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Proceedings of OFW4 4th OpenFOAM Workshop

June 1-4, Montreal, QC, Canada

USING OPENFOAM TO MODEL ENERGY TAKEN FROM THE SWIRL

BEHIND A CAR

Louis Gagnon, louis.gagnon.10@ulaval.ca

Marc J. Richard, marc.richard@gmc.ulaval.ca

Benoît Lévesque, benoit.levesque@gmc.ulaval.ca

Dept. of Mechanical Engineering

Laval University

Québec (Québec) Canada

Abstract. A two-dimensional numerical analysis of the Ahmed body was performed using the k-ω-SST turbulence model

from the OpenFOAM software. The analysis was then modiﬁed to include a rotating paddle wheel that captures energy

from the swirl that forms behind the vehicle. The rotating wheel is modeled using a General Grid Interface (GGI) and the

energy captured is calculated with the help of the forces library of the OpenFOAM software. Power generation reached

16.1 watts at optimal conditions. Total drag reductions up to 8.2% were found. Most computations were run in parallel

on 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 drag

and that the scientiﬁc community still questions whether the optimal drag reduction on a vehicle would equate to a null

pressure drag coefﬁcient, it is attempted in this paper to show how moving parts can be added to an automobile model

to reduce the energy it consumes to overcome wind resistance. That is achieved by capturing energy from the swirls and

modifying the ﬂow that exists behind a hatchback car. The modiﬁcation is triggered by a rotating device located in the

detached ﬂow behind the vehicle. It is suggested that the energy should be recaptured in the form of electricity because

of the current trend toward hybrid vehicles. The moving parts in question are inspired by paddle wheels and their purpose

is to recapture energy from the vortices located behind a moving vehicle. Although the simulations were performed on a

car model, tractor-trailer rigs would be ideal candidates for the type of energy capture presented in this paper, as well as

any 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 widespread

attention from the scientiﬁc community since its ﬁrst appearance when Ahmed, Ramm and Faltin (1984) used it in a wind

tunnel to mimic the ﬂow found around a typical car. This model was also chosen by the European Research Community

On Flow, Turbulence, And Combustion (ERCOFTAC) to benchmark different CFD codes. The ﬁrst goal was thus to create

a mesh-model combination that would reproduce the generally accepted ﬂow characteristics of the Ahmed body and, most

important, its drag coefﬁcient with a minimal error. Reproducing the experimental drag coefﬁcient of the Ahmed body has

been a challenge for many researchers that studied the Ahmed body because of the difﬁculty to precisely locate the start

of the separation bubble on the rear slant angle of the body. However, a general idea of the appropriate drag coefﬁcient

was grasped from the published research to be in the range of 0.25 to 0.35 when the rear slant angle is 25 degrees. It

must also be pointed out that between the two widely used angles of 25 and 35 degrees there is a drag crisis that occurs

at 30 degrees where the experimental drag value reaches 37.8 (Ahmed, Ramm and Faltin, 1984). Several attempts were

done by different authors to reproduce the transition phenomenon that occurs between those two angles where the ﬂow

actually goes from having its longitudinal vortices start on the rear slant angle of the vehicle to having them start only

on the lower, vertical, rear end. Those vortices have a signiﬁcant inﬂuence on the three-dimensional drag on the Ahmed

body 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 the

model 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 middle

of the rear vertical wall of the car. The energy lost to the top vortex is what is recaptured by the paddle wheels used in this

paper.

Proceedings of OFW4 4th OpenFOAM Workshop

June 1-4, Montreal, QC, Canada

Figure 1. The Ahmed body, adapted with permission from (Hinterberger, García-Villalba and Rodi, 2004). Throughout

this 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 vertical

wall.

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 strong

capability to model attached and detached ﬂows as well as ﬂows subjected to adverse pressure gradients. LES models

were considered but were not deemed appropriate for two-dimensional modeling even though some authors have reported

successful use of LES in two dimensions (Bouris and Bergeles, 1999). Many reports of RANS models being used with

a reasonable error to model the Ahmed body are available in the literature. The k-ω-SST model features an automatic

wall treatment and uses a k-ωtype of model within the boundary layer and a k-type of model in the free-stream ﬂow.

Considering that Bayraktar found good results using the RNG k-model on the Ahmed body (Bayraktar, Landman and

Baysal, 2001), use of k-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).

Proceedings of OFW4 4th OpenFOAM Workshop

June 1-4, Montreal, QC, Canada

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 Reynolds

number of this analysis, based on model length is thus Re = 4.25×106. Boundary conditions based on a 0.5% turbulence

intensity (Ahmed, Ramm and Faltin, 1984) and turbulent length scale of 0.05 m were used to estimate k and ωinlet

boundary conditions.

