International Journal of Automotive Technology, Vol. 20, No. 5, pp. 9971008 (2019)

DOI 10.1007/s1223901900948

Copyright © 2019 KSAE/ 11014

pISSN 12299138/ eISSN 19763832

997

EFFECT OF CROSSWINDS ON THE AERODYNAMICS OF TWO

PASSENGER CARS CROSSING EACH OTHER

Ahmad Hammad1), Tao Xing1)*, Ahmed Abdel-Rahim2), Vibhav Durgesh1) and John C. Crepeau1)

1)Department of Mechanical Engineering, University of Idaho, Moscow, ID 83844-0902, USA2)Department of Civil and Environmental Engineering, University of Idaho, Moscow, ID 83844-1022, USA

(Received 2 July 2018; Revised 9 February 2019; Accepted 25 February 2019)

ABSTRACTThe impact of aerodynamics on vehicle safety during crossing of passenger cars is investigated, in the absence

and presence of 30o crosswind. Three-dimensional, unsteady computational fluid dynamics (CFD) simulations were used to

simulate these maneuvers. The vortical structures surrounding one car in the case without crosswind were analyzed,

establishing the connection between force and moment fluctuations pre-interaction and the shedding frequency of these

vortices. The forces and moments acting on a passenger car during a crossing maneuver may change by up to 43 %, with the

maximum change associated with the windward car in the presence of crosswind. However, the duration of this increase in

forces is at most 0.01 s, which will not affect the stability of vehicles under normal conditions. The presence of crosswind

increased the rate of fluctuation of forces and moments. Wind tunnel experimental results are in good agreement with the

simulations, and the data available in literature. The analysis results do not show the necessity of enacting new safety policies

on highways, but future parametric studies are needed to fully investigate the impact of different crosswind speeds and

directions, the impact of discrepancy in vehicles sizes, and different vehicle lateral separating distances during crossing and

overtaking.

KEY WORDS : Car-car crossing, Vehicle aerodynamics, Computational fluid dynamics, Vortical structures

NOMENCLATURE

CFD : computational fluid dynamics

DES : detached-eddy simulation

DDES : delayed detached-eddy simulation

IDDES : improved delayed detached-eddy simulation

LES : large-eddy simulation

RANS : Reynolds-averaged Navier-Stokes equations

SUBSCRIPTS

x, y, z : coordinates

d : drag (in Cd)

1. INTRODUCTION

Rural roads in the US, compared to urban roads, see a

proportionately higher number of fatalities with respect to

traffic volume. This risk is most apparent on two-lane,

undivided rural highways shared by fast-moving cars and

trucks, especially in twisty sections of these roads where

winds are more variable in terms of speed and direction.

These vehicles impart aerodynamic forces and moments on

one another, and the significance of these forces and

moments in affecting vehicle stability has increased with

the trend towards lighter, more fuel-efficient vehicles. In an

overtaking or crossing maneuver on a highway involving

two vehicles, the flow fields around the two vehicles

interact generating transient aerodynamic forces that can

affect car handling and stability (Corin et al., 2008). When

the relative size difference between the two vehicles is

large (e.g., a car and a truck), these forces increase on the

smaller vehicle, and increase further under the influence of

crosswinds, (Howell et al., 2014). A vehicle is more stable

when its geometric center, center of gravity and stagnation

point are all in line. Under crosswind conditions, the air

flow around the vehicle becomes asymmetric and the

stagnation point shifts towards the direction of crosswind,

affecting the stability of the vehicle (Altinisik et al.,

2015b). As the computational power of commercially

available computers doubles approximately every two

years (famously observed and predicted by Gordon Moore

(Moore, 1998)), high quality transient computational fluid

dynamics (CFD) simulations of the complex interactions

between moving vehicles were not feasible until the late

2000s. In a transient CFD study on two vehicles crossing

each other using k-ε turbulence model (Zhang et al., 2010),

however, it is not clear if the geometries used are two-

dimensional (2D) or three-dimensional (3D). The study did

not include experimental validation of the results.

Instrumented experiments on a proving ground measured

the surface pressure distribution of a passenger car during*Corresponding author. e-mail: xing@uidaho.edu

998 Ahmad Hammad et al.

both a passing and an overtaking (Kremheller, 2015).

These experiments showed that the asymmetric pressure

distribution induced by these maneuvers influenced lateral

acceleration and yawing rates, being pronounced in

vehicles with a larger frontal area. The change in surface

pressure increased when the lateral distance between

vehicles was decreased. A good correlation between CFD

and experimental data was found, however, only a brief

explanation of the comparison between CFD results and

experimental measurements was presented in this paper.

