Обучение чтению литературы на английском языке по специальности «Аэродинамика». В 2 ч. Ч. 1 (96

Drag is a mechanical force. It is generated by the interaction and contact of a solid body with a fluid (liquid or gas). For drag to be gener& ated, the solid body must be in contact with the fluid. If there is no fluid, there is no drag. Drag is generated by the difference in velocity between the solid object and the fluid. There must be motion between the object and the fluid. If there is no motion, there is no drag. It makes no differ& ence whether the object moves through a static fluid or whether the fluid moves past a static solid object. Drag acts in a direction that opposes the motion. (Lift acts perpendicular to the motion.)

We can think of drag as aerodynamic friction, and one of the sources of drag is the skin friction between the molecules of the air and the solid surface of the aircraft. Because the skin friction is an interaction between a solid and a gas, the magnitude of the skin friction depends on properties of both solid and gas. For the solid, a smooth, waxed surface produces less skin friction than a roughened surface. For the gas, the magnitude depends on the viscosity of the air and the relative magnitude of the viscous forces to the motion of the flow, expressed as the Reynolds number. Along the solid surface, a boundary layer of low energy flow is generated. And the magnitude of the skin friction depends on the state of this flow.

We can also think of drag as aerodynamic resistance to the motion of the object through the fluid. This source of drag depends on the shape of the aircraft and is called form drag. As air flows around a body, the local velocity and pressure are changed. Since pressure is a measure of the mo& mentum of the gas molecules and a change in momentum produces a force, a varying pressure distribution will produce a force on the body. We can determine the magnitude of the force by integrating (or adding up) the local pressure times the surface area around the entire body. The component of the aerodynamic force that is opposed to the motion is the drag; the component perpendicular to the motion is the lift. Both the lift and drag force act through the center of pressure of the object.

There is an additional drag component caused by the generation of lift . Aerodynamicists have named this component the induced drag. This drag occurs because the flow near the wing tips is distorted spanwise as a result of the pressure difference from the top to the bottom of the wing. Swirling vortices are formed at the wing tips, and there is an energy associated with these vortices. The induced drag is an indication of the amount of energy lost to the tip vortices. The magnitude of induced drag depends on the amount of lift being generated by the wing and on

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the wing geometry. Long, thin (chordwise) wings have low induced drag; short wings with a large chord have high induced drag.

Additional sources of drag include wave drag and ram drag. As an aircraft approaches the speed of sound, shock waves are generated along the surface. There is an additional drag penalty (called wave drag) that is associated with the formation of the shock waves. The magnitude of the wave drag depends on the Mach number of the flow. Ram drag is associated with slowing down the free stream air as air is brought inside the aircraft. Jet engines and cooling inlets on the aircraft are sources of ram drag.

Text IIC. What Is Lift?

Lift is the force that holds an aircraft in the air. Lift can be generated by any part of the airplane, but most of the lift on a normal airliner is generated by the wings. Lift is an aerodynamic force produced by the motion of a fluid past an object. Lift acts through the center of pressure of the object and is defined to be perpendicular to the flow direction.

How Is Lift Generated?

There are many explanations for the generation of lift found in encyclopedias, in basic physics textbooks, and on Web sites. Unfortunately, many of the explanations are misleading and incorrect. Theories on the generation of lift have become a source of great controversy and a topic for heated arguments. To help you understand lift and it’s origins, a series of pages will describe The various theories and how some of The popular theories fail.

Lift occurs when a flow of gas is turned by a solid object. The flow is turned in one direction, and the lift is generated in the opposite direction, according to Newton’s Third Law of action and reaction. Because air is a gas and the molecules are free to move about, any solid surface can deflect a flow. For an airfoil, both the upper and lower surfaces contribute to the flow turning. Neglecting the upper surface’s part in turning the flow leads to an incorrect theory of lift.

