# Simulation of a Hydrostatic Pressure Machine with Caffa3d Solver: Numerical Model Characterization and Evaluation

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Rotation of the Wheel

#### 2.2. Free Surface Flow

#### 2.3. Model Geometry and Meshing

#### 2.4. Boundary Conditions

#### 2.5. Other Configuration Parameters

#### 2.6. Power Calculation

## 3. Results and Discussion

#### 3.1. VOF Assessment

#### 3.2. Simulation of a HPM

## 4. Conclusions

- to add the vertical wall normal to the flow at the section of the rotation axis, in order to reduce the gap between the wheel and the lateral walls, while maintaining the channel wider than the wheel, in order to enable the filling and emptying process;
- to perform a mesh independence analysis while maintaining low values of ${y}^{+}$;
- to assess other turbulence techniques and associated models (particularly the $\kappa -\u03f5$ model for RANS already implemented in the solver);
- to incorporate the continuous calculation (at each time step) of torque and shaft power into the solver.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Explanation of the operation of a generic HPM, taken from HYLOW Internal Task Report 2.3 [19].

**Figure 3.**Sketch of the sliding interface, showing the relative displacement angle $\alpha $ between stationary blocks (painted) and rotating blocks (white).

**Figure 6.**Computational mesh of the region surrounding the HPM (

**left**) and around a blade (

**right**) with dimensions in meters.

**Figure 8.**Comparison of free surface profile in the channel over the semicylindrical dam: (

**a**) obtained with caffa3d and (

**b**) presented in [33] through exprimental (o) and numerical (-).

**Figure 9.**Comparison of streamlines in the channel over the semicylindrical dam: (

**a**) obtained with caffa3d and (

**b**) presented in [33].

**Figure 10.**Horizontal velocity profiles obtained with caffa3d for sections: (

**a**) $x=0.8$ m; (

**b**) $x=1.0$ m; (

**c**) $x=1.3$ m, and by experiments and simulations [33] for sections: (

**d**) $x=0.8$ m; (

**e**) $x=1.0$ m; (

**f**) $x=1.3$ m.

**Figure 13.**Magnitude of the velocity at the section of the rotation axis ($x=0.0$ m), at time $t=4.0$ s.

**Figure 18.**Sequence of fraction of volume (

**left**) and pressure (

**right**) around the HPM at times $t=$ 2 s (

**up**), 3 s (

**middle**) and 4 s (

**down**).

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**MDPI and ACS Style**

Pienika, R.; Usera, G.; Ramos, H.M.
Simulation of a Hydrostatic Pressure Machine with Caffa3d Solver: Numerical Model Characterization and Evaluation. *Water* **2020**, *12*, 2419.
https://doi.org/10.3390/w12092419

**AMA Style**

Pienika R, Usera G, Ramos HM.
Simulation of a Hydrostatic Pressure Machine with Caffa3d Solver: Numerical Model Characterization and Evaluation. *Water*. 2020; 12(9):2419.
https://doi.org/10.3390/w12092419

**Chicago/Turabian Style**

Pienika, Rodolfo, Gabriel Usera, and Helena M. Ramos.
2020. "Simulation of a Hydrostatic Pressure Machine with Caffa3d Solver: Numerical Model Characterization and Evaluation" *Water* 12, no. 9: 2419.
https://doi.org/10.3390/w12092419