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1
Savin, S., J. Büchner, G. Consolini, B. Nikutowski, L. Zelenyi, E. Amata, H. U. Auster, et al. "On the properties of turbulent boundary layer over polar cusps." Nonlinear Processes in Geophysics 9, no. 5/6 (December 31, 2002): 443–51. http://dx.doi.org/10.5194/npg-9-443-2002.
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Abstract. We study properties of nonlinear magnetic fluctuations in the turbulent boundary layer (TBL) over polar cusps during a typical TBL crossing on 19 June 1998. Interball-1data in the summer TBL are compared with that of Geotail in solar wind (SW) and Polar in the northern TBL. In the TBL two characteristic slopes are seen: ~ - 1 at (0.004- 0.08) Hz and ~ - 2.2 at (0.08-2) Hz. We present evidences that random current sheets with features of coherent solitons can result in: (i) slopes of ~ - 1 in the magnetic power spectra; (ii) demagnetization of the SW plasma in "diamagnetic bubbles"; (iii) nonlinear, presumably, 3-wave phase coupling with cascade features; (iiii) departure from the Gaussian statistics. We discuss the above TBL properties in terms of intermittency and self-organization of nonlinear systems, and compare them with kinetic simulations of reconnected current sheet at the nonlinear state. Virtual satellite data in the model current sheet reproduce valuable cascade-like spectral and bi-spectral properties of the TBL turbulence.
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Leehey, P. "Structural Excitation by a Turbulent Boundary Layer: An Overview." Journal of Vibration and Acoustics 110, no. 2 (April 1, 1988): 220–25. http://dx.doi.org/10.1115/1.3269502.
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Thirty years of theoretical and experimental research have yet to resolve a number of questions regarding the vibratory response of, and acoustic radiation from, a structure excited by a turbulent boundary layer (TBL). The most important questions are: (a) Can the TBL be characterized as a Thevenin source—particularly when vibratory power flow into the structure is maximized at hydrodynamic coincidence? Alternatively, at what level does structural vibration fundamentally change the character of the TBL? (b) Is the low wave number portion of the wall pressure spectrum of dominant importance in structural excitation away from hydrodynamic coincidence? Or do structural discontinuities cause the convective ridge of wall pressure to be of greater practical interest? (c) Can one quantify the radiation from a turbulent boundary layer about a rigid finite body? Is it dipole or quadrupole? What is the role of fluctuating wall shear stress? Current research on dense fluid loading and on modeling the behavior of the TBL is yielding new, and sometimes surprising, answers to some of these questions. Free resonant structural vibration in the dense fluid limit and the use of a bounded, non-causal, Green function representing the TBL are two of the surprises discussed.
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Zhang, Jiaojiao, Shengna Liu, and Liancun Zheng. "Turbulent boundary layer heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary." Zeitschrift für Naturforschung A 77, no. 4 (December 21, 2021): 369–77. http://dx.doi.org/10.1515/zna-2021-0268.
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Abstract The turbulent boundary layer (TBL) heat transfer of CuO–water nanofluids on a continuously moving plate subject to convective boundary are investigated. Five different shapes of nanoparticles are taken into account. Prandtl mixing length theory is adopted to divide the TBL into two parts, laminar sub-layer and turbulent region. The numerical solutions are obtained by bvp4c and accuracy is verified with previous results. It is found that the transfer of momentum and heat in the TBL is more obvious in laminar sub-layer than in turbulent region. The rise of velocity ratio parameter increases the velocity and temperature while decreases the local friction coefficient. The heat transfer increases significantly with the increase of velocity ratio parameter, Biot number, and nanoparticles volume fraction. For nanoparticles of different shapes, the heat transfer characteristics are Nu x (sphere) < Nu x (hexahedron) < Nu x (tetrahedron) < Nu x (column) < Nu x (lamina).
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Satcunanathan, Sutharsan, Matthias Meinke, and Wolfgang Schröder. "Impact of Porous Media on Boundary Layer Turbulence." Fluids 7, no. 4 (April 13, 2022): 139. http://dx.doi.org/10.3390/fluids7040139.
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The subsonic flows around NACA 0012 aerofoils with a solid, a porous, and a poro-serrated trailing edge (TE) at a Reynolds number of 1 × 106 are investigated by a hybrid Reynolds-averaged Navier–Stokes (RANS)/large-eddy simulation (LES) approach. The porosity is treated by the method-of-volume averaging. In the RANS, a two-equation low Reynolds number k-ε turbulence model is modified to include the porous treatment. Similarly the equations in the LES are extended by the Darcy–Forchheimer model. The simulation is set up with the broadband turbulent boundary layer trailing edge (TBL-TE) noise prediction as a future objective in mind, i.e., the noise sources in the trailing edge region are captured by the LES. To enforce a physically realistic transition from an averaged RANS solution towards a resolved turbulent flow field, at the inflow of the LES coherent structures are generated by means of the reformulated synthetic turbulence generation (RSTG) method. For the poro-serrated TE, turbulence statistics vary in the spanwise direction between the two extremes of a pure solid and a rectangular porous TE, where porosity locally increases the level of turbulence intensity and alters the near wall turbulence anisotropy.
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LEE, SEUNG-HYUN, and HYUNG JIN SUNG. "Direct numerical simulation of the turbulent boundary layer over a rod-roughened wall." Journal of Fluid Mechanics 584 (July 25, 2007): 125–46. http://dx.doi.org/10.1017/s0022112007006465.
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The effects of surface roughness on a spatially developing turbulent boundary layer (TBL) are investigated by performing direct numerical simulations of TBLs over rough and smooth walls. The Reynolds number based on the momentum thickness was varied in the range Reθ = 300 ∼ 1400. The roughness elements were periodically arranged two-dimensional spanwise rods, and the roughness height was k = 1.5θin, where θin is the momentum thickness at the inlet, which corresponds to k/δ = 0.045 ∼ 0.125, δ being the boundary layer thickness. To avoid generating a rough-wall inflow, which is prohibitively difficult, a step change from smooth to rough was placed 80θin downstream from the inlet. The spatially developing characteristics of the rough-wall TBL were examined. Along the streamwise direction, the friction velocity approached a constant value, and self-preserving forms of the turbulent Reynolds stress tensors were obtained. Introduction of the roughness elements affected the turbulent stress not only in the roughness sublayer but also in the outer layer. Despite the roughness-induced increase of the turbulent Reynolds stress tensors in the outer layer, the roughness had only a relatively small effect on the anisotropic Reynolds stress tensor in the outer layer. Inspection of the triple products of the velocity fluctuations revealed that introducing the roughness elements onto the smooth wall had a marked effect on vertical turbulent transport across the whole TBL. By contrast, good surface similarity in the outer layer was obtained for the third-order moments of the velocity fluctuations.
