#### Introduction

Expansion is the size variation of a body when the temperature at which is exposed changes. It’s very important to treat properly the **absorption of expansion in thermal fluid installations.**

In the facilities of heat transmission, either steam or overall thermal fluid, operating temperatures that can be achieved are high and therefore, the piping expansion phenomenon and the possible consequences should be properly treated.

#### Some theory

Following, there is an example of the magnitude of the forces that expansions produce and the importance of a proper design that eliminates any risk by this cause. Please, suppose a pipe section of 10 meters length l, diameter 3 “, material ASME SA 106 Gr. B – specific carbon steel for high temperature service -, fully fixed at its ends and therefore no possibility of dilating freely.

The pipe assembly was carried out at room temperature, 20 °C, being the expected maximum operating temperature 300 ° C.

Under these conditions and the characteristics of the material, its linear thermal expansion coefficient α (2), has an average value in these temperatures of 1.44E-05 m/(m•°C) and the expected expansion at the moment of reaching the maximum temperature will be:

With this expansion of 40.4 mm, the stress to which the pipe is subjected is:

where E is the module of elasticity (3) or, Young’s module of the material

This tension applied to the pipe is much higher than the elastic limit (1) at the working temperature of Sy/ T = 188.06 N / mm² .

If we talk in terms of pressure, the piping makes **7444 bar** of pressure on the points to which it is subjected. As a result, they apply a force of equal magnitude – compressive forces -.

These values are not surprising, since the force associated to the produced stress is **362 Tons-force**:

being S the interior section of 3 “ pipe, S= 4768.56 mm2

If we can not reach to absorb the dilation produced, the pipe would suffer permanent deformation – plastic deformations – with buckling and rupture of it, because the overcoming of the material breaking stress at the operating temperature Su/T= 413.69 N/mm².

An Excel sheet is attached for calculation of expansions.

#### Types of dilations

There are different possibilities for the absorption of the expansions in thermal fluid installations:

- About the installation design or also called self-compensation system. It is only involved the pipe line to absorb the expansion.
- Deformation figures. Being impossible to adopt a self-compensating system, we can use pipe curves and artificial performances. We can consider three types according to their geometric shape, “U”, “V” and “Z”
- Compensators or expansion joints. Specific element of mechanical deformation which takes small space

In the next chapters we will explain more specifically these solutions and the advantages and disadvantages of each.

#### NOTES:

- The elastic limit is the maximum stress that a material can withstand without permanent deformation. Above these stress, the material entails a plastic behavior, permanent deformations and it can not spontaneously recover its original shape when the tensions are removed
- The expansion coefficient is the change in length per unit of length and temperature degree, characteristic of each material
- Characteristic of an elastic material indicating the behavior of it, according the direction in which a force is applied