# A Validated Thermal Computational Fluid Dynamics Model of Wine Warming in a Glass
## 4 Validation  
The presented simulation approach was validated for warming wine and water at a room temperature of \(T_{\mathrm{R}}=23\,^{\circ}\mathrm{C}\). The simulation results for the initial temperature of \(T_{0}=8\,^{\circ}\mathrm{C}\) and \(T_{0}=12\,^{\circ}\mathrm{C}\) were compared to the experimental data from Sections 2.2 and 2.3. Detailed validation was first performed for water rather than wine to reduce the possibility of modeling errors for the liquid. The following investigates the importance of modeling different physical heating mechanisms closely. Then, the simulation of wine was evaluated, and the effects of the liquid properties are discussed. Figure 6 presents the results for warming water. The simulated temperature increase, see Figure 6a, and fits the experimental data accurately in all three positions. The temperature is computed slightly too low only for \(y_{2}\). The initial rapid temperature increase starts with a delay of about 40 s. Minor differences in the initial conditions between the experiment and simulation are probably the reason for this. The pouring process in the experiment presumably introduces a small initial motion in the water so that the heat is transported faster from the glass wall to the middle of the liquid. The simulation takes a few seconds to establish the natural convection since starting from a zero velocity field. Nevertheless, the agreement is surprisingly accurate, considering the comparison in single discrete positions of the underlying complex physical system. Figure 6b compares the average water temperatures. The simulation matches the experimental data for all investigated periods well. The simulated temperature is slightly overpredicted for \(T_{0}=12\,^{\circ}\mathrm{C}\). However, the difference is only \(0.08\,^{\circ}\mathrm{C}\) after 5 min and \(0.09\,^{\circ}\mathrm{C}\) after 40 min. This corresponds to a relative error of 5.5% and 1.8% in relation to the corresponding temperature change, respectively. It should be noted that the discrepancy is within the range of the thermometer's measurement accuracy. The comparison for \(T_{0}=8\,^{\circ}\mathrm{C}\) shows slightly larger errors for \(t=5\,\mathrm{min}\) and \(t=20\,\mathrm{min}\). This could be due to the relatively small number of measurements, and the experiment's higher error sensitivity at lower temperatures. At \(t=20\,\mathrm{min}\), the maximum difference is still relatively small with 4.4% or \(0.21\,^{\circ}\mathrm{C}\), while the prediction for \(t=10\,\mathrm{min}\) and \(t=40\,\mathrm{min}\) is accurate. Overall, the simulation agrees very well with the experimental data and accurately represents the physical process of water warming in a glass. The importance of including the physical effects of convection and radiation in the simulation is investigated hereafter. The influence of modeling both mechanisms on the total heat transfer is examined for the warming of water with \(T_{0}=12\,^{\circ}\mathrm{C}\). The convection of the air and the liquid in the glass are involved in the physical process. The simulation approach can disregard the convection of the liquid and the air by not calculating the  
Figure 5: Quarter section of the discretized problem domain and two relevant close-ups. corresponding velocity field. A simulation without radiation neglects Equation (9). All simulation variations still model heat conduction. The comprehensive baseline simulation, including all physical phenomena, is compared to the simulation without taking into account (1) the convection of the air, (2) the convection of the water, (3) the radiation, and (4) the radiation and convection of the air. Figure 7 shows the resulting average water temperatures compared to the experimental data. The baseline simulation computes the temperature only \(0.09\,\mathrm{\SIUnitSymbolCelsius}\) higher than the experiment at \(t=40\,\mathrm{min}\). Leaving out one of the mechanisms reduces the temperature increase over time.