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1
MORRISON, J. F., B. J. McKEON, W. JIANG, and A. J. SMITS. "Scaling of the streamwise velocity component in turbulent pipe flow." Journal of Fluid Mechanics 508 (June 10, 2004): 99–131. http://dx.doi.org/10.1017/s0022112004008985.
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Hellström, Leo H. O., and Alexander J. Smits. "Structure identification in pipe flow using proper orthogonal decomposition." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2089 (March 13, 2017): 20160086. http://dx.doi.org/10.1098/rsta.2016.0086.
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The energetic motions in direct numerical simulations of turbulent pipe flow at Re τ =685 are investigated using proper orthogonal decomposition. The procedure is extended such that a pressure component is identified in addition to the three-component velocity field for each mode. The pressure component of the modes is shown to align with the streamwise velocity component associated with the large-scale motions, where positive pressure coincides with positive streamwise velocity, and vice versa. The streamwise evolution of structures is then visualized using a conditional mode, which exhibit a strong similarity to the large-scale, low-momentum motions. A low-pressure region is present in the downstream section of the structure, and a high-pressure region is present in the upstream section. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.
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Antonia, R. A., L. W. B. Browne, and D. A. Shah. "Characteristics of vorticity fluctuations in a turbulent wake." Journal of Fluid Mechanics 189 (April 1988): 349–65. http://dx.doi.org/10.1017/s0022112088001053.
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Measurements of the lateral components of the vorticity fluctuation have been made in the self-preserving turbulent wake of a circular cylinder. Each component was obtained separately using two X-wires separated in the appropriate lateral directions. The two velocity derivatives which make up the streamwise vorticity component were also determined but not simultaneously. An approximation to the streamwise vorticity was made from these measurements. Moments, probability density functions and spectra of the three vorticity components across the wake are presented and discussed. The high-wavenumber behaviour of the spectra is compared with calculations, based on local isotropy. Satisfactory agreement with the calculations is obtained for the lateral vorticity components over a significant high-wavenumber range. The approximated streamwise vorticity spectrum tends towards the isotropic calculation at very large wavenumbers.
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Nygaard, K. J., and A. Glezer. "Evolution of stream wise vortices and generation of small-scale motion in a plane mixing layer." Journal of Fluid Mechanics 231 (October 1991): 257–301. http://dx.doi.org/10.1017/s0022112091003397.
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The evolution of streamwise vortices in a plane mixing layer and their role in the generation of small-scale three-dimensional motion are studied in a closed-return water facility. Spanwise-periodic streamwise vortices are excited by a time-harmonic wavetrain with span wise-periodic amplitude variations synthesized by a mosaic of 32 surface film heaters flush-mounted on the flow partition. For a given excitation frequency, virtually any span wise wavelength synthesizable by the heating mosaic can be excited and can lead to the formation of streamwise vortices before the rollup of the primary vortices is completed. The onset of streamwise vortices is accompanied by significant distortion in the transverse distribution of the streamwise velocity component. The presence of inflexion points, absent in corresponding velocity distributions of the unforced flow, suggests the formation of locally unstable regions of large shear in which broadband perturbations already present in the base flow undergo rapid amplification, followed by breakdown to small-scale motion. Furthermore, as a result of spanwise-non-uniform excitation the cores of the primary vortices are significantly altered. The three-dimensional features of the streamwise vortices and their interaction with the base flow are inferred from surfaces of r.m.s. velocity fluctuations and an approximation to cross-stream vorticity using three-dimensional single component velocity data. The striking enhancement of small-scale motion and the spatial modification of its distribution, both induced by the streamwise vortices, can be related to the onset of the mixing transition.
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Lee, Jae Hwa, Hyung Jin Sung, and Ronald J. Adrian. "Space–time formation of very-large-scale motions in turbulent pipe flow." Journal of Fluid Mechanics 881 (October 25, 2019): 1010–47. http://dx.doi.org/10.1017/jfm.2019.786.
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We examine the origin of very-large-scale motions (VLSMs) in fully developed turbulent pipe flow at friction Reynolds number, $\mathit{Re}_{\unicode[STIX]{x1D70F}}=934$, using data from a direct numerical simulation. The VLSMs and the packet-like large-scale motions (LSMs) found in this study are very similar to those found in earlier studies. Three-dimensional time-evolving instantaneous fields show that one component of the process leading to the large streamwise length of VLSMs is the concatenation of adjacent streamwise LSMs caused by the continuous elongation of LSMs due to the strain component of the mean shear. Spatial organization patterns of the VLSMs and LSMs and their properties are studied by separating auto-correlation of the streamwise velocity fluctuations into the components of the VLSM and the LSM defined by low-pass/high-pass filtering in the streamwise direction. The structures of the two-point spatial correlations of the streamwise velocity component of the VLSMs and the LSMs in the streamwise-azimuthal plane are characterized by multiple maxima and complex patterns that beg explanation in terms of patterned coherent arrangements of the LSMs. Using proper orthogonal decomposition (POD), it is found that the X-shape correlation pattern of the VLSMs results from the superposition of very long helically inclined structures and streamwise-aligned structures. Further explanation of the patterns in the correlations of the VLSMs and LSMs is provided through the study of synthetically constructed arrangements of simple hairpin packet models of the LSM. Head-to-tail alignment of the model packets along streamwise and helical directions suggested by the eigenvalues of the POD creates a pair of long roll-cells centred above the logarithmic layer, and bracketing the LSMs. These roll-cells are pure kinematic consequences of the induction within the LSM packets, but they may also serve to organize smaller packets.
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BIRCH, DAVID M., and JONATHAN F. MORRISON. "Similarity of the streamwise velocity component in very-rough-wall channel flow." Journal of Fluid Mechanics 668 (December 3, 2010): 174–201. http://dx.doi.org/10.1017/s0022112010004647.
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The streamwise velocity component is studied in fully developed turbulent channel flow for two very rough surfaces and a smooth surface at comparable Reynolds numbers. One rough surface comprises sparse and isotropic grit with a highly non-Gaussian distribution. The other is a uniform mesh consisting of twisted rectangular elements which form a diamond pattern. The mean roughness heights (±) the standard deviation) are, respectively, about 76(±42) and 145(±150) wall units. The flow is shown to be two-dimensional and fully developed up to the fourth-order moment of velocity. The mean velocity profile over the grit surface exhibits self-similarity (in the form of a logarithmic law) within the limited range of 0.04≤y/h≤0.06, but the profile over the mesh surface does not, even though the mean velocity deficit and higher moments (up to the fourth order) all exhibit outer scaling over both surfaces. The distinction between self-similarity and outer similarity is clarified and the importance of the former is explained. The wake strength is shown to increase slightly over the grit surface but decrease over the mesh surface. The latter result is contrary to recent measurements in rough-wall boundary layers. Single- and two-point velocity correlations reveal the presence of large-scale streamwise structures with circulation in the plane orthogonal to the mean velocity. Spanwise correlation length scales are significantly larger than corresponding ones for both internal and external smooth-wall flows.
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McKeon, B. J., and J. F. Morrison. "Asymptotic scaling in turbulent pipe flow." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 365, no. 1852 (January 16, 2007): 771–87. http://dx.doi.org/10.1098/rsta.2006.1945.
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The streamwise velocity component in turbulent pipe flow is assessed to determine whether it exhibits asymptotic behaviour that is indicative of high Reynolds numbers. The asymptotic behaviour of both the mean velocity (in the form of the log law) and that of the second moment of the streamwise component of velocity in the outer and overlap regions is consistent with the development of spectral regions which indicate inertial scaling. It is shown that an ‘inertial sublayer’ in physical space may be considered as a spatial analogue of the inertial subrange in the velocity spectrum and such behaviour only appears for Reynolds numbers R + >5×10 3 , approximately, much higher than was generally thought.
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WARHOLIC, MICHAEL D., GAVIN M. SCHMIDT, and THOMAS J. HANRATTY. "The influence of a drag-reducing surfactant on a turbulent velocity field." Journal of Fluid Mechanics 388 (June 10, 1999): 1–20. http://dx.doi.org/10.1017/s0022112099004498.
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A two-component laser-Doppler velocimeter, with high spatial and temporal resolution, was used to study how the introduction of a drag-reducing surfactant to water changes the fully-developed velocity field in an enclosed rectangular channel. Measurements were made for four different Reynolds numbers, Re = 13300; 19100; 32000, and 49100 (based on the bulk viscosity, the half-height of the channel, and the viscosity of water). For a fixed volumetric flow the pressure drop was reduced by 62 to 76% when compared to a Newtonian flow with an equal wall viscosity. Measurements were made of the mean streamwise velocity, the root mean square of two components of the fluctuating velocity, the Reynolds shear stress and the spectral density function of the fluctuating velocity in the streamwise direction. The Reynolds shear stress is found to be zero over the whole channel and the spectra of the streamwise velocity fluctuations show a sharp cutoff at a critical frequency, fc. The ratio of the cutoff frequency to the root mean square of the streamwise velocity fluctuations is found to be approximately equal to 1 mm−1. The observation of a zero Reynolds shear stress indicates the existence of additional mean shear stresses (or mean transfers of momentum) that are not seen with a Newtonian fluid. Furthermore, the presence of a random fluctuating velocity field suggests a production of turbulence by a mechanism other than that usually found for a fully developed flow. Possible explanations for this behaviour are presented.
