study of the properties of liquid and gas flows is very important for the industry and public utilities.The laminar and turbulent flows affects the speed of the transport of water, oil, natural gas pipelines for various applications, affects the other parameters.These problems do science hydrodynamics.
Classification
The scientific environment flow regimes of liquids and gases are divided into two completely different classes:
- laminar flow (jet);
- turbulent.
also distinguish transitional stage.Incidentally, the term "liquid" has a broad meaning: it can be incompressible (it is actually a liquid), compressible (gas), conducting, and so on. D.
Background
Another Mendeleev in 1880, it was suggestedthe existence of two opposing modes trends.More details on this issue examined the British physicist and engineer Osborne Reynolds, completed a study in 1883.First, virtually, and then use the formula, he found that at low speed the flow becomes laminar flow of liquids form: layers (streams of particles) is almost mixed and move along parallel paths.However, after overcoming a certain critical value (for different conditions it is different), called the Reynolds number of fluid flow regimes are changing the jet stream becomes chaotic vortex - that is turbulent.It was found that these parameters are peculiar to a certain extent and gases.
practical calculations British scientists have shown that the behavior of, for example, water, is highly dependent on the shape and size of the tank (pipes, channels, capillaries, etc.), in which it flows.The tubes having a circular cross-section (these are used for mounting pressure pipelines), its Reynolds number - the formula of the critical state is described as: Re = 2300. For the flow of open channels Reynolds number more: Re = 900. At lower values of Re for is ordered,at large - chaotic.
Laminar flow
difference between laminar flow turbulence is in the nature and direction of the water (gas) flows.They move layers, without mixing and without pulsations.In other words, the movement takes place uniformly without erratic jumps in the pressure direction and speed.
laminar flow is formed, for example, in the narrow blood vessels of living creatures and plants capillaries under comparable conditions, at a current of very viscous fluids (oil pipelines).To visualize the jet stream, quite a bit to reveal the tap - water will flow quietly, evenly, without mixing.If you unscrew the faucet until the end, the system pressure will rise and the flow will become chaotic.
Turbulent flow
Unlike laminar in which the particles move along the nearby virtually parallel paths, turbulent fluid flow is random in nature.If we use the Lagrangian approach, the trajectories of the particles can be arbitrarily interfere and behave quite unpredictably.Movement of liquids and gases in these conditions is always transient, and the parameters of these non-stationary can have a very wide range.
How laminar gas flow becomes turbulent, can be traced on the example of wisps of smoke of a burning cigarette in the still air.Initially, the particles move almost parallel paths unchanged in time.Smoke seems fixed.Then at some point suddenly emerge large eddies that move completely randomly.These vortices disintegrate into smaller ones - for even smaller and so on.Finally, the smoke is almost mixed with ambient air.
Cycles turbulence
The above example is a textbook, and from his observations scientists have made the following conclusions:
- Laminar and turbulent flow are probabilistic in nature: the transition from one regime to another is not in exactly the right place, and in a rather arbitrary, randomlocation.
- first large vortices occur that are larger than the size of wisps of smoke.Movement becomes unsteady and strongly anisotropic.Large flows become unstable and break up into smaller and smaller.Thus, there is a hierarchy of eddies.The energy of motion is transferred from large to small, and at the end of this process disappears - there is energy dissipation at small scales.
- turbulent flow is erratic: a particular vortex can be in a completely random, unpredictable place.
- Mixing smoke with ambient air does not take place in laminar and in turbulent - is very intense.
- Despite the fact that the boundary conditions are stationary, the turbulence itself has a pronounced transient in nature - all gas-dynamic parameters change over time.
There is another important property of turbulence: it is always three-dimensional.Even if we consider the one-dimensional flow in a pipe or two-dimensional boundary layer, it is still the movement of turbulent vortices occur in the directions of the three axes.
