3. Generation of three-dimensional geometry

The first step in the numerical procedure was to prepare the 3-D geometry of the 17-km-long Sulejow reservoir. Gambit Program 2.2.30 (ANSYS, USA) was employed to generate geometry of the water body.

On the basis of the most accurate, available data of the reservoir, geometry was generated using segmentation technique with 36 cross-sectional profiles of the artificial lake. Methodology adopted to determine parameters of the sections was based on the field measurements by using an integrated system: digital depth sounder RESON PC-100 and GPS Trimble 5700. The cross-sectional spacing ranged from 400 to 600 m. Figure 2 shows an example and locations of the measured sections in the water body.

Figure 2. The cross-sectional profiles of the Sulejow reservoir.

Figure 3. Example of the cross sections generated with Gambit program.

Poland was built by impounding the Pilica river on 138.9 km with a dam in the years 1969– 1973. The reservoir is a shallow water body (mean depth 3.3 m) covering a large area (22 km<sup>2</sup>

Sulejow reservoir is a ribbon-type reservoir, which can be divided into two morphological zones each influenced by different forcing agents. The first one (consisting of a riverine zone and a transition zone) is the narrow, shallower part of the reservoir, dominated by the river inflows. The second zone, the wide lacustrine part of the reservoir, is located near the dam. This zone is quite open and behaves like a lake, and the main driving force mechanism causes the movement of water masses wind. The main axis runs from southwest to northeast which is close to the direction of winds that ripple and mix the water. A result is the formation of places with stagnant water on the southern bank of the middle and lower part of the reservoir.

The first step in the numerical procedure was to prepare the 3-D geometry of the 17-km-long Sulejow reservoir. Gambit Program 2.2.30 (ANSYS, USA) was employed to generate geometry

On the basis of the most accurate, available data of the reservoir, geometry was generated using segmentation technique with 36 cross-sectional profiles of the artificial lake. Methodology adopted to determine parameters of the sections was based on the field measurements by using an integrated system: digital depth sounder RESON PC-100 and GPS Trimble 5700. The cross-sectional spacing ranged from 400 to 600 m. Figure 2 shows an example and locations of

3. Generation of three-dimensional geometry

the measured sections in the water body.

Figure 2. The cross-sectional profiles of the Sulejow reservoir.

of the water body.

42 Dam Engineering

).

In this study, the "bottom-up" approach was implemented in order to obtain a three-dimensional geometry from the set of separated surfaces. Each measured cross section was defined by the information of the distance between two banks (connection length between probing points in the section was 5 m) and elevation (normal impoundment level in the Sulejow reservoir is 166.6 m amsl). Figure 3 illustrates an example of the cross section built in the Gambit Program.

The vertices which determine the reservoir bed were connected to form the edges. Subsequently, edges were combined into faces. The last stage consisted in stitching the faces in order to obtain the volumes. After completion of the segmentation procedure, rendering process was conducted, which facilitated generation of three-dimensional geometry of the reservoir, using the faces obtained from the segmentation. Figure 4 presents the complete geometry that consists of 36 volumes totally.

Terminal berm of the reservoir consists of earth dam and weir, with integrated hydroelectric power station (Figure 5). The length of the dam with a weir is 1200 m, the maximum height is 16 m, and the total volume is 567,000 m3 . The jazz is concrete, in the overflow riffle span, middle and left of the weir, drain pipes have been built. Weirs are closed with the oval valves. Cross section of earth dam and weir is shown in Figure 6a and b. Geometry and computational mesh of the dam are shown in Figure 7.

Figure 4. Sulejow reservoir geometry.

Figure 5. Front step of the weir. (1) Earth dam, (2) weir, (3) electric power station, (4) switching station, (5) operating settlement, (6) buildings, (7) clay band, (8) foil-sealing of the reservoir bottom, and (9) marina.

The final verification of the accuracy of the reservoir shape was feasible on the basis of satellite photographs, which confirm the correct approximation of the geometry. Figure 8 shows the satellite image of the Sulejow reservoir with marked cross sections, according to which the 3-D geometry was prepared. Due to the fact that sections were determined every 500 m, it could not be possible to precisely map the shape of the shoreline; however, this approximation does not affect the nature of the flow throughout the 17-km-long dam reservoir. The generated 3-D

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Three-dimensional grid generation for a complex geometry is not a straightforward task, as the grid type has a significant influence upon the quality of the simulations [20]. The crucial issues controlling grid quality are the type of grid, that is, structured and unstructured, grid spacing, and skewness. To apply a finite volume method in CFD model of the reservoir, the 3-D computational domain must be subdivided into a large number of cells. However, the high ratio of the breadth to depth dimensions and irregular shape of the reservoir make this process difficult. Appropriate mesh resolution is linked to the hydrodynamic conditions, the flow

In finite volume methods for numerical simulations, the hexahedral mesh (hex mesh) is preferred, as compared to the tetrahedral mesh (tet mesh), owing to the reduced error and smaller number of elements [21]. Typically, tet mesh is preferred for filling irregular spaces, since existing algorithms can semiautomatically subdivide most of the spaces [15]. Structured meshes are better suited to shallow reservoirs, while an unstructured mesh matches better to deeper (or with smaller aspect ratio) reservoirs. On the other hand, generating a hex mesh, with desirable qualities, often requires significant geometric decomposition, which makes the

geometry of the artificial lake was discretized to perform the numerical solutions.

