Laminar is an air flow in which the streams of air move in the same direction and are parallel to each other. When the speed increases to a certain value, the air stream trickles, in addition to the translational speed, also acquire rapidly changing speeds perpendicular to the direction of translational motion. A flow is formed, which is called turbulent, that is, chaotic.

boundary layer

The boundary layer is the layer in which the air velocity varies from zero to a value close to the local air velocity.

When an air flow flows around a body (Fig. 5), air particles do not slide over the surface of the body, but are decelerated, and the air velocity near the body surface becomes equal to zero. When moving away from the surface of the body, the air speed increases from zero to the speed of the air flow.

The thickness of the boundary layer is measured in millimeters and depends on the viscosity and pressure of the air, on the profile of the body, the state of its surface and the position of the body in the air stream. The thickness of the boundary layer gradually increases from the leading to the trailing edge. In the boundary layer, the nature of the movement of air particles differs from the nature of the movement outside it.

Consider an air particle A (Fig. 6), which is located between air streams with velocities U1 and U2, due to the difference in these velocities applied to opposite points of the particle, it rotates and the more, the closer this particle is to the surface of the body (where the difference the highest speed). When moving away from the surface of the body, the rotational motion of the particle slows down and becomes equal to zero due to the equality of the air flow velocity and the air velocity of the boundary layer.

Behind the body, the boundary layer passes into a wake, which blurs and disappears as it moves away from the body. The turbulence in the wake hits the tail of the aircraft and reduces its efficiency, causing shaking (Buffing phenomenon).

The boundary layer is divided into laminar and turbulent (Fig. 7). With a steady laminar flow of the boundary layer, only internal friction forces appear due to the viscosity of the air, so the air resistance in the laminar layer is small.

Rice. 5

Rice. 6 Air flow around a body - flow deceleration in the boundary layer

Rice. 7

In a turbulent boundary layer, there is a continuous movement of air streams in all directions, which requires more energy to maintain the chaotic vortex motion and, as a result, a greater resistance of the air flow to the moving body is created.

The coefficient Cf is used to determine the nature of the boundary layer. A body of a certain configuration has its own coefficient. So, for example, for a flat plate, the drag coefficient of the laminar boundary layer is:

for turbulent layer

where Re is the Reynolds number, which expresses the ratio of inertial forces to frictional forces and determines the ratio of two components - profile resistance (shape resistance) and frictional resistance. The Reynolds number Re is determined by the formula:

where V is the air flow velocity,

I - character of body size,

kinetic coefficient of viscosity of air friction forces.

When an air flow flows around a body at a certain point, the boundary layer changes from laminar to turbulent. This point is called the transition point. Its location on the surface of the body profile depends on the viscosity and pressure of the air, the speed of the air streams, the shape of the body and its position in the air flow, and also on the surface roughness. When creating wing profiles, designers tend to take this point as far as possible from the leading edge of the profile, thereby reducing the friction drag. For this purpose, special laminated profiles are used to increase the smoothness of the wing surface and a number of other measures.

With an increase in the speed of the air flow or an increase in the angle of the body relative to the air flow to a certain value, at some point, the boundary layer is separated from the surface, while the pressure behind this point sharply decreases.

As a result of the fact that the pressure at the trailing edge of the body is greater than behind the separation point, there is a reverse flow of air from the zone of higher pressure to the zone of lower pressure to the separation point, which entails separation of the air flow from the body surface (Fig. 8).

A laminar boundary layer separates more easily from the body surface than a turbulent one.

Continuity equation for an air stream jet

The equation of the continuity of the jet of air flow (the constancy of air flow) is an equation of aerodynamics, which follows from the basic laws of physics - the conservation of mass and inertia - and establishes the relationship between the density, speed and cross-sectional area of ​​the jet of air flow.

Rice. eight

Rice. nine

When considering it, the condition is accepted that the studied air does not have the property of compressibility (Fig. 9).

In a jet of variable cross section, a second volume of air flows through section I for a certain period of time, this volume is equal to the product of the air flow velocity and cross section F.