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LEE, JAE HWA, HYUNG JIN SUNG, and PER-ÅGE KROGSTAD. "Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall." Journal of Fluid Mechanics 669 (January 12, 2011): 397–431. http://dx.doi.org/10.1017/s0022112010005082.
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Direct numerical simulation (DNS) of a spatially developing turbulent boundary layer (TBL) over a wall roughened with regularly arrayed cubes was performed to investigate the effects of three-dimensional (3-D) surface elements on the properties of the TBL. The cubes were staggered in the downstream direction and periodically arranged in the streamwise and spanwise directions with pitches of px/k = 8 and pz/k = 2, where px and pz are the streamwise and spanwise spacings of the cubes and k is the roughness height. The Reynolds number based on the momentum thickness was varied in the range Reθ = 300−1300, and the roughness height was k = 1.5θin, where θin is the momentum thickness at the inlet, which corresponds to k/δ = 0.052–0.174 from the inlet to the outlet; δ is the boundary layer thickness. The characteristics of the TBL over the 3-D cube-roughened wall were compared with the results from a DNS of the TBL over a two-dimensional (2-D) rod-roughened wall. The introduction of cube roughness affected the turbulent Reynolds stresses not only in the roughness sublayer but also in the outer layer. The present instantaneous flow field and linear stochastic estimations of the conditional averaging showed that the streaky structures in the near-wall region and the low-momentum regions and hairpin packets in the outer layer are dominant features in the TBLs over the 2-D and 3-D rough walls and that these features are significantly affected by the surface roughness throughout the entire boundary layer. In the outer layer, however, it was shown that the large-scale structures over the 2-D and 3-D roughened walls have similar characteristics, which indicates that the dimensional difference between the surfaces with 2-D and 3-D roughness has a negligible effect on the turbulence statistics and coherent structures of the TBLs.
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Tian, Hai Ping, Shao Qiong Yang, and Nan Jiang. "Topological Characteristics of Coherent Structures in the Turbulent Boundary Layer Measured by Tomo-PIV." Advanced Materials Research 718-720 (July 2013): 801–6. http://dx.doi.org/10.4028/www.scientific.net/amr.718-720.801.
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Database of time series of the instantaneous three-dimensional three-component (3D-3C) velocity vector field, measured by tomographic time-resolved PIV(Tomo-PIV) in a water tunnel, was analyzed to investigate spatial topologies of coherent structures in the turbulent boundary layer (TBL). A new concept of spatial locally averaged velocity structure function of turbulence is put forward to describe the spatial dilation or compression of the multi-scale coherent structures in the TBL. According to the physical mechanism of dilation or compression of multi-scale coherent vortex structures in the turbulent flow, a new conditional sampling method was proposed as well to extract the spatial topological characteristics of physical quantities of coherent structures, such as fluctuating velocities, velocity gradients, velocity strain rates and vorticity during the bursting process in the Tomo-PIV database. Furthermore, the anti-symmetric structures are the typical spatial topologies characteristics for the velocity gradients and vorticity during coherent structures burst.
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Shehzad, M., B. Sun, D. Jovic, Y. Ostovan, C. Cuvier, J. M. Foucaut, C. Willert, C. Atkinson, and J. Soria. "Intense large-scale motions in zero and adverse pressure gradient turbulent boundary layers." Proceedings of the International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics 20 (July 11, 2022): 1–9. http://dx.doi.org/10.55037/lxlaser.20th.169.
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Proper orthogonal decomposition (POD) is used to study coherent structures in wall-bounded turbulent flows. The present study uses POD in turbulent boundary layers to determine the contributions of the intense large-scale motions (LSMs) to the Reynolds stresses. This study uses the 2C-2D PIV measurements of zero pressure gradient turbulent boundary layers (ZPG-TBL) at Re_{δ2} = 7750, and adverse pressure gradient turbulent boundary layer (APG-TBL) at β = 2.27 and Re_{δ2}= 16240, where Re_{δ2} is the momentum thickness based Reynolds number and β is the Clauser’s pressure gradient parameter. The measurements were obtained in the Laboratoire de Mécanique des Fluides de Lille (LMFL) High-Reynolds-Number (HRN) Boundary Layer Wind Tunnel, Lille, France. The snapshots of the flow field are segregated into those dominated by the intense and mild LSMs based on the intensity of the temporal coefficients of the first POD mode. The intense LSMs are further decomposed into high-momentum (HM) and low-momentum (LM) motions. The relative contributions of the HM motions to the Reynolds stresses are larger near the wall as compared to the LM motions. At the wall-normal distance of the displacement thickness (δ1), HM and LM motions have similar contributions. Beyond δ1, the LM motions have larger contributions with their peaks located closer to the displacement thickness height. This shows that in the presence of an APG, the turbulence activity is shifted closer to the displacement thickness height.
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Stroh, A., Y. Hasegawa, P. Schlatter, and B. Frohnapfel. "Global effect of local skin friction drag reduction in spatially developing turbulent boundary layer." Journal of Fluid Mechanics 805 (September 20, 2016): 303–21. http://dx.doi.org/10.1017/jfm.2016.545.
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A numerical investigation of two locally applied drag-reducing control schemes is carried out in the configuration of a spatially developing turbulent boundary layer (TBL). One control is designed to damp near-wall turbulence and the other induces constant mass flux in the wall-normal direction. Both control schemes yield similar local drag reduction rates within the control region. However, the flow development downstream of the control significantly differs: persistent drag reduction is found for the uniform blowing case, whereas drag increase is found for the turbulence damping case. In order to account for this difference, the formulation of a global drag reduction rate is suggested. It represents the reduction of the streamwise force exerted by the fluid on a plate of finite length. Furthermore, it is shown that the far-downstream development of the TBL after the control region can be described by a single quantity, namely a streamwise shift of the uncontrolled boundary layer, i.e. a changed virtual origin. Based on this result, a simple model is developed that allows the local drag reduction rate to be related to the global one without the need to conduct expensive simulations or measurements far downstream of the control region.
