# Valve Geometry and Flow Optimization through an Automated DOE Approach

^{1}

^{2}

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## Abstract

**:**

^{®}associated with SimericsMP+

^{®}allows us to easily study many different geometrical variants and work out a design of experiments (DOE) sequence that gives evidence of the most impactful aspects of a design. Moreover, the result can be further optimized to obtain the best possible solution in terms of the constraints defined.

## 1. Introduction

^{®}(Friendship Systems AG, Postdam, Germany) and a commercial computational fluid dynamics (CFD) code: SimericsMP+

^{®}(Simerics Inc.

^{®}, Bellevue, WA, USA).

^{®}(an optimization tool with integrated parametric geometry modelling capabilities) and SimericsMP+

^{®}, a commercial CFD solver. This approach greatly reduced the set-up effort and allowed for a leaner and more efficient project layout.

## 2. Materials and Methods

^{®}on similar Duplomatic MS S.p.A. valves and experimental tests performed at the Industrial Engineering Department of the University of Naples, Federico II are reported in different publications (e.g., [1,8]).

^{®}(developed by Simerics Inc.

^{®}, Bellevue, WA, USA)).

^{®}tool was chosen as a general purpose CFD software that numerically solves the fundamental conservation equations of mass, momentum and energy as described below [14,15].

- $\Omega \left(t\right)$ is the control volume,
- σ is the control volume surface,
- n is the surface normal pointed outwards,
- ρ is the fluid density,
- p is the pressure,
- f is the body force,
- v is the fluid velocity,
- v
_{σ}is the surface motion velocity.

_{i}(i = 1,2,3) is the velocity component and ${\delta}_{ij}$ is the Kronecker delta function.

_{1}= 1.44, c

_{2}= 1.92, σ

_{k}= 1, σ

_{ε}= 1.3; where σ

_{k}e σ

_{ε}are the turbulent kinetic energy and the turbulent kinetic energy dissipation rate Prandtl numbers.

_{i}’ (i = 1,2,3) being components of v’.

_{t}is calculated by:

_{μ}= 0.09.

_{t can}be expressed as a function of velocity and the shear stress tensor as:

^{®}grid generator (Figure 4).

- The parent–child tree architecture allows for an expandable data structure with reduced memory storage;
- Binary refinement is optimal for transitioning between different length scales and resolutions within the model;
- Most cells are cubes, which is the optimum cell type in terms of orthogonality, aspect ratio and skewness, thereby reducing the influence of numerical errors and improving speed and accuracy;
- It can be automated, greatly reducing the set-up time.

^{®}mismatched grid interface (MGI, see Figure 5) is a very efficient implicit algorithm that identifies the overlap areas and matches them without interpolation. During the simulation process, the matching area is treated no differently than an internal face between two neighboring cells in the same grid domain.

- Fluid: oil at 45 °C (constant)
- Oil kinematic viscosity: 4.42 × 10
^{−5}[m^{2}/s] = 44.2 cSt - Oil density: 876 [kg/m
^{3}] - Inlet, Port P: fixed static absolute pressure 50 bar
- Outlet, Port A: fixed static absolute pressure of 45 bar

^{®}.

^{®}stands for “CAE System Empowering Simulation” and its ultimate goal is to design optimal flow-exposed products [17]. Starting from a baseline geometry, it is possible within CAESES

^{®}to modify the geometry, using different strategies and imposing constraints and parameters to obtain a set of geometries and boundary conditions that will be treated as a design of experiments (DOE) set.

- Fully parametric modeling: It allows the user to build the geometry from scratch in CAESES
^{®}, using a proprietary “Meta Surface technology”. This technology gives the possibility of modifying the built-in geometry in all possible ways (Figure 7). - Partially parametric modeling: It lets the user import existing geometries and morph or deform these geometries. This means that the original geometry can be “distorted and modified” using a sort of surrounding grid, with control points that drive the geometry modifications (Figure 8).

^{®}calculated all the possible shapes within the defined constraints and calculated a DOE sequence for the valid geometrical solutions.

^{®}using the “fully parametric modelling” approach. The “partial parametric modeling” approach was used for other parts of the model (spool and other ports), although these parts have not been included in this phase of the project.

^{®}and different geometrical modifications of the valve ports A and B were taken into consideration.

^{®}allows the user to select the geometry control parameters that are deemed relevant for the problem.

^{®}: Port A and Port P volumes were monitored not to exceed predefined values.

^{®}.

^{®}is that the code drives all the process automatically; this means that CAESES

^{®}generates the geometry that has to be tested on the base of the “design variables”.