The second mass air flow m is equal to the product of the second air flow and the air flow density p of the jet. According to the law of conservation of energy, the mass of the air flow of the stream m1 flowing through section I (F1) is equal to the mass m2 of this flow flowing through section II (F2), provided that the air flow is steady:

m1=m2=const, (1.7)

m1F1V1=m2F2V2=const. (1.8)

This expression is called the equation of the continuity of the jet of the air stream of the stream.

F1V1=F2V2= const. (1.9)

So, it can be seen from the formula that the same volume of air passes through different sections of the stream in a certain unit of time (second), but at different speeds.

We write equation (1.9) in the following form:

It can be seen from the formula that the airflow velocity of the jet is inversely proportional to the cross-sectional area of ​​the jet and vice versa.

Thus, the equation of the continuity of the jet of air flow establishes the relationship between the cross section of the jet and the speed, provided that the air flow of the jet is steady.

Static pressure and velocity head Bernoulli equation

air plane aerodynamics

The aircraft, which is in a stationary or moving air flow relative to it, experiences pressure from the latter, in the first case (when the air flow is stationary) it is static pressure and in the second case (when the air flow is moving) it is dynamic pressure, it is often called speed pressure. The static pressure in a stream is similar to the pressure of a liquid at rest (water, gas). For example: water in a pipe, it can be at rest or in motion, in both cases the walls of the pipe are under pressure from the water. In the case of water movement, the pressure will be somewhat less, since a velocity pressure has appeared.

According to the law of conservation of energy, the energy of an air stream in various sections of an air stream is the sum of the kinetic energy of the stream, the potential energy of the pressure forces, the internal energy of the stream and the energy of the body position. This amount is a constant value:

Ekin+Ep+Evn+En=const (1.10)

Kinetic energy (Ekin) - the ability of a moving air stream to do work. She is equal

where m is the mass of air, kgf s2m; V-speed of air flow, m/s. If instead of the mass m we substitute the mass density of air p, then we get the formula for determining the velocity head q (in kgf / m2)

Potential energy Ep - the ability of the air flow to do work under the influence of static pressure forces. It is equal to (in kgf-m)

where Р - air pressure, kgf/m2; F is the cross-sectional area of ​​the air flow filament, m2; S is the path traveled by 1 kg of air through a given section, m; the product SF is called the specific volume and is denoted by v, substituting the value of the specific volume of air into formula (1.13), we obtain

The internal energy Evn is the ability of a gas to do work when its temperature changes:

where Cv is the heat capacity of air at a constant volume, cal / kg-deg; T-temperature on the Kelvin scale, K; A is the thermal equivalent of mechanical work (cal-kg-m).

It can be seen from the equation that the internal energy of the air flow is directly proportional to its temperature.

Position energy En is the ability of air to do work when the position of the center of gravity of a given air mass changes when it rises to a certain height and is equal to

where h is the change in height, m.

In view of the scanty small values ​​of the separation of the centers of gravity of air masses along the height in a trickle of the air flow, this energy is neglected in aerodynamics.

Considering all types of energy in relation to certain conditions, it is possible to formulate Bernoulli's law, which establishes a relationship between the static pressure in a trickle of the air flow and the velocity pressure.

Consider a pipe (Fig. 10) of variable diameter (1, 2, 3) in which an air flow moves. Manometers are used to measure the pressure in the sections under consideration. Analyzing the readings of pressure gauges, we can conclude that the lowest dynamic pressure is shown by a pressure gauge of section 3-3. This means that when the pipe narrows, the speed of the air flow increases and the pressure drops.

Rice. ten

The reason for the pressure drop is that the air flow does not produce any work (friction is not taken into account) and therefore the total energy of the air flow remains constant. If we consider the temperature, density and volume of the air flow in different sections to be constant (T1=T2=T3; p1=p2=p3, V1=V2=V3), then the internal energy can be ignored.

This means that in this case, the transition of the kinetic energy of the air flow into potential energy and vice versa is possible.

When the speed of the air flow increases, then the velocity head increases and, accordingly, the kinetic energy of this air flow.

We substitute the values ​​from formulas (1.11), (1.12), (1.13), (1.14), (1.15) into formula (1.10), taking into account that we neglect the internal energy and position energy, transforming equation (1.10), we obtain

This equation for any section of a trickle of air is written as follows:

This type of equation is the simplest mathematical Bernoulli equation and shows that the sum of the static and dynamic pressures for any section of a steady air flow stream is a constant value. Compressibility is not taken into account in this case. Appropriate corrections are made when compressibility is taken into account.

