# A Simulation of Tire Hydroplaning Based on Laser Scanning of Road Surfaces
## 3 Test Methods
### Simulation Model
#### 3.2.3 Water Body Modeling  
In the analysis of tire-fluid-road interaction, there are two models [38]: the water flow model and the tire rolling model, as shown in Figure 12. The water flow model simplifies calculations by setting the tire rotation speed and applying reverse translational velocities to the road surface and water flow, making it efficient and easy to converge, but unable to accurately simulate water flow patterns. The tire rolling model pre-sets a water film on the road surface, assigning rotational and translational speeds to the tires, which more realistically reflects the working state of the tires and water flow patterns, but has low computational efficiency and is prone to non-convergence. Studies have shown that the two models differ little when simulating mechanical indicators such as tire-road contact forces [23]. Given that this study focuses on the contact characteristics of tires and roads under water accumulation conditions, with non-water flow patterns being less critical, the more computationally efficient water flow model is selected. Figure 11: Finite element mesh model of road surface: (**a**) AC-13; (**b**) SMA-13; (**c**) OGFC-13. In the tire-water-road coupling analysis, water flow is impacted by the high-speed rotation of tires, resulting in complex mechanical responses. Abaqus provides a variety of state equations to describe the behavior of water flow. In this paper, the MIE-GRUNEISEN state equation [35; 36] is selected to describe the relationship between water flow density and pressure, with the basic form as follows:  
\[\mathrm{P}=\mathrm{P_{H}}(1-\frac{\Gamma_{0}\eta}{2})+\Gamma_{0}\rho_{0} \mathrm{E_{m}} \tag{10}\]  
In the formula, \(\mathrm{P}\) is the stress of the fluid; \(\mathrm{P}\) is the impact pressure; \(\Gamma 0\) is the material parameter; \(\eta=1-\rho_{0}/\rho\), where \(\rho_{0}\) is the initial density of the fluid, \(\mathrm{kg/m^{3}}\); \(\rho\) is the density of the fluid after impact, \(\mathrm{kg/m^{3}}\); Em is the specific internal energy of the fluid, \(\mathrm{P}\)H is the impact pressure, and the specific relationship is shown in Formula (11):  
\[\mathrm{P_{H}}=\frac{\rho_{0}\varsigma\eta}{(1-\mathrm{s}\eta)^{2}} \tag{11}\]  
In this formula, \(\mathrm{C_{0}}\) is the sound velocity of the fluid, \(\mathrm{m/s}\); \(\mathrm{s}\) is the material constant, and the relationship between \(\mathrm{C_{0}}\) and \(\mathrm{s}\) is shown in Formula (12). \[\mathrm{U_{s}}=c_{0}+\mathrm{sU_{P_{V}}} \tag{12}\]  
In the formula, \(\mathrm{Up}\) is the impact velocity, where \(\mathrm{Up}\) refers to the motion velocity of the particle. By applying the law of conservation of energy to the above (9)-(11) formulas, the relationship between fluid stress and fluid density can be obtained as shown in Formula (13). \[\mathrm{P}=\frac{\rho_{0}c_{0}\eta}{(1-\mathrm{s}\eta)^{2}}(1-\frac{\Gamma_{0 }\eta}{2})+\Gamma_{0}\eta\mathrm{E_{m}} \tag{13}\]  
In this study, the parameters in the MIE-GRUNEISEN state equation were determined [39] by referring to the relevant literature, as shown in Table 7.  
The water film finite element model uses a water-air composite model, with dimensions of 300 mm \(\times\) 300 mm \(\times\) 100 mm. It includes a lower water film area (height varies with the thickness of the water film) and an upper air area (ensuring space for water flow). The modeling steps are as follows: first, meshing is performed in Hypermesh using Eulerian elements EC3D8R; second, the tire-water flow coupling region is refined, with a total of 62,209 nodes and 56,687 elements; finally, the mesh is imported into Abaqus (Figure 13). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & \(\mathbf{\rho_{0}}\) (\(\mathrm{kg/m^{3}}\)) & \(\mathbf{c_{0}}\) (\(\mathrm{m/s}\)) & \(\mathbf{s}\) & \(\mathbf{\Gamma_{0}}\) \\ \hline water & 1000 & 1484 & 1.979 & 0.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameters of the MIE–GRUNEISEN state equation. Figure 12: Water film model type: (**a**) the scrolling model; (**b**) water flow model.