Commercial CFD Code Validation for HeavyVehicle External Aerodynamics Simulation
W. David Pointer, Tanju Sofu, and David Weber
Argonne National Laboratory, Nuclear Engineering Division
The issue of energy economy in transportation has grown beyond traditional
concerns over environment, safety and health to include new concerns over
national security and energy self-sufficiency. As part of the U.S. Department
of Energy Office of FreedomCAR and Vehicle Technologies’ Working Group
on Aerodynamic Drag of Heavy Vehicles, Argonne National Laboratory is independently investigating the accuracy of aerodynamic drag predictions generated by commercial Computational Fluid Dynamics (CFD) Software. In this
validation study, computational predictions from two commercial CFD codes,
Star-CD [1] and PowerFLOW [2], will be compared with detailed velocity,
pressure and force balance data from experiments completed in the 7 ft. by 10
ft. wind tunnel at NASA Ames [3,4] using a Generic Conventional Model
(GCM) that is representative of typical current-generation tractor-trailer geometries. This paper highlights results from evaluations of drag coefficient predictions using standard two-equation steady RANS turbulence models and
logarithmic wall functions that were completed as part of the first phase of
these studies.
Introduction
The commercial CFD software validation effort undertaken by Argonne National Laboratory is currently nearing the completion of the first phase of a
multi-stage project that will culminate in an evaluation of the capabilities of
selected commercial CFD software for the simulation of aerodynamic drag of
actual truck geometries. In the first phase, a roadmap is being developed for
the more rigorous validation efforts to be completed in the remaining components of the study. This phase includes preliminary evaluations of solution
sensitivity to the computational mesh construction, selection of turbulence
model, and other simulation parameters. The evaluations completed in the
development of the roadmap use simulations of the standard configuration of
a Generic Conventional Model (GCM), which is a representative simplification of current generation tractor-trailer geometries. These simulations will
use the commercial CFD software package Star-CD, which is a finite volume
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code using a predictor-corrector-type solver. Computational meshes for these
studies are developed using Star-CD’s automatic meshing capabilities and
problem set up is completed using the aerodynamic problem definition tool,
ES-Aero. The software package provides a wide variety of turbulence modeling options as part of the standard commercial release and allows for the use of
alternative turbulence models through user-subroutine programming. Initial
studies completed in this phase have focused upon the applicability of standard
two-equation high Reynolds number steady-RANS (Reynolds-averaged Navier
Stokes) turbulence models using wall functions in the near wall region for the
prediction of aerodynamic drag. Future efforts may include evaluations of socalled two-layer models, which use the standard two-equation high Reynolds
number models in the far field coupled with a low-Reynolds number model in
the near wall field, or transient simulation methodologies.
In the second phase, the agreement between simulations of the standard
configuration of the GCM using Star-CD and the commercial CFD software
package PowerFLOW will be evaluated. Since PowerFLOW is a latticeBoltzmann based code, the extensive modeling options available in a finite
volume code are neither available nor necessary. Standard PowerFLOW modeling options will be employed in these evaluations.
In the final phase of the studies using the GCM geometry, computational
predictions of velocity fields, pressure fields, and drag coefficients will be compared with experimental measurements for four different configurations of the
GCM. All wind tunnel tests considered in the study provide a Reynolds
number of 1.1 million. In each experiment, three-axis Particle Image Velocimetry (PIV) and 490 pressure sensors are employed to record the velocity and
pressure fields around the vehicle. A standard aerodynamic force balance is
employed to capture drag force data. All cases will be treated as “blind” validation studies with no prior knowledge of the details of the experimental results.
A set of best practice guidelines will be developed from the GCM studies for
application to the simulation of a real truck geometry complete with mirrors,
door handles and all standard decorative details. Through a cooperative research and development agreement, PACCAR Technical Center will provide
detailed geometric data and experimental measurements of drag coefficient
and surface pressure distributions for a 1/8th scale model of a commercial
tractor and generic trailer under a range of yaw angles. Blind validation studies will be completed using standard options available within selected commercial CFD software.