Previous studies in this area appear to have one or more

of the following limitations: (a) using 2D geometries; (b)

low grid resolutions; and (c) inappropriate turbulence

models that are too dissipative, destroying details of the

important vortical structures in the flow.

2. OBJECTIVE AND APPROACH

This study uses 3D CFD models to investigate variations in

forces and moments associated with car-car crossings, with

and without 30o crosswind (the drag coefficient is not

sensitive to yawing angle change after a critical yaw angle

of 25 ~ 30o (Altinisik et al. (2015b) influenced by vehicle

shape), influenced by vehicle shape, with complimentary

experiments on a single car model in the wind tunnel, to

validate the CFD results. The vortical structures in the

flowfield around the car were analyzed, and their

relationship with forces and moments were investigated.

To address the shortcomings mentioned in the literature

review section, the CFD simulations of vehicle interaction

used: (a) 3D, model scale geometries of vehicles; (b) fine

grids with up to 5.8 million grid points; and (c) Improved

Delayed Detached Eddy Simulation (IDDES) turbulence

model (Gritskevich et al., 2012). IDDES is a hybrid

RANS/LES (Reynolds-Averaged Navier-Stokes equations/

Large-Eddy Simulation) model that accurately resolves

small flow structures near the solid boundaries of the

vehicles and larger flow structures further away from the

boundaries, while avoiding grid induced separation of the

boundary layer.

3. METHODOLOGY

All simulations and experiments involving the passenger

car were run at 1 : 25 scale.

3.1. Car Geometry

A generic passenger car model (Figure 1) was designed

based on the average dimensions of mid-size family sedans

in the US market (e.g., Toyota Camry, Honda Accord, Ford

Fusion, etc.), in terms of overall length, height, width, track

width and wheelbase length. Other important proportions

(cabin length, beltline height, etc.) are also in line with

typical mid-size sedans. The vehicle lacks a wheel gap

between the wheels and the fenders, and wheel motion was

not considered in this study.

3.2. Experimental Methodology

The purpose of the experiments was to measure the drag

forces on a single car model. The drag force was used to

validate a 3D unsteady simulation of the same geometry.

The subsonic wind tunnel in the Department of Mechanical

Figure 1. True dimensions of car model (model dimensions

in parentheses). All dimensions in meters.

Figure 2. Car model setup in wind tunnel. Air is moving in

the negative X-direction. Schematic shows the orientation

of force (red) and moment coefficients (blue) obtained in

the simulations.

EFFECT OF CROSSWINDS ON THE AERODYNAMICS OF TWO PASSENGER CARS CROSSING EACH OTHER 999

Engineering at The University of Idaho was used to

conduct the experiment, and the vehicle model was 3D-

printed using the department’s facilities, with the necessary

attachments manufactured in the machine shop. The 3D-

printed car model is accurately sized to within 1 % in all

dimensions. Figure 2 shows the details of the experimental

set-up. The force balance uses strain gauges and the data is

fed to a Newport Electronics INFS4 Strain Gauge meter.

The balance was calibrated using standard weights.

In each experimental run, a data acquisition device

(National Instruments USB-6002) recorded the drag force

after the air velocity stabilized inside the wind tunnel. Each

data sample was 5 seconds long at 1,000 Hz. Force data

was averaged for each run, and the standard deviation

calculated. The wind tunnel came to a complete stop before

commencing the next run. Air velocity inside the wind

tunnel was changed by adjusting the variable-speed drive

frequency. The frontal area of the car (0.004408 m2) was

used to calculate the drag coefficient.

3.3. CFD Methodology

3.3.1. Simulation design and grid topology

Commercial mesh generating software, Pointwise

(V17.2R3), was used to generate the mesh. The dimensions

of the vehicles were scaled down to 4 % of their original

sizes. An unstructured grid was used on the surfaces of the

vehicles. The volume immediate to the vehicle surfaces

was filled with structured, triangular-aspect prisms to

provide enough grid points to resolve the boundary layer

(Figure 3). The first grid point away from the wall is at a

distance of 0.0001 m, for an approximate y+ value of 2.

