Aeroacoustics of square finite wall-mounted cylinders with different aspect ratios in pressure-gradient flows.

Flow-induced noise produced by finite wall-mounted cylinders (FWMCs) is a major noise source for aircraft landing gear, rail pantographs and submarine appendages. These applications often encounter flows with various pressure gradients, however, there is little information in the literature on the effects of pressure gradients. Our recent work has demonstrated that the presence of a pressure gradient can significantly affect the near-wake flow structures of a square FWMC with a low aspect ratio of 2.4, thereby suppressing/enhancing the vortex-shedding tones. The current study extends this work to square FWMCs with varying aspect ratios, focusing on the role that aspect ratio plays in the noise generation of square FWMCs in pressure gradient flows. Experiments were undertaken using the open-jet pressure-gradient test rig in the UNSW anechoic wind tunnel, where the square FWMC model was immersed in flows with favourable-, near-zero-, and adverse-pressure gradients at a width-based Reynolds number of 28800. The square FWMC model was installed on a traversing system to realize the change in cylinder aspect ratio. Inside the test model, a series of channels and surface pressure taps were created to measure the unsteady surface pressure using a remote microphone technique. Far-field noise and unsteady surface pressure signals were simultaneously acquired to characterize the combined effects of aspect ratio and pressure gradient on the far-field noise production and reveal the noise generation mechanisms.

Single normal hot-wire measurements of the streamwise component of velocity were taken in boundary layer flows subjected to pressure gradients at matched friction Reynolds numbers Reτ ≈ 3000. To evaluate spatial resolution effects, the sensor lengths are varied in both adverse pressure gradient (APG) and favorable pressure gradient (FPG). A control boundary layer flow in zero pressure gradient ZPG is also presented. It is shown here that, when the sensor length is maintained a constant value, in a contant Reynolds number, the near-wall peak increases with (adverse) pressure gradient. Both increased contributions of the small- and especially large-scale features are attributed to the increased broadband turbulence intensities. The two-mode increase, one centreing in the near-wall region and the other one in the outer region, makes spatial resolution studies in boundary layer flow more complicated. The increased large-scale features in the near-wall region of an APG flow is similar to large-scales increase due to Reynolds number in ZPG flow. Additionally, there is also an increase of the small-scales in the near-wall region when the boundary layer is exposed to adverse pressure gradient (while the Reynolds number is constant). In order to collapse the near-wall peaks for APG, ZPG and FPG flows, the APG flow has to use the longest sensor and conversely, the FPG has to use the shortest sensor. This study recommends that the empirical prediction by Huthins et. al. (2009) to be reevaluated if pressure gradient flows were to be considered such that the magnitude of the near-wall peak is also a function of the adverse pressure gradient parameter.

Measurements were made in rough-wall boundary layers subject to favourable, zero and adverse pressure gradients. Profiles of mean velocity and turbulence quantities were acquired and velocity fields were measured in multiple planes to document flow structure. Comparisons were made to equivalent smooth-wall cases with the same free stream velocity distributions. Outer layer similarity was observed between the rough- and smooth-wall cases in all quantities in the favourable and zero pressure gradient regions, but large differences were observed with adverse pressure gradients. In both the smooth- and rough-wall cases, the favourable pressure gradient reduced the turbulence in the boundary layer, and increased the size of turbulence structures relative to the boundary layer thickness in both the streamwise and spanwise directions, while lowering their inclination angle with respect to the wall. When the boundary layer was returned to a zero pressure gradient following the favourable pressure gradient region, the turbulence level and the size and inclination of the structures returned to their canonical zero pressure gradient condition. The response of the boundary layer was somewhat faster in the rough-wall case, causing it to reach equilibrium in a shorter streamwise distance after the changes in pressure gradient than in the smooth-wall case. The adverse pressure gradient increased turbulence levels relative to the wall friction velocity, reduced the size of turbulence structures relative to the boundary layer thickness and increased their inclination angle. The changes with the adverse pressure gradient were significantly larger with the rough wall than the smooth. The results suggest that similarity might be achieved with adverse pressure gradients if smooth- and rough-wall cases with the same Clauser pressure gradient parameter history are compared.

