- The most important characteristic of turbulent motion is the fact that velocity and pressure at a point fluctuate with time in a random manner.
Fig. 32.1 Variation of horizontal components of velocity for laminar and turbulent flows at a point P
- The mixing in turbulent flow is more due to these fluctuations. As a result we can see more uniform velocity distributions in turbulent pipe flows as compared to the laminar flows .
Fig. 32.2 Comparison of velocity profiles in a pipe for (a) laminar and (b) turbulent flows
- Turbulence can be generated by -
- frictional forces at the confining solid walls
- the flow of layers of fluids with different velocities over one another
The turbulence generated in these two ways are considered to be different.
Turbulence generated and continuously affected by fixed walls is designated as wall turbulence , and turbulence generated by two adjacent layers of fluid in absence of walls is termed as free turbulence . One of the effects of viscosity on turbulence is to make the flow more homogeneous and less dependent on direction.
- Turbulence can be categorised as below -
- Homogeneous Turbulence: Turbulence has the same structure quantitatively in all parts of the flow field.
- Isotropic Turbulence: The statistical features have no directional preference and perfect disorder persists.
- Anisotropic Turbulence: The statistical features have directional preference and the mean velocity has a gradient.
- Homogeneous Turbulence : The term homogeneous turbulence implies that the velocity fluctuations in the system are random but the average turbulent characteristics are independent of the position in the fluid, i.e., invariant to axis translation.
Consider the root mean square velocity fluctuations
,
,
In homogeneous turbulence, the rms values of u', v' and w' can all be different, but each value must be constant over the entire turbulent field. Note that even if the rms fluctuation of any component, say u' s are constant over the entire field the instantaneous values of u necessarily differ from point to point at any instant.
- Isotropic Turbulence: The velocity fluctuations are independent of the axis of reference, i.e. invariant to axis rotation and reflection. Isotropic turbulence is by its definition always homogeneous . In such a situation, the gradient of the mean velocity does not exist, the mean velocity is either zero or constant throughout.
In isotropic turbulence fluctuations are independent of the direction of reference and=
=
or
It is re-emphasised that even if the rms fluctuations at any point are same, their instantaneous values necessarily differ from each other at any instant.
- Turbulent flow is diffusive and dissipative . In general, turbulence brings about better mixing of a fluid and produces an additional diffusive effect. Such a diffusion is termed as "Eddy-diffusion ".( Note that this is different from molecular diffusion)
At a large Reynolds number there exists a continuous transport of energy from the free stream to the large eddies. Then, from the large eddies smaller eddies are continuously formed. Near the wall smallest eddies destroy themselves in dissipating energy, i.e., converting kinetic energy of the eddies into intermolecular energy.
