Surface roughness effects on flow noise

We report high-resolution measurements of the properties of the velocity boundary layer in turbulent thermal convection using the particle image velocimetry (PIV) technique and measurements of the temperature profiles and the thermal boundary layer. Both velocity and temperature measurements were made near the lower conducting plate of a rectangular convection cell using water as the convecting fluid, with the Rayleigh numberRavarying from 109to 1010and the Prandtl numberPrfixed at 4.3. From the measured profiles of the horizontal velocity we obtain the viscous boundary layer thickness δυ. It is found that δυfollows the classical Blasius-like laminar boundary layer in the present range ofRa, and it scales with the Reynolds numberReas δυ/H= 0.64Re−0.50±0.03(whereHis the cell height). While the measured viscous shear stress and Reynolds shear stress show that the boundary layer is laminar forRa< 2.0 × 1010, two independent extrapolations, one based on velocity measurements and the other on velocity and temperature measurements, both indicate that the boundary layer will become turbulent atRa~ 1013. Just above the thermal boundary layer but within the mixing zone, the measured temperature r.m.s. profiles σT(z) are found to follow either a power law or a logarithmic behaviour. The power-law fitting may be slightly favoured and its exponent is found to depend onRaand varies from −0.6 to −0.77, which is much larger than the classical value of −1/3. In the same region, the measured profiles of the r.m.s. vertical velocity σw(z) exhibit a much smaller scaling range and are also consistent with either a power-law or a logarithmic behaviour. The Reynolds number dependence of several wall quantities is also measured directly. These are the wall shear stress τw~Re1.55, the viscous sublayer δw~Re−0.91, the friction velocityuτ~Re0.80, and the skin-friction coefficientcf~Re−0.34. All of these scaling properties are very close to those predicted for a classical Blasius-type laminar boundary layer, except that ofcf. Similar to classical shear flows, a viscous sublayer is also found to exist in the present system despite the presence of a nested thermal boundary layer. However, velocity profiles normalized by wall units exhibit no obvious logarithmic region, which is likely to be a result of the very limited distance between the edge of the viscous sublayer and the position of the maximum velocity. Compared to traditional shear flows, the peak position of the wall-unit-normalized r.m.s. profiles is found to be closer to the plate (atz+=z/δw≃ 5). Our overall conclusion is that a Blasius-type laminar boundary condition is a good approximation for the velocity boundary layer in turbulent thermal convection for the present range of Rayleigh number and Prandtl number.

An experimental investigation has been conducted to identify the effects of pressure gradient and surface roughness on turbulent boundary layers. In Part II, smooth- and rough-surface turbulent boundary layers with and without adverse pressure gradient (APG) are presented at a fixed Reynolds number (based on the length of flat plate) of 900,000. Flat-plate boundary layer measurements have been conducted using a single-sensor, hot-wire probe. For smooth surfaces, compared to the zero pressure gradient (ZPG) boundary layer, the APG boundary layer has a higher mean velocity defect throughout the boundary layer and lower friction coefficient. APG decreases the streamwise normal Reynolds stress for y less than 0.4 times the boundary layer thickness and increases it slightly in the outer region. For rough surfaces, APG reduces the roughness effects of increasing the mean velocity defect and normal Reynolds stress for y less than 23 and 28 times the average roughness height, respectively. Consistently, for the same roughness, APG decreases the integrated streamwise turbulent kinetic energy. APG also decreases the roughness effect on the friction coefficient, roughness Reynolds number, and roughness shift. Compared to the ZPG boundary layers, the roughness effects on integral boundary layer parameters—boundary layer thickness and momentum thickness—are weaker under APG. Thus, contrary to the favorable pressure gradient (FPG) in part I, APG reduces the roughness effects on turbulent boundary layers.

A fully turbulent channel flow with smooth and rod-roughened walls has been investigated using hot-wire anemometry and direct numerical simulations (DNS). The mean flow follows the law of the wall for both surfaces and the velocity defect suggests that the outer layer is very little affected by the roughness. The Reynolds stresses appear to be very similar for the two surface geometries outside $y\,{\approx}\,5k$, where $k$ is the roughness height. A quadrant analysis shows that the structural differences close to the wall extend somewhat further out. The turbulence structure is further investigated using stress ratios and the anisotropy tensor, which corroborate the findings from the Reynolds stresses. Many of the recent investigations on boundary layers seem to find large differences between smooth and rough wall data in the outer layer also. A tentative explanation for the apparent dependence on flow type of the surface roughness effects is given.