Generic Conventional Model
The Generic Conventional Model (GCM) is a simplified representation of a
conventional U.S. tractor-trailer truck. The model is 1/8th scale and can be
configured in four different geometries as illustrated in Fig. 1. The nominal
configuration is a representative model of a current-generation tractor-trailer
truck. Alternate configurations include the addition of a low-boy device under
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Standard truck
Low boy trailer
Faired truck
Faired truck with low boy trailer
Fig. 1. Generic Conventional Model (GCM) geometric configurations
the length of the trailer, a full fairing between the cab and the trailer, and the
combination of the fairing and low-boy device.
Computational Model
The computational model employed in these studies was developed using the
ES-Aero tool for aerodynamic drag simulation that is available as part of the
Star-CD software package. The mesh is developed using a semi-automated
process that progresses in seven stages:
1. A three-dimensional hexahedral mesh is created that completely fills the
volume of the wind tunnel.
2. The mesh is refined in successively smaller zones surrounding the vehicle
until the mesh in a small region surrounding the vehicle reaches the pro-
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scribed near-vehicle cell size. The result is an unstructured mesh of hexahedral cells which exhibit 2-to-1 matching at the unstructured interfaces.
3. The near-vehicle mesh is locally refined based upon features of the vehicle
surface definition. Local refinements are determined by both minimum
feature size limits and by user identification of feature zones of interest.
4. The surfaces that define the vehicle are “wrapped” by projecting the refined
hexahedral mesh onto the surface. In this manner, the multiple components of the vehicle are merged into a single surface, and a quadrilateral
surface definition is created.
5. The quadrilateral surface definition is spatially expanded to create a subsurface.
6. The sub-surface is used to cut away the parts of the unstructured hexahedral
mesh that fall within the sub-surface.
7. A brick and prism extrusion layer is created to fill the gap between the subsurface and the quadrilateral surface definition. Thus, the polyhedral
trimmed cells are not in the critical boundary layer region of the problem.
8. Upon completion of the basic mesh, the wake and ground layer regions are
automatically further refined to better capture important flow features.
In this study, the generated mesh has a near-wall cell size of 8.0 mm. The
minimum cell size used in local refinements is 0.5 mm, and a minimum of 16
points are required to define any full circle. In addition to automatic refinements, cells adjacent to the surface are refined to a size of 2.0 mm in order to
preserve the quality of the surface in the wrapping stage and improve the quality of the trimmed cells. The extrusion layer consists of two layers of brick and
prism cells where the outer layer has a thickness of 1.0 mm and the inner layer
has a thickness of 0.5 mm. A sample computational mesh is illustrated in Fig.
2. In order to reduce computational cost for these preliminary studies, only
half of the GCM is included in the model and a symmetric boundary condition is employed at the centerline.
In all simulations discussed herein, the GCM is centered at zero yaw on the
floor of a wind tunnel test section that is 2.133 m (7 ft.) tall by 3.048 m (10
ft.) wide. Since the GCM is approximately 2.5 m long, a total test section
length of 10.0 m is assumed, where one model length is included upstream of
the model and two model lengths are included downstream of the model.
Based upon a Reynolds number of 1.1 million, a uniform velocity of 51.5 m/s
is enforced at the inlet boundary. A uniform pressure condition is applied at
the outlet boundary. In these studies, the surface of the standard configuration
GCM is defined using approximately 500,000 triangular surface elements that
are based upon CAD data representations taken from optical scans of the actual model.
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Fig. 2. Two-dimensional projection of the near-vehicle region of the computational
mesh employed in these studies.
Turbulence Modeling
While commercial CFD technology relies heavily upon traditional steady
RANS turbulence modeling in combination with logarithmic wall functions
for most flow field simulation applications, the applicability of these models to
aerodynamic drag simulations is often questioned. Numerous studies have
demonstrated mediocre predictions of separation regions under adverse pressure gradients such as those seen in backward facing steps or bluff bodies in
cross flow when using these models. However, as with any problem, the applicability of these models to the heavy vehicle problem should be independently considered. These studies evaluate three formulations of this type of turbulence model:
1. the standard high Reynolds number k-e model,
2. the Menter k-e SST model [5], and
3. the renormalization group (RNG) formulation of the k-e model [6].