No Fluid, No Lift. Lift is a mechanical force. It is generated by the interaction and contact of a solid body with a fluid (liquid or gas). It is not generated by a force field, in the sense of a gravitational field, or an electromagnetic field, where one object can affect another object

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without being in physical contact. For lift to be generated, the solid body must be in contact with the fluid: no fluid, no lift. (The space shuttle does not stay in space because of lift from its wings but because of orbital mechanics related to its speed. Space is nearly a vacuum. Without air, there is no lift generated by the wings.)

No Motion, No Lift. Lift is generated by the difference in velocity between the solid object and the fluid. There must be motion between the object and the fluid: no motion, no lift. It makes no difference whether the object moves through a static fluid, or the fluid moves past a static solid object. Lift acts perpendicular to the motion. (Drag acts in the direction opposed to the motion.)

Text IID. What Is Weight?

Weight is the force generated by the gravitational attraction of the earth, on the airplane. We are more familiar with weight than with the other forces acting on an airplane, because each of us have our own weight which we can measure every another thing is light. But weight, the gravitational force, is fundamentally different from the aerodynamic forces, lift and drag. Aerodynamic forces are mechanical forces and the airplane has to be in physical contact with the air which generates the force. The gravitational force is a field force; the source of the force does not have to be in physical contact with the object (The airplane).

The nature of the gravitational force has been studied by scientists for many years and is still being investigated by theoretical physicists. For an object the size of an airplane, the descriptions given three hundred years ago by Sir Isaac Newton work quite well. Newton developed his theory of gravitation when he was only 23 years old and published the theories with his laws of motion some years later. The gravitational force between two objects depends on the mass of the objects and the inverse of the square of the distance between the objects. Larger objects create greater forces and the farther apart the objects are the weaker the attraction. Newton was able to express the relationship in a single weight equation.

For an airplane, weight is a force which is always directed towards the center of the earth. The magnitude of this force depends on the mass of all of the parts of the airplane itself, plus the amount of fuel, plus any payload on board (people, baggage, freight...). The weight is distributed throughout the airplane, but we can often think of it as collected and

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acting through a single point called the center of gravity. In flight, the airplane rotates about the center of gravity, but the direction of the weight force always remains toward the center of the earth. During a flight the aircraft burns up its fuel, so the weight of the airplane constantly changes. Also, the distribution of the weight and the center of gravity can change, so the pilot must constantly adjust the controls to keep the airplane balanced.

The dream remains that, if we could really understand gravity, we could create anti&gravity devices which would revolutionize travel through the sky. Unfortunately, anti&gravity devices only exist in science fiction. Machines like airplanes, or magnetic levitation devices, create forces opposed to the gravitational force, but they do not block out or eliminate the gravitational force.

UNIT III

New Words and Word Combinations

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1. Translate the following words and word combinations:

the value – the stream value – the free steam value; the drag – the friction drag – the skin friction drag;

the inlet – the aircraft inlet – the high speed aircraft inlet;

the variation – the velocity variation – the steamwise velocity variation.

2. Read and translate the text.

Text IIIA. Boundary Layer

As an object moves through a fluid, or as a fluid moves past an object, the molecules of the fluid near the object are disturbed and move around the object. Aerodynamic forces are generated between the fluid and the object. The magnitude of these forces depend on the shape of the object, the speed of the object, the mass of the fluid going by the object and on two other important properties of the fluid; the viscosity, or stickiness, and the compressibility, or springiness, of the fluid. Òî model these effects ðroðårly, aerodynamicists use similarity parameters which are ratios of these effects to other forces present in the problem. If two experiments have the same values for the similarity parameters, then the relative importance of the forces are being correctly modeled.

Aerodynamic forces depend in a complex way on the viscosity of the fluid. As the fluid moves past the object, the molecules right next to the surface stick to the surface. The molecules just above the surface are slowed down in their collisions with the molecules sticking to the surface. These molecules in turn slow down the flow just above them. The farther one moves away from the surface, the fewer the collisions affected by the object surface. This creates a thin layer of fluid near the surface in which the velocity changes from zero at the surface to the free stream value away from the surface. Engineers call this layer the boundary layer because it occurs on the boundary of the fluid.

