3D numerical simulation of dam-break flow over different obstacles in a dry bed

Dams are one of the most important artificial structures to protect human lives and preserve water supplies. Therefore, the constructors commonly attempt to ensure the safety of the dams during the operation period. The designers are faced with the dam-break because it is a possible accidental problem. From this point of view, numerous experimental, numerical modeling and analytical studies have been conducted on dam failure (Lobovský et al. 2014). Ritter (1892) used an analytical solution with the Saint-Venant equations to the dam-break flow, in which the resistance was neglected. Dressler (1952) considered the Chezy resistance formula added to the nonlinear shallow water equations for the dam-break solution when resistance is neglected. Lauber & Hager (1998) studied dam-break waves in a smooth rectangular and horizontal channel. Goater & Hogg (2011) used the nonlinear shallow water equations for a collapse of a reservoir into an initially stationary layer of fluid. Maghsoodi et al. (2012) investigated dam-break with a stationary object using Computational Fluid Dynamics (CFD). Wang & Pan (2015) used shallow water equations to model the dam-break down a uniform slope. Akkerman et al. (2011) investigated dam-break with a stationary object using isogeometric analysis. Amini et al. (2016) used isogeometric analysis so that the governing Navier-Stokes (NS) equations using a pressure projection method are solved in a Lagrangian form. Shobeyri & Afshar (2010) offered a discrete least squares meshless method for the simulation of incompressible free surface flows in a Lagrangian form using a pressure projection method. Yu et al. (2016) proposed a Coupled Level Set (CLS)/Immersed Boundary (IB) method developed in Cartesian grids. In recent years, numerous experimental tests have been carried out on dam-break. Morris (2000) employed a triangular bump for numerical verification of dam-break flow propagation. Ozmen-Cagatay & Kocaman (2011) presented an experimental and numerical investigation of dam-break flow over initially dry bed with a trapezoidal obstacle. They used Flow-3D for solving the Reynolds Averaged Navier Stokes (RANS) equations with the k-ω turbulence model and the Shallow Water Equations (SWE). Soares-Frazão & Zech (2007) presented data about the effect of such an obstacle on a dam-break wave. The experimental setup consisted in a channel with a rectangular shaped obstacle, which was a representation of a building. Issakhov et al. (2018) presented the effect of water on obstacles in the dam-break flow problem.

Yang et al. (2018) utilized FLOW-3D software to investigate the distribution and differences of turbulence kinetic energy and also presented a comprehensive understanding of dam-break wave generation and propagation. Gu et al. (2018) used a 3D interface-preserving level set method to simulate dam-break flow problems. In this paper dam-break problems either with or without obstacles were studied to confirm the coupled two-phase incompressible flow and level set method solver. Seyedashraf et al. (2017) proposed a novel technique based on Artificial Neural Network (ANN) along with an equation and detailed solution of the 1D dam-break problems without source terms. Celis et al. (2017) investigated dam breaking and sloshing forces based on Finite Difference Method (FDM). Heo et al. (2017) developed a CLS-VOF (volume of fluid) and IB method, and applied it to simulating the interaction between dam-break flow and stationary obstacles. Munoz & Constantinescu (2020) investigated a 3D, non-hydrostatic, RANS model using the VOF approach to simulate dam-break flows. Vosoughi et al. (2020) evaluated multiphase flood waves caused by failure of silted-up dams experimentally and numerically. Ye et al. (2020) employed a mesh-free method to simulate dam-break wave spreading in different bed configurations.

Although several studies have been made on the analysis of the dam-break, there is a lack of information on the effect of different obstacle geometries on flood flow. For this purpose, in the current study the dam-break flow was investigated by solving the NS and multiphase flow equations for an incompressible fluid. Also, various forms of obstacles were considered in a dry bed. Finally, results were compared with other researches.

In this contribution, three experimental dam-break cases were considered in order to numerically investigate the turbulent water flow surfaces over the obstacles after dam-break. The first case was an experimental model (Akkerman et al. 2011) with a rectangular tank consisting of a 1.22 m × 1 m × 0.55 m column of water with the object located at 2.315 m from the beginning of the channel with dimensions 0.161 m × 0.161 m × 0.403 m (Figure 1).

