L. W. B. Browne

Low-Reynolds-number effects in a fully developed turbulent channel flow

Low-Reynolds-number effects are observed in the inner region of a fully developed turbulent channel flow, using data obtained either from experiments or by direct numerical simulations. The Reynolds-number influence is observed on the turbulence intensities and to a lesser degree on the average production and dissipation of the turbulent energy. In the near-wall region, the data confirm Wei & Willmarths (1989) conclusion that the Reynolds stresses do not scale on wall variables. One of the reasons proposed by these authors to account for this behaviour, namely the ‘geometry’ effect or direct interaction between inner regions on opposite walls, was investigated in some detail by introducing temperature at one of the walls, both in experiment and simulation. Although the extent of penetration of thermal excursions into the opposite side of the channel can be significant at low Reynolds numbers, the contribution these excursions make to the Reynolds shear stress and the spanwise vorticity in the opposite wall region is negligible. In the inner region, spectra and co-spectra of the velocity fluctuations u and v change rapidly with the Reynolds number, the variations being mainly confined to low wavenumbers in the u spectrum. These spectra, and the corresponding variances, are discussed in the context of the active/inactive motion concept and the possibility of increased vortex stretching at the wall. A comparison is made between the channel and the boundary layer at low Reynolds numbers.

Turbulent energy dissipation in a wake

The average turbulent energy dissipation is often estimated by assuming isotropy and measuring the temporal derivative of the longitudinal velocity fluctuation. In this paper, the nine major terms that make up the total dissipation have been measured in the self-preserving region of a cylinder wake for a small turbulence Reynolds number. The results indicate that local isotropy is not satisfied; the isotropic dissipation, computed by assuming isotropic relations, being smaller than the total dissipation by about 45% on the wake centreline and by about 80% near the wake edge. Indirect verification of the dissipation measurements is provided by the budget of the turbulent kinetic energy. This budget leads to a plausible distribution for the pressure diffusion term, obtained by difference.

Some characteristics of small-scale turbulence in a turbulent duct flow

The fine-scale structure of turbulence in a fully developed turbulent duct flow is examined by considering the 3D velocity derivative field obtained from direct numerical simulations at two relatively small Reynolds numbers. The magnitudes of all mean-square derivatives (normalized by wall variables) increase with the Reynolds number, the increase being largest at the wall. These magnitudes are not consistent with the assumption of local isotropy except perhaps near the duct center-line. When the assumption of local isotropy is relaxed to one of local axisymmetry, or invariance with respect to rotation about a coordinate axis (here chosen in the streamwise direction), satisfactory agreement is indicated by the data outside the wall region. Support for axisymmetry is demonstrated by anisotropy invariant maps of the dissipation and vorticity tensors.

Calibration ofX-probes for turbulent flow measurements

We compare two methods of calibrating the yaw response of hot-wire probes: (i) the assumption that an effective angle, independent of the flow speed, can be deduced; (ii) the more general approach of determining the yaw response at a number of different speeds. The first, simpler, approach is shown to give surprisingly reasonable results for the usual turbulence statistics, even in high turbulence intensity flows. Some differences in the distribution of the inclination of the instantaneous velocity vector are observed. There is no advantage in using thek2 factor to allow for longitudinal cooling.

On the organized motion of a turbulent plane jet

Measurements of space–time correlations of longitudinal and normal velocity fluctuations and of temperature fluctuations support the existence of counter-rotating spanwise structures appearing alternately on opposite sides of the jet centreline in the self-preserving region of the flow. The frequency of these structures closely satisfies self-preservation. The asymmetric arrangement of the structures is first observed downstream of the position where the jet mixing layers nominally merge but upstream of the onset of self-preservation. Closer to the jet exit, the space–time correlations indicate the existence of spanwise structures that are symmetrical about the centreline.