The volume between these cells and the inner surfaces of

a cuboid containing each vehicle is populated with

unstructured, pyramid-shaped cells. The high-resolution

dynamic mesh zones behind and in front of each vehicle is

populated by structured cubes with the dimensions (X × Y

× Z) 0.004 × 0.004 × 0.004 m (see Figure 4 for a vertical

slice through the car mesh). The number of grid points in

each mesh is sufficient to resolve all small and large-scale

flow structures. A grid dependency study involving 3

single-car meshes (the fine grid resolution is identical to

the two-car simulations used in this study) showed

monotonic convergence on the grid triplet (refer to Section

4.1 for details).

A large, rectangular, low-resolution zone encloses the

dynamic mesh zones. The lateral distance separating the

two vehicles is approximately half-lane width (1.6 m). The

velocity of each vehicle is 30 m/s (67 mph), moving in

opposite directions parallel to the X-axis.

3.3.2. Numerical method

The commercial CFD software, ANSYS Fluent 17.1 &

17.2 were used in the simulations, using a least squares

cell-based discretization method, and a transient solver.

The SIMPLE algorithm was used for the pressure-velocity

coupling. A second order scheme was used for pressure

discretization. The momentum equations were discretized

using bounded central differencing. An implicit second

order scheme was used for temporal discretization. The

overall simulation design is shown in Table 1.

3.3.3. Dynamic mesh method

The sliding mesh model in Fluent was used to simulate the

relative motion between the vehicles involved. This model

is a special case of general dynamic mesh motion wherein

the nodes move rigidly in a given dynamic mesh zone, i.e.,

all the boundaries and the cells of a given mesh zone move

together in a rigid-body motion. In this situation, the nodes

of the mesh move in space (relative to the fixed, global

coordinates), but the cells defined by the nodes (the zones

behind and in front of the vehicles) do not deform.

Furthermore, mesh zones moving adjacent to one another

are linked across non-conformal interfaces (the zones

separating the imaginary “tunnels” in which the vehicles

move relative to one another, and the zones separating

these tunnels and the larger zone enclosing them,) thatFigure 3. Triangular prisms in the boundary layer close to

the car surface.

Figure 4. Slice through the mesh showing the unstructured

grid surrounding the car.

Table 1. Simulation matrix.

Simulation ReNo. of points

Initial separating distance (m)

No crosswind 4 × 105 5.2 × 106

2.787 (14.26 car lengths)Crosswind 4.5 × 105 5.8 × 106

1000 Ahmad Hammad et al.

allows for fluid flow from one mesh to the other (ANSYS,

2016).

3.3.4. Turbulence model

In all simulations, the flow around the vehicles involved

was modeled using Improved Delayed Detached-Eddy

Simulation “IDDES” (Shur et al., 2008). For 3D, high

Reynolds number turbulent flows, using RANS for

analysis results in the loss of vortical structure details,

especially the smaller, high-frequency eddies. DES

(Detached-Eddy Simulation, (Spalart et al., 1997)) and its

modification, DDES (Delayed DES (Spalart et al., 2006))

are models developed with the aim of accurately predicting

massively separated flows at a manageable computational

cost (Strelets, 2001). DES combines RANS in the attached

boundary layers, which are populated with small eddies

that have a length-scale much less than the boundary layer

thickness (δ), with LES in the complex, massively

separated regions away from the wall, where large,

unsteady turbulent scales play a dominant role. DES can

produce artificial separation of the boundary layer, in an

effect termed Grid Induced Separation, when the switch

from RANS to LES happens inside the boundary layer, due

to a refinement in the grid in that region (Menter et al.,

2003). This occurs when geometric features demand a fine

grid inside the boundary layer, resulting in wall-parallel

grid spacings in the upper regions of the boundary layer

that are smaller than the distance from the wall. This also

occurs when the boundary layer is thicker as it nears

separation. This motivated the development of DDES to

avoid the switch from RANS to LES in regions inside the

boundary layer which are not fine enough to resolve

velocity fluctuations (LES content) (Spalart et al., 2006).

Further improvement of DDES was proposed, the

IDDES model, combining DDES with an improved

RANS-LES hybrid model that enables Wall-Modeled LES

(WMLES) when unsteadiness is present in the boundary

layer (Shur et al., 2008). The presence of obstacles (for

example: sharp, backwards facing angles in car

geometries) can induce this unsteadiness. WMLES

resolves the inner-most part of the boundary layer using

RANS, switching over to LES formulation when the grid

spacing is sufficient to resolve the local scales. The IDDES

model surpasses both DES and DDES in simulating mixed

flows with both attached and separated regions.

