Laminar flow - what it looks like. Airway resistance. Lung resistance. Air flow. Laminar flow. Turbulent airflow Laminar airflow in clean rooms

Over the past ten years, abroad and in our country, the number of purulent-inflammatory diseases due to infections has increased, which have acquired the name "nosocomial" (nosocomial infections) - as defined by the World Health Organization (WHO). According to the analysis of diseases caused by nosocomial infections, we can say that their duration and frequency directly depend on the state of the air environment in hospital premises. In order to provide the required microclimate parameters in operating rooms (and industrial clean rooms), unidirectional air diffusers are used. As shown by the results of environmental monitoring and analysis of the movement of air flows, the operation of such distributors can provide the required microclimate parameters, but negatively affects the bacteriological composition of the air. To achieve the required degree of protection of the critical zone, it is necessary that the air flow that exits the device does not lose the shape of the boundaries and maintains a straight line of motion, in other words, the air flow should not narrow or expand over the zone selected for protection, in which the surgical table is located.

In the structure of the hospital building, operating rooms require the greatest responsibility due to the importance of the surgical process and the provision of the necessary microclimate conditions for this process to be successfully carried out and completed. The main source of the release of various bacterial particles is directly from the medical staff, which generates particles and excretes microorganisms while moving around the room. The intensity of the appearance of new particles in the airspace of the room depends on the temperature, the degree of mobility of people, and the speed of air movement. The nosocomial infection, as a rule, moves around the operating room with air currents, and the probability of its penetration into the vulnerable wound cavity of the operated patient never decreases. As observations have shown, improper organization of ventilation systems usually leads to such a rapid accumulation of infection in the room that its level can exceed the permissible norm.

For several decades, foreign specialists have been trying to develop system solutions to ensure the necessary conditions for the air environment in operating rooms. The air flow that enters the room should not only maintain the microclimate parameters, assimilate harmful factors (heat, odor, humidity, harmful substances), but also maintain the protection of the selected zones from the possibility of infection, and therefore ensure the required air purity in operating rooms ... The area in which invasive operations are performed (penetration into the human body) is called the "critical" or operating area. The standard defines such a zone as an "operating sanitary protection zone", this concept means the space in which the operating table, equipment, instrument tables are located, and medical personnel are located. In there is such a thing as "technological core". It refers to the area in which production processes are carried out under sterile conditions, this area can be meaningfully related to the operating room.

In order to prevent the penetration of bacterial contamination into the most critical areas, screening methods based on the use of air displacement have been widely used. For this purpose, laminar air diffusers of various designs have been developed. Later, "laminar" came to be called "unidirectional" flow. Today you can find a variety of options for the name of air distribution devices for clean rooms, for example, "laminar ceiling", "laminar", "clean air operating system", "operating ceiling" and others, but this does not change their essence. The air distributor is built into the ceiling structure above the protected area of \u200b\u200bthe room. It can be of various sizes, depending on the air flow rate. The optimal area of \u200b\u200bsuch a ceiling should not be less than 9 m 2, so that it can completely cover the area with tables, personnel and equipment. The displacing air flow in small portions slowly flows from top to bottom, thus separating the aseptic field of the operating area, the area where the sterile material is transferred from the environment. Air is removed from the lower and upper zones of the protected room simultaneously. HEPA filters (class H po) are built into the ceiling, which let the air flow through them. Filters only trap live particles without disinfecting them.

Recently, at the global level, attention has increased to the issues of air disinfection of hospital premises and other institutions in which there are sources of bacterial contamination. The documents set out the requirements that it is necessary to decontaminate the air of operating rooms with a particle deactivation efficiency of 95% and higher. Equipment of climatic systems and air duct are also subject to disinfection. Bacteria and particles that are released by the surgical personnel enter the air environment of the room continuously and accumulate in it. In order to prevent the concentration of harmful substances in the room from reaching the maximum permissible level, it is necessary to constantly monitor the air environment. This control is carried out without fail after the installation of the climate system, repair or maintenance, that is, at the time when the cleanroom is used.

Designers have already become accustomed to the use of ultrafine unidirectional air diffusers with built-in ceiling-type filters in operating rooms.

Air currents with large volumes move slowly down the premises, thus separating the protected area from the surrounding air. However, many specialists do not worry that these solutions alone cannot be enough to maintain the required level of air disinfection during surgical operations.

A large number of design options for air distribution devices have been proposed, each of which has received its own application in a specific area. Special operating rooms among themselves within their class are divided into subclasses depending on the purpose of the degree of cleanliness. For example, operating rooms for cardiac surgery, general surgery, orthopedic, etc. Each class has its own requirements for ensuring cleanliness.

