Table 2 Summary of erosion models based on experiments

Liu et al. [69]

2012

Needle tip (ZG230-450):

\(E = 5.45 \times 10^{ - 9} \cdot W^{3.16} \cdot C_{s}^{0.98}\)

Needle shaft (42CrMo):

\(E = 1.47 \times 10^{ - 9} \cdot W^{3.41} \cdot C_{s}^{1.02}\)

Runner bucket (X3CrNiMo13-4):

\(E = 8.82 \times 10^{ - 9} \cdot W^{3.51} \cdot C_{s}^{1.01}\)

\(E\) is the erosion rate of mass loss for the test sample, g/h

\(W\) is the resultant velocity, m/s

\({C}_{s}\) is the sediment concentration, kg/m³

Liu et al. [44]

2019

Runner bucket (04Cr13Ni5Mo):

\(E = 3.45 \times 10^{ - 9} \cdot W^{4.31} \cdot C_{s}^{1.05}\)

Needle tip (ADB610):

\(E = 5.32 \times 10^{ - 9} \cdot W^{4.28} \cdot C_{s}^{0.95}\)

Nozzle ring (42ZG230-450):

\(E = 1.07 \times 10^{ - 8} \cdot W^{4.07} \cdot C_{s}^{1.06}\)

\(E\) is erosion rate, μm/h

\(W\) is the resultant velocity, m/s

\({C}_{s}\) is the sediment concentration, kg/m³

Padhy et al. [5]

2009

Runner (brass):

\(W = 4.02 \times 10^{ - 12} S^{0.0567} C^{1.2267} V^{3.79} t\)

\(W\) is normalized wear, g/g; per unit discharge, m³/s

\(S\) is silt particle size, m

\(C\) is silt concentration, ppm

\(V\) is silt concentration, m/s

Padhy et al. [6]

2011

Turbine (brass):

\(\eta \% = 2.43 \times 10^{ - 10} t^{0.75} S^{0.099} C^{0.93} V^{3.40}\)

\(\eta\) is efficiency loss, %

\(S\) is silt particle size, m

\(C\) is silt concentration, ppm

\(V\) is silt concentration, m/s

Thakur et al. [71]

2017

Runner blades (Aluminum):

\(W = 3.733 \times 10^{ - 11} S^{0.1159} C^{0.9096} V^{2.285} t^{1.1317}\)

W is normalized wear, g/g

S is silt size, μm

C is the silt concentration, ppm

V is the jet velocity, m/s

\(t\) is operating time, h

Rai et al. [45]

2020

Bucket (Bronze):

\(\left( {E_{n} } \right)_{BGi} = 5.74 \times 10^{ - 12} (SSC)^{1.03} \left( {d_{50} } \right)^{ - 0.085} (C)^{3.10} (t)^{1.09}\)

Bucket (16Cr-5Ni):

\(\left( {E_{n} } \right)_{BGi} = 9.09 \times 10^{ - 13} (SSC)^{1.09} \left( {d_{50} } \right)^{0.004} (C)^{3.36} (t)^{1.11}\)

Bucket (16Cr-4Ni):

\(\left( {E_{n} } \right)_{BGi} = 7.02 \times 10^{ - 13} (SSC)^{1.08} \left( {d_{50} } \right)^{ - 0.009} (C)^{3.42} (t)^{1.12}\)

Bucket (13Cr-4Ni):

\(\left( {E_{n} } \right)_{BGi} = 6.25 \times 10^{ - 13} (SSC)^{1.08} \left( {d_{50} } \right)^{0.000} (C)^{3.47} (t)^{1.11}\)

Bucket (13Cr-4Ni with plasma sprayed Cr2O3 coating):

\(\left( {E_{n} } \right)_{BGi} = 7.14 \times 10^{ - 12} (SSC)^{1.25} \left( {d_{50} } \right)^{0.376} (C)^{2.42} (t)^{1.18}\)

Bucket (13Cr-4Ni with WC-Co-Cr HVOF coating):

\(\left( {E_{n} } \right)_{BGi} = 1.38 \times 10^{ - 14} (SSC)^{1.12} \left( {d_{50} } \right)^{0.314} (C)^{4.09} (t)^{0.96}\)

\({\left({E}_{n}\right)}_{BGi}\) is normalized erosion for the bucket, g

\(SSC\) is silt concentration, ppm

\({d}_{50}\) is median sediment size in a particle size distribution, mm

\(C\) is relative flow velocity, m/s

\(t\) is the time duration of erosion, h