Experimental investigation of turbulent flow in a channel with rough walls
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This thesis focuses on the effects of surface roughness on the turbulent structure in a two-dimensional channel flow. Various turbulence quantities have been investigated for a rough surface generated by either spanwise mounted rods or a perforated plate, covering both the ceiling and the floor of the channel. Results from a smooth wall channel flow have been used as a reference. Conclusions from investigations in rough wall boundary layers have so far been ambiguous. This is, inter alia, connected to the difficulty of obtaining reliable estimates of the friction velocity, uτ , which is believed to be the main scaling parameter. However, in a channel flow, uτ may be obtained directly from the streamwise pressure gradient, which is relatively easy to measure. The present study was therefore initiated with the aim to reduce the uncertainties in the results and enable firmer conclusions to be drawn. Hot-wire anemometry has been used as the primary measurement technique. For the calibration of the yaw-response of X-wires at low velocities a velocity dependent effective angle method has been developed. This method has been verified to give similar results as a full velocity vs. yaw-angle calibration method, which is considerably more laborious to use. Compared to the more common fixed effective angle method this new method has been shown to improve the estimates of the Reynolds stresses considerably. The mean velocity profile in the rough wall cases display the expected shift in the logarithmic law, ∆U+, which for both roughnesses is shown to follow the behaviour of a k-type roughness. The velocity defect profiles indicate similarity between the smooth and rough surfaces in the outer region. The measured distributions of the Reynolds stresses are similar for all surfaces outside y ≈5 k. Estimates of stress ratios and the anisotropy tensor indicate that the rough wall turbulence structure differs from the smooth wall flow only in the roughness sublayer, where it is more isotropic. This is believed to be connected to a break-up of the highly organized streamwise vortices. Support for this may be found in profiles of the streamwise integral scale, which is shown to be attenuated for the rough surfaces. A quadrant analysis indicate that differences in the turbulent structure extend somewhat further out than what is suggested by the stresses. The rough surfaces inhibit ejection events near the wall, presumably because low momentum fluid is trapped between the roughness elements. The most apparent feature of the rough surfaces is, however, the enhancement of sweeps, caused by a reduction in the damping of the wall normal motion because of the open nature of the surfaces. As is observed for some of the structural features over the rough surfaces, the transport properties are also affected to a certain degree outside the roughness sublayer. This is documented through the third order moments. An analysis of the Reynolds number dependency in both the physical and wavenumber domain support the concept of a universal ‘active’ motion and an ‘inactive’ motion which varies with Reynolds number. However, this conjecture seems to be valid only for relatively high Reynolds numbers. Estimates of the streamwise small scale intermittency exponent indicates that the large scale forcing penetrates through to the small scales at the low Reynolds numbers that are presently investigated. This means that the small scales over the rough surfaces are more isotropic than over a smooth surface. However, in the central region of the channel flow the small scale behaviour for all the surfaces is very similar to that measured in homogenous and isotropic turbulence. The present results indicate collectively that there are only minor differences in the statistical and structural quantities outside the roughness sublayer between the smooth and rough channel flows. This is in support of the classical ‘wall similarity hypothesis’.