# Wake Structures and Surface Patterns of the DrivAer Notchback Car Model under Side Wind Conditions

^{*}

## Abstract

**:**

## 1. Introduction

^{TM}” and a “BMW 3 series

^{TM}”. The aim is to develop a realistic vehicle geometry that is freely available to the research community. The model geometry is available in fastback, notchback, and fullback versions. The underbody is available in a flat and a detailed version. Further information on general model design can be found in the literature [9,16]. The effect of crosswinds on this DrivAer model has already been investigated in previous studies by means of force and pressure measurements [10,17,18]. The successive increase in drag was attributed to the significant change in pressure distribution at the rear of the vehicle. Significantly lower surface pressures were measured particularly at the rear window and the vehicle base. However, there are only a few data on the external flow field available in order to identify the flow structures which are responsible for this modified behavior. This deficit is addressed in this study.

## 2. Experimental Setup

^{−1}; and was the same in previous studies to maintain comparability. The freestream turbulence intensity was less than 0.5%. The Reynolds number ($Re$) was approximately $3\times {10}^{6}$ based on the overall vehicle length L. For the velocity measurements, a pitot tube was used, which was installed upstream of the model at the ceiling of the test section, and the air temperature was monitored by means of a thermocouple. The boundary layer effect acting on the model was minimized by a splitter plate that cuts off the boundary layer of the wind tunnel. This is required because the wind tunnel has no ground simulation system. The model was investigated at yaw angles of ${0}^{\circ}$, ${5}^{\circ}$, and ${10}^{\circ}$. The inflow $Re$ was always set at ${0}^{\circ}$. The zero yaw angle was determined as the angle where no side force occurred. The model was mounted on an external balance located beneath the test section, which also enabled the yaw movement of the model in the wind tunnel. The mounting strut between the balance and the model was aerodynamically shielded without physical contact using two NACA0025 profiles to minimize the aerodynamic force acting on the strut. A small vertical clearance of approximately 2 between the slightly flattened tires and the splitter plate as well as between the model under-floor and the tip of the NACA profile was required to avoid termination of the force and to allow yawing conditions. The blockage ratio of the model $\phi $ in the test section at ${0}^{\circ}$ was ≈5.4% based on the frontal area of the model A of 0.135 m. The coefficients were corrected by adjusting the freestream velocity, e.g., for the drag coefficient.

^{−1}. A previously applied disparity correction eliminated minor mismatches between camera viewing areas. The software used was PIVview (Version 3.60, PIVTEC GmbH, Göttingen, Germany).

## 3. Results

#### 3.1. Surface Traces without Crosswind

#### 3.2. Surface Traces with Crosswind

#### 3.3. Wake Flow Field without Side Wind

#### 3.4. Wake Flow Field with Side Wind

^{−1}shrank significantly under high crosswind conditions (Figure 9d). For a clear illustration of the isocontours shown here and the recirculation area for all investigated inflow directions, a qualitative representation of top and side views is given at later stage.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Abbreviations | |

CCD | Charge-coupled device |

HFI | Hermann–Föttinger Institut |

NACA | National Advisory Committee for Aeronautics |

PIV | Particle Image Velocimetry |

OP | Oil paint/flow visualization |

SBES | Stress-Blended Eddy Simulation |

SW | Side wind |

Greek Letters | |

${\alpha}_{xy}$ | Projected angle on the x–y plane |

${\alpha}_{xz}$ | Projected angle on the x–z plane |

${\beta}_{SW}^{OP}$ | Side wind angle for oil paint experiment |

${\beta}_{SW}$ | Side wind angle for PIV experiment |

$\Delta $ | Difference |

${\lambda}_{2}$ | Vortex criterion |

$\rho $ | Density of air |

$\phi $ | Blockage ratio in the test section |

$\overrightarrow{\Omega}$ | Vorticity |

$\overrightarrow{\omega}$ | Nondimensional vorticity |

$\overrightarrow{{c}_{\infty}}$ | Freestream velocity |

Latin Letters | |

A | Frontal area of the model |

${C}_{D}$ | Drag coefficient |

${C}_{P}$ | Pressure coefficient |

L | Total length of the model |

p | Static pressure |

q | Dynamic pressure |

$Re$ | Reynolds number |

$u,v,w$ | Cartesian components of vector $\overrightarrow{c}$ |

$x,y,z$ | Axis of coordinates |

B | Bifurcation line |

F | Focus point |

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**Figure 1.**${C}_{D}$ for the notchback driver model at varying side wind conditions of ${0}^{\circ}\le {\beta}_{SW}\le {10}^{\circ}$ and at $Re=3.2\times {10}^{6}$.

