Skin friction topology on ground vehicle models

Abstract

Global luminescent oil-film skin friction meter is used to extract the skin friction topology on two generic ground vehicle models: the Ahmed body and the DrivAer model notchback configuration. Topological structures of skin friction on the top and side surfaces are extracted on both the models at different Reynolds numbers (2.68 $\times$ 10⁵, 5.35 $\times$ 10⁵, and 8.03 $\times$ 10⁵ for the Ahmed body and 2.92 $\times$ 10⁵ and 5.84 $\times$ 10⁵ for the DrivAer model, corresponding to freestream velocities of 10, 20, and 30 m/s for the Ahmed body and 10 and 20 m/s for the DrivAer model). For the Ahmed body, important features such as forebody separation bubble, longitudinal vortex, and C-pillar vortices and vortex bursting on the rear slant angle are identified. Similarly, for the DrivAer model, in addition to separation and reattachment lines and vortex bursting, more complex vortex interactions in the rear window are revealed. Comparisons of the results obtained for both the models with existing flow visualizations and numerical results are discussed.

Graphical abstract

Appendix: Uncertainties

Despite the numerous advantages of the GLOF skin-friction meter, just like any experimental technique, this approach is subject to multiple elemental error sources. The following section provides a summary of the most significant error sources presented by Brown and Naughton (1999), Liu and Shen (2008), and Lee et al (2019).

According to Brown and Naughton (1999) and Lee et al. (2019), the most relevant error sources associated with the GLOF technique are: oil properties (i.e., viscosity, density, and temperature), model geometry (i.e., model curvature and camera orientation), illumination source (i.e., non-uniform illumination and reflection from the model and/or the oil surface), camera (i.e., acquisition frame rate, spatial resolution, noise, and lens distortion), calibration (oil droplet volume and scale reading on image), flow field (i.e., pressure gradient, body forces, surface tension, unsteady flow, and surface roughness), and data reduction (i.e., derivative approximations, image down-sampling, analytical method, and thin oil-film modeling). It is important to mention that when performing uncertainty analysis, only the error sources that can be quantitatively evaluated are considered.

In addition, according to Liu et al. (2008), although the effects of pressure gradient and gravity are not considered in the approach presented in Sect. 2, in order to improve the accuracy of skin-friction measurements, a correction scheme for these effects near critical points should be consider, especially in three-dimensional separated flows. Furthermore, in this work, a simple perspective projection transformation is used to transform the thin oil-film equation from the object space to the image plane such that the data processing can be conveniently carried out in the image plane. However, this transformation is only valid when the image plane is approximately parallel to a flat or relatively flat measurement surface. For a highly curved surface that is viewed by a camera from a large angle, a general mapping between the surface and image plane should be considered.

The Lagrange multiplier $\propto$ in Eq. (4) acts as an effective diffusion coefficient controlling the smoothness of the field, i.e., the larger Lagrange multiplier tends to smooth out finer features. In order to quantitatively demonstrate the effect of the Lagrange multiplier, a parametric study on the effect of this parameter on the overall results is performed. Using the top-view GLOF images of the Ahmed body at 10 m/s, the effect of the Lagrange multiplier was quantified using the relative root-mean-square error (RMSE) for x- and y-components of skin friction for $\propto ={10}^{-4}-{10}^{6}$ using a reference value of $\propto =\mathrm{1,000}$. As shown in Fig. 11

Fig. 11

Skin friction RMSE as a function of the Lagrange multiplier for the Ahmed body at 10 m/s: a x-component and b y-component

, the results obtained do not change significantly for $\propto \cong 800-\mathrm{3,000}$; therefore, throughout this work, $\propto =\mathrm{1,000}$ is used. In addition, the skin friction lines obtained for $\propto ={10}^{-4},\propto ={10}^{ 3}$, and $\propto ={10}^{6}$ are shown in Fig. 12

Fig. 12

Skin friction lines for the top view of the Ahmed body at 10 m/s for: a $\propto$ =10 ^{− 4}, b $\propto$ =10 ³, and c $\propto$ = 10⁶

.