using openfoam to model energy taken from the swirl behind a car

Proceedings of OFW44th OpenFOAM Workshop

June 1-4, Montreal, QC, Canada

USING OPENFOAM TO MODEL ENERGY TAKEN FROM THE SWIRLBEHIND A CAR

Louis Gagnon, [email protected] J. Richard, [email protected]ît Lévesque, [email protected]. of Mechanical EngineeringLaval UniversityQuébec (Québec) Canada

Abstract. A two-dimensional numerical analysis of the Ahmed body was performed using the k-ω-SST turbulence modelfrom the OpenFOAM software. The analysis was then modified to include a rotating paddle wheel that captures energyfrom the swirl that forms behind the vehicle. The rotating wheel is modeled using a General Grid Interface (GGI) and theenergy captured is calculated with the help of the forces library of the OpenFOAM software. Power generation reached16.1 watts at optimal conditions. Total drag reductions up to 8.2% were found. Most computations were run in parallelon a dual core computer.

1. INTRODUCTION

In the perspective that a large portion of the energy consumed by ground vehicles is used to overcome pressure dragand that the scientific community still questions whether the optimal drag reduction on a vehicle would equate to a nullpressure drag coefficient, it is attempted in this paper to show how moving parts can be added to an automobile modelto reduce the energy it consumes to overcome wind resistance. That is achieved by capturing energy from the swirls andmodifying the flow that exists behind a hatchback car. The modification is triggered by a rotating device located in thedetached flow behind the vehicle. It is suggested that the energy should be recaptured in the form of electricity becauseof the current trend toward hybrid vehicles. The moving parts in question are inspired by paddle wheels and their purposeis to recapture energy from the vortices located behind a moving vehicle. Although the simulations were performed on acar model, tractor-trailer rigs would be ideal candidates for the type of energy capture presented in this paper, as well asany vehicle involved in a lot of highway driving.

2. THE CAR MODEL

The Ahmed car model was chosen as the shape to analyze in the simulations because it has received widespreadattention from the scientific community since its first appearance when Ahmed, Ramm and Faltin (1984) used it in a windtunnel to mimic the flow found around a typical car. This model was also chosen by the European Research CommunityOn Flow, Turbulence, And Combustion (ERCOFTAC) to benchmark different CFD codes. The first goal was thus to createa mesh-model combination that would reproduce the generally accepted flow characteristics of the Ahmed body and, mostimportant, its drag coefficient with a minimal error. Reproducing the experimental drag coefficient of the Ahmed body hasbeen a challenge for many researchers that studied the Ahmed body because of the difficulty to precisely locate the startof the separation bubble on the rear slant angle of the body. However, a general idea of the appropriate drag coefficientwas grasped from the published research to be in the range of 0.25 to 0.35 when the rear slant angle is 25 degrees. Itmust also be pointed out that between the two widely used angles of 25 and 35 degrees there is a drag crisis that occursat 30 degrees where the experimental drag value reaches 37.8 (Ahmed, Ramm and Faltin, 1984). Several attempts weredone by different authors to reproduce the transition phenomenon that occurs between those two angles where the flowactually goes from having its longitudinal vortices start on the rear slant angle of the vehicle to having them start onlyon the lower, vertical, rear end. Those vortices have a significant influence on the three-dimensional drag on the Ahmedbody because they interact with the separation bubble located on the slant angle. However, Beaudoin and Aider (2008)have experimentally demonstrated that those vortices could be avoided by use of side wings on the slant angle wall of themodel and that removing them can also reduce drag. The goal of this project is to deal with the middle, two-dimensional,separation bubble which exists behind the body and hosts two span-wise vortices that meet approximately in the middleof the rear vertical wall of the car. The energy lost to the top vortex is what is recaptured by the paddle wheels used in thispaper.



Figure 1. The Ahmed body, adapted with permission from (Hinterberger, García-Villalba and Rodi, 2004). Throughoutthis paper, the x, y, z axes represent stream-wise, vertical, and span-wise directions, respectively.