3.3.4.1. Governing equations

The incompressible continuity and momentum equations

for Cartesian coordinates read as (Xing, 2014):

(1)

(2)

where V is the velocity vector, is the density, is the

dynamic viscosity, p is the pressure and g is gravitational

acceleration.

RANS equations in Cartesian tensor form are given by:

(3)

(4)

where and and are the mean and

fluctuating velocity components, respectively.

IDDES is a hybrid RANS-LES model, based on the

BSL/ST (baseline/standard) model (Gritskevich et al.,

2012).

SST IDDES formulation: Transport equations for k and

ω:

(5)

(6)

where k is the turbulent kinetic energy, ω is the specific

dissipation rate, Pk is the production term, and F1 is one of

the two SST blending functions.

3.3.5. Boundary and initial conditions

The faces of the large rectangular zone surrounding the

dynamic mesh zones have different boundary conditions

depending on the case (Figure 5, Table 2). Car 1 moves in

the positive X-direction.

• Constant pressure-outlet boundaries are defined by the

following conditions:

Gauge pressure = 0

Backflow turbulent intensity = 1 %

Backflow turbulent viscosity ratio = 0.1

( ) 0 V

2 T( ) ( ) ( )pt

V V V V g

i

i

( ) 0u

t x

i i j

j

ji

ij i j

j j j

k

ki j

( (

2(

)

3

)

)

u u u

t x

uu uu u

x x x x x x

i i iu u u

iu

iu

3

k t k

IDDES

( ) ( )k k

Uk k Pt l

2

ω t

2

1 k k

t

( ) (

2( )1

)Ut

kF P

Figure 5. Boundary conditions.

EFFECT OF CROSSWINDS ON THE AERODYNAMICS OF TWO PASSENGER CARS CROSSING EACH OTHER 1001

• In crosswind cases, two pressure-outlet boundaries are

replaced by velocity inlets, which have the following

conditions:

Turbulent intensity = 1 %

Turbulent viscosity ratio = 0.1

Velocity = 17.32 m/s, in the Z-direction

• All cases are initialized with the following conditions:

Time-step size: 0.0001 s

Initial separating distance between vehicles: 2 m

Initial air velocity inside domain: 0 m/s

3.3.6. Convergence criteria

All the simulations were determined to be converged when

the residuals of the continuity; x, y and z velocity; k; and ω

equations are lower than 1e-05.

3.3.7. CFD analysis method

In each simulation, forces and moments acting on the

vehicle surfaces were recorded at each time step. These

forces and moments are non-dimensionalized to form

coefficients using the following formulas:

(7)

, (8)

where F and M' are the force (N) and moment (Nm),

respectively, is the air density (1.1 kg/m3), u is the

relative velocity magnitude of air with respect to the

vehicle (m/s), A is the frontal area of the vehicle (m2), and L

is the total length of the vehicle (m). Fd is the magnitude of

the drag force, while Fy and Fz are the projected force

components in the y and z directions, respectively. Cd, Cy

and Cz are the drag, lift and side-force coefficients,

respectively. Mx, My and Mz

are the roll, yaw and pitching

moment coefficients, respectively.

Fast Fourier transform analysis was conducted on the

time histories of forces to identify their power spectrum.

The frequencies of different vortical structures can then be

associated with the FFT analysis. The flow around the

vehicles, and in particular the shedding vortices, where

visualized using the isosurfaces of Q-Criterion (Hunt et al.,

1988): in an incompressible flow, a vortex is a connected

fluid region with a positive second invariant of u, where

the vorticity magnitude is greater than the magnitude of

rate of strain:

(9)

where Q represents the local balance between shear strain

rate and vorticity magnitude. This criterion also requires

the pressure to be lower than the ambient pressure in the

vortex (Kolář, 2007; Holmén, 2012).

4. RESULTS AND DISCUSSION

4.1. Solution Verification and Experimental Validation

Wind tunnel experimental results for the drag coefficient

(Cd) of a single passenger car are clustered around an

average value of 0.349. The variability in each

experimental test is small, with a maximum standard

deviation of about 1 % from the average value. The

uncertainty in each drag force measurement after wind

tunnel calibration is around 12 %.

The mesh size (fine mesh) and time-step size used in the

simulations were determined using rigorous verification

(Xing and Stern, 2010, 2011) & validation (Xing et al.,

2008) for a single, stationary car (resembling conditions in

the wind tunnel). The results are summarized in Table 3.

