1425 Drag coefficients and various body shapes Fig 1415af

A comparison of the air flow resistance for different shapes in terms of drag coefficients is presented as follows:

(a) Circular plate (Fig. 14.15(a)) Air flow is head on, and there is an immediate end on pressure difference. Flow separation takes place at the rim; this provides a large vortex wake and a correspondingly high drag coefficient of 1.15.

(b) Cube (Fig. 14.15(b)) Air flow is head on but a boundary layer around the sides delays the flow separation; nevertheless there is still a large vortex wake and a high drag coefficient of 1.05.

(c) Sixty degree cone (Fig. 14.15(c)) With the piecing cone shape air flows towards the cone apex and then spreads outwards parallel to the shape of the cone surface. Flow separation however still takes place at the periphery thereby producing a wide vortex wake. This profile halves the drag coefficient to about 0.5 compared with the circular plate and the cube block.

Flow separation

Turbulent volume

Flow separation

Turbulent volume

Fig. 14.15(a-e) Drag coefficient for various shaped solids

Fig. 14.15(a-e) Drag coefficient for various shaped solids

(d) Sphere (Fig. 14.15(d)) Air flow towards the sphere, it is then diverted so that it flows outwards from the centre around the diverging surface and over a small portion of the converging rear half before flow separation occurs. There is therefore a slight reduction in the vortex wake and similarly a marginal decrease in the drag coefficient to 0.47 compared with the 60° cone.

(e) Hemisphere (Fig. 14.15(e)) Air flow towards and outwards from the centre of the hemisphere. The curvature of the hemisphere gradually aligns with the main direction of flow after which flow separation takes place on the periphery. For some unknown reason (possibly due to the very gradual alignment of surface curvature with the direction of air movement near the rim) the hemisphere provides a lower drag coefficient than the cone and the sphere shapes this, being of the order of 0.42.

(f) Teardrop (Fig. 14.15(f)) If the proportion of length to diameter is well chosen, for example 0.25, the streamline shape can maintain a boundary layer before flow separation occurs almost to the end of its tail. Thus the resistance to body movement will be mainly due to viscous air flow and little to do with vortex wake suc tion. With these contours the drag coefficient can be as low as 0.05.

14.2.6 Base drag (Fig. 14.16(a and b)) The shape of the car body largely influences the pressure drag. If the streamline contour of the body is such that the boundary layers cling to a converging rear end, then the vortex area is considerably reduced with a corresponding reduction in rear end suction and the resistance to motion. If the body was shaped in the form of a tear drop, the contour of the body would permit a boundary layer to continue a considerable way towards the tail before flow separation occurs, see Fig. 14.16(a), consequently the area heavily subjected to vortex swirl and negative pressure will be at a minimum. However, it is impractical to design a tear drop body with an extended tapering rear end, but if the tail is cut off (bobtailed) at the point where the air flow separates from the contour of the body (see Fig. 14.16(b)), the same vortex (negative pressure) exists as if the tail was permitted to converge. The cut off cross-section area where flow separation would occur is known as the 'base area' and the negative vortex pressure produced is referred to as the 'base drag'. Thus there is a trend

Point of Separation

Airstreamlines

Point of Separation

Airstreamlines

(a) Tear drop shaped body

Base area

1 to

Base area

(b) Bobtailed tear drop

Fig. 14.16 (a and b) Base drag for car manufacturers to design bodies that taper slightly towards the rear so that flow separation occurs just beyond the rear axle.

Vortices are created around various regions of a vehicle when it is in motion. Vortices can be described as a swirling air mass with an annular cylindrical shape, see Fig. 14.17. The rotary speed at the periphery is at its minimal, but this increases inversely with the radius so that its speed near the centre is at a maximum. However, there is a central core where there is very little movement, consequently viscous shear takes place between adjacent layers of the static core and the fast moving air swirl; thus the pressure within the vortex will be below atmospheric pressure, this being much lower near the core than in the peripheral region.

14.2.8 Trailing vortex drag (Fig. 14.18(a and b)) Consider a car with a similar shape to a section of an aerofoil, see Fig. 14.18(a), when air flows from the front to the rear of the car, the air moves between the underside and ground, and over the raised upper body profile surfaces. Thus if the upper and lower airstreams are to meet at the rear at a common speed the air moving over the top must move further and therefore faster than the more direct underfloor airstream. The air pressure will therefore be higher in the slower underfloor airstream than that for the faster air-stream moving over the top surface of the car. Now air moves from high to low pressure regions so that the high pressure airstream underneath the car will tend to move diagonally outwards and upwards towards the low pressure airstream flowing over the top of the body surface (see Fig. 14.18(b)). Both the lower and the upper airstreams eventually interact along the side-to-top profile edges on opposite sides of the body to form an inward rotary air motion that continues to whirl for some distance beyond the rear end of the forward moving car, see Fig. 14.18(a and b). The magnitude and intensity of these vortices will to a great extent depend upon the rear styling of the

Outer rim

Inner region

High angular speed and low pressure

or rar = a constant

Outer rim or rar = a constant

Where V = Liner velocity ra = Angular velocity r = Radius

Outer region

Low angular speed and high pressure

Inner core air mass no movement

Where V = Liner velocity ra = Angular velocity r = Radius

Fig. 14.17 The vortex

Fig. 14.17 The vortex

Slower airstream and higher air pressure underneath body

(a) Pictorial view Diagonal airstream

Direction of motion a

(a) Pictorial view Diagonal airstream a

Trailing vortex ' cone

Negative pressure

Fig. 14.18(a and b) Establishment of trailing vortices car. The negative (below atmospheric) pressure created in the wake of the trailing vortices at the rear of the car attempts to draw it back in the opposite direction to the forward propelling force; this resistance is therefore referred to as the 'trailing vortex drag'.

14.2.9 Attached transverse vortices (Fig. 14.19(a and b))

Separation bobbles which form between the bonnet (hood) and front windscreen, the rear screen and boot (trunk) lid and the boot and rear light panel tend to generate attached transverse vortices (see Fig. 14.19(a and b)). The front attached vortices work their way around the 'A' post and then extend along the side windows to the rear of the car and beyond. Any overspill from the attached vortices in the rear window and rear light panel regions merges and strengthens the side panel vortices (see Fig. 14.19(b)); in turn the products of these secondary transverse vortices combine and enlarge the main trailing vortices.

Side vortex
Fig. 14.19 (a and b) Notch back transverse and trailing vortices
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