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Computational Methods of Erosion Wear in Centrifugal Pump: A State-of-the-Art Review

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Abstract

Erosion wear of the centrifugal pump components is considered one of the principal hurdles for pumping and transporting the particle-fluid flow in the hydraulic system. Although the particles in the multiphase flow can behave like a continuum fluid at times, their irregular pattern cannot be predicted by traditional continuum-based modeling. The computational numerical methods have been extensively used in engineering, where its application is starting to achieve popularity in hydraulic pumping systems. As a result, the Discrete Phase Modeling (DPM) or the Discrete Element Method (DEM) integrated with Computational Fluid Dynamics (CFD) is considered a promising numerical technique that can model the multiphase flow by tracking the movement of each particle in the fluid flow accurately. Further, the CFD predicts and provides the characteristics of the fluid flow field via transport phenomena equations of mass, momentum, and energy. This work reviews the current strategies and the existing applications of the computational modeling approach for predicting and locating the erosion wear in the centrifugal pumps. It mainly represents three principal aspects: the concepts of a centrifugal pump with the erosion wear problem, the modeling approaches of particle-fluid motion including the turbulence and the wear models used in the hydraulic systems, and the computational methodologies for modeling the fluid-particle coupling and their applications for predicting the erosion wear in the centrifugal pumps. The existing published literature indicates that computational numerical modeling is a promising technique to predict and locate the erosion wear in the centrifugal pump components. The collected data could be benefiting from developing and optimizing the pump design and the operating conditions. The main findings are discussed and summarized as a part of the review, where future developments and challenges are highlighted.

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Abbreviations

\(A\) :

Contact area between particles and flow

\({A}_{face}\) :

Unit area of the surface

\(a\) :

Separation distance between particles

\({B}_{h}\) :

Brinell’s hardness number of wall material

\({C}_{D}\) :

Particle drag correlation

\(C\) :

Empirical constant

\({d}_{p}\) :

Particle diameter

\({E}_{w}\) :

Erosion wear rate

\({D}_{\omega }\) :

Cross-diffusion term

\({d}^{^{\prime}}\) :

Particle reference diameter

\({E}_{w}\) :

Erosion wear rate

\({E}_{i}\) :

Young's modulus of particle i

\({E}_{j}\) :

Young's modulus of particle j

\({E}^{*}\) :

Equivalent Young's modulus

\({E}_{c}\) :

Wear due to cutting

\({E}_{D}\) :

Wear due to deformation

\(F\) :

Particle sharpness factor

\({F}_{drag}\) :

Fluid drag force

\({F}_{m}\) :

Magnus force

\({F}_{pg}\) :

Fluid-particle interaction forces

\({F}_{n}\) :

Applied normal load

\({F}_{f}\) :

Force of the fluid phase

\({F}_{p}\) :

Body force of the particle phase

\({F}_{Lf}\) :

Fluid lift force

\({F}_{Lp}\) :

Saffman's lift force

\({F}_{vmf}\) :

Fluid virtual mass force per unit mass

\({F}_{vmp}\) :

Particle virtual mass force per unit mass

\({F}_{C}\) :

Contact force

\({F}_{{i}_{adh}}^{n}\) :

Normal adhesive contact force

\({F}_{ij}^{n}\) :

Normal contact force on a particle

\({T}_{f}\) :

Torque produced by fluid

\(t\) :

Time

\({T}_{C}\) :

Contact torque

\({u}_{p}\) :

Particle translation velocity

\({U}_{p}\) :

Relative impact velocity of the particle

\({u}_{f}\) :

Average velocity component of the fluid

\({v}^{^{\prime}}\) :

Particle reference velocity

\({\nu }_{i}\)y:

Poisson's ratios of the of particle i

\({\nu }_{j}\) :

Poisson's ratios of the of particle j

\({\nu }_{n}\) :

Normal velocity of the particle

\({\nu }_{t}\) :

Tangential velocity of the particle

\({V}_{w}\) :

Volume of the removed material

\(v\) :

Velocity

\(W\) :

Wear rate

\({Y}_{M}\) :

Fluctuating turbulence to the dissipation rate

\({Y}_{k}\) :

Dissipation of k due to turbulence

\({Y}_{\omega }\) :

