Modern developments in shear-stress measurement ☆

An outline of the techniques available for the measurement of skin friction in turbulent boundary layers

This thesis deals with the problem of high Reynolds number zero pressuregradient turbulent boundary layers in an incompressible flow without any effects of heat-transfer. The zero-pressure gradient turbulent boundary layer is one of the canonical shear flows important in many applications and of large theoretical interest. The investigation was carried out through an experimental study in the MTL wind-tunnel at KTH, where the fluctuating velocity components and the fluctuating wall-shear stress in a turbulent boundary layer were measured using hot-wire and hot-film anemometry. Attempts were made to answer some basic and “classical” questions concerning turbulent boundary boundary layers. The classical two layer theory was confirmed and constant values of the slope of the logarithmic overlap region (i.e. the von Karman constant) and the additive constants were found and estimated to κ = 0.38, B = 4.1 and B1 = 3.6 (δ = δ95). The inner limit of overlap region was found to scale on the viscous length scale (ν/uτ) and was estimated to be y = 200, i.e. considerably further out compared to previous knowledge. The outer limit of the overlap region was found to scale on the outer length scale and was estimated to be y/δ = 0.15. This also means that a universal overlap region only can exist for Reynolds numbers of at least Reθ ≈ 6000. The values of the newly determined limits explain the Reynolds number variation found in some earlier experiments. Measurements of the fluctuating wall-shear stress using the hot-wire-onthe-wall technique and a MEMS hot-film sensor show that the turbulence intensity τr.m.s./τw is close to 0.41 at Reθ ≈ 9800. A numerical and experimental investigation of the behavior of double wire probes were carried out and showed that the Peclet number based on wire separation should be larger than about 50 to ensure an acceptably low level of thermal interaction. Results are presented for two-point correlations between the wall-shear stress and the streamwise velocity component for separations in both the wallnormal-streamwise plane and the wall-normal-spanwise plane. Turbulence producing events are further investigated using conditional averaging of isolated shear-layer events. Comparisons are made with results from other experiments and numerical simulations. Descriptors: Fluid mechanics, turbulence, boundary layers, high Reynolds number, zero-pressure gradient, hot-wire, hot-film anemometry, oil-film interferometry, structures, streak spacing, micro-electro-mechanical-systems.

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Experimental studies of zero pressure-gradient turbulent boundary layer flow

This article is concerned with the mean velocity distributions of two-dimensional fully developed turbulent plane-channel flows. To yield reliable information, the authors performed detailed hot-wire measurements for more than 12 Reynolds numbers. The experimental investigations covered a wide range of the Reynolds numbers up to Reτ≈5×103, where Reτ is based on the wall friction velocity and the channel half-height. From the distribution of the mean velocity gradient (dU+/dy+)=f(y+) the entire flow field was analyzed, resulting in a logarithmic region for the mean velocity profile in the inertial sublayer, extending almost up to the center of the channel at higher Reynolds numbers. The analysis of the experimental results yield a value of the von Karman constant, κ, close to 0.37(≈1/e) independent of the Reynolds number and the additive constant B=3.70, which is close to 10/e, i.e., U+=e ln y++10/e=(1/0.37)ln y++3.70.

Evaluating the law of the wall in two-dimensional fully developed turbulent channel flows

This survey covers recent developments and applications of four skin-friction measurement techniques (oil-film interferometry, wall hot wire, surface fence and wall pulsed wire). Comparisons of the techniques with each other and with other methods are presented. Applications in attached and separated fully turbulent boundary layers and in highly accelerated laminar-like flows will be shown to demonstrate the application range and the limits of the various techniques.

https://iopscience.iop.org/article/10.1088/0957-0233/7/10/010/pdf

New developments and applications of skin-friction measuring techniques

An oil film on a solid surface moves under the action of gravity or of the pressure gradient and skin friction resulting from the flow of air over the oil surface. Such oil flows are studied experimentally and theoretically. If the film is thin enough, the dominant force is the skin friction, and a simple relation is obtained between the film thickness variation and the skin friction distribution. The other forces give a perturbation which may be estimated and which decreases with time. The appropriate film thickness is of the order of 10 mu m and so is conveniently measured by interferometry. Experimental results confirm the theory and show that the method gives reasonably accurate measurements of skin friction distribution in low speed flows.

https://iopscience.iop.org/article/10.1088/0022-3735/9/3/015/pdf

L H Tanner

Papers

A study of the motion of oil films on surfaces in air flow, with application to the measurement of skin friction