3.3 Mesh

A Reynolds number of 4.25 ×106requires a very ﬁne mesh. It was initially attempted to make use of a structured

boundary layer mesh around the whole vehicle. However, due to the diverse behavior of the ﬂow near the body, a structured

boundary layer mesh was only used at locations of very small longitudinal variations of the ﬂow properties. Thus, only

two small zones of the mesh are structured and use about 500 less cells than an equivalent unstructured mesh. Using

a boundary layer mesh on the front was not appropriate because the pressure gradient along the tangent of the surface

is as strong as along the normal. On the rear slant-angle and vertical surfaces a structured mesh was also inappropriate

due to sudden changes in pressure at speciﬁc locations and a velocity distribution typical of detached ﬂows. It was also

necessary to have a well resolved mesh behind the car to properly simulate the wake. The mesh on the wall of the vehicle

also required a ﬁne resolution because of its inﬂuence on the drag coefﬁcient. The zone just upstream of the vehicle was

meshed slightly coarser than the wake because there are no vortices in front of the car: only a saddle point that affects the

upstream ﬂow. Considering that it is generally recommended to have at least 15 nodes in the boundary layer and that the

ﬂat plate boundary layer is estimated to be 2 cm thick (Cousteix, 1989), it is not possible to precisely resolve the said layer

and the simulations rely mostly on wall models from the solver. In his three-dimensional numerical analysis of the Ahmed

body, Bayraktar settled for a 4.4M cells unstructured mesh because it yielded a ﬁne correlation between experimental and

numerical drag coefﬁcients (Bayraktar, Landman and Baysal, 2001). From that number of cells and the assumption that

the relative numbers of cells in longitudinal, lateral, and vertical directions were a, 0.25a, and 0.2a, respectively it was

found using Eq. (1) that an equivalent 2D mesh would have 40K cells. Ncells,2Dis the number of cells of the equivalent

two-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 with

respect to the car. This is accomplished by having the solver interpolate the values at a virtual interface which is indicated

Proceedings of OFW4 4th OpenFOAM Workshop

June 1-4, Montreal, QC, Canada

to the solver by the deﬁnition of two coincident circles that delimit the inner (rotating part) and outer (ﬁxed car) parts of

the mesh. As seen in Fig. 2, the mesh resolution at the interface is increased in order to make the interface as close as

possible to a perfect circle and reduce to a minimum the empty zones that occur between the inner and outer parts of the

mesh.

3.5 Validation

The results from the unaltered two-dimensional Ahmed body simulations ran were used to calculate the drag coefﬁcient

differences between the energy-recapturing and the reference model. It was thus necessary to have a certain level of

conﬁdence towards the solution of the ﬂow around that particular body. This level of assurance was gained by running

a mesh reﬁnement test with a mesh that contained twice as many nodes in each direction. The reﬁned mesh has 111.5K

cells. The results from the two meshes matched, within a reasonable error, for all of the ﬂow characteristics. An accurate

enough correlation between the two mesh’s drag coefﬁcients was also found. The simulation with the ﬁner mesh yielded

a slightly higher drag coefﬁcient which interestingly makes the calculation of total drag reduction by use of the paddle

wheel conservative. The reﬁned mesh gives a ﬁner view of the ﬂow properties but both clearly share the same general

ﬂow characteristics.

4. ENERGY CAPTURE

As mentioned in the introduction, the goal is to have an added part that captures energy from the ﬂow. For results

to be interesting the total drag with the added piece cannot be higher than that of the unaltered Ahmed body; or, in case

that the total drag is increased then the energy captured from the ﬂow would have to surpass the energy lost to drag. To

calculate how much power is extracted from the ﬂow, the moment around the z-axis (Mz) is taken from the analysis and

equated into ecapture according to Eq. (2). Also, Eq. (3) serves as a measure of how much power is required to overcome

a speciﬁc drag coefﬁcient at the traveling velocity of the car.

ecapture =Mz×R×2π

60 ×w

T(2)

edrag = ( 1

2×ρU2ACD)×U(3)

A= 0.288 ×0.389 (4)

