Thermal Bowing

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Thermal bowing occurs in horizontal pipes partially filled with hot or cold fluids such as LNG. This phenomenon can cause unexpected damage to piping and supporting structures. Since thermal bowing typically happens during transient conditions like startup, it may remain undetected until damage is discovered.

Thermal bowing can also result from uneven solar heating when one side of the pipe is exposed to sunlight while the other remains shaded.

This effect occurs when significant temperature differences exist between the top and bottom of the pipe cross-section, creating a thermal gradient. The resulting differential thermal expansion causes pipe curvature known as thermal bowing.

Assumptions:

• Thermal strain distribution across the pipe cross-section is linear
• Applies only to horizontal pipes meeting horizontal tolerance criteria: |DZ| / (DX² + DY² + DZ²)^0.5 < Tolerance. Default tolerance is 0.0001, adjustable in Project Settings (Horizontal Tolerance)
• Bowing occurs only in the vertical plane

Thermal gradient values can vary for each pipe element and across different operating conditions.

Pipe curvature due to thermal bowing:

r - curvature radius

D - pipe outside diameter

α - thermal expansion coefficient at operating temperature

T_top - temperature at pipe top

T_bottom - temperature at pipe bottom

Specify thermal gradient (T_top-T_bottom) in pipe properties. Enable thermal bowing analysis in Project Settings.

Bending moment in restrained pipe due to thermal bowing:

E - elastic modulus at operating temperature

I - moment of inertia

Operating temperature equals (T_top + T_bottom)/2