experimental aerodynamicsvehicle aerodynamics · 2011-01-13 · drag force •!as already discussed...

Experimental Aerodynamics

Lecture 3: Performance and stability

G. Dimitriadis

Experimental Aerodynamics Vehicle Aerodynamics


Car performance •! Car performance is a function of the

complete design of a car. •! Aerodynamics plays a significant part

but there are many other factors that are important.

•! As the main function of aerodynamics is to improve fuel efficiency, we will concentrate on fuel performance in this part of the course.


Car equation of motion

•! Use Newton’s 2nd Law of Motion:

!"

FT"

R"mg"

D"

FT: Traction force D: Drag force R: Rolling resistance"V: Speed mg: weight !: climb angle

FT = D + R + m dVdt

+ mgsin!


Drag force

•! As already discussed in the previous section, the drag force can be expressed as

•! This expression is deceptively simple because it includes all of the internal and external sources of drag in the drag coefficient.

D =12!V 2CDS


Rolling resistance •! The rolling resistance can be

approximated as R=fRmg, where fR is the coefficient of rolling resistance.

•! fR can be approximated as a function of speed.

Typical variation of rolling resistance coefficient with speed.

fR = 2.80 !10"7V 2 +1.97 !10"6V + 0.012

fR = a2V2 + a1V + a0

In this example:


Car inertia •! The inertia of the car depends primarily on its

mass but also on the moment of inertia of all rotating parts of the powertrain.

•! The total inertia can be expressed as an effective mass, meff=m(1+#i), where #i depends on the chosen gear: –! 1st gear: #1=0.25 –! 2nd gear: #2=0.15 –! 3rd gear: #3=0.10 –! 4th gear: #4=0.075 –! 5th gear: #5=0.063


Complete traction force

•! A complete (but approximate) equation for the traction force can then be written as:

•! Notice that the acceleration term is defined as a ‘resistance to acceleration’ and therefore has a sign opposite to that of the traction force.

FT =12!V 2CDS + a2V

2 + a1V + a0( )mg + m 1+ " i( ) dVdt + mgsin#


Fuel consumption

•! The fuel consumption of a car running over a certain period of time T is usually defined as the ratio:

•! Where is the volume fuel rate and the denominator is simply the distance travelled in T seconds.

•! The fuel consumption is usually measured in L/100 km.

B =˙ b dt

0

T

!Vdt

0

T

!

˙ b


Powered driving •! Consider the case where the engine is

providing a traction force, i.e. FT>0. •! The traction power necessary to produce the

required traction force is given by PT=FTV. •! The traction power is related to the engine

power by PT=Pb,T$D, where is the $D drivetrain efficiency.

•! The volume fuel rate can be expressed as

•! Where be is the specific fuel consumption.

˙ b =be

!fuel"D

PT =be

!fuel"D

FTV


Specific fuel consumption

•! The specific fuel consumption (brake specific fuel consumption for reciprocating engines) is defined as:

•! The brake specific fuel consumption (bsfc) is not a constant; it varies with the speed of rotation of the engine.

•! However, the minimum bsfc for most engines is of the same order, between 200 and 300 g/Kwh

be =˙ m fuel

Pb,T= !fuel

˙ b Pb,T


Sample bsfc map for an engine Minimum bsfc


Fuel consumption in powered driving •! The fuel consumption in powered driving is then given as

•! For constant speed operation on a level road over a short period of time (little fuel is burned so the car weight does not change much), this becomes

•! or,

B =1!fuel

be"D

FTVdt0

T

#Vdt0

T

#

B =be

!fuel"D

FT

B =be

!fuel"D

12!V 2CDS + a2V

2 + a1V + a0( )mg# $

% &


Application example •! Apply this equation to a luxury car with S=2m2,

m=1500kg at V=150kph (i.e. fR=0.018).

•! Substituting gives

•! We can simplify a bit by noting that 0.94CD>>0.018 and that 0.94!1:

B =bemg!fuel"D

12mg

!V 2CDS + a2V2 + a1V + a0( )#

$ % & ' (

B =bemg!fuel"D

0.94CD + 0.018( )

B =bemg!fuel"D

CD


Drag effect on fuel consumption

•! This simple example demonstrates that, all other factors remaining equal, fuel consumption is directly proportional to the drag coefficient.

•! Therefore, a 10% decrease in the drag coefficient of the car could bring about a 10% decrease in non-dimensional fuel consumption.

