I. Core Calculation Principles for Thermal Expansion Displacement

1. Basic Formula for Thermal Expansion$\Delta L=\alpha \cdot L\cdot \Delta T$
   • α: Linear expansion coefficient of steel (carbon steel: $12\times 10^{-6}{/}^{\circ }C$; stainless steel: $16\times 10^{-6}{/}^{\circ }C$)
   • L: Pipeline length (m)
   • ΔT: Temperature difference (operating temperature - ambient temperature, °C)
2. Example Calculation
   • For a DN200 carbon steel steam pipeline ($L=50m$), operating at $250^{\circ }C$ (ambient temperature $20^{\circ }C$):$\Delta L=12\times 10^{-6}\times 50\times (250-20)=138mm$

II. Spacing Standards Based on Pipeline Nominal Diameter (DN)

III. Key Influencing Factors and Adjustment Principles

1. Temperature & Medium Parameters
   • High-temperature steam ($>300^{\circ }C$): Reduce spacing by 20% (e.g., DN200 spacing adjusted from 30m to 24m)
   • Superheated steam with large temperature fluctuations: Add temperature compensation calculation factors ($K_T=1.2-1.5$)
2. Pipeline Layout & Support Conditions
   • Straight pipeline sections: Adopt standard spacing;
   • L-shaped/bent sections:
     • $90^{\circ }$ elbow: The allowable expansion length is calculated as $L=\sqrt{\frac{6EID}{P}}$ (E: Young's modulus, I: moment of inertia, D: outer diameter, P: design pressure);
     • For $L=10m$ carbon steel elbow ($P=1.6MPa$), the allowable displacement is ~60mm.
3. Compensator Type & Performance
   • Axial compensators: Limited to ≤100mm displacement, requiring reduced spacing for large displacements;
   • Universal hinged compensators: Can compensate for lateral displacement, allowing 10-15% increased spacing.

IV. Engineering Design Case (PN1.6MPa Steam Pipeline)

1. Pipeline Parameters
   • Material: 20# carbon steel (α = $12\times 10^{-6}{/}^{\circ }C$)
   • Length: 80m, operating temperature: $220^{\circ }C$, ambient temperature: $25^{\circ }C$
   • Calculated displacement: $\Delta L=12\times 10^{-6}\times 80\times (220-25)=187.2mm$
2. Compensator Configuration Plan
   • Option 1: Install 2 axial compensators (spacing 40m each), each bearing 93.6mm displacement (within ≤100mm limit);
   • Option 2: Use a single large-displacement compensator (pre-stretched 50% during installation), but require fixed supports at both ends (thrust force ~80kN).

V. Special Installation Requirements to Ensure Effectiveness

1. Support System Matching
   • Fixed supports: Install within 8-10D of the compensator, load-bearing capacity ≥1.5×thermal expansion thrust;
   • Guide supports: Set every 3-5D, clearance ≤3mm to prevent lateral misalignment.
2. Temperature Expansion Allowance Verification
   • Check the pipeline's natural compensation capacity (e.g., Z-shaped sections can compensate for ΔL ≤80mm/100m);
   • For insufficient natural compensation, add compensators to ensure the total displacement ≤70% of the compensator's rated value.

VI. Design Codes & Engineering Standards Reference

• Chinese Standards:
  • GB 50316-2000 (2008 Edition) Design Code for Industrial Piping
  • GB/T 14525-2010 Metallic Bellows Expansion Joints for Piping
• International Standards:
  • ASME B31.1 Power Piping (Clause 107 on expansion compensation)
  • EN 13480-5 Metallic Industrial Piping - Expansion Joints