Studying the properties of fluid and gas flows is very important for industry and utilities. Laminar and turbulent flow affects the speed of transportation of water, oil, natural gas through pipelines for various purposes, affects other parameters. The science of hydrodynamics deals with these problems.
Classification
In the scientific community, the regimes of fluid and gas flow are divided into two completely different classes:
The transition stage is also distinguished. By the way, the term “liquid” has a wide meaning: it can be incompressible (this is actually a liquid), compressible (gas), conductive, etc.
Background
Even in 1880, Mendeleev expressed the idea of the existence of two opposite regimes of currents. The British physicist and engineer Osborne Reynolds studied this question in more detail, completing research in 1883. At first, practically, and then using formulas, he established that at a low flow velocity, the movement of liquids acquires a laminar form: the layers (particle flows) hardly mix and move along parallel trajectories. However, after overcoming a certain critical value (for different conditions, it is different), called the Reynolds number, the modes of fluid flow change: the jet stream becomes chaotic, vortex - that is, turbulent. As it turned out, these parameters are to some extent also characteristic of gases.
The practical calculations of the English scientist showed that the behavior, for example, of 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 (they are used for mounting pressure pipelines), their Reynolds number — the critical state formula is described as follows: Re = 2300. For an open channel, the Reynolds number is different: Re = 900. At lower Re values, the flow will be ordered. at large - chaotic.
Laminar flow
The difference between a laminar flow and a turbulent one is in the nature and direction of the water (gas) flows. They move in layers, without mixing and without ripple. In other words, the movement runs uniformly, without random jumps in pressure, direction and speed.
Laminar fluid flow is formed, for example, in the narrow blood vessels of living creatures, plant capillaries and under comparable conditions, during the flow of very viscous fluids (fuel oil through the pipeline). To visually see the jet stream, it is enough to slightly open the water tap - the water will flow calmly, evenly, without mixing. If the faucet is turned away completely, the pressure in the system will increase and the flow will become chaotic.
Turbulent flow
In contrast to the laminar one, in which nearby particles move along almost parallel trajectories, the turbulent fluid flow is disordered. If we use the Lagrange approach, then the particle trajectories can intersect arbitrarily 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.
As the laminar gas flow regime changes to turbulent one can be traced on the example of a stream of smoke from a burning cigarette in still air. Initially, particles move almost parallel along time-invariant trajectories. The smoke seems motionless. Then in some place large eddies suddenly appear that move completely randomly. These vortices break up into smaller ones, those into even smaller ones, and so on. In the end, smoke almost mixes with the surrounding air.
Turbulence cycles
The above example is a textbook, and from his observation, scientists made the following conclusions:
- Laminar and turbulent flows are probabilistic in nature: the transition from one regime to another does not occur in a precisely specified place, but in a rather arbitrary, random place.
- First, large vortices arise, the size of which is larger than the size of a stream of smoke. The movement becomes unsteady and highly anisotropic. Large flows lose stability and break up into 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 disappears - energy is dissipated at small scales.
- The turbulent flow regime is random in nature: this or that vortex can appear in a completely arbitrary, unpredictable place.
- Mixing of smoke with ambient air practically does not occur in the laminar regime, and in turbulent mode it is very intense.
- Despite the fact that the boundary conditions are stationary, the turbulence itself is pronounced non-stationary in nature - all gas-dynamic parameters change in 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, still the movement of turbulent vortices occurs in the directions of all three coordinate axes.
Reynolds number: formula
The transition from laminarity to turbulence is characterized by the so-called critical Reynolds number:
Re cr = (ρuL / µ) cr,
where ρ is the flux density, u is the characteristic flow velocity; L is the characteristic flow size, µ is the dynamic viscosity coefficient , cr is the flow through the pipe with a circular cross section.
For example, for a flow with a velocity u in a pipe, the pipe diameter is used as L. Osborne Reynolds showed that in this case 2300 <Re cr <20000. The spread is very large, almost an order of magnitude.
A similar result is obtained in the boundary layer on the plate. The distance from the leading edge of the plate is taken as a characteristic size, and then: 3 × 10 5 <Re cr <4 × 10 4 . If L is defined as the thickness of the boundary layer, then 2700 <Re cr <9000. There are experimental studies that have shown that the value of Re cr can be even greater.
The concept of speed disturbance
The laminar and turbulent fluid flow, and, accordingly, the critical value of the Reynolds number (Re) depend on a larger number of factors: pressure gradient, height of roughness tubercles, turbulence intensity in the external flow, temperature difference, etc. For convenience, these total factors are also called velocity perturbations , since they have a certain effect on the flow rate. If this disturbance is small, it can be extinguished by viscous forces that tend 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 inertia forces and viscosity forces, the flow perturbation falls under the action of the formula:
Re = ρuL / µ = ρu 2 / (µ × (u / L)).
In the numerator is doubled the pressure head, and in the denominator is a value that has the order of the friction stress, if the thickness of the boundary layer is taken as L. The pressure head tends to destroy the balance, and friction forces counteract this. However, it is not clear why the inertia forces (or pressure head) lead to changes only when they are 1000 times more than the viscosity forces.
Calculations and facts
It would probably be more convenient to use, as a characteristic velocity in Re cr, not the absolute flow velocity u, but the velocity perturbation. In this case, the critical Reynolds number will be about 10, that is, when the perturbation of the velocity head over viscous stresses is 5 times higher, the laminar fluid flow flows into a turbulent one. According to a number of scientists, this definition of Re well explains the following experimentally confirmed facts.
For a perfectly uniform velocity profile on an ideally smooth surface, the traditionally determined number Re cr tends to infinity, that is, a transition to turbulence is practically not observed. But the Reynolds number, determined by the magnitude of the velocity perturbation is less than critical, which is 10.
In the presence of artificial turbulizers, causing a speed surge comparable to the main speed, the flow becomes turbulent at much lower Reynolds numbers than Re cr , determined by 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 flows are common to all types of liquids and gases under different conditions. In nature, laminar flows are rare and characteristic, for example, for narrow underground flows in flat conditions. Much more this question worries scientists in the context of practical applications for transporting pipelines of water, oil, gas and other technical fluids.
The question of the stability of the laminar flow is closely related to the study of the perturbed motion of the main flow. It is established that it is exposed to the so-called small perturbations. Depending on whether they fade away or grow over time, the mainstream is considered stable or unstable.
Compressible and non-compressible fluids
One of the factors affecting the laminar and turbulent flow of a fluid is its compressibility. This property of the liquid is especially important when studying the stability of non-stationary processes with a rapid change in the main flow.
Studies show that the laminar flow of an incompressible fluid in cylindrical tubes is resistant to relatively small axisymmetric and non-axisymmetric perturbations in time and space.
Recently, calculations have been performed on the effect of axisymmetric disturbances on the stability of the flow in the inlet of a cylindrical pipe, where the main flow is dependent 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.
Output
Despite centuries of study, it cannot be said that both laminar and turbulent flows are thoroughly studied. Experimental studies at the micro level raise new questions that require well-reasoned calculation justification. The nature of research is also of practical use: thousands of kilometers of water, oil, gas, and product pipelines have been laid in the world. The more technical solutions will be introduced to reduce turbulence during transportation, the more effective it will be.