U is the velocity of the car and the free-stream ﬂow. ρis the density of the ambient air, taken as 1.2kg/m3. R is the

rotational velocity of the paddle wheel. A is the frontal area of the car and CDis the drag coefﬁcient considered for

conversion into equivalent energy. wis the width of the three-dimensional Ahmed body and Tis the thickness of the two-

dimensional model used in the analysis. In a practical application, the power captured from the ﬂow would be converted

into electricity. This assumption is made for two reasons, which are the current trend towards electric and hybrid vehicles

and the ability of an electric generator to regulate the forces applied on the paddle wheel while harvesting electrical power

from it. Old fashion paddle wheels are used to keep the analysis of energy capture from the swirl simple. A constant

rotating velocity of the wheel is imposed and power generated is calculated from the average of moments acting on the

paddle wheel. To apply this to practical implementation one could use a paddle wheel with a relatively large moment

of inertia but that creates a problem of added weight to the vehicle. The other approach, more realistic, is to have the

generator programmed to "damp" velocity ﬂuctuations by making it respond to ﬂuctuations of Mzby giving or taking

power 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. ecaptur e is energy in watts

captured 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 = 0.3requires 4.36kW when the

three-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 0.19

m below the top edge of the body. All wheels have 4 blades.

Proceedings of OFW4 4th OpenFOAM Workshop

June 1-4, Montreal, QC, Canada

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

Case 1 2 3 4 5 6

Center 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 0.05

RPM 2500 2000 2000 4000 2000 2300

CD,body 0.3084 0.2939 0.3122 0.2954 0.3130 0.3122

CD,part -0.0323 -0.0148 -0.0335 -0.0207 -0.0353 -0.0334

CD,saved 0.0240 0.0209 0.0213 0.0252 0.0227 0.0213

CD,power 348 304 309 366 324 309

ecapture 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

ecapture (W)

Time (s)

Figure 4. Plot of ecaptur e 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,saved

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 of

the paddle wheel in case 3. The data is taken from t= 1.45sto t= 1.48s. To illustrate how the ﬂow stabilizes in the

ﬁrst tenths of second of the simulation, the output power from case 6 is plotted against time in Fig. (6). Each calculation

is done on one full revolution of the paddle wheel, which is equivalent to 4 geometric cycles. After time t= 0.26sthe

power output stabilizes at ecapture = 10.38 ±0.01Wthoughout 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 results

are reported here and they are both based on the geometry of case 3, reported in the ﬁxed rotational velocity cases. Case

7 and case 8 have rotational velocity functions, Rvar, deﬁned in Eq. (6) and Eq. (7), respectively. Ris the base rotational

velocity, which is 2000 RPM for both cases, and t is time in seconds. The only difference between the two cases is the

phase angle of the sinusoidal function. Rvar was designed so that the paddle wheel moves at maximum rotational velocity

when the maximum energy, and thus maximum Mz, are seen from the ﬁxed rotational velocity cases. This was done in an

attempt to reduce ﬂuctuations in the energy generated. Since the energy production has a period exactly equal to a fourth

of the period of oscillation of the wheel the frequency of the sinusoidal function is also chosen as a fourth of the period

of the wheel. The phase of the sinusoidal function comes from a graphical approximation to match the peaks of power

Proceedings of OFW4 4th OpenFOAM Workshop

June 1-4, Montreal, QC, Canada

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0

10

20

Time (s)

Power output (W)

Figure 6. Plot of power output vs time calculated per paddle-wheel revolution starting at t= 0. Each cycle is 0.0261

seconds 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×π

7.5×t)(6)

Rvar,8=R×(1.0+0.2×sin(−2.3 + R×π

7.5×t)(7)

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

Case 7 8

CD,body 0.3095 0.3104

CD,part -0.0342 -0.0335

CD,saved 0.0248 0.0231

CD,power 359 336

ecapture 12.0 16.1

1.8 1.9 2 2.1 2.2 2.3 2.4

14

15

16

17

Time (s)

Power output (W)

Figure 7. Plot of power output vs time calculated per paddle-wheel revolution starting at t= 0. Each cycle is 0.03 seconds

long 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 the

rotating paddle wheels was exclusive to their rotation or could be achieved by a similar but non-rotating object. Results

of these cases are summarized in Tab. 3. The added parts have center positions of (1.077, -0.19), radii of 0.05 m, and

Proceedings of OFW4 4th OpenFOAM Workshop

June 1-4, Montreal, QC, Canada

2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2

0

5

10

15

Time (s)

Power output (W)

Figure 8. Plot of power output vs time calculated per paddle-wheel revolution starting at t= 0. Each cycle is 0.03 seconds

long 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 horizontal

position, respectively. Case A models a paddle wheel whose inner radius was enlarged to 0.045 m which makes it almost

a cylinder. Case B is a copy of case A but the paddle wheel revolves at 2500 RPM. Power consumed by the paddle wheel

in 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 making

the rear of the Ahmed body more streamline in order to compare the drag reduced by this streamline rear with the drag

reduced by various wheel conﬁgurations. Graphical representation of the comparison cases are given in Tab. 3 to simplify

comprehension.