For clarity of Bernoulli's law, you can conduct an experiment. Take two sheets of paper, holding them parallel to each other at a short distance, blow into the gap between them.

Rice. eleven

The leaves are getting closer. The reason for their convergence is that on the outer side of the sheets the pressure is atmospheric, and in the gap between them, due to the presence of a high-speed air pressure, the pressure decreased and became less than atmospheric. Under the influence of the pressure difference, the sheets of paper bend inward.

wind tunnels

An experimental setup for studying the phenomena and processes that accompany the flow of gas around bodies is called a wind tunnel. The principle of operation of wind tunnels is based on the principle of Galileo's relativity: instead of the motion of a body in a stationary medium, a gas flow around a stationary body is studied. In wind tunnels, the aerodynamic forces acting on the aircraft and the moments are experimentally determined, the pressure and temperature distributions over its surface are studied, the flow pattern around the body is observed, aeroelasticity is studied etc.

Wind tunnels depending on the range of Mach numbers M are divided into subsonic (M=0.15-0.7), transonic (M=0.7-13), supersonic (M=1.3-5) and hypersonic (M= 5-25), according to the principle of operation - into compressor rooms (continuous operation), in which the air flow is created by a special compressor, and balloon ones with increased pressure, according to the layout of the circuit - into closed and open ones.

Compressor pipes have high efficiency, they are easy to use, but require the creation of unique compressors with big expenses gas and high power. Balloon wind tunnels are less economical than compressor wind tunnels, since part of the energy is lost when gas is throttled. In addition, the duration of operation of balloon wind tunnels is limited by the gas supply in the cylinders and ranges from tens of seconds to several minutes for various wind tunnels.

The wide distribution of balloon wind tunnels is due to the fact that they are simpler in design and the compressor power required to fill the balloons is relatively small. In wind tunnels with a closed loop, a significant part of the kinetic energy remaining in the gas flow after its passage through the working area is used, which increases the efficiency of the wind tunnel. In this case, however, it is necessary to increase the overall dimensions of the installation.

In subsonic wind tunnels, the aerodynamic characteristics of subsonic helicopters, as well as the characteristics of supersonic aircraft in takeoff and landing modes, are studied. In addition, they are used to study the flow around cars and other ground Vehicle, buildings, monuments, bridges and other objects Figure shows a diagram of a subsonic wind tunnel with a closed loop.

Rice. 12

1 - honeycomb 2 - grids 3 - prechamber 4 - confuser 5 - flow direction 6 - working part with model 7 - diffuser, 8 - bend with rotary blades, 9 - compressor 10 - air cooler

Rice. thirteen

1 - honeycomb 2 - screens 3 - prechamber 4 confuser 5 perforated working part with model 6 ejector 7 diffuser 8 elbow with guide vanes 9 air outlet 10 - air supply from cylinders

Rice. fourteen

1 - compressed air cylinder 2 - pipeline 3 - control throttle 4 - leveling grids 5 - honeycomb 6 - deturbulent grids 7 - prechamber 8 - confuser 9 - supersonic nozzle 10 - working part with model 11 - supersonic diffuser 12 - subsonic diffuser 13 - release into the atmosphere

Rice. fifteen

1 - cylinder with high pressure 2 - pipeline 3 - control throttle 4 - heater 5 - prechamber with honeycomb and grids 6 - hypersonic axisymmetric nozzle 7 - working part with model 8 - hypersonic axisymmetric diffuser 9 - air cooler 10 - flow direction 11 - air supply into ejectors 12 - ejectors 13 - shutters 14 - vacuum vessel 15 - subsonic diffuser

The study of the properties of liquid and gas flows is very important for industry and public utilities. Laminar and turbulent flow affects the speed of transportation of water, oil, natural gas through pipelines for various purposes, and affects other parameters. The science of hydrodynamics deals with these problems.

Classification

In the scientific community, the flow regimes of liquids and gases are divided into two completely different classes:

• laminar (jet);
• turbulent.