The details of the flow within the boundary layer are very important for many problems in aerodynamics, including the development of a wing stall, the skin friction drag of an object, the heat transfer that occurs in high speed flight, and the performance of a high speed aircraft inlet. Unfortunately, the physical and mathematical details of boundary layer theory are beyond the scope of this article and are usually studied in late

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undergraduate or graduate school in college. We will only present some of the effects of the boundary layer.

On the figure we show the streamwise velocity variation from free stream to the surface. In reality, the effects are three dimensional. From the conservation of mass in three dimensions, a change in velocity in the streamwise direction causes a change in velocity in the other directions as well. There is a small component of velocity perpendicular to the surface which displaces or moves the flow above it. One can define the thickness of the boundary layer to be the amount of this displacement. The displacement thickness depends on the Reynolds number which is the ratio of inertial (resistant to change or motion) forces to viscous (heavy and gluey) forces and is given by the equation: Reynolds number (Re) equals velocity (V) times density (r) times a characteristic length (1) divided by the viscosity coefficient (µ):

Re = V · r · 1 / µ.

Boundary layers may be either laminar (layered), or turbulent (disordered) depending on the value of the Reynolds number. For lower Reynolds numbers, the boundary layer is laminar and the streamwise velocity changes uniformly as one moves away from the wall, as shown on the left side of the figure. For higher Reynolds numbers, the boundary layer is turbulent and the streamwise velocity is characterized by unsteady (changing with time) swirling flows inside the boundary layer. The external flow reacts to the edge of the boundary layer just as it would to the physical surface of an object. So the boundary layer gives any object an “effective” shape which is usually slightly different from the physical shape. To make things more confusing, the boundary layer may lift off or “separate” from the body and create an effective shape much different from the physical shape. This happens because the flow in the boundary has very low energy (relative to the free stream) and is more easily driven by changes in pressure. Flow separation is the reason for wing stall at high angle of attack. The effects of the boundary layer on lift are contained in the lift coefficient and the effects on drag are contained in the drag coefficient.

Historical note: The theory which describes boundary layer effects was first presented by Ludwig Prandtl in the early 1900’s. The general fluids equations had been known for many years, but solutions to the equations did not properly describe observed flow effects (like wing stalls) . Prandtl was the first to realize that the relative magnitude of

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the inertial and viscous forces changed from a layer very near the surface to a region far from the surface. He first proposed the interactively coupled, two layer solution which properly models many flow problems.

3.Answer the questions.

1.What does the term boundary layer stand for?

2.What does the magnitude of aerodynamic forces depend on?

3.What do aerodynamicists use to model the effects in the fluid?

4.When can the boundary layers be laminar? When can they be turbulent?

5.Where are the effects of the boundary layer on lift contained?

6.Who was the first to present the theory describing boundary layer affects?

4.Fill in the blanks with the words and word combinations from the box:

laminar, uniformly, angle of attack, boundary layer, lift coefficient, disturbed

1.Engineers call this layer the ______ because it occurs on the boundary of the fluid.

2.The molecules of the fluid near the object are ______ and move around the object.

3.For lower Reynolds numbers, the boundary layer is ______ .

4.Velocity changes from zero at the surface to the _______ away from the surface.

5.Flow separation is the reason for wing stall at high _______ .

6.The streamwise velocity changes _______ as one moves away from the wall.

7.The effects of the boundary layer on lift are contained in the ______ .

5.Complete the sentences using the information from the text.

1.Aerodynamic forces depend on _____.

2.In reality the effects in the boundary layer are _____.

3.The Reynolds number is ______.

4.Boundary layers may be either ______.

5.The boundary layer may lift off the body and create an effective shape different from the physical shape because ______.

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6.Translate the sentences into English.

1.Теория пограничного слоя не изучается в нашем курсе.

2.Это зависит от числа Рейнольдса.

3.Воздействие трехмерно.

4.Разделение потока было причиной этого явления.

