4 results
The viscous flow on surfaces with longitudinal ribs
- D. W. Bechert, M. Bartenwerfer
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- Journal:
- Journal of Fluid Mechanics / Volume 206 / September 1989
- Published online by Cambridge University Press:
- 26 April 2006, pp. 105-129
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The viscous sublayer of a turbulent boundary layer on a surface with fine longitudinal ribs (riblets) is investigated theoretically. The mean flow constituent of this viscous flow is considered. Using conformal mapping, the velocity distributions on various surface configurations are calculated. The geometries that were investigated include sawtooth profiles with triangular and trapezoidal grooves as well as profiles with thin blade-shaped ribs, ribs with rounded edges and ribs having sharp ridges and U-shaped grooves. (This latter riblet configuration is also found on the tiny scales of fast sharks.) Our calculations enable us to determine the location of the origin of the velocity profile that lies somewhat below the tips of the ridges. The distance between this origin and the tip of the ridge we call ‘protrusion height’. The upper limit for the protrusion height is found to be 22% of the lateral rib spacing; the coefficient 0.22 being the value of the expression π−1 In 2. This limit is valid for two-dimensional riblet geometries. Analogous experiments with an electrolytic tank are carried out as an additional check on the theoretical calculations. This is also an easy way to determine experimentally the location of the origin of the velocity profile for arbitrary new riblet geometries. A possible connection between protrusion height and drag reduction in a turbulent boundary layer flow is discussed. Finally, the present theory also produces an orthogonal grid pattern above riblet surfaces which may be utilized in future numerical calculations of the whole turbulent boundary layer.
Excitation of instability waves in free shear layers Part 2. Experiments
- D. W. Bechert, B. Stahl
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- Journal:
- Journal of Fluid Mechanics / Volume 186 / January 1988
- Published online by Cambridge University Press:
- 21 April 2006, pp. 63-84
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The acoustical excitation of shear layers is investigated experimentally. Acoustical excitation causes, for example, the so-called ‘orderly structures’ in shear layers and jets. Also, the deviations in the spreading rate between different turbulent-shear-layer experiments are due to the same excitation mechanism. The present investigations focus on measurements in the linear interaction region close to the edge from which the shear layer is shed. We report on two sets of experiments (Houston 1981 and Berlin 1983/84). The measurements have been carried out with laminar shear layers in air using hot-wire anemometers and microphones. The agreement between these measurements and the theory is good. Even details of the fluctuating flow field correspond to theoretical predictions, such as the local occurrence of negative phase speeds.
Excitation of instability waves in free shear layers. Part 1. Theory
- D. W. Bechert
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- Journal:
- Journal of Fluid Mechanics / Volume 186 / January 1988
- Published online by Cambridge University Press:
- 21 April 2006, pp. 47-62
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The generation of instability waves in free shear layers is investigated theoretically. The model assumes an infinitesimally thin shear layer shed from a semi-infinite plate which is exposed to sound excitation. For this model the forced instability waves are calculated. The shear-layer excitation by a source farther away from the plate edge in the downstream direction is very weak while upstream from the plate edge the excitation is relatively efficient. A special solution is given for the source at the plate edge. Any type of source farther away from the plate edge produces a parabolic pressure field near the edge. For this latter, fairly general case, a reference quantity is found for the magnitude of the excited instability waves. The theory is then extended to two streams, one on each side of the shear layer, having different velocities and densities. Furthermore, the excitation of a shear layer in a channel is calculated. The limitations to the theory and some aspects related to experiments are discussed. In particular, for a comparison with measurements, numerical computations of the velocity field outside the shear layer have been carried out.
Experiments on drag-reducing surfaces and their optimization with an adjustable geometry
- D. W. BECHERT, M. BRUSE, W. HAGE, J. G. T. VAN DER HOEVEN, G. HOPPE
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- Journal:
- Journal of Fluid Mechanics / Volume 338 / 10 May 1997
- Published online by Cambridge University Press:
- 10 May 1997, pp. 59-87
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Previous research has established that surfaces with tiny ribs (riblets) aligned in the streamwise direction can reduce the turbulent wall-shear stress below that of a smooth surface. Typical skin-friction reductions have been found to be about 5%. The results of the present investigation, however, demonstrate a considerable improvement over this value. This improvement is achieved by a systematic experimental optimization which has been guided by theoretical concepts.
A key feature of our experiments is the utilization of an oil channel. Previous experiments in wind tunnels had to contend with very small riblet dimensions which typically had a lateral rib spacing of about 0.5 mm or less. By contrast, in our oil channel, the ribs can have a lateral spacing of between about 2 and 10 mm. This increased size of the surface structures enables test surfaces to be manufactured with conventional mechanical methods, and it also enables us to build test surfaces with adjustable geometry. In addition, the Berlin oil channel has a novel shear stress balance with an unprecedented accuracy of ±0.3%. This latter feature is a prerequisite for a systematic experimental optimization.
In the present investigation, surfaces with longitudinal ribs and additional slits are studied. The experiments cover a fairly large range of parameters so that the drag reduction potential of a surface with ribs and/or slits is worked out conclusively. A large parameter range is made possible because of the adjustability of the surfaces as well as the automatic operation of the oil channel. In particular, the following tests were run:
(i) Shear stress measurements with conventional riblet configurations, i.e. with triangular and semi-circular grooves, have been carried out. These measurements were necessary in order to establish the connection between our oil channel data and previous data from wind tunnels. As was previously established, we found a drag reduction of about 5%.
(ii) An adjustable surface with longitudinal blade ribs and with slits was built and tested. Both groove depth and slit width could be varied separately and continuously during the experiment. It turned out, that slits in the surface did not contribute to the drag reduction. Nevertheless, these investigations show how perforated surfaces (e.g. for boundary-layer control) can be designed for minimal parasitic drag. On the other hand, with closed slits, an optimal groove depth for the rib surface could be determined, i.e. half of the lateral rib spacing. For this configuration, we found an 8.7% skin-friction reduction. By carefully eliminating deleterious effects (caused by little gaps, etc.), the skin-friction reduction could be improved to a record value of 9.9%.
(iii) A quantitative comparison between theory and experiment was carried out. The theory is based on the assumption that riblets impede the fluctuating turbulent crossflow near the wall. In this way, momentum transfer and shear stress are reduced. The simplified theoretical model proposed by Luchini (1992) is supported by the present experiments.
(iv) For technological applications of riblets, e.g. on long-range commercial aircraft, the above thin-blade ribs are not practical. Therefore, we have devised a surface that combines a significantly improved performance (8.2 %) with a geometry which exhibits better durability and enables previously developed manufacturing methods for plastic riblet film production to be used. Our riblet geometry exhibits trapezoidal grooves with wedge-like ribs. The flat floor of the trapezoidal grooves permits an undistorted visibility through the transparent riblet film which is essential for crack inspection on aircraft.