Figure 2. The two-dimensional representation of the Ahmed body with the paddle wheel located behind its rear verticalwall.

3. CFD ANALYSIS

3.1 Turbulence model

The turbulence model that yielded the most appropriate result is the k-ω-SST model; it is also known for its strongcapability to model attached and detached flows as well as flows subjected to adverse pressure gradients. LES modelswere considered but were not deemed appropriate for two-dimensional modeling even though some authors have reportedsuccessful use of LES in two dimensions (Bouris and Bergeles, 1999). Many reports of RANS models being used witha reasonable error to model the Ahmed body are available in the literature. The k-ω-SST model features an automaticwall treatment and uses a k-ω type of model within the boundary layer and a k-ε type of model in the free-stream flow.Considering that Bayraktar found good results using the RNG k-ε model on the Ahmed body (Bayraktar, Landman andBaysal, 2001), use of k-ε equations in the free-stream flow should give reliable results. For more information on the k-ω-SST model the reader is encouraged to see the paper by Menter which mathematically describes the turbulence model(Menter and Esch, 2001).



3.2 Parameters and boundary conditions

The air velocity used in the analysis is U = 60 m/s and kinematic viscosity is ν = 14.75× 10−6m2/s. The Reynoldsnumber of this analysis, based on model length is thusRe = 4.25×106. Boundary conditions based on a 0.5% turbulenceintensity (Ahmed, Ramm and Faltin, 1984) and turbulent length scale of 0.05 m were used to estimate k and ω inletboundary conditions.

3.3 Mesh

A Reynolds number of 4.25 × 106 requires a very fine mesh. It was initially attempted to make use of a structuredboundary layer mesh around the whole vehicle. However, due to the diverse behavior of the flow near the body, a structuredboundary layer mesh was only used at locations of very small longitudinal variations of the flow properties. Thus, onlytwo small zones of the mesh are structured and use about 500 less cells than an equivalent unstructured mesh. Usinga boundary layer mesh on the front was not appropriate because the pressure gradient along the tangent of the surfaceis as strong as along the normal. On the rear slant-angle and vertical surfaces a structured mesh was also inappropriatedue to sudden changes in pressure at specific locations and a velocity distribution typical of detached flows. It was alsonecessary to have a well resolved mesh behind the car to properly simulate the wake. The mesh on the wall of the vehiclealso required a fine resolution because of its influence on the drag coefficient. The zone just upstream of the vehicle wasmeshed slightly coarser than the wake because there are no vortices in front of the car: only a saddle point that affects theupstream flow. Considering that it is generally recommended to have at least 15 nodes in the boundary layer and that theflat plate boundary layer is estimated to be 2 cm thick (Cousteix, 1989), it is not possible to precisely resolve the said layerand the simulations rely mostly on wall models from the solver. In his three-dimensional numerical analysis of the Ahmedbody, Bayraktar settled for a 4.4M cells unstructured mesh because it yielded a fine correlation between experimental andnumerical drag coefficients (Bayraktar, Landman and Baysal, 2001). From that number of cells and the assumption thatthe relative numbers of cells in longitudinal, lateral, and vertical directions were a, 0.25a, and 0.2a, respectively it wasfound using Eq. (1) that an equivalent 2D mesh would have 40K cells. Ncells,2D is the number of cells of the equivalenttwo-dimensional mesh. The mesh that was used for the present analysis is slightly rougher and has 27.5K cells.

a× 0.2a× 0.25a = 4.4× 106 =⇒ a = 444.80 ∴ Ncells,2D = a× 0.2a ≈ 40000 (1)

3.4 Rotating interface

Figure 3. Mesh on the rear of the vehicle and paddle wheel

The General Grid Interface (GGI) of the OpenFOAM software was used to allow the paddle wheel to rotate withrespect to the car. This is accomplished by having the solver interpolate the values at a virtual interface which is indicated



to the solver by the definition of two coincident circles that delimit the inner (rotating part) and outer (fixed car) parts ofthe mesh. As seen in Fig. 2, the mesh resolution at the interface is increased in order to make the interface as close aspossible to a perfect circle and reduce to a minimum the empty zones that occur between the inner and outer parts of themesh.

