# A Novel Surge Damping Method for Hydraulic Transients with Operating Pump Using an Optimized Valve Control Strategy

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Simulation Model

#### 2.1. One-Dimensional Unsteady Friction Model

- (1)
- The liquid fluid complies with cross-section-averaged properties.
- (2)
- The water liquid is considered to be single phase without entrained air.
- (3)
- The pipe is elastic, and the fluid is compressible.
- (4)
- The pipe flow is assumed to be adiabatic flow.

_{d}is the second viscosity coefficient that is relevant to Reynolds number, which can be determined using the trial-and-error method. With the incorporation of the modified unsteady friction term, the one-dimensional governing equations for unsteady flow can be obtained, which are known as the water hammer equations:

#### 2.2. Physical Model and Solution Method

^{+}and C

^{−}can be expressed as

_{S}was 165.92, the coefficient constant a

_{1}was 7.07, and a

_{2}was −1.09.

^{−}, the flow rate ${Q}_{E}$can be obtained as follows

^{−}, which is the reversal of the centrifugal pump case.

_{F}and Q

_{0}are the transient and steady flow rate through the valve, respectively, and H

_{F}and H

_{0}are the hydraulic head in the transient and steady state, respectively.

^{+}, in opposition to C

^{−}, as follows:

## 3. Optimization Scheme Using ASFA

_{V}of all visible fish is better than that at the current position Xi while also satisfying the crowdedness standard, it steps forward to the swarm center and reaches a new position X

_{c},

_{p}:

^{−}

^{4}.

_{c}, X

_{p}, and X

_{F}

_{.}If an individual fish position is superior, then the bulletin board is updated with the position of the optimal fish. This evaluation continues until evaluation for all fish has been completed. Finally, when the termination criteria are satisfied by means of an acceptable error or the iteration limit being reached, the algorithm ends with the optimized results being output.

## 4. Model Validation

^{D}

^{=30}. With an acceptance of 0.01, the minimum value 0 was obtained at (0, 0) for this function. The second test function was $f2\left(x\right)={{\displaystyle \sum}}_{i=1}^{D}100{({x}_{i+1}-{x}_{i}{}^{2})}^{2}+{({x}_{i}-1)}^{2},$ which is also a unimodal function, and is known as the Rosenbrock function. In the searching range of [−10, 10]

^{D}

^{=30}, the minimum value 0 was found at (1, 1) with an acceptance of 100 [41]. As can be seen, the minimum values obtained from the presented optimization method were 1.89 × 10

^{−6}in Figure 6a and 3.17 × 10

^{−5}in Figure 6b, respectively.

## 5. Results

#### 5.1. Wave Damping Case without Pump Operation

#### 5.2. Wave Damping Case with Centrifugal Pump Operation

#### 5.3. Wave Damping Case with Positive Displacement Pump Operation

## 6. Conclusions

- (1)
- The transient wave surge can be reduced through nonlinear valve closure without adding additional damping devices. For transient flow with and without a centrifugal pump running, surge reduction of 9.3% and 11.4% could be obtained in the most severe valve closure case. Even with increasing pressure with positive displacement pump operation, the surge damping method was able to achieve a 34% time margin for reaching the head limit and a maximum reduction in the surge amplitude of 75.2%.
- (2)
- With increasing valve closing time, the surge amplitude caused by valve closure decreases for the transient flow with and without the centrifugal pump running, and the rate of surge amplitude decrease also decreases. For positive displacement pumps, the surge amplitude increases with increasing valve closing time, but at a significantly slower rate of increase with the optimized nonlinear valve closure.
- (3)
- For rapid valve closure in 0.1 s, the optimized nonlinear closing motion performs a similar “И” shape. For other valve closure cases in the present study, the optimized valve opening curves show a relatively smooth variation during the initial stage before decreasing rapidly to full closure during valve operation.
- (4)
- The valve closure process can be abstracted into a traveling salesman problem, and further optimization using an artificial fish swarm algorithm was demonstrated to be beneficial for wave damping. The strategy proposed in the present study could help for either guiding real-time valve control or serve as a design reference for novel valve structures for the purpose of surge protection.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AFSA | artificial fish swarm algorithm |

