# Research on the Relationship between Sediment Concentration and Centrifugal Pump Performance Parameters Based on CFD Mixture Model

^{*}

## Abstract

**:**

^{3}/s, Q = 2.5 m

^{3}/s, 1.2 Q = 3 m

^{3}/s) by the polynomial least-square method. Calculated values of fitting equations were compared with the measured values in centrifugal pump operation. The results show that, as the sediment concentration increases from 0.1% to 1%, the maximum volume fraction of sediment at blade outlet increased from 0.14% to 1.14%, and the maximum volume fraction of sediment at blade outlet increased from 0.7% to 2.29%. The turbulent kinetic energy inside the centrifugal pump increased from 8.74 m

^{2}/s

^{2}to 10.78 m

^{2}/s

^{2}. The calculated values of fitting equation are in good agreement with the measured values in centrifugal pump operation, and the maximum errors of head, flow rate, and efficiency are 6.48%, 3.54%, and 2.87%, respectively. Therefore, the reliability of the fitting equations is verified. The research method can provide a reference for the calculation of performance parameters for centrifugal pumps in other water supply pumping stations with sediment-laden flow.

## 1. Introduction

^{3}, and the sediment particle size is 0.05~0.002 mm in the middle reaches of the Yellow River. At present, double-suction is the device most widely used in centrifugal pump operation. Centrifugal pumps are heavily used in pumping irrigation projects in the Yellow River Basin because of their characteristics to pump high flow rate [3]. Double-suction centrifugal pumps are mostly designed and manufactured under the condition of clean water. However, as the Yellow River has high sediment content, the sediment is moved by the action of water in centrifugal pumps, and in turn, the moving sediment affects the flow structure. This situation affects the flow rate, head, and efficiency of centrifugal pumps to varying degrees, and the structure of centrifugal pumps also produces varying degrees of abrasion. This situation does not only affect the flow and head of centrifugal pumps, but also destroys the structure of the centrifugal pumps, thus shortening their life. In addition, the above effects also reduce the efficiency of centrifugal pumps, cause energy waste, and increase economic losses [4,5,6,7]. Such problems occur not only in the Yellow River Basin, but also in other water supply engineering sites with sediment-laden flow. Therefore, it is necessary to study the characteristic parameters of centrifugal pumps under the condition of sediment-laden flow.

## 2. Materials and Methods

#### 2.1. Research Object

^{3}/s, and total installed capacity of 30,880 kW. The 800S-76 centrifugal pump of the pumping station was selected to explore the performance parameters of the centrifugal pump under different sediment concentrations. The centrifugal pump is a double-suction centrifugal pump with a design flow rate of 2.5 m

^{3}/s, and rotational speed of 750 r/min. The impeller has eight groups of blades. The working parameters of the centrifugal pump at 0.8 Q, Q, and 1.2 Q working conditions are shown in Table 1. Based on the measured data, the weight sediment concentration of the water flowing through the pump is less than 0.5%, for there is a sedimentation tank in front of the pumping station.

#### 2.2. Mixture Model

^{3}; ${v}_{m}$ is mass average velocity, m/s; ${\mu}_{m}$ is mixture viscous coefficient, Pa·s; $F$ is body force, Pa; $n$ is number of phases (there are only water phase and sediment phase, so $n=2$); ${\alpha}_{k}$ is volume fraction of the kth phase; ${\rho}_{k}$ is density of the kth phase, kg/m

^{3}; and ${v}_{dr,k}$ is drift velocity of the kth phase, m/s.

^{2}.

^{3}; ${d}_{p}$ is particle diameter of the second phase p, m; and ${\mu}_{q}$ is relative dynamic viscosity coefficient of the second phase p, Pa·s.

#### 2.3. Meshing and Calculation Method

#### 2.4. Polynomial Least-Squares Fitting Principle

**m + 1**data points $\left({x}_{i},{y}_{i}\right)\left(i=0,1,2,\cdots ,m\right)$, an approximate polynomial function f(x) of order

**n**can be introduced for fitting. That is,

_{k}in the polynomial function f(x). Thus, the minimum sum of squares of deviation should be a function of coefficient ${a}_{k}\left(0\le k\le n\right)$. That is,

**A**uncertainty ${U}_{a,A}$, ${U}_{a,B}$ is

_{a}and s

_{b}. That is,

## 3. Results and Discussion

#### 3.1. Model Validation

#### 3.2. Analysis of Simulated Results of Internal and External Characteristics of Centrifugal Pump with Sediment-Laden Flow

^{3}) in the front pool of the pumping station was selected based on the actual operation of Jiamakou water supply pumping station. The performance of the centrifugal pump at the design flow is studied under the conditions of clean water (the sediment concentration of 0%) and different sediment concentrations, and the effects of those sediment concentrations on internal characteristics and performance parameters of the centrifugal pump, are analyzed.