3.5 Validation

The results from the unaltered two-dimensional Ahmed body simulations ran were used to calculate the drag coefficientdifferences between the energy-recapturing and the reference model. It was thus necessary to have a certain level ofconfidence towards the solution of the flow around that particular body. This level of assurance was gained by runninga mesh refinement test with a mesh that contained twice as many nodes in each direction. The refined mesh has 111.5Kcells. The results from the two meshes matched, within a reasonable error, for all of the flow characteristics. An accurateenough correlation between the two mesh’s drag coefficients was also found. The simulation with the finer mesh yieldeda slightly higher drag coefficient which interestingly makes the calculation of total drag reduction by use of the paddlewheel conservative. The refined mesh gives a finer view of the flow properties but both clearly share the same generalflow characteristics.

4. ENERGY CAPTURE

As mentioned in the introduction, the goal is to have an added part that captures energy from the flow. For resultsto be interesting the total drag with the added piece cannot be higher than that of the unaltered Ahmed body; or, in casethat the total drag is increased then the energy captured from the flow would have to surpass the energy lost to drag. Tocalculate how much power is extracted from the flow, the moment around the z-axis (Mz) is taken from the analysis andequated into ecapture according to Eq. (2). Also, Eq. (3) serves as a measure of how much power is required to overcomea specific drag coefficient at the traveling velocity of the car.

ecapture = Mz ×R× 2π

60× w

T(2)

edrag = (12× ρU2ACD)× U (3)

A = 0.288× 0.389 (4)

U is the velocity of the car and the free-stream flow. ρ is the density of the ambient air, taken as 1.2kg/m3. R is therotational velocity of the paddle wheel. A is the frontal area of the car and CD is the drag coefficient considered forconversion into equivalent energy. w is the width of the three-dimensional Ahmed body and T is the thickness of the two-dimensional model used in the analysis. In a practical application, the power captured from the flow would be convertedinto electricity. This assumption is made for two reasons, which are the current trend towards electric and hybrid vehiclesand the ability of an electric generator to regulate the forces applied on the paddle wheel while harvesting electrical powerfrom it. Old fashion paddle wheels are used to keep the analysis of energy capture from the swirl simple. A constantrotating velocity of the wheel is imposed and power generated is calculated from the average of moments acting on thepaddle wheel. To apply this to practical implementation one could use a paddle wheel with a relatively large momentof inertia but that creates a problem of added weight to the vehicle. The other approach, more realistic, is to have thegenerator programmed to "damp" velocity fluctuations by making it respond to fluctuations of Mz by giving or takingpower to the wheel. It is probably preferable to have a steady rotation velocity for design considerations.

5. RESULTS

In the results, CD,body and CD,part represent the drag coefficients on the Ahmed body and on the added part, respec-tively. CD,power is the energy saved by the avoided drag when vehicle travels at 60 m/s. ecapture is energy in wattscaptured by the rotating paddle wheel. The reference case gives a CD,body of 0.300 and that value is used when quanti-fying the amount of drag saved by the various configurations. The reference CD,body = 0.3 requires 4.36kW when thethree-dimensional Ahmed car is moving at 60m/s. CD,saved is the coefficient of the avoided drag and is defined in Eq.(5).

CD,saved = 0.3− CD,body − CD,part (5)

5.1 Selected cases

5.1.1 Fixed rotational velocity

In Tab. 1, results from cases of rotating paddle wheels are reported. The wheel’s center of rotation y-position is 0.19m below the top edge of the body. All wheels have 4 blades.



Table 1. Results from selected cases with fixed rotational velocity.