Verification is used to estimate the numerical errors by

systematically refining the grid spacing and time-step sizes

on three meshes (coarse, medium and fine) using a

refinement ratio in three directions. As shown by

Figure 6, the grid triplet demonstrates monotonic

convergence and therefore the fine mesh (5.8 million) was

adopted for all the car-car crossing simulations. In Table 3,

RG defines the convergence ratio which is the ratio of the

solution differences for medium-fine and coarse-medium

solution pairs. PG is the observed order of accuracy, UG is

the numerical uncertainty estimate as a percentage of

experimental data, and |E| is the absolute relative error

between the fine mesh solution and experimental data. UV

is the validation uncertainty and UD is the experimental

uncertainty. UG is only 0.633 % based on the experimental

d,y,z

d,y,z 2

2 F

Cu A

x,y,z

x,y,z 2

2 M

Mu AL

2

i, j i, j j,i

2 2

i, j j,i

1(

2

1

)

)1( 0

2 2

Q u u u

u u S

‖ ‖ ‖ ‖

2

Table 2. Boundary conditions for simulation cases.

Faces Boundary conditions

ABCD All cases Slip wall

EFGH All cases Slip wall

ABFENo crosswind Constant pressure outlet

Crosswind Slip wall

DCGHNo crosswind Constant pressure outlet

Crosswind Slip wall

ADHE, BCGF

No crosswind Constant pressure outlet

CrosswindConstant velocity inlet

(17.32 m/s to simulate 30o crosswind)

Table 3. Verification & validation (V&V) study for Cd. All

percentages are based on experimental data D.

RG PG UG (%) |E| (%) UV

(%) UD

(%)

0.111 3.169 0.633 11.174 12.017 12

1002 Ahmad Hammad et al.

data. After solution verification is completed, validation is

performed by comparing |E| (11.174 %) with the validation

uncertainty UV (12.017 %). Since |E| < UV, the CFD model

was validated.

The aerodynamic blockage inside the wind tunnel was

corrected using the following proposed formula (Sykes,

1973):

(10)

where w is the blockage correction factor, m is an empirical

constant (m = 1.22 (Stafford, 1981)) B is the blockage ratio

and defined as:

(11)

where Am and Aw are the model frontal area and wind tunnel

cross-sectional area respectively. The corrected drag

coefficient is defined using the formula:

(12)

where Cdc and Cdm are the corrected and measured drag

coefficients respectively. The blockage correction method

used by Sykes is one of three methods that give the most

accurate results (Altinisik et al., 2015a) and applicable for

blockage ratios less than 5 %. The current blockage ratio,

B, of the passenger car inside the wind tunnel is 2 %.

The CFD result on the fine mesh is 11 % lower than the

experimental data. The discrepancy between CFD

simulation result and experimental results can be explained

by: a) the effect of skin friction inside the wind tunnel, and

b) the nature of the simulation design. The two vehicles are

separated by a certain separating distance at the start of

each simulation. This distance is necessary to give the

airflow around the vehicle a chance to fully develop, and

the forces and moments to stabilize, before interaction

between the vehicles start. However, this distance is limited

by the computational affordability of CFD simulations.

Even though forces and moments in the simulation are

stable before interaction starts, it appears that there is still a

small aerodynamic effect of each vehicle on the other,

reflected in the lateral shifting of the stagnation point on

each vehicle by a small distance.

4.2. CFD Results

4.2.1. Two cars crossing without crosswind (Case 1)

4.2.1.1. Before interaction between the two vehicles starts

The vortical structures in the airflow surrounding Car 1 can

be seen in Figure 7. The main vortices and their

frequencies are defined in Table 4. The vortices are defined

such that “Right” and “Left” refer to the right and left sides

of the car along the direction of travel, respectively.

Vortices are abbreviated by T, B, W, and S, standing for

“Top”, “Bottom”, “Wake” and “Side”. Vortices T1, T2 and

T3 (Figure 7 (a)) are formed along the sharp roofline along

each side of the car. They are visually dominant, but they

are stable before the interaction. Along each side, these 3

vortices weaken towards the end of the roofline, forming 2

top vortices in the wake of the car, T4 and W (Figure 7 (b)).

Along the bottom surface of the car, a vortex, B, sheds off

the entire width of the rear bumper (Figure 7 (c)).