Air diffusers for clean rooms were first used in the mid 50s of the last century. Since that time, the distribution of air in industrial premises has become traditional in those cases when it is necessary to ensure reduced concentrations of microorganisms or particles, all this is done through a perforated ceiling. The air flow moves in one direction through the entire volume of the room, while the speed remains uniform - approximately 0.3 - 0.5 m / s. The air is supplied through a group of high efficiency air filters that are located on the ceiling of the cleanroom. The air flow is supplied according to the principle of an air piston, which rapidly moves downward through the entire room, removing harmful substances and dirt. Air is removed through the floor. This movement of air can remove aerosol contamination from processes and personnel. The organization of such ventilation is aimed at ensuring the necessary air purity in the operating room. Its disadvantage is that it requires a large air flow, which is not economical. For clean rooms of ISO class 6 (according to ISO classification) or class 1000, air exchange of 70-160 times / h is allowed. Later, more efficient modular-type devices with smaller dimensions and low costs came to replace, which allows you to choose an air inlet, starting from the size of the protection zone and the required air exchange rates in the room, depending on its purpose.

Operation of laminar air distributors

Laminar flow devices are intended for use in clean rooms for the distribution of large volumes of air. The implementation requires specially designed ceilings, room pressure control and floor hoods. If these conditions are met, laminar flow distributors will necessarily create the necessary unidirectional flow with parallel streamlines. Due to the high rate of air exchange, conditions close to isothermal are maintained in the supply air flow. Designed for air distribution during extensive air changes, ceilings provide low starting flow rates due to their large footprint. The control of the change in air pressure in the room and the result of the operation of the exhaust devices ensure the minimum dimensions of the air recirculation zones, here the principle of "one passage and one outlet" works. Suspended particles fall to the floor and are removed, making it virtually impossible to recirculate them.

However, in the operating room, such air heaters work somewhat differently. In order not to exceed the permissible levels of bacteriological purity of the air in the operating rooms, according to calculations, the air exchange values \u200b\u200bare about 25 times / h, and sometimes even less. In other words, these values \u200b\u200bare not comparable to the values \u200b\u200bcalculated for production facilities. To maintain a stable air flow between the operating room and adjacent rooms, overpressure is maintained in the operating room. The air is removed through exhaust devices that are installed symmetrically in the walls of the lower zone. To distribute smaller volumes of air, laminar devices of a smaller area are used; they are installed directly above the critical area of \u200b\u200bthe room as an island in the middle of the room, and do not occupy the entire ceiling.

Based on the observation results, such laminar air distributors may not always be able to provide unidirectional flow. Since the difference between the temperature in the supply air stream and the ambient air temperature of 5-7 ° C is unavoidable, the colder air leaving the supply device will descend much faster than the unidirectional isothermal flow. This is a common feature of ceiling diffusers installed in public spaces. The opinion that laminars provide a unidirectional stable air flow in any case, regardless of where and how they are used, is wrong. Indeed, under real conditions, the speed of the vertical low-temperature laminar flow will increase as it descends to the floor.

With an increase in the supply air volume and a decrease in its temperature in relation to the room air, the acceleration of its flow increases. As shown in the table, thanks to the use of a laminar system, the area of \u200b\u200bwhich is 3 m 2, and the temperature difference is 9 ° C, the air velocity at a distance of 1.8 m from the outlet increases three times. At the exit from the laminar device, the air velocity is 0.15 m / s, and in the area of \u200b\u200bthe operating table - 0.46 m / s, which exceeds the permissible level. Many studies have proven long ago that at an increased supply flow rate, its “unidirectionality” is not preserved.

	Air consumption, m 3 / (h m 2)	Pressure, Pa	Air speed at a distance of 2 m from the panel, m / s
			3 ° C T	6 ° C T	8 ° C T	11 ° C T	NC
Single panel	183	2	0,10	0,13	0,15	0,18	<20
	366	8	0,18	0,20	0,23	0,28	<20
	549	18	0,25	0,31	0,36	0,41	21
	732	32	0,33	0,41	0,48	0,53	25
1.5 - 3.0 m 2	183	2	0,10	0,15	0,15	0,18	<20
	366	8	0,18	0,23	0,25	0,31	22
	549	18	0,25	0,33	0,41	0,46	26
	732	32	0,36	0,46	0,53	–	30
More than 3 m 2	183	2	0,13	0,15	0,18	0,20	21
	366	8	0,20	0,25	0,31	0,33	25
	549	18	0,31	0,38	0,46	0,51	29
	732	32	0,41	0,51	–	–	33

Lewis (1993) and Salvati (1982) analyzes of air control in operating theaters found that in some cases, the use of laminar systems with high air velocities leads to an increase in the level of contamination of air in the area of \u200b\u200bthe surgical incision, which can lead to to its infection.

