fluid mechanics final project report

Determination of Drag Force Exertedon Pickup Truck Tailgate Position

using CFD AnalysisJoe Brindle

Soumini Mohandas

Surya Yamujala

CHEN 6353 - University of Utah

December 15, 2016

Abstract

It is of numerous peoples interest to mitigate the fuel costs of their vehicles. One of the common, andvery high consuming fuel vehicles out there is a Pickup truck. Many people try to mitigate this by tryingvarying the aerodynamics of their vehicles. On a pickup truck some lower their tailgate to improve fuelefficiency. The computational fluid dynamics package Comsol was used to determine the efficacy of theseactions at 35 and 65 mph. The forces exerted on the vehicle were used to calculate the required powernecessary to keep the vehicle at that velocity. The final power requirements are 22.47 kW and 4.12 (2.76hp) at 65 mph and 35 mph for the tailgate up, respectively, and 22.02 kW and 4.06 kW (2.72 hp) for 65mph and 35 mph for the tailgate down, respectively.

I. Introduction

Rising fuel price and the emissions mitigation has perpetuated an interest in improvingfuel economy both among automobile manufacturers and consumers. Aerodynamics is animportant aspect to improve the vehicles fuel efficiency. Some of the most common fuel

consuming vehicles are larger vehicles, for apparent reasons such as larger mass and larger crosssectional area. A pickup truck is one of the most popular vehicles used today and it accountsfor about 14.9 per cent of the vehicles on the road. A pickup is very valuable for both personaland businesses because of the utility of the bed. The bed is also theorized to be a source of dragon the pickup due to the tailgate position. There is some controversy over the tailgate position,whether more force is exerted in the vertical position, with the air being forced onto the normalof the tailgate than in the horizontal position where there is both a normal and shear force. Thetailgate of the pickup truck plays an important role in the aerodynamic performance. In thisstudy, we examine the change in the flow characteristics of a pickup truck by varying its tailgatepositions and determine the stresses and forces exerted to qualify the controversy and determinethe validity of each argument.

II. Methods

Geometry

The geometry was implemented by using the dimensions of a 2017 Chevrolet Silverado 1500.The dimensions that were used to implement the geometry are provided in the supplementary

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Determination of Drag Force Exerted on Pickup Truck• Dec 2016 • CHEN 6353

files. The vehicle geometry was made using the CAD package in Comsol. There is a domainbox implemented around the vehicle to simulate a wind tunnel like effect. Then the geometry ofvehicle was subtracted from the domain so that there is no unnecessary meshing of the inside ofthe vehicle.Two separate models were used to change the geometry of the tailgate position and to convergethe two simulations in parallel.

Figure 1: Velocity Contour Plot

Model Selection

The vehicle was modeled in the Turbulent flow regime. The Reynold’s number is of the order ofthe 109 when the velocity and characteristic length and being the x-direction length and velocityof the vehicle and the fluid properties are air at standard temperature and pressure. The Reynoldsnumber calculation is presented below with the unit conversions inferred.

vDν

=227in ∗ 65mph

18.90 m2

s

= 1.13 ∗ 109

The κ-ε model was used as the coupling method to converge the turbulent flow regimes. Rigorousflow convergence models were unnecessary for this simulation as there was only from turbulentflow conditions.

The boundary conditions applied are as follows:

• Inlet Velocity (normal to x-direction) - Varied as 35 mph and 65 mph• Outlet Pressure (normal to x-direction) - Set as 0 pa to set the relative pressure difference• Open Boundary (parallel to x-direction) - This is to simulate a semi-infinite domain• Wall Conditions (vehicle shape boundary)- Comsol’s Turbulent Flow wall functions1

A symmetry boundary condition is used in the halfway point to mitigate the computationalintensity of the model. Therefore, all stresses are doubled to find the true force exerted on the

1Wall functions implements the multilayer theory where there is a laminar boundary layer, a transitional layer, inertiallayer and the turbulent layer. This model is relevant to our study as we would like to analyze the forces exerted onto thesurface of the vehicle

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vehicle.Relative motion is a major construct of this model. In the simulation, the geometry is stationarywhile the fluid is in motion, however, in reality the fluid is stationary and the vehicle is in motion.Although a trivial assumption but this is something to consider when reviewing the direction ofthe force and velocity vectors.

Meshing

This model made use of user defined meshing so some custom meshing options could be used.This model was primarily concerned with the forces exerted on the boundaries of the vehicle,therefore the surface meshing and the domain were meshed separately. The following describesour meshing options.

Surface Mesh Free Triangular NormalDomain Mesh Free Tetrahedral Coarser

Boundary Layer Mesh Rectangular 5 layers

The boundary layer mesh was implemented to characterize the flow near the surfaces as accuratelyas possible. Any change in flow normal to the plane surface will be very slight so a thin rectangularmesh is best to model these areas.

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III. Results

Velocity Results

Figure 2: Velocity Contour Plot at 35 mph

The velocity profile propagates like a wake with increasing velocity as the distance from thevehicle increases. This is expected with a semi infinite domain. Because of the relative motionassumption, where the velocity is zero, it is actually at a maximum and vice versa with thedirection of velocity vectors reversed in the x-direction. The contour velocity plots can be seen inFigure 2 and Figure 3. These plots reflect a few interesting points where the velocity is high andlow and what type of stresses are exerted on particular areas described in sections below.

