Uniform Distortion Research Articles

A ν-fluid model of homogeneous turbulence subjected to uniform mean distortion

In two previous papers (Proudman 1970; Dowden 1972) it has been shown that some of the phenomena of turbulence a t high Reynolds numbers can be modelled by a suitable chosen member of the class of ν-fluids. These are non-Newtonian fluids all of whose properties depend only on a single dimensional constant whose dimensions are those of viscosity. The purpose of this paper is to construct an equation to model homogeneous turbulence in the presence of a spatially constant rate of deformation in the limit of infinite Reynolds number.The equation employed is that of a doubly degenerate third-order v-fluid (in Proudman's classification) in the limit ν → 0. In such a fluid the stress tensor S is governed by an equation of the form \[ A\dot{S}\ddot{S}+B\dot{S}^2+Cu^{\prime}S\dot{S}+D\dot{u}^{\prime}S^2 + Eu^{\prime 2}S^2 = 0, \] where A, B,…, E are isotropic tensor constants of the fluid, u′ is the total rate of deformation tensor and dots denote time derivatives. A list of properties required of the equation and its solution is proposed, and the most general form of A, B,…, E is given consistent with these requirements. Computed solutions of this equation are compared with the results of experiments on homogeneous turbulence, and are found to agree well with them.

The uniform distortion of a turbulent flame

The influence of uniform and constant strain rate on the structure of turbulence in duct flow and the combustion process of homogeneous mixtures at high Reynolds numbers has been examined experimentally. The distortion of the flow produces a change in the distribution of turbulence and a certain decrease in its intensity, introduces a small anisotropy, and strengthens considerably the microstructure of the turbulence therefore also the vorticity of low. At the same time there is a considerable increase in the intensity of combustion in the strained turbulent flame depending on the value and the rate of strain.

The uniform distortion of a turbulent wake

The effect of a uniform and constant rate of strain imposed upon a turbulent wake which is generated behind a circular cylinder has been examined experimentally. The strain field, produced by passing the flow through a distorting duct of constant cross-sectional area, simultaneously compresses the wake in the plane of the cylinder and extends it in the other lateral direction but applies no strain in the direction of the main stream. The investigation shows the existence of a large-scale, periodic eddy structure within the strained wake, similar to, but more intense than, that which was observed for the undistorted wake. These large lateral convective motions appear to be the primary mechanism controlling the development of the flow, and are responsible for the failure of the wake to attain the theoretically predicted self-preservation state. It is shown that the strain rate, which acts favourably upon these large eddies, is sufficient to produce a net increase in vorticity in spite of the ordinary processes of turbulent viscous decay. At the same time, however, the rate of viscous dissipation of the smallest eddies in the flow is augmented by the strain, and the resulting wake structure is almost entirely dominated by the large-eddy motions. A possible means by which the large eddies are initiated is discussed.

The effect of uniform distortion on weak homogeneous turbulence

The effect of uniform distortion on weak homogeneous turbulence