The dependence of the change in the air flow rate on the supply air temperature and the size of the laminar panel area is shown in the table. When the air moves from the starting point, the streamlines will run parallel, then the flow boundaries will change, there will be a narrowing towards the floor, and, therefore, it will no longer be able to protect the area that was determined by the dimensions of the laminar installation. With a speed of 0.46 m / s, the air flow will capture the sedentary air of the room. And since bacteria continuously enter the room, infected particles will enter the air stream leaving the air inlet. This is facilitated by air recirculation, which occurs due to the pressurized air in the room.

To maintain the cleanliness of the operating rooms, according to the standards, it is necessary to ensure the imbalance of air by increasing the inflow by 10% more than the hood. Excess air enters adjacent, uncleaned rooms. In modern operating rooms, sealed sliding doors are often used, then excess air cannot escape and circulates through the room, after which it is taken back into the air inlet using built-in fans, then it is cleaned in filters and re-supplied to the room. The circulating air stream collects all contaminated substances from the room air (if it moves close to the supply air stream, it can pollute it). Since there is a violation of the boundaries of the flow, it is inevitable that air from the space of the room is mixed into it, and, consequently, the penetration of harmful particles into the protected sterile zone.

The increased mobility of air entails intensive exfoliation of dead skin particles from open areas of the skin of medical personnel, after which they enter the surgical incision. However, on the other hand, the development of infectious diseases during the rehabilitation period after surgery is a consequence of the patient's hypothermic state, which is aggravated when exposed to mobile streams of cold air. So, a well-functioning traditional laminar flow diffuser in a clean room can be beneficial as well as harmful in an operation performed in a conventional operating room.

This feature is typical for laminar devices with an average area of \u200b\u200babout 3 m 2 - optimal for protecting the operating area. According to American requirements, the air flow rate at the outlet of the laminar device should not be higher than 0.15 m / s, that is, 14 l / s of air should come into the room from an area of \u200b\u200b0.09 m 2. In this case, 466 l / s (1677.6 m 3 / h) or about 17 times / h will flow. Since, according to the standard value of air exchange in operating rooms, it should be 20 times / h, according to - 25 times / h, then 17 times / h is fully consistent with the required standards. It turns out that a value of 20 times / h is suitable for a room with a volume of 64 m 3.

According to current standards, the area of \u200b\u200bthe general surgical profile (standard operating room) should be at least 36 m 2. However, for operating rooms designed for more complex operations (orthopedic, cardiological, etc.), higher requirements are imposed, often the volume of such operating rooms is about 135 - 150 m 3. For such cases, an air distribution system with a large area and air capacity will be required.

If airflow is provided for larger operating rooms, it poses the problem of maintaining laminar flow from the outlet level to the operating table. Airflow studies have been conducted in several operating rooms. In each of them laminar panels were installed, which can be divided into two groups according to the occupied area: 1.5 - 3 m 2 and more than 3 m 2, and experimental installations for air conditioning were built, which allow changing the value of the supply air temperature. In the course of the study, the speed of the incoming air flow was measured at various flow rates and temperature changes; these measurements can be seen in the table.

Cleanliness criteria for operating rooms

For the correct organization of air circulation and distribution in the room, it is necessary to choose a rational size of the supply panels, to ensure the standard flow rate and supply air temperature. However, these factors do not guarantee absolute air disinfection. For more than 30 years, scientists have been solving the issue of disinfecting operating rooms and suggesting various anti-epidemiological measures. Today, the requirements of modern regulatory documents for the operation and design of hospital premises are faced with the goal of air disinfection, where HVAC systems are the main way to prevent the accumulation and spread of infections.

For example, according to the standard, the main goal of its requirements is disinfection, and it says that "a properly designed HVAC system minimizes the airborne spread of viruses, fungal spores, bacteria and other biological contaminants", the main role in the control of infections and other harmful factors plays the HVAC system. The requirements for room air conditioning systems are defined, which indicate that the design of the air supply system should ensure that bacteria, along with the air, enter the clean areas to be minimized and maintain the highest possible level of cleanliness in the rest of the operating room.