•! Remember that non-dimensional fuel consumption is given by

B!fuel"D

bemg


More realistic data

•! A more realistic estimate of the decrease in fuel consumption due to a decrease in drag is the following: –!Gasoline engines:

–!Diesel Engines:

!BB0

= 0.40 !CD

CD0

!BB0

= 0.50 !CD

CD0


European car classes •! A classification of European car classes

is as follows:

•! With the following representative cars:


Fuel effect on European cars •! Estimate of fuel consumption reduction

due to drag, mass and power reductions


Statistics

•! These fuel consumption effects depend on the choice of car usage, what is known as the Driving Cycle.

•! The Driving Cycle is a definition of how much time the average car spends driving in a city, on a regional road or on a motorway.

•! The old European Driving Cycle specified that B=1/3(Bcity+B90+B120).

•! The diagrams of the previous slide were obtained using this definition.


NEDC •! The new European Driving Cycle is

called NEDC and is as complicated as anything that European bureaucrats can produce.

•! Using this Driving Cycle, car weight decreases become more important to fuel savings than drag reductions.

•! Therefore, it must be right...


NEDC fuel consumption savings

"G denotes change in car weight

Car weight reductions have a much bigger effect on fuel consumption under the new standard.

Conversely, drag reductions have a significantly smaller effect.


Lowest fuel consumption •! Decreasing the drag coefficient can increase

the maximum speed of a car. •! Further fuel savings can be obtained if the

engine power is decreased so that the maximum speed remains at its original value.

•! A reduction in power will worsen the car’s acceleration and climbing performance. Therefore, the car’s weight must also be reduced.

•! Of course, reducing mass is not necessarily very easy.


Potential mass reductions

•! This is where the process becomes even more hypothetical.

•! We can assume that the mass reduction potential is 10% for class A cars up to 20% for class E cars.

•! Then we can determine how much we can reduce the power in order to preserve the same acceleration and climb performance.

•! Finally, this gives us the estimate of how much we need to decrease the drag coefficient so that the maximum speed remains the same.


Optimal fuel savings Optimal CD

Class

0.32 A

0.28 B

0.24 C

0.23 D

0.24 E


Discussion •! The optimal drag coefficients seem reasonable. •! However, it must be kept in mind that their

calculation started from a very weak assumption about the weight reduction possibilities.

•! If such weight reductions are not possible, then the optimal drag coefficients values are wrong.

•! Therefore, the value of such calculations is debatable.

•! You can’t just wish for fuel savings. There must be a concrete mechanism by which they are achieved!


Directional stability •! At high speeds, the yawing moment caused by

aerodynamic forces during turning or because of a crosswind can be quite significant.

•! In the early years of the automobile era (up to the 1920s) car performance and road quality limited the top speeds.

•! Therefore, there was little correlation between aerodynamics and yawing moment.

•! However, as car performance and road quality improved, the aerodynamic yawing moment became increasingly important.


6 degrees of freedom •! A car has 6 degrees of freedom:

Up#

Front#Side#

Pitch#

Yaw#

Roll#

3 Displacements: Front, side, up

3 Rotations: Yaw, pitch, roll

C.G.: Centre of gravity

C.G.#


Centre of pressure •! The resultant aerodynamic force can be seen

as the integral of the pressure distribution over the entire surface of the car.

•! This resultant force acts on the centroid of the pressure distribution, known as the Centre of Pressure.

•! The centre of pressure is not coincident with the car’s centre of gravity.

•! As a consequence, the aerodynamic force creates an aerodynamic moment around the centre of gravity.


Aerodynamic forces and moments

•! The resultant aerodynamic force and moment around the centre of gravity can be decomposed in the direction of the three car axes, yielding:

•! 3 Forces: –! Lift –! Drag –! Side force

•! 3 Moments: –! Pitching moment –! Yawing moment –! Rolling moment


Streamlining

•! Streamlining reduced drag but also decreased lateral stability.

•! Furthermore, many cars of the interwar years had the engine installed in the rear.

•! The combination of rear lift and rear positions of the centre of gravity greatly reduced the directional stability of cars.

•! Vehicles with low aerodynamic drag were generally sensitive to crosswinds


Effect of lift •! Many cars produce lift at high airspeeds.

The lift coefficients are much smaller than those of aircraft but they are positive.

•! This lift decreases the wheel load and increases the sensitivity of the steering response to small disturbances.

•! If the lift is higher towards the rear of the car, it can cause oversteer, i.e. the sideslip angle of the rear wheels becomes greater than that of the front wheels.