For instance, in Figure 2 and Figure 3 there is a large stagnation zone where the velocity is

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Figure 3: Velocity Contour Plot at 65 mph

very low in the front of the vehicle (roughly the speed of the vehicle in reality). Any stress exertedin this area will be a normal component and will have little shear contribution to the x-directionstress.

An interesting aspect to the velocity contour plots is velocity profile in the bed of the pickup.With the tailgate down, the contour lines dip down into the bed then come back to a more constantgradient as the flow continues towards the outlet of the domain. This is indicative of a normalstress at this point to push the flow upwards and straighten the flow. Likewise, in the Tailgate upgeometry there is a low flow cavity that forms in the bed of the pickup. However, there is a slightdip down right before the tailgate. This might be indicative of both a normal and shear stressexerted onto this point as there is both a change in direction and squeezing the velocity profile.

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Stress Results

The stresses are plotted on the surface of the vehicle as well. The Stresses (x-direction only) exertedon the surface are presented in Figure 4 and Figutre 5.

Figure 4: Stress profile at 35 mph

The more notable aspects of these plots are the negative x-direction stress in the region thattransitions the windshield to the roof as well as the grill to the hood. The stress in the x-directionis negative in this place because of bernoulli’s principle which states that where the velocity ishigh there must be low pressure at this point. There is a high shear at this point, but since theviscosity is so small, there is a small impact on the low pressure and therefore the overall stress atthis place on the domain.

The difference between the stresses at 35 mph and 65 mph show a much larger stress profile.

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Figure 5: Stress profile at 65 mph

The stress at 35 mph is in the range of .5 > stressx > −.5 while at the stress at 65 mph the stressranges from 1 > stressx > −3 so the stress dramatically increased.

Force and Power results

The surface integral tool was used to calculate the forces in the x and y direction. The z directionforce was inferred to be zero as the forces would be symmetric as per the symmetry boundarycondition. The surface integral was used to calculate the power

Power =∫ v ∫ A(vehicle)

τ · dA · dv

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Table 1: Force Vector Components and Power Required

Force Vector Components and PowerFx (N) Fy (N) FMagnitude (N) Power (kW)

35 mph Tailgate Down 259.4 136.4 293.1 4.0635 mph Tailgate Up 263.4 116.5 288.0 4.12

65 mph Tailgate Down 757.7 395.8 854.8 22.0265 mph Tailgate Up 773.5 342.0 845.7 22.47

Since there is only one component of velocity for the vehicle (in reality) only the x directionstresses contibute to the power needed to keep the vehicle at that velocity.

Drag Coefficient

The drag force is strongly a function of velocity so we determined if stokes law is appropriate forthis model to evaluate if the drag coefficient is constant for both cases.

Fdrag =Cdρu2 A

2

The drag coefficients are presented in the table below

Table 2: Drag coefficients

35 mph 65 mphTailgate Up .465 .396

Tailgate Down .473 .400

IV. Discussion

This study has presented several insights into the motion of a vehicle and the drag that wasexerted onto the vehicle. One interesting and unexpected result was that the power required wasless for the tailgate position being down. This conflicts with anecdotal and experimental work. Itwas expected that the tailgate up would require less power at a given velocity. The low velocitycavity shown in Figure 2 and Figure 3 for the tailgate up would mitigate much of the drag exertedon the vehicle. However there are two considerations to qualify this and provide an explanationfor the discrepancy. The assumptions made when modeling for turbulence with this model andthe other forces that are at play when considering power consumption and fuel economy.

Comsol uses the Reynold’s Averaged Navier-Stokes (RANS) to model turbulence. If this iscompared to reality, there actually exists a gaussian distribution of velocity fluctuations thatoccurs around the predicted value. So if inferential statistics were used to calculate the statisticaldifference between the velocity distributions and then the resulting distributions of forces thatcould be present. There would likely not be a statistically significant difference in the forces

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between the two geometry configurations.

The force vector in the y-direction was drastically increased by 15% with the tailgate positiondown as shown in Table 1. This may be significant enough to increase other forces that wouldresist the velocity of the vehicle. A larger downward y-direction force would result in a largerfriction force in the wheels. The wheel in contact with the ground is in static friction, but thewheel sliding on the hub is in kinetic friction and would be amplified by 15% (assuming the car isweightless) due to the equation Ff = µk ∗ Fnormal .The drag coefficients are very similar for both geometries. However the drag coefficient is stronglyinfluenced by speed. One reason may be the compressible flow will alter the density throughoutits flow around the vehicle. The result is that stokes law can vary for compressible, turbulent flowregimes. The density could vary making the Fdrag not constant The higher the velocity, the lowerthe pressure, the lower the density and therefore the lower the drag coefficient.

V. Conclusion

This model brought numerous insights of applied drag forces in common applications like thedrag exerted on vehicles. The added power necessary to keep the pickup truck at a particularvelocity is slightly more however likely statistically insignificant. There are normal stresses exertedthat could increase the friction to produce the added power and consequently lower the gasmileage which is generally reported when the tailgate is down.

References

[COMSOL, 2016] COMSOL Multiphysics, COMSOL (2016). COMSOL Multiphysics Software

[GM, 2016] 2017 Chevrolet Silverado 1500 Features & Specs

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fluid mechanics final project report

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