However, the regulatory documents do not contain direct requirements reflecting the definition and control of the efficiency of disinfection of premises with various ventilation methods. Therefore, when designing, you have to engage in searches that take a lot of time and do not allow you to do your main job.

A large amount of regulatory literature has been published on the design of HVAC systems for operating rooms, it describes the requirements for air disinfection, which are difficult for a designer to meet for a number of reasons. For this, it is not enough just to know modern disinfecting equipment and the rules for working with it; it is also necessary to maintain further timely epidemiological control of indoor air, which creates an idea of \u200b\u200bthe quality of the HVAC systems. Unfortunately, this is not always the case. If the assessment of the cleanliness of industrial premises is based on the presence of particles (suspended solids) in it, then the indicator of cleanliness in clean hospital premises is represented by live bacterial or colony-forming particles, their permissible levels are given in. In order not to exceed these levels, regular monitoring of indoor air for microbiological indicators is required, for this it is required to count microorganisms. The collection and calculation methodology for assessing the level of air purity has not been given in any regulatory document. It is very important that the counting of microorganisms must be done in the work area during the operation. But this requires a complete design and installation of an air distribution system. It is impossible to determine the degree of disinfection or the efficiency of the system before starting work in the operating room; this is established only during at least several operations. This raises a number of difficulties for engineers, because the necessary research is contrary to the observance of the anti-epidemic discipline of hospital premises.

Air curtain method

Correctly organized joint work of air supply and air removal provides the required air regime in the operating room. To improve the nature of the movement of air flows in the operating room, it is necessary to ensure a rational mutual arrangement of the exhaust and supply devices.

Figure: 1. Analysis of the air curtain operation

Using both the entire ceiling area for air distribution and the entire floor for discharge is not possible. Floor extractors are unhygienic as they get dirty quickly and are difficult to clean. Complex, bulky and expensive systems have not been widely adopted in small operating rooms. Therefore, the most rational is the "island" placement of laminar panels over the protected area and the installation of exhaust openings in the lower part of the room. This makes it possible to organize air flows by analogy with clean industrial premises. This method is cheaper and more compact. Air curtains are successfully used as a protective barrier. The air curtain connects with the supply air flow, forming a narrow "shell" of air at a higher speed, which is specially created around the perimeter of the ceiling. Such a curtain constantly operates on the hood and does not allow contaminated ambient air to enter the laminar flow.

To better understand how the air curtain works, you can imagine an operating room with a hood installed on all four sides of the room. The inflow of air, which comes from the "laminar island" located in the center of the ceiling, can only go down, while expanding towards the walls as it approaches the floor. This solution will reduce the recirculation zones and the size of stagnant areas where harmful microorganisms gather, prevent mixing of the room air with the laminar flow, reduce its acceleration, stabilize the speed and get the entire sterile zone overlapped by the downward flow. This helps to isolate the protected area from ambient air and allows biological contaminants to be removed from it.

Figure: 2 shows a standard air curtain design with slots around the room. If the extraction is organized around the perimeter of the laminar flow, it will stretch, the air flow will expand and fill the entire area under the curtain, and as a result, the effect of "narrowing" is prevented and the required laminar flow rate stabilizes.

Figure: 2. Diagram of the air curtain

In fig. 3 shows the actual air speed values \u200b\u200bwith a properly designed air curtain. They clearly show the interaction of an air curtain with a laminar flow that moves evenly. The air curtain avoids the installation of a bulky exhaust system throughout the entire perimeter of the room. Instead, as is customary in operating rooms, a traditional hood is installed in the walls. The air curtain protects the area surrounding the surgical staff and the table, preventing contaminated particles from returning to the initial airflow.

Figure: 3. Actual velocity profile in the cross-section of the air curtain

What level of disinfection can be achieved using an air curtain? If it is poorly designed, then it will not bring more effect than a laminar system. It is possible to make a mistake at a high air speed, then such a curtain can "pull" the air flow faster than necessary, and it will not have time to reach the operating table. Uncontrolled flow behavior can pose a threat of contaminated particles entering the protected area from floor level. Also, a curtain with an insufficient suction speed will not be able to fully impede the air flow and may be drawn into it. In this case, the air mode of the operating room will be the same as when using only the laminar device. During design, it is necessary to correctly identify the speed range and select the appropriate system. The calculation of disinfection characteristics depends on this.

Air curtains have a number of clear advantages, but they should not be used everywhere, because it is not always necessary to create a sterile flow during the operation. The decision on how necessary to ensure the level of air disinfection is made in conjunction with the surgeons involved in these operations.