An experimental investigation was undertaken to study the salient features of adverse and favourable pressure gradient turbulent flows over a smooth wall and gravel roughness in asymmetric diverging and converging channels. Reference experiments were also performed in a parallel walled channel for which the pressure gradient was nearly zero. A high resolution particle image velocimetry system was used to conduct the velocity measurements. From these measurements, both one-point and two-point statistics were extracted and used to determine the effects of combined roughness and pressure gradient on the turbulence structure. It was found that adverse pressure gradient and surface roughness increased the turbulence intensities and Reynolds shear stress over the entire boundary layer, while favourable pressure gradient increased the turbulent intensities in the wall region and decreased the turbulence level in the outer layer. The Reynolds shear stress was decreased substantially by the favourable pressure gradient resulting in a considerable decay in the levels of the stress ratios over the smooth surface and gravel roughness. The distributions of the turbulent diffusion terms show considerable transport of turbulent kinetic energy and Reynolds shear stress towards the wall in the presence of adverse pressure gradient and surface roughness, while these terms are attenuated by favourable pressure gradient. In the diverging channel, it was found that surface roughness increases the spatial extents of the two-point streamwise velocity auto-correlation contour in the inner layer and increases the extents of the wall-normal velocity correlation in the outer layer.

Interfacial instability in two-layer Couette–Poiseuille flow of viscoelastic fluids

Abstract

The complex surface of an aircraft generates a nonzero pressure gradient flow. In this study, the boundary conditions of favorable and adverse pressure gradients are constructed in a small low-turbulence wind tunnel test section. Hot-wire anemometers and time-resolved image velocimetry are used to analyze the flow structure in a fully developed turbulent boundary layer with porous media. The effects of the porous surface on the statistical characteristics of the turbulent flow field and turbulent flow structure are analyzed and discussed. The results show that porous media reduce the velocity gradient in the linear layer, and the friction drag reduction effect is higher downstream of the porous wall. The drag reduction effect decreases along the flow direction. A wall with a 10 pores per inch produces a slightly better drag reduction effect than smooth wall. The maximum local drag reduction effect of a 10-pores-per-inch porous wall is 43.7% under a favorable pressure gradient and 42.3% under an adverse pressure gradient. The velocity streaks in the inner layer show that the porous wall widens the low-velocity streaks, making them more stable, while the high-speed streaks decrease in size under the pressure gradient. In the case of the adverse pressure gradient, the structure of the streaks becomes blurred, and their strength weakens. Under both favorable and adverse pressure gradients, the porous media lift up the coherent structures near the wall, thus weakening the large-scale coherent wall structures.

The current work presents computational studies of a compressible boundary layer in the presence of non zero pressure gradients. The aim of this investigation is to study and analyse the behaviour of near-wall compressible flows under the effects of both favourable and adverse pressure gradients. Results are reported using two alternative two-equation turbulence closures and a second order closure in order to provide an evaluation of the various models. These calculations, conducted through the boundary layer, have allowed a better understanding of the mechanisms controlling this kind of flow. The effects of streamwise pressure gradients on the mean and turbulent quantities and on the turbulence anisotropy, are studied, particularly in the viscous sublayer. It is concluded that there are a specific pressure gradient effects present in the bondary layer. The results of the analysis show that the effects found in incompressible flows are also present in this case, and have been qualitatively reproduced. There are, in addition, other influences due to the compressibility. From a comparative analysis with the various models, we find that the results with the Chien model containing the Nichols correction gave a better prediction than Chien model under a favourable pressure gradient.