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Lee, Myoungkyu, and Robert D. Moser. "Direct numerical simulation of turbulent channel flow up to." Journal of Fluid Mechanics 774 (June 10, 2015): 395–415. http://dx.doi.org/10.1017/jfm.2015.268.
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A direct numerical simulation of incompressible channel flow at a friction Reynolds number ($\mathit{Re}_{{\it\tau}}$) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant ${\it\kappa}=0.384\pm 0.004$. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $k^{-1}$ dependence over a short range in wavenumber $(k)$. Further, consistent with previous experimental observations, when these spectra are multiplied by $k$ (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the $k^{-1}$ range.
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GAYME, D. F., B. J. McKEON, A. PAPACHRISTODOULOU, B. BAMIEH, and J. C. DOYLE. "A streamwise constant model of turbulence in plane Couette flow." Journal of Fluid Mechanics 665 (October 19, 2010): 99–119. http://dx.doi.org/10.1017/s0022112010003861.
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Streamwise and quasi-streamwise elongated structures have been shown to play a significant role in turbulent shear flows. We model the mean behaviour of fully turbulent plane Couette flow using a streamwise constant projection of the Navier–Stokes equations. This results in a two-dimensional three-velocity-component (2D/3C) model. We first use a steady-state version of the model to demonstrate that its nonlinear coupling provides the mathematical mechanism that shapes the turbulent velocity profile. Simulations of the 2D/3C model under small-amplitude Gaussian forcing of the cross-stream components are compared to direct numerical simulation (DNS) data. The results indicate that a streamwise constant projection of the Navier–Stokes equations captures salient features of fully turbulent plane Couette flow at low Reynolds numbers. A systems-theoretic approach is used to demonstrate the presence of large input–output amplification through the forced 2D/3C model. It is this amplification coupled with the appropriate nonlinearity that enables the 2D/3C model to generate turbulent behaviour under the small-amplitude forcing employed in this study.
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ARNDT, R. E. A., D. F. LONG, and M. N. GLAUSER. "The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet." Journal of Fluid Mechanics 340 (June 10, 1997): 1–33. http://dx.doi.org/10.1017/s0022112097005089.
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It is shown that the pressure signal measured at the outer edge of a jet mixing layer is entirely hydrodynamic in nature and provides a good measure of the large-scale structure of the turbulent flow. Measurement of the pressure signal provides a unique opportunity to utilize proper orthogonal decomposition (POD) to deduce the streamwise structure. Since pressure is a scalar, a significant reduction in the numerical and experimental complexity inherent in the analysis of velocity vector fields results.The POD streamwise eigenfunctions show that the structure associated with any frequency–azimuthal mode number combination displays the general characteristics of amplification–saturation–decay of an instability wave, all within about three wavelengths. High-frequency components saturate early in x and low-frequency components saturate further downstream, indicative of the inhomogeneous character of the flow in the streamwise direction. Application of the POD technique allows the phase velocity to be determined taking into account the inhomogeneity of the flow in the streamwise direction. The phase velocity of each instability wave (POD eigenvector) is constant and equal to 0.58Uj, indicating that the jet structure is non-dispersive.Using the shot-noise decomposition, a characteristic event is constructed. This event is found to contain evidence of both pairings and triplings of vortex structures. The tripling results in a rapid increase in the first asymmetric (m=1) component. On average, pairing occurs once every four Uj/D while tripling occurs once every 13Uj/D.
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Ruiz-Chavarria, G., S. Ciliberto, C. Baudet, and E. Lévêque. "Scaling properties of the streamwise component of velocity in a turbulent boundary layer." Physica D: Nonlinear Phenomena 141, no. 3-4 (July 2000): 183–98. http://dx.doi.org/10.1016/s0167-2789(00)00028-2.
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HILL, REGHAN J., and DONALD L. KOCH. "The transition from steady to weakly turbulent flow in a close-packed ordered array of spheres." Journal of Fluid Mechanics 465 (August 25, 2002): 59–97. http://dx.doi.org/10.1017/s0022112002008947.
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The sequence of transitions in going from steady to unsteady chaotic flow in a close-packed face-centred cubic array of spheres is examined using lattice-Boltzmann simulations. The transition to unsteady flow occurs via a supercritical Hopf bifurcation in which only the streamwise component of the spatially averaged velocity fluctuates and certain reflectional symmetries are broken. At larger Reynolds numbers, the cross-stream components of the spatially averaged velocity fluctuate with frequencies that are incommensurate with those of the streamwise component. This transition is accompanied by the breaking of rotational symmetries that persisted through the Hopf bifurcation. The resulting trajectories in the spatially averaged velocity phase space are quasi-periodic. At larger Reynolds numbers, the fluctuations are chaotic, having continuous frequency spectra with no easily identified fundamental frequencies. Visualizations of the unsteady flows in various dynamic states show that vortices are produced in which the velocity and vorticity are closely aligned. With increasing Reynolds number, the geometrical structure of the flow changes from one that is dominated by extension and shear to one in which the streamlines are helical. A mechanism for the dynamics is proposed in which energy is transferred to smaller scales by the dynamic interaction of vortices sustained by the underlying time-averaged flow.
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HODA, NAZISH, MIHAILO R. JOVANOVIĆ, and SATISH KUMAR. "Frequency responses of streamwise-constant perturbations in channel flows of Oldroyd-B fluids." Journal of Fluid Mechanics 625 (April 14, 2009): 411–34. http://dx.doi.org/10.1017/s0022112009006223.
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Non-modal amplification of disturbances in streamwise-constant channel flows of Oldroyd-B fluids is studied from an input–output point of view by analysing the responses of the velocity components to spatio-temporal body forces. These inputs into the governing equations are assumed to be harmonic in the spanwise direction and stochastic in the wall-normal direction and in time. An explicit Reynolds number (Re) scaling of frequency responses from different forcing to different velocity components is developed, showing the same Re dependence as in Newtonian fluids. It is found that some of the frequency response components peak at non-zero temporal frequencies. This is in contrast to Newtonian fluids, where peaks are always observed at zero frequency, suggesting that viscoelastic effects introduce additional time scales and promote development of flow patterns with smaller time constants than in Newtonian fluids. The temporal frequencies, corresponding to the peaks in the components of frequency response, decrease with an increase in viscosity ratio (ratio of solvent viscosity to total viscosity) and show maxima for non-zero elasticity number. Our analysis of the Reynolds–Orr equation demonstrates that the energy-exchange term involving the streamwise/wall-normal polymer stress component τxy and the wall-normal gradient of the streamwise velocity ∂yu becomes increasingly important relative to the Reynolds-stress term as the elasticity number increases and is thus the main driving force for amplification in flows with strong viscoelastic effects.
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GANAPATHISUBRAMANI, B. "Statistical structure of momentum sources and sinks in the outer region of a turbulent boundary layer." Journal of Fluid Mechanics 606 (July 10, 2008): 225–37. http://dx.doi.org/10.1017/s0022112008001675.
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The spatial structure of momentum sources and sinks (T > 0 and T < 0; where T is the streamwise component of the Lamb vector) is examined in a turbulent boundary layer by using dual-plane particle image velocimetry data obtained in streamwise–spanwise planes at two wall-normal locations (x2/δ = 0.1 and 0.5, where x2 is the wall-normal location and δ is the boundary layer thickness). Two-point correlations of T indicate that the size of source motions remains relatively constant while the size of sink motions increases with increasing wall-normal distance. The relative strength of sink motions also increases away from the wall. The velocity field in the vicinity of source/sink motions was explored by computing cross-correlations of T with the velocity components. Source-like motions are correlated with elongated low-momentum zones that possess regions of upwash embedded within them and appear to be the strongest in areas where these low-momentum zones meander in the spanwise direction. Momentum sinks appear to be located within low-speed regions that are within larger high-momentum zones. The velocity fluctuations undergo rapid transitions between quadrants in the vicinity of sinks (i.e. both streamwise and wall-normal velocity fluctuations change sign). The length scales, over which the fluctuations change sign, are much larger at x2/δ = 0.5 than at x2/δ = 0.1.
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Kwon, Y. S., N. Hutchins, and J. P. Monty. "On the use of the Reynolds decomposition in the intermittent region of turbulent boundary layers." Journal of Fluid Mechanics 794 (March 30, 2016): 5–16. http://dx.doi.org/10.1017/jfm.2016.161.