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Ismail, Umair. "Direct Numerical Simulation of a Turbulent Boundary Layer Encountering a Smooth-to-Rough Step Change." Energies 16, no. 4 (February 8, 2023): 1709. http://dx.doi.org/10.3390/en16041709.
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Using a direct numerical simulation (DNS), we investigate the onset of non-equilibrium effects and the subsequent emergence of a self-preserving state as a turbulent boundary layer (TBL) encounters a smooth-to-rough (STR) step change. The rough surface comprises over 2500 staggered cuboid-shaped elements where the first row is placed at 50 θ0 from the inflow. A Reθ=4500 value is attained along with δk≈35 as the TBL develops. While different flow parameters adjust at dissimilar rates that further depend on the vertical distance from the surface and perhaps on δSTR/k, an equilibrium for wall stress, mean velocity, and Reynolds stresses exists across the entire TBL by 35 δSTR after the step change. First-order statistics inside the inner layer adapt much earlier, i.e., at 10–15 δSTR after the step change. Like rough-to-smooth (RTS) scenarios, an equilibrium layer develops from the surface. Unlike RTS transitions, a nascent logarithmic layer is identifiable much earlier, at 4 δSTR after the step change. The notion of equivalent sandgrain roughness does not apply upstream of this fetch because non-equilibrium advection effects permeate into the inner layer. The emergent equilibrium TBL is categorized by a fully rough state (ks+≈120–130; ks/k≈2.8). Decomposition of wall stress into constituent parts reveals no streamwise dependence. Mean velocity in the outer layer is well approximated by Coles’ wake law. The wake parameter and shape factor are enhanced above their smooth-wall counterparts. Quadrant analysis shows that shear-stress-producing motions adjust promptly to the roughness, and the balance between ejections and sweeps in the outer layer remains impervious to the underlying surface.
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Morrill-Winter, Caleb, Jimmy Philip, and Joseph Klewicki. "An invariant representation of mean inertia: theoretical basis for a log law in turbulent boundary layers." Journal of Fluid Mechanics 813 (January 20, 2017): 594–617. http://dx.doi.org/10.1017/jfm.2016.875.
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A refined scaling analysis of the two-dimensional mean momentum balance (MMB) for the zero-pressure-gradient turbulent boundary layer (TBL) is presented and experimentally investigated up to high friction Reynolds numbers, $\unicode[STIX]{x1D6FF}^{+}$. For canonical boundary layers, the mean inertia, which is a function of the wall-normal distance, appears instead of the constant mean pressure gradient force in the MMB for pipes and channels. The constancy of the pressure gradient has led to theoretical treatments for pipes/channels, that are more precise than for the TBL. Elements of these analyses include the logarithmic behaviour of the mean velocity, specification of the Reynolds shear stress peak location, the square-root Reynolds number scaling for the log layer onset and a well-defined layer structure based on the balance of terms in the MMB. The present analyses evidence that similarly well-founded results also hold for turbulent boundary layers. This follows from transforming the mean inertia term in the MMB into a form that resembles that in pipes/channels, and is constant across the outer inertial region of the TBL. The physical reasoning is that the mean inertia is primarily a large-scale outer layer contribution, the ‘shape’ of which becomes invariant of $\unicode[STIX]{x1D6FF}^{+}$ with increasing $\unicode[STIX]{x1D6FF}^{+}$, and with a ‘magnitude’ that is inversely proportional to $\unicode[STIX]{x1D6FF}^{+}$. The present analyses are enabled and corroborated using recent high resolution, large Reynolds number hot-wire measurements of all the terms in the TBL MMB.
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Rao, V. Bhujanga, P. V. S. Ganesh Kumar, and P. K. Gupta. "Viscous Effects on Turbulent Boundary-Layer Noise of Ship's Sonar Dome in a Water Tunnel." Journal of Ship Research 35, no. 04 (December 1, 1991): 331–38. http://dx.doi.org/10.5957/jsr.1991.35.4.331.
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Turbulent boundary-layer (TBL) wall pressure fluctuations of a body measured in a water tunnel need correction to obtain unbounded free-field values. Besides blockage effects in a tunnel which are easily accounted for, viscous effects on TBL noise are to be evaluated to quantify this correction. An analytical method using suitable wave vector spectrum modeling to estimate the correction needed due to viscous effects is presented. A sonar dome body is considered as a typical example.
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Guillon, Corentin, Emmanuel Redon, and Laurent Maxit. "Vibroacoustic simulations with non-homogeneous TBL excitations: Synthesis of wall pressure fields with the Continuously-varying Uncorrelated Wall Plane Waves approach." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 7 (February 1, 2023): 544–51. http://dx.doi.org/10.3397/in_2022_0075.
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A numerical method is presented to predict the vibro-acoustic response of a vibrating structure excited by a spatially inhomogeneous turbulent boundary layer(TBL). It is based on the synthesis of different realizations of the random pressure fluctuations that can be introduced as loadings of a vibro-acoustic model (such as a finite element model). To generate the pressures of the non-homogeneous turbulent boundary layer, the Uncorrelated Wall Plane Wave(UWPW) approach used so far for homogeneous TBL is extended. On a first step, this extension is based on a decomposition of the excited surface into sub-areas and on the averaged TBL parameters for each sub-area. In a second step, it consists in taking into account the interaction between the sub-areas and a refinement of the sub-area decomposition. This leads to the Continuously-varying Uncorrelated Wall Plane Waves (C-UWPW) approach. The accuracy of the proposed approach is investigated on a panel with a varying thickness and excited by a growing TBL triggered at one edge of the plate. The interests of the proposed approach in terms of accuracy and computation time are discussed. Finally, an illustration of the proposed approach to predict the radiated noise from a blade immersed in a water flow is proposed.
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Shi, Beiji, Zhaoyue Xu, and Shizhao Wang. "A non-equilibrium slip wall model for large-eddy simulation with an immersed boundary method." AIP Advances 12, no. 9 (September 1, 2022): 095014. http://dx.doi.org/10.1063/5.0101010.
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A non-equilibrium wall model for large-eddy simulation with the immersed boundary (IB) method is proposed to reduce the required number of grid points in simulating wall-bounded turbulence. The proposed wall model is presented as an appropriate slip velocity on the wall. The slip velocity is constructed by integrating the simplified turbulent boundary layer (TBL) equation along the wall-normal direction, which enhances the integral momentum balance near the wall on a coarse grid. The effect of pressure gradient on the near wall flow is taken into account by retaining the pressure gradient term in the simplified TBL equation. The proposed model is implemented in the form of a direct-forcing IB method with moving-least-square reconstruction near the wall. The benchmarks of plane channel turbulence and the flows over a backward-facing step are used for validation. The proposed model improves the wall stresses and velocity profiles in the region where the pressure gradient dominates the near wall flows.