Car shape effect on lift Influence of stagnation point position and separation height on lift and pitching moment.

Clearly, a high stagnation point and slow separation tend to create higher lift and, hence, more directional instability.


50s bathtubs

•! The bathtub cars of the 1950s did not really improve the directional problems.

•! They generated significant amounts of rear lift and many of them had rear-mounted engines.

•! The situation became so bad that some cars started featuring double fins at the back.


Effect of fins •! Car fins act exactly like aircraft fins

V"

V" C.G.#

Yf"

Df"

%"

Y"

D"C.P.#

C.P.: Centre of pressure C.G.: Centre of gravity Y: Side force D: Drag force %: Yaw angle Yf: Fin side force Df: Fin drag

The airflow is coming at an angle %, causing a side force and drag acting on the centre of pressure. These forces cause a destabilizing moment around the centre of gravity.

The fins create side and drag forces on their centers of pressure. These provide a stabilizing moment around the centre of gravity.


Front-mounted engines •! Eventually, the directional stability problems

started being resolved by mounting the engines at the front on most cars.

•! Furthermore, as aerodynamics started becoming important again in the 70s, aerodynamically induced directional instability started to be investigated.

•! Finally, spoilers started to get installed on the rear of high performance cars, pushing the rear of the car down and thus increasing directional stability.


Spoilers •! Spoilers can have several functions:

–!Create downforce to improve the grip of the tyres on the road.

–!Create downforce to counter body-generated lift and overcome directional stability problems.

–!Smooth out and direct the airflow in order to decrease turbulence and drag

–!Decorate. •! In general, downforce-producing spoilers

are only required for racing vehicles.


Passenger car spoilers •! Several non-racing cars (usually

Sports Coupes like the Toyota Celica and the Toyota MR2) feature factory-installed front and rear spoilers. Their functions usually are: –! Front spoiler: decrease drag by

diverting the flow away from the wheels

–! Rear spoiler: smooth the flow to reduce turbulence

•! Both these functions help to reduce drag.

Toyota Celica

Toyota MR2


Yawing moment •! The aerodynamic yawing moment acting around

the centre of gravity is denoted by N. •! For yaw stability, the rate of change of this moment

with yaw angle must be negative, i.e.

•! This condition can also be written in coefficient form

•! Where CN is defined as:

!N!"

< 0

!CN

!"< 0

CN =N

12!V 2Sl

l is the wheelbase, i.e. the distance between the front and rear wheels.


Effect of flow separation •! For car directional stability, larger areas

of separation are actually good!

Case A: Rear separation Case B: Front separation

!CN

!"#

$ %

&

' ( A

> 0

!CN

!"#

$ %

&

' ( B

> 0

!CN

!"#

$ %

&

' ( B

<!CN

!"#

$ %

&

' ( A

But


Controlled separation •! Case A occurs at smaller yaw angles, case B at

bigger ones. •! At a critical yaw angle, the flow jumps from

case A to B.

%"

CD"

%"

CN"


Crosswind

•! When a crosswind Vc acts on a vehicle at an angle &, the resultant airspeed seen by the vehicle is Vr and its direction angle is %, the yaw angle.

Vr Vc

V % &


Side force and Yawing moment

•! The side force and yawing moment coefficients can be assumed to be linear with yaw angle, at least for %<20o. Then, –! CY=C’Y%"–! CN=C’N%#

•! The total side force becomes

•! The total yawing moment becomes

•! Where e is the distance between the centre of pressure and the centre of gravity

Y =12!Vr

2S " C Y#

N =12!Vr

2S " C Y#e


Gusts •! Crosswind is rarely sustained.

Atmospheric turbulence can be seen as a noisy background signal peppered with discrete powerful events known as gusts.

•! Gusts are sudden and last a short time. The response of cars to gusts is different to the response to sustained crosswinds; the former is dynamic, the latter is static.

•! Gusts excite the yaw dynamics of the car and can cause oscillations to occur.


Measurement of crosswind effects

Such measurements are carried out using crosswind blowers.

Open loop test

Closed loop test


Effect of yaw angle on all six aerodynamic load coefficients for three different car families (hatchback, notchback and estate)

All 6 aerodynamic load components


Overtaking

•! Effect of crosswind on car overtaking a bus

!: %=0o

*: %=5o

x: %=10o

Encountering bus wake

Recovery to steady state conditions

Encountering bus wake

Recovery to steady state conditions

experimental aerodynamicsvehicle aerodynamics · 2011-01-13 · drag force •!as already discussed...

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