**3. Results**

Simulations have been conducted on a single heat storage tank both in the charge and discharge phase in order to investigate the effects of overall node number on time-temperature profiles, both during charge and discharge, and the effect of the flow rates only during discharge.

The TES tank model behavior was analyzed by comparing it with the experimental data found in the literature regarding reproducible fully-instrumented laboratory tests, i.e., given by González-Altozano et al. [17] for charging and Li et al. [18] for discharging. Then the model was applied to the simulation of a large storage tank monitored in an operating environment [38].

For all the simulation sets, a variable-step ode45 (Dormand-Prince) solver was used, since it represents a good compromise between calculation time and results accuracy.

#### *3.1. Model Analysis—Charge Phase*

First, the charge maneuver of a thermal energy storage tank was simulated. The tank, initially at low temperature, was heated up with a hot water flow fed at the top of the tank. A grid sensitivity analysis on node number and dimension was performed.