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In the analysis of velocity fields in turbulent boundary layers, the traditional Reynolds decomposition is universally employed to calculate the fluctuating component of streamwise velocity. Here, we demonstrate the perils of such a determination of the fluctuating velocity in the context of structural analysis of turbulence when applied in the outer region where the flow is intermittently turbulent at a given wall distance. A new decomposition is postulated that ensures non-turbulent regions in the flow do not contaminate the fluctuating velocity components in the turbulent regions. Through this new decomposition, some of the typical statistics concerning the scale and structure of turbulent boundary layers are revisited.
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IQBAL, M. O., and F. O. THOMAS. "Coherent structure in a turbulent jet via a vector implementation of the proper orthogonal decomposition." Journal of Fluid Mechanics 571 (January 4, 2007): 281–326. http://dx.doi.org/10.1017/s0022112006003351.
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The coherent structure in the near-field of an axisymmetric turbulent jet at a Reynolds number of 3.8 × 105 and Mach number of 0.3 is experimentally characterized by a vector implementation of the proper orthogonal decomposition (POD). The POD eigenfunctions and associated eigenvalues are extracted at several selected streamwise locations in the initial region. The focus on the near-field is motivated by its importance in numerous technical applications. Results show a rapid energy convergence with POD mode number. Examination of the relative energy contained in the combined azimuthal and radial components of the POD modes reveals that it is comparable to that in the streamwise component. The streamwise evolution of the eigenvalue spectra is characterized by a remarkable variation in the azimuthal mode number energy distribution, leading to the dominance of azimuthal mode m = 1 beyond the end of the jet core. In contrast, a scalar implementation using only the streamwise component shows the dominance of mode m = 2 which is consistent with previous scalar implementations of the POD. For a given azimuthal mode number, the eigenvalue spectra exhibit a broad peak which occurs at a constant value of Strouhal number based on local shear layer momentum thickness and local jet maximum velocity. The phase information required for a local reconstruction of the jet structure is obtained by projecting the POD eigenmodes onto instantaneous realizations of the flow at fixed streamwise locations. The instantaneous realizations are obtained by utilizing cross-stream arrays of multi-sensor probes in conjunction with linear stochastic estimation (LSE). Results clearly show the local dynamic behaviour of each component of the jet structure.
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Hwang, Jinyul, and Hyung Jin Sung. "Wall-attached structures of velocity fluctuations in a turbulent boundary layer." Journal of Fluid Mechanics 856 (October 12, 2018): 958–83. http://dx.doi.org/10.1017/jfm.2018.727.
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Wall turbulence is a ubiquitous phenomenon in nature and engineering applications, yet predicting such turbulence is difficult due to its complexity. High-Reynolds-number turbulence arises in most practical flows, and is particularly complicated because of its wide range of scales. Although the attached-eddy hypothesis postulated by Townsend can be used to predict turbulence intensities and serves as a unified theory for the asymptotic behaviours of turbulence, the presence of coherent structures that contribute to the logarithmic behaviours has not been observed in instantaneous flow fields. Here, we demonstrate the logarithmic region of the turbulence intensity by identifying wall-attached structures of the velocity fluctuations ($u_{i}$) through the direct numerical simulation of a moderate-Reynolds-number boundary layer ($Re_{\unicode[STIX]{x1D70F}}\approx 1000$). The wall-attached structures are self-similar with respect to their heights ($l_{y}$), and in particular the population density of the streamwise component ($u$) scales inversely with $l_{y}$, reminiscent of the hierarchy of attached eddies. The turbulence intensities contained within the wall-parallel components ($u$ and $w$) exhibit the logarithmic behaviour. The tall attached structures ($l_{y}^{+}>100$) of $u$ are composed of multiple uniform momentum zones (UMZs) with long streamwise extents, whereas those of the cross-stream components ($v$ and $w$) are relatively short with a comparable width, suggesting the presence of tall vortical structures associated with multiple UMZs. The magnitude of the near-wall peak observed in the streamwise turbulent intensity increases with increasing $l_{y}$, reflecting the nested hierarchies of the attached $u$ structures. These findings suggest that the identified structures are prime candidates for Townsend’s attached-eddy hypothesis and that they can serve as cornerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.
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Pramanik, Shantanu, and Manab Kumar Das. "Computational study of a turbulent wall jet flow on an oblique surface." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 2 (February 25, 2014): 290–324. http://dx.doi.org/10.1108/hff-01-2012-0005.
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Purpose – The purpose of the present study is to investigate the flow and turbulence characteristics of a turbulent wall jet flowing over a surface inclined with the horizontal and to investigate the effect of variation of the angle of inclination of the wall on the flow structure of the wall jet. Design/methodology/approach – The high Reynolds number two-equation κ− model with standard wall function is used as the turbulence model. The Reynolds number considered for the present study is 10,000. The Reynolds averaged Navier-Stokes (RANS) equations are used for predicting the turbulent flow. A staggered differencing technique employing both contravariant and Cartesian components of velocity has been applied. Results for distribution of wall static pressure and skin friction, decay of maximum streamwise velocity, streamwise variation of integral momentum and energy flux have been compared for the cases of α=0°, 5°, and 10°. Findings – Flow field has been represented in terms of streamwise and lateral velocity contours, static pressure contour, vorticity contour and streamwise velocity and static pressure profiles at different locations along the oblique offset plate. Distribution of Reynolds stresses in terms of spanwise, lateral and turbulent shear stresses, and turbulent kinetic energy and its dissipation rate have been presented to describe the turbulent characteristics. Similarity of streamwise velocity and the velocity parallel to the oblique wall has been observed in the developed region of the wall jet flow. A decaying trend is observed in the variation of total integral momentum flux in the developed region of the wall jet which becomes more evident with increase in oblique angle. Developed flow region has indicated trend of similarity in profiles of streamwise velocity as well as velocity component parallel to the oblique wall. A depression in wall static pressure has been observed near the nozzle exit when the wall is inclined and the depression increases with increase in inclination. Effect of variation of oblique angles on skin friction coefficient has indicated that it decreases with increase in oblique angle. Growth of the outer and inner shear layers and spread of the jet shows linear variation with distance along the oblique wall. Decay of maximum streamwise velocity is found to be unaffected by variation in oblique angle except in the far downstream region. The streamwise variation of spanwise integral energy shows increase in oblique angle and decreases the magnitude of energy flux through the domain. In the developed flow region, streamwise variation of centreline turbulent intensities shows increased values with increase in oblique angle, while turbulence intensities along the jet centreline in the region X<12 remain unaffected by change in oblique angles. Normalized turbulent kinetic energy distribution highlights the difference in turbulence characteristics between the wall jet and reattached offset jet flow. Near wall velocity distribution shows that the inner region of boundary layer of the developed oblique wall jet follows a logarithmic profile, but it shows some difference from the standard logarithmic curve of turbulent boundary layers which can be attributed to an increase in skin friction coefficient and a decrease in thickness of the wall attached layer. Originality/value – The study presents an in-depth investigation of the interaction between the jet and the inclined wall. It is shown that due to the Coanda effect, the jet follows the nearby wall. The findings will be useful in the study of combined flow of wall jet and offset jet and dual offset jet on oblique surfaces leading to a better design of some mechanical jet flow devices.
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Pratomo, Hariyo P. S., and Klaus Bremhorst. "Velocity Statistics of a Fully Pulsed Round Jet in Streamwise Direction." Applied Mechanics and Materials 534 (February 2014): 117–23. http://dx.doi.org/10.4028/www.scientific.net/amm.534.117.
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In this paper, statistical quantities of a fully pulsed round jet along the jet centerline are reported. A range of the Reynolds (1.5 x 104 < Re < 4 x 104) and Strouhal (0.0064 < St < 0.0076) numbers is used to generate the jet. Physically this unsteady jet produces a series of distinct pulses due to the excitations. The mechanically excitations lead to the appearance of pulse dominated and high turbulence steady jet region in which their existence is of a strong dependence on the level of the controlled parameters. After the pulse merging completes the pulsed jet alters to a self-preserving steady jet with a significantly higher turbulence intensity. Under a constant mass flow rate the pulsed jet tends to be more fluctuating at a less intense pulsation thus permitting the endurance of the normalized periodic component and a more rapid velocity decay in the pulse-dominated region.
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Zhang, Shengqi, Zhenhua Xia, Yipeng Shi, and Shiyi Chen. "A two-dimensional-three-component model for spanwise rotating plane Poiseuille flow." Journal of Fluid Mechanics 880 (October 9, 2019): 478–96. http://dx.doi.org/10.1017/jfm.2019.715.