5.Величина этой силы зависит от формы объекта.

6.Поток движется вдоль объекта.

7.Match the beginnings of the sentences with their ends.

8.Give the verbs in the brackets in the correct form.

1.Aerodynamic forces (to generate) between the fluid and the ob& ject.

2.The molecules (to slow down) the flow just above them.

3.The streamwise velocity (to change) uniformly.

4.The theory of boundary layer (to present) first by Ludwig Prandtl in 1900’s.

5.Solutions to the equations (not to describe) properly observed flow effects.

6.The effects of the boundary layer on lift (to contain) in the lift coefficient.

7.A change in velocity in the streamwise direction (to cause) a change in velocity in the other directions as well.

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8.The flow in the boundary (to have) low energy and easily (to drive) by changes in pressure.

9.Reynolds number (to give) by the equation.

9.Read and translate the text. Write out the terms from it.

Text IIIB. Equation of State

Ideal Gas. Properties

V = C2 · T

Density = r, Pressure = p, Temperature = Ò, Volume = V, Mass = m. Observation.

Boil: For a given mass, at constant temperature, the pressure times the volume is a constant:

p · V = Ñ1.

Charles and Gay&Lussañ: For a given mass, at constant pressure, the volume is directly proportional to the temperature:

Combine:

pV / Ò = nR R = 8.31 J / mole / K(Universal)

pV = nRT, n = number of moles.

Divide by mass:

Specific Volume = v = volume / mass = 1 / r

pv = nRT / m or pv = RT op = RrT,

R = Constant value for each gas = 286 kJ / kg / K (for air).

Air is a gas. Gases have various properties that we can observe with our senses, including the gas pressure (p), temperature (Ò), mass (m), and volume (V) that contains the gas. Careful, scientific observation has determined that these variables are related to one another, and the values of these properties determine the state of the gas.

If we fix any two of the properties we can determine the nature of the relationship between the other two. If the pressure and temperature are held constant, the volume of the gas depends directly on the mass, or amount of gas. This allows us to define a single additional property called the gas density (r), which is the ratio of mass to volume. If the mass and

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temperature are held constant, the product of the pressure and volume are observed to be nearly constant for a real gas. (The product of pressure and volume is exactly a constant for an ideal gas.) This relationship between pressure and volume is called Boyle’s Law in honor of Robert Boyle who first observed it in 1660. Finally, if the mass and pressure are held constant, the volume is directly proportional to the temperature for an ideal gas. This relationship is called Charles and Gay&Lussac’s Law in honor of the two French scientists who discovered the relationship.

The gas laws of Boyle and Charles and Gay&Lussac can be combined into a single equation of state: p · V / Ò = n · R where “ · ” denotes multi& plication and / denotes division. To account for the effects of mass, we have defined the constant to contain two parts: a universal constant (R) and the mass of the gas expressed in moles (n).

Performing a little algebra, we obtain the more familiar form:

p · V = n · R · T.

Aerodynamicists use a slightly different form of the equation of state that is specialized for air. If we divide both sides of the general equation by the mass of the gas, the volume becomes the specific volume, which is the inverse of the gas density. We also define a new gas constant (R), which is equal to the universal gas constant divided by the mass per mole of the gas. The value of the new constant depends on the type of gas as opposed to the universal gas constant, which is the same for all gases. The value of the equation of state for air is given as 286 kilo Joule per kilogram per degree Kelvin . The equation of state can be written in terms of the specific volume or in terms of the air density as

p · v = R · T or p = r · R · T.

Notice that the equation of state given here applies only to an ideal gas, or a real gas that behaves like an ideal gas. There are in fact many different forms for the equation of state for different gases. Also be aware that the temperature given in the equation of state must be an absolute temperature that begins at absolute zero. In the metric system of units, we must specify the temperature in degrees Kelvin (not Celsius). In the English system, absolute temperature is in degrees Rankine (not Fahrenheit).

10.Give a summary of text IIIB.

11.Read and translate the text using a dictionary if necessary.

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