Conclusion

Vertical laminar flow is not always predictable depending on the conditions of its use. Laminar panels that are used in clean production rooms often do not provide the required level of decontamination in operating rooms. The installation of air curtain systems helps to control the movement pattern of vertical laminar air flows. Air curtains help to monitor the bacteriological air in operating rooms, especially during long-term surgical procedures and the constant presence of patients with weak immune systems, for whom airborne infections are at great risk.

The article was prepared by A. P. Borisoglebskaya using materials from the magazine "ASHRAE".

Literature

1. SNiP 2.08.02–89 *. Public buildings and structures.
2. SanPiN 2.1.3.1375-03. Hygienic requirements for the placement, arrangement, equipment and operation of hospitals, maternity hospitals and other medical hospitals.
3. Instructive and methodological guidelines for organizing air exchange in ward departments and operating rooms of hospitals.
4. Instructional and methodological guidelines on hygienic issues of design and operation of infectious diseases hospitals and departments.
5. Manual to SNiP 2.08.02–89 * for the design of healthcare institutions. GiproNIZdrav of the USSR Ministry of Health. M., 1990.
6. GOST ISO 14644-1-2002. Cleanrooms and associated controlled environments. Part 1. Classification of air purity.
7. GOST R ISO 14644-4-2002. Cleanrooms and associated controlled environments. Part 4. Design, construction and commissioning.
8. GOST R ISO 14644-5-2005. Cleanrooms and associated controlled environments. Part 5. Operation.
9. GOST 30494–96. Residential and public buildings. Indoor microclimate parameters.
10. GOST R 51251–99. Air purification filters. Classification. Marking.
11. GOST R 52539-2006. Air purity in hospitals. General requirements.
12. GOST R IEC 61859-2001. Radiation therapy rooms. General safety requirements.
13. GOST 12.1.005–88. System of standards.
14. GOST R 52249-2004. Rules for the production and quality control of medicines.
15. GOST 12.1.005–88. Occupational safety standards system. General sanitary and hygienic requirements for the air in the working area.
16. Instructive and methodological letter. Sanitary and hygienic requirements for dental treatment and prophylactic institutions.
17. MGSN 4.12-97. Treatment-and-prophylactic institutions.
18. MGSN 2.01-99. Standards for thermal protection and heat and water power supply.
19. Methodical instructions. MU 4.2.1089-02. Control methods. Biological and microbiological factors. Ministry of Health of Russia. 2002.
20. Methodical instructions. MU 2.6.1.1892-04. Hygienic requirements for ensuring radiation safety during radionuclide diagnostics using radiopharmaceuticals. Classification of medical facilities premises.

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

Laminar fluid flow is observed at low speeds of its movement. In a laminar flow, the trajectories of all particles are parallel and their shape follows the flow boundaries. In a round pipe, for example, the liquid moves in cylindrical layers, the generatrices of which are parallel to the walls and axis of the pipe. In a rectangular, infinite width channel, the fluid moves in layers parallel to its bottom. At each point of the flow, the speed remains constant in the direction. If the speed does not change with time and magnitude, the motion is called steady. For laminar motion in a pipe, the cross-sectional velocity distribution diagram has the form of a parabola with the maximum velocity on the pipe axis and with zero value at the walls, where an adhered 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 motionless. The speeds of subsequent layers are the greater, the greater their distance to the pipe surface, and the highest speed is possessed by the layer moving along the pipe axis. The profile of the averaged velocity of the turbulent flow in pipes (Fig. 53) differs from the parabolic profile of the corresponding laminar flow by a more rapid 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 circular pipe with a steady laminar flow is determined by the Hagen - Poiseuille law:

(8)

where p 1 and p 2 are the pressure in two cross-sections of the pipe spaced apart from each other at a distance of Δx; r is the radius of the pipe; 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 fulfilled only for small values \u200b\u200bof the Reynolds number:

(9)

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

The English scientist Osborne Reynolds (1842 - 1912) in 1883 performed 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 opening was on the axis of the tube. Paint was fed into the liquid stream through a tube. While 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 the velocity, which Reynolds called critical, wave-like disturbances and separate rapidly decaying vortices appeared on the strip. As the speed increased, their number increased and they began to develop. At a certain value of the velocity, the strip disintegrated into separate vortices, which spread over the entire thickness of the fluid flow, causing intense mixing and coloration of the entire fluid. This flow was called turbulent .