#### 3.2.1. Internal Characteristic Analysis

- Influence of sediment concentrations on solid particle distribution in the centrifugal pump

- (2)
- Effect of sediment concentrations on the turbulent kinetic energy in centrifugal pump

**ab**(X = −0.35 m) is selected to analyze the influence of sediment concentrations on the variation of turbulent kinetic energy in the centrifugal pump, and the results are shown in Figure 8.

^{2}/s

^{2}to 10.78 m

^{2}/s

^{2}. Finally, loss of pressure and energy also increase continuously in the process of centrifugal pump operation.

#### 3.2.2. External Characteristic Analysis

#### 3.3. Establishment of Fitting Equations between Performance Parameters of Centrifugal Pump and Sediment Concentration at Different Working Conditions

^{3}/s; ${N}_{{\rho}_{sc}}$ is shaft power at Q under the sediment concentration ${\rho}_{sc}$, Kw; and ${\eta}_{{\rho}_{sc}}$ is centrifugal pump efficiency at Q under the sediment concentration ${\rho}_{sc}$, %;

^{3}/s; ${N}_{Q}$ is shaft power at Q under the condition of clean water, Kw; and ${\eta}_{Q}$ is centrifugal pump efficiency at Q under the condition of clean water, %.

^{3}/s; ${N}_{0.8{\rho}_{sc}}$, ${N}_{1.2{\rho}_{sc}}$ are shaft power at 0.8 Q and 1.2 Q under the sediment concentration ${\rho}_{sc}$, Kw; ${\eta}_{0.8{\rho}_{sc}}$, ${\eta}_{1.2{\rho}_{sc}}$ are centrifugal pump efficiency at 0.8 Q and 1.2 Q under the sediment concentration ${\rho}_{sc}$, %; ${H}_{0.8Q}$, ${H}_{1.2Q}$ are centrifugal pump head at 0.8 Q and 1.2 Q under the condition of clean water, m; ${Q}_{0.8Q}$, ${Q}_{1.2Q}$ are centrifugal pump flow rate at 0.8 Q and 1.2 Q under the condition of clean water, m

^{3}/s; ${N}_{0.8Q}$, ${N}_{1.2Q}$ are shaft power at 0.8 Q and 1.2 Q under the condition of clean water, Kw; and ${\eta}_{0.8Q}$, ${\eta}_{1.2Q}$ are centrifugal pump efficiency at 0.8 Q and 1.2 Q under the condition of clean water, %.

#### 3.4. Verification and Application of Fitting Equations

#### 3.4.1. Comparison and Error Analysis of Measured Data and Calculated Values

^{3}/s, and ${\eta}_{0.8Q}$ = 82%). The results are shown in Table 6.

#### 3.4.2. Comparison of Similar Calculation Equations

^{3}/s; ${H}_{\rho}$ is the head of pumps with sediment-laden flow in old equations, m; ${N}_{\rho}$ is the shaft power of pumps with sediment-laden flow in old equations, kW; ρ is sediment concentration in old equations, %; ${Q}_{0}$ is the flow rate of pumps with clean water in old equations, m

^{3}/s; ${H}_{0}$ is the head of pumps with clean water in old equations, m; and ${N}_{0}$ is the shaft power of pumps with clean water in old equations, kW.

#### 3.4.3. Characteristic Curves of Centrifugal Pump with Different Sediment Concentrations

_{sc}= 0%, 0.5%, and 1%) are substituted into Equations (22)–(24). The calculation results are shown in Table 8.

## 4. Conclusions

- The volume fraction of sediment at impeller outlet and volute wall is relatively large under the condition of sediment-laden flow, leading to the wear of blade edge and volute wall being relatively serious. Moreover, the wear of blade edge and volute wall increases with the increase of sediment concentration.
- In the impeller inlet, blade back, impeller outlet, and cochlea tongue of the centrifugal pump, there are high turbulent kinetic energy regions in different degrees under the condition of sediment-laden flow, resulting in loss of pressure and energy in the centrifugal pump. With the increase of sediment concentration, the loss of pressure and energy in the centrifugal pump also increase.
- With the increase of sediment concentration in the centrifugal pump, the head, flow rate, and efficiency of the centrifugal pump all show downward trends, while the shaft power shows a rising trend.
- The fitting equations are established between the performance parameters of the centrifugal pump and sediment concentration by the polynomial least-squares method, which can provide a simple and efficient method for the calculation of performance parameters of the centrifugal pump with different sediment concentrations. However, it can be seen from the error analysis results that, as the service time of the centrifugal pump increases, it is necessary to constantly calibrate fitting equations to ensure its calculation accuracy.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