A three-dimensional computation was conducted to understand effects of the inlet boundary layer thickness on the internal flow and the loss characteristics in a low-speed axial compressor operating at the design condition (φ = 85%) and near stall condition (φ = 65%). At the design condition, independent of the inlet boundary layer thickness, flows in the axial compressor show similar characteristics such as the pressure distribution, size of hub corner-stall, tip leakage flow trajectory, limiting streamlines on the blade suction surface, etc. But, as the load is increased, for the thick inlet boundary layer at hub and casing, the hub corner stall grows to make a large separation region between the hub and suction surface, and the tip leakage flow is more vortical than that observed in the case with thin inlet boundary layer and has the critical point where the trajectory of the tip leakage flow is suddenly turned to the downstream. For the thin inlet boundary layer, the hub corner stall decays to form the thick boundary layer from hub to midspan on the suction surface owing to the blockage of the tip leakage flow and the tip leakage flow leans to the circumferential direction more than at the design condition. In addition to these, the severe reverse flow, induced by both boundary layers on the blade surface and the tip leakage flow, can be found to act as the blockage of flows near the casing, resulting in a heavy loss. As a result of these differences of the internal flow made by the different inlet boundary layer thickness, the spanwise distribution of the total loss is changed dramatically. At the design condition, total pressure losses for two different boundary layers are almost alike in the core flow region but the larger losses are generated at both hub and tip when the inlet boundary layer is thin. At the near stall condition, however, total loss for thick inlet boundary layer is found to be greater than that for thin inlet boundary layer on most of the span except the region near the hub and casing. In order to analyze effects of inlet boundary layer thickness on total loss in detail, total loss is scrutinized through three major loss categories available in a subsonic axial compressor such as profile loss, tip leakage loss and endwall loss.

The endwall flow features are heavily dependent on the incoming boundary layer. It was particularly important to increase understanding the effect of inlet boundary layer thickness on endwall secondary flow under unsteady conditions. In present study, the influences of incoming wakes and various boundary layer thickness on endwall secondary flow were studied in a typical high-lift low-pressure turbine cascade, numerical calculation and experiment measurement of seven-hole probe were adopted at Re = 25,000 (based on the inlet velocity and the axial chord). Upstream wakes were simulated through moving rods upstream of the cascade. Detailed analysis was focused on the mechanisms of periodic wake influencing on the endwall vortex structures under thick endwall boundary layer condition. Influences of two different endwall boundary layer thickness on endwall secondary vortices structures were also comparatively analyzed. Under steady condition without wake, although thick incoming boundary layer reduces the cross-passage pressure gradient near endwall, more low momentum fluid inside thick endwall boundary layer is drawn into secondary vortices, finally resulting in stronger the pressure side leg of the leading edge horseshoe vortex and passage vortex, compared to the results of thin boundary layer condition. Under unsteady condition with thick inlet boundary layer, the “negative jet” effect of incoming wakes delays intersection of pressure side leg and suction side leg of leading edge horseshoe vortex on blade suction surface. The time-averaged strength of passage vortex and counter vortex core decreases by about 32%, and the underturning and overturning of endwall secondary flow is suppressed. The instantaneous results also indicate the endwall secondary vortices are reduced periodically at the position of wakes passing.

The oblique shock impinging on the supersonic turbulent boundary layer leads to a mixing layer and the emergence of large-scale coherent structures within the interaction zone which leave significant velocity defect and turbulence amplification downstream. In the present study, we investigate the turbulence recovery in the post-shock region by exploiting direct numerical simulation data of the oblique-shock/turbulent boundary layer interaction flow at the incoming Mach number of $2.28$ and the shock angle of $33.2^\circ$ , with special attention paid to the contribution of the mixing layer and large-scale structures to flow dynamics. For that purpose, we propose to split the mean velocity, Reynolds stresses and spanwise spectra into a canonical portion that is constructed according to the statistics of canonical turbulent boundary layers, and a mixing-layer-induced portion. We found that the hidden mixing layer grows with the boundary layer thickness and that the induced mean shear and Reynolds stresses decay at different rates. The mean velocity recovers to the canonical profiles at a distance of 13 boundary layer thicknesses downstream where the mixing-layer-induced mean shear ceases to have strong impacts. The recovery of Reynolds stresses requires 10 boundary layer thicknesses in the near-wall region but a much longer streamwise extent in the outer region due to the slow decay of large-scale motions. These large-scale motions superpose on the near-wall turbulence, intensifying the turbulent fluctuations, yet having a trivial impact on the skin friction, for the contribution of the mixing-layer-induced mean shear and Reynolds shear stress are balanced by the advection term. We further establish a simple physical model capable of approximately predicting the streamwise evolution of mixing-layer-induced mean shear and turbulent kinetic energy. This model suggests that the complete recovery of turbulence in the outer region requires a streamwise extent of approximately 50 boundary layer thicknesses.