**Figure 4.**Surface traces at $\beta ={0}^{\circ}$ in the frontal view (

**a**), rear view (

**b**), and side view (

**c**).

**Figure 5.**Surface traces at side wind condition of ${5}^{\circ}$: (

**a**) front view, (

**b**) rear view, (

**c**) leeward side, and (

**d**) windward side. The color indicates the changes in the oil trace directions in relation to the baseline case.

**Figure 6.**Surface traces at side wind condition of ${10}^{\circ}$: (

**a**) front view, (

**b**) rear view, (

**c**) leeward side, and (

**d**) windward side. The color indicates the changes in the oil trace directions in relation to the baseline case.

**Figure 7.**Vortical structures along the downstream direction of the rear window and the vehicle base surface without side wind: (

**a**–

**d**) streamwise vortices, (

**e**) ${\lambda}_{2}$-criterion, and (

**f**) recirculation area.

**Figure 8.**Vortical structures at side wind direction of $-{5}^{\circ}$: (

**a**,

**b**) streamwise vortices, (

**c**) ${\lambda}_{2}$-criterion, and (

**d**) recirculation area.

**Figure 9.**Vortical structures at side wind direction of $-{10}^{\circ}$: (

**a**,

**b**) streamwise vortices, (

**c**) ${\lambda}_{2}$-criterion, and (

**d**) recirculation area.

**Figure 10.**A-pillar and C-pillar vortices at the leeward side of the model at a side wind of (

**a**) $-{5}^{\circ}$ and (

**b**) $-{10}^{\circ}$.

**Figure 11.**Centerlines of the vortex cores and the size of the recirculation area in the upper part of the model at changing side wind directions.

**Figure 12.**Centerlines of the vortex cores and the size of the recirculation area in the lower part of the model at changing side wind directions.

**Table 1.**Courses of selected vortical structures and wake length values depending on the inflow direction.

${\mathit{\beta}}_{\mathit{SW}}={0}^{\circ}$ | ${\mathit{\beta}}_{\mathit{SW}}=-{5}^{\circ}$ | ${\mathit{\beta}}_{\mathit{SW}}=-{10}^{\circ}$ | |
---|---|---|---|

top view | ${\alpha}_{xy,\u2460}=-{4}^{\circ}$ | ${\alpha}_{xy,\u2460}=-{10}^{\circ}$ | ${\alpha}_{xy,\u2460}=-{12}^{\circ}$ |

${\alpha}_{xy,\u2461}={7}^{\circ}$ | ${\alpha}_{xy,\u2461}={3}^{\circ}$ | − | |

− | ${\alpha}_{xy,\u2462}=-{3}^{\circ}$ | ${\alpha}_{xy,\u2462}=-{8}^{\circ}$ | |

$\frac{{x}_{u=0m/s}^{max}}{L}\approx 0.15$ | $\frac{{x}_{u=0m/s}^{max}}{L}\approx 0.17$ | $\frac{{x}_{u=0m/s}^{max}}{L}\approx 0.14$ | |

side view | ${\alpha}_{xz,1}={10}^{\circ}$ | ${\alpha}_{xz,1}={7}^{\circ}$ | ${\alpha}_{xz,1}={0}^{\circ}$ |

${\alpha}_{xz,2}={9}^{\circ}$ | ${\alpha}_{xz,2}={20}^{\circ}$ | − | |

− | ${\alpha}_{xz,3}={17}^{\circ}$ | ${\alpha}_{xz,3}={15}^{\circ}$ |

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## Share and Cite

**MDPI and ACS Style**

Wieser, D.; Nayeri, C.N.; Paschereit, C.O. Wake Structures and Surface Patterns of the DrivAer Notchback Car Model under Side Wind Conditions. *Energies* **2020**, *13*, 320.
https://doi.org/10.3390/en13020320

**AMA Style**

Wieser D, Nayeri CN, Paschereit CO. Wake Structures and Surface Patterns of the DrivAer Notchback Car Model under Side Wind Conditions. *Energies*. 2020; 13(2):320.
https://doi.org/10.3390/en13020320

**Chicago/Turabian Style**

Wieser, Dirk, Christian Navid Nayeri, and Christian Oliver Paschereit. 2020. "Wake Structures and Surface Patterns of the DrivAer Notchback Car Model under Side Wind Conditions" *Energies* 13, no. 2: 320.
https://doi.org/10.3390/en13020320