There is also a transitional stage. By the way, the term "liquid" has a broad meaning: it can be incompressible (this is actually a liquid), compressible (gas), conductive, etc.

Background

Even Mendeleev in 1880 expressed the idea of ​​the existence of two opposite regimes of currents. The British physicist and engineer Osborne Reynolds studied this issue in more detail, completing his research in 1883. First, practically, and then with the help of formulas, he established that at a low flow velocity, the movement of liquids acquires a laminar shape: layers (particle flows) almost do not mix and move along parallel trajectories. However, after overcoming a certain critical value (it is different for different conditions), called the Reynolds number, the fluid flow regimes change: the jet stream becomes chaotic, vortex - that is, turbulent. As it turned out, these parameters are also characteristic of gases to a certain extent.

The practical calculations of the English scientist showed that the behavior of, for example, water, strongly depends on the shape and size of the reservoir (pipe, channel, capillary, etc.) through which it flows. In pipes with a circular cross section (such are used for the installation of pressure pipelines), their Reynolds number - the formula is described as follows: Re \u003d 2300. For flow along an open channel, it is different: Re \u003d 900. At lower values ​​of Re, the flow will be ordered, at large - chaotic .

laminar flow

The difference between a laminar flow and a turbulent flow is in the nature and direction of water (gas) flows. They move in layers without mixing and without pulsations. In other words, the movement is even, without erratic jumps in pressure, direction and speed.

The laminar flow of a liquid is formed, for example, in narrow living beings, capillaries of plants and, under comparable conditions, in the flow of very viscous liquids (fuel oil through a pipeline). To visually see the jet stream, it is enough to slightly open the tap - the water will flow calmly, evenly, without mixing. If the faucet is turned off to the end, the pressure in the system will increase and the flow will become chaotic.

turbulent flow

Unlike laminar flow, in which nearby particles move along almost parallel trajectories, the turbulent flow of a fluid is disordered. If we use the Lagrange approach, then the trajectories of particles can arbitrarily intersect and behave quite unpredictably. The motions of liquids and gases under these conditions are always unsteady, and the parameters of these unsteadiness can have a very wide range.

How the laminar flow of a gas turns into a turbulent one can be traced by the example of a wisp of smoke from a burning cigarette in still air. Initially, the particles move almost in parallel along trajectories that do not change in time. The smoke seems to be still. Then, in some place, large vortices suddenly appear, which move completely randomly. These vortices break up into smaller ones, those into even smaller ones, and so on. Eventually, the smoke practically mixes with the surrounding air.

Cycles of turbulence

The above example is textbook, and from his observation, scientists have drawn the following conclusions:

1. Laminar and turbulent flow are probabilistic in nature: the transition from one regime to another does not occur at a precisely specified place, but at a rather arbitrary, random place.
2. First, large eddies appear, the size of which is larger than the size of the smoke plume. The motion becomes unsteady and strongly anisotropic. Large streams lose their stability and break up into smaller and smaller ones. Thus, a whole hierarchy of vortices arises. The energy of their movement is transferred from large to small, and at the end of this process it disappears - energy dissipation occurs at small scales.
3. The turbulent flow regime is random in nature: one or another vortex can be in a completely arbitrary, unpredictable place.
4. The mixing of smoke with the surrounding air practically does not occur in the laminar regime, and in the turbulent regime it is very intense.
5. Despite the fact that the boundary conditions are stationary, the turbulence itself has a pronounced non-stationary character - all gas-dynamic parameters change with time.

There is another important property of turbulence: it is always three-dimensional. Even if we consider a one-dimensional flow in a pipe or a two-dimensional boundary layer, the motion of turbulent eddies still occurs in the directions of all three coordinate axes.

Reynolds number: formula

The transition from laminar to turbulent is characterized by the so-called critical Reynolds number:

Re cr = (ρuL/µ) cr,

where ρ is the flux density, u is the characteristic flux velocity; L is the characteristic size of the flow, µ is the coefficient cr is the flow through a pipe with a circular cross section.