Reynolds number: the formula
transition from laminar to turbulence characterized by the so-called critical Reynolds number:
Recr = (ρuL / μ) cr,
where ρ - density of the flow, u - the characteristic velocity of the flow;L - characteristic size of the flow, μ - dynamic viscosity coefficient, cr - over on a pipe with a circular cross-section.
example, to flow with velocity u in the pipe as the pipe diameter L is used.Osborne Reynolds demonstrated that in this case 2300 & lt; Recr & lt;20000. The spread is very large, nearly an order of magnitude.
similar result is obtained in the boundary layer on a plate.The characteristic dimension is taken away from the front edge of the plate, and then the 3 × 105 & lt; Recr & lt;4 × 104.If L is defined as the thickness of the boundary layer, 2700 & lt; Recr & lt;9000. There are experimental studies that have shown that the value of Recr may be even greater.
concept of velocity perturbation
laminar and turbulent fluid flow, and accordingly, the critical value of the Reynolds number (Re) depends on many factors: the pressure gradient, the height of hillocks roughness, turbulence intensity in the external flow, temperature and so forth. For convenience,These factors are called total indignation rate, as they have a certain influence on the flow rate.If this perturbation is small, it can be repaid viscous forces seeking to align the velocity field.For large perturbations within may become unstable, and there is turbulence.
Given that the physical meaning of the Reynolds number - the ratio of inertial forces and viscous forces, flow disturbances covered by the formula:
Re = ρuL / μ = ρu2 / (μ × (u / L)).
The numerator is twice the velocity head, and the denominator - the value of having the procedure friction stress, if L is taken as the thickness of the boundary layer.Dynamic pressure tends to destroy the balance and friction forces oppose this.However, it is unclear why the inertia force (or dynamic pressure) changes only when they are 1,000 times more viscous forces.
calculations and facts
probably more convenient to be used as a characteristic speed Recr not absolute flow velocity u, and the velocity perturbation.In this case, the critical Reynolds number will be about 10, that is in excess of dynamic pressure perturbation over the viscous stresses 5 times the laminar flow to a turbulent fluid flows.This definition Re according to some scientists is well explained by the following experimentally proven facts.
to perfectly uniform velocity profile on a perfectly smooth surface is traditionally determined by the number Recr tends to infinity, ie the transition to turbulence is not actually there.But Reynolds number is determined from the velocity perturbation is less than the critical value, which is equal to 10.
the presence of artificial turbulence, causing a surge of speed, comparable to the prime rate, the flow becomes turbulent at much lower Reynolds number than Recr, certain absolutespeed value.This allows to use the value of the coefficient Recr = 10, where the characteristic velocity is the absolute value of the velocity perturbation caused by the above reasons.
stability of laminar flow regime in the pipeline
Laminar and turbulent flow characteristic of all kinds of liquids and gases in different environments.In nature, laminar flows are rare and characterized, for example, to narrow underground streams in the plains.Much more concerned about this issue in the context of scientific applications for the pipeline transportation of water, oil, gas and other fluids.
question the stability of laminar flow is closely related to the study of the disturbed motion of the main flow.It is found to be affected by so-called small perturbations.Depending on whether they are growing or fading over time, the basic flow is considered stable or unstable.
compressible and compressible fluids
One of the factors influencing the laminar and turbulent flow of the fluid is its compressibility.This property of the fluid is especially important in the study of the stability of non-stationary processes in a rapid change of the main flow.
Studies show that the laminar flow of an incompressible fluid in a cylindrical pipe section resistant to relatively small axisymmetric and non-axisymmetric perturbations in space and time.
Recently, calculations are carried out on the influence of disturbances on the axisymmetric flow resistance in the inlet part of the cylindrical tube where the main current is dependent on the two coordinates.The coordinate axis of the pipe is considered as a parameter, which depends on the velocity profile of the main flow pipe radius.
Conclusion Despite centuries of study, one can not say that laminar and turbulent flow thoroughly studied.Experimental studies on the micro level pose new issues requiring a reasoned calculation justification.The nature of research is applied and the benefit: the world laid thousands of kilometers of water, oil, gas and product.The more technical solutions implemented to reduce turbulence during transport, the more effective it will be.
