Numerical Simulation and Structural Optimization of Gas-Solid Two-Phase Flow Erosion in Combined Elbows

Literature Overview

This paper, published in the Proceedings of the CSEE in 2018 (Vol. 38, Issue 3, pp. 832-839) by Wang Yu, He Qi, Yu Fei, Liu Ming, and Yan Junjie from the State Key Laboratory of Multiphase Flow in Power Engineering at Xi'an Jiaotong University, addresses a critical engineering problem in coal-fired power plants: the erosion wear behavior of gas-solid two-phase flow within closely spaced combined elbows. The research was supported by the National Basic Research Program of China (2015CB251504) and the National Natural Science Foundation of China (51406006). The study employs the Discrete Phase Model (DPM) combined with the Erosion/Corrosion Research Center (E/CRC) wear model from the University of Tulsa to numerically simulate flow fields, wall erosion distributions, and maximum wear locations in two configurations of combined elbows. The findings provide actionable structural optimization recommendations for duct layout design in flue gas and pulverized coal systems.

Core Technical Methodology

The numerical simulation framework integrates three key components: a gas-phase turbulence model, a particle trajectory model based on DPM, and an empirical erosion wear model derived from the E/CRC database. The DPM tracks individual particle trajectories through the continuous gas phase, accounting for particle inertia, gravity, drag forces, and inter-particle collisions. The E/CRC erosion model correlates erosion rate with particle impact velocity, impact angle, particle mass flux, particle hardness, and material properties through an empirical function calibrated against extensive experimental data.

The two combined elbow configurations studied are the Z-type (sequential 180-degree reversal) and the Pi-type (inverted U-shaped) arrangements, where the straight section length between elbows is parameterized by the ratio L/D. The study systematically varies this ratio to identify optimal spacing for minimum wall erosion. The simulation domain is discretized using unstructured meshes with boundary layer refinement near walls to resolve the near-wall velocity gradients critical for erosion prediction.

Key Findings and Technical Insights

The simulation results reveal that the spacing between consecutive elbows has a profound and non-intuitive effect on the erosion distribution. For the Z-type configuration, an L/D ratio of 2 is recommended to achieve the lowest wall erosion. This is because at L/D = 2, the particle trajectories have sufficient straight-pipe distance to partially re-distribute after the first elbow, reducing the concentration of high-impact particles at the second elbow's outer wall. However, excessively large L/D values do not further reduce erosion because the particle kinetic energy is largely preserved in the straight section.

For the Pi-type configuration, the optimal arrangement is L/D = 0, meaning the two elbows are directly connected without an intervening straight section. This counter-intuitive result can be explained by the flow dynamics: when the two elbows are directly connected, the flow field at the exit of the first elbow directly feeds into the second elbow with a more uniform velocity profile, avoiding the formation of recirculation zones and secondary flow structures that would otherwise concentrate particles at critical impact locations.

The maximum erosion locations are consistently found on the outer wall of each elbow, as expected from centrifugal force effects. However, the severity distribution is asymmetric along the elbow arc, with peak erosion occurring at approximately 45 to 90 degrees from the inlet, depending on the specific configuration and particle properties.

Engineering Practice Integration

From a practical standpoint, these findings have direct implications for the design of flue gas ducts, pulverized coal pipelines, and induced draft fan inlet ducts in coal-fired power plants. In retrofitting projects where space constraints force tight elbow spacing, engineers can now make informed decisions about whether to adopt Z-type or Pi-type configurations and what spacing to use. The recommendation to use L/D = 2 for Z-type elbows is particularly valuable in boiler furnace exit duct designs where 180-degree reversals are common due to space limitations.

For pipe manufacturers and fitting suppliers, these results suggest that providing standard-length straight pipe spools matching the optimal L/D ratios could add value. Additionally, the erosion distribution data can inform the placement of wear-resistant overlays or sacrificial inserts on the inner surface of elbows, allowing for targeted protection rather than full-length lining.

Study Insights and Implications

This research demonstrates that the interaction between consecutive elbows is not merely a superposition of individual elbow effects but a coupled phenomenon governed by particle trajectory memory and flow field development. The concept of "flow field memory" is critical: particles entering the second elbow carry momentum and spatial distribution characteristics determined by the first elbow and the intervening straight section. This insight extends beyond the specific configurations studied and suggests that any multi-elbow arrangement should be evaluated as a system rather than as isolated components.

The study also highlights an important limitation: the E/CRC erosion model, while extensively validated for single-particle impacts, may not fully capture multi-particle interaction effects at high solid loading concentrations typical of coal-fired boiler applications. Future work should incorporate particle-particle collision models and consider the effect of wall roughness evolution on erosion progression over time.

In summary, this paper provides a rigorous numerical framework and clear design guidelines for combined elbow arrangements in gas-solid two-phase flow systems. The practical recommendations regarding L/D ratios for Z-type and Pi-type configurations offer immediate value to power plant designers and maintenance engineers seeking to extend the service life of critical ductwork components.