For example, for a flow with a velocity u in a pipe, Osborne Reynolds is used as L and showed that in this case 2300

A similar result is obtained in the boundary layer on the plate. As a characteristic dimension, the distance from the leading edge of the plate is taken, and then: 3 × 10 5

The concept of speed perturbation

Laminar and turbulent fluid flow, and, accordingly, the critical value of the Reynolds number (Re) depend on a larger number of factors: on the pressure gradient, the height of roughness bumps, the intensity of turbulence in the external flow, temperature difference, etc. For convenience, these total factors are also called velocity perturbation , since they have a certain effect on the flow rate. If this perturbation is small, it can be extinguished by viscous forces tending to equalize the velocity field. With large disturbances, the flow can lose stability, and turbulence occurs.

Considering that the physical meaning of the Reynolds number is the ratio of inertial and viscous forces, the perturbation of flows falls under the formula:

Re = ρuL/µ = ρu 2 /(µ×(u/L)).

The numerator contains twice the velocity head, and the denominator is a value that is of the order of the friction stress if the thickness of the boundary layer is taken as L. Velocity pressure tends to destroy the balance, and counteract this. However, it is not clear why (or velocity head) lead to changes only when they are 1000 times greater than the viscous forces.

Calculations and facts

It would probably be more convenient to use as the characteristic velocity in Re cr not the absolute flow velocity u, but the perturbation of the velocity. In this case, the critical Reynolds number will be about 10, that is, when the velocity pressure perturbation exceeds viscous stresses by a factor of 5, the laminar flow of the fluid flows into a turbulent one. This definition of Re, in the opinion of a number of scientists, explains well the following experimentally confirmed facts.

For an ideally uniform velocity profile on an ideally smooth surface, the traditionally determined number Re cr tends to infinity, i.e., no transition to turbulence is actually observed. But the Reynolds number, determined by the magnitude of the velocity perturbation, is less than the critical one, which is 10.

In the presence of artificial turbulators that cause a speed surge comparable to the main speed, the flow becomes turbulent at much lower values ​​of the Reynolds number than Re cr , determined from the absolute value of the speed. This makes it possible to use the value of the coefficient Re cr = 10, where the absolute value of the velocity perturbation caused by the above reasons is used as the characteristic velocity.

Stability of the laminar flow regime in the pipeline

Laminar and turbulent flow is characteristic of all types of liquids and gases under different conditions. In nature, laminar flows are rare and are typical, for example, for narrow underground flows in flat conditions. Scientists are much more concerned about this issue in the context of practical application for transporting water, oil, gas and other technical liquids through pipelines.

The question of the stability of a laminar flow is closely related to the study of the perturbed motion of the main flow. It is established that it is subjected to the influence of so-called small perturbations. Depending on whether they fade or grow over time, the main current is considered stable or unstable.

The flow of compressible and incompressible fluids

One of the factors affecting the laminar and turbulent flow of a fluid is its compressibility. This property of a fluid is especially important when studying the stability of unsteady processes with a rapid change in the main flow.

Studies show that the laminar flow of an incompressible fluid in cylindrical pipes is resistant to relatively small axisymmetric and nonaxisymmetric perturbations in time and space.

Recently, calculations have been carried out on the effect of axisymmetric perturbations on the stability of the flow in the inlet part of a cylindrical pipe, where the main flow depends on two coordinates. In this case, the coordinate along the pipe axis is considered as a parameter on which the velocity profile along the radius of the main flow pipe depends.

Conclusion

Despite centuries of study, it cannot be said that both laminar and turbulent flow have been thoroughly studied. Experimental studies at the microlevel raise new questions that require a reasoned calculation justification. The nature of research is also of practical use: thousands of kilometers of water, oil, gas, product pipelines have been laid in the world. The more technical solutions are introduced to reduce turbulence during transportation, the more effective it will be.

To reduce pollution in high class clean rooms, special ventilation systems are used, in which the air flow moves from top to bottom without turbulences, i.e. laminar. With laminar air flow, dirt particles from people and equipment do not scatter throughout the room, but are collected by the flow near the floor.

Constructions

In general, cleanrooms include the following basic elements:

enclosing wall structures (framework, blind and glazed wall panels, doors, windows);

hermetic panel and cassette ceilings with built-in grid lights;

antistatic floors;

Clean-Zone Floor Covering Clean-Zone is supplied in standard rolls, to be professionally installed as a wall-to-wall floor covering, creating a permanent and unavoidable trap for dirt.

air preparation system (supply, exhaust and recirculation ventilation units, air intake devices, air distributors with final filters, air control devices, sensor equipment and automation elements, etc.);

control system for engineering systems of clean rooms;

air locks;

transfer windows;

filter-fan modules for creating clean zones inside clean rooms.