ρ_{m} | mixture density (kg/m^{3}) |

ν_{m} | mass average velocity (m/s) |

μ_{m} | mixture viscous coefficient (Pa·s) |

F | body force (Pa) |

n | number of phases (there are only water phase and sediment phase, so n = 2) |

α_{k} | volume fraction of the kth phase (kg/m^{3}) |

ρ_{k} | density of the kth phase (kg/m^{3}) |

ν_{dr,k} | drift velocity of the kth phase (m/s) |

τ_{q,p} | relaxation time of particles (s) |

a | acceleration of second-phase particle (m/s^{2}) |

ρ_{p} | density of the second phase p (kg/m^{3}) |

d_{p} | particle diameter of the second phase p (m) |

μ_{q} | relative dynamic viscosity coefficient of the second phase p (Pa·s) |

A | uncertainty of intercept a |

B | uncertainty of slope b |

ρ_{sc} | sediment concentration (%) |

${H}_{0.8{\rho}_{sc}}$ | centrifugal pump head at 0.8 Q under the sediment concentration ρ_{sc} (m) |

${H}_{{\rho}_{sc}}$ | centrifugal pump head at Q under the sediment concentration ρ_{sc} (m) |

${H}_{1.2{\rho}_{sc}}$ | centrifugal pump head at 1.2 Q under the sediment concentration ρ_{sc} (m) |

${Q}_{0.8{\rho}_{sc}}$ | centrifugal pump flow rate at 0.8 Q under the sediment concentration ρ_{sc} (m^{3}/s) |

${Q}_{{\rho}_{sc}}$ | centrifugal pump flow rate at Q under the sediment concentration ρ_{sc} (m^{3}/s) |

${Q}_{1.2{\rho}_{sc}}$ | centrifugal pump flow rate at 1.2 Q under the sediment concentration ρ_{sc} (m^{3}/s) |

${N}_{0.8{\rho}_{sc}}$ | shaft power at 0.8 Q under the sediment concentration ρ_{sc} (kW) |

${N}_{{\rho}_{sc}}$ | shaft power at Q under the sediment concentration ρ_{sc} (kW) |

${N}_{1.2{\rho}_{sc}}$ | shaft power at 1.2 Q under the sediment concentration ρ_{sc} (kW) |

${\eta}_{0.8{\rho}_{sc}}$ | centrifugal pump efficiency at 0.8 Q under the sediment concentration ρ_{sc} (%) |

${\eta}_{{\rho}_{sc}}$ | centrifugal pump efficiency at Q under the sediment concentration ρ_{sc} (%) |

${\eta}_{1.2{\rho}_{sc}}$ | centrifugal pump efficiency at 1.2 Q under the sediment concentration ρ_{sc} (%) |

H_{0.8Q} | centrifugal pump head at 0.8 Q under the condition of clean water (m) |

H_{Q} | centrifugal pump head at Q under the condition of clean water (m) |

H_{1.2Q} | centrifugal pump head at 1.2 Q under the condition of clean water (m) |

Q_{0.8Q} | centrifugal pump flow rate at 0.8 Q under the condition of clean water (m^{3}/s) |

Q_{Q} | centrifugal pump flow rate at Q under the condition of clean water (m^{3}/s) |

Q_{1.2Q} | centrifugal pump flow rate at 1.2 Q under the condition of clean water (m^{3}/s) |

N_{0.8Q} | shaft power at 0.8 Q under the condition of clean water (kW) |

N_{Q} | shaft power at Q under the condition of clean water (kW) |

N_{1.2Q} | shaft power at 1.2 Q under the condition of clean water (kW) |

η_{0.8Q} | centrifugal pump efficiency at 0.8 Q under the condition of clean water (%) |

η_{Q} | centrifugal pump efficiency at Q under the condition of clean water (%) |

η_{1.2Q} | centrifugal pump efficiency at 1.2 Q under the condition of clean water (%) |

Q_{ρ} | flow rate of pumps with sediment-laden flow in old models (m^{3}/s) |

H_{ρ} | head of pumps with sediment-laden flow in old models (m) |

N_{ρ} | shaft power of pumps with sediment-laden flow in old models (kW) |

ρ | sediment concentration in old models (%) |

Q_{0} | flow rate of pumps with clean water in old models (m^{3}/s) |

N_{0} | head of pumps with clean water in old models (m) |

N_{0} | shaft power of pumps with clean water in old models (kW) |

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**Figure 4.**Physical picture of wear and cloud diagram of volume fraction of sediment particles: (

**a**) physical picture of wear; (

**b**) cloud diagram of volume fraction of sediment particles.

**Figure 5.**Cloud diagram of the variation of solid particle volume fraction in centrifugal pump with different sediment concentrations: (

**a**) sediment concentration ρ

_{sc}= 0.1%; (

**b**) sediment concentration ρ

_{sc}= 1%.