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Spanwise rotating plane Poiseuille flow (RPPF) is one of the canonical flow problems to study the effect of system rotation on wall-bounded shear flows and has been studied a lot in the past. In the present work, a two-dimensional-three-component (2D/3C) model for RPPF is introduced and it is shown that the present model is equivalent to a thermal convection problem with unit Prandtl number. For low Reynolds number cases, the model can be used to study the stability behaviour of the roll cells. It is found that the neutral stability curves, critical eigensolutions and critical streamfunctions of RPPF at different rotation numbers ($Ro$) almost collapse with the help of a rescaling with a newly defined Rayleigh number $Ra$ and channel height $H$. Analytic expressions for the critical Reynolds number and critical wavenumber at different $Ro$ can be obtained. For a turbulent state with high Reynolds number, the 2D/3C model for RPPF is self-sustained even without extra excitations. Simulation results also show that the profiles of mean streamwise velocity and Reynolds shear stress from the 2D/3C model share the same linear laws as the fully three-dimensional cases, although differences on the intercepts can be observed. The contours of streamwise velocity fluctuations behave like plumes in the linear law region. We also provide an explanation to the linear mean velocity profiles observed at high rotation numbers.
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Matsuda, Hisashi, Sei-ichi Iida, and Michio Hayakawa. "Coherent Structures in a Three-Dimensional Wall Jet." Journal of Fluids Engineering 112, no. 4 (December 1, 1990): 462–67. http://dx.doi.org/10.1115/1.2909428.
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The formation mechanism of streamwise vortices in the near field of the three-dimensional wall jet discharging from a circular nozzle along a flat plate is studied experimentally using a conditional sampling technique. Ensemble-averages of the lateral velocity component indicate the presence of large-scale horseshoe-like structures, whose legs are inclined and stretched to form the streamwise vortices in the mixing region of the jet. Based on the present result, a coherent structure model for the near field of the wall jet is proposed.
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Balachandar, Ram, B. S. Hyun, and V. C. Patel. "Effect of depth on flow over a fixed dune." Canadian Journal of Civil Engineering 34, no. 12 (December 2007): 1587–99. http://dx.doi.org/10.1139/l07-068.
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Laser Doppler velocimeter (LDV) measurements were carried out to study the effect of depth on the flow over a train of fixed two-dimensional dunes. Conventionally averaged velocity and turbulence parameters reveal large peaks in the streamwise and vertical components of turbulent intensities and shear stress, along the shear layer emanating from the dune crest. A secondary peak in the streamwise turbulence profiles some distance beyond the shear layer indicates maintenance of turbulence generated on the previous dune and convection of the flow history from one dune to the next. Analyses based on triple products and quadrant decomposition of velocity fluctuations reveals the central role of the shear layer in dictating the flow properties over the entire depth. The depth influences the flow in the near-bed region and the length of the separation zone is longer at a shallower depth. The streamwise mean profiles collapse onto a single curve in the outer region beyond the shear layer, indicating a degree of similarity and independence from the near-bed flow. The profiles of the vertical component of turbulence reveal a systematic dependence on flow depth, with lower turbulence intensity at larger depths. The quantitative effect of flow depth is evident in the measurements at all levels, including triple products and quadrant decomposition.
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O’Brien, J. E., and S. P. Capp. "Two-Component Phase-Averaged Turbulence Statistics Downstream of a Rotating Spoked-Wheel Wake Generator." Journal of Turbomachinery 111, no. 4 (October 1, 1989): 475–82. http://dx.doi.org/10.1115/1.3262296.
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Measurements of the axial and tangential components of the unsteady turbulent flow downstream of a rotating spoked-wheel wake generator have been obtained. The results of this study have implications for the use of this type of wake generator to produce simulated turbine guide vane wakes. Instantaneous velocity information was phase averaged based on a signal synchronized with the bar-passing frequency. Mean velocity profiles and phase-averaged Reynolds stress results were found to be consistent with measurements obtained behind a stationary cylinder. Reynolds stresses were significantly higher than corresponding measurements obtained in large-scale research turbomachines, however. Phase-averaged triple velocity correlations, also calculated from the digital velocity records, reveal the sign and magnitude of skewness in the velocity probability density distributions for the two components. Large crossflow gradients observed in the triple correlations in the wake indicate the importance of the tangential-component fluctuations in the net turbulent transport of turbulent energy across the wake. Streamwise-component wake velocity spectra for low values of reduced bar-passing frequency include a peak associated with vortex shedding from the cylindrical wake-generating bars at a shedding Strouhal number of 0.2. For higher bar-passing frequencies, the energy associated with vortex shedding is shifted to lower frequencies and becomes broadband from the stationary reference frame viewpoint.
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Mansy, Hussein, Pan-Mei Yang, and David R. Williams. "Quantitative measurements of three-dim ensional structures in the wake of a circular cylinder." Journal of Fluid Mechanics 270 (July 10, 1994): 277–96. http://dx.doi.org/10.1017/s0022112094004271.
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The fine scale three-dimensional structures usually associated with streamwise vortices in the near wake of a circular cylinder have been studied at Reynolds numbers ranging from 170 to 2200. Spatially continuous velocity measurements along lines parallel to the cylinder axis were obtained with a scanning laser anemometer. To detect the streamwise vortices in the amplitude modulated velocity field, it was necessary to develop a spatial decomposition technique to split the total flow into a primary flow component and a secondary flow component. The primary flow is comprised of the mean flow and Strouhal vortices, while the secondary flow is the result of the three-dimensional streamwise vortices that are the essence of transition to turbulence. The three-dimensional flow amplitude increases in the primary vortex formation region, then saturates shortly after the maximum amplitude in the primary flow is reached. In the near-wake region the wavelength decreases approximately like Re−0.5, but increases with downstream distance. A discontinuous increase in wavelength occurs below Re = 300 suggesting a fundamental change in the character of the three-dimensional flow. At downstream distances (x/D = 10-20), the spanwise wavelength decreases from 1.42D to 1.03D as the Reynolds number increases from 300 to 1200.
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GOLDSTEIN, M. E., ADRIAN SESCU, PETER W. DUCK, and MEELAN CHOUDHARI. "Algebraic/transcendental disturbance growth behind a row of roughness elements." Journal of Fluid Mechanics 668 (January 26, 2011): 236–66. http://dx.doi.org/10.1017/s0022112010004726.
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This paper is a continuation of the work begun in Goldstein et al. (J. Fluid Mech., vol. 644, 2010, p. 123), who constructed an asymptotic high-Reynolds-number solution for the flow over a spanwise periodic array of relatively small roughness elements with (spanwise) separation and plan form dimensions of the order of the local boundary-layer thickness. While that paper concentrated on the linear problem, here the focus is on the case where the flow is nonlinear in the immediate vicinity of the roughness with emphasis on the intermediate wake region corresponding to streamwise distances that are large in comparison with the roughness dimension, but small in comparison with the distance between the roughness array and the leading edge. An analytical O(h2) asymptotic solution is obtained for the limiting case of a small roughness height parameter h. These weakly nonlinear results show that the spanwise variable component of the wall-pressure perturbation decays as x−5/3 ln x when x → ∞ (where x denotes the streamwise distance scaled on the roughness dimension), but the corresponding component of the streamwise velocity perturbation (i.e. the wake velocity) exhibits an O(x1/3 ln x) algebraic/transcendental growth in the main boundary layer. Numerical solutions for h = O(1) demonstrate that the wake velocity perturbation for the fully nonlinear case grows in the same manner as the weakly nonlinear prediction – which is considerably different from the strictly linear result obtained in Goldstein et al. (2010).
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BURATTINI, P., S. LEONARDI, P. ORLANDI, and R. A. ANTONIA. "Comparison between experiments and direct numerical simulations in a channel flow with roughness on one wall." Journal of Fluid Mechanics 600 (March 26, 2008): 403–26. http://dx.doi.org/10.1017/s0022112008000657.
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The turbulent flow in a two-dimensional channel with roughness on one wall is investigated using experiments and direct numerical simulations (DNS). The elements have a square cross-section with height k=0.1H (H is the channel half-width) and a streamwise spacing of 4k. The Reynolds number Reτr, based on the friction velocity at the rough wall and H, is in the range 300–1100. Particular attention is given to the rough-wall side. Measured turbulence intensities, length scales, leading terms in the turbulent kinetic energy budget, and velocity spectra are compared with those obtained from the DNS. Close agreement is found, yielding support for the simplifying assumptions in the experiment (notably local isotropy and Taylor's hypothesis) and the adequacy of the spatial resolution in the simulation. Overall, the profiles of the Reynolds normal stresses on the roughness side are almost independent of Reτr, when normalized by outer variables. Energy spectra at different locations above the rough wall collapse well at high wavenumbers, when normalized by Kolmogorov scales. In contrast to previous studies, a region of negative energy production near the location of the maximum streamwise velocity is not observed. Comparison with a smooth-wall channel, at similar values of the friction-velocity Reynolds number, highlights differences only in the streamwise velocity component near the wall.