Boundary layer transition was measured in zero, favorable, and adverse pressure gradients at Mach 8 using heat transfer. Models consisted of 7° half angle forecones 0.4826 m long, followed by flared or ogive aft bodies 0.5334 m long. The flares and ogives produced constant pressure gradients. For the cases examined, favorable pressure gradients delay transition and adverse pressure gradients promote transition, but transition zone lengths are shorter in favorable pressure gradient. Results of the effect of adverse pressure gradient on transition zone lengths were inconclusive.

Experimental investigation on the effects of complex pressure gradients on the film cooling effectiveness of a serpentine nozzle

Spectral density, magnitude of the normalized longitudinal and lateral cross-spectral-density functions, and convection-velocity ratio as a function of longitudinal separation and frequency of wall-pressure fluctuations were measured with small flush-mounted transducers. These measurements were accomplished in both mild adverse and mild favorable pressure gradients in a low-turbulence subsonic wind tunnel. To establish a basis of comparison, similar measurements were made for the zero pressure gradient, and agreement with published measurements was excellent. The effect of an adverse pressure gradient on the nondimensionalized spectral density was an increase in the low-frequency content without influencing the high-frequency portion appreciably; a sharp decrease in the high-frequency portion was observed for the favorable pressure gradient. At similar nondimensionalized longitudinal separations and frequencies, the convection velocity ratio was higher in the favorable and lower in the adverse pressure gradients. The longitudinal decay of a particular eddy was more rapid in the adverse and slower in the favorable pressure gradients. No differences were found in the lateral cross-spectral density for the different pressure gradients.

Spectral density, magnitude of the normalized longitudinal and lateral cross-spectral density functions, and convection velocity ratio as a function of longitudinal separation and frequency of wall-pressure fluctuations were measured with small flush-mounted transducers. These measurements were accomplished in both mild adverse and mild favorable pressure gradients in a low-turbulence subsonic wind tunnel. To establish a basis of comparison, similar measurements were made for the zero-pressure gradient, and agreement with published measurements was excellent. The effect of an adverse pressure gradient on the nondimensionalized spectral density was an increase in the low-frequency content without influencing the high-frequency portion appreciably; a sharp decrease in the high-frequency portion was observed for the favorable pressure gradient. At similar nondimensionalized longitudinal separation and frequencies the convection velocity ratio was higher in the favorable and lower in the adverse pressure gradients. The longitudinal decay of a particular eddy was more rapid in the adverse and slower in the favorable pressure gradients. No differences were found in the lateral cross-spectral density for the different pressure gradients.

This study focuses on the effects of mean (favourable) and large-scale fluctuating pressure gradients on boundary layer turbulence. Two-dimensional (2D) particle image velocimetry (PIV) measurements, some of which are time-resolved, have been performed upstream of and within a sink flow for two inlet Reynolds numbers, ${Re}_{\theta }(x_{1})=3360$ and 5285. The corresponding acceleration parameters, $K$, are ${1.3\times 10^{-6}}$ and ${0.6\times 10^{-6}}$. The time-resolved data at ${Re}_{\theta }(x_{1})=3360$ enables us to calculate the instantaneous pressure distributions by integrating the planar projection of the fluid material acceleration. As expected, all the locally normalized Reynolds stresses in the favourable pressure gradient (FPG) boundary layer are lower than those in the zero pressure gradient (ZPG) domain. However, the un-scaled stresses in the FPG region increase close to the wall and decay in the outer layer, indicating slow diffusion of near-wall turbulence into the outer region. Indeed, newly generated vortical structures remain confined to the near-wall region. An approximate analysis shows that this trend is caused by higher values of the streamwise and wall-normal gradients of mean streamwise velocity, combined with a slightly weaker strength of vortices in the FPG region. In both boundary layers, adverse pressure gradient fluctuations are mostly associated with sweeps, as the fluid approaching the wall decelerates. Conversely, FPG fluctuations are more likely to accompany ejections. In the ZPG boundary layer, loss of momentum near the wall during periods of strong large-scale adverse pressure gradient fluctuations and sweeps causes a phenomenon resembling local 3D flow separation. It is followed by a growing region of ejection. The flow deceleration before separation causes elevated near-wall small-scale turbulence, while high wall-normal momentum transfer occurs in the ejection region underneath the sweeps. In the FPG boundary layer, the instantaneous near-wall large-scale pressure gradient rarely becomes positive, as the pressure gradient fluctuations are weaker than the mean FPG. As a result, the separation-like phenomenon is markedly less pronounced and the sweeps do not show elevated small-scale turbulence and momentum transfer underneath them. In both boundary layers, periods of acceleration accompanying large-scale ejections involve near-wall spanwise contraction, and a high wall-normal momentum flux at all elevations. In the ZPG boundary layer, although some of the ejections are preceded, and presumably initiated, by regions of adverse pressure gradients and sweeps upstream, others are not. Conversely, in the FPG boundary layer, there is no evidence of sweeps or adverse pressure gradients immediately upstream of ejections. Apparently, the mechanisms initiating these ejections are either different from those involving large-scale sweeps or occur far upstream of the peak in FPG fluctuations.