Starting from the critical value of the velocity, the Hagen - Poiseuille law was also violated. Repeating experiments with pipes of different diameters, with different liquids, Reynolds found that the critical speed at which the parallelism of the flow velocity vectors was violated changed depending on the flow size and fluid viscosity, but always in such a way that the dimensionless number
took 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 \u003d η / ρ is the kinematic viscosity, ρ is the density of the liquid, υ av is the average velocity of the liquid over the pipe section, l - characteristic linear dimension, for example pipe diameter.

Thus, up to a certain value of the number Re, there is a stable laminar flow, and then, in a certain range of values \u200b\u200bof this number, the laminar flow ceases to be stable and separate, more or less rapidly damped disturbances arise in the flow. Reynolds called these values \u200b\u200bof the number critical Re cr. With a further increase in the value of the Reynolds number, the motion becomes turbulent. The range of critical Re values \u200b\u200busually 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 entrance to the pipe, the critical value of the Reynolds number could be raised to 20,000, and if the entrance to the pipe has sharp edges, burrs, etc. or the pipe walls are rough, the Re cr value can drop to 800-1000 ...

In a turbulent flow, fluid particles acquire velocity components perpendicular to the flow, so they can pass from one layer to another. The velocity of the liquid particles rapidly increases with distance from the pipe surface, then changes quite insignificantly. Since liquid particles pass from one layer to another, their velocities in different layers differ little. Due to the large velocity gradient at the pipe surface, vortices usually form.

Turbulent flow of liquids is most common in nature and technology. Air flow in. atmosphere, water in seas and rivers, in canals, in pipes, it is always turbulent. In nature, laminar motion occurs when water is filtered in fine pores of fine-grained soils.

The study of turbulent flow and the construction of its theory is extremely complicated. The experimental and mathematical difficulties of these studies have so far been only 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.) must either be solved approximately, or by testing the corresponding models in special hydrodynamic tubes. The so-called similarity theory serves to move from the results obtained on a model to a phenomenon in nature. The Reynolds number is one of the main criteria for the similarity of the flow of a viscous fluid. Therefore, its definition is very important in practice. In this work, a transition from a laminar flow to a turbulent one is observed and several values \u200b\u200bof the Reynolds number are determined: in the laminar flow region, in the transition region (critical flow), and during turbulent flow.

In fluid dynamics, laminar (streamlined) flow occurs when a fluid flows in layers without breaking between layers.

At low speeds, the liquid tends to flow without lateral mixing - adjacent layers slide past each other like playing cards. There are no transverse currents perpendicular to the direction of flow, eddies or pulsations.

In a laminar flow, the movement of fluid particles occurs in an orderly manner, in straight lines, parallel to the surface. Laminar flow is a flow regime with high momentum diffusion and low momentum convection.

If a fluid flows through a closed channel (tube) or between two flat plates, a laminar or turbulent flow may occur - this depends on the speed and viscosity of the fluid. Laminar flow occurs at lower speeds, which are below the threshold at which it becomes turbulent. Turbulent flow is a less ordered flow pattern, with vortices or small packets of fluid particles resulting in lateral mixing. In non-scientific terms, laminar flow is called smooth.

However, in order to better understand what a "laminar" flow is, it is better to see once what this "plate" flow looks like. Fluid moves and does not move - this is a very characteristic description of laminar flow. The stream is like a frozen stream, but it is enough to put your hand under this stream to see the movement of water (any other liquid).

When a liquid flows through a closed channel such as a pipe or between two flat plates, either of two types of flow can take place depending on the speed and viscosity of the liquid: laminar flow or turbulent flow. Laminar flow tends to occur at lower speeds, below the threshold at which it becomes turbulent. Turbulent flow is a less orderly flow pattern that is characterized by eddies or small packets of liquid particles that result in lateral mixing. In non-scientific terms, laminar flow is smooth , while the turbulent flow is rude .

Relationship with Reynolds number

The type of flow occurring in the fluid in the channel is important in fluid dynamics problems and is then affected by heat and mass transfer in the fluid systems. The dimensionless Reynolds number is an important parameter in equations that describe whether to bring fully developed flow conditions into laminar or turbulent flow. The Reynolds number is the ratio of the inertial force to the shear force of a fluid: how fast a fluid moves relative to how viscous it is, regardless of the scale of the fluid system. Laminar flow usually occurs when the fluid is moving slowly or the fluid is very viscous. As the Reynolds number increases, for example, by increasing the fluid flow rate, the flow will transition from laminar to turbulent flow in a certain range of Reynolds numbers of laminar-turbulent range transition depending on small levels of interference in the fluid or imperfections in the flow system. If the Reynolds number is very small, much less than 1, then the fluid will exhibit Stokes, or creeping, flow, where the force of the fluid's viscosity is dominated by inertial forces.