Case 1 2 3 4 5 6Center x 1.077 1.11 1.077 1.11 1.077 1.077

Wheel radius 0.05 0.04 0.05 0.04 0.04 0.05RPM 2500 2000 2000 4000 2000 2300CD,body 0.3084 0.2939 0.3122 0.2954 0.3130 0.3122CD,part -0.0323 -0.0148 -0.0335 -0.0207 -0.0353 -0.0334CD,saved 0.0240 0.0209 0.0213 0.0252 0.0227 0.0213CD,power 348 304 309 366 324 309ecapture 0.9 8.2 12.8 -4.6 6.0 10.38

-20

-10

0

10

20

30

40

50

1.45 1.455 1.46 1.465 1.47 1.475 1.48

e cap

ture

(W

)

Time (s)

Figure 4. Plot of ecapture vs Time for one full revolution of the paddle wheel from case 3

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

1.45 1.455 1.46 1.465 1.47 1.475 1.48

CD

,sav

ed

Time (s)

Figure 5. Plot of CD,saved vs Time for one full revolution of the paddle wheel from case 3

Figures (4) and (5) illustrate the energy captured and the drag coefficient avoided, respectively, for a full revolution ofthe paddle wheel in case 3. The data is taken from t = 1.45s to t = 1.48s. To illustrate how the flow stabilizes in thefirst tenths of second of the simulation, the output power from case 6 is plotted against time in Fig. (6). Each calculationis done on one full revolution of the paddle wheel, which is equivalent to 4 geometric cycles. After time t = 0.26s thepower output stabilizes at ecapture = 10.38± 0.01W thoughout the simulation.

5.1.2 Variable rotational velocity

The OpenFOAM GGI code was modified to allow the wheel to rotate according to a sinusoidal function. Two resultsare reported here and they are both based on the geometry of case 3, reported in the fixed rotational velocity cases. Case7 and case 8 have rotational velocity functions, Rvar, defined in Eq. (6) and Eq. (7), respectively. R is the base rotationalvelocity, which is 2000 RPM for both cases, and t is time in seconds. The only difference between the two cases is thephase angle of the sinusoidal function. Rvar was designed so that the paddle wheel moves at maximum rotational velocitywhen the maximum energy, and thus maximum Mz , are seen from the fixed rotational velocity cases. This was done in anattempt to reduce fluctuations in the energy generated. Since the energy production has a period exactly equal to a fourthof the period of oscillation of the wheel the frequency of the sinusoidal function is also chosen as a fourth of the periodof the wheel. The phase of the sinusoidal function comes from a graphical approximation to match the peaks of power



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

10

20

Time (s)

Pow

er o

utpu

t (W

)

Figure 6. Plot of power output vs time calculated per paddle-wheel revolution starting at t = 0. Each cycle is 0.0261seconds long based on a rotational velocity of 2300 RPM. Data taken from case 6.

generation and variable rotational velocity.

Rvar,7 = R× (1.0 + 0.2× sin(−2.9249 +R× π7.5

× t) (6)

Rvar,8 = R× (1.0 + 0.2× sin(−2.3 +R× π7.5

× t) (7)

Table 2. Results from selected cases with variable rotational velocity.

Case 7 8CD,body 0.3095 0.3104CD,part -0.0342 -0.0335CD,saved 0.0248 0.0231CD,power 359 336ecapture 12.0 16.1

1.8 1.9 2 2.1 2.2 2.3 2.414

15

16

17

Time (s)

Pow

er o

utpu

t (W

)

Figure 7. Plot of power output vs time calculated per paddle-wheel revolution starting at t = 0. Each cycle is 0.03 secondslong based on a rotational velocity of 2000 RPM. Data taken from case 7.

5.2 Comparison cases

Some cases of non-rotating paddle wheels and modified wheels were run to test whether the drag reduction from therotating paddle wheels was exclusive to their rotation or could be achieved by a similar but non-rotating object. Resultsof these cases are summarized in Tab. 3. The added parts have center positions of (1.077, -0.19), radii of 0.05 m, and



2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.20

5

10

15

Time (s)

Pow

er o

utpu

t (W

)

Figure 8. Plot of power output vs time calculated per paddle-wheel revolution starting at t = 0. Each cycle is 0.03 secondslong based on a rotational velocity of 2000 RPM. Data taken from case 8.

