# Investigation of Pressure Variations in Hose Pumps under Different Flow Regimes Using Bidirectional Fluid–Structure Interaction

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

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## Abstract

**:**

## 1. Introduction

## 2. Simplified Model and Numerical Computational Methods

#### 2.1. Geometric Model

#### 2.2. Mesh Generation

^{5}. We placed five monitoring points at the outlet and used pressure as a reference quantity independent of the grid. We set the grid numbers at 3.0 × 10

^{5}, 4.0 × 10

^{5}, 5.0 × 10

^{5}, and 6.0 × 10

^{5}, respectively. The study revealed that when the grid number exceeded 4.0 × 10

^{5}, the pressure difference at the monitoring points was relatively small. Therefore, it is considered that grid independence has been achieved when the grid number is 4.0 × 10

^{5}. Hence, the model grid meets the requirements for computational accuracy and speed.

#### 2.3. Simulation Model Establishment

_{1}and I

_{2}are invariants of the strain tensor C

_{ij}, and C

_{10}and C

_{01}are Mooney–Rivlin model material constants determined by the material properties as shown in Table 3.

#### 2.4. Contact Settings

#### 2.5. Observation Surface Settings

## 3. Experimental Setup

#### Description of the Experimental Rig

## 4. Results and Analysis

#### 4.1. Experimental Result Validation

_{d}is the conversion coefficient due to hose deformation (typically taken as 0.7–0.8), n is the rotor speed in rad/s, and r is the rotor radius (typically taken as 0.121 m).

_{d}= 0.74 was used, resulting in inlet velocities of 0.32 m/s and 0.6 m/s. The outlet pressure was set to 0.1 MPa, and water was selected as the fluid material. A comparison of the experimental and simulated volume flow rates of the hose pump is shown in Figure 5.

#### 4.2. Simulation Results Analysis

^{5}Pa, while the maximum inlet pressure is 1.39859 × 10

^{5}Pa. This results in an outlet pressure lower than the inlet pressure, resulting in a pressure difference of −0.39212 × 10

^{5}Pa. At 2.12 s, the maximum outlet pressure is 1.00337 × 10

^{5}Pa, and the maximum inlet pressure is 1.28868 × 10

^{5}Pa. Once again, the outlet pressure is lower than the inlet pressure, with a pressure difference of −0.28531 × 10

^{5}Pa. At 2.5 s, the maximum outlet pressure is 1.00259 × 10

^{5}Pa, and the maximum inlet pressure is 1.11278 × 10

^{5}Pa. The outlet pressure remains lower than the inlet pressure, resulting in a pressure difference of −0.11019 × 10

^{5}Pa. Overall, the pressure difference exhibits an initial increase followed by a decrease trend.

^{5}Pa, and the maximum inlet pressure is 1.0053 × 10

^{5}Pa. The outlet pressure is lower than the inlet pressure, leading to a pressure difference of −0.00439 × 10

^{5}Pa. At 2.12 s, the maximum outlet pressure is 1.00117 × 10

^{5}Pa, and the maximum inlet pressure is 1.03652 × 10

^{5}Pa. The outlet pressure remains lower than the inlet pressure, with a pressure difference of −0.03535 × 10

^{5}Pa. At 2.5 s, the maximum outlet pressure is 0.99999 × 10

^{5}Pa, and the maximum inlet pressure is 1.00193 × 10

^{5}Pa. Once again, the outlet pressure is lower than the inlet pressure, with a pressure difference of −0.001937 × 10

^{5}Pa. The overall trend of the pressure difference shows an initial increase followed by a decrease, similar to the laminar flow case, but with smaller variations.

^{5}Pa, while the maximum inlet pressure is 1.21998 × 10

^{5}Pa. The outlet pressure is lower than the inlet pressure, resulting in a pressure difference of −0.21623 × 10

^{5}Pa. At 1.73 s, the maximum outlet pressure is 1.01118 × 10

^{5}Pa, and the maximum inlet pressure is 1.74994 × 10

^{5}Pa. The outlet pressure is lower than the inlet pressure, with a pressure difference of −0.73876 × 10

^{5}Pa. At 1.83 s, the maximum outlet pressure is 1.00378 × 10

^{5}Pa, and the maximum inlet pressure is 1.31568 × 10

^{5}Pa. Once again, the outlet pressure is lower than the inlet pressure, resulting in a pressure difference of −0.3119 × 10

^{5}Pa. The overall trend of pressure difference exhibits an initial increase followed by a decrease, and in this case, the pressure difference is significantly smaller compared to the 35 Hz case.

^{5}Pa, and the maximum inlet pressure is 0.98796 × 10

^{5}Pa. The outlet pressure is lower than the inlet pressure, resulting in a pressure difference of −0.0119 × 10

^{5}Pa. At 1.73 s, the maximum outlet pressure is 1.00223 × 10

^{5}Pa, and the maximum inlet pressure is 1.07033 × 10

^{5}Pa. The outlet pressure is lower than the inlet pressure, with a pressure difference of −0.0681 × 10

^{5}Pa. At 1.83 s, the maximum outlet pressure is 0.99882 × 10

^{5}Pa, and the maximum inlet pressure is 0.95147 × 10

^{5}Pa. However, in this case, the outlet pressure is higher than the inlet pressure, resulting in a positive pressure difference of 0.04735 × 10

^{5}Pa. Once again, the overall trend of pressure difference exhibits an initial increase followed by a decrease, and the flow field instability is more pronounced compared to the previous cases.

