141 Viscous air flow fundamentals

14.1.1 Boundary layer (Fig. 14.2) Air has viscosity, that is, there is internal friction between adjacent layers of air, whenever there is relative air movement, consequently when there is sliding between adjacent layers of air, energy is dissipated. When air flows over a solid surface a thin boundary layer is formed between the main airstream and the surface. Any relative movement between the main airstream flow and the surface of e

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Vehicle speed (km/h)

Fig. 14.1 Comparison of low and high aerodynamic drag forces with rolling resistance

Outer layer

Full velocity of air flow

~7 Inner layer

Fig. 14.2 Boundary layer velocity gradient

Outer layer

Full velocity of air flow

Parabolic rise in air layer velocity from inner to outer boundary layer

Viscous shear

~7 Inner layer

Parabolic rise in air layer velocity from inner to outer boundary layer

Viscous shear

plate drag /

Flat plate Rollers

Fig. 14.3 Apparatus to demonstrate viscous drag the body then takes place within this boundary layer via the process of shearing of adjacent layers of air. When air flows over any surface, air particles in intimate contact with the surface loosely attach themselves so that relative air velocity at the surface becomes zero, see Fig. 14.2. The relative speed of the air layers adjacent to the arrested air surface film will be very slow; however, the next adjacent layer will slide over an already moving layer so that its relative speed will be somewhat higher. Hence the relative air velocity further out from the surface rises progressively between air layers until it attains the unrestricted main airstream speed.

14.1.2 Skin friction (surface friction drag) (Fig. 14.3)

This is the restraining force preventing a thin flat plate placed edgewise to an oncoming airstream being dragged along with it (see Fig. 14.3), in other words, the skin friction is the viscous resistance generated within the boundary layer when air flows over a solid surface. Skin friction is dependent on the surface area over which the air flows, the degree of surface roughness or smoothness and the air speed.

Air particles in contact with a surface tend to be attracted to it, thus viscous drag will retard the

Spring scale layer of air moving near the surface. However, there will be a gradual increase in air speed from the inner to the outer boundary layer. The thickness of the boundary layer is influenced by the surface finish. A smooth surface, see Fig. 14.4(b), allows the free air flow velocity to be reached nearer the surface whereas a rough surface, see Fig. 14.4(a), widens the boundary so that the full air velocity will be reached further out from the surface. Hence the thicker boundary layer associated with a rough surface will cause more adjacent layers of air to be sheared, accordingly there will be more resistance to air movement compared with a smooth surface.

When air flows through a diverging and converging section of a venturi the air pressure and its speed changes, see Fig. 14.5. Initially at entry the unrestricted air will be under atmospheric conditions where the molecules are relatively close together, consequently its pressure will be at its highest and its speed at its minimum.

As the air moves into the converging section the air molecules accelerate to maintain the volume flow. At the narrowest region in the venturi the random air molecules will be drawn

Fig. 14.5 Venturi

High flow pressure

Accelerating Low Decelerating High pressure flow pressure

Airstream

High flow pressure

Accelerating Low Decelerating High pressure flow pressure

Airstream

High Errtry speed

Exit

Low speed

High Errtry speed

Exit

Low speed

Stagnation

Stagnation

apart thus creating a pressure drop and a faster movement of the air. Further downstream the air moves into the diverging or expanding section of the venturi where the air flow decelerates, the molecules therefore are able to move closer together and by the time the air reaches the exit its pressure will have risen again and its movement slows down.

14.1.5 Air streamlines (Fig. 14.6) A moving car displaces the air ahead so that the air is forced to flow around and towards the rear. The pattern of air movement around the car can be visualized by airstreamlines which are imaginary lines across which there is no flow, see Fig. 14.6. These streamlines broadly follow the contour of the body but any sudden change in the car's shape

High pressure low speed

Converging accelerating flow

Low pressure high speed

Diverging decelerating flow

High pressure low speed

High pressure low speed

Converging accelerating flow

Low pressure high speed

Diverging decelerating flow

Low pressure (subatmospheric pressure) high speed

Fig. 14.7 Relative air speed and pressure conditions over the upper profile of a moving car

Low pressure (subatmospheric pressure) high speed

Fig. 14.7 Relative air speed and pressure conditions over the upper profile of a moving car compels the streamlines to deviate, leaving zones of stagnant air pockets. The further these streamlines are from the body the more they will tend to straighten out.