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OWEIS, GHANEM F., ERIC S. WINKEL, JAMES M. CUTBRITH, STEVEN L. CECCIO, MARC PERLIN, and DAVID R. DOWLING. "The mean velocity profile of a smooth-flat-plate turbulent boundary layer at high Reynolds number." Journal of Fluid Mechanics 665 (December 6, 2010): 357–81. http://dx.doi.org/10.1017/s0022112010003952.
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Smooth flat-plate turbulent boundary layers (TBLs) have been studied for nearly a century. However, there is a relative dearth of measurements at Reynolds numbers typical of full-scale marine and aerospace transportation systems (Reθ = Ueθ/ν > 105, where Ue = free-stream speed, θ = TBL momentum thickness and ν = kinematic viscosity). This paper presents new experimental results for the TBL that forms on a smooth flat plate at nominal Reθ values of 0.5 × 105, 1.0 × 105 and 1.5 × 105. Nominal boundary layer thicknesses (δ) were 80–90mm, and Karman numbers (δ+) were 17000, 32000 and 47000, respectively. The experiments were conducted in the William B. Morgan Large Cavitation Channel on a polished (k+ < 0.2) flat-plate test model 12.9m long and 3.05m wide at water flow speeds up to 20ms−1. Direct measurements of static pressure and mean wall shear stress were obtained with pressure taps and floating-plate skin friction force balances. The TBL developed a mild favourable pressure gradient that led to a streamwise flow speed increase of ~2.5% over the 11m long test surface, and was consistent with test section sidewall and model surface boundary-layer growth. At each Reθ, mean streamwise velocity profile pairs, separated by 24cm, were measured more than 10m from the model's leading edge using conventional laser Doppler velocimetry. Between these profile pairs, a unique near-wall implementation of particle tracking velocimetry was used to measure the near-wall velocity profile. The composite profile measurements span the wall-normal coordinate range from y+ < 1 to y > 2δ. To within experimental uncertainty, the measured mean velocity profiles can be fit using traditional zero-pressure-gradient (ZPG) TBL asymptotics with some modifications for the mild favourable pressure gradient. The fitted profile pairs satisfy the von-Kármán momentum integral equation to within 1%. However, the profiles reported here show distinct differences from equivalent ZPG profiles. The near-wall indicator function has more prominent extrema, the log-law constants differ slightly, and the profiles' wake component is less pronounced.
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Savin, S., L. Zelenyi, S. Romanov, I. Sandahl, J. Pickett, E. Amata, L. Avanov, et al. "Magnetosheath-cusp interface." Annales Geophysicae 22, no. 1 (January 1, 2004): 183–212. http://dx.doi.org/10.5194/angeo-22-183-2004.
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Abstract. We advance the achievements of Interball-1 and other contemporary missions in exploration of the magnetosheath-cusp interface. Extensive discussion of published results is accompanied by presentation of new data from a case study and a comparison of those data within the broader context of three-year magnetopause (MP) crossings by Interball-1. Multi-spacecraft boundary layer studies reveal that in ∼80% of the cases the interaction of the magnetosheath (MSH) flow with the high latitude MP produces a layer containing strong nonlinear turbulence, called the turbulent boundary layer (TBL). The TBL contains wave trains with flows at approximately the Alfvén speed along field lines and "diamagnetic bubbles" with small magnetic fields inside. A comparison of the multi-point measurements obtained on 29 May 1996 with a global MHD model indicates that three types of populating processes should be operative: large-scale (∼few RE) anti-parallel merging at sites remote from the cusp; medium-scale (few thousandkm) local TBL-merging of fields that are anti-parallel on average; small-scale (few hundredkm) bursty reconnection of fluctuating magnetic fields, representing a continuous mechanism for MSH plasma inflow into the magnetosphere, which could dominate in quasi-steady cases. The lowest frequency (∼1–2mHz) TBL fluctuations are traced throughout the magnetosheath from the post-bow shock region up to the inner magnetopause border. The resonance of these fluctuations with dayside flux tubes might provide an effective correlative link for the entire dayside region of the solar wind interaction with the magnetopause and cusp ionosphere. The TBL disturbances are characterized by kinked, double-sloped wave power spectra and, most probably, three-wave cascading. Both elliptical polarization and nearly Alfvénic phase velocities with characteristic dispersion indicate the kinetic Alfvénic nature of the TBL waves. The three-wave phase coupling could effectively support the self-organization of the TBL plasma by means of coherent resonant-like structures. The estimated characteristic scale of the "resonator" is of the order of the TBL dimension over the cusps. Inverse cascades of kinetic Alfvén waves are proposed for forming the larger scale "organizing" structures, which in turn synchronize all nonlinear cascades within the TBL in a self-consistent manner. This infers a qualitative difference from the traditional approach, wherein the MSH/cusp interaction is regarded as a linear superposition of magnetospheric responses on the solar wind or MSH disturbances. Key words. Magnetospheric physics (magnetopause, cusp, and boundary layers) – Space plasma physics (turbulence; nonlinear phenomena)
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SCHLATTER, PHILIPP, and RAMIS ÖRLÜ. "Assessment of direct numerical simulation data of turbulent boundary layers." Journal of Fluid Mechanics 659 (July 16, 2010): 116–26. http://dx.doi.org/10.1017/s0022112010003113.
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Statistics obtained from seven different direct numerical simulations (DNSs) pertaining to a canonical turbulent boundary layer (TBL) under zero pressure gradient are compiled and compared. The considered data sets include a recent DNS of a TBL with the extended range of Reynolds numbers Reθ = 500–4300. Although all the simulations relate to the same physical flow case, the approaches differ in the applied numerical method, grid resolution and distribution, inflow generation method, boundary conditions and box dimensions. The resulting comparison shows surprisingly large differences not only in both basic integral quantities such as the friction coefficient cf or the shape factor H12, but also in their predictions of mean and fluctuation profiles far into the sublayer. It is thus shown that the numerical simulation of TBLs is, mainly due to the spatial development of the flow, very sensitive to, e.g. proper inflow condition, sufficient settling length and appropriate box dimensions. Thus, a DNS has to be considered as a numerical experiment and should be the subject of the same scrutiny as experimental data. However, if a DNS is set up with the necessary care, it can provide a faithful tool to predict even such notoriously difficult flow cases with great accuracy.