**Figure 6.**Cross-section ab solid particle volume fraction variation trend diagram: (

**a**) sediment concentration ρ

_{sc}= 0.1%; (

**b**) sediment concentration ρ

_{sc}= 1%.

**Figure 7.**Cloud diagram of the variation of turbulence kinetic energy in centrifugal pump with different sediment concentrations: (

**a**) clear water; (

**b**) sediment concentration ρ

_{sc}= 0.1%; (

**c**) sediment concentration ρ

_{sc}= 1%.

**Figure 8.**Cross-section ab shows the variation trend of turbulence kinetic energy with different sediment concentrations.

**Figure 9.**The variation trend diagram of performance parameters of centrifugal pump with different sediment concentrations at the design flow rate Q.

**Figure 10.**Variation trend diagram of performance parameters of centrifugal pump with different sediment concentrations at 0.8 Q and 1.2 Q conditions: (

**a**) 0.8 Q working condition; (

**b**) 1.2 Q working condition.

**Figure 11.**Characteristic curves of centrifugal pump with sediment concentrations of 0%, 0.5%, and 1%: (

**a**) flow-head (Q-H) curve; (

**b**) flow-shaft power (Q-N) curve; (

**c**) flow-efficiency (Q-η) curve.

Working Conditions | Head (m) | Flow Rate (m^{3}/s) | Shaft Power (kW) | Efficiency (%) |
---|---|---|---|---|

0.8 Q | 79 | 2 | 1886.82 | 82 |

Q | 75 | 2.5 | 2160.08 | 85 |

1.2 Q | 64 | 3 | 2292.84 | 82 |

Working Condition | Head (m) | Shaft Power (kW) | ||||
---|---|---|---|---|---|---|

Working Parameter | Simulated Value | Relative Error | Working Parameters | Simulated Value | Relative Error | |

0.8 Q | 79 | 79.64 | 0.81% | 1886.82 | 1921.66 | 1.85% |

Q | 75 | 76.68 | 2.25% | 2160.08 | 2230.52 | 3.26% |

1.2 Q | 64 | 65.26 | 1.97% | 2292.84 | 2358.43 | 2.86% |

**Table 3.**Performance parameters of centrifugal pump with different sediment concentrations at design flow rate Q.

ρ_{sc} (%) | Head (m) | Flow Rate (m^{3}/s) | Shaft Power (kW) | Efficiency (%) |
---|---|---|---|---|

0 | 76.68 | 2.528 | 2230.52 | 85.09 |

0.1 | 76.66 | 2.525 | 2234.17 | 84.84 |

0.2 | 76.58 | 2.523 | 2237.85 | 84.53 |

0.3 | 76.50 | 2.520 | 2241.52 | 84.22 |

0.5 | 76.34 | 2.515 | 2248.89 | 83.60 |

0.7 | 76.18 | 2.510 | 2256.25 | 82.99 |

1 | 75.95 | 2.502 | 2267.30 | 82.08 |

**Table 4.**The errors between the numerical simulation results at the condition of clean water and the performance parameters of centrifugal pump at different flows.

Working Condition | Flow Rate (m^{3}/s) | Efficiency (%) | ||||
---|---|---|---|---|---|---|

Performance Parameters | Simulated Value | Relative Error | Performance Parameters | Simulated Value | Relative Error | |

0.8 Q | 2 | 2.022 | 1.12% | 82 | 82.08 | 0.10% |

Q | 2.5 | 2.528 | 1.10% | 85 | 85.09 | 0.11% |

1.2 Q | 3 | 3.033 | 1.09% | 82 | 82.18 | 0.22% |

**Table 5.**Errors between actual data of shaft power and calculated values of shaft power equation at 0.8 Q working condition.