Dissipation of ω due to turbulence

\({\mu }_{f}\) :

Turbulent fluid viscosity

\({F}_{i}^{f}\) :

Interaction force of the fluid on the particle i

g:

Gravitational acceleration

\(G\) :

Mean rate of the strain tensor

\({G}_{k}\) :

Generation of turbulence kinetic energy

\({G}_{b}\) :

Generation of turbulence due to buoyancy

\({G}_{\omega }\) :

Generation of

\({H}_{V}\) :

Vickers hardness of the wall surface

\({I}_{p}\) :

Moment of inertia of the particle

\(k\) :

Interphase exchange coefficient

\(K\) :

Particle vertical to horizontal force ratio

\({K}_{W}\) :

Wear constant associated with the material

\({k}_{1}\) :

Function of particle properties

\({k}_{2}\) :

Velocity constant

\({k}_{3}\) :

Particle size constant

\(L\) :

Turbulent boundary or the mixing length

\({m}_{p}\) :

Particle mass

\(\dot{{m}_{p}}\) :

Mass flow rate of the particles

\(\widehat{{n}_{c}}\) :

Unit vector in the normal contact

\(p\) :

Plastic flow stress of the eroded material

\(P\) :

Pressure shared by two phases

\({P}_{max}\) :

Maximum liquid bridge tensile force

\({r}^{*}\) :

Equivalent particle radius

\({r}_{i}\) :

Radius of particle i

\({r}_{j}\) :

Radius of particle j

\({Re}_{p}\) :

Particle Reynolds number

\({R}_{\epsilon }\) :

Dissipation of swirl effect on turbulence

\({S}_{L}\) :

yFriction or sliding distance

\({S}^{n}\) :

Normal overlapping

\({s}^{t}\) :

Tangential relative displacement

\({s}_{max}^{t}\) :

Maximum relative tangential displacement

\({\mu }_{t}\) :

Eddy viscosity

\({\mu }_{{f}_{eff}}\) :

Fluid effective turbulent viscosity

\(\tau\) :

Stress tensor

\({\tau }_{f}\) :

Viscous stress tensor

\({\rho }_{f}\) :

Fluid density

\({\rho }_{m}\) :

Density of the pump surface material

\(\varphi\) :

Ratio of depth of contact to the depth of cut

\({\omega }_{p}\) :

Particle rotational velocity

\(\eta\) :

Damping ratio

\({\eta }^{t}\) :

Tangential damping ratio

\(\Gamma\) :

Surface energy

\({\Gamma }_{k}\) :

Effective diffusivity of k

\({\Gamma }_{\omega }\) :

Effective diffusivity of ω

\({\sigma }_{k}\) :

Turbulent Prandtl numbers for k

\({\sigma }_{\epsilon }\) :

Turbulent Prandtl numbers for ϵ

\({\alpha }_{f}\) :

Fluid volume fraction

\({\alpha }_{p}\) :

Particle volume fraction

\({\alpha }_{k}\) :

Inverse Prandtl number for k

\({\alpha }_{\epsilon }\) :

Inverse Prandtl number for ϵ

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 52079058 and 51979138), Zhenjiang Key Research and Development Project (Grant No. GY2020008), Nature Science Foundation for Excellent Young Scholars of Jiangsu Province (Grant No. BK20190101), National Key Research and Development Project (Grant No. 2020YFC1512404), “Pioneer” and “Leading Goose” R&D Program of Zhejiang (2022C03170).

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  1. Research Center of Fluid Machinery Engineering & Technology, Jiangsu University, Zhenjiang, 212013, China

    Mahmoud A. El-Emam, Ling Zhou, Eman Yasser & Ling Bai

  2. Department of Agricultural and Biosystems Engineering, Alexandria University, Shatby, 21526, Egypt

    Mahmoud A. El-Emam

  3. School of Mechanical Engineering, Nantong University, Nantong, 226019, China

    Weidong Shi

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El-Emam, M.A., Zhou, L., Yasser, E. et al. Computational Methods of Erosion Wear in Centrifugal Pump: A State-of-the-Art Review. Arch Computat Methods Eng 29, 3789–3814 (2022). https://doi.org/10.1007/s11831-022-09714-x

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