The interaction region of a turbulent plane jet

All three velocity fluctuations and the temperature fluctuation have been measured in a slightly heated turbulent plane jet. Attention is focused on the interaction region of the flow, which is situated between the location where the two mixing layers nominally merge and that which corresponds to approximate self-preservation. For the jet considered here the mixing-layer structures are symmetrical with respect to the centreline, and when they meet in the interaction region the redistribution of turbulence quantities is dramatic. This redistribution is examined in detail. Also examined is the effect of the generation, in the interaction region, of new structures, asymmetric with respect to the centreline, which evolve into the self-preserving flow region downstream. Turbulence parameters, such as the turbulent Prandtl number, probability density functions, skewness and flatness factors, are also presented, primarily to guide computer simulations of this flow. The superposition procedure of Weir, Wood & Bradshaw (1981), which assumes that the turbulence structure of each mixing layer is not significantly altered by the interaction, is not appropriate to the present flow.

Spatial organization of large structures in the turbulent far wake of a cylinder

Using an array of x-probes aligned in the plane of mean shear in the turbulent far wake of a circular cylinder, instantaneous velocity vector patterns are obtained from which stream-function approximations and sectional streamlines are derived. Conditional patterns obtained using different methods for detecting the organised motion are essentially independent of the particular method used. The spatial arrangement of the organised motion about the flow centreline varies in a continuous manner between opposing and alternating modes. Results presented include conditional patterns for the opposing and alternating modes and the relative contributions made by each mode to the Reynolds stresses. A modified Rankine vortex kinematic model based as much as possible on experimental data and incorporating both modes, yields mean velocity and Reynolds stress distributions which agree well with experiment. A quasi-three-dimensional version of the model implies that large spanwise vortices and shear-aligned double rollers represent the same three-dimensional organised motion from two different viewpoints.

Organized structures in a turbulent plane jet: topology and contribution to momentum and heat transport

In the self-preserving region of a slightly heated turbulent plane jet, conventional isocorrelation contours of velocity and temperature fluctuations support the existence of organized large-scale structures. Temperature fronts associated with these structures were visually detected using a spanwise rake of cold wires. This method of detection was then used to condition velocity and temperature fluctuations and products of these fluctuations. Ensemble-averaged velocity vectors, constructed in the plane of main shear, suggest a topology for the organized motion in which the temperature front is identified with the diverging separatrix connecting adjacent structures on the same side of the centreline. Coherent stresses and heat fluxes are particularly significant near the diverging separatrix. Contributions by the coherent and random motions to the averaged momentum and heat transports are generally of the same order of magnitude.

A DESCRIPTION OF THE ORGANIZED MOTION IN THE TURBULENT FAR WAKE OF A CYLINDER AT LOW REYNOLDS NUMBER

The topology of the organized motion has been obtained in the slightly heated self-preserving far wake of a circular cylinder at a Reynolds number, based on the cylinder diameter, of about 1200. In a frame of reference moving with the organized motion, the toplogy in the plane of main shear reduces to a succession of centres and saddles, located at about the wake half-width. Centres are identifiable by large values of spanwise vorticity associated with the coherent large-scale motion. Saddles occur at the intersection of converging and diverging separatrices, the latter being identifiable with the high strain rate due to the large-scale motion. Large values of the longitudinal turbulence intensity associated with the smaller-scale motion occur at the centres. High values of the normal and shear stresses, the temperature variance and heat fluxes associated with the large-scale motion occur on either side of each saddle point along the direction of the diverging separatrix. Contours for the production of energy and temperature variance associated with the small-scale motion are aligned along the diverging separatrices, and have maxima near the saddle point. Contours for one component of the dissipation of small-scale temperature variance also have a high concentration along the diverging separatrix. Flow visualizations in the far wake suggest the existence of groups of three-dimensional bulges which are made up of clusters of vortex loops.

Determination of time constants of cold wires

The time constant of a fine cold wire used as a resistance thermometer can be obtained by a technique which is based on ideas developed for the pulsed‐wire technique for velocity measurement in highly turbulent flows and in regions of flow reversal. The cold wire is placed downstream of, and at right angles to, a wire of larger diameter which is pulsed with a short duration voltage pulse. The response of the cold wire to the change in the temperature of the flow is used to determine the time constant of the wire, once the pulsed wire time constant is known. Frequency responses based on measured time constants for cold wires of 2.5, 1.3, and 0.63 μm diameters are presented as a function of flow velocity.