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BAKAS, NIKOLAOS A. "Mechanisms underlying transient growth of planar perturbations in unbounded compressible shear flow." Journal of Fluid Mechanics 639 (October 16, 2009): 479–507. http://dx.doi.org/10.1017/s0022112009991273.
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Non-modal mechanisms underlying transient growth of propagating acoustic waves and non-propagating vorticity perturbations in an unbounded compressible shear flow are investigated, making use of closed form solutions. Propagating acoustic waves amplify mainly due to two mechanisms: growth due to advection of streamwise velocity that is typically termed as the lift-up mechanism leading for large Mach numbers to an almost linear increase in streamwise velocity with time and growth due to the downgradient irrotational component of the Reynolds stress leading to linear growth of acoustic wave energy for large times. Synergy between these mechanisms along with the downgradient solenoidal component of the Reynolds stress produces large and robust energy amplification.On the other hand, non-propagating vorticity perturbations amplify due to kinematic deformation of vorticity by the mean flow. For weakly compressible flows, an initial vorticity perturbation abruptly excites acoustic waves with exponentially small amplitude, and the energy gained by vorticity perturbations is transferred back to the mean flow. For moderate Mach numbers, a strong coupling between vorticity perturbations and acoustic waves is found with the energy gained by vorticity perturbations being transferred to acoustic waves that are abruptly excited by the vortex.Calculation of the optimal perturbations for a viscous flow shows that for low Mach numbers, acoustic wave excitation by vorticity perturbations and the subsequent growth of acoustic waves leads to robust energy growth of the order of Reynolds number, while for large Mach numbers, synergy between the lift-up mechanism and the downgradient solenoidal component of the Reynolds stress dominates the growth and leads to a comparable large amplification of streamwise velocity.
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Zhao, Lihao, Helge I. Andersson, and Jurriaan J. J. Gillissen. "Interphasial energy transfer and particle dissipation in particle-laden wall turbulence." Journal of Fluid Mechanics 715 (January 9, 2013): 32–59. http://dx.doi.org/10.1017/jfm.2012.492.
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AbstractTransfer of mechanical energy between solid spherical particles and a Newtonian carrier fluid has been explored in two-way coupled direct numerical simulations of turbulent channel flow. The inertial particles have been treated as individual point particles in a Lagrangian framework and their feedback on the fluid phase has been incorporated in the Navier–Stokes equations. At sufficiently large particle response times the Reynolds shear stress and the turbulence intensities in the spanwise and wall-normal directions were attenuated whereas the velocity fluctuations were augmented in the streamwise direction. The physical mechanisms involved in the particle–fluid interactions were analysed in detail, and it was observed that the fluid transferred energy to the particles in the core region of the channel whereas the fluid received kinetic energy from the particles in the wall region. A local imbalance in the work performed by the particles on the fluid and the work exerted by the fluid on the particles was observed. This imbalance gave rise to a particle-induced energy dissipation which represents a loss of mechanical energy from the fluid–particle suspension. An independent examination of the work associated with the different directional components of the Stokes force revealed that the dominating energy transfer was associated with the streamwise component. Both the mean and fluctuating parts of the Stokes force promoted streamwise fluctuations in the near-wall region. The kinetic energy associated with the cross-sectional velocity components was damped due to work done by the particles, and the energy was dissipated rather than recovered as particle kinetic energy. Componentwise scatter plots of the instantaneous velocity versus the instantaneous slip-velocity provided further insight into the energy transfer mechanisms, and the observed modulations of the flow field could thereby be explained.
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Van Buren, Tyler, Owen Williams, and Alexander J. Smits. "Turbulent boundary layer response to the introduction of stable stratification." Journal of Fluid Mechanics 811 (December 13, 2016): 569–81. http://dx.doi.org/10.1017/jfm.2016.775.
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The response of an initially neutral rough-wall turbulent boundary layer to a change in wall temperature is investigated experimentally. The change causes a localized peak in stable stratification that diffuses and moves away from the wall with downstream distance. The streamwise and wall-normal components of turbulent velocity fluctuations are damped at similar rates, even though the stratification only directly impacts the wall-normal component. The Reynolds shear profiles reveal the growth of an internal layer that scales approximately with the bulk Brunt–Väisälä frequency.
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Krug, Dominik, Xiang I. A. Yang, Charitha M. de Silva, Rodolfo Ostilla-Mónico, Roberto Verzicco, Ivan Marusic, and Detlef Lohse. "Statistics of turbulence in the energy-containing range of Taylor–Couette compared to canonical wall-bounded flows." Journal of Fluid Mechanics 830 (October 6, 2017): 797–819. http://dx.doi.org/10.1017/jfm.2017.625.
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Considering structure functions of the streamwise velocity component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva et al. (J. Fluid Mech., vol. 823, 2017, pp. 498–510) observed that remarkably the large-scale (energy-containing range) statistics in canonical wall-bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor–Couette flow. In doing so, we find that also the transversal structure function of the spanwise velocity component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached-eddy contributions. By taking the effect of streamwise alignment into account, the attached-eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS framework – both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high Reynolds number data are currently available.
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N., Bustamante-Penagos, and Niño Y. "Flow–Sediment Turbulent Ejections: Interaction between Surface and Subsurface Flow in Gravel-Bed Contaminated by Fine Sediment." Water 12, no. 6 (June 3, 2020): 1589. http://dx.doi.org/10.3390/w12061589.
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Several researchers have studied turbulent structures, such as ejections, sweeps, and outwards and inwards interactions in flumes, where the streamwise velocity dominates over vertical and transversal velocities. However, this research presents an experimental study in which there are ejections associated with the interchange between surface and subsurface water, where the vertical velocity dominates over the streamwise component. The experiment is related to a surface alluvial stream that is polluted with fine sediment, which is percolated into the bed. The subsurface flow is modified by a lower permeability associated with the fine sediment and emerges to the surface current. Quasi-steady ejections are produced that drag fine sediment into the surface flow. Particle image velocimetry (PIV) measured the velocity field before and after the ejection. The velocity data were analyzed by scatter plots, power spectra, and wavelet analysis of turbulent fluctuations, finding changes in the distribution of turbulence interactions with and without the presence of fine deposits. The flow sediment ejection changes the patterns of turbulent structures and the distribution of the turbulence interactions that have been reported in open channels without subsurface flows.
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Suga, Kazuhiko, Yuki Okazaki, Unde Ho, and Yusuke Kuwata. "Anisotropic wall permeability effects on turbulent channel flows." Journal of Fluid Mechanics 855 (September 21, 2018): 983–1016. http://dx.doi.org/10.1017/jfm.2018.666.
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Streamwise–wall-normal ( $x$ – $y$ ) and streamwise–spanwise ( $x$ – $z$ ) plane measurements are carried out by planar particle image velocimetry for turbulent channel flows over anisotropic porous media at the bulk Reynolds number $Re_{b}=900{-}13\,600$ . Three kinds of anisotropic porous media are constructed to form the bottom wall of the channel. Their wall permeability tensor is designed to have a larger wall-normal diagonal component (wall-normal permeability) than the other components. Those porous media are constructed to have three mutually orthogonal principal axes and those principal axes are aligned with the Cartesian coordinate axes of the flow geometry. Correspondingly, the permeability tensor of each porous medium is diagonal. With the $x$ – $y$ plane data, it is found that the turbulence level well accords with the order of the streamwise diagonal component of the permeability tensor (streamwise permeability). This confirms that the turbulence strength depends on the streamwise permeability rather than the wall-normal permeability when the permeability tensor is diagonal and the wall-normal permeability is larger than the streamwise permeability. To generally characterize those phenomena including isotropic porous wall cases, modified permeability Reynolds numbers are discussed. From a quadrant analysis, it is found that the contribution from sweeps and ejections to the Reynolds shear stress near the porous media is influenced by the streamwise permeability. In the $x$ – $z$ plane data, although low- and high-speed streaks are also observed near the anisotropic porous walls, large-scale spanwise patterns appear at a larger Reynolds number. It is confirmed that they are due to the transverse waves induced by the Kelvin–Helmholtz instability. By the two-point correlation analyses of the fluctuating velocities, the spacing of the streaks and the wavelengths of the Kelvin–Helmholtz (K–H) waves are discussed. It is then confirmed that the transition point from the quasi-streak structure to the roll-cell-like structure is characterized by the wall-normal distance including the zero-plane displacement of the log-law velocity which can be characterized by the streamwise permeability. It is also confirmed that the normalized wavelengths of the K–H waves over porous media are in a similar range to that of the turbulent mixing layers irrespective of the anisotropy of the porous media.