CB | convolution-based |

CE | compression–expansion |

CFD | computational fluid dynamics |

IAB | instantaneous accelerations-based |

MOC | method of characteristics |

ODE | ordinary differential equation |

TSP | traveling salesman problem |

1-D | one-dimensional |

Notation | |

a | wave speed (m∙s^{−1}) |

a_{1}, a_{2} | pump coefficient constants (-) |

A | cross sectional area (m^{2}) |

B | pipeline characteristic impedance (-) |

D | pipe diameter (m) |

f | Darcy–Weisbach friction factor (-) |

g | gravitational acceleration (m∙s^{−2}) |

H | pressure head (m) |

J_{s} | steady friction loss term (-) |

J_{u} | unsteady friction loss term (-) |

k | empirical decay coefficient (-) |

k_{d} | second viscosity coefficient (-) |

L | pipe length (m) |

n | artificial fish number (-) |

P | cross-section-average pressure (Pa) |

Q | flowrate (m^{3}∙s^{−}^{1}) |

R | pipeline resistance coefficient (-) |

r | radial coordinate (m) |

Re | Reynolds number (-) |

V | cross-section-average velocity (m∙s^{−1}) |

ϖ | phase velocity in fluctuation (rad∙s^{−1}) |

t | time (s) |

τ | valve opening (-) |

ρ | fluid density (kg∙m^{−3}) |

$\mu $ | dynamic viscosity (Pa∙s) |

${\mu}^{\prime}$ | the second viscosity (Pa∙s) |

x | coordinate along the pipe axis (m) |

X | artificial fish position (-) |

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**Figure 4.**The calculation flow chart for the surge damping optimization. (

**a**) Optimization procedures using ASFA; (

**b**) Hydraulic transient calculation procedures.

**Figure 6.**Validation results using different test functions. (

**a**) optimization for sphere function; (

**b**) optimization for Rosenbrock function; (

**c**) optimization for Schwefel function.

**Figure 9.**Comparison of the pressure fluctuation with a valve closing time of 0.1 s with no pump operation.

**Figure 10.**Comparison of the pressure fluctuation with a valve closing time of 0.5 s with no pump operation.

**Figure 13.**Comparison of the pressure fluctuation with a valve closing time of 0.1 s with centrifugal pump operation.

**Figure 14.**Comparison of the pressure fluctuation with a valve closing time of 0.5 s with centrifugal pump operation.

**Figure 15.**Pressure surge amplitude at different valve closing times with centrifugal pump operation.

**Figure 17.**Comparison of the pressure rise in 0.1 s valve closing time with positive displacement pump operation.

**Figure 18.**Comparison of the pressure increase with a 0.5 s valve closing time with positive displacement pump operation.

**Figure 19.**Pressure surge amplitude at different valve closing times with positive displacement pump operation.

Parameters (Unit) | Values |
---|---|

Initial tank head, H_{res} (m) | 128 |

Initial flow velocity, V_{0} (m/s) | 0.94 |

Pipeline length, L (m) Wave speed, a (m/s) | 98.11 1298.4 |

Pump rotational speed, n_{pump} (r/min)Pump designed head, H _{pump} (m)Pump designed velocity, V _{pump} (m/s) | 8000 165.9 0.88 |

blade numbers | 8 |

Valve closing time, tc (s) | 0.1~0.5 |

$\mathrm{Water}\mathrm{density},\rho $ (kg/m^{3}) | 997.59 |

$\mathrm{Dynamic}\mathrm{viscosity},\mu $$(\mathrm{Pa}\xb7\mathrm{s}$) | 0.947 × 10^{−3} |

empirical coefficient k second viscosity coefficient k _{d} Darcy–Weisbach friction factor, f | 0.0138 20.258 0.0224 |

Parameters | Description | Values |
---|---|---|

Vision | visual radius | 0.1 |

step | moving distance | 0.01 |

n | artificial fish quatities | 30 |

dim | artificial fish dimension | 10 |

delta Trail _{max}Gen _{max} | fish swarm crowdness maximum trial number maximum iteration number | 27 30 500 |

error | convergence error | 1 × 10^{−4} |

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**MDPI and ACS Style**

Cao, Z.; Xia, Q.; Guo, X.; Lu, L.; Deng, J.
A Novel Surge Damping Method for Hydraulic Transients with Operating Pump Using an Optimized Valve Control Strategy. *Water* **2022**, *14*, 1576.
https://doi.org/10.3390/w14101576

**AMA Style**

Cao Z, Xia Q, Guo X, Lu L, Deng J.
A Novel Surge Damping Method for Hydraulic Transients with Operating Pump Using an Optimized Valve Control Strategy. *Water*. 2022; 14(10):1576.
https://doi.org/10.3390/w14101576

**Chicago/Turabian Style**

Cao, Zheng, Qi Xia, Xijian Guo, Lin Lu, and Jianqiang Deng.
2022. "A Novel Surge Damping Method for Hydraulic Transients with Operating Pump Using an Optimized Valve Control Strategy" *Water* 14, no. 10: 1576.
https://doi.org/10.3390/w14101576