Table 3. Results from comparison cases.

Case 0◦30◦A B C D

CD,body 0.3111 0.3063 0.3099 0.3288 0.3107 0.2151

CD,part -0.0046 -0.0069 -0.0392 -0.0351 -0.0551 -

CD,saved -0.0065 0.0006 0.0292 0.0061 0.0445 0.0849

CD,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 case

with paddle wheels rotating at 2000 RPM and having a radius of 0.05 m and the power generated is 12.8 watts. The

conﬁguration that reduces the drag coefﬁcient the most is a paddle wheel rotating at roughly 4000 RPM, located slightly

upwind of the maximum turbulent kinetic energy location, and having a radius of 0.04 m. A full center serves to avoid

incoming ﬂow from being diverted between the paddles and wasting some of its kinetic energy in doing so. Cases that

do not have a full center paddle wheel do not yield as much energy and are not documented in this paper. It was also

noticed that the paddles should not interfere, or at least the least possible, with the ﬂow outside the separation bubble

since doing so signiﬁcantly increases drag without increasing the amount of power generated. It was not expected that

the drag would be reduced by the rotating paddle wheels. Therefore, it is questioned whether the reduced drag might

be 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 the

vehicle. Non-rotating paddle wheel tests show that the beneﬁcial effect of the rotating paddle wheels is stronger. The

test with the non-rotating cylinder of 0.05 m radius (comparison case C) drastically reduces the total drag coefﬁcient of

the vehicle-cylinder assembly; however, when looking at Fig. 8 one can question whether the results are valid since the

CD,saved strongly ﬂuctuates. The result from the non-rotating cylinder is somewhat troubling because it shows a positive

Proceedings of OFW4 4th OpenFOAM Workshop

June 1-4, Montreal, QC, Canada

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 of

the explanation why the drag coefﬁcient is reduced. Also, the vortex is still present and creates a suction on the paddle

wheel thus further increasing CD,saved . The streamlines also show that the ﬂow circulates around the paddle wheel and

from the moments one sees that some of the energy of those streamlines is transferred to the wheel. Finally, those two

ﬁgures also show that the maximum turbulent kinetic energy is lower in the case with the paddle wheel, which very likely

indicates that less energy is lost by viscous dissipation. From, the analysis, it seems clear that RPM is highly inﬂuent on

the output energy of the system. The best results are obtained at 2000 RPM. As expected, when the RPM of the paddle

wheel reaches a certain value, the power generated turns into power that has to be fed to the wheel. On the other hand, the

problem associated with a too low RPM is that the forces on the paddle wheel do not increase enough to compensate for

the lower velocity of the wheel and thus the power generated falls. The ﬂuctuations in energy captured and drag respond

to the rotation of the paddle wheel as seen on Fig. 7. Four force cycles are noticeable for each revolution of the paddle

wheel. Consider that a full revolution of the paddle wheel corresponds to four quarter cycles which are each geometrically

identical. Also, in the published literature, most of all Ahmed body analyses are ran with a ﬁxed ﬂoor, and that is different

from real-world situations where the ﬂoor has a relative velocity with respect to the car equal to the velocity of the car

itself. 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 slant

angle. That zone is where this paper is focused; however, the purpose of this paper is to show how ﬂow structures found

on a typical car can be used to generate energy. Speciﬁc car models are not analyzed yet and the Ahmed body is only used

as a reference to create typical car ﬂows and validate the calculations. Finally, it should be noted that more tests have to be

run in order to ﬁgure out the best combination of energy capture and drag reduction. The authors believe that it is possible

to get a positive energy capture to accompany results of large drag reduction given buy the non-moving cylinder; the good

combination of rotational velocity and blade geometry only has to be found. So far the best results come from a variable

rotational speed case which shows that the energy capture can be adapted to the ﬂow and motivates the implementation of

a 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 reduce

drag 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. As

for future plans, ﬁner meshes, three-dimensional analyses, different blade shapes, ﬂow driven RPM, and the effects of

friction, are considered for study.

8. ACKNOWLEDGEMENTS

The authors would like to thank all those who contributed to the development of the OpenFOAM software which made

the 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 for

ground 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 Engineering

and 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, and

Trains, 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 Brazilian

Congress of Mechanical Engineering, Vol.20, pp. 117-127.