This papers discusses an probe into the aerodynamic behavior of a rider vehicle. The theoretical account chosen is a BMW MINI. A simplified CAD theoretical account is generated and used to make a CFD mesh in Gambit. The assorted factors of puting up a CFD theoretical account are so investigated to find the right methodological analysis.
The consequence of altering the forepart and rear screen angles on the vehicle ‘s retarding force is investigated. It is found that retarding force can be reduced by increasing the incline of the forepart screen to 150o and utilizing a 90o incline on the rear terminal.
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The vehicle is so analysed with a side air current, to find the consequence on retarding force, side and lift forces. It is found that a greater angle of cross air current additions side force on the vehicle and reduces drag.
The consequence of the flow development length is so investigated, based on the theory of stagnancy force per unit area constructing up in forepart of the vehicle. The lengths tested are found to both be long plenty for the flow at the recess to be unaffected, and hence give really similar consequences. Flow field breadth is investigated, and it is found to hold really small consequence with the breadths tested. The theory is similar to that of the development length, but both breadths tested are sufficiently broad for the flow around the vehicle to non impact the flow at the sphere walls. The greatest difference in these probes is seen in down force. It is thought that these consequences are undependable due to the simplified auto theoretical account holding a level floor.
The testing is validated by a figure of methods, and is found to be inaccurate to a factor of around two. This is attributed to the terrible simplification the theoretical account required to enable engagement.
The optimised vehicle form is so evaluated against the standard auto, and it is found to give betterments in both power ingestion ( retarding force ) and stableness ( down force ) . It is noted that these angles may non be practical or aesthetically pleasing, and hence likely non deserving altering for the little benefit, when it could hold a big negative consequence on the desirableness of the vehicle.
This papers contains synergistic 3d theoretical accounts and is best viewed electronically utilizing Adobe Reader 9 or subsequently.
A CAD theoretical account of a vehicle was created for the simulation. The auto chosen was a BMW MINI. This was because the form of the vehicle was rather ‘boxy ‘ , and had pronounced forepart and rear windscreen angles. This geometry meant it would be suited for the analysis as it would import into Gambit moderately easy and be straightforward to alter the screen angles.
Simplification of Model Geometry
The theoretical account was ab initio created following the process lineation in Section A.3, but with complex geometry to follow the curves of the vehicle. Wheel arches and door mirrors were besides included. This theoretical account was so imported into Gambit for engagement, where issues were found with the complex geometry taking to skewed elements, or the demand for really all right mesh spacing. The all right mesh spacing created a batch of elements, which caused Gambit to run out of available memory and clang. This meant that the theoretical account had to be simplified to let dependable engaging with the system memory and clip restraints. It was hence decided to pattern the vehicle without door mirrors or wheel arches, and to simplify the curves and general geometry of the organic structure. The simplification of form besides allowed the production of a rapid paradigm theoretical account, which would non hold been possible if door mirrors and properly dimension wheel arches were included, as they would hold made to pattern excessively weak.
The form of the existent vehicle is far less additive than the form of the theoretical account created. It could be argued that the theoretical account should include the vehicle ‘s door mirrors, which can hold a big consequence on the air flow around the organic structure, but as the analysis was chiefly interested in the effects of forepart and rear windscreen angles it was decided that these parts would be left out of the theoretical account. It was thought that the consequences should non be affected dramatically as the theoretical accounts were all based around the same initial organic structure, intending that all comparings were still valid.
Final Model Generation
The theoretical account was generated by ‘tracing ‘ an outline drawing of the vehicle to make its profile, and so squeeze outing it across the breadth of the auto. The outline study used is shown in Figure 1. – Mini Side Profile ( miniguy.com, 2007 ) .
Figure 1. – Mini Side Profile ( miniguy.com, 2007 )
This image was used to make a study in SolidWorks, as it was non known how to import a image in to Gambit. The traced image was really little, which meant that profiled study had to be scaled up to fit the dimensions of the existent vehicle. The study was constrained in such a manner as to let easy change of the forepart and rear windscreen angles, without changing the tallness ( and hence projected frontal country ) of the vehicle ( another advantage to making the initial geometry in SolidWorks ) . The study is shown in Figure 1. – Profile Sketch.