ρ_{sc} (%) | Shaft Power (kW) | ||
---|---|---|---|

Actual Data | Equation Calculated Value | Relative Error | |

0.15 | 1853.78 | 1891.52 | 2.04% |

0.16 | 1839.33 | 1891.83 | 2.85% |

0.22 | 1860.66 | 1893.71 | 1.78% |

0.27 | 1875.76 | 1895.28 | 1.04% |

0.39 | 1848.96 | 1899.04 | 2.71% |

ρ_{sc} (%) | Head (m) | Flow Rate (m^{3}/s) | Effective (%) | ||||||
---|---|---|---|---|---|---|---|---|---|

Actual Data | Equation Calculation | Relative Error | Actual Data | Equation Calculation | Relative Error | Actual Data | Equation Calculation | Relative Error | |

0.15 | 75.32 | 78.88 | 4.73% | 2.03 | 1.9969 | 1.63% | 80.77 | 81.57 | 0.99% |

0.16 | 74.59 | 78.87 | 5.74% | 2.07 | 1.9967 | 3.54% | 82.20 | 81.54 | 0.81% |

0.22 | 74.03 | 78.83 | 6.48% | 2.03 | 1.9955 | 1.70% | 79.09 | 81.36 | 2.87% |

0.27 | 75.16 | 78.79 | 4.83% | 2.02 | 1.9944 | 1.27% | 79.26 | 81.22 | 2.47% |

0.39 | 74.88 | 78.69 | 5.09% | 2.01 | 1.9920 | 0.90% | 79.71 | 80.87 | 1.46% |

ρ_{sc} (%) | Head (m) | Flow Rate (m^{3}/s) | ||||||
---|---|---|---|---|---|---|---|---|

Actual Data | Error of old Equations | Error of Fitting Equations | Difference Volume of Error | Actual Data | Error of Old Equations | Error of Fitting Equations | Difference Volume of Error | |

0.15 | 75.32 | 4.50% | 4.73% | 0.23% | 2.03 | 11.34% | 1.62% | 9.72% |

0.16 | 74.59 | 5.50% | 5.75% | 0.25% | 2.07 | 13.65% | 3.53% | 10.11% |

0.22 | 74.03 | 6.15% | 6.48% | 0.33% | 2.03 | 15.41% | 1.69% | 13.72% |

0.27 | 75.16 | 4.45% | 4.83% | 0.38% | 2.02 | 17.71% | 1.25% | 16.46% |

0.39 | 74.88 | 4.59% | 5.10% | 0.51% | 2.01 | 23.14% | 0.88% | 22.26% |

ρ_{sc} (%) | Shaft Power (kW) | |||||||

Actual Data | Error of OldEquations | Error of Fitting Equations | Difference Volume of Error | |||||

0.15 | 1853.78 | 1.81% | 2.03% | 0.22% | ||||

0.16 | 1839.33 | 2.61% | 2.85% | 0.23% | ||||

0.22 | 1860.66 | 1.47% | 1.77% | 0.29% | ||||

0.27 | 1875.76 | 0.69% | 1.03% | 0.33% | ||||

0.39 | 1848.96 | 2.28% | 2.69% | 0.41% |

ρ_{sc} (%) | Head (m) | Flow Rate (m^{3}/s) | Shaft Power (kW) | Efficiency (%) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

0.8 Q | Q | 1.2 Q | 0.8 Q | Q | 1.2 Q | 0.8 Q | Q | 1.2 Q | 0.8 Q | Q | 1.2 Q | |

0 | 79 | 75 | 64 | 2 | 2.5 | 3 | 1886.82 | 2160.08 | 2292.84 | 82 | 85 | 82 |

0.5 | 78.61 | 74.63 | 63.68 | 1.99 | 2.487 | 2.985 | 1937.13 | 2178.01 | 2377.89 | 80.55 | 83.50 | 80.55 |

1 | 78.23 | 74.26 | 63.36 | 1.98 | 2.474 | 2.969 | 1952.60 | 2195.94 | 2397.34 | 79.11 | 82.00 | 79.11 |

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Wu, X.; Su, P.; Wu, J.; Zhang, Y.; Wang, B. Research on the Relationship between Sediment Concentration and Centrifugal Pump Performance Parameters Based on CFD Mixture Model. *Energies* **2022**, *15*, 7228.
https://doi.org/10.3390/en15197228

**AMA Style**

Wu X, Su P, Wu J, Zhang Y, Wang B. Research on the Relationship between Sediment Concentration and Centrifugal Pump Performance Parameters Based on CFD Mixture Model. *Energies*. 2022; 15(19):7228.
https://doi.org/10.3390/en15197228

**Chicago/Turabian Style**

Wu, Xinhao, Peilan Su, Jianhua Wu, Yusheng Zhang, and Baohe Wang. 2022. "Research on the Relationship between Sediment Concentration and Centrifugal Pump Performance Parameters Based on CFD Mixture Model" *Energies* 15, no. 19: 7228.
https://doi.org/10.3390/en15197228