The standard high Reynolds number k-e model and the k-e SST model are
identical in the far field, but the SST model uses a blending function that is
dependent on the distance from the surface to incorporate the additional detail
of the Wilcox k-e model in separation regions and near the walls. For the high
Reynolds number k-e model, the near wall turbulence parameters are specified
using the logarithmic “law of the wall” function. For the k-e SST, the w of
the near wall cell is also fixed using a wall function dependent on the coefficients of the turbulence model. The SST model may be more sensitive to
separation than the standard k-e model, but the two should show reasonable
agreement. The RNG model is also similar to the standard k-e model, but the
RNG model contains an additional term to account for the mean flow distortion of the dissipation. It is expected that a larger discrepancy will be seen
between the standard k-e model and the RNG model.
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Simulation Results
For each turbulence model considered, a steady-state simulation consisting of
3000 iterations was completed. Convergence parameters that define the desired limits of the velocity, mass and pressure residuals were set to small values
to allow the simulation to continue to the 3000th iteration before the standard
flow parameter convergence criteria were satisfied. In addition to the standard
flow parameter residuals, the convergence of the vehicle drag coefficient was
monitored interactively. Although the drag coefficient shows slight oscillatory
behavior in each simulation, near-constant drag-coefficients were obtained by
the 1800th iteration in all three cases. At the 3000th iteration, the normalized
global residual of each of the individual flow parameters have converged to less
than 1x10-4. The normalized change in the drag coefficient has also con-
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verged to less than 1x10-4 by the 3000th iteration. Since velocity and pressure
data from the wind tunnel experiments will not be available for comparison
with the computational studies until the “blind” validation phase of the projects, comparisons with the measured experimental pressure and velocity data
have not yet been made. Only comparisons between the three computational
cases can be made for the pressure and velocity distributions at this time.
However, comparisons with experimental drag coefficient measurements are
made herein since this data provides little information that could potentially
be used to produce “tuned” solutions.
Velocity Distribution Predictions
Since the current simulations have employed a steady-state methodology, the
predicted flow fields cannot be expected to capture such temporal behaviors as
vortex shedding in the wake behind the trailer. However, such steady-state
simulations may still provide useful insights about the general character of the
flow field.
Velocity magnitude profiles at the centerline of the GCM are
shown in Fig. 3. In these figures, recirculation zones are clearly outlined by
the regions of near-zero velocity magnitude, which are shown in violet. The
simulations all show a large recirculation zone downstream of the trailer which
in reality is a large unsteady wake. While a steady-state simulation cannot
capture such a wake, these phenomena are characterized as steady recirculation
zones which provide some insight into the location and distribution of vortex
shedding and other wake field phenomena within the flow field.
As one should expect, the predictions of the simulations using the standard
k-e model and the SST model are very similar. However, the length of the recirculation zone following the trailer is somewhat reduced by the SST model,
and the length of the recirculation under the trailer is extended by the SST
model. The application of the RNG model leads to a more significant deviation from the case using the standard k-e model. The length of the recirculation zone at the base of the trailer is significantly increased and the interaction
of the underbody flow with both the wake flow and the ground plane is much
more significant.
Pressure Distribution Predictions
The accurate prediction of surface pressure distributions is critical for the prediction of drag forces acting on the vehicle. While comparisons will not be
made with experimental measurements of surface pressure distributions, the
surface pressure distributions should be consistent with flow field predictions.
Furthermore, the predictions from the simulations using different turbulence
models should show reasonable consistency since the differences between the
selected models are not large.
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A sample surface pressure distribution taken from the simulation using the
standard k-e model is shown in Fig. 4. Data shown in the contour plot of surface pressure was generated by reflecting the calculated values across the symmetric boundary plane of the half-vehicle model. The surface pressure data
clearly captures that stagnation of flow in front of the vehicle. Also seen are
the regions of separated flow along the A-pillar, along the top of the cab fairing, along the sides of the cylindrical wheels, and along the expansion feature
that would be located just downstream of the cab doors. Consistent with expectations, negative pressures are predicted along the rear surface of the cab
and the trailer, but no large pressure gradients are seen observed within those
regions. The largest pressure gradients are observed along the leading edge of
the sides of the tires and along the recirculation region just under the front
bumper. Significant stagnation and negative base pressure regions are observed on all tires and axels in this simulation. This is consistent with the
static nature of the GCM model, but this distribution would be altered for real
Cab Front View
Trailer Base View
Side View
Fig. 4. Predicted pressure distributions on the surface of the GCM model as seen in isometric, front, side and back views. Data is taken from simulations using the k-e model and
data has been reflected across the symmetric centerline boundary to generate a data set representing the full vehicle.
