Steel Flue-Gas Ducts – Effects of Temperature

The design of steel flue-gas ducts is relatively complex, both in terms of structural analysis and detailing. One of the key design considerations is thermal action, which is the focus of this article.

Thermal Actions on Steel Flue-Gas Ducts

Temperature is typically one of the governing actions in the design of steel flue-gas ducts. Thermal actions cause structural components to deform. These deformations may be axial, due to a uniform temperature change, or flexural, due to a temperature gradient through the cross-section. If the structure is unable to deform freely, thermal restraint generates additional stresses and internal forces.

The effects of thermal actions in flue-gas ducts are, of course, reduced by internal insulation, which significantly lowers the temperature at the inner surface of the structural steelwork. Nevertheless, the steel temperature may still remain relatively high. The effects of a uniform temperature increase can be largely eliminated through appropriate structural detailing. Typical measures include the correct selection and arrangement of supports and bearings, together with the provision of expansion joints (compensators) at suitable locations. Both solutions are intended to allow free thermal movement and thereby prevent the development of additional axial forces (normal forces) due to restraint.

Due to their large dimensions, flue-gas ducts often require both longitudinal and transverse stiffening, for example by means of I-section beams. Depending on the dimensions of the duct, IPE, HEA or HEB sections may be used. Such stiffeners increase the temperature difference within the structural system between the inner part of the duct and the external part exposed to ambient conditions. Consequently, the flanges of a stiffening beam may be subjected to different temperatures, with the outer flange remaining cooler. The resulting differential thermal strains tend to bend the stiffener. If this deformation is restrained, the beam cannot develop its free thermal curvature, and significant bending stresses arise in the stiffeners. In other words, internal forces develop within the structure to counteract the free thermal deformation. The highest bending moments typically occur in the support regions, as shown in the screenshot below, where stiffer reinforcing sections are often provided. It is therefore the temperature difference—the thermal gradient—that generates additional bending effects, which may govern the durability and structural safety of the duct. It should also be noted that, in a stiffener-to-duct wall configuration, temperature differences between the stiffener and the duct wall (with the stiffener remaining at a lower temperature) lead to different axial deformations. As a result, significant axial stresses (normal stresses) can develop within the structure. Neglecting the impact of temperature differences in this type of structure can lead to failure conditions and costly remedial works after the installation has been commissioned.

Temperature Gradient

A temperature gradient is a non-uniform temperature distribution within a structural member. In the example considered here, it is defined as the temperature difference between the duct shell plate and the outermost surface of the stiffener.

To illustrate the effects of a temperature gradient, consider a simple beam fixed at both ends and subjected to a temperature difference over the depth of its cross-section.

Because the beam is restrained against free deformation, additional bending stresses develop. The higher temperature at the upper flange causes it to expand. Since this expansion is restrained, compressive stresses develop in the upper flange. The lower flange, which is exposed to a lower temperature, tends to contract relative to the upper flange. Due to the restraint of thermal deformation, tensile stresses develop in the flange. As a consequence, bending stresses are induced in the cross-section. Determining the bending moment induced by the temperature gradient requires knowledge of the coefficient of thermal expansion α. It should be noted that, if the beam were free to deform, it would develop a natural thermal curvature and no restraint-induced thermal stresses would arise.

Determination of the Temperature Gradient

Determining the temperature gradient is not straightforward. The most reliable method would be to measure the temperatures while the installation is operating. This is not possible during the design stage unless relevant monitoring data from comparable existing installations are available.

Where such data are unavailable, advanced computational fluid dynamics (CFD) analyses can support the design process. CFD analyses can be used to determine:

• the flue-gas temperature distribution throughout the entire duct volume;
• the temperature distribution within the duct structure, taking the thermal insulation into account.

The resulting temperature field can then be applied as a thermal load case in the finite element analysis (FEA) model of the structure.

Summary

When designing steel flue-gas ducts, knowing the operating temperature of the installation alone is not sufficient. The temperature distribution within the structure is equally important. The stiffeners supporting the duct shell may remain significantly cooler than the shell plate itself. As a result, due to the lack of freedom for thermal deformation, significant bending stresses as well as normal stresses caused by axial forces are generated in these members. Taking these stresses into account is important with regard to the load-bearing capacity of the stiffeners themselves, the capacity of their connections, and the stability of the shell plate.

In the design of large steel flue-gas ducts, the assessment of temperature gradients should be treated as a standard part of the structural analysis process, in the same way as the assessment of wind and seismic actions.