Figure 1. – Profile Sketch
This profile was so extruded to a deepness of half the auto ‘s breadth ( Parker ‘s, 2006 ) to make the full organic structure of the auto. Extruding in both waies meant the auto was centred in the co-ordinate system. Wheels were so added with mention to the organic structure shapes. The full theoretical account is shown in Figure 1. – Full moon Car Model.
Figure 1. – Full moon Car Model
A more realistic representation is shown in Figure 1. – Actual 3d Model ( DMI, n.d. ) for comparing. STEP files were so created for a figure of different forepart and rear windscreen angles, to let the theoretical account to be imported into Gambit.
Figure 1. – Actual 3d Model ( DMI, n.d. )
Mesh File Generation
The theoretical account was imported into Gambit for engaging. Due to the simple geometry and exportation as a STEP file, there were no issues with importing the theoretical account.
Flow Domain Creation
The flow sphere must be big plenty that the flow can be to the full developed before hitting the vehicle, and that it can re-converge after go throughing the organic structure. There is a balance between sphere size and figure of mesh elements, so a via media must be used. Some initial sphere sizes were tested and it was found that the flow at the mercantile establishment was still non-laminar with a short sphere, and that computational clip and memory use increased with a larger sphere. An overall sphere size of 8000x7000x25000 was settled upon as a sensible balance. The vehicle organic structure was so subtracted from the sphere to make a individual fluid part with a nothingness stand foring the auto form. This means that the vehicle organic structure does non necessitate to be set as a solid part.
Flow Domain Discretisation
Due to the engagement demands around the complex geometry of the vehicle form, a high figure of elements is needed. This mesh denseness is non required at the far extends of the sphere, and introduces unneeded computational clip and memory use if it is excessively all right. The sphere was hence split into five smaller volumes, with the vehicle organic structure to the full enclosed in one volume. The flow sphere used for the initial screen effects probe is shown in Figure 1. – Discretised Flow Domain.
Figure 1. – Discretised Flow Domain
The mesh scaling is an of import portion of CFD analysis, as it can hold a big consequence on the quality of the consequences. There is a trade off between truth and figure of elements, with an increased mesh density/number of elements taking to increased memory use and calculation clip. The memory restrictions of the systems used ( limited by 32bit runing systems ) were a big factor in finding the optimal mesh size. The general process followed was to engage the country of involvement ( the auto organic structure ) with a all right mesh, which became finer towards the extents of the flow sphere.
It was ab initio attempted to engage the theoretical account with a mesh spacing of 10 on the auto organic structure faces, but Gambit ran out of memory. The mesh spacing was increased somewhat to 15 on the auto faces ; to 200 at the utmost terminals of the flow sphere ( intermediate zones were meshed with rating in between ) . This meshed successfully in Gambit, but failed during the low-level formatting phase in FLUENT. The mesh denseness was hence decreased to 20 on the auto faces. This allowed the analysis to run successfully, although it took a long clip. It was hence decided to look into a somewhat coarser mesh to cut down work outing clip due to the needed figure of theoretical accounts to be run and tight university clip restraints. A mesh rating runing from 50 on the auto faces, to 800 at the sphere extends was used and the consequences compared to the old theoretical account. The drag force on the organic structure was within 5 % of the theoretical account with the finer mesh, but calculating clip was reduced dramatically. It was hence decided to utilize this mesh scaling as a via media between truth, memory use and solving clip. The mesh is shown in Figure 1. – Mesh Grading. Tetrahedral elements were used so that the vehicle geometry could be approximated more accurately.
Figure 1. – Mesh Rating
The recess face of the sphere was set to a Velocity Inlet. This allowed the specification of a flow speed moving as a headwind.
Pressure Mercantile establishment
The rear face of the sphere was set to a Pressure Outlet. This is coincident with the usage of a Velocity Inlet – the Pressure Outlet is set to atmospheric force per unit area, so as to merely see the effects of the flow speed in the simulation.
The faces that split the flow sphere were set to Interior boundaries. This means FLUENT will let flow of air through them un-inhibited. They were set separately so as to let single analysis of them utilizing FLUENT ( FLUENT looks at the boundary groups instead than single faces ) .
The faces of the vehicle and outer faces of the flow sphere were set as walls. This is so that flow can non perforate them during the analysis. They are once more set separately to let single analysis and scene of boundary conditions in FLUENT.
