the channel slope and ground slope. Thus the flow structure is comprised of a falling jet (free overfall), a sliding or skimming jet and a circulating or mixing zone. This pattern causes the significant portion of flow energy to be dissipated through jet impact and turbulent mixing. In this study the complex flow pattern in the vertical drop with different forms of downstream channel was studied numerically. The two dimensional RANS equations accompanied with volume of fluid (VOF) method are applied. The results of the simulation are then compared to the experimental results. The details of energy loss and velocity profiles in different locations are also scrutinized.
In this study three different data sets were used. The first data set presented (case A) was measured by Lin et al. (2007). Their experiments were conducted in a flume of 8.85 m length with a glass-walled and glass-bottomed test section of 3.05 m length, 0.50 m width and 0.54 m depth. Two vertical drops with heights of 11.0 and 20.0 cm were chosen. Another set of data (case B) were collected by Chamani et al. (2005) in a ventilated vertical drop with subcritical flow at the upstream channel and sloping aprons at the downstream channel. Flow characteristics such as pool depth, downstream depth, and energy loss were measured in an 11 m length, 0.401 m width ?ume. The drop height was 0.21 m and inverse slope was set at 5 degrees. The last data set (case C) was measured by Lin et al. (2009) in a vertical drop with an end sill. The flume size was the same as in case A. Three vertical drop pools were used in this study with drop height H of 14.0 cm, pool length (L) of 16.0 cm, and end sill heights (h) of 0, 1.7 and 6.0 cm, such that the end sill ratios (h/H) were 0, 0.12, and 0.43 respectively. For the case A, four different grids (7908, 18901, 32729 and 57512 nodes) with identical flow properties were used. Instead of setting the depth and velocity, at the upstream end of the channel, a tank was set up so that the contracted flow depth and the average velocity (after the gate) match the selected critical depth and velocity. Pressure outlet boundary conditions (BC) were set at top of the channel, the channel outlet and at the air vent. The flow depth results were converging and a good agreement with experimental data was observed with the two smallest grids. However, to access better resolution, the 57512-node grid was preferred and grids with almost the same cell size were adopted for other numerical simulations. The laminar model did not produce satisfactory flow depth and velocity along the drop structure. The results of the most commonly used two-equation turbulence models (k-? and k-?) were identical. Furthermore, the standard wall function produced better results compared to non-equilibrium wall function. Thus the standard k-? with the standard wall function was preferred for other simulations.
Grid study showed that numerical results of a 57512-node grid had the best agreement with the experimental values. The desired downstream channel length was preferred to be 1.5 meter, and the standard k-? turbulence model produced the best results in a horizontal apron drop. The numerical free-surface profiles followed the theoretical equations very well. Due to higher circulation ratio and occurring a hydraulic jump in the pool, the greatest energy dissipation was obtained in the drop with an end sill. The drop with adverse apron was in the second position and the minimum dissipation occurred in the horizontal apron drop. The numerically calculated velocity profiles mimicked the experimental results all over the falling, sliding or skimming jet regions. The numerical model was not so successful in the mixing region behind the nappe which is possibly due to weakness of the turbulence models. Using enhanced turbulence model will decrease discrepancies in this region. It can be concluded that the 2D numerical model is able to produce satisfactory results in order to design and evaluate a vertical drop, which in turn can aviate the need to endeavor too much effort and financial cost to construct a suitable experimental model in the laboratory.