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Aerodynamics of Boomerang. Chapter 1

APR 21, 2006

by Saulius Pakalnis

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The purpose of the article is to give you fundamental knowledge of aerodynamics of boomerangs and explain principles which let  you to build your own boomerang constructions. This will encourage you to make high quality returning boomerangs for sport. 

Introduction

Ideal and Real gases. Ref (pdf).

Ideal gases

Basic assumptions of Ideal gases model:
1. Gas consists of molecules in ceaseless motion.
2. The size of the molecules is negligible in the sense that their diameters are much smaller than the average distance travelled between collisions.
3. The molecules do no interact, except during collisions.

Real gases

Typical interactional potential between molecules of real gases. Attractive Van der Waals forces have a very complex character at distances about 10^-7 cm. They decrease with distance as ~1/(r^7). At long distance, molecules attract each other. This attraction is also a response for the condensation of gases into liquids at low temperatures. At a short distance, molecules repel each other. This repulsion is a response for the definite volumes of liquids and solids, not to collapse to a point.

From the ideal gas equation:
• For 1 mol of an ideal gas, PV/RT = 1 for all pressures.
• In a real gas, PV/RT varies from 1 significantly.
• The higher the pressure - the bigger deviation from the ideal behavior.
• For 1 mol of  ideal gas, PV/RT = 1 for all temperatures.
• As temperature increases, the gases behave in a more ideal way.
The assumptions of the kinetic-molecular theory show where ideal gas behavior breaks down:
• The molecules of gas have finite volume.
• Molecules of gas do attract each other.
• As the pressure on gas increases, the molecules are forced closer together.
• As the molecules get closer together, the volume of the container gets smaller.
• The smaller the container, the more of the total space the gas molecules occupy.
• Therefore, the higher the pressure, the less the gas resembles the ideal gas.
• As gas molecules get closer together, the intermolecular distances decrease.
• The smaller the distance between the gas molecules, the more likely that attractive forces will
develop between the molecules.
• Therefore, the less probability the gas resembles the ideal gas.
• As temperature increases, the gas molecules move faster and further apart.
• Also, higher temperatures mean more energy available to break intermolecular forces.
• As temperature increases, the negative departure from ideal gas behavior disappears.

Although the ideal gas model is very useful, it is only an approximation of the real nature of gases, and the equations derived from its assumptions are not entirely dependable. As a consequence, the measured properties of a real gas will very often differ from the properties predicted by calculations. Ref.

Real gases sometimes don't obey the ideal gas laws because the ideal gas model is based on some assumptions that aren't completely true. The main flaw in the ideal gas model is the assumption that gas molecules do not attract or repel each other. Attractions and repulsions are negligible when the distance between molecules is large, but they do become larger as the molecules become closer together. If you can contrive conditions that force the molecules into close contact, so that attractions and repulsions can't be neglected, you will likely see deviations from ideal behavior. Ref.

Viscosity of air

It seems natural to see the origin of viscosity in terms of the attractive and repulsive forces between molecules. However, gases have substantial viscosity even though their inter-molecular forces are weak, suggesting some other mechanism. Viscosity in gases arises principally from the molecular diffusion that transports momentum between layers of flow. A lot of fluid dynamics is concerned with inviscid flow, but the role of viscosity is crucial to understanding some of the most important fluid phenomena, such as lift produced by a wing. (Author: Fred Senese senese@antoine.frostburg.edu). Ref.

Touch a lift force in water 

Inner surface
The water "reflects" from spoon surface. According to the third  Newton's law ("For every action there is an equal and opposite reaction") spoon moves to the opposite direction. The motion is shown by arrows.

Outer surface
The water follows the surface of the spoon. According to the third  Newton's law the spoon moves to the opposite direction.

Why water sticks to the surface of spoon?
You can replace the surface tension's attractive force by a repulsive one. Just put oil or fat film on spoon surface. See that static forces (as capillarity) make no changes to water stream. It still  attracts the spoon. The effect has a dynamic origin. It is explained by Coanda effect.