As the theoretical account is set up as a sphere with a nothingness stand foring the form of the auto, merely one continuum type is needed – this is a zone of air. If the vehicle was left as a solid organic structure, the volumes would hold to be set otherwise.
FLUENT Model Setup
The grid was scaled a factor of 1×10-3 as it was created in millimeter.
The theoretical account was solved utilizing the Pressure Based solver. This because the theoretical accounts were to be tested at velocities up to 80m/s ( good above take off velocity of most aircraft ) , and the Pressure Based method is the preferable convergent thinker for high velocity aeromechanicss ( Fluent Inc. , 2006 ) . It is besides quicker than the Density Based solver as it solves a force per unit area equation instead than work outing continuity and impulse equations at the same time ( Fluent Inc. , 2006 ) .
The theoretical account was solved utilizing the Green-Gauss Node Based gradient option. This is because it retains a 2nd order truth when compared to the Cell Based option, and is hence more accurate, particularly for tetrahedral meshes ( Fluent Inc. , 2006 ) and predicts drag more accurately ( Fluent Inc. , 2006 ) .
The Spalart-Allmaras turbulency theoretical account was considered, this theoretical account was developed specifically for aerospace applications with wall bounded flows ( Fluent Inc. , 2006 ) . This is really similar to the theoretical account tested, although the aerospace applications may be at somewhat higher velocities. It besides gives good consequences for boundary beds with high force per unit area gradients, which are likely with the form of the vehicle, and a cardinal country of the probe. The theoretical account solves turbulency with one equation, and hence has speedy calculating times. The realizable k-Iµ theoretical account was besides tested, and it was found that the excess truth from the two equation theoretical account outweighed the addition in calculating clip. This theoretical account is besides by and large recommended for external automotive aeromechanicss, and does non hold the badly increased resource demand of the Reynolds Stress Model ( Lanfrit, 2005 ) .
Solution Controls Discretisation
These options were set to Second Order Upwind. This improves the truth of the consequences as fluctuations are solved as 2nd order equations instead than first order. It is similar to utilizing quadratic elements alternatively of additive elements in Finite Element Analysis.
The sphere recess was set as a speed recess for the flow velocity tested. This is a simple user-created status based on the coveted vehicle velocity to be simulated.
Pressure Mercantile establishment
The force per unit area mercantile establishment was set to atmospheric force per unit area. This is to imitate merely the flow from the vehicle velocity and non present any other force per unit area alterations.
All walls of the sphere were set to travel with the initial flow. This was to give a more realistic representation of the flow over a traveling vehicle, and avoid any induced shear emphasiss caused by no faux pas boundary conditions. The importance of a traveling floor in aerodynamic simulations is confirmed by Krajnovic and Davidson ( 2005 ) .
As the wheels are revolving when the vehicle moves, the angular speed must be calculated. This was performed utilizing ( 1. ) for each of the flow speeds tested.
( 1. )
I‰ = Angular Velocity ( rad/s )
V = Linear Velocity ( m/s )
R = Wheel Radius = 0.32m
The orientation of the theoretical account in the coordinate system meant that the rotary motion axis was specified as x=1 ( utilizing right manus clasp regulation ) . Centres of rotary motion were determined from the original CAD geometry as Y=0.22m for both forepart and rear, and Z=0.565m and Z=-1.93m for forepart and rear wheels severally.
Windscreen and Rear Screen Effectss
The windshield and rear screen effects theoretical accounts were analyzing simple headwind flow, so were set up utilizing the boundary conditions discussed in Section A.5.3, STEP files were created in SolidWorks for each of the geometry combinations for proving. These were all meshed in the same method described in Section A.4 so as to give comparable consequences.
The standard vehicle geometry was tested at velocities of 20, 50 and 80 m/s so as to supply a benchmark ( the comparings to the standard theoretical account are discussed in ) . Models were so run at all velocities with combinations of 90o and 150o front screen angles, and 90o and 30o rear screen angles. This scope of angles was chosen to demo the dramatic consequence of big alterations, utilizing the appendages of the scope allowed. The speeds were chosen for the same grounds – to give a wider overall image of the alterations. The consequences were so analysed to find the consequence the angles had on the retarding force force moving on the vehicle. The drag force study by each analysis is shown in Table 2. – Consequence of Screen Angles on Drag Force.