The specific calculation of the Reynolds number, and the values \u200b\u200bwhere laminar flow occurs, will depend on the geometry of the flow system and the flow structure. A general example of a flow through a pipe where the Reynolds number is defined as

R e \u003d ρ u DH μ \u003d u DH ν \u003d QDH ν A, (\\ displaystyle \\ mathrm (Re) \u003d (\\ frac (\\ rho uD _ (\\ text (H))) (\\ mu)) \u003d (\\ frac ( uD _ (\\ text (H))) (\\ nu)) \u003d (\\ frac (QD _ (\\ text (H))) (\\ nu A)),) D H is the hydraulic pipe diameter (m); Q is the volumetric flow rate (m 3 / s); This is the area of \u200b\u200bthe pipe in cross section (m 2); U is the average fluid velocity (SI units: m / s); μ is the dynamic viscosity of the liquid (Pa · s \u003d N · s / m 2 \u003d kg / (m · s)); ν is the kinematic viscosity of the fluid, ν = μ / p (m 2 / s); ρ represents the density of the liquid (kg / m 3).

For such systems, laminar flow occurs when the Reynolds number is below the critical value of approximately 2040, although the transition range is typically between 1,800 and 2,100.

For hydraulic systems occurring on external surfaces, such as flow around objects suspended in a fluid, other definitions for Reynolds numbers can be used to predict the type of flow around an object. Particles Reynolds number Re p will be used for particles suspended in a fluid fluid, for example. As with pipe flow, laminar flow tends to occur at lower Reynolds numbers, while turbulent flow and related phenomena such as eddies occur at higher Reynolds numbers.

Examples of

A common application of laminar flow is in the smooth flow of a viscous fluid through a tube or pipe. In this case, the flow velocity changes from zero at the walls of the maximum along the center of the cross section of the vessel. The flow profile of laminar flow in a pipe can be calculated by dividing the flow into thin cylindrical elements and applying a viscous force to them.

Another example would be the flow of air over an aircraft wing. The boundary layer is a very thin sheet of air lying on the surface of the wing (and all other surfaces of the aircraft). Since air is viscous, this layer of air tends to stick to the wing. As the wing moves forward through the air, the boundary layer first flows smoothly over the streamlined shape from the airfoil. Here the flow is laminar and the boundary layer is the laminar layer. Prandtl applied the concept of a laminar boundary layer with aerodynamic surfaces in 1904.

laminar flow barriers

Laminar air flow is used to separate air volumes, or prevent airborne contaminants from entering an area. Laminar flow hoods are used to eliminate contamination from sensitive processes in science, electronics and medicine. Air curtains are often used in commercial environments to allow heated or cooled air to pass through doorways. A laminar flow reactor (LFR) is a reactor that uses laminar flow to study chemical reactions and process mechanisms.

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

Boundary layer

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

When the air flow around the body (Fig. 5), air particles do not slide over the body surface, but are decelerated, and the air velocity near the body surface becomes zero. With distance 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 flow. The boundary layer thickness gradually increases from the leading edge to the trailing edge. In the boundary layer, the nature of the movement of air particles differs from the nature of 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 of 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 speeds). 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 transforms into a wake stream, which, with distance from the body, is blurred and disappears. Swirls in the wake jet hit the tail unit of the aircraft and reduce its efficiency and cause shaking (buffet 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 are manifested due to the viscosity of the air; therefore, the air resistance in the laminar layer is small.

Figure: 5

Figure: 6 Air flow around a body - flow deceleration in the boundary layer

Figure: 7

In a turbulent boundary layer, there is a continuous movement of air streams in all directions, which requires more energy to maintain an irregular vortex movement and, as a consequence, 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 resistance coefficient of the laminar boundary layer is:

for a turbulent layer

where Re is the Reynolds number, which expresses the ratio of inertial forces to friction 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 rate,

I - character of body size,

kinetic coefficient of viscosity of air friction forces.

When the air flow around the body at a certain point, the boundary layer transitions 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 air streams, the shape of the body and its position in the air flow, as well as on the surface roughness. When creating wing profiles, designers strive to place this point as far as possible from the leading edge of the profile, thereby reducing frictional resistance. 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 air flow velocity or an increase in the angle of position of the body relative to the air flow up to a certain value, at a certain point, the boundary layer is separated from the surface, and 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 beyond the point of separation, there is a reverse flow of air from the zone of higher pressure to the zone of lower pressure to the point of separation, which entails separation of the air flow from the surface of the body (Fig. 8).

The laminar boundary layer detaches more easily from the body surface than the turbulent one.

