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Aerodynamics - 2

Reynolds Numbers

Osborne Reynolds was responsible for discovering many of the principles of fluid viscosity and boundary layers. He discovered that the condition of the boundary layer, laminar or turbulent, depend on the fluid velocity, the distance downstream, and a characteristic of fluid known as kinematic viscosity. Reynolds numbers are used to measure the viscous (Having a thick, sticky consistency between solid and liquid)qualities of a fluid. The symbol Re is used for this number and can be expressed as the equation:

Re = V x s

√

Where V = Fluid velocity

d = distance downstream from leading edge

√ = kinematic viscosity of the fluid (these are standard figures which are given with respect to air temperature)

Figure: (Scott, 2005)

At low Reynolds numbers the flow is laminar, and at high Reynolds numbers it is turbulent.

Interested fact: Spheres are not a good shape for aerodynamics. A blade or fin or wing works much better at controlling air flow for flight by maximizing lift and minimizing drag forces. Dimples on a ball help reduce drag, while spin mostly promotes lift. Without dimples, golf balls wouldn't fly half as far as they do.

Form Drag

The figure to the right shows how form drag (also known as pressure drag) is affected by the streamlined shape of the body. For a flat blocky shape, the form drag will be high and for a streamlined low-profile body, the form drag will be minimized. The separation of the fluid creates turbulence and results in pockets of low and high pressure that leave a wake behind the body, thus the term pressure drag. The pressure drag opposes forward motion and is a component of the total drag.

Wake

Awakeis the region of recirculating flow immediately behind a moving or stationary solid body, caused by the flow of surrounding fluid around the body.

The figure below shows the large wake generated behind the a small boat. This wake is in essence "wasted" energy that the ship generates. This wasted energy was not used to propel the boat forward, but rather to generate waves.

Figure: (Cortana, 2006)

Wake Turbulence

Wake turbulenceforms behind anaircraftas it passes through the air. This turbulence includes various components, the most important of which arewingtip vorticesand jetwash. Jetwash refers simply to the rapidly moving gases expelled from a jet engine; it is extremely turbulent, but of short duration.See image below.

Figure: (Edmont, 2009)

Figure:(NASA, 1990)

Drag Coefficient

The amount of drag on an object is proportional to the dynamic pressure times the area and will vary with the shape of the body, the roughness of the surface, and other factors. Drag, like lift, is proportional to the dynamic pressure of the air and to the area on which it is acting. Therefore, a drag coefficient is used to describe how much of the dynamic pressure is converted into drag. The equation looks a lot like the lift equation, except that it measures the force in a stream wise direction, which is parallel to the airflow.

Drag=Cdx (1/2 p V2) x A

Where: Figure: (Aquaphoenix, 2012)

-Cd= Drag coefficient

-P= Density

-V= Velocity

-A= Area

The term ½ p V2 , remember, is the dynamic pressure, referred to by the symbol q. Thus, using this notation:

Drag= Cdx q x A

There is a similarity between lift coefficient and drag coefficient in that the lift coefficient, CL , is a measure of how much of the dynamic pressure gets converted into lift, and the drag coefficient is a measure of how well a wing (or other body) converts dynamic pressure force into drag.

Both are an indication of efficiency. When generating lift, however, we want as much as possible, but, when generating drag, we want the least possible.

A low drag coefficient, then, is what we want. The efficiency is determined by how little of the pressure force is turned into drag.

The drag coefficient can also be expressed as the ratio of drag force to dynamic pressure force, or:

Cd= Drag/q x A

This is the formula that is used to calculate CD from wind tunnel tests. The drag force is measured using some sort of scale or balance. The force is then divided by q x A which is determined from a measurement of the air speed, density, and the area of the body.

Figure: (Magda, 2006)

Testing the Racer Shapes in a Wind Tunnel

Using a wind tunnel to test different shapes and designs of our racer is a fantastic way to predict how our racer is likely to behave in an F1inSchools race.If we test our models in our wind tunnel and determine the different racer’s Reynolds numbers we can determine the designs which create the least turbulence and therefore move with the best laminar airflow.

Figure: (PITSCO, 2002)

Obviously the designs with the lowest Reynolds numbers will then potentially be the fastest cars. Of course all other contributing factors between cars would have to be equal. We can use the Pitsco Scout, to test our racer designs.We can read the Reynolds number directly from the digital readout which makes this very useful for determining which of our designs is the best aerodynmically.

Bernoulli's principle

The production of the lift force by an aerofoil is explained by Bernoulli's principle. Daniel Bernoulli (170082) was a Swiss scientist who discovered that the total pressure in a fluid remained constant. This total pressure consists of:

• static pressure (the weight of the molecules)• dynamic pressure (due to motion) Figure: (OTEN, 2002)

If air was accelerated through a shaped tube called a `venturi', then at the narrowest point, where the speed of the flow was fastest, the static pressure was least. The relationship between the velocity and pressure exerted by a moving fluid is described by Bernoulli's principle(OTEN, 2002):

as the velocity of a fluid increases, the pressure exerted by that fluid decreases.

See Bernoullis’s Principle Experiments YouTube

Air foils and Lift

Air foils are the wings on aeroplanes and the spoiler type sections on cars. In planes we all know that the wings allow the plane to be supported in the air, however on cars they are not just for show they have a very important purpose.

In the diagram to the left differences in shape and the direction of the force produced is shown when the wing is inverted in powered car racing where the aim is to produce down force (so that the cars can “stick “ to the road and grip so that the power produced by the engine can be transferred to the track). This is the direct opposite to a plane wing where the aim is to create lift to keep the plane in the air.

CO2 Powered Race Car Resource Folio 1