Table 2. – Consequence of Screen Angles on Drag Force
The consequences suggest a complex relationship between the two angles. The ‘Gradient ‘ values represent the incline of a consecutive line suiting the two points – while this produces a quantitative relationship of retarding force force to test angle, the Numberss are likely to be extremely inaccurate due to merely holding two values. For a 90o forepart screen angle, increasing the incline of the rear screen decreases the retarding force force by around 2-5 % for each velocity tested. This is at odds with the consequence when a 150o forepart screen angle is used, where the retarding force force additions by 1-2 % as the rear incline is increased. This could be explained by the big consequence that the forepart screen angle has on the retarding force force. Increasing the forepart screen angle to 150o shows considerable decreases in retarding force force for both rear screen angles. The retarding force forces increase dramatically with increased velocity, which is to be expected given the standard equation for aerodynamic retarding force shown in ( 2. ) .
( 2. )
D = Drag Force ( N )
I? = Density of Air ( kg/m3 )
Cadmium = Drag Coefficient
A = Frontal Area ( M2 )
V = Velocity ( m/s )
The effects can be analysed farther by looking at the flow speed over the roof of the vehicle for each instance.
Figure 2. – Flow Velocity Variation ( m/s ) ( 20 m/s )
The consequence of altering the rear screen angle is clear to see, with the sharper roofline making a larger country of low velocity aftermath behind the vehicle, the increased aftermath behind the vehicle has a dramatic addition on the retarding force created ( Fukuda et al. , 1995 ) .
The sharper forepart screen angle creates a much larger country of aftermath ( and a thicker boundary bed ) above the vehicle, explicating the addition in retarding force.
Sloping the rear screen shows a lessening in retarding force with a square front terminal, but an addition in retarding force with a aslant front terminal. Hucho ( 1998 ) suggests that retarding force additions with increasing rear screen angle up to around 45-60o. This suggests that the lessening in retarding force with a square front terminal has more to make with the interaction of the forepart and rear screen angles, than merely the rear screen.
The addition in retarding force from inclining the rear terminal with a 150o front screen can be explained by the ensuing shortness of the roof. The corners where the screens meet the roof create turbulency, and with the shorter roofline it can be seen that these countries interact with each other, which is likely to increase the retarding force farther. This consequence can be seen in Figure 2. – Turbulence Intensity ( % age ) ( 80 m/s ) on Page 15 where the more aslant rear terminal shows a more disruptive boundary bed.
These effects can besides be seen by analyzing the pathlines shown in Figure 2.. The crisp forepart screen angles show much greater flow withdrawal where the bonnet meets the forepart screen, which is so continued over the roof of the vehicle. This explains the addition in retarding force when compared to the slanted forepart screens, which show virtually no withdrawal. This is confirmed by the work of Hucho ( 1998 ) , who suggests that the optimal windscreen angle for cut downing separation ( and hence retarding force ) is around 150o, when sing the via medias of visibleness and rider compartment temperatures.
Degree centigrades: UsersChrisPDocumentsUniHuddersfieldYear 5Vehicle Aerodynamics and Air ManagementAngles Pathlines.jpg
Figure 2. – Pathlines Coloured by Velocity ( m/s ) ( 80 m/s )
Figure 2. – Turbulence Intensity ( % age ) ( 80 m/s ) shows the turbulency strength of the flow over the roof of the vehicle. It is clear to see that the sharper screen angles create a disruptive boundary bed ; this contributes further to the addition in retarding force. The 90o rear screen angles besides show whirls behind the vehicle where the flows from underneath and above meet and interact.
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Figure 2. – Turbulence Intensity ( % age ) ( 80 m/s )
Side Wind Effectss
The theoretical account was created utilizing the standard vehicle geometry, as no dimensions were being altered for the trial. The basic process outlined in was used with some little versions. The usage of side air currents meant that the flow sphere had to be made much wider, so as to give the flow opportunity to re-converge after go throughing the vehicle organic structure. Adjacent sides were set as recesss ( forepart and left ) and mercantile establishments ( rear and right ) to give a to the full developed flow, without go forthing any nothingnesss near to walls.
The air current magnitudes were calculated utilizing trigonometry and vectors as shown in ( 3. ) and ( 3. ) .