3.1. Computational mesh

Figure 7. Outflow of the Sulejow reservoir.

features, and the discretization schemes.

Figure 6. (a) Cross section of the earth dam. (1) reinforced concrete shield, (2) clay band, (4) grass slope, (5) drainage, (6) embankment, and (7) national road on the dam crest. (b) Cross section of the weir. (1) Elevated sill, (2) oval valve, (3) weir pool, and (4) artificial pothole.

Three-Dimensional CFD Simulations of Hydrodynamics for the Lowland Dam Reservoir http://dx.doi.org/10.5772/intechopen.80377 45

Figure 7. Outflow of the Sulejow reservoir.

The final verification of the accuracy of the reservoir shape was feasible on the basis of satellite photographs, which confirm the correct approximation of the geometry. Figure 8 shows the satellite image of the Sulejow reservoir with marked cross sections, according to which the 3-D geometry was prepared. Due to the fact that sections were determined every 500 m, it could not be possible to precisely map the shape of the shoreline; however, this approximation does not affect the nature of the flow throughout the 17-km-long dam reservoir. The generated 3-D geometry of the artificial lake was discretized to perform the numerical solutions.

#### 3.1. Computational mesh

Figure 5. Front step of the weir. (1) Earth dam, (2) weir, (3) electric power station, (4) switching station, (5) operating

Figure 6. (a) Cross section of the earth dam. (1) reinforced concrete shield, (2) clay band, (4) grass slope, (5) drainage, (6) embankment, and (7) national road on the dam crest. (b) Cross section of the weir. (1) Elevated sill, (2) oval valve, (3) weir

pool, and (4) artificial pothole.

44 Dam Engineering

settlement, (6) buildings, (7) clay band, (8) foil-sealing of the reservoir bottom, and (9) marina.

Three-dimensional grid generation for a complex geometry is not a straightforward task, as the grid type has a significant influence upon the quality of the simulations [20]. The crucial issues controlling grid quality are the type of grid, that is, structured and unstructured, grid spacing, and skewness. To apply a finite volume method in CFD model of the reservoir, the 3-D computational domain must be subdivided into a large number of cells. However, the high ratio of the breadth to depth dimensions and irregular shape of the reservoir make this process difficult. Appropriate mesh resolution is linked to the hydrodynamic conditions, the flow features, and the discretization schemes.

In finite volume methods for numerical simulations, the hexahedral mesh (hex mesh) is preferred, as compared to the tetrahedral mesh (tet mesh), owing to the reduced error and smaller number of elements [21]. Typically, tet mesh is preferred for filling irregular spaces, since existing algorithms can semiautomatically subdivide most of the spaces [15]. Structured meshes are better suited to shallow reservoirs, while an unstructured mesh matches better to deeper (or with smaller aspect ratio) reservoirs. On the other hand, generating a hex mesh, with desirable qualities, often requires significant geometric decomposition, which makes the

The total basin volume was 74,721,600 m3

generated for the Sulejow reservoir geometry.

of the basin volume 1%.

, which reflects the real value. Four layers of ele-

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Three-Dimensional CFD Simulations of Hydrodynamics for the Lowland Dam Reservoir

ments across the wall thickness were added to confirm the numerical stability by specifying

The process of generating structured grid was much more labor intensive than creating an unstructured mesh; however, elaborated model was more stable and converged quickly.

Exclusion from the model of some near-shore regions of the basin, with the shallow depth (<0.3 m) and inconsiderable slope, was necessary to avoid generation of cells with highly acute angles. Removal of strongly skewed elements from the computational domain would have minimal impact on the overall circulation patterns in the basin due to the high ratio of bottom area to the water volume, resulting with minimal flow and very low velocity in this region. This operation removed approximately 10% of the basin surface area but only a small fraction

A post-processing check on mesh quality, based on assessing the skewness of the generated cells, indicated that the mesh is of high quality and would not compromise solution stability. The use of a coarser grid (<10<sup>5</sup> and 10<sup>6</sup> elements) caused rapid solution divergence. However, increasing the mesh number to 18 <sup>10</sup><sup>6</sup> had no further influence on the results especially on the location of swirl flows. Figure 9 shows the hexahedral, structured mesh which has been

Figure 9. Example of the computational domain with the structural mesh generated in GAMBIT 2.2.30 program. Under

magnification, hexahedral elements included in the boundary layer are visible.

the height of the first layer, nearest to the wall (0.01), and the growth factor (0.1).

Figure 8. Satellite photograph of the Sulejow reservoir with the cross sections. Source: geoportal.gov.pl.

meshing process extremely difficult to perform and automate. As a result, it requires considerable user efforts and may take days or even weeks to develop the proper grid in the case of complex shapes.

