I. Core Calculation Basis: Thermal Expansion and Compensation Capacity

1. Thermal Expansion Formula
   The axial expansion of steam pipelines due to temperature changes can be calculated using the formula:
   $\Delta L=\alpha \times L\times \Delta T$

• $\Delta L$: Expansion amount (mm)
• $\alpha$: Linear expansion coefficient of the material (e.g., carbon steel $\alpha$ ≈ 12×10⁻⁶/°C)
• $L$: Pipeline length (m)
• $\Delta T$: Temperature difference (°C, operating temperature - installation temperature)

2. Compensation Capacity of Bellows Compensators
   The axial compensation per corrugation of common bellows compensators is approximately 2–6 mm. The number of corrugations is determined by the total expansion. For example:

• Expansion of a carbon steel pipeline (L = 50m, ΔT = 200°C):
  $\Delta L=12\times 10^{-6}\times 50\times 200=120\text{mm}$
  If the compensation per corrugation is 4 mm, a compensator with 30 corrugations is required.

II. Industry-Recommended Spacing Standards (Empirical Values)

III. Scenarios Requiring Compensators

1. Inadequate Natural Compensation

• Natural bends (e.g., L-shape, Z-shape) have limited compensation capacity. Add compensators when the bend length exceeds:
  • L-shaped bend: Arm length > 40D (D = pipe diameter, mm)
  • Z-shaped bend: Long arm > 20D, short arm > 10D

2. Special Working Conditions

• Straight pipeline length > 50m (carbon steel, ΔT = 150°C);
• Pipelines passing through vibrating areas or building expansion joints;
• Connections between branch and main pipelines with a temperature difference > 50°C.

IV. Key Points for Installation Design

1. Fixed Support Arrangement

• Install fixed supports at both ends of the compensator, within ≤10D spacing, to prevent compensator deflection;
• Install guide supports on both sides of the compensator, within ≤4D spacing, to ensure smooth axial displacement.

2. Compensator Type Selection

• Axial type: For straight pipelines, compensation per corrugation ≤6 mm;
• Lateral type: For L-shaped pipelines, compensates lateral displacement (requires limit devices);
• Angular type: For Z-shaped pipelines, requires 2–3 sets installed in combination.

3. Temperature Difference Correction Example

• Example: DN100 carbon steel pipeline (L = 60m), operating temperature 220°C, installation temperature 20°C:
  • $\Delta T=200°C$, $\Delta L=12\times 10^{-6}\times 60\times 200=144\text{mm}$
  • Select a compensator with 4 mm compensation per corrugation, requiring 36 corrugations, or install 2 sets of 18-corrugation compensators in sections (spacing 30m).

V. Reference Specifications and Standards

• Chinese Standards: GB/T 12777-2019 General Technical Conditions for Metal Bellows Expansion Joints
• US Standards: EJMA Expansion Joint Manufacturers Association Standards
• Calculation Basis: Thermal expansion section in ASME B31.1 Power Piping

Conclusion