( 3. )
Ten = X Component of Velocity ( m/s )
V = Overall Velocity Magnitude = 40m/s
I? = Wind Angle = 15o, 30o or 45o
( 3. )
Z = Z Component of Velocity ( m/s )
V = Overall Velocity Magnitude = 40m/s
I? = Wind Angle = 15o, 30o or 45o
It was simulated in this manner ( instead than revolving the auto ) to maintain the theoretical account aligned with the co-ordinate system and hence do the force outputs easier to compare. All side wind theoretical accounts were created in the same manner, with the lone difference being the air current vector magnitude values. The theoretical account in the larger flow sphere is shown in Figure 3..
Degree centigrades: UsersChrisPDocumentsUniHuddersfieldYear 5Vehicle Aerodynamics and Air Managementcrosswind mesh.jpg
Figure 3. – Cross Wind Mesh
The effects of side air current angle on retarding force, lift and side forces are shown in Figure 3. – Side Wind Angle Effects.
Figure 3. – Side Wind Angle Effects on Forces
The fluctuations are shown with the equations for their tendency lines – while they set up quantitative relationships for the information available, they are non likely to be accurate due to the little scope of readings taken. The most obvious alteration is the fluctuation in side force moving on the vehicle. This is to be expected, as the vector way of the air current moving on the side of the vehicle increases with air current angle. These side forces are generated due to the asymmetrical force per unit area distribution created by the air current angle. These consequences can be compared with the theory put frontward by Gilhaus and Hoffmann ( 1998 ) , which suggests that a air current angle of 200 gives ensuing retarding force and side forces with an angle of 60o. Reading off the graph, the side and retarding force forces would be around 2500N and 1400N severally. The attendant angle can so be calculated utilizing ( 3. ) .
( 3. )
I? = Resultant Angle ( grades )
S = Side Force ( N )
D = Drag Force ( N )
This suggests that the consequences match the proposed theory, and should hence be dependable and comparable.
The big side forces introduced are besides likely to be due to the crisp A pillar angles of the auto theoretical account, which have been found to take to additions in side force fluctuation and hence yaw minute ( Gohlke et al. , 2010 ) . It is likely that these could be reduced to more realistic degrees by swerving the borders to be more similar to the existent vehicle.
The effects of side air current angle on pitch, swerve and axial rotation minutes are shown in Figure 3..
Figure 3. – Side Wind Angle Effects on Moments
The fluctuations are shown with the equations for their tendency lines – while they set up quantitative relationships for the information available, they are non likely to be accurate due to the little scope of readings taken. These minutes have a great consequence on the vehicle ‘s stableness, and the inputs that would be required from the driver to maintain the auto traveling in the coveted way. They can be explained by analyzing the vehicle surface force per unit area distributions shown in Figure 3. ( 15, 30 and 45 grades left to compensate ) .
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Figure 3. – Crosswind Surface Static Pressure Distributions
The lessening in pitch can be explained by the forepart screen force per unit area alterations. The 15o air current Acts of the Apostless more on the forepart screen ( as would be expected due to its angle ) . This pushes the top of the auto backwards, making a pitching minute similar to difficult acceleration.
Yaw minute is at its upper limit with a air current angle of 30o, this can be explained by the force per unit area distribution on the side of the auto, which shows more of a alteration over the surface compared to the other two theoretical accounts, with high force per unit area on the forepart left corner and lower force per unit area on the rear left. The 15o theoretical account shows a more symmetrical distribution, with the 45o theoretical account being comparatively changeless across the surface. This besides explains the addition in rolled minute at 30o flow angle, with a larger difference between the force per unit area at the top and bottom than the other two theoretical accounts.
The flow Fieldss for the different side air currents ( 15o, 30o, 45o top to bottom ) are shown in Figure 3. – Side Wind Flow Field.
Figure 3. – Side Wind Flow Field Velocities ( m/s )
The plane taken for each instance is through the beginning, coincident with the air current angle. The flow Fieldss show the consequence of the vehicle form in the air current way. For illustration the 30o air current creates a big country of aftermath behind the vehicle. This suggests that the 30o air current hits the vehicle at one of its most ‘bluff ‘ angles. This can be compared to the flow with a 45o air current, which appears to hit the vehicle at a sharper border, likely to be around the A Pillar.
Consequence of Length of Development of Flow
The theoretical accounts were created utilizing the process outlined in, and adapted by widening the sphere length in forepart of the vehicle to give development lengths of 56,200 millimeters and 112,400 millimeter. These spheres are shown in Figure 4. and Figure 4. severally.