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Elsinga, G. E., C. Poelma, A. Schröder, R. Geisler, F. Scarano, and J. Westerweel. "Tracking of vortices in a turbulent boundary layer." Journal of Fluid Mechanics 697 (March 6, 2012): 273–95. http://dx.doi.org/10.1017/jfm.2012.60.
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AbstractThe motion of spanwise vortical elements and large-scale bulges has been tracked in the outer region between wall-normal distance $z/ \delta = 0. 11$ and 0.30 of a turbulent boundary layer at ${\mathit{Re}}_{\theta } = 2460$. The experimental dataset of time-resolved three-dimensional velocity fields used has been obtained by tomographic particle image velocimetry. The tracking of these structures yields their respective average trajectories as well as the variations thereof, quantified by the root mean square of the trajectory coordinates as a function of time. It is demonstrated that the variation in convection can be described by a dispersion model for infinitesimal particles in homogeneous turbulence, which suggests that these vortical structures and bulges are transported passively by the external velocity field without significant changes in their topology, at least over the present observation time of $1. 2\delta / {U}_{e} $. However, this does not mean that the structure’s convection velocity is equal to the local flow velocity at each instant. Differences of the order of the Kolmogorov or wall friction velocity have been observed for the spanwise vortical elements. In addition, the simultaneous detection and tracking of multiple structures allows an evaluation of the relative velocity between two spanwise vortex elements, which are approximately aligned along the streamwise direction. The typical streamwise distance between such neighbouring structures is found to be around $0. 2\delta $. Their relative velocities are small, especially the streamwise component, which shows less variation as may be expected based on the relative flow velocity statistics for the same separation distance. This appears consistent with the hairpin packet model, which comprises a set of streamwise aligned hairpins travelling coherently. In exceptional cases, however, the structures approach each other rapidly, forcing an interaction on a time scale of the order of $1\delta / {U}_{e} $. It is shown that the measured variation in convection velocity can further be used successfully to predict the temporal development of space–time correlation functions starting from the instantaneous correlation map. In this prediction the structures are assumed to convect without change, following our observations.
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Vanstone, Leon, Mustafa Nail Musta, Serdar Seckin, and Noel Clemens. "Experimental study of the mean structure and quasi-conical scaling of a swept-compression-ramp interaction at Mach 2." Journal of Fluid Mechanics 841 (February 19, 2018): 1–27. http://dx.doi.org/10.1017/jfm.2018.8.
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This study investigates the mean flow structure of two shock-wave boundary-layer interactions generated by moderately swept compression ramps in a Mach 2 flow. The ramps have a compression angle of either $19^{\circ }$ or $22.5^{\circ }$ and a sweep angle of $30^{\circ }$. The primary diagnostic methods used for this study are surface-streakline flow visualization and particle image velocimetry. The shock-wave boundary-layer interactions are shown to be quasi-conical, with the intermittent region, separation line and reattachment line all scaling in a self-similar manner outside of the inception region. This is one of the first studies to investigate the flow field of a swept ramp using particle image velocimetry, allowing more sensitive measurements of the velocity flow field than previously possible. It is observed that the streamwise velocity component outside of the separated flow reaches the quasi-conical state at the same time as the bulk surface flow features. However, the streamwise and cross-stream components within the separated flow take longer to recover to the quasi-conical state, which indicates that the inception region for these low-magnitude velocity components is actually larger than was previously assumed. Specific scaling laws reported previously in the literature are also investigated and the results of this study are shown to scale similarly to these related interactions. Certain limiting cases of the scaling laws are explored that have potential implications for the interpretation of cylindrical and quasi-conical scaling.
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Pouagare, M., J. M. Galmes, and B. Lakshminarayana. "An Experimental Study of the Compressor Rotor Blade Boundary Layer." Journal of Engineering for Gas Turbines and Power 107, no. 2 (April 1, 1985): 364–72. http://dx.doi.org/10.1115/1.3239731.
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The three-dimensional turbulent boundary layer developing on a rotor blade of an axial flow compressor was measured using a minature “x” configuration hot-wire probe. The measurements were carried out at nine radial locations on both surfaces of the blade at various chordwise locations. The data derived includes streamwise and radial mean velocities and turbulence intensities. The validity of conventional velocity profiles such as the “power law profile” for the streamwise profile, and Mager and Eichelbrenner’s for the radial profile, is examined. A modification to Mager’s crossflow profile is proposed. Away from the blade tip, the streamwise component of the blade boundary layer seems to be mainly influenced by the streamwise pressure gradient. Near the tip of the blade, the behavior of the blade boundary layer is affected by the tip leakage flow and the annulus wall boundary layer. The “tangential blockage” due to the blade boundary layer is derived from the data. The profile losses are found to be less than that of an equivalent cascade, except in the tip region of the blade.
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LARCHEVÊQUE, LIONEL, PIERRE SAGAUT, and ODILE LABBÉ. "Large-eddy simulation of a subsonic cavity flow including asymmetric three-dimensional effects." Journal of Fluid Mechanics 577 (April 19, 2007): 105–26. http://dx.doi.org/10.1017/s0022112006004502.
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Large-eddy simulations of a cavity configuration yielding a mean flow that exhibits spanwise asymmetry are carried out. Results from the computations reveal that the asymmetry is due to a bifurcation of the whole flow field inside the cavity. It is demonstrated that the bifurcation originates in an inviscid confinement effect induced by the lateral walls. The branch of the bifurcation can be selected by slightly altering the incoming mean flow. Further investigations show that underlying steady spanwise modulations of velocity are amplified under the influence of the lateral walls. The modulation of the streamwise velocity component has the largest energy content and its dominant wavelength contaminates both vertical velocity and pressure. Complementary to these linear interactions, nonlinear energy transfers from streamwise velocity to pressure are also found. A transient analysis highlights the stiff transition from a symmetrical two-structure non-bifurcated flow to a stable unsymmetrical one-and-a-half-structure bifurcated flow. The switch to the bifurcated flow induces an alteration of the Rossiter aero–acoustic loop yielding a change in the dominant Rossiter mode and the appearance of a nonlinear harmonic of the first mode.
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Wall, D. P., and M. Nagata. "Three-dimensional exact coherent states in rotating channel flow." Journal of Fluid Mechanics 727 (June 28, 2013): 533–81. http://dx.doi.org/10.1017/jfm.2013.242.
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AbstractThree-dimensional exact, finite-amplitude solutions are presented for the problem of channel flow subject to a system rotation about a spanwise axis. The solutions are of travelling wave form, and may bifurcate as tertiary flows from the two-dimensional streamwise-independent secondary flow, or as secondary flows directly from the basic flow. For the tertiary flows, we consider solutions of spanwise superharmonic and subharmonic type. We distinguish flows on the basis of symmetry, originating eigenmode and major solution branch, and thus identify 15 distinct flows: 5 superharmonic tertiary, 5 subharmonic tertiary and 5 secondary flows. The tertiary flows all feature a single layer of vortical structures in the spanwise–wall-normal plane, the secondary flows feature single-, double-, triple- or quadruple-layer flow structures in this plane. All flows feature low-speed streamwise-orientated streaks in the streamwise velocity component and/or pulses of low-speed streamwise velocity. The streaks may be sinusoidal or varicose. Sinusoidal streaks are flanked by staggered streamwise vortices, varicose streaks and pulses are flanked by aligned vortices. A comparison with previous simulation and experimental studies finds that the simplest three-dimensional flows observed previously correspond to superharmonic tertiary flows bifurcating from the upper branch of the secondary flow. The mean absolute vorticity of the present flows is also considered. A flattening of the profile of this vorticity is observed in the central region of the channel for two-dimensional secondary and many of the three-dimensional flows, with two-step profiles also observed. This phenomenon is attributed to mixing of the vorticity across zones of the channel in which streamwise vortex structures exist, and is demonstrated by a two-dimensional model. The phenomenon appears to be distinct to that observed in fully turbulent rotating channel flows.
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Ninto, Y., and M. H. Garcia. "Experiments on particle—turbulence interactions in the near–wall region of an open channel flow: implications for sediment transport." Journal of Fluid Mechanics 326 (November 10, 1996): 285–319. http://dx.doi.org/10.1017/s0022112096008324.
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A high-speed video system was used to study the interaction between sediment particles and turbulence in the wall region of an open channel flow with both smooth and transitionally rough beds. In smooth flows, particles immersed within the viscous sublayer were seen to accumulate along low-speed wall streaks; apparently due to the presence of quasi-streamwise vortices in the wall region. Larger particles did not tend to group along streaks, however their velocity was observed to respond to the streaky structure of the flow velocity in the wall region. In transitionally rough flows particle sorting was not observed. Coherent flow structures in the form of shear layers typically observed in the near-wall region interacted with sediment particles lying on the channel bottom, resulting in the particles being entrained into suspension. Although there has been some speculation that this process would not be effective in entraining particles totally immersed in the viscous sublayer, the results obtained demonstrate the opposite. The entrainment mechanism appears to be the same independent of the roughness condition of the bottom wall, smooth or transitionally rough. In the latter case, however, hiding effects tend to preclude the entrainment of particles with sizes finer than that of the roughness elements. The analysis of particle velocity during entrainment shows that the streamwise component tends to be much smaller than the local mean flow velocity, while the vertical component tends to be much larger than the local standard deviation of the vertical flow velocity fluctuations, which would indicate that such particles are responding to rather extreme flow ejection events.