The influence of the boundary layer (BL) thickness on the tonal noise generated by subsonic impinging jets is investigated. For that, initially laminar jets at Mach numbers$0.6$and$0.9$with BL thicknesses$0.05r_0$,$0.1r_0$and$0.2r_0$, where$r_0$is the pipe-nozzle radius, impinging on a plate at$6r_0$from the nozzle, are simulated. For Mach number$0.9$, acoustic tones due to feedback loops of axisymmetric nature between the nozzle and the plate are generated at frequencies that do not vary with the BL thickness. The two dominant tones are, however,$17$and$26\ \mathrm {dB}$stronger for the thickest BL compared with the thinnest one. For Mach number$0.6$, for the thinnest BL no acoustic peaks appear, as observed in the experiments of the literature, but narrow peaks resulting from axisymmetric feedback loops emerge for thicker BLs. Therefore, low subsonic impinging jets can be resonant for specific nozzle-exit conditions. The increase in tone amplitude for Mach number$0.9$, and the establishment of feedback loops for Mach number$0.6$with increasing BL thickness, are found to result from two changes in the jet flow. The first change is that the shear-layer laminar–turbulent transition occurs farther downstream for a thicker BL, leading to a greater predominance of the axisymmetric aerodynamic fluctuations near the plate. The second change is that the amplification of the flow fluctuations between the nozzle and the plate at the tone frequencies is stronger for thicker BLs.

One of the purposes of this investigation is to throw some additional light on the question of how to correlate between the experimental data from different sources and the theoretical approaches for the study of incompressible turbulent boundary layers development on rough surface. Moreover, the study developed included the presence of adverse pressure gradient; as well as a discussion about the effect of surface roughness on the boundary layer parameters which control the flow behaviour. On the basis of Zancow experimental work with rough surface and the velocity law of Rotta, this study has been developed. In order to obtain the numerical results for the mathematical solution outlined in this work, a computer program is constructed to perform all the necessary calculations. These results are represented in charts and can be utilised for the geometric shape of roughness.

Circulation control can greatly enhance lift on a xed wing. However, the introduction of a high-speed Coanda jet is theorized to signi cantly increase noise, which is a growing concern for a variety of potential circulation control applications. The sound produced by a circulation control airfoil is measured using a phased microphone array and freeeld microphones in an open-jet anechoic wind tunnel. The phased array maps reveal dominant high-frequency noise sources at the sidewall-trailing edge interfaces. These three-dimensional sources prohibit the accurate measurement of two-dimensional circulation control trailing edge noise by a single microphone. Hence, an integrated phased array spectrum is computed and compared with a theory that identi es three potential noise sources: the interaction of the freestream boundary layer with the slot lip edge, the interaction of boundary layer turbulence with the rounded trailing edge, and the interaction of the jet with the surrounding slot geometry. The theory requires detailed ow eld information, including friction velocities, boundary layer thicknesses, displacement thicknesses, and local mean velocities. These parameters are estimated using particle image velocimetry measurements. A quantitative comparison of the measured and theoretical spectra reveal large di erences. The model predicts that the interaction of the freestream boundary layer with the slot lip is the dominant noise source mechanism over most frequencies.