Degree centigrades: UsersChrisPDocumentsUniHuddersfieldYear 5Vehicle Aerodynamics and Air Management56200 length mesh.jpg
Figure 4. – 56,200 millimeter Development Length Mesh
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Figure 4. – 112,400 millimeter Development Length Mesh
The consequence of altering the development lengths was investigated at 20 m/s and 80 m/s. The retarding force forces reported are shown in Table 4. – Consequence of Development Length on Drag Force ( N ) .
Table 4. – Consequence of Development Length on Drag Force ( N )
The differences in reported retarding force forces are negligible for the development length alteration. There is hence no quantitative relationship for the scope tested, as the consequences are virtually indistinguishable. This is non, nevertheless the instance with down force. The down force values reported are shown in Table 4. – Consequence of Development Length in Down Force ( N ) .
Table 4. – Consequence of Development Length in Down Force ( N )
This shows a much larger alteration, proposing the importance of a long flow development length when analyzing down force. As with the retarding force consequences, a quantitative relationship can non be established for the little alteration at 20m/s. One could be established for 80m/s, but it is non likely that it would be accurate. The consequences will nevertheless be significantly affected by the simplified vehicle geometry holding a level floor ( unrealistic and generates land consequence ( Scibor-Rylski, 1975 ) ) , and the highly high velocity analysed ( the top velocity of the fastest Miniskirt is around 65m/s ) . The big sum of down force generated is besides likely to be due to the fact that the wheel arches are non modelled – these typically create high sums of lift ( Regert & A ; Lajos, 2007 ) .
The demand for a long development length of flow is the physique up of inactive force per unit area in forepart of the vehicle. This is shown in Figure 4. – Consequence of Development Lengths on Inactive Pressure ( Pa ) 20 m/s and Figure 4. – Consequence of Development Lengths on Inactive Pressure ( Pa ) 80 m/s ( shorter development lengths on top ) . It is clear to see that some sphere is needed in forepart of the vehicle, as the inactive force per unit area builds up and could finally make the recess, but both domain lengths tested are more than adequate in length, and therefore demo virtually no difference. This is to be expected when sing the recommendation of three auto lengths development length in FLUENT ( Lanfrit, 2005 ) and typical full graduated table air current tunnel lengths of 10-20m ( Hucho, 1998 ) .
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Figure 4. – Consequence of Development Lengths on Inactive Pressure ( Pa ) 20 m/s
Degree centigrades: UsersChrisPDocumentsUniHuddersfieldYear 5Vehicle Aerodynamics and Air Managementlength 80ms.jpg
Figure 4. – Consequence of Development Lengths on Inactive Pressure ( Pa ) 80 m/s
Consequence of Flow Field Width
The standard auto theoretical account discussed in was used and the flow sphere widened to give analyses with breadths of 8,000 ( same breadth used for the probe in ) millimeter and 30,000 millimeter. These theoretical accounts were so run at 20m/s and 80m/s. The mesh for the wider sphere is shown in Figure 5..
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Figure 5. – Wider Flow Field Mesh
The fluctuation in drag force is shown in Table 5. – Consequence of Flow Field Width on Drag Force ( N ) .
Table 5. – Consequence of Flow Field Width on Drag Force ( N )
It is clear to see that the alteration in flow field breadth has a really little consequence on the retarding force force reported. There is hence no quantitative relationship for the scope tested, as the consequences are virtually indistinguishable. This is as one would anticipate sing the typical breadths of air current tunnels and comparatively little consequence that a narrow tunnel has on the consequences ( Barnard, 2001 ) .
The fluctuation in down force is shown in Table 5. – Consequence of Flow Field Width on Down Force ( N ) .
Table 5. – Consequence of Flow Field Width on Down Force ( N )
As with the development length trial in, down force shows a well larger difference, particularly at 80 m/s where the 3.75x addition in flow field width gives a 1.45x addition in down force. Looking at the surface parts to these forces shows that the chief differences come from the roof and floor of the vehicle. This difference could be attributed to the narrower theoretical account holding the geometry closer to the walls of the sphere. As the walls have a fixed boundary status, the flow is near to them is affected. Therefore if the theoretical account is excessively close to the walls, both the vehicle form and sphere walls will hold an consequence on the flow in the country between them. The consequences are nevertheless likely to be unrealistic due to the modeling simplifications discussed earlier – chiefly the level floor and deficiency of wheel arches – which both increase down force dramatically.