14.1.6 Relative air speed and pressure conditions over the upper profile of a moving car (Figs 14.7 and 14.8)

The space between the upper profile of the horizontal outer streamlines relative to the road surface generated when the body is in motion can be considered to constitute a venturi effect, see Fig. 14.7. Note in effect it is the car that moves whereas air remains stationary; however, when wind-tunnel tests are carried out the reverse happens, air is drawn through the tunnel with the car positioned inside on a turntable so that the air passes over and around the parked vehicle. The air gap between the horizontal airstreamlines and front end bonnet (hood) and windscreen profile and the back end screen and boot (trunk) profile produces a diverging and converging air wedge, respectively. Thus the air scooped into the front wedge can be considered initially to be at atmospheric pressure and moving at car speed. As the air moves into the diverging wedge it has to accelerate to maintain the rate of volumetric displacement. Over the roof the venturi is at its narrowest, the air movement will be at its highest and the air molecules will be stretched further apart, consequently there will be a reduction in air pressure in this region. Finally the relative air movement at the rear of the boot will have slowed to car speed, conversely its pressure will have again risen to the surrounding atmospheric pressure conditions, thus allowing the random network of distorted molecules to move closer together to a more stable condition. As the air moves beyond the roof into the diverging wedge region it decelerates to cope with the enlarged flow space.

As can be seen in Fig. 14.8 the pressure conditions over and underneath the car's body can be plotted from the data; these graphs show typical pressure distribution trends only. The pressure over the rear half of the bonnet to the mid-front windscreen region where the airstream speed is slower is positive (positive pressure coefficient Cp), likewise the pressure over the mid-position of the rear windscreen and the rear end of the boot where the airstream speed has been reduced is also positive but of a lower magnitude. Conversely the pressure over the front region of the bonnet and particularly over the windscreen/roof leading edge and the horizontal roof area where the airstream speed is at its highest has a negative pressure (negative pressure coefficient Cp). When considering the air movement underneath the car body, the restricted airstream flow tends to speed up the air movement thereby producing a slight negative pressure distribution along the whole underside of the car. The actual pattern of pressure distribution above and below the body will be greatly influenced by the car's profile style, the vehicle's speed and the direction and intensity of the wind.

14.1.7 Lamina boundary layer (Fig. 14.9(a)) When the air flow velocity is low sublayers within the boundary layer are able to slide one over the other at different speeds with very little friction; this kind of uniform flow is known as lamina.

14.1.8 Turbulent boundary layer (Fig. 14.9(b))

At higher air flow velocity the sublayers within the boundary layer also increase their relative sliding speed until a corresponding increase in interlayer friction compels individual sublayers to randomly

Fig. 14.8 Pressure distribution above and below the body structure

Low velocity

Lamina flow

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(a) Lamina air flow (low velocity)

Fig. 14.9(a and b) Lamina and turbulent air flow

Outer layer

High velocity

Outer layer

High velocity

Eddies (vortices)

Inner layer

(b) Turbulent air flow (high velocity)

TP

(b) High speed

Fig. 14.10 (a and b) Lamina/turbulent boundary layer transition point

(b) High speed

Fig. 14.10 (a and b) Lamina/turbulent boundary layer transition point break away from the general direction of motion; they then whirl about in the form of eddies, but still move along with the air flow.

14.1.9 Lamina/turbulent boundary layer transition point (Fig. 14.10(a and b)) A boundary layer over the forward surface of a body, such as the roof, will generally be lamina, but further to the rear a point will be reached called the transition point when the boundary layer changes from a lamina to a turbulent one, see Fig. 14.10(a). As the speed of the vehicle rises the transition point tends to move further to the front, see Fig. 14.10(b), therefore less of the boundary layer will be lamina and more will become turbulent; accordingly this will correspond to a higher level of skin friction.

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