4 blades for cases with blades. Cases 0 and 30 model a fixed paddle wheel rotated by 0 ◦and 30 from the horizontalposition, respectively. Case A models a paddle wheel whose inner radius was enlarged to 0.045 m which makes it almosta cylinder. Case B is a copy of case A but the paddle wheel revolves at 2500 RPM. Power consumed by the paddle wheelin case B is 1.28 watts. Case C is a 0.05 m radius cylinder that does not rotate. Case D is a rough attempt at makingthe rear of the Ahmed body more streamline in order to compare the drag reduced by this streamline rear with the dragreduced by various wheel configurations. Graphical representation of the comparison cases are given in Tab. 3 to simplifycomprehension.

Table 3. Results from comparison cases.

Case 0◦ 30◦ A B C DCD,body 0.3111 0.3063 0.3099 0.3288 0.3107 0.2151CD,part -0.0046 -0.0069 -0.0392 -0.0351 -0.0551 -CD,saved -0.0065 0.0006 0.0292 0.0061 0.0445 0.0849CD,power -94.5 8.8 445 87.9 645 1233

6. DISCUSSION

Several configurations of the paddle wheel were tested. The most power captured from the flow is from the casewith paddle wheels rotating at 2000 RPM and having a radius of 0.05 m and the power generated is 12.8 watts. Theconfiguration that reduces the drag coefficient the most is a paddle wheel rotating at roughly 4000 RPM, located slightlyupwind of the maximum turbulent kinetic energy location, and having a radius of 0.04 m. A full center serves to avoidincoming flow from being diverted between the paddles and wasting some of its kinetic energy in doing so. Cases thatdo not have a full center paddle wheel do not yield as much energy and are not documented in this paper. It was alsonoticed that the paddles should not interfere, or at least the least possible, with the flow outside the separation bubblesince doing so significantly increases drag without increasing the amount of power generated. It was not expected thatthe drag would be reduced by the rotating paddle wheels. Therefore, it is questioned whether the reduced drag mightbe due to the effective body of the modified Ahmed model being more streamline. Thus, tests were run to see if a non-rotating paddle wheel also reduces the drag coefficient. Tests were also run with a non-rotating cylinder fixed behind thevehicle. Non-rotating paddle wheel tests show that the beneficial effect of the rotating paddle wheels is stronger. Thetest with the non-rotating cylinder of 0.05 m radius (comparison case C) drastically reduces the total drag coefficient ofthe vehicle-cylinder assembly; however, when looking at Fig. 8 one can question whether the results are valid since theCD,saved strongly fluctuates. The result from the non-rotating cylinder is somewhat troubling because it shows a positive