In the second case, the model (Ozmen-Cagatay & Kocaman 2011) consisted of a rectangular tank as a horizontal channel 8.9 m long and 0.30 m wide. The column of water was 4.65 m × 0.3 m × 0.25 m. In this model a symmetrical trapezoidal-shaped obstacle was assumed. The obstacle's dimensions were 0.075 m high and 1 m base length located 1.53 m away from the plate (Figure 2).

In the third case (Soares Frazao & Testa 1999), experiments were conducted in a smooth prismatic channel of rectangular cross-section over a triangular bottom sill on the downstream bed. The column of water was 0.75 m × 15.5 m × 1.75 m. In this model the symmetrical trapezoidal-shaped bottom sill was utilized, 0.4 m high and 6 m base length, that was located 10 m downstream from the gate (Figure 3).

Figure 4 illustrates the computational grid in the vicinity of the obstacles. Due to the major effects of the computational mesh on the accuracy of the obtained results, a wide range of sensitivity analyses were conducted in order to validate the suitable number of meshes. Through running the models with refined mesh sizes in various conditions, the smallest size of the mesh was approximately 1, 1.6, and 2 cm, for rectangular, trapezoidal and triangle obstacles, respectively. Figure 5 depicts the computational domains and considered channel boundaries.

Before analyzing the results, it was necessary to ensure the accuracy of the numerical model by comparing its results with experimental measurements. For this purpose, the height of water at different points, height of free surface in the channel and pressure in different locations were investigated.

Figure 6 represents the predicted and measured time series of the water level at different gauging points H1, H2, H3 and H4 (Figure 1) for the dam-break flow with rectangle obstacle.

As can be seen from Figure 6, in point H1, it takes nearly 1 s for water to reach this point. Then the height of water at this point is increased. After about 2.5 s of breaking the dam, the water height decreases and, after 5 s, the water level rises again. Point H2, located on the obstacle, it takes about 0.43 s for water to reach this point. Then the height of water at this point is increased. Until approximately 3 s after the dam-break, the water height decreases and again, after 5 s, the water level rises. Point H3, located before the obstacle, it takes about 0.18 s for water to reach this point. Then the height of water increases at this point. Until approximately 2 s, the water height decreases, and at 2.3 s the water height reaches 0.281 m, and after 4.4 s, the water level rises again. At point H3, all these water level fluctuations were in very good agreement with the experimental evidence. Point H4 depicts the water level fluctuations (Point H4, located on the column of water) and illustrates, first the height of water decreases, and consequently in 2.72 s the height of water falls 0.082 m. The water height decreases until 2.88 s, after that the water height reaches 0.2 m, and up to 3.62 s the water height remains stable. Then the height of water decreases again up to 3.9 s. At the time of 3.9 s the water height rises to 0.386 m and again the height of water decreases to approximately 0.2 m. In order to demonstrate the accuracy of the numerical simulations, the water pressures at different points are shown. Figure 7 represents the water pressure changes at four different locations for dam-break flow with rectangle obstacle. Figure 7 also shows the predicted and measured time histories of the water pressure at different gauging points P1 and P2 (Figure 1) for the dam-break flow with rectangle obstacle. The pressure changes over time are the same for two points. When the water reaches points 1 and 2, the pressure increases and then the pressure decreases and after a few seconds (4.82 s) the pressure rises again.

In this section the sudden breaking dam flow in a channel of water with a trapezoidal obstacle is considered. Figure 8 presents the predicted and measured water flow according to the four different times (based on the assumption of the model in Figure 2). Also, the effect of the trapezoidal obstacle in the case of dam-break was determined. The resulting water surface was consistent with those of laboratory results. The results indicate that after the dam-break phenomenon, a water wave moves upward in the upstream direction.