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Goldstein, M. E., and David W. Wundrow. "Interaction of oblique instability waves with weak streamwise vortices." Journal of Fluid Mechanics 284 (February 10, 1995): 377–407. http://dx.doi.org/10.1017/s0022112095000401.
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This paper is concerned with the effect of a weak spanwise-variable mean-flow distortion on the growth of oblique instability waves in a Blasius boundary layer. The streamwise component of the distortion velocity initially grows linearly with increasing streamwise distance, reaches a maximum, and eventually decays through the action of viscosity. This decay occurs slowly and allows the distortion to destabilize the Blasius flow over a relatively large streamwise region. It is shown that even relatively weak distortions can cause certain oblique Rayleigh instability waves to grow much faster than the usual two-dimensional Tollmien–Schlichting waves that would be the dominant instability modes in the absence of the distortion. The oblique instability waves can then become large enough to interact nonlinearly within a common critical layer. It is shown that the common amplitude of the interacting oblique waves is governed by the amplitude evolution equation derived in Goldstein & Choi (1989). The implications of these results for Klebanoff-type transition are discussed.
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Talluru, K. M., J. Philip, and K. A. Chauhan. "Local transport of passive scalar released from a point source in a turbulent boundary layer." Journal of Fluid Mechanics 846 (May 4, 2018): 292–317. http://dx.doi.org/10.1017/jfm.2018.280.
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Simultaneous measurements of streamwise velocity ($\tilde{U}$) and concentration ($\tilde{C}$) for a horizontal plume released at eight different vertical locations within a turbulent boundary layer are discussed in this paper. These are supplemented by limited simultaneous three-component velocity and concentration measurements. Results of the integral time scale ($\unicode[STIX]{x1D70F}_{c}$) of concentration fluctuations across the width of the plume are presented here for the first time. It is found that$\unicode[STIX]{x1D70F}_{c}$has two distinct peaks: one closer to the plume centreline and the other at a vertical distance of plume half-width above the centreline. The time-averaged streamwise concentration flux is found to be positive and negative, respectively, below and above the plume centreline. This behaviour is a resultant of wall-normal velocity fluctuations ($w$) and Reynolds shear stress ($\overline{uw}$). Confirmation of these observations is found in the results of joint probability density functions of$u$(streamwise velocity fluctuations) and$\tilde{C}$as well as that of$w$and$\tilde{C}$. Results of cross-correlation coefficient show that high- and low-momentum regions have a distinctive role in the transport of passive scalar. Above the plume centreline, low-speed structures have a lead over the meandering plume, while high-momentum regions are seen to lag behind the plume below its centreline. Further examination of the phase relationship between time-varying$u$and$c$(concentration fluctuations) via cross-spectrum analysis is consistent with this observation. Based on these observations, a phenomenological model is presented for the relative arrangement of a passive scalar plume with respect to large-scale velocity structures in the flow.
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Bertram, C. D., and S. A. Godbole. "LDA Measurements of Velocities in a Simulated Collapsed Tube." Journal of Biomechanical Engineering 119, no. 3 (August 1, 1997): 357–63. http://dx.doi.org/10.1115/1.2796101.
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A perspex (plexiglas) tube was locally deformed into an almost bi-lobar interior cross section, representative of the localized throat at the downstream end of a collapsed tube conveying a flow. The axial and transverse (parallel to the long axis of the deformed cross section) components of fluid velocity were measured in a dense rectangular grid of points covering the whole cross section, at 15 axial sites between one diameter upstream of and three diameters downstream of the center of the constriction. The Reynolds number based on undeformed tube diameter and mean velocity was 705. Results are presented both as surfaces showing the variation of each component over the cross section and as velocity vector profiles. The overall changes in velocity in the streamwise direction are presented in terms of the variation of the maximum and minimum of each component with axial position. Flow downstream of the throat consisted of two parallel side-jets with a broad region of reverse flow in between. This pattern persisted until beyond 2.5 diameters downstream, by which point transverse inflow at the top and bottom of the cross section had converted the side jets into a complete annulus of axial velocity surrounding a central deficit. Jet velocities and reverse flow disappeared relatively abruptly before three diameters downstream.
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Tamano, Shinji, Takuya Kitao, and Yohei Morinishi. "Turbulent drag reduction of boundary layer flow with non-ionic surfactant injection." Journal of Fluid Mechanics 749 (May 15, 2014): 367–403. http://dx.doi.org/10.1017/jfm.2014.225.
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AbstractWe experimentally investigated streamwise variations of turbulent dynamics in drag-reducing turbulent boundary layer flows following the injection of non-ionic surfactant solutions, which mainly consisted of oleyldimethylamine oxide. We focus on the comparison of turbulence statistics between injected (i.e. heterogeneous) and premixed (i.e. homogeneous) surfactant solutions, in which the maximum drag reduction ratio of 50 % is the same at the most downstream position for both cases. The wall-normal profiles of turbulence statistics, such as streamwise and wall-normal turbulence intensities, seem to be noticeably different between heterogeneous and homogeneous surfactant solutions. However, streamwise variations in these maxima and the wall-normal locations are essentially similar to one another, except for the maximum of streamwise turbulence intensity, which is not arranged by the amount of drag reduction and is also dependent on the normalization due to outer and inner variables. Such complex behaviour of streamwise turbulence intensity would be caused by the formation of near-wall layered structures that are parallel to the wall. For both heterogeneous and homogeneous surfactant solutions, the streamwise variation in the drag reduction ratio corresponds well to those of the mean velocity in wall units and the wall-normal locations of maxima of streamwise and wall-normal turbulence intensities with both outer and inner scaling. Unlike the Reynolds shear stress, the correlation coefficient of the streamwise and wall-normal turbulent fluctuations is correlated well with the drag reduction ratio. We present plausible pictures of the development of turbulence structures such as hairpin vortices and low-speed streaks for the drag-reducing turbulent boundary layer in heterogeneous and homogeneous surfactant solutions, which are comprehensively derived from the present set of experimental measurements such as flow visualization, planar laser-induced fluorescence, two-component laser-Doppler velocimetry and particle image velocimetry on the streamwise and wall-normal plane and the streamwise and spanwise plane.
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Nie, J. H., B. F. Armaly, W. Q. Tao, and Q. W. Wang. "Three-Dimensional Turbulent Flow in the Exit Head Section of a Heat Exchanger." Journal of Fluids Engineering 126, no. 1 (January 1, 2004): 72–80. http://dx.doi.org/10.1115/1.1637635.
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Measurements of three-dimensional turbulent flow in the exit head section of a shell-and-tube heat exchanger were performed using three-component laser Doppler velocimeter. The test geometry is half of a hemispherical cap with two outlet-tubes and with a cylindrical inlet section. Distributions of the velocity vector field, the three mean velocity components, and the Reynolds stress components are reported, and the complex nature of flow in the head section and in the neighborhood of the outlet-tube is quantified. The radial and the streamwise velocity components are of the same order of magnitude in the neighboring region of the outlet-tubes, and they are not symmetric relative to the center plane intersection of the outlet-tubes. The friction factor that was measured across the exit head section of the heat exchanger decreases as the Reynolds number increases from 25,000 to 50,000. These results are useful for validating turbulent flow simulation codes and are needed for improving the design of the exit head section of shell-and-tube heat exchangers.
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Elsnab, John R., Jason P. Monty, Christopher M. White, Manoochehr M. Koochesfahani, and Joseph C. Klewicki. "High-fidelity measurements in channel flow with polymer wall injection." Journal of Fluid Mechanics 859 (November 26, 2018): 851–86. http://dx.doi.org/10.1017/jfm.2018.873.
