Abstract
The mass flow of abrasive is one of the significant factors, which affects the erosion rate of abrasive gas jet eroding rock and coal, because it affects rebounding abrasives and the shielding effect. However, the effect of abrasive mass flow on abrasive acceleration has been little studied in favor of research on abrasive particle erosion, which is of prime importance for the determination of how the mass flow affects the erosion rate. Therefore, in this study, the effect of mass flow on erosion rates was investigated by numerical simulation and experiment, to analyze the effect of mass flow on abrasive acceleration. It can be concluded that the influence of pressure cannot be ignored, as it determines the time and distance of abrasive acceleration. Each pressure has a corresponding optimal mass flow that can achieve the maximum erosion rate. The erosion rate begins to decrease when the mass flow exceeds the optimal value. The wave-like flow-field structure of free jets influences the distribution character of the abrasive, and leads to the formation of the annular structure of the abrasive flow field. The mass flow barely affects the distribution of abrasive, but clearly affects the abrasive velocity. As the mass flow increases, the distance and time of acceleration of the abrasive decrease, which causes the amount of high-speed abrasive on both sides of the jet axis to decrease and the velocity also decreases.
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Abbreviations
- a :
-
The acoustic velocity
- A :
-
Brinell hardness of the material
- C 1ε, C 2ε, C 3ε :
-
Empirical constants
- \({C_{\text{D}}}\) :
-
Drag coefficient
- \({C_{\text{L}}}\) :
-
Lift coefficient
- \({C_{{\text{VM}}}}\) :
-
Virtual mass coefficient
- \({C_\mu }\) :
-
Constant
- \({d_{\text{p}}}\) :
-
Diameter of the particle
- \(\vec {e}\) :
-
Unit vector
- E R :
-
Target erosion
- \({\vec {F}_{\text{B}}}\) :
-
Magus buoyancy force vector
- \({\vec {F}_{\text{D}}}\) :
-
Drag force vector
- \({\vec {F}_{\text{G}}}\) :
-
Gravity force vector
- \({\vec {F}_{\text{L}}}\) :
-
Lift force vector
- \({\vec {F}_{\text{P}}}\) :
-
Pressure gradient force vector
- F s :
-
Particle shape coefficient
- \({\vec {F}_{{\text{VM}}}}\) :
-
Virtual mass force vector
- G b :
-
The generation term of the turbulent kinetic energy owing to buoyancy
- g i :
-
The component of gravitational acceleration in the i direction
- G k :
-
The generation term of the turbulent kinetic energy resulting from the mean velocity gradient
- i, j :
-
Subscripts of tensors
- \(I\) :
-
Moment of inertia
- k :
-
Turbulent kinetic energy
- m 1, m 2, m 3, m 4 :
-
Empirical constants of erosion rate equation
- \({m_{\text{p}}}\) :
-
The particle mass
- m t−p :
-
Total quality of abrasive
- P 0 :
-
Atmospheric pressure
- P c−a :
-
Pressure of the compressed air
- P ra :
-
Price of abrasive
- P re :
-
Price of electricity
- Prt :
-
The turbulence Prandtl number
- Q inlet :
-
Rate of flow of air compressor inlet
- Q p :
-
Mass flow of abrasive
- \(R{e_{\text{p}}}\) :
-
Relative Reynolds number
- \({\text{S}}\) :
-
Is the modulus of the mean rate-of-strain tensor
- \({S_k}\), \({S_\varepsilon }\) :
-
User-defined source terms
- t :
-
Time
- t r :
-
Erosion time
- \(\vec {T}\) :
-
Torque
- \({u_f}\) :
-
Velocity of the fluid
- u i, u j :
-
Velocity components along i and j
- \({\vec {u}_{\text{p}}}\) :
-
Particle velocity
- \({V_{\text{p}}}\) :
-
Particle volume
- w :
-
Empirical constant of erosion rate equation
- W ac :
-
Power of the air compressor
- x i :
-
Cartesian coordinates
- Y M :
-
The contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate
- z :
-
Empirical constant of erosion rate equation
- \(\alpha\) :
-
Empirical constant of erosion rate equation
- \({\alpha _{\text{f}}}\) :
-
Porosity of continuous phase
- \({\alpha _k}\), \({\alpha _\varepsilon }\) :
-
The reciprocals of the effective Prandtl numbers for turbulent kinetic energy and dissipation rate
- θ :
-
Impingement angle
- \(\varepsilon\) :
-
Dissipation rate of k
- \({\eta _0}\) :
-
Constant
- \(\mu\) :
-
Gas viscosity
- \({\mu _m}\) :
-
Dynamic viscosity
- \({\mu _t}\) :
-
Eddy viscosity
- \({\rho _p}\) :
-
The density of the particle
- \(\tau\) :
-
Time variable
- \(\varphi\) :
-
The thermal expansion coefficient
- \(\vec {\omega }\) :
-
Particle angular velocity
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Acknowledgements
This paper was jointly funded by the National Science Foundation of China, (51704096, 51574112), the Program for Innovative Research Team in University (IRT_16R22), the National Key R&D Program of China (2017YFC0804207), the Science Research Funds for the Universities of Henan Province (J2018-4), and Scientific Research Foundation of State Key Laboratory Cultivation Base for Gas Geology and Gas Control (WS2017A02).
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Ranjith, P.G., Liu, Y., Wei, J. et al. Effect of abrasive mass flow on the abrasive acceleration and erosion rates of abrasive gas jets. Rock Mech Rock Eng 52, 3085–3102 (2019). https://doi.org/10.1007/s00603-019-01746-3
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DOI: https://doi.org/10.1007/s00603-019-01746-3