In this section a comparison between the numerical modeling and the experimental data for the case of dam-break flow with a triangle obstacle is presented. Figure 9 shows the predicted and measured time-dependent water level at different gauging points G4, G10, G13 and G20 (Figure 3) for the dam-break flow with triangle obstacle.

From Figure 9, in point G4, located before the obstacle, it takes about 1.32 s for water to reach this point. Then the height of water at this point increases. Until approximately 13.16 s after the dam-break the water height increases sharply, consequently at 14.26 s, the water height is 0.512 m, and then the water height decreases. Point G10 which is located at the beginning of the obstacle, it takes about 1.32 s for water to reach this point. Then the height of water at this point increases until approximately 13.16 s after breaking the dam. The water height increases drastically, at 14.26 s the water height is 0.512 m, then the water height decreases gradually over time up to almost 40 s. In point G13, located above the obstacle, it takes about 4.27 s for water to reach this point. The water height is constant between 6.99 s and 16.42 s then the water height decreases near to zero. In point G20, located after the obstacle, the height of water is very low.

Dam-break flows with solid obstacle were successfully simulated through the comparison of the predicted results with their corresponding experimental evidence. The resulting water pressure distributions and the water surfaces at different times indicate that the standard k-ω model is an appropriate model to simulate the dam-break phenomenon with various types of obstacles.

After verification, some applied results and discussions from the performed simulations are presented in this section.

One of the most challenging issues during dam failure is the water level in different places, particularly in the case of an existing obstacle. For this reason, in this section the 3D water levels are investigated as follows.

Figure 10 illustrates the water profile in the case of a rectangular obstacle. Dam-break causes an unsteady flow. In less than 1 s after dam-break, the water flow faces the obstacle and immediately, the stream hits the end wall of the canal and the water bounces back. Then, after near 2 s back water flow overtops the rectangular obstacle and almost all of the obstacle is submerged. At the time of 3.5 s, the water flow hits again the beginning wall of the canal and creates a second water wave which propagates throughout the longitudinal direction of the canal. Consequently, the second wave reaches the obstacle again at the time of 4.5 s. Obviously, the second water wave has lower intensity than the first wave. However, according to Figure 10, the secondary water wave (at time 6 s) hits the end wall of the canal with lower water height. Figure 11 depicts the water surface profile at different times by considering a trapezoidal obstacle. The obstacle was located 6.18 m from the beginning wall.

In this case, in less than 1.5 s after dam breakage the water wave passes the obstacle. Moreover, at the time of 3 s due to the assumed obstacle, a wave is generated that moves upward. The wave intensity decreases when it travels to the beginning of the canal. Then after 11.5 s, the back water wave again hits the wall at the beginning of the canal. The generated water surface profile in the case of a triangle obstacle is shown in Figure 12.

In this case the obstacle was located at 10 m from the beginning wall. Less than 4 s after dam breakage the water wave passes the obstacle. In 7 s after breakage, the water wave reaches the end of the canal and disappears. At approximately 10 s a wave forms behind the obstacle that moves upward. After 24 s all the water in front of the obstacle totally disappeared. Figure 12 demonstrates that after 26 s from the dam breakage the back water wave reaches the beginning wall.

Among all mechanical phenomena during a dam breakage, determining the pressure in different situations is much more challenging. Due to the presence of an obstacle the variation of the pressure will be in an oscillatory manner. In this regard, the variation of the pressure on the canal walls was studied (the pressures are relative to P_o = γh_o).

According to the Figure 13, due to the reciprocating wave of water, the amount of pressure varies in different locations with respect to time. At time 1 s, the pressure reaches to 0.9γh₀ at the end of the canal. However, negative pressure reaches almost −0.25γh₀ in the vicinity of the obstacle. The induced pressure due to the dam breakage decreases with increasing time. As a consequence, at time 3.5 s over a limited area of the canal bed the pressure is equal to 0.67γh₀. However, at 4.5 s, the area subjected to 0.67γh₀ pressure increases. Therefore, at 6 s after breakage the pressure at the canal bed decreases near to 0.67γh₀ and at the same time other bed surfaces experience pressure lower than 0.67γh₀.

