# A Validated Thermal Computational Fluid Dynamics Model of Wine Warming in a Glass
## 3 Simulation Model
### Computational Methods  
The problem was implemented in ANSYS CFX 2021R1, a commercial CFD solver applying the finite volume method with a second-order spatial and temporal discretization. It was assumed that all liquid domains exhibit incompressible flow, as no flows with a high Mach number (\(Mn>0.3\)) occurred in the study. The temperature-dependent density was still taken into account in order to resolve the natural convection phenomena [23]. The surrounding room was modeled as a spherical dome with a diameter of 2 m over a circular virtual table of the same dimension; see Figure 4. Exploiting symmetry, only one-half of the model needed to be resolved computationally and symmetry conditions were imposed. Smaller sector models produced distorted mesh elements at the symmetry axis and, consequently, were not used. The following boundary conditions were assigned: On the half-sphere and the lower side of the table, the temperature was fixed to the room temperature \(T_{\mathrm{R}}\). All air and wine boundaries had no slip conditions for the fluid flow. At the interfaces air-table, air-glass, air-wine, wine-glass, and glass-table, the conjugate heat transfer capability of ANSYS CFX 2021R1. ensured the continuity of temperatures and heat fluxes. Symmetry conditions were applied on all boundaries in the cut plane of the half model. The half-sphere surface was modeled as a wall, and, as the utilized solver, was sensitive to pressure head differences in open-cavity natural convection scenarios. The default inclusion of hydro-static pressures in the buoyancy forces induced spurious flows for open domains, as demonstrated in [35]. Concerning initial conditions, the initial velocities and relative pressures of air, water, or wine were zero. Air, wine glass, table, and room walls are initialized with the room temperature \(T_{\mathrm{R}}\), while the fluid temperature was initially set to \(T_{0}\).  
The computational domain was discretized with hexahedral elements having a height of 2, 2, 0.5, and 1 mm for the domains table, air, glass, and wine, respectively. Figure 5 illustrates relevant sections of the final computational mesh. Inflation layers (15 and 11 layers for air and wine domain, stretch factor 1.2, and first layer height 0.1 mm) captured wall-bounded gradients in the domains of air and wine. Generalized Richardson extrapolation [36] was employed to estimate the grid-independent solution of the average heat fluxes at the domain interfaces. The relative discretization errors of 0.49 %, 1.04 %, and 0.29 % compared to the grid-independent solution were calculated for the domains air, glass, and wine. The resulting system was discretized into 492,042 control volumes. The initial 150 s were solved with a time step of 0.1 s, while the residual simulation utilized a time step of 0.5 s, as results did not differ significantly for smaller time steps. The system of equations was solved block-coupled for momentum and mass conservation and segregated for the  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Solid** & \(\rho/\mathbf{kg\,m^{-3}}\) & \(\mathbf{c_{p}/J\,kg^{-1}\,K^{-1}}\) & \(\mathbf{\kappa/W\,m^{-1}\,K^{-1}}\) & \(\epsilon/-\) \\ \hline Glass & 2640 & 850 & 1.12 & 0.84 [31] \\ Spruce & 430 [27] & 2300 [32] & 0.11 [33] & 0.89 [34] \\ \hline \end{tabular}
\end{table}
Table 2: Transport properties of solids. Material data are kindly provided by Stölzle Lausitz GmbH if not marked otherwise.  
Figure 4: Computational domain of the half-model using symmetry boundary conditions in 2D view (**left**) and 3D view (**right**) (dimensions in mm).  
energy equation. The target scaled residuals of ANSYS CFX reached \(R<1\times 10^{-6}\) for each time step, and imbalances were monitored to remain below 1 %. One simulation of 45 min real time took approximately 18 h on 16 cores of a cluster PC with two Intel Xeon E5-2687W v4 (3.2 GHz) CPUs (Santa Clara, CA, USA).