The equation of continuity of an air stream

The equation of continuity of an air stream (constant air flow) is an aerodynamic equation that follows from the basic laws of physics - conservation of mass and inertia - and establishes the relationship between the density, velocity and cross-sectional area of \u200b\u200ban air stream.

Figure: 8

Figure: nine

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

In a trickle 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 by the cross-section F.

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

m1 \u003d m2 \u003d const, (1.7)

m1F1V1 \u003d m2F2V2 \u003d const. (1.8)

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

F1V1 \u003d F2V2 \u003d 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 is seen from the formula that the speed of the air flow of the jet is inversely proportional to the cross-sectional area of \u200b\u200bthe jet and vice versa.

Thus, the equation of continuity of the jet of the 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

An aircraft located 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 mobile) it is dynamic pressure, it is more often called high-speed pressure. The static pressure in the trickle 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 pipe walls are under pressure from the water side. In the case of water movement, the pressure will be slightly less, since a high-speed 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 pressure forces, the internal energy of the stream and the energy of the body position. This sum is a constant value:

Ekin + Ep + Eun + En \u003d 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 the air stream, m / s. If instead of mass m we substitute the mass density of air p, then we obtain the formula for determining the velocity head q (in kgf / m2)

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

where Р - air pressure, kgf / m2; F is the cross-sectional area of \u200b\u200bthe air stream stream, 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 air volume into the formula (1.13), we get

The internal energy Eun 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 - thermal equivalent of mechanical work (cal-kg-m).

The equation shows that the internal energy of the air flow is directly proportional to its temperature.

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

where h is the change in height, m.

Due to the scanty small values \u200b\u200bof the distance between the centers of gravity of air masses along the height in the jet of the air flow, this energy is neglected in aerodynamics.

Considering in interconnection 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 air flow and the velocity head.

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

Figure: ten

The reason for the pressure drop is that the air flow does not do any work (friction is not included) and therefore the total energy of the air flow remains constant. If the temperature, density and volume of the air flow in different sections are considered constant (T1 \u003d T2 \u003d T3; p1 \u003d p2 \u003d p3, V1 \u003d V2 \u003d V3), then the internal energy can be disregarded.

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

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

Substituting the values \u200b\u200bfrom 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 the energy of position, transforming equation (1.10), we obtain

This equation for any section of the air stream is written as follows:

This kind of equation is the simplest mathematical Bernoulli equation and shows that the sum of static and dynamic pressures for any section of a stream of a steady air flow is a constant value. The compressibility is not taken into account in this case. Corresponding amendments are made to take into account the compressibility.

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.

Figure: eleven

The sheets move closer together. The reason for their convergence is that on the outside 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 has decreased and becomes 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 accompanying the flow of gas around bodies is called a wind tunnel. The principle of operation of wind tunnels is based on Galileo's principle of relativity: instead of the motion of a body in a stationary medium, the flow of gas around a stationary body is studied.In wind tunnels, the aerodynamic forces acting on an aircraft are experimentally determined and the distributions of pressure and temperature over its surface are investigated, a picture of the flow around the body is studied, and aeroelasticity is studied. etc.

Wind tunnels, depending on the range of Mach numbers M, are divided into subsonic (M \u003d 0.15-0.7), transonic (M \u003d 0.7-1 3), supersonic (M \u003d 1.3-5) and hypersonic (M \u003d 5-25), according to the principle of operation - on compressor (continuous), in which the air flow is created by a special compressor, and cylinder with increased pressure, according to the layout of the circuit - on closed and open.

Compressor pipes have high efficiency, they are easy to use, but they require unique compressors with high gas flow rates and high power. Balloon wind tunnels are less economical compared to compressor wind tunnels, since part of the energy is lost during gas throttling. 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 widespread use of balloon wind tunnels is due to the fact that they are simpler in design and the compressor power required for filling the cylinders is relatively small. Closed-loop wind tunnels use a significant part of the kinetic energy remaining in the gas flow after it passes through the working area, which increases the efficiency of the pipe. This, however, has to increase the overall dimensions of the installation.

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

Figure: 12

1- honeycomb 2 - mesh 3 - prechamber 4 - confuser 5 - direction of flow 6 - working part with model 7 - diffuser, 8 - elbow with swivel blades, 9 - compressor 10 - air cooler

Figure: 13

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

Figure: 14

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

Figure: 15

1 - high pressure cylinder 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 - direction of flow 11 - air supply into ejectors 12 - ejectors 13 - gates 14 - vacuum tank 15 - subsonic diffuser