The asymmetry of the periods of similar vortices located

on the left and right sides (S, right and left) of the car is

explained by the location of the stagnation pressure point

(Figure 8). This point is slightly shifted away (on the

horizontal XZ-plane) from the symmetry plane of the car,

indicating that the incoming airflow impacts the car at an

angle that is not quite perpendicular. As shown in Figure 9,

spectral analysis of the drag coefficient during the pre-

interaction period (0.015 ~ 0.045 s in the simulation),

indicates dominant frequencies at 100, 170, 200 and 300

Hz, each corresponding to the shedding frequency ( f ) of

one or more vortices. Not all vortices influence the

1w mB

m

w

AB

A

dc dmC wC

Figure 6. Solution verification and comparison with

experimental data for a stationary, single car simulation

using simulations on 3 mesh sizes.

Table 4. Main vortices shedding frequency before

interaction between vehicles.

Vortex Frequency (Hz)

T4 163, 192

B 200

W (left) 159

W (right) 294

S (left) 435

S (right) 170

EFFECT OF CROSSWINDS ON THE AERODYNAMICS OF TWO PASSENGER CARS CROSSING EACH OTHER 1003

fluctuations in drag coefficient. Vortices T1, T2 and T3 are

longitudinal and continuously shedding, and the side

vortices (S) are too weak to influence the drag coefficient.

The rear top center vortex (T4) is influenced by the two

inner roofline vortices (T1 & T3). This results in a

shedding pattern dominated by two frequencies (163, 192

Hz). At 0.0276 s (Figure 10), a massive vortex spanning

the width of the car starts shedding, while further

downstream of it a small helical vortex is present. This

pattern is repeated starting at 0.0328 s.

The other two rear top vortices have different shedding

frequencies, (159 and 294 Hz for the left and right sided

vortices, respectively).

Figures 11 and 12 show the progression of each vortex,

shedding from the top edge of the trunk, then joined by the

Figure 7. Vortical structures using isosurfaces of Q-

criterion.

Figure 8. Horizontal slice through Car 1 highlighting the

shifted position of the stagnation point at the front of the

car.

Figure 9. Two cars crossing without crosswind: FFT

analysis of drag coefficient before vehicle interaction.

Figure 10. Rear center vortex (Figure 7 (b)), shown by

isosurfaces of Q-criterion = 5e6. The shedding frequency

(corresponding to fluctuations in drag coefficient)

alternates between ~ 170 and ~ 200 Hz.

1004 Ahmad Hammad et al.

longitudinal vortex T2 after it breaks down to form helical,

counter-rotating vortical structures.

Figures 13 and 14 show the asymmetrical side helical

vortices. The left-side vortex has a much higher frequency

(435 Hz) compared to the right-side vortex (~ 170 Hz).

This left-side vortex also contributes to the formation of the

left-side rear vortex.

4.2.1.2. During interaction between the two vehicles

From this point forward, the distance between the two cars

will be denoted by D, where D is the horizontal distance

along the X-axis between two vertical planes tangential to

the front of each car, measured in car lengths (the length of

each car is 0.192 m). Initially, D = 14.26 car lengths and

decreases when the two cars are approaching each other

and becomes negative when the two vertical planes pass

each other, i.e., the two cars leaving each other.

The interaction doesn’t start until D ~ 1.8 car lengths (t ~

0.04 s) and continues after crossing until D ~ − 4.5 (t = 0.06

s). This interaction duration is evident in the fluctuation of

the drag force (Figure 15 (a)) and side force coefficients for

both cars (Figure 15 (b)), before returning to the pre-

interaction average values.

Figure 11. Rear left vortex, shown by isosurfaces of Q-

criterion = 5e6. The shedding frequency of this vortex

(~ 150 Hz) is half that of the equivalent vortex at the other

side of the car.

Figure 12. Rear right vortex, shown by isosurfaces of Q-

criterion = 5e6.

Figure 13. Helical right side vortex, shown by isosurfaces

of Q-criterion = 3e5. The vortex starts forming at the edge

of the front bumper.

Figure 14. Helical left-side vortex.

Figure 15. Two cars crossing without crosswind: time

histories of (a) Drag force coefficient; (b) Side force

coefficient.

EFFECT OF CROSSWINDS ON THE AERODYNAMICS OF TWO PASSENGER CARS CROSSING EACH OTHER 1005

One noticeable observation is the alternation of these

force fluctuations from one set of force coefficients to the

other: at D = − 0.59 (t = 0.0475s (P1)), the drag coefficient

of both cars decreases to its minimum value (almost 20 %

less than average), at the same moment, the side-force

coefficient is at its average value. This coefficient climbs

up to its maximum value at D = − 1.21 (t = 0.0495 s (P2))

when the drag coefficient is at its average value (Cd = 0.32).

