General

Is it necessary to initialise the temperatures of solid elements in the Initial Phase and use them in the subsequent phases, even though a thermal flow analysis is only intended to be performed in the last phase of the project? The quick answer to the question is: yes, it is.

According to the principles of the finite element (FE) method, changes in internal forces and, therefore, in stresses, strains and material state result from out-of-balance forces. These out-of-balance forces may result from changes in geometry, loading conditions (in either their configuration or magnitude), flow and thermal conditions (generically, changes in geometry and boundary conditions). Due to this, the solution to a given boundary-value problem using the FE method involves:

1. the definition of the initial conditions of the problem (i.e., generating the initial stress and strain states, pore pressures, temperatures and other state variables at the start of the analysis);
2. the definition of the geometry and boundary conditions in each phase of the problem.

As changes in (2) are performed from a given phase to the subsequent one, a new equilibrium is searched and, therefore, an updated solution for the problem is obtained.

When accounting for thermal effects, this means that temperatures of solid elements should be initialised at the start of the project and be used in the subsequent phases (either remaining constant or changing according to newly imposed thermal boundary conditions). Among other possibilities (such as a steady-state thermal analysis), the “earth gradient” option can be used to define the initial temperature distribution in the model, as illustrated in Figure 1. Supposing that a thermal flow analysis is only intended to be performed at a later stage (e.g., in Phase_3 of the project illustrated in Figure 1), the option “use temperatures from the previous phase” can be selected as “thermal calculation type” for the intermediate phases (e.g., Phase_1 and Phase_2 of the project shown in Figure 1) to ensure that temperature values are kept during these phases and, therefore, can be used in the subsequent phase involving a thermal flow analysis.

Figure 1 Application of the earth gradient option to initialise the temperature of solid elements.

Furthermore, whenever new solid elements are activated (meaning that changes in the geometry are applied), the initial temperatures of those solid elements should be defined. Among other possibilities, an earth gradient analysis may be performed once more, possibly complemented with “user-defined” temperature conditions when the temperature of the solid elements depart from those given by the earth gradient option.

Practical example

Let us assume that a construction of a tank designed to contain a hot fluid is simulated, with the following phases being defined (note that the construction sequence described here is very simplified, since the only purpose is to highlight the importance of initialising the temperatures in the Initial Phase of the project and, subsequently, using the “temperatures from previous phase” option up to the phase where a thermal analysis is performed):

• Initial Phase: generation of the initial state of the soil deposits;
• Phase_1: excavation required to shape the base for the foundations of the tank;
• Phase_2: construction of the tank;
• Phase_3: operation, consisting of filling the tank with a hot fluid.

Let us assume now that the temperatures of the soil deposits are not explicitly initialised at the start of the analysis (i.e., the “thermal calculation type” is set to “ignore temperatures” in Initial Phase, Phase_1 and Phase_2), and a steady-state thermal analysis is performed in Phase_3. In such a case, since information about the temperature of solid elements at the start of Phase_3 is unavailable, an internal assumption (*) is required (note that initial conditions for the problem under analysis are required in a FE analysis, as discussed before). Naturally, this internal assumption may not represent adequately the field conditions and, therefore, the changes in the temperatures of the solid elements occurring during the thermal steady state analysis performed in Phase_3 might lead to unexpected results, such as excessive thermal expansion.

As illustrated in Figure 1, the adequate procedure would consist of initialising the temperature of the solid elements during the “Initial Phase” and using the option “use temperatures from the previous phase” in Phase_1 and Phase_2, where thermal effects are not considered. Following this strategy, the initial temperatures of solid elements are properly defined and kept in the analysis to be used in Phase_3, where a steady-state analysis is performed.

(*) Since PLAXIS 2D CONNECT Edition V21, when nothing else is specified by the user, the initial temperature of a solid element is set, by default, to the reference temperature, T_ref, specified in Project properties.