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ELBING, BRIAN R., MICHAEL J. SOLOMON, MARC PERLIN, DAVID R. DOWLING, and STEVEN L. CECCIO. "Flow-induced degradation of drag-reducing polymer solutions within a high-Reynolds-number turbulent boundary layer." Journal of Fluid Mechanics 670 (February 22, 2011): 337–64. http://dx.doi.org/10.1017/s0022112010005331.
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Polymer drag reduction, diffusion and degradation in a high-Reynolds-number turbulent boundary layer (TBL) flow were investigated. The TBL developed on a flat plate at free-stream speeds up to 20ms−1. Measurements were acquired up to 10.7m downstream of the leading edge, yielding downstream-distance-based Reynolds numbers up to 220 million. The test model surface was hydraulically smooth or fully rough. Flow diagnostics included local skin friction, near-wall polymer concentration, boundary layer sampling and rheological analysis of polymer solution samples. Skin-friction data revealed that the presence of surface roughness can produce a local increase in drag reduction near the injection location (compared with the flow over a smooth surface) because of enhanced mixing. However, the roughness ultimately led to a significant decrease in drag reduction with increasing speed and downstream distance. At the highest speed tested (20ms−1) no drag reduction was discernible at the first measurement location (0.56m downstream of injection), even at the highest polymer injection flux (10 times the flux of fluid in the near-wall region). Increased polymer degradation rates and polymer mixing were shown to be the contributing factors to the loss of drag reduction. Rheological analysis of liquid drawn from the TBL revealed that flow-induced polymer degradation by chain scission was often substantial. The inferred polymer molecular weight was successfully scaled with the local wall shear rate and residence time in the TBL. This scaling revealed an exponential decay that asymptotes to a finite (steady-state) molecular weight. The importance of the residence time to the scaling indicates that while individual polymer chains are stretched and ruptured on a relatively short time scale (~10−3s), because of the low percentage of individual chains stretched at any instant in time, a relatively long time period (~0.1s) is required to observe changes in the mean molecular weight. This scaling also indicates that most previous TBL studies would have observed minimal influence from degradation due to insufficient residence times.
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Sanmiguel Vila, C., R. Vinuesa, S. Discetti, A. Ianiro, P. Schlatter, and R. Örlü. "On the identification of well-behaved turbulent boundary layers." Journal of Fluid Mechanics 822 (May 31, 2017): 109–38. http://dx.doi.org/10.1017/jfm.2017.258.
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This paper introduces a new method based on the diagnostic plot (Alfredsson et al., Phys. Fluids, vol. 23, 2011, 041702) to assess the convergence towards a well-behaved zero-pressure-gradient (ZPG) turbulent boundary layer (TBL). The most popular and well-understood methods to assess the convergence towards a well-behaved state rely on empirical skin-friction curves (requiring accurate skin-friction measurements), shape-factor curves (requiring full velocity profile measurements with an accurate wall position determination) or wake-parameter curves (requiring both of the previous quantities). On the other hand, the proposed diagnostic-plot method only needs measurements of mean and fluctuating velocities in the outer region of the boundary layer at arbitrary wall-normal positions. To test the method, six tripping configurations, including optimal set-ups as well as both under- and overtripped cases, are used to quantify the convergence of ZPG TBLs towards well-behaved conditions in the Reynolds-number range covered by recent high-fidelity direct numerical simulation data up to a Reynolds number based on the momentum thickness and free-stream velocity $Re_{\unicode[STIX]{x1D703}}$ of approximately 4000 (corresponding to 2.5 m from the leading edge) in a wind-tunnel experiment. Additionally, recent high-Reynolds-number data sets have been employed to validate the method. The results show that weak tripping configurations lead to deviations in the mean flow and the velocity fluctuations within the logarithmic region with respect to optimally tripped boundary layers. On the other hand, a strong trip leads to a more energized outer region, manifested in the emergence of an outer peak in the velocity-fluctuation profile and in a more prominent wake region. While established criteria based on skin-friction and shape-factor correlations yield generally equivalent results with the diagnostic-plot method in terms of convergence towards a well-behaved state, the proposed method has the advantage of being a practical surrogate that is a more efficient tool when designing the set-up for TBL experiments, since it diagnoses the state of the boundary layer without the need to perform extensive velocity profile measurements.
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Mazzeo, G., M. Ichchou, G. Petrone, O. Bareille, S. De Rosa, and F. Franco. "Pseudo-equivalent deterministic excitation method application for experimental reproduction of a structural response to a turbulent boundary layer excitation." Journal of the Acoustical Society of America 152, no. 3 (September 2022): 1498–514. http://dx.doi.org/10.1121/10.0013424.
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In the transportation engineering field, the turbulent boundary layer over a structure is one of the most relevant sources of structural vibration and emitted noise. Wind tunnels are still one of the best options for vibroacoustic experimental analyses for this specific problem. However, it is also true that this experimental method is not always affordable, due to several limitations—settings hard to control, time and money consumption, discrepancies among laboratories—that wind tunnel facilities present. It has already developed different methodologies to address this necessity, most of them based on the use of loudspeakers or shakers. In this work, an existing numerical method, called the pseudo-equivalent deterministic excitation method (PEDE M), is further developed for the experimental purpose of reproducing the experimental structural response of a panel subjected to a turbulent boundary layer (TBL) excitation, by using an equivalent rain-on-the-roof excitation instead; different formulations are used for the application of this approximated TBL excitation. The experimental application of PEDE M, here called X-PEDE M, is validated by comparison with experimental results of two different panels analysed in two different wind tunnel facilities.
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Kitsios, V., A. Sekimoto, C. Atkinson, J. A. Sillero, G. Borrell, A. G. Gungor, J. Jiménez, and J. Soria. "Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation." Journal of Fluid Mechanics 829 (September 20, 2017): 392–419. http://dx.doi.org/10.1017/jfm.2017.549.