pressure downstream of the body; usually the pressure downstream of a body subjected to a moving flow is negative.Also, by comparing the velocity streamlines of the reference case with those of the paddle wheel cases on Fig. 9 and 10,respectively, one notices how the upper vortex is much smaller when the rotating paddle wheel is present; this is part ofthe explanation why the drag coefficient is reduced. Also, the vortex is still present and creates a suction on the paddlewheel thus further increasing CD,saved. The streamlines also show that the flow circulates around the paddle wheel andfrom the moments one sees that some of the energy of those streamlines is transferred to the wheel. Finally, those twofigures also show that the maximum turbulent kinetic energy is lower in the case with the paddle wheel, which very likelyindicates that less energy is lost by viscous dissipation. From, the analysis, it seems clear that RPM is highly influent onthe output energy of the system. The best results are obtained at 2000 RPM. As expected, when the RPM of the paddlewheel reaches a certain value, the power generated turns into power that has to be fed to the wheel. On the other hand, theproblem associated with a too low RPM is that the forces on the paddle wheel do not increase enough to compensate forthe lower velocity of the wheel and thus the power generated falls. The fluctuations in energy captured and drag respondto the rotation of the paddle wheel as seen on Fig. 7. Four force cycles are noticeable for each revolution of the paddlewheel. Consider that a full revolution of the paddle wheel corresponds to four quarter cycles which are each geometricallyidentical. Also, in the published literature, most of all Ahmed body analyses are ran with a fixed floor, and that is differentfrom real-world situations where the floor has a relative velocity with respect to the car equal to the velocity of the caritself. This should not greatly modify the results but it still was reported to have a 8% influence on the drag coefficient(Krajnovic and Davidson, 2005). Krajnovic reported that a moving floor actually influences the flow around the rear slantangle. That zone is where this paper is focused; however, the purpose of this paper is to show how flow structures foundon a typical car can be used to generate energy. Specific car models are not analyzed yet and the Ahmed body is only usedas a reference to create typical car flows and validate the calculations. Finally, it should be noted that more tests have to berun in order to figure out the best combination of energy capture and drag reduction. The authors believe that it is possibleto get a positive energy capture to accompany results of large drag reduction given buy the non-moving cylinder; the goodcombination of rotational velocity and blade geometry only has to be found. So far the best results come from a variablerotational speed case which shows that the energy capture can be adapted to the flow and motivates the implementation ofa GGI code that has a rotating velocity dependent on the flow properties or forces acting upon it.

7. CONCLUSION

It was found that the rotating paddle wheel can generate 16.1 watts while reducing drag by 7.7%. It can also reducedrag by 8.4% if power is supplied to the paddle wheel. This reduction is calculated from the extrapolation of two-dimensional simulations. This extrapolation should hold as long as a device such as the one that Beaudoin and Aider(2008) experimented with is used to eliminate the influence of the longitudinal vortices on the span-wise vortices. Asfor future plans, finer meshes, three-dimensional analyses, different blade shapes, flow driven RPM, and the effects offriction, are considered for study.

8. ACKNOWLEDGEMENTS

The authors would like to thank all those who contributed to the development of the OpenFOAM software which madethe simulations reported in this paper possible.

9. REFERENCES

Ahmed, S. R., Ramm, G. and Faltin, G., 1984, "Some salient features of the time averaged ground vehicle wake", Tech-nical Report TP-840300, Society of Automotive Engineers, Warrendale, Pa., 31 p.

Bayraktar, I., Landman, D. and Baysal, O., 2001, "Experimental and computational Investigation of Ahmed body forground vehicle aerodynamics", SAE Transactions: Journal of Commercial Vehicles, Vol.110, No. 2, pp. 613-626.

Bouris, D. and Bergeles, G., 1999, "2D LES of vortex shedding from a square cylinder", Journal of Wind Engineeringand Industrial Aerodynamics, Vol.80, pp.31-46.

Beaudoin, J.-F. and Aider, J.-L., 2008, "Drag and lift reduction of a 3d bluff body using flaps", Experiments in Fluids,Vol.44, No. 4, pp. 491-501.

Cousteix, J., 1989, "Turbulence et couche limite", Cépaduès Éditions, PARIS?? pp. XX166.Hinterberger, C., García-Villalba, M. and Rodi, W., 2004, "Large Eddy Simulation of flow around the Ahmed body",

Lecture Notes in Applied and Computational Mechanics, The Aerodynamics of Heavy Vehicles: Trucks, Buses, andTrains, R. McCallen, F. Browand, J. Ross (Eds.), Springer Verlag, pp..

Krajnovic, S. and Davidson, L., 2005, "Influence of floor motions in wind tunnels on the aerodynamics of road vehicles",Journal of Wind Engineering and Industrial Aerodynamics, Vol.93, pp. 677-696.

Menter, F. and Esch, T., 2001, "Elements of industrial heat transfer predictions", Proceedings of the 16th BrazilianCongress of Mechanical Engineering, Vol.20, pp. 117-127.

using openfoam to model energy taken from the swirl behind a car

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