Does Coanda effect also "work" in free streams?


 See interaction of oil and water streams. The streams are centered. They pull each other below a point of convergence. The pull turns into push when speed of both streams becomes equal. Then oil begins to collapse into drops, and the two phase system becomes unstable. Second picture shows oil drops, which split from water. Note, that static surface tension force is repulsive for water - oil interface.

The streams are directed  in the way, that oil stream just touches surface of water stream. Above the convergence point water stream is more slow than oil one.  An attractive force of water and oil streams is explained by Coanda effect.

Touch a lift force in air

Take a shield of paper (A4 format). Cut it into 2 pieces.


Take hair dryer and one of the paper strips. Make an experiment.

Inner surface
Direct air blow to inner surface. Lift force pushes the strip up.

Outer surface
Air is blowed at small angle to a curved surface. Lift force pushes the strip up.

Outer surface
Almost no lift? You can push the strip down, but how to pull it up?
Note1: Lift force appears as the result of surface and air flow interaction. It seems that some special conditions should be met to get a lift.

 

Peculiarities of dynamic ant static pressure

Dynamic pressure is the component of fluid pressure that represents fluid kinetic energy (i.e., motion), while static pressure represents hydrostatic effects.

Static pressure is isotropic - the same in all x,y,x directions. In air it equals the atmospheric pressure and does not depend on the wing speed.

Dynamic pressure of a fluid stream with density and speed u is given by
Dynamic pressure represents the fluid stream motion at a certain direction. Air speed u is evaluated as a relative speed of the wing.

Note1. Pillow phenomenon may explain why air flow speed near the curved upper surface is accelerated and is higher if compared to the air flow  near the lower surface.

Note2: Air stream "sticks" to surface and bends down the near upper surface of the wing not due to Pillow phenomenon but due to Coanda effect.

Note3: Do not confuse Dynamic pressure with a pressure near airfoil surfaces. Air stream interaction with both airfoil surfaces has a complex dependence and gives some relative pressure, which may be applied to the normal of surface.

Ref:

Weltner, Klaus and Ingelman-Sundberg, Martin. Ref.. Misinterpretations of Bernoulli's Law:

Static pressure in a free air stream.
Static pressure is the pressure inside the stream measured by a manometer moving with the flow. At the same time, the static pressure is the pressure which is excerted on a plane parallel to the flow. Thus the static pressure within an air stream has to be measured carefully using a special probe. A thin disk must cover the probe except for the opening. The disk must be positioned parallel to the streaming flow, so that the flow is not interfered with.

If the static pressure is measured in the way outlined above within a free air stream generated by a fan or a hair dryer it can be shown that the static pressure is the same as in the surrounding atmosphere. Bernoulli's law cannot be applied to a free air stream because friction plays an important role. It may be noted that the situation is similar to the laminar flow of a liquid with viscosity inside a tube. The different velocity of the stream layers is caused by viscosity. The static pressure is the same throughout the whole cross-section. A free air stream in the atmosphere is exclusively decelerated by friction. If static pressure in a free air stream is equal to atmospheric pressure, some of the striking lecture demonstrations are interpreted incorrectly since the effects observed are not caused by Bernoulli's law.

Measurement of static pressure within a free stream 

A sufficiently sensitive manometer can be produced easily if not available in the lab. A fine pipe of glass is bent at one side to dip in a cup and to be fixed according to figure 7. The meniscus must be positioned in the middle of the pipe. The suitable inclination should be 1:15 - 1:30. A rubber tube connects the glass pipe with a probe. As has been pointed out before a flat disk must be glued on top of the probe leaving the opening free. The disk has to be held parallel to the streaming. If the static pressure is measured in such a way it can be shown that it is equal to the pressure in the environmental atmosphere.