The generalized wall function by Shih et al. [Report No. M-1999-209398 (1999)], which accounts for non-equilibrium effects by the presence of favorable and adverse pressure gradients in turbulent flows, is addressed with the aim of performing high Reynolds number large-eddy simulations of the wall-bounded flow. The model uses a corrected law of the wall with a pressure gradient contribution to approximate the wall stress and applies to the entire viscous layer, buffer layer, and inertial region. A fully developed channel flow is first tested to validate the solver and model implementation, and then the wall function is assessed for the flow over a periodic hill. Wall-resolved simulations are in good agreement with reference results. A priori investigation with own experimental results corroborates the mathematical form of the model and suggests using different coefficients. The wall-modeled simulations show that the implemented wall model is able to improve the wall shear stress predictions compared to a standard equilibrium wall model. It corrects the underestimation of wall shear stresses by equilibrium models in the favorable pressure gradient region and the overestimation of wall shear stresses in the adverse pressure gradient region. The positions of the separation and reattachment points are also in good agreement with reference results. Furthermore, the prediction of the wall shear stress maximum in the favorable pressure gradient zone at the windward side of the hill is quite robust against coarsening the wall-normal grid spacing.

Three dimensional instantaneous velocity data were taken in a turbulent corner flow with smooth walls under zero, a favorable, and an adverse pressure gradient. The favorable pressure gradient was −26.5 Pa/m (K = 0.15E−6) and the adverse gradient was 34.9 Pa/m (K = −0.20E−6). This paper will concentrate on effects of the favorable and adverse pressure gradients. Zero pressure gradient results were published in an earlier manuscript [1]. Experiments were carried out in air with a free stream inlet velocity of 13 m/s and an axial Reynolds number of about one million. The data were collected using a three-component LDV system that was configured in a nearly orthogonal setup. Measurements were made down to a y+ of approximately 5, and should provide a valuable data set in developing models and predictive codes. Data were collected at two axial locations, 0.93 and 1.26 m measured from the virtual origin. The boundary layer thickness was 20.90 mm and 24.91 mm respectively at these locations for the zero gradient case. The favorable gradient had thicknesses of 19.35 mm and 22.53 mm respectively, whereas the thicknesses of adverse pressure gradient were 28.89 mm and 36.81 mm. At each position, instantaneous velocity profiles were measured at 6.35, 12.7, 20.6, 41.2, 82.3, 121.9, 164.5, 184.8, and 205.1 mm from the corner. The centerline profiles agree well with classical flat plate data. Three mean velocity and six Reynolds stress components have been calculated. The instantaneous velocity field data set is sufficient to compute higher order correlations. The data will be very valuable for development of computer codes and models for corner flows of all kinds and for heat transfer studies in the internal cooling channels of gas turbine blades and turbine end wall flow. An analysis of the data is presented and will provide a detailed database for this complex three dimensional flow fields.