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The statistical properties are presented for the direct numerical simulation of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) at the verge of separation. The APG TBL has a momentum thickness-based Reynolds number range from $Re_{\unicode[STIX]{x1D6FF}_{2}}=570$ to 13 800, with a self-similar region from $Re_{\unicode[STIX]{x1D6FF}_{2}}=10\,000$ to 12 300. Within this domain the average non-dimensional pressure gradient parameter $\unicode[STIX]{x1D6FD}=39$, where for a unit density $\unicode[STIX]{x1D6FD}=\unicode[STIX]{x1D6FF}_{1}P_{\!e}^{\prime }/\unicode[STIX]{x1D70F}_{w}$, with $\unicode[STIX]{x1D6FF}_{1}$ the displacement thickness, $\unicode[STIX]{x1D70F}_{w}$ the mean shear stress at the wall and $P_{\!e}^{\prime }$ the far-field pressure gradient. This flow is compared with previous zero pressure gradient and mild APG TBL ($\unicode[STIX]{x1D6FD}=1$) results of similar Reynolds number. All flows are generated via the direct numerical simulation of a TBL on a flat surface with far-field boundary conditions tailored to apply the desired pressure gradient. The conditions for self-similarity, and the appropriate length and velocity scales, are derived. The mean and Reynolds stress profiles are shown to collapse when non-dimensionalised on the basis of these length and velocity scales. As the pressure gradient increases, the extent of the wake region in the mean streamwise velocity profiles increases, whilst the extent of the log-layer and viscous sublayer decreases. The Reynolds stress, production and dissipation profiles of the APG TBL cases exhibit a second outer peak, which becomes more pronounced and more spatially localised with increasing pressure gradient. This outer peak is located at the point of inflection of the mean velocity profiles, and is suggestive of the presence of a shear flow instability. The maximum streamwise velocity variance is located at a wall normal position of $\unicode[STIX]{x1D6FF}_{1}$ of spanwise wavelength of $2\unicode[STIX]{x1D6FF}_{1}$. In summary as the pressure gradient increases the flow has properties less like a zero pressure gradient TBL and more akin to a free shear layer.
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Ono, Marie, Noriyuki Furuichi, Yuki Wada, Noboru Kurihara, and Yoshiyuki Tsuji. "Reynolds number dependence of inner peak turbulence intensity in pipe flow." Physics of Fluids 34, no. 4 (April 2022): 045103. http://dx.doi.org/10.1063/5.0084863.
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Streamwise turbulence statistics in the range from Reτ = 990 to Reτ = 20 750 at the High Reynolds Number Actual Flow Facility at the National Metrology Institute of Japan are presented, specifically focusing on the Reynolds number dependence of the inner peak turbulence intensity. Velocity measurements are conducted using laser Doppler velocimetry (LDV), taking account of problems specific to this method, with the aim of providing reliable experimental results. The control volume and the fringe pattern of LDV, both of which influence turbulence statistics, are directly measured using a rotary wire device, and they are used to correct the measured turbulence intensity using methods developed in this study. The present results for mean velocity and turbulence intensity profiles agree well with direct numerical simulation data. The inner peak turbulence intensity in this pipe experiment increases with the increasing Reynolds number. It is found that the Reynolds number dependence of the inner peak up to Reτ = 20 750 is very similar to that in a turbulent boundary layer (TBL). The slope of the outer logarithmic region in the turbulence intensity profile is twice the slope obtained from the relation between the inner peak and the Reynolds number. This relation is also consistent with that for TBL flow.
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Biplab Ranjan Adhikary, Ananya Majumdar, Atanu Sahu, and Partha Bhattacharya. "Sensitivity of TBL Wall-Pressure over the Flat Plate on Numerical Turbulence Model Parameter Variations." CFD Letters 15, no. 7 (May 29, 2023): 148–74. http://dx.doi.org/10.37934/cfdl.15.7.148174.
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A two-fold sensitivity of the zero-pressure gradient (ZPG) turbulent boundary layer (TBL) wall-pressure spectrum to different RANS model parameters is investigated for a flat plate case, which is a close approximation to the aircraft fuselage or wing. The alteration in the mean square pressure fluctuations due choice of semi-empirical pressure model and the choice of computational model parameters like solver, near wall grid clustering, measuring location, and flow velocity are separately studied. The underlying effect of different TBL parameters in the said sensitivity has been studied while numerically replicating wind tunnel experiments and in-flight tests considering different RANS configurations. Initially, the best-predicting pressure spectrum models are selected by comparing them with available in-flight and wind tunnel test data. Subsequently, the accuracy of all the individual model parameters in predicting mean TBL flow quantities like wall shear stress, boundary layer thickness, displacement thickness, momentum thickness, etc., and eventually mean square pressure (MSP) is estimated. The sensitivity of the mean square pressure fluctuations value to the TBL flow quantities and the near-wall grid clustering is observed to be significant. In general, family of models is found to be best in terms of numerical convergence and closeness when compared to the experimental MSP values. family of models is suggested to be avoided while estimating MSP in flat plate TBL case
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Hu, Jinge, and Zhaohui Yao. "Drag reduction of turbulent boundary layer over sawtooth riblet surface with superhydrophobic coat." Physics of Fluids 35, no. 1 (January 2023): 015104. http://dx.doi.org/10.1063/5.0132403.
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The application of drag reduction tech holds great significance to energy saving. To achieve better drag reduction, we investigated the flow characteristics of the turbulent boundary layer (TBL) over a composite surface made of sawtooth riblets with superhydrophobic coat (rib&SHS), a superhydrophobic surface (SHS), and a smooth surface using particle image velocimetry. The results showed that the drag reduction rate of the composite surface was higher than that of the superhydrophobic surface at the same Reynolds number. When the Reynolds number reached 2015, the drag reduction effect of SHS was almost ineffective (drag reduction was only 1.2%), whereas rib&SHS maintained satisfactory results (drag reduction was 20.2%). By proper orthogonal decomposition (POD), the second-order POD mode showed the tilt angles of the interface of Q2 and Q4 events inside the TBL over rib&SHS, and SHS were reduced compared with the smooth surface in the drag reduction cases. With drag reduction of rib&SHS and SHS, the hairpin vortexes were lifted away from the wall and the distances of vortexes within hairpin vortex packets decreased. Compared with SHS, rib&SHS had a greater effect on hairpin vortexes and hairpin vortex packets because the riblets made the Q2 events of rib&SHS weaker than that of SHS. So, the rib&SHS has a higher drag reduction rate and a larger drag reduction Reynolds number range than the SHS. It can be used to guide the drag reduction design of underwater vehicles.
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Schau, H. C. "Planar turbulent boundary layer (TBL) pressure field emulation with a reduced degree of freedom array." Journal of the Acoustical Society of America 80, S1 (December 1986): S27. http://dx.doi.org/10.1121/1.2023728.
