CFD-DEM Analysis of Slurry Shield Tunneling Discharge Pipe Elbow Pressure Loss

Literature Overview

This 2021 paper by Guo Yidong, Li Xinggao, Yang Yi, and Gan Congyu, published in Modern Tunneling Technology (Vol. 58, No. S1, pp. 191-198), investigates the along-pipe pressure loss at elbow locations in slurry shield tunneling discharge pipelines using CFD-DEM (Computational Fluid Dynamics - Discrete Element Method) coupled simulation. The authors are affiliated with Beijing Jiaotong University's Key Laboratory of Urban Underground Engineering and China Communications Tunnel Engineering Bureau Co., Ltd. The study establishes a three-dimensional curved pipe model for slurry-rock debris two-phase flow, considering the geometric shape of rock debris, and analyzes the effects of pipe bending angle and curvature radius on pressure loss.

Technical Background: Slurry Shield Tunneling and Discharge Pipe Systems

Slurry shield tunneling (also known as slurry support shield tunneling) is a method used for tunneling through water-rich ground conditions. The excavation face is supported by a slurry medium (typically bentonite or polymer-based fluid) that maintains face stability while excavated material (muck) is transported to the surface through a discharge pipeline. The discharge pipe system must handle a complex two-phase flow consisting of the slurry fluid and solid rock debris particles of varying sizes and shapes.

The presence of elbows in the discharge pipeline introduces additional pressure losses beyond the frictional losses in straight pipe sections. These local losses are critical because they directly affect the pumping power requirement and the hydraulic capacity of the slurry transport system. Understanding the pressure loss characteristics at elbows is essential for optimizing the pipeline layout and pump selection.

CFD-DEM Coupled Simulation Methodology

Model Configuration

The CFD-DEM method couples the fluid dynamics simulation (CFD) with the discrete element simulation (DEM) to capture the interaction between the slurry fluid and the solid rock debris particles. The model includes:

Rock Debris Geometric Characteristics

A key innovation of this study is the explicit consideration of rock debris geometric shape in the DEM model. Unlike simplified spherical particle models, the actual rock debris from tunneling operations has irregular shapes that significantly affect the flow behavior and pressure loss. The irregular geometry leads to:

• Increased drag forces compared to spherical particles
• Particle-particle interlocking and jamming effects
• Non-uniform stress distribution on pipe walls
• Enhanced turbulence generation

Control Variable Method

The study employs a control variable approach to systematically analyze the effects of individual geometric parameters:

1. Bending angle (θ): Varied from 20° to 90° in incremental steps
2. Curvature radius (r): Varied across a range of practical values
3. Other parameters held constant: Particle size distribution, slurry properties, flow velocity

Key Results and Quantitative Relationships

The study's primary findings establish the following relationships between pipe geometry and pressure loss:

The along-pipe pressure loss (ΔP) was found to be approximately linearly related to both the bending angle (θ) and the curvature radius (r), with the bending angle having a more pronounced effect on pressure loss.

Analysis of the Non-Linear Transition at 50°

The transition from slow to rapid pressure loss increase at approximately 50° bending angle is a critical finding with important engineering implications. Below 50°, the flow deflection is gradual enough that the slurry and rock debris can follow the pipe curvature without significant separation or accumulation. Above 50°, the centrifugal force becomes large enough to cause:

• Flow separation at the inner wall
• Particle accumulation and deposition at the inner wall
• Increased turbulence intensity
• Enhanced fluid-particle momentum exchange

Curvature Radius Effect

The finding that larger curvature radius leads to greater pressure loss is counterintuitive at first glance, as conventional single-phase flow theory suggests that larger radius reduces local losses. However, in the context of two-phase slurry-rock debris flow, the larger curvature radius may allow particles to travel further along the pipe before reaching the outer wall, potentially causing:

• Greater particle-fluid interaction zone
• More extended flow disturbance region
• Larger separation zone at the inner wall

This result highlights the importance of considering the specific flow regime (two-phase vs. single-phase) when interpreting geometric effects on pressure loss.

Connection to Steel Pipe and Fitting Engineering Practice

Pipe Elbow Design for Slurry Transport

The findings of this study have direct implications for the design and selection of steel pipe elbows used in slurry transport systems:

1. Bending angle optimization: For slurry transport applications, the use of multiple smaller-angle elbows (each less than 50°) may be preferred over a single large-angle elbow to minimize pressure loss. This translates to a preference for 45° elbows over 90° elbows in slurry pipeline layouts.
2. Curvature radius selection: The non-intuitive finding regarding curvature radius suggests that the optimal radius for slurry transport elbows may differ from that for single-phase fluid transport. Engineers must consider the specific two-phase flow characteristics when selecting elbow geometry.
3. Material selection for erosion resistance: The high-velocity two-phase flow at elbow locations creates erosion potential, particularly at the outer wall where particles impinge. Materials with enhanced erosion resistance (such as hardfacing overlays or wear-resistant alloy pipes) may be required.

Manufacturing Considerations

Quality Control for Slurry Service Elbows

The demanding operating conditions of slurry transport systems require enhanced quality control for elbows:

• Dimensional inspection: Verify inner and outer diameters, wall thickness, and radius of curvature
• Surface finish: Smooth internal surface reduces pressure loss and erosion
• Weld quality: For welded elbows, full RT or UT of the weld seam is essential
• Wall thickness verification: UT or eddy current testing to ensure uniform wall thickness
• Hardness testing: Verify material hardness for erosion resistance

Key Questions and Reflections

The study raises several important questions for engineers designing slurry transport systems:

• How does the pressure loss at elbows change with varying slurry concentrations (solid content percentage), and at what concentration does the transition from Newtonian to non-Newtonian behavior occur?
• What is the effect of particle size distribution on pressure loss, and is there a critical particle size above which deposition and blockage become likely?
• How do the findings translate to different pipe diameters, and are there scale effects that must be considered when applying the results to full-scale systems?
• What is the long-term effect of particle erosion on the elbow geometry, and how does the changing internal surface affect pressure loss over the service life?

The CFD-DEM methodology used in this study represents a powerful tool for understanding complex multiphase flow phenomena in curved pipes. However, the accuracy of the simulation depends on the quality of the input parameters (particle shape, fluid properties, boundary conditions) and the validity of the coupling algorithms. Validation against experimental data is essential to ensure the reliability of the simulation results.

Study Insights and Implications

The CFD-DEM analysis of slurry shield tunneling discharge pipe elbow pressure loss provides valuable quantitative insights for the design and optimization of slurry transport systems. The key finding that pressure loss increases significantly above 50° bending angle has direct practical implications: pipeline layouts should minimize the use of large-angle elbows and instead employ multiple smaller-angle bends to reduce pumping power requirements.

For steel pipe elbow manufacturers and piping engineers, the study highlights the importance of considering the specific service conditions (two-phase flow, particle-laden slurry) when selecting elbow geometry. The conventional wisdom of using larger curvature radii to reduce pressure loss may not apply to two-phase flows, and engineers must evaluate the specific flow regime before making design decisions. The linear relationship between pressure loss and bending angle provides a useful design tool for estimating pressure drops in pipeline systems with multiple elbows, enabling more accurate pump sizing and system optimization. The CFD-DEM methodology itself represents a significant advancement in the ability to simulate complex multiphase flows, providing a complement to experimental testing and enabling the evaluation of design alternatives before physical fabrication. This computational approach can be extended to other complex flow scenarios in steel pipe systems, including slurry transport in mining applications, wastewater treatment plant piping, and dredging operations, where understanding two-phase flow behavior in curved pipe sections is critical for system design and operation.