^{®}creates the STL file that is used by SimericsMP+

^{®}to generate the mesh. SimericsMP+

^{®}is then run in batch and generates the new mesh, sets up the simulation and solves the case.

^{®}are read, via a .txt file, from CAESES

^{®}, that evaluates the obtained mass flux value.

^{®}’ shared memory parallel solver on a single processor, eight cores workstation, the whole DOE sequence calculation took 22.5 h; less than one day.

## 3. Results

#### 3.1. Baseline Computational Fluid Dynamics (CFD) Results

#### 3.2. Optimizaion Results

^{®}provides a detailed table of all the data used in the calculations. For each simulated design, the corresponding geometric characteristics as well as calculations results are provided. In this specific project, as previously mentioned, 90 design variants were tested. A chart mapping 67 solutions versus the obtained flow rate can be visualized in Figure 16.

#### Optimized Geometry

#### 3.3. CFD Results on Optimized Geometry

## 4. Discussion

^{®}and then evaluated by Simerics MP+

^{®}. Answers can be obtained in very short time, also with different optimization techniques.

^{®}and SimericsMP+

^{®}.

## 5. Conclusions

^{®}and CAESES

^{®}were used for this project.

^{®}directly handles the automated process, including geometric modifications, simulations set up and run.

^{®}, is necessary, as it accelerates the process to obtain the best geometry.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations/Nomenclature

CAD | Computer Aided Design |

CFD | Computational Fluid Dynamics |

DOE | Design of Experiments |

MGI | Mismatched Grid Interface |

STL | Stereolithography |

RNG | Re-Normalization Group |

## References

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Parameter | Lower Value | Upper Value | Initial Value |
---|---|---|---|

Box shift for Port A | −2.5 [mm] | −1.8 [mm] | −2 [mm] |

Box rotation for Port A | 5 [°] | 10 [°] | 10 [°] |

Outer circle radius for Port A | 1.45 [mm] | 1.6 [mm] | 1.5 [mm] |

Outer fillet radius for Port A | 10 [mm] | 35 [mm] | 30 [mm] |

Box shift for Port P | −2.5 [mm] | −1 [mm] | −1.1 [mm] |

Box rotation for Port P | 5 [°] | 10 [°] | 9 [°] |

Outer circle radius for Port P | 1.45 [mm] | 1.6 [mm] | 1.482 [mm] |

Outer fillet radius for Port P | 10 [mm] | 35 [mm] | 34.61 [mm] |

Parameter | Baseline | Optimized |
---|---|---|

Box height for Port A | −2 [mm] | −1.871 [mm] |

Box rotation for Port A | 10 [°] | 7.617 [°] |

Outer circle radius for Port A | 1.5 [mm] | 1.592 [mm] |

Outer fillet radius for Port A | 30 [mm] | 17.62 [mm] |

Box height for Port P | −1.1 [mm] | −1.949 [mm] |

Box rotation for Port P | 9 [°] | 8.555 [°] |

Outer circle radius for Port P | 1.482 [mm] | 1.5847 [mm] |

Outer fillet radius for Port P | 34.61 [mm] | 14.88 [mm] |

Volume Port A | 158,242 [mm^{3}] | 175,369 [mm^{3}] |

Volume Port B | 158,967 [mm^{3}] | 178,111 [mm^{3}] |

Parameter | Baseline | Best Design |
---|---|---|

Mass Flow rate [kg/s] | 13.47 | 14.70 |

Outer radius Port A [mm] | 1.5 | 1.595 |

Outer radius Port P [mm] | 1.5 | 1.595 |

Volume Port A [m^{3}] | 0.000168 | 0.000176 |

Volume Port P [m^{3}] | 0.000170 | 0.000180 |

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## Share and Cite

**MDPI and ACS Style**

Olivetti, M.; Monterosso, F.G.; Marinaro, G.; Frosina, E.; Mazzei, P.
Valve Geometry and Flow Optimization through an Automated DOE Approach. *Fluids* **2020**, *5*, 17.
https://doi.org/10.3390/fluids5010017

**AMA Style**

Olivetti M, Monterosso FG, Marinaro G, Frosina E, Mazzei P.
Valve Geometry and Flow Optimization through an Automated DOE Approach. *Fluids*. 2020; 5(1):17.
https://doi.org/10.3390/fluids5010017

**Chicago/Turabian Style**

Olivetti, Micaela, Federico Giulio Monterosso, Gianluca Marinaro, Emma Frosina, and Pietro Mazzei.
2020. "Valve Geometry and Flow Optimization through an Automated DOE Approach" *Fluids* 5, no. 1: 17.
https://doi.org/10.3390/fluids5010017