insured that contact between the tube and wall occurred at the shoulder of the bevel. Very light contact could be detected by a change in electrical resistance with no bending of the tube. A micrometer attached to the tube-traversing mechanism could be set at zero at this point. Velocities in the boundary layer were determined from pitot pressure and tunnel supply pressure assuming constant total temperature. The data for all five surveys are tabulated in Ref. 4. The velocity profiles shown on Figs. 2 and 3 were obtained with the D = 0.020-in. and D = 0.095-in. tubes. The curve faired through the D = 0.020-in. data of Fig. 2 is reproduced on Fig. 3 for comparison with the D = 0.095-in. data. The D = 0.020-in. tube gives very nearly the correct results. Figure 3 demonstrates that the interference effects with a tube as large as D = 0.095 in. are quite small. The boundary-layer momentum thickness, 0, and displacement thickness, 6*, were determined from the data for each survey. In order to carry the integrations all the way to the wall, the velocity was assumed to vary with the |th root of distance in the region between the wall and the first survey point. Values of 0 and H = 6*/0 from Ref. 4, nondimensiona lized by values for zero tube diameter, are plotted on Fig. 4. Even with the largest tube (about 25% of the boundary-layer thickness), the error in 0 is only 2% and the error in H only 1%. In plotting the data from Ref. 4 vs D/S, it should be noted that S was taken as the thickness of a boundary layer with the entire velocity profile given by a ^th-root distribution. This fictitious boundary layer had the same 9 as the boundary layer surveyed.

The acoustic impedance of an orifice under a turbulent boundary layer with a pressure gradient was measured. A single orifice was tested in a wind tunnel with freestream velocity varied from 10 to 30 m/s with an imposed pressure gradient which varied from mildly separating to strongly accelerating. The impedance of the orifice as a function of frequency was correlated with variations in the boundary layer parameters. The impedance was insensitive to changes in the outer layer variables, i.e., the boundary layer thickness and pressure gradient. Using inner layer variables, a nondimensional resistance R/ρu* and end correction δe/δeo could be correlated with ωd/u*. It was found that the nondimensional impedance asymptotically approaches a constant value when ωd/u* is greater than 40.

The effects of surface roughness on a spatially developing turbulent boundary layer (TBL) are investigated by performing direct numerical simulations of TBLs over rough and smooth walls. The Reynolds number based on the momentum thickness was varied in the range Reθ = 300 ∼ 1400. The roughness elements were periodically arranged two-dimensional spanwise rods, and the roughness height was k = 1.5θin, where θin is the momentum thickness at the inlet, which corresponds to k/δ = 0.045 ∼ 0.125, δ being the boundary layer thickness. To avoid generating a rough-wall inflow, which is prohibitively difficult, a step change from smooth to rough was placed 80θin downstream from the inlet. The spatially developing characteristics of the rough-wall TBL were examined. Along the streamwise direction, the friction velocity approached a constant value, and self-preserving forms of the turbulent Reynolds stress tensors were obtained. Introduction of the roughness elements affected the turbulent stress not only in the roughness sublayer but also in the outer layer. Despite the roughness-induced increase of the turbulent Reynolds stress tensors in the outer layer, the roughness had only a relatively small effect on the anisotropic Reynolds stress tensor in the outer layer. Inspection of the triple products of the velocity fluctuations revealed that introducing the roughness elements onto the smooth wall had a marked effect on vertical turbulent transport across the whole TBL. By contrast, good surface similarity in the outer layer was obtained for the third-order moments of the velocity fluctuations.

Recent research has shown that 2-D roughness of finite height can damp the second mode instability under certain conditions. For instance, it has been shown that the relative location of 2-D roughness element and the synchronization point is important in determining the 2-D roughness effect on modal growth. It was found that if a roughness element is placed downstream of a disturbance's synchronization point, the disturbance is damped. In this paper, an extensive DNS parametric study on the effect of second mode instability from roughness height, width and spacing between roughness elements are conducted. The results reveal that a taller roughness within one boundary layer thickness height results a stronger damping effect on the second mode. On the other hand, the roughness width effect is relatively insignificant compared with the height effect. Lastly, the spacing between roughness elements has been studied. The results show the increasing in spacing of roughness elements has both advantages and disadvantages. For the second mode control using 2-D roughness elements, roughness elements spacing of 10 times the roughness width has been shown to have the best overall damping effect in a broad frequency bandwidth. Overall, our extensive study has shown that roughness height is an important factor for the amplification/damping effect. For a second mode control design using 2-D roughness, the roughness height of 50% boundary layer thickness, width of 2 boundary layer thicknesss and spacing of 10 have been chosen to optimize the damping mechanism.

Unsteady separation and vortex shedding from a laminar separation bubble over a bluff body

Boundary layer laminarization by convex curvature and acceleration