^{5}Pa, with the minimum around 0.999 × 10

^{5}Pa. The maximum average inlet pressure is around 1.4 × 10

^{5}Pa, with the minimum around 1.1 × 10

^{5}Pa. When transporting water at the same power frequency, the maximum average outlet pressure is around 1.00125 × 10

^{5}Pa, with the minimum around 0.995 × 10

^{5}Pa, and the maximum average inlet pressure is around 1.4 × 10

^{5}Pa, with the minimum around 0.985 × 10

^{5}Pa. In turbulent conditions, both flow materials exhibit more fluctuations and smaller amplitude compared to laminar conditions. Overall, turbulent conditions lead to more minor but frequent fluctuations, while laminar conditions result in larger but less frequent fluctuations.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**Flow lines and turbulent kinetic energy distribution at the intermediate observation plane in the flow field. (

**a**) Transporting liquid fertilizer for 2.5 s at a power frequency of 35 Hz; (

**b**) Transporting liquid fertilizer for 1.83 s at a power frequency of 65 Hz; (

**c**) Transporting water for 2.5 s at a power frequency of 35 Hz; (

**d**) Transporting water for 1.83 s at a power frequency of 65 Hz.

**Figure 7.**Pressure distribution contour plots at different power frequencies and for different transported materials at the outlet and inlet. (

**a**) Pressure contour plots at the outlet for liquid fertilizer at a power frequency of 35 Hz and an outlet pressure of 0.1 MPa; (

**b**) Pressure contour plots at the inlet for liquid fertilizer at a power frequency of 35 Hz and an outlet pressure of 0.1 MPa; (

**c**) Pressure contour plots at the outlet for water at a power frequency of 35 Hz and an outlet pressure of 0.1 MPa; (

**d**) Pressure contour plots at the inlet for water at a power frequency of 35 Hz and an outlet pressure of 0.1 MPa; (

**e**) Pressure contour plots at the outlet for liquid fertilizer at a power frequency of 65 Hz and an outlet pressure of 0.1 MPa; (

**f**) Pressure contour plots at the inlet for liquid fertilizer at a power frequency of 65 Hz and an outlet pressure of 0.1 MPa; (

**g**) Pressure contour plots at the outlet for water at a power frequency of 65 Hz and an outlet pressure of 0.1 MPa; (

**h**) Pressure contour plots at the inlet for water at a power frequency of 65 Hz and an outlet pressure of 0.1 MPa.

**Figure 8.**Pressure variations at the inlet and outlet. (

**a**) Transporting liquid fertilizer at a power frequency of 35 Hz; (

**b**) Transporting water at a power frequency of 35 Hz; (

**c**) Transporting liquid fertilizer at a power frequency of 65 Hz; (

**d**) Transporting water at a power frequency of 65 Hz.

**Figure 9.**Pressure contours at the midsection for different power frequencies and transported materials. (

**a**) Pressure contour at the midsection of liquid fertilizer at an outlet pressure of 0.1 MPa and a power frequency of 35 Hz; (

**b**) Pressure contour at the midsection of water at an outlet pressure of 0.1 MPa and a power frequency of 35 Hz; (

**c**) Pressure contour at the midsection of liquid fertilizer at an outlet pressure of 0.1 MPa and a power frequency of 65 Hz; (

**d**) Pressure contour at the midsection of water at an outlet pressure of 0.1 MPa and a power frequency of 65 Hz.

**Figure 10.**Pressure distribution across the entire cycle. (

**a**) Transporting liquid fertilizer at a power frequency of 35 Hz; (

**b**) Transporting water at a power frequency of 35 Hz; (

**c**) Transporting liquid fertilizer at a power frequency of 65 Hz; (

**d**) Transporting water at a power frequency of 65 Hz.

Power Supply Frequency (Hz) | Number of Rollers | Drum Diameter (mm) | Outer Circle Diameter (mm) | Hose Inlet Diameter (mm) | Hose Outer Diameter (mm) |
---|---|---|---|---|---|

35/65 | 3 | 69 | 260 | 25 | 25 |

Density (kg/m^{3}) | Dynamic Viscosity (kg/(m s)) | |
---|---|---|

Liquid Fertilizer | 1300 | 0.7 |

Water | 998.2 | 0.001003 |

Density (kg/m^{3}) | Material Constant C_{10} | Material Constant C_{01} |
---|---|---|

1100 | 5.2 × 10^{7} | 1.3 × 10^{7} |

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**MDPI and ACS Style**

Wang, M.; Zhang, L.; Wang, W.; Ma, X.; Hu, X.; Zhao, J.; Chao, X.
Investigation of Pressure Variations in Hose Pumps under Different Flow Regimes Using Bidirectional Fluid–Structure Interaction. *Processes* **2023**, *11*, 3079.
https://doi.org/10.3390/pr11113079

**AMA Style**

Wang M, Zhang L, Wang W, Ma X, Hu X, Zhao J, Chao X.
Investigation of Pressure Variations in Hose Pumps under Different Flow Regimes Using Bidirectional Fluid–Structure Interaction. *Processes*. 2023; 11(11):3079.
https://doi.org/10.3390/pr11113079

**Chicago/Turabian Style**

Wang, Mengfan, Lixin Zhang, Wendong Wang, Xiao Ma, Xue Hu, Jiawei Zhao, and Xuewei Chao.
2023. "Investigation of Pressure Variations in Hose Pumps under Different Flow Regimes Using Bidirectional Fluid–Structure Interaction" *Processes* 11, no. 11: 3079.
https://doi.org/10.3390/pr11113079