Numerical Simulation of Coke Particle Erosion on Elbows with Different Bend Radii

Literature Overview

This paper by Jiang Chen, Sun Wei, Wang Li, Ren Pingping, Zhang Xiaofei, and Ji Mingyan (2025), published in Pipeline Technology and Equipment (Issue 3, pp. 57-62), investigates the erosion behavior of coke particles on elbow walls using computational fluid dynamics (CFD) coupled with discrete phase modeling. The study examines nine different bend radius configurations and employs the Realizable k-ε turbulence model to analyze fluid characteristics, pressure distribution, and particle trajectories within the elbows.

Simulation Methodology

The numerical framework combines continuous phase simulation with discrete phase modeling:

Component	Model/Method	Purpose
Continuous phase	Realizable k-ε turbulence model	Fluid flow field prediction
Discrete phase	Coke particle tracking	Particle trajectory and impact
Erosion model	Particle impact velocity and angle	Maximum erosion rate calculation
Bend radii studied	9 configurations (2D to 7D+)	Comparative analysis
Output parameters	Pressure distribution, impact velocity, erosion rate	Design optimization

The Realizable k-ε model was selected over the standard k-ε model because it better captures the behavior of swirling and curved flows, which are prevalent in elbow geometries. This model accounts for the effects of mean rotation and strain rate on turbulence production.

Key Findings

The simulation reveals systematic trends in the relationship between bend radius and erosion behavior:

Bend Radius (R/D)	Flow Stability	Particle Impact Pressure	Maximum Erosion Rate	Recommendation
2D	Highly unstable	High	Very high	Avoid
3D	Unstable	High	High	Avoid
4D	Moderately stable	Moderate	Moderate	Acceptable for space-constrained applications
5D	Moderately stable	Moderate	Moderate	Avoid (not optimal)
6D	Moderately stable	Moderate	Moderate	Avoid (not optimal)
7D	Stable	Low	Low	Optimal cost-performance ratio

The study identifies a critical finding regarding secondary flow development:

Centrifugal force effects: The continuous phase experiences centrifugal forces that generate secondary flow patterns within the elbow
Local disturbance creation: Secondary flows create localized turbulence and flow instability
Radius-dependent stabilization: As the bend radius increases, the internal flow field stabilizes, fluid relative velocity decreases, and wall impact intensity reduces
Discrete phase response: Coke particle erosion is significantly influenced by the bend radius due to changes in particle impact velocity and angle

Erosion Mechanism Analysis

The erosion behavior of coke particles on elbow walls follows established erosion mechanisms:

Impact velocity: Higher particle velocities at the outer wall of the elbow increase erosive energy
Impact angle: Particles impacting at angles between 20-30 degrees typically cause maximum erosion for brittle materials
Particle size distribution: Larger particles carry more kinetic energy and cause more severe localized damage
Collision frequency: Higher particle concentrations increase the frequency of erosive impacts

The secondary flow patterns within the elbow create complex particle trajectories where particles may impact the wall multiple times within a single elbow passage, compounding the erosive damage.

Engineering Recommendations

Based on the simulation results, the following design guidelines are proposed:

Space-constrained applications: Use 4D radius elbows as a compromise between space requirements and erosion resistance
Optimal performance: 7D radius elbows provide the best balance of erosion resistance, pressure drop, and cost
Avoid configurations: 2D, 3D, 5D, and 6D radius elbows are not recommended due to suboptimal performance
Material selection: For coke transport systems, consider erosion-resistant lining materials (e.g., ceramic coatings, hardfacing) in conjunction with appropriate radius selection
Maintenance planning: Elbows with smaller radii require more frequent inspection and replacement schedules

Practical Considerations for Coke Transport Systems

Coke transport systems in steel plants and chemical facilities present unique challenges:

Particle characteristics: Coke particles are angular, brittle, and heterogeneous in size distribution
Flow conditions: Typically high-velocity pneumatic conveying with particle concentrations of 20-60% by volume
Temperature effects: Hot coke transport may involve elevated temperatures affecting particle properties and wall material behavior
Abrasive wear patterns: Outer wall erosion at the elbow exit is the most common failure mode

The simulation results should be validated against field data from actual coke transport systems to confirm the predicted erosion patterns and rates. Discrepancies between simulation and reality may arise from particle-particle interactions, wall roughness effects, and material property variations that are difficult to model accurately.

Reflections

This study provides valuable design guidance for engineers working on pneumatic conveying systems handling abrasive particulate materials. The identification of 7D as the optimal radius represents a practical recommendation that balances performance with spatial constraints. However, the study's limitation lies in its purely numerical approach—experimental validation with physical erosion testing would strengthen the conclusions and provide confidence factors for engineering design.

The finding that 4D is acceptable for space-constrained applications while 7D is optimal provides engineers with flexibility in design decisions. In practice, the choice between these options should consider not only erosion resistance but also pressure drop requirements, system layout constraints, and maintenance access considerations.

The research contributes to the growing body of CFD-based erosion prediction methodology and demonstrates the value of parametric studies in identifying optimal design parameters for industrial applications.