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tractor-trailer vehicles while in service as a result of the rotation of these elements.
Pressure distributions along the front of the tractor and the base of the
trailer at the model centerline are shown in Fig. 5 for each of the turbulence
models employed. As expected, there is very little deviation between the standard k-e model and the SST model. In a manner consistent with the deviations observed in the velocity field between the simulations using the standard
k-e model and the RNG model, the pressure profiles from the RNG case show
larger negative pressures in the separation zones. While a small difference is
seen between the RNG model and the other models in the predictions along
the trailer base, larger contributions to the difference in total body drag are
found along the components in the under body flow.
Drag Coefficient Predictions
For each simulation, the vehicle drag coefficient was calculated using a
frontal surface area of 0.158 m2. The experimental drag coefficient is reported
as 0.4076 where a frontal area of 0.1544 m2 was assumed. However, the value
frontal area used in the calculation of the experimental coefficient does not account for the area of the tires. When this area is accounted for, as in the calculation of the drag coefficient for the numerical predictions, the experimental
drag coefficient becomes 0.398. As shown in Table 1, excellent agreement
with the experimental result is obtained for all of the turbulence models employed. The best agreement is seen in the simulation using the k-e SST
model, where the error in the prediction is 0.75 percent. Efforts are currently
underway to establish the sensitivity of these results to the computational mesh
structure and refinement.
Table 1. Summary of drag coefficient predictions for each of the turbulence
models employed.
Predicted Drag
Coefficient
Percent Error in
Prediction
Experiment
0.398
--
High-Reynolds number
k-epsilon model
0.402
1.00
Menter k-e SST model
0.401
0.75
RNG model
0.389
2.29
Turbulence Model
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W.D. Pointer, T. Sofu, and D. Weber
(a) Front of Tractor
(b) Base of Trailer
Fig. 5. Predicted pressure distributions along the centerline of the tractor front and trailer base
surfaces of the GCM for each turbulence model considered.
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Summary and Conclusion
Argonne National Laboratory is currently investigating the accuracy of commercial CFD software for the prediction of the aerodynamic drag coefficient of
heavy vehicles. Initial studies have examined drag coefficient prediction using
standard two-equation steady-state RANS turbulence models in conjunction
with wall functions in the commercial CFD software package Star-CD. These
initial studies appear to indicate that these basic models can be used in conjunction with the computational mesh generated by Star-CD’s automatic
meshing tools to make accurate predictions of the vehicle drag coefficient. Indeed, predicted drag coefficients are within as little as 0.75 percent of the
measured wind tunnel value. Extensive mesh sensitivity analyses are currently
underway to further establish the validity of these results. At the conclusion of
“blind” numerical simulation activities using the GCM standard truck geometry, pressure and velocity field predictions will be compared with detailed
pressure and velocity data from wind tunnel experiments. These results will be
used to develop a set of best practice guidelines that will be employed in the
simulation of a real tractor-trailer truck geometry for comparison with wind
tunnel data collected for that system.
References
1. Star-CD, version 3.150A, CD-Adapco Group, Melville, NY.
2. PowerFLOW, version 3.4, Exa Corporation, Lexington, MA.
3. Dale Satran, “ An Experimental Study of the Generic Conventional Model
(GCM) in the NASA Ames 7-by-10-Foot Wind Tunnel,” United Engineering Foundation Conference on The Aerodynamics of Heavy Vehicles:
Trucks, Buses, and Trains, Monterey, CA, Dec 2-6, 2002.
4. J. T. Heineck, Stephen Walker, Dale Satran, “The Measurement of Wake
and Gap Flows of a 1/8th Scale Generic Truck Using Three-Component
Particle Image Velocimetry,” United Engineering Foundation Conference
on The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains,
Monterey, CA, Dec 2-6, 2002.
5. Yakhot, V., Orszag, S.A., Thangam, S., Gatski, T.B., and Speziale, C.G.
“Development of turbulence models for shear flows by a double expansion
technique”, Phys. Fluids, A4, No. 7, pp. 1510–1520, 1992
6. F. R. Menter, “Zonal Two Equation k-_ Turbulence Models for Aerodynamic Flows” in 24th Fluid Dynamics Conference (Orlando), AIAA paper
93-2906, July 1993.