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KATZ, R. A., T. GALIB, and J. CEMBROLA. "Mechanisms underlying transitional and turbulent boundary layer (TBL) flow-induced noise in underwater acoustics (II)." Le Journal de Physique IV 04, no. C5 (May 1994): C5–1063—C5–1066. http://dx.doi.org/10.1051/jp4:19945233.
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She, Zhen-Su, Xi Chen, and Fazle Hussain. "Quantifying wall turbulence via a symmetry approach: a Lie group theory." Journal of Fluid Mechanics 827 (August 22, 2017): 322–56. http://dx.doi.org/10.1017/jfm.2017.464.
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First-principle-based prediction of mean-flow quantities of wall-bounded turbulent flows (channel, pipe and turbulent boundary layer (TBL)) is of great importance from both physics and engineering standpoints. Here we present a symmetry-based approach which yields analytical expressions for the mean-velocity profile (MVP) from a Lie-group analysis. After verifying the dilatation-group invariance of the Reynolds averaged Navier–Stokes (RANS) equation in the presence of a wall, we depart from previous Lie-group studies of wall turbulence by selecting a stress length function as a similarity variable. We argue that this stress length function characterizes the symmetry property of wall flows having a simple dilatation-invariant form. Three kinds of (local) invariant forms of the length function are postulated, a combination of which yields a multi-layer formula giving its distribution in the entire flow region normal to the wall and hence also the MVP, using the mean-momentum equation. In particular, based on this multi-layer formula, we obtain analytical expressions for the (universal) wall function and separate wake functions for pipe and channel, which are validated by data from direct numerical simulations (DNS). In conclusion, an analytical expression for the entire MVP of wall turbulence, beyond the log law or power law, is developed in this paper and the theory can be used to describe the mean turbulent kinetic-energy distribution, as well as a variety of boundary conditions such as pressure gradient, wall roughness, buoyancy, etc. where the dilatation-group invariance is valid in the wall-normal direction.
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Kaminski, P., and A. Tyliszczak. "Numerical analysis of the influence of wall roughness on the turbulent boundary layer separation." Journal of Physics: Conference Series 2367, no. 1 (November 1, 2022): 012011. http://dx.doi.org/10.1088/1742-6596/2367/1/012011.
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Abstract Passive control of turbulent boundary layer (TBL) separation in a channel with adverse pressure gradient (APG) condition towards the outlet is investigated using Reynolds-averaged Navier-Stokes (RANS) methods and Large Eddy simulations (LES) with the help of commercial ANSYS software. Isothermal and incompressible flow in the near-wall area of the flat plate as well as various configurations of wavy wall is studied. It is shown that the amplitude and period of the waviness significantly influence the near wall region and point of separation.
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Xiao, Meng-Juan, and Zhen-Su She. "Precise drag prediction of airfoil flows by a new algebraic model." Acta Mechanica Sinica 36, no. 1 (November 16, 2019): 35–43. http://dx.doi.org/10.1007/s10409-019-00911-9.
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AbstractWe report the results of accurate prediction of lift ($$C_L$$CL) and drag ($$C_D$$CD) coefficients of two typical airfoil flows (NACA0012 and RAE2822) by a new algebraic turbulence model, in which the eddy viscosity is specified by a stress length (SL) function predicted by structural ensemble dynamics (SED) theory. Unprecedented accuracy of the prediction of $$C_D$$CD with error of a few counts (one count is $$10^{-4}$$10-4) and of $$C_L$$CL with error under 1%-2% are uniformly obtained for varying angles of attack (AoA), indicating an order of magnitude improvement of drag prediction accuracy compared to currently used models (typically around 20 to 30 counts). More interestingly, the SED-SL model is distinguished with fewer parameters of clear physical meaning, which quantify underlying turbulent boundary layer (TBL) with a universal multi-layer structure, and is thus promising to be more easily generalizable to complex TBL. The use of the new model for the calibration of flow condition in experiment and the extraction of flow physics from numerical simulation data of aeronautic flows are discussed.
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Wang, Cong, and Morteza Gharib. "On the Turbulent Drag Reduction Effect of the Dynamic Free-Slip Surface Method." Journal of Marine Science and Engineering 10, no. 7 (June 27, 2022): 879. http://dx.doi.org/10.3390/jmse10070879.
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The turbulent boundary layer (TBL) over the hull surface of a water vehicle significantly elevates the drag force on the water vehicle. In this regard, effectively controlling the TBL can lead to a drag reduction (DR) effect and therefore improve the energy efficiency of water transportation. Many DR methods have demonstrated promising DR effects but face challenges in implementation at the scale of engineering application. In this regard, the recently developed dynamic free-slip surface method can resolve some of the critical challenges. It employs an array of freely oscillating air–water interfaces to manipulate the TBL and can achieve a substantial DR effect under certain control conditions. However, the optimal setting of the control parameters that would maximize the DR effect remains unclear. To answer these questions, this study systematically investigates the effects of multiple control parameters for the first time, including the geometric size and curvature of the interface, the frequency of active oscillation, and the Reynolds number of TBL. Digital Particle Image Velocimetry was used to non-invasively measure the velocity and vorticity field of the TBL, and the Charted Clauser method was used to calculate the DR effect. The presented results suggest that the oscillating free-slip interfaces reduce the flow velocity near the wall boundary and lift the transverse vorticity (and the viscous shear stress) away from the wall. In addition, the shape factor of the TBL is elevated by the oscillating interfaces and slowly relaxes back in the downstream regions, which implies a partial relaminarization process induced in the TBL. Up to 36% DR effect was achieved within the current scope range of the control parameters. All of the results consistently suggest that a large DR effect is achieved when the free-slip interfaces oscillate with large Weber numbers. These discoveries shed light on the underlying DR mechanism and provide guidance for the future development of an effective drag control technique based on the dynamic free-slip surface method.
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Shepherd, Micah. "Excitation of structures by partially correlated pressures: A review of diffuse acoustic field and turbulent boundary layer models." Journal of the Acoustical Society of America 153, no. 3_supplement (March 1, 2023): A75. http://dx.doi.org/10.1121/10.0018211.