Electronics industry is one of the largest consumers of clean rooms in the world. The purity requirements in this industry are the most stringent. The trend of constant growth of these requirements has led to qualitatively new approaches to the creation of clean environments. The essence of these approaches is to create isolating technologies, i.e. in the physical separation of a certain volume of clean air from the environment. This division, as a rule, hermetic, made it possible to exclude the influence of one of the most intense sources of pollution - man. The use of isolation technologies entails the widespread introduction of automation and robotics. The use of clean rooms in microelectronics has its own characteristics: the requirements for the cleanliness of the air in terms of aerosol particles come to the fore. Increased requirements are also placed on the cleanroom grounding system, especially in terms of ensuring the absence of static electricity. In microelectronics, it is required to create clean rooms of the highest purity classes with perforated raised floors to improve air flow lines, i.e. increase the unidirectional flow.

Clean production facilities should provide conditions for maximum cleanliness of production; provide insulation of the internal volume; entrance to clean rooms through a special vestibule (gateway).

The pressure in a clean room should be greater than atmospheric pressure to push dust out of the room. In the lock, personnel clothes are blown to remove dust particles.

Clean rooms create laminar air flows, and turbulent flows, which are created by rotating and moving parts of the equipment, are unacceptable. It is required to ensure that there are no heated things that contribute to the formation of convection currents.

Usually used slatted floor and slatted ceiling.

Minimal equipment is placed in clean rooms

Since the production of clean rooms is very expensive, local dedusting zones are used.

One of the effective ways to reduce costs when creating cleanroom complexes is zoning of a clean room into local areas, which may differ from each other both in terms of air purity class and functional purpose (protection of the product only, or protection of both the product and the environment).

Thus, inside a clean room of a low cleanliness class, clean zones with a higher cleanliness class than the room where they are located can be created above the critical places of the technological process.

The main purpose of clean zones:

maintaining the specified parameters of the air environment in the local working space;

protecting the product from environmental influences.

According to the definition given in GOST R ISO 14644-1-2000, a clean area is a defined space in which the concentration of airborne particles is controlled, designed and used to minimize the entry, exit and retention of particles within the area, and allowing other parameters, such as temperature, humidity and pressure, to be controlled as necessary.

Clean zones can be structurally implemented either as part of the overall cleanroom ventilation system or as stand-alone products.

The first method is applicable when the location of clean zones is laid down at the design stage of creating a clean room and is not subject to change for the entire period of its operation, as well as if it is necessary to supply fresh air to the working space of a clean zone.

The second method involves the possibility of changing the location of clean zones, which provides more opportunities for changing the technological process and upgrading equipment. At the same time, clean zones, made as independent products, can either be fixed to the load-bearing structures of the clean room, or be mobile autonomous products that can move inside the clean room.

Most often, clean production conditions are used with a minimum use of personnel, using semi-automatic machines. Often use local settings. Recently, cluster installations (cluster) have been used.

Specifications:

1 Ultimate pressure in a clean, empty and degassed chamber, Pa 1.33x10-3

2 Pressure recovery time 1.33x10-3 Pa, min 30

3 Working chamber dimensions, mm Diameter Height 900 1000

4 Number of plasma accelerators with metal cathodes (SPU-M) with plasma flow separation, pcs 3

5 Number of pulsed plasma accelerators with graphite cathodes (IPU-S) with plasma flow separation, pcs 4

6 Number of extended ion sources for cleaning and assistance (RIF type), pcs 1

7 Substrate heating, 0С 250

8 Technological equipment: Single planetarium, pcs. Double planetary, pcs 1 1

9 Process gas purge system

10 System of control and management of the technological cycle

11 High vacuum pumping: two diffusion pumps operating in parallel NVDM-400 with a capacity of 7000 l/s each

12 Fore-vacuum pumping: AVR-150 fore-vacuum unit with a capacity of 150 l/s

13 Maximum electrical power consumed by the vacuum unit, kW, not more than 50

14 Area occupied by the vacuum unit, m2 25

Lung distensibility quantitatively characterizes the extensibility of lung tissue at any moment of change in their volume during the inhalation and exhalation phases. Therefore, extensibility is a static characteristic of the elastic properties of lung tissue. However, during breathing, there is resistance to the movement of the external respiration apparatus, which determines its dynamic characteristics, among which the most important is resistance the flow of air as it moves through the airways of the lungs.

