# A Novel Shape-Adjustable Surface and Its Applications in Car Design
## 4 Modeling Optimization  
In CFD feedback and optimization processes of automobile design, the model template and the SQ-Coons surface have two design levels. The first is that designers determine the overall shape of the car through the model template and the control points in it. The other is that shape parameters are used as variables to optimize vehicle aerodynamic coefficients while maintaining the overall car shape. In addition, due to the differences, each surface has its own optimal combination of shape parameters. The hood surface of model M0 is taken as an example in this section. M0 is the common template from the analysis and statistics of dozens of existing vehicle models, and is also the initial template for obtaining more models by changing parameters. It has the same topological relationship of surface stitching as other models. Therefore, the optimization ideas implemented on it can also be applied to other models. In the following optimization process, all the control points (the integral car modeling) of the hood surface in M0 are kept unchanged while the shape parameters (surface details) of the hood surface are optimized as variables for its CFD result. The coordinates of 12 control points on the four boundaries and the \(u\) and \(v\) directions of the hood surface are illustrated in Table 2 and Figure 12, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(p_{ij}\) & \multicolumn{4}{c}{\(i\)} \\ \cline{3-6}  & & **0** & **1** & **2** & **3** \\ \hline \multirow{4}{*}{\(j\)} & **0** & 6.73, \(-\)41.30, 50.34 & 43.44, \(-\)59.96, 72.99 & 91.17, \(-\)69.67, 74.53 & 136.73, \(-\)72.79, 78.75 \\ \cline{2-6}  & **1** & \(-\)2.32, \(-\)15.18, 50.98 & & & 117.38, \(-\)27.68, 82.37 \\ \cline{2-6}  & **2** & \(-\)2.32, 15.18, 50.98 & & & 117.38, 27.68, 82.37 \\ \cline{2-6}  & **3** & 6.73, 41.30, 50.34 & 43.44, 59.96, 72.99 & 91.17, 69.67, 74.53 & 136.73, 72.79, 78.75 \\ \hline \hline \end{tabular}  
* The contact point between the vehicle fore-end and ground is taken as the coordinate origin the driving direction is taken as the negative direction of the \(X\)-axis; the right-direction of the driver is taken as the positive direction of the \(Y\)-axis; the upward direction is taken as the positive direction of the \(Z\)-axis; the measuring unit is cm.  
\end{table} 
Table 2: The coordinates of 12 control points of the SQ-Coons hood surface *. Figure 11: Numerical distribution statistics of three difference degrees \(d\) in 50 vehicle models: (**a**) Type-1 difference degree; (**b**) Type-2 difference degree; (**c**) Type-3 difference degree. In the outflow field simulation of an automobile in CFD, the model is required to be closed. As the model template is composed of only 25 unclosed surfaces, five planes, including four nearly circular planes at the wheels and a large plane at the chassis, need to be generated to enclose the whole body. The next step of CFD pretreatment is the generation of a computational grid, which is carried out in Gambit 2.4.6. The shape of the computational domain resembled a rectangular wind-tunnel test section. Its cross section covered 5 times the length upstream and 10 times the length downstream of the CAD vehicle model, 4 times the width on both left and right sides, and the height was 5 times the height of the model. The corresponding blockage ratio was about 1.12% according to our measurements, which is within the scope of 5% in typically accepted automobile aerodynamic testing (see [29]). The triangle mesh was set as 10 mm, and the hybrid tetrahedron was 10-200 mm. In addition, five layers of prism mesh were generated from the surface of the automobile model, and the thickness of the first layer was set as 8 mm. The two steps of the CFD pretreatment processes of the whole vehicle are shown in Figure 13.  
To obtain the total pressure \(D\) in the upwind direction of the models, Ansys Fluent 16.2 and the \(k\)-\(\varepsilon\) turbulence model are used for aerodynamic computations.