Another peak for both drag and side force coefficients is

observed at D = − 4.34 (t = 0.0595 s (P3)). The pressure

distribution on the sides of each car during the crossing

contributes to the fluctuations in the side-force coefficient.

At the maximum side force value (P2), the low-pressure

region between the two cars reaches its maximum extent

and strength (Figure 16). This low-pressure region grows

as the two cars approach each other, pulling the two cars

towards each other and contributing to the fluctuations in

side force (Figure 15 (b)). The main vortical structures

around the two vehicles do not change in shape or direction

during the interaction, but they lose their periodicity

(Figure 17).

The lift coefficient (Figure 18 (a)) hovers close to zero

for both cars and does not show significant variation during

interaction compared to its average fluctuation frequency.

The roll coefficient for both cars (Figure 18 (b)) is small,

which is expected, as the car geometry is symmetrical

around the vertical plane passing through its centerline,

consequently, the streamwise vortical structures are

symmetrical around that same plane. The vortices are

oriented along the longitudinal axis, not the vertical axis:

there is little variation between the vertical forces acting on

each side of the car to cause a significant roll moment. Still,

within that small magnitude of roll moment (less than

Figure 16. Horizontal slice at y = 0.02 showing the

pressure distribution around the cars at maximum side

force (P2 in Figure 15).

Figure 17. Overall flow pattern surrounding the cars and

pressure distribution on car surfaces during interaction

without crosswind.

Figure 18. Two cars crossing without crosswind: time

histories of (a) Lift; (b) Roll; (c) Yaw; (d) Pitch

coefficients.

1006 Ahmad Hammad et al.

0.0075 for either car), the interaction causes a spike at D =

− 1.21 (t = 0.0495 s) before returning to normal.

The yaw moment coefficient (Figure 18 (c)) does not

show a periodic pattern before the interaction starts,

varying between 0 and 0.075 for either car, which can be

attributed to the large number of symmetrical, streamwise

vortical structures of varying shedding frequencies on each

side of the car, with no particular vortex having a dominant

effect over the others. Again, there is a small spike at D =

− 0.12 (t = 0.0460 s), but this peak is in the same order of

magnitude of the largest fluctuation of the coefficient

before the interaction starts. There is no effect on the pitch

moment coefficient (Figure 18 (d)).

4.2.2. Two cars crossing with 30-degree crosswind (Case 2)

4.2.2.1. Before interaction between the two vehicles starts

The vortical structures in the airflow surrounding Car 1 can

be seen in Figure 19. Compared to the case without

crosswinds, the top vortices T1 (left & right) and the

downwind side vortex T3 (right) disappear. Side vortex S

only appears on the downwind (right) side of the vehicle.

All the other vortices keep their shape and structure, tilted

30o to the X-axis.

The mean drag coefficient of both cars before the

crossing is 0.41, a 34 % increase over the same car’s drag

coefficient without crosswind (Figure 20 (a)). The car is

less streamlined when the airflow is impacting it at an

angle, and an increase in drag force is expected. The lift

coefficient shows two stages, the first with a mean value of

0.14 between D = 9.57 and D = 4.88 (0.15 s to 0.03 s in the

simulation), and a second phase with a mean value of

− 0.10 between D = 4.88 and D = 1.76 (0.03 s to 0.04 s in

the simulation) (Figure 20 (b)). The side force coefficient

stabilizes later than the other two force coefficients. The

mean value for both cars is 1.47. This is an indication of the

stronger side forces acting on the vehicles by the crosswind

(Figure 20 (c)), when compared to the side forces

experienced in the similar case without crosswind.

4.2.2.2. During interaction between the two vehicles

As the vehicles approach each other, one car experiences a

jump in its drag coefficient to 0.54, a 35 % increase (Car 2)

(Figure 20 (a)). The other car (Car 1) is momentarily

shielded from the effect of crosswind, and the drag forces

acting on it drop by 15 % compared to the pre-interaction

mean value. The windward car (Car 2) also experiences the

largest deviation of side forces. Its side force coefficient

changes from a mean value of ~ 1.47 to 0.84 (Figure 20

(c)). The side force coefficient of the car on the leeward

side drops to 1.23. This pattern is repeated with the lift

Figure 19. Vortical structures using isosurfaces of Q-

criterion.