The flow field around the vehicle for 80 m/s is shown in Figure 5. – Flow Velocity Around Vehicle ( m/s ) ( 80 m/s ) , but the consequence of the flow field breadth is hard to see – the xanthous country around the side of the vehicle.
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Figure 5. – Flow Velocity Around Vehicle ( m/s ) ( 80 m/s )
The part of the roof can be seen by analyzing the inactive force per unit area, as shown in Figure 5. – Inactive Pressure Variation ( Pa ) ( 80 m/s ) ( narrow flow sphere on top ) .
Degree centigrades: UsersChrisPDocumentsUniHuddersfieldYear 5Vehicle Aerodynamics and Air Managementwidth inactive force per unit area 80ms.jpg
Figure 5. – Inactive Pressure Variation ( Pa ) ( 80 m/s )
There is a little fluctuation towards the rear of the roof, which when multiplied by the big country gives a big difference in force.
The retarding force force outputted by the analysis of the standard auto was used to cipher the drag coefficient of the vehicle. This is shown in ( 6. ) for the standard vehicle geometry.
( 6. )
Cadmium = Drag Coefficient
D = Drag Force ( N )
I? = Density of Air = 1.22kg/m3
A = Frontal Area = 1.92m2
V = Flow Velocity ( m/s )
The drag coefficient of the existent vehicle is 0.35 ( BMW MINI, 2010 ) . This suggests that the analysis gives a drag force of around 1.7 times ( 69 % addition ) what would be expected. It was possible that this was due to the comparatively bold organic structure from the simplified geometry, but it was decided to formalize the theoretical account against known geometry to corroborate or dismiss this theory.
Validation against Known Geometry
To formalize the CFD package ‘s truth, a theoretical account was created with the same flow sphere and mesh denseness as discussed in, but for a domain of radius 200mm, it is shown in Figure 6..
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Figure 6. – Sphere Validation Model Mesh
This was tested utilizing the same methods as the vehicle theoretical accounts to find its drag coefficient and compare it to the theoretical value. The retarding force force predicted by the theoretical account was 24N, giving a drag coefficient of 0.78 ( utilizing ( 6. ) as earlier ) . The theoretical value can be found from the chart shown in Figure 6. – Typical Drag Coefficients ( freestudy.co.uk, 2002 ) . The Reynolds figure must foremost be calculated utilizing ( 6. ) .
( 6. )
I? = Density of Air ( kg/m3 )
V = Flow Velocity ( m/s )
D = Diameter of Sphere ( m )
Aµ = Viscosity of Air ( Pas )
This gives a retarding force coefficient value of around 0.4, proposing that it is a similar factor of inaccuracy to the vehicle theoretical accounts. This is likely to be caused by the mesh come closing the form of a smooth surface to a figure of tetrahedral elements. While it is likely that the consequences are inaccurate, the comparings drawn from the modeling are still valid, as they are all based on the same mesh scaling and flow parametric quantities, doing them straight comparable and precise instead than accurate.
Figure 6. – Typical Drag Coefficients ( freestudy.co.uk, 2002 )
Use of Alternative CFD Package
Dassault Systemes ‘ SolidWorks Flow Simulation was used to analyze the standard vehicle geometry at 20 m/s, to formalize the apparatus process used in Gambit and FLUENT.
Table 6. – Comparison of FLUENT and SolidWorks Results
In footings of retarding force, SolidWorks appears to bring forth a much more accurate consequence, with the retarding force coefficient being much closer to the right value ( 0.35 ) . There is besides a big difference in down force. This may be attributed to the manner SolidWorks defines the flow sphere. The vehicle theoretical account is centralised in a big rectangular sphere, instead than being close to the ‘floor ‘ . This would hold a big consequence on the flow underneath the vehicle, and therefore bring forth different down forces. This is shown in the force per unit area distribution secret plan in Figure 6..
Figure 6. – SolidWorks Pressure Distribution
A speed secret plan is besides shown in Figure 6.. The two figures show similar distributions to the trials carried out in FLUENT, proposing the consequences should be comparable.