In Figure 14, unlike the rectangular obstacle, due to the drainage of water flow from the downstream and also because of the rather long distance between the dam axis and the obstacle, the induced pressure decreases over time. Hence, at 1.5 s the pressure at the bed of the canal reaches near to γh₀ and at the moment lower pressure occurs at the obstacle. After water wave completion impact at about 3 s after breakage, the induced pressure reaches near to 0.6γh₀ in the vicinity of the obstacle. As time progresses and associated with the returning of the wave water to the upstream, the pressure at the bed of the canal increases; however, the pressure decreases with increasing time.

In Figure 15, similar to the trapezoidal obstacle, in the case of a triangle obstacle with disappearing water from the downstream side, the pressure at different times decreased. Hence, at 4 s, the pressure at the bed of the canal reaches near to γh₀ and at this time lower pressure occurs at the obstacle. After water wave completion impact at about 10 s after breakage, the induced pressure reaches near to 0.8γh₀ in the vicinity of the obstacle. After a time and by returning the wave water to the upstream, the pressure at the bed of the canal increases; however, the pressure decreases with increasing time.

When there is a dam-break, by considering the water depths and presence of the obstacle, variation of the water flow velocities, particularly around the obstacle is of significant importance.

Figure 16 depicts the water velocities throughout a canal with a rectangular obstacle. At the time of 1 s, the velocity equal to 3 m/s is observed. At time 2 s and after the water wave hits the downstream wall, the velocity decreases near to 1.2 m/s. At 3.5 s, when the water wave reaches the initial wall, a uniform distribution of velocities occurred. However, at 4.5 s due to the wave traveling in the downstream direction, the velocity of the upper layer of the water wave reaches again 1.8 m/s. Consequently, by decreasing the water wave energy, some time after the dam-break the velocities decreased.

Figure 17 illustrates the water velocities throughout a canal with a trapezoidal obstacle. Due to the presence of an obstacle, the nature of the velocity distribution in time is oscillatory. After 1.5 s of dam-break the velocity is 2 m/s. At time 3 s, the situation of the maximum velocity moves forward along the downstream. Consequently, by completion of the reflected water wave, maximum downstream velocity decreased to a value near to 1.6 m/s. At this moment, the maximum upstream velocity also decreased to 0.4 m/s with some local velocities near to 0.8 m/s.

Like the trapezoidal obstacle, when a triangle obstacle is considered against water flow, an oscillatory flow results. Figure 18 shows the variation of velocity over time for a triangle obstacle. At 4 s, the velocity approaches 3.25 m/s around the obstacle. After the obstacle and due to the similar bed slope, the velocity remains at about 3.25 m/s until 10 s from the dam-break. However, after about 24 s, the downstream flow completely disappeared and only upstream back flow in front of the obstacle continues with 1.3 m/s velocity.

In this paper, a 3D model of dam-break flow over different obstacles with dry beds was developed. To verify the Fluent software performance, the height of water at different points, the height of free surface in the channel and pressure in different locations with rectangular, triangular and trapezoidal obstacles were investigated. Simulations were performed with the standard k-ω turbulent model, the PISO pressure-velocity coupling scheme and the VOF method for tracking the free surface. By comparing the 3D-simulation results with dam-break flows over the different obstacles, it was found that the numerical models have sufficient accuracy and were in agreement with experimental data and results of other researches. Furthermore, the results showed that if there was a wall at the end of the channel and the distance between the barriers at the end wall was small (Case 1), maximum water height occurred after the flow collided with the end wall. If the end of the channel was open (Cases 2 and 3), the maximum water height occurred after the current hit the obstacle. In the rectangular obstacle, negative pressure happened in the vicinity of the obstacle, while in the trapezoidal and triangular obstacles, the pressure was always positive. The maximum velocity happened at the front of the wave causing dam-break. Over time and by the return of the water wave, the velocity decreased dramatically.

All relevant data are included in the paper or its Supplementary Information.