The movement of air from the external environment through the respiratory tract to the alveoli and vice versa is influenced by the pressure gradient: in this case, air moves from an area of ​​high pressure to an area of ​​low pressure. When inhaling, the air pressure in the alveolar space is less than atmospheric pressure, and when exhaling, vice versa. Airway resistance air flow depends on the pressure gradient between the oral cavity and the alveolar space.

Airflow through the respiratory tract can be laminar, turbulent and transitional between these types. Air moves in the airways mainly in a laminar flow, the speed of which is higher in the center of these tubes and lower near their walls. With laminar air flow, its velocity is linearly dependent on the pressure gradient along the airways. In places where the airways divide (bifurcations), the laminar air flow becomes turbulent. When turbulent flow occurs in the airways, a breath noise is produced that can be heard in the lungs with a stethoscope. The resistance to laminar gas flow in a pipe is determined by its diameter. Therefore, according to Poiseuille's law, the amount of airway resistance to air flow is proportional to their diameter raised to the fourth power. Since the resistance of the airways is inversely related to their diameter to the fourth power, this indicator most significantly depends on changes in the diameter of the airways caused, for example, by the release of mucus from the mucous membrane or narrowing of the bronchial lumen. The total cross-sectional diameter of the airways increases in the direction from the trachea to the periphery of the lung and becomes as large as possible in the terminal airways, which causes a sharp decrease in the resistance to air flow and its speed in these parts of the lungs. Thus, the linear velocity of the inhaled air flow in the trachea and main bronchi is approximately 100 cm/s. At the border of the airway and transition zones of the respiratory tract, the linear velocity of the air flow is about 1 cm / s, in the respiratory bronchi it decreases to 0.2 cm / s, and in the alveolar passages and sacs - up to 0.02 cm / s. Such a low airflow rate in the alveolar ducts and sacs causes a slight resistance moving air and is not accompanied by a significant expenditure of energy of muscle contraction.

On the contrary, the largest airway resistance air flow occurs at the level of segmental bronchi due to the presence in their mucous membrane of the secretory epithelium and a well-developed smooth muscle layer, i.e., factors that most affect both the diameter of the airways and the resistance to air flow in them. One of the functions of the respiratory muscles is to overcome this resistance.

There are two different forms, two modes of fluid flow: laminar and turbulent flow. The flow is called laminar (layered) if each selected thin layer slides along the flow relative to the neighboring ones without mixing with them, and turbulent (vortex) if intensive vortex formation and liquid (gas) mixing occur along the flow.

Laminar fluid flow is observed at low velocities of its movement. In laminar flow, the trajectories of all particles are parallel and follow the flow boundaries in their shape. In a round pipe, for example, the liquid moves in cylindrical layers, the generatrix of which is parallel to the walls and axis of the pipe. In a rectangular, infinitely wide channel, the liquid moves, as it were, in layers parallel to its bottom. At each point in the flow, the velocity remains constant along the direction. If the speed at the same time does not change with time and in magnitude, the movement is called steady. For laminar motion in a pipe, the diagram of the distribution of velocity in the cross section has the form of a parabola with a maximum velocity on the axis of the pipe and with a zero value at the walls, where an adhering liquid layer is formed. The outer layer of liquid adjacent to the surface of the pipe in which it flows, due to the forces of molecular cohesion, adheres to it and remains immobile. The velocities of subsequent layers are the greater, the greater their distance from the pipe surface, and the layer moving along the pipe axis has the highest speed. The profile of the average velocity of the turbulent flow in pipes (Fig. 53) differs from the parabolic profile of the corresponding laminar flow by a faster increase in the velocity υ.