To fill the shallow space representing the reservoir area, with minimally skewed, hexahedral cells, the typical cell dimension must be small compared to the depth of the water. Thus, the meshing process becomes computationally expensive due to the requirement of a large number of elements.

While developing the CFD model of flow hydrodynamics, preliminary simulations allowed us to select proper density of the numerical grid, at which a convergent and stable solution can be obtained. In order to generate a mesh for the Sulejow reservoir geometry, the capacity of Gambit 2.2.30 commercial software was used. The domain surface was discretized using structural (hexahedral) mesh with 16,787,820 active cells and 17,717,364 nodes, respectively. The total basin volume was 74,721,600 m3 , which reflects the real value. Four layers of elements across the wall thickness were added to confirm the numerical stability by specifying the height of the first layer, nearest to the wall (0.01), and the growth factor (0.1).

The process of generating structured grid was much more labor intensive than creating an unstructured mesh; however, elaborated model was more stable and converged quickly.

Exclusion from the model of some near-shore regions of the basin, with the shallow depth (<0.3 m) and inconsiderable slope, was necessary to avoid generation of cells with highly acute angles. Removal of strongly skewed elements from the computational domain would have minimal impact on the overall circulation patterns in the basin due to the high ratio of bottom area to the water volume, resulting with minimal flow and very low velocity in this region. This operation removed approximately 10% of the basin surface area but only a small fraction of the basin volume 1%.

A post-processing check on mesh quality, based on assessing the skewness of the generated cells, indicated that the mesh is of high quality and would not compromise solution stability. The use of a coarser grid (<10<sup>5</sup> and 10<sup>6</sup> elements) caused rapid solution divergence. However, increasing the mesh number to 18 <sup>10</sup><sup>6</sup> had no further influence on the results especially on the location of swirl flows. Figure 9 shows the hexahedral, structured mesh which has been generated for the Sulejow reservoir geometry.

meshing process extremely difficult to perform and automate. As a result, it requires considerable user efforts and may take days or even weeks to develop the proper grid in the case of

Figure 8. Satellite photograph of the Sulejow reservoir with the cross sections. Source: geoportal.gov.pl.

To fill the shallow space representing the reservoir area, with minimally skewed, hexahedral cells, the typical cell dimension must be small compared to the depth of the water. Thus, the meshing process becomes computationally expensive due to the requirement of a large num-

While developing the CFD model of flow hydrodynamics, preliminary simulations allowed us to select proper density of the numerical grid, at which a convergent and stable solution can be obtained. In order to generate a mesh for the Sulejow reservoir geometry, the capacity of Gambit 2.2.30 commercial software was used. The domain surface was discretized using structural (hexahedral) mesh with 16,787,820 active cells and 17,717,364 nodes, respectively.

complex shapes.

46 Dam Engineering

ber of elements.

Figure 9. Example of the computational domain with the structural mesh generated in GAMBIT 2.2.30 program. Under magnification, hexahedral elements included in the boundary layer are visible.


Table 1. Values of parameter: y+ , skewness, and aspect ratio for the analyzed numerical grid.

The quality of the numerical grid was determined by the shape and the size of the computing field and the total number of elements used in the generated numerical grid and through the position of the first node relative to the plane of the wall. To assess the quality of the numerical grid elements, three parameters were used (Gambit User Guide):


Ranges of parameters: y<sup>+</sup> , skewness, and aspect ratio for the numerical grid generated in this work are given in Table 1.

(159,116 hexahedra, 126 wedges) and 321,872 nodes, respectively. A boundary layer was

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Figure 10. Fragment of the structured, hexahedral mesh generated with Gambit program.

Wind accelerates surface fluid particles by imparting momentum to the fluid, through surface stresses. In the analysis, the water flows through the air momentum. In the computational domain, the water phase has two outlets that allow for fluid reversing. Analysis of flow in 2-D model was intended to determine which boundary condition best describes the situation that

For two-dimensional CFD model, the following boundary conditions were imposed:.

Inlet boundary conditions applied for the analyzed domain were two tributaries (Pilica and

Simulated inflow boundaries were specified with mass flow rates, normal to the boundary. Velocities at each inlet were calculated from the inlet area measurements of stream flow for the Pilica and Luciaza rivers, made by the Regional Board and Water Management in Warsaw in 2007. The monthly values of mass flow rates in the Pilica and Luciaza rivers are presented in

The definition of the inlet requires the values of the velocity vectors and turbulence properties. For the air inlet, the simulations were first conducted at a speed of 3 m/s. Velocity profile obtained at the outlet of the computational domain was loaded as an input file to receive the velocity profile at the inlet. This approach allows to obtain a fully developed velocity profile

Implementation of volume of fluid model requires an additional boundary condition to be specified, namely, the turbulence intensity at the inlet and turbulent viscosity ratio. Introduc-

tion of disturbance into the flow reflects the real features of the flow pattern.

generated consisting of 10 rows.

4.2. Boundary conditions

Table 2.

for a small domain.

prevails over the water surface by the effect of wind.

Luciaza rivers) and outlet (dam) as given in Figure 11.