Full textAbstract:
Streamwise velocity profiles and their wall-normal derivatives were used to investigate the properties of turbulent channel flow in the low polymer drag reduction$(DR)$regime ($DR=6.5\,\%$to$26\,\%$), as realized via polymer injection at the channel surface. Streamwise velocity data were obtained over a friction Reynolds number ranging from$650$to$1800$using the single-velocity-component version of molecular tagging velocimetry (1c-MTV). This adaptation of the MTV technique has the ability to accurately capture instantaneous profiles at very high spatial resolution (${\gtrsim}850$data points per wall-normal profile), and thus generate well-resolved derivative information as well. Owing to this ability, the present study is able to build upon and extend the recent numerical simulation analysis of Whiteet al. (J. Fluid Mech., vol. 834, 2018, pp. 409–433) that examined the mean dynamical structure of polymer drag-reduced channel flow at friction Reynolds numbers up to$1000$. Consistently, the present mean velocity profiles indicate that the extent of the logarithmic region diminishes with increasing polymer concentration, while statistically significant increases in the logarithmic profile slope begin to occur for drag reductions less than$15\,\%$. Profiles of the r.m.s. streamwise velocity indicate that the maximum moves farther from the wall and increases in magnitude with reductions in drag. Similarly, with increasing drag reduction, the profile of the combined Reynolds and polymer shear stress exhibits a decrease in its maximum value that also moves farther from the wall. Correlations are presented that estimate the location and value of the maximum r.m.s. streamwise velocity and combined Reynolds and polymer shear stress. Over the range of$DR$investigated, these effects consistently exhibit approximately linear trends as a function of$DR$. The present measurements allow reconstruction of the mean momentum balance (MMB) for channel flow, which provides further insights regarding the physics described in the study by Whiteet al. In particular, the present findings support a physical scenario in which the self-similar properties on the inertial domain identified from the leading-order structure of the MMB begin to detectably and continuously vary for drag reductions less than$10\,\%$.
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Vukoslavcevic, Petar, and James Wallace. "On the accuracy of measurement of turbulent velocity gradient statistics with hot-wire probes." Thermal Science 21, suppl. 3 (2017): 533–51. http://dx.doi.org/10.2298/tsci160210116v.
Full textAbstract:
A very high resolution minimal channel flow direct numerical simulation was used to examine, virtually, the ability of various multi-sensor hot-wire probe configurations to measure the statistics of velocity gradient components. Various array and sensor configurations and the spatial resolution of probes with these configurations were studied, building on designs and investigations of various authors. In contrast to our previous studies, which focused on turbulent vorticity, vorticity-velocity correlations, dissipation and production rate, here the measurement accuracy of each component of the velocity vector gradient tensor is analyzed separately. The results of the study show that the virtual experiments compare well with a physical experiment, and that such virtual experiments are a powerful tool to examine the accuracy of velocity gradient measurements. The cross-stream gradients needed to determine the vorticity components can be measured with sufficient accuracy with most of the array and sensor configurations of vorticity probes used so far. A systematic error of some of the gradient measurements can appear due to the array or sensor configurations. None of the examined probe designs can measure, with sufficient accuracy, the streamwise velocity gradients, directly or indirectly, using the continuity equation.
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Gustavsson, L. Hårkan. "Energy growth of three-dimensional disturbances in plane Poiseuille flow." Journal of Fluid Mechanics 224 (March 1991): 241–60. http://dx.doi.org/10.1017/s002211209100174x.
Full textAbstract:
The development of a small three-dimensional disturbance in plane Poiseuille flow is considered. Its kinetic energy is expressed in terms of the velocity and vorticity components normal to the wall. The normal vorticity develops according to the mechanism of vortex stretching and is described by an inhomogeneous equation, where the spanwise variation of the normal velocity acts as forcing. To study specifically the effect of the forcing, the initial normal vorticity is set to zero and the energy density in the wavenumber plane, induced by the normal velocity, is determined. In particular, the response from individual (and damped) Orr–Sommerfeld modes is calculated, on the basis of a formal solution to the initial-value problem. The relevant timescale for the development of the perturbation is identified as a viscous one. Even so, the induced energy density can greatly exceed that associated with the initial normal velocity, before decay sets in. Initial conditions corresponding to the least-damped Orr–Sommerfeld mode induce the largest energy density and a maximum is obtained for structures infinitely elongated in the streamwise direction. In this limit, the asymptotic solution is derived and it shows that the spanwise wavenumbers at which the largest amplification occurs are 2.60 and 1.98, for symmetric and antisymmetric normal vorticity, respectively. The asymptotic analysis also shows that the propagation speed for induced symmetric vorticity is confined to a narrower range than that for antisymmetric vorticity. From a consideration of the neglected nonlinear terms it is found that the normal velocity component cannot be nonlinearly affected by the normal vorticity growth for structures with no streamwise dependence.
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Gao, Xiufang, and Bengt Sunde´n. "Effects of Inclination Angle of Ribs on the Flow Behavior in Rectangular Ducts." Journal of Fluids Engineering 126, no. 4 (July 1, 2004): 692–99. http://dx.doi.org/10.1115/1.1778715.
Full textAbstract:
The flow behavior in rib-roughened ducts is influenced by the inclination of ribs and the effect is investigated in the present study by Particle Image Velocimetry (PIV). The local flow structures between two adjacent ribs were measured. The Reynolds number was fixed at 5800. The flow field description was based on the PIV results in planes both parallel and perpendicular to the ribbed walls at various locations. The rib angle to the main flow direction was varied as 30 deg, 45 deg, 60 deg and 90 deg. The ribs induce three dimensional flow fields. The flow separation and reattachment between adjacent ribs are clearly observed. In addition, the inclined ribs are found to alter the spanwise distribution of the streamwise velocity component. The streamwise velocity component has its highest values at the upstream end of the ribs, and decreases continuously to its lowest values at the downstream end. Strong secondary flow motion occurs over the entire duct cross section for the inclined ribs. The flow structures between two consecutive ribs show that the fluid flows along the ribs from one end of the ribs to the other end, and then turns back at the transverse center. Downwash and upwash flows are observed at the upstream end and downstream end of the ribs, respectively.
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Blair, M. F. "Boundary-Layer Transition in Accelerating Flows With Intense Freestream Turbulence: Part 1—Disturbances Upstream of Transition Onset." Journal of Fluids Engineering 114, no. 3 (September 1, 1992): 313–21. http://dx.doi.org/10.1115/1.2910032.
Full textAbstract:
Hot-wire anemometry was employed to examine the laminar-to-turbulent transition of low-speed, two-dimensional boundary layers for two (moderate) levels of flow acceleration and various levels of grid-generated freestream turbulence. Flows with an adiabatic wall and with uniform-flux heat transfer were explored. All of the experimental test cases resulted in bypass-mode transitions, a conclusion based upon the observance of spots upstream of the theoretical minimum critical Reynolds number (three cases) or, for one case, upon the evidence that T-S mode amplification played no apparent role in the transition. Data obtained for the preonset stage indicate that the streamwise-component fluctuation-amplitude distributions, frequency distributions and outer-region waveforms of these bypass-mode transitions were similar to those reported in the literature for low-freestream-turbulence transitions. Within the zone upstream of the first appearance of turbulent spots: (1) The near-wall (Y<δ/2) fluctuations were predominantly low-frequency (frequency approximately 1/5 of that of the most amplified T-S disturbances). (2) The maximum streamwise-component fluctuations occurred over the altitude band 0.3<Y/δ<0.4. (3) Very strong negative “spikes” in streamwise velocity were observed, just upstream of spot initiation, at boundary-layer altitudes near Y/δ=0.6.
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Kuwata, Y., and K. Suga. "Direct numerical simulation of turbulence over anisotropic porous media." Journal of Fluid Mechanics 831 (October 13, 2017): 41–71. http://dx.doi.org/10.1017/jfm.2017.619.
Full textAbstract:
To investigate which component of the anisotropic permeability tensor of porous media influences turbulence over porous walls, direct numerical simulation of anisotropic porous-walled channel flows is performed by the D3Q27 multiple-relaxation-time lattice Boltzmann method. The presently considered anisotropic permeable walls have square pore arrays aligned with the Cartesian axes. Vertical, streamwise and spanwise pore arrays are systematically introduced to the walls to impose anisotropic permeability. Simulations are carried out at a friction Reynolds number of 111 and 230, which is based on the averaged friction velocity of the porous bottom and the smooth top walls. It is found that streamwise and spanwise permeabilities enhance turbulence whilst vertical permeability itself does not. In particular, the enhancement of turbulence is remarkable over porous walls with streamwise permeability. Over streamwise permeable walls, development of high- and low-speed streaks is prevented whilst large-scale intermittent patched patterns of ejection motions are induced. It is revealed by two-point correlation analysis that streamwise permeability allows the development of streamwise large-scale perturbations induced by Kelvin–Helmholtz instability. Spectral analysis reveals that this perturbation contributes to the enhancement of the Reynolds shear stress, leading to significant skin friction of the porous interface. Through the comparison between the two different Reynolds-number cases, it is found that, as the Reynolds number increases, the streamwise perturbation becomes larger and more organized. Consequently, owing to the enhancement of the large-scale perturbation, a significant Reynolds-number dependence of the skin friction of the porous interface can be observed over the streamwise permeable wall. It is also implied that the wavelength of the perturbation can be reasonably scaled by the outer-layer length scale.