Statistical theory of turbulence IV-Diffusion in a turbulent air stream

Abstract

It was pointed out in Part I that experiments on the spread of heat from a line source ( e.g ., an electrically heated wire) in a turbulent air stream may be expected to give two elements of the statistical specification of turbulence. If the spread is measured near the source the value of the mean transverse component of velocity √¯ v 2 or v ' in the notation of Part I, can be found. If the spread is examined further down-stream it should be possible to analyse the results to find the correlation function R η , which is the principal element of the representation of turbulence in the Lagrangian system. Spread of heat nearer line source Recently the spread of heat from a heated wire in a wind tunnel has been measured at points near to the source by Schubauer. The stream was made turbulent by means of grids of round bars arranged in square pattern. Their diameters were 1 /5 of the mesh length and M varied from 5 inches to 1/2 inch. The width of the heat wake was found by measuring the angle subtended at the source by the two positions where the temperature rise was half that in the centre of the wake. This angle, denoted by α, depends partly on the amount of turbulence and to a less extent on the spread of heat due to the thermal conductivity of the air. By assuming that the effect of turbulence is to communicate to the air an eddy conductivity β, which is additive to, and obeys the same law as, true thermal conductivity, a virtual angle α turb can be deduced by the relation α 2 turb = α 2 — α 2 0 ,

Testing Premixed Turbulent Combustion Models by Studying Flame Dynamics

“…If the diffusivity D in eqn (10) is associated with the developing turbulent diffusivity resulted from the Taylor theory [14,15] (21) then eqn (15) yields eqn (2), which is well supported by experimental data (cf. symbols and curve in Figure 2a).…”

“…For instance, a quasi-linear growth of ∆ t with flame development time has been documented in many experiments (e.g. see Figure 2a) reviewed elsewhere [1,6], with the growth of ∆ t being well approximated by the Taylor [14,15] turbulent diffusion theory (2) (cf. solid line and symbols in Figure 2a).…”

“…Second, the mean flame brush thickness yielded by the gradient models is controlled by the diffusivity D, see eqn (15), and is independent of the turbulent burning velocity U t . Therefore, the growth of δ t = ∆ t /∆ t, ∞ may differ substantially from the development of u t .…”

Concepts, observations, and simulation of refractive index turbulence in the lower atmosphere

“…Much of the original motivation for studying turbulent flows in engineering and in the environment stemmed from what Taylor [1935aTaylor [ , 1935bTaylor [ , 1935cTaylor [ , 1935d called their "virtual mean stresses." These and other virtual fluxes are now better known as Reynolds fluxes after turbulence pioneer O. Reynolds.…”

On the Large Eddy Simulation of the Taylor–Green vortex

“…Experiments show that this length is 0.1M. Complete sets of measurements (see [32,33]) allow also to define a length λ η which may be regarded as a measure of the 'smallest size of eddy' in the Lagrangian system; this is connected (in a channel along the y-axis) with the average change in pressure by ∂p ∂y for isotropic turbulence.…”