Turbulence

Question 1

what is Turbulence

Answer 1

Fluid flow with random velocity fluctuations characterised by high diffusivity of mass, momentum and energy.

vortices of different length scales.

At a Reynolds number less than critical, the kinetic energy of the flow is not enough to sustain the random fluctuation against the viscous damping and in such laminar flow continues to exits. At somewhat higher Reynolds number than the critical Reynolds number, the kinetic energy of flow supports the growth of fluctuations and transition to turbulence is induced.

Question 2

Consequences

Answer 2

The turbulence promotes improved mixing. Increased skin friction, pressure drop. High transfer rate of momentum, heat, and mass by fluctuating turbulent motion, are practically the most important feature of turbulence.

Question 3

Types

Answer 3

Homogeneous and Isotropic Turbulence
Homogeneous - statistical properties are invariant of axis translation
Isotropic - statistical properties are invariant of axis rotation and reflection along-with translation

In homogeneous turbulence the rms values of the velocity components can all be different, but each value must be constant over the entire turbulent field.

In isotropic turbulence fluctuations are independent of the direction of reference.

Question 4

Energy Cascade

Answer 4

The large eddies break down into smaller eddies. Smaller eddies break down into still smaller eddies, and so on

Question 5

Types of Turbulent Fluctuations

Answer 5

Stationary turbulence
Turbulence in Periodic Mean Flows
Intermittent Turbulence (Laminar to Turbulent transition Flows)

Question 6

friction velocity

Answer 6

turbulent intensity distributions are scaled with friction velocity
max. of u’2 is related to u_tau

Question 7

Methods of studying turbulence

Answer 7

The methods for calculating turbulence can be grouped into the three broad categories.

Reynolds averaged Navier-Stokes (RANS) equations of turbulence. The RANS approach includes eddy-viscosity based models, such as the k- e models and its variants on one hand and the Reynolds Stress Model (RSM) on the other. Usually the RSM consists of the second moment turbulence modeling.

The most elegant approach to the solution of turbulent flows is the direct numerical simulation (DNS) of turbulence, in which the governing equations are discretized and solved numerically using extremely fine grid mesh. If the grid size is fine enough to resolve the smallest scale of motion, and the solution scheme is designed to minimize the numerical diffusion and dissipation errors, one can achieve an accurate three-dimensional, time-dependent solution of the governing equations completely free of modeling assumptions. Thus DNS has been a very useful tool, over the past ten years, for the study of transitional and turbulent flow physics, but it has a severe limitation. In order to resolve all scales of motion, one requires a number of grid points N ~ L / η , where L is the dimension of computational domain (basically the largest scale in the system) and η is the smallest scale in motion, the Kolmogorov length scale. Since this ratio is proportional to Re3/4 , the number of grid point needed by a DNS is order of N3 ~ Re9/4 . On the other hand the solutions of Reynolds-averaged equations using k - ε and any other suitable model have basic limitations because of the non-linear, non-local and non-Gaussian properties of turbulence. Large-Eddy Simulation (LES) is a technique, which draws the advantages of the direct simulation of turbulent flows and the solution of the Reynolds-averaged equations through closure assumptions. In LES, the contribution of the large-scale structures to momentum and energy transfer is computed exactly and the effect of the smallest scales of turbulence is modeled.
Large Eddy Simulation (LES) techniques.
Direct Numerical Simulation (DNS) of turbulence.