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Structures are sometimes excited by pressure distributions which exhibit complex spatial correlation. This differs from common acoustic excitations since the pressure at one location is only partially correlated with the pressure at another location due to inherent spatial randomness within the forcing function. Two forcing functions which exhibit partially-correlated pressures are the diffuse acoustic field (DAF) and turbulent boundary layer (TBL) flow. A basic model for representing the spatial correlation for these two forcing functions will be reviewed in both the spatial and wavenumber domains. Recent approaches for computing the vibration of structures excited by DAF or TBL flow will then be summarized. Interesting physical effects, such as intermodal coupling, will be highlighted to illustrate the importance of properly modeling partial correlations when they exist.
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Djenidi, L., K. M. Talluru, and R. A. Antonia. "Can a turbulent boundary layer become independent of the Reynolds number?" Journal of Fluid Mechanics 851 (July 18, 2018): 1–22. http://dx.doi.org/10.1017/jfm.2018.460.
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This paper examines the Reynolds number ($Re$) dependence of a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) which develops over a two-dimensional rough wall with a view to ascertaining whether this type of boundary layer can become independent of $Re$. Measurements are made using hot-wire anemometry over a rough wall that consists of a periodic arrangement of cylindrical rods with a streamwise spacing of eight times the rod diameter. The present results, together with those obtained over a sand-grain roughness at high Reynolds number, indicate that a $Re$-independent state can be achieved at a moderate $Re$. However, it is also found that the mean velocity distributions over different roughness geometries do not collapse when normalised by appropriate velocity and length scales. This lack of collapse is attributed to the difference in the drag coefficient between these geometries. We also show that the collapse of the $U_{\unicode[STIX]{x1D70F}}$-normalised mean velocity defect profiles may not necessarily reflect $Re$-independence. A better indicator of the asymptotic state of $Re$ is the mean velocity defect profile normalised by the free-stream velocity and plotted as a function of $y/\unicode[STIX]{x1D6FF}$, where $y$ is the vertical distance from the wall and $\unicode[STIX]{x1D6FF}$ is the boundary layer thickness. This is well supported by the measurements.
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Wang, Chengyue, Qi Gao, Jinjun Wang, Biao Wang, and Chong Pan. "Experimental study on dominant vortex structures in near-wall region of turbulent boundary layer based on tomographic particle image velocimetry." Journal of Fluid Mechanics 874 (July 9, 2019): 426–54. http://dx.doi.org/10.1017/jfm.2019.412.
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Vortex structures are very popular research objects in turbulent boundary layers (TBLs) because of their prime importance in turbulence modelling. This work performs a tomographic particle image velocimetry measurement on the near-wall region ($y<0.1\unicode[STIX]{x1D6FF}$) of TBLs at three Reynolds numbers $Re_{\unicode[STIX]{x1D70F}}=1238$, 2286 and 3081. The main attention is paid to the wall-normal evolution of the vortex geometries and topologies. The vortex is identified with swirl strength ($\unicode[STIX]{x1D706}_{ci}$), and its orientation is recognized by using the real eigenvector of the velocity gradient tensor. The vortex inclination angles in the streamwise–wall-normal plane and in the streamwise–spanwise plane as functions of wall-normal positions are investigated, which provide useful information to speculate on the three-dimensional shape of the vortex tubes in a TBL. The difference between the orientations of vorticity and swirl is discussed and their inherent relationship is revealed based on the governing equation of vorticity. Linear stochastic estimation (LSE) is further deployed to directly extract three-dimensional vortex models. The LSE velocity fields for ejection events happening at different wall-normal positions shed light on the evolution of the topologies for the vortices dominating ejection events. LSE based on a centred prograde spanwise vortex provides a typical packet model, which indicates that the population density of the packets in a TBL is large enough to leave footprints in conditionally averaged flow fields. This work should help to settle the severe debate on the existence of packet structures and also lays some foundation for the TBL model theory.
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Mourão Bento, Hugo F., Colin P. VanDercreek, Francesco Avallone, Daniele Ragni, and Mirjam Snellen. "Lattice Boltzmann very large eddy simulations of a turbulent flow over covered and uncovered cavities." Physics of Fluids 34, no. 10 (October 2022): 105120. http://dx.doi.org/10.1063/5.0100001.
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Microphone measurements in a closed test section wind tunnel are affected by turbulent boundary layer (TBL) pressure fluctuations. These fluctuations are mitigated by placing the microphones at the bottom of cavities, usually covered with a thin, acoustically transparent material. Prior experiments showed that the cavity geometry affects the propagation of TBL pressure fluctuations toward the bottom. However, the relationship between the cavity geometry and the flowfield within the cavity is not well understood. Therefore, a very large-eddy simulation was performed using the lattice Boltzmann method. A cylindrical, a countersunk and a conical cavity are simulated with and without a fine wire-cloth cover, which is modeled as a porous medium governed by Darcy's law. Adding a countersink to an uncovered cylindrical cavity is found to mitigate the transport of turbulent structures across the bottom by shifting the recirculation pattern away from the cavity bottom. Covering the cavities nearly eliminates this source of hydrodynamic pressure fluctuations. The eddies within the boundary layer, which convect over the cover, generate a primarily acoustic pressure field inside the cavities and thus suggesting that the pressure fluctuations within covered cavities can be modeled acoustically. As the cavity diameter increases compared to the eddies' integral length scale, the amount of energy in the cut-off modes increases with respect to the cut-on modes. Since cut-off modes decay as they propagate into the cavity, more attenuation is seen. The results are in agreement with experimental evidence.
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ELSINGA, G. E., and I. MARUSIC. "Universal aspects of small-scale motions in turbulence." Journal of Fluid Mechanics 662 (September 22, 2010): 514–39. http://dx.doi.org/10.1017/s0022112010003381.
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Two aspects of small-scale turbulence are currently regarded universal, as they have been reported for a wide variety of turbulent flows. Firstly, the vorticity vector has been found to display a preferential alignment with the eigenvector corresponding to the intermediate eigenvalue of the strain rate tensor; and secondly, the joint probability density function (p.d.f.) of the second and third invariant of the velocity gradient tensor, Q and R, has a characteristic teardrop shape. This paper provides an explanation for these universal aspects in terms of a spatial organization of coherent structures, which is based on an evaluation of the average flow pattern in the local coordinate system defined by the eigenvectors of the strain rate tensor. The approach contrasts with previous investigations, which have relied on assumed model flows. The present average flow patterns have been calculated for existing experimental (particle image velocimetry) or numerical (direct numerical simulation) datasets of a turbulent boundary layer (TBL), a turbulent channel flow and for homogeneous isