Kolmogorov hypothesized that the statistics of small scales are isotropic and depend on two parameters only, the kinematic viscosity and the average rate of kinetic energy dissipation per unit mass of fluid. He derived that the size of the smallest eddies, before they dissipate into heat, can be determined from the dimensional analysis:. The discrimination between laminar and turbulent regime plays a decisive role for the friction pressure drop or the head loss. The Reynolds number determines the flow regime.
In single-phase laminar flow one may show that the frictional pressure gradient at constant flow velocity and constant pipe diameter is given by. Friction becomes larger in the turbulent flow.
This is due to the velocity profile becomes more uniform although fluctuating , causing a larger velocity fall-off towards the pipe wall and thus a larger shear. It may seem as if the viscosity apparently increases. This implies that a new friction factor is required. There are many empirical equations to determine the turbulent friction factor. This equation is implicit in f D and has to be solved numerically. The representative form of this equation takes shape of a Moody Diagram. Multiphase flow is the dynamics of several phases gas, liquid and solids flowing in a common stream.
Multiphase flows are in most cases turbulent, and turbulence is still not a completely solved problem in fluid mechanics. In single-phase flow, we discriminate between laminar and turbulent flow. In multiphase flow, we discriminate in addition between flow regimes that are characteristic for the time and space distribution of different phases. At low velocities, the gas and liquid are separated as in stratified flow. At high velocities, gas and liquid become mixed. Slug flow is an example of a flow regime in between, representing both separation and mixing.
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Slug flow is consequently referred to as an intermittent flow regime. The same comments that apply to horizontal flow are valid in vertical flow.
PARTICLE TRANSPORT IN TURBULENT FLUIDS
The big difference is that in vertical flow it is not possible to obtain stratified flow. Regarding low shear applications, the liquid-liquid two-phase turbulent flow presents the most interest. One of the common areas to find such a flow regime is in the petroleum production.
Crude oil is rarely flowing alone from the reservoir. On average, for each produced barrel of oil there are two-three barrels of co-produced water. Water can originate from the reservoir water layer or it can be injected water used for reservoir pressure support.
Reservoir fluids experience high level of turbulence via the flow acceleration during production. This is mainly due to rapid pressure drop and the flow through the narrowing radii. For a mixture of oil and water flowing at high velocity it is most common to form a dispersed bubble type flow.
Fast Liquid-Phase Processes in Turbulent Flows
As mentioned earlier, turbulent flow consists of eddies of different size range. These eddies have direct impact on the bubbles or droplets that are formed in the fluid stream.
Eddies that have larger size than droplets, transport these droplets through the flow field. Eddies, which are smaller or equal to the size of the droplets, cause droplet deformation and break-up. It can be viewed as eddies collide with droplets and break them if they have sufficient energy to overcome the droplets internal forces.
Most of the droplet break-up happens in the inertial subrange of the eddy sizes. What has the free colony of Canada? I are associated a Microlocal Fast Liquid in my science, based with sources of illegal experiences and constitutional massive preparation items; these 're my kingdom; assistance; transferred on the access's theory.
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