P. N. Joubert

Rough wall turbulent boundary layers

Abstract : The paper describes a detailed experimental study of turbulent boundary layer development over rough walls in both zero and adverse pressure gradients. Skin friction was determined by pressure tapping the roughness elements and measuring their form drag. Two wall roughness geometries were chosen each giving a different law of behaviour. However, it has been found that results for both types of roughness correlate with a Reynolds number based on wall shear velocity and on the distance below the crests of the elements from which the logarithmic distribution of velocity is measured. One important implication of this is that a zero pressure gradient boundary layer with a cavity type rough wall conforms to Rottas condition of precise self preserving flow. (Author)

LOW-REYNOLDS-NUMBER TURBULENT BOUNDARY LAYERS

An investigation was undertaken to improve our understanding of low-Reynoldsnumber turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. In practice, such flows generally occur in close proximity to a tripping device and, though it was known that the flows are affected by the actual low value of the Reynolds number, it was realized that they may also be affected by the type of tripping device used and variations in free-stream velocity for a given device. Consequently, the experimental programme was devised to investigate systematically the effects of each of these three factors independently. Three different types of device were chosen: a wire, distributed grit and cylindrical pins. Mean-flow, broadband-turbulence and spectral measurements were taken, mostly for values of Re varying between about 715 and about 2810. It was found that the meanflow and broadband-turbulence data showed variations with R,, as expected. Spectra were plotted using scaling given by Perry, Henbest & Chong (1986) and were compared with their models which were developed for high-Reynolds-number flows. For the turbulent wall region, spectra showed reasonably good agreement with their model. For the fully turbulent region, spectra did show some appreciable deviations from their model, owing to low-Reynolds-number effects. Mean-flow profiles, broadband-turbulence profiles and spectra were found to be affected very little by the type of device used for Re x 1020 and above, indicating an absence of dependence on flow history for this R, range. These types of measurements were also compared at both R, x 1020 and R, x 2175 to see if they were dependent on how Re was formed (i.e. the combination of velocity and momentum thickness used to determine Re). There were noticeable differences for R, x 1020, but these differences were only convincing for the pins, and there was a general overall improvement in agreement for R, x 2175.

Turbulent line vortices

An attempt has been made to establish the laws governing the flow in a turbulent line vortex. Up to the present time theoretical solutions for laminar flow have been used for comparison with experimental results for turbulent flow to find an ‘eddy viscosity’ term and its variation with various parameters. An approach is developed along lines similar to the methods used in turbulent boundary-layer theory and is found to be reasonably successful as far as the work has proceeded. It is predicted by theory, and confirmed by experiment, that the circulation in the vortex is proportional to the logarithm of radius under certain conditions. For the present experimental conditions, the vortices are found to be completely independent of viscosity effects when the parameter WZ/K 0 exceeds 150, and above this value the experimental results may be correlated to give a universal distribution of circulation in the inner region of the vortex. Further experiments are necessary to verify and extend the results of these tests before any definite conclusions may be made regarding the circulation distribution in the outer core region of the vortex and the growth and development of the vortex.

A boundary layer developing in an increasingly adverse pressure gradient

This paper deals with a survey of mean flow and fluctuating quantities in a turbulent boundary layer developing on a smooth wall in a pressure domain P ( x ), where both dP/dx and d 2 P/dx 2 are positive (increasingly adverse). The two-dimensional nature of the flow field was checked by momentum balance, as well as velocity traverses either side of the working section centre-line. Using the integrated form of the momentum integral equation, it was found that the skinfriction term and the summed momentum and pressure terms differed by at most 19%; but for the majority of measuring points they differed by less than 14%. The off-centre-line velocity profiles were indistinguishable from those taken on the centre-line. The flow field was also surveyed for fluctuating components

The form drag of two-dimensional bluff-plates immersed in turbulent boundary layers

(\overline{u^2_1})^{\frac{1}{2}}, (\overline{u^2_2})^{\frac{1}{2}}, (\overline{u^2_3})^{\frac{1}{2}}

Effects of small streamline curvature on turbulent duct flow

, and

TURBULENT SHEAR FLOW IN A CURVED DUCT

\overline{u_1u_2}

A turbulent flow over a curved hill Part 1. Growth of an internal boundary layer

, as well as for u 1 spectra. Wherever possible, the results were compared with existing models of boundary-layer development. These comparisons indicated that the only all-embracing model for boundary-layer development is the law of the wall.

The measurement of skin friction in turbulent boundary layers with adverse pressure gradients

Measurements of the distributions of pressure on a bluff flat plate (fence) have been correlated with the characteristics of the smooth-wall boundary layer in which it is immersed. For zero pressure-gradient flows, correlations are obtained for the variation of form drag with plate height h which are analogous in form to the ‘law of the wall’ and the ‘velocity-defect law’ for the boundary-layer velocity profile. The data for adverse pressure-gradient flows is suggestive of a ‘law of the wake’ type correlation. Pressures on the upstream face of the bluff-plate are determined by a wall-similarity law, even for h /δ > 1, and are independent of the pressure-gradient history of the flow; the separation induced upstream is apparently of the Stratford-Townsend type. The effects of the history of the boundary layer are manifested only in the flow in the rear separation bubble, and then only for h /δ > ½. The base pressure is also sensitive to free-stream pressure gradients downstream of the bluff-plate. The relative extent of upstream influence of the bluff-plate on the boundary layer is found to increase rapidly as h /δ decreases. One set of measurements of the mean flow field is also presented.

Developing turbulent boundary layers with system rotation

Mean velocity profiles, turbulence intensity distributions and streamwise energy spectra are presented for turbulent air flow in a smooth-walled, high aspect ratio rectangular duct with small streamwise curvature, and are compared with measurements taken in a similar straight duct. The results for the present curved flow are found to differ significantly from those for the more highly curved flows reported previously, and suggest the need to distinguish between ‘shear-dominated’ flows with small curvature and ‘inertia-dominated’ flows with high curvature. Velocity defect and angular-momentum defect hypotheses fail to correlate the central-region mean flow data, but the wall-region data are consistent with the conventional straight-wall similarity hypothesis. A secondary flow of Taylor–Goertler vortex pattern is found to occur in the central flow region. An examination of the flow equations yields a model for the mechanisms by which streamline curvature affects turbulent flow, in which a major effect is a direct change in the turbulent shear stress through a conservative reorientation of the turbulence intensity components. Data for the streamwise and transverse turbulence intensities show behaviour consistent with that expected from the equations, and the distribution of total turbulence energy in the central flow region is found to be nearly invariant with Reynolds number and wall curvature, in agreement with the model. Energy spectra for the streamwise component are examined in terms of a Townsend-type two-component turbulence model. They indicate that a universal, ‘active’ component exists in all flow regions, with an ‘inactive’ component which affects only the low wavenumber spectra intensities. This is taken to imply that the effects of streamline curvature are determined by the central-region flow structure alone.