Figure 9Profiles (diagrams) of laminar and turbulent fluid flows in pipes

The average value of the velocity in the cross section of a round pipe with a steady laminar flow is determined by the Hagen-Poiseuille law:

(8)

where p 1 and p 2 - pressure in two cross sections of the pipe spaced from each other at a distance Δx; r - pipe radius; η is the viscosity coefficient.

The Hagen-Poiseuille law can be easily verified. It turns out that for ordinary liquids it is valid only at low flow rates or small pipe sizes. More precisely, the Hagen-Poiseuille law is satisfied only for small values ​​of the Reynolds number:

(9)

where υ is the average speed in the cross section of the pipe; l- characteristic size, in this case - the diameter of the pipe; ν - coefficient of kinematic viscosity.

The English scientist Osborne Reynolds (1842 - 1912) in 1883 made an experiment according to the following scheme: at the entrance to a pipe through which a steady stream of liquid flows, a thin tube was placed so that its hole was on the axis of the tube. Paint was fed through the tube into the liquid stream. As long as the laminar flow existed, the paint moved approximately along the axis of the pipe in the form of a thin, sharply limited strip. Then, starting from a certain value of velocity, which Reynolds called critical, undulating perturbations and individual rapidly damping vortices arose on the strip. As the speed increased, their number became greater, and they began to develop. At a certain velocity, the strip broke up into separate vortices, which propagated throughout the entire thickness of the liquid flow, causing intense mixing and coloring of the entire liquid. This flow has been called turbulent .

Starting from the critical value of the speed, the Hagen-Poiseuille law was also violated. Repeating experiments with pipes of different diameters, with different liquids, Reynolds found that the critical velocity at which the parallelism of the flow velocity vectors is violated varied depending on the size of the flow and the viscosity of the liquid, but always in such a way that the dimensionless number
took on a certain constant value in the region of transition from laminar to turbulent flow.

The English scientist O. Reynolds (1842 - 1912) proved that the nature of the flow depends on a dimensionless quantity called the Reynolds number:

(10)

where ν = η/ρ is the kinematic viscosity, ρ is the liquid density, υ av is the liquid velocity averaged over the pipe section, l- characteristic linear dimension, for example, the diameter of the pipe.

Thus, up to a certain value of the number Re, a stable laminar flow exists, and then, in a certain range of values ​​of this number, the laminar flow ceases to be stable and separate, more or less rapidly damping perturbations appear in the flow. Reynolds called these values ​​of the number critical Re cr. With a further increase in the value of the Reynolds number, the motion becomes turbulent. The area of ​​critical Re values ​​usually lies between 1500-2500. It should be noted that the value of Re cr is influenced by the nature of the entrance to the pipe and the degree of roughness of its walls. With very smooth walls and a particularly smooth pipe entry, the critical value of the Reynolds number could be raised to 20,000, and if the pipe entrance has sharp edges, burrs, etc., or the pipe walls are rough, the Re cr value can drop to 800-1000 .

In turbulent flow, fluid particles acquire velocity components perpendicular to the flow, so they can move from one layer to another. The velocity of liquid particles increases rapidly as they move away from the pipe surface, then changes quite slightly. Since the particles of the liquid pass from one layer to another, their velocities in different layers differ little. Due to the large velocity gradient near the pipe surface, vortices are usually formed.

Turbulent flow of liquids is the most common in nature and technology. The flow of air in atmosphere, water in the seas and rivers, in channels, in pipes is always turbulent. In nature, laminar motion occurs during water filtration in fine pores of fine-grained soils.

The study of turbulent flow and the construction of its theory are extremely complicated. The experimental and mathematical difficulties of these investigations have so far only been partially overcome. Therefore, a number of practically important problems (the flow of water in canals and rivers, the movement of an aircraft of a given profile in the air, etc.) have to be solved either approximately or by testing the corresponding models in special hydrodynamic tubes. For the transition from the results obtained on the model to the phenomenon in nature, the so-called similarity theory is used. The Reynolds number is one of the main criteria for the similarity of a viscous fluid flow. Therefore, its definition is practically very important. In this work, a transition from laminar to turbulent flow is observed and several values ​​of the Reynolds number are determined: in the region of laminar flow, in the transition region (critical flow), and in turbulent flow.