Figure 20. Two cars crossing with 30-degree crosswind:

time histories of (a) Drag; (b) Lift; (c) Side force; (d) Yaw;

(e) Roll; (f) Pitch coefficients.

EFFECT OF CROSSWINDS ON THE AERODYNAMICS OF TWO PASSENGER CARS CROSSING EACH OTHER 1007

coefficient: the windward car’s coefficient changes to

− 0.45, with no appreciable change for the leeward car.

The yaw moment coefficients (Figure 20 (d)) show the

same trend as the force coefficients: the windward car

shows a greater deviation from average (− 0.17 to − 0.10)

compared to the leeward car (0.20 to 0.18). Both roll and

pitch moment coefficients show no appreciable change

from the pre-interaction average (Figure 20 (e) and (f)).

5. CONCLUSION AND FUTURE WORK

Unsteady, three-dimensional CFD simulations were

performed to investigate the aerodynamic effects of vehicle

interaction in two cases: (1) two passenger cars crossing

each other without crosswind, and (2) two passenger cars

crossing each other with 30-degree crosswind. The

simulations investigated the change in forces and moments

associated with these vehicle encounters. Wind tunnel

experimental measurements of the drag coefficient of a

single car model without crosswind were used to validate

the simulation. The vortical structures surrounding one car

in case (1) were analyzed, establishing the connection

between force and moment fluctuations pre-interaction and

the shedding frequency of these vortices. A total of twelve

vortices were identified and analyzed. Ten vortices are

pairs on each side of the car: two vortices along the car

doors, six on the top, and two in the wake. The other two

vortices are central on the top and bottom of the car. The

six vortices on the top of the vehicle are stable and have no

effect on the unsteadiness of the forces and moments. The

two vortices along the doors are unstable but have minimal

effect on the forces and moments. The two vortices in the

wake and the two central vortices are the ones that have the

most significant impact on the forces and moments.

Two cars crossing without crosswind (Case 1): During

interaction, the most significant effect of one car on the

other is on the side force and the yaw moment. While the

side force is minimal before interaction, its magnitude

increases gradually, and its direction continuously changes

during interaction. The side force coefficient increases in

magnitude from an initial value of 0.01 to a maximum

value of 0.09. The yaw moment coefficient does not show a

periodic pattern before interaction. There is a peak in its

value when the cars are side by side, but this peak is in the

same order of magnitude of the largest fluctuation of the

coefficient before interaction starts. Under the conditions

analyzed, these effects last for ~ 0.02 s, and no fluctuation

lasts more than 0.005 s, so the impulse of any change in

side force is small. The two cars affect each other similarly,

and the interaction does not change the shape or direction

of the vortical structures surrounding each car.

Two cars crossing with 30-degree crosswind (Case 2):

As in the case without crosswind, the most significant

effect of one car on the other is on the side force and the

yaw moment. However, unlike Case 1 where each car

experiences roughly the same changes in force and

moment magnitudes, in Case 2 the windward car

experiences the largest changes in these magnitudes,

especially in the side force, which drops by 43 % during

interaction. The yaw moment coefficient also drops by 42

%. The leeward car experiences a smaller drop in the side

force of 16 % because it is shielded from the effects of

crosswind. However, the duration of these changes is

small, similar to the overall trends seen in Case 1.

5.1. Future work

This study involves two identical passenger cars interacting

with each other. The analysis of forces and moments, as

well as the identification and definition of major vortical

structures serves as a baseline for further studies involving

vehicles of disparate sizes, e.g., a car and truck, under a

range of scenarios and minimum lateral distance between

the two vehicles for safety concerns.

To fully investigate the effects of crosswinds on vehicle

interactions, more CFD simulations need to be run with

incrementally larger crosswind angles. Additionally, the

current V&V methodology and procedures were developed

for RANS models. In the IDDES model, RANS is used

inside boundary layer but large eddy simulation (LES) is

used in the separation region. It would be interesting to use

the recently developed general framework of LES (Xing,

2015; Dutta and Xing, 2017), and the five-equation and

robust three-equation methods for LES (Dutta and Xing,

2018) to not only evaluate the numerical errors but also the

modeling and total errors.

ACKNOWLEDGEMENTThis work has been funded by the

US Department of Transportation's University Transportation

Center program, Grant #DTRT13-G-UTC4O through the Pacific

Northwest Regional University Transportation Center (PacTrans).

The authors would like to thank PacTrans for their support.

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