Figure 6. – SolidWorks Velocity Distribution
Overall the consequences look similar to the 1s produced by FLUENT, although with predicted retarding force closer to the existent Numberss. This suggests that SolidWorks may hold produced more accurate consequences than FLUENT, although calculation clip would hold been increased significantly. The consequences obtained from FLUENT, whilst non needfully being accurate are still likely to be precise due to the same process being followed. They should therefore still give valid comparings. The deficiency of solid floor ( route ) in the SolidWorks simulation may besides hold had a dramatic consequence on the decrease in retarding force, as skin clash would be neglected.
Wind Tunnel Testing
A theoretical account of the standard vehicle geometry was created utilizing the university ‘s rapid prototyping machine ; a exposure of which is shown in Figure 6..
Tocopherol: Year 5Vehicle Aerodynamics and Air ManagementRapid Prototype Model.JPG
Figure 6. – Rapid Prototype Model
The theoretical account was to be tested in the university ‘s air current tunnel, utilizing a cobra investigation to find the speed behind the vehicle. This so allows the retarding force force to be calculated utilizing the impulse method shown in ( 6. ) .
( 6. )
D = Drag Force ( N )
I? = Density of Air = 1.22kg/m3
B = Model Width ( m )
H = Maximum Height of Velocity Measurement ( m )
ux = Measured Velocity ( m/s )
Y = Height of Measurement ( m )
= Free Stream Velocity ( m/s )
Using this method with experimental informations requires averaging of speed values and a summing up to find the value of the built-in. This drag force can so be compared against the anticipation in FLUENT, and used to cipher the estimated retarding force coefficient. The speed profile produced is shown in Figure 6..
Figure 6. – Speed Profile
The information from the proving are shown in Table 6..
Table 6. – Wind Tunnel Testing Results
The built-in values are calculated utilizing ( 6. ) and the retarding force coefficient calculated utilizing ( 6. ) .
The predicted retarding force coefficient is 0.95, compared to a anticipation of 0.59 from FLUENT – an addition of 61 % . This could propose that either method has mistakes of around this degree or that both theoretical accounts have some mistake and are wrong.
As the theoretical account is so far off from the existent vehicle geometry, it can non be faithfully determined whether the air current tunnel or CFD analysis is the most accurate. Both methods have built-in inaccuracies, and therefore could bring forth undependable consequences. Any comparings made should still nevertheless be valid, due to all the CFD theoretical accounts being created and meshed in the same manner, giving a high degree of preciseness.
Standard Vehicle Geometry
The simulation was performed utilizing the standard vehicle geometry, to compare it to the ‘optimum ‘ angled form determined in. The consequences are shown in Table 7..
Table 7. – Comparison of Standard and Optimised Model Forces ( N )
The power required to travel a vehicle depends really strongly on the retarding force force ; it is hence really good to cut down the retarding force force on a vehicle and therefore cut down its fuel ingestion. The consequences shown in Table 7. show that drag force is reduced by utilizing the optimised screen angles determined in. It is likely that the absolute optimal values lie someplace in between these angles and the standard vehicle dimensions, so farther experimentation would be required. Curvature of the roof could besides be introduced to cut down retarding force ( Hucho, 1998 ) , but the consequence on frontal country must besides be considered.
The stableness of the vehicle depends greatly on the down force generated. Cars typically create lift at high velocity, efficaciously cut downing their weight moving on the land and hence doing them unstable. The theoretical accounts analysed created down force due to the simplified level floor of the theoretical account. Table 7. shows a considerable addition in down force from the optimised screen angles, although as with power ingestion, it is likely that the genuinely optimal dimensions are somewhat different. The consequences may non besides be genuinely dependable due to the big consequence of holding an unrealistic level floor. Fliping minute is besides decreased well with the optimised form.
The consequences suggest that the power ingestion and stableness of the vehicle could be improved by inclining the forepart screen to 150o and altering the rear screen to 90o. While this would be good, there are many other factors which must be considered when planing a vehicle. Increasing the forepart screen incline could cut down headway for illustration, and holding a 90o rear screen could be seen by many as aesthetically unpleasing. These factors are really of import to auto purchasers, particularly a ‘fashionable ‘ trade name such as the MINI. It is hence improbable that the little additions in fuel economic system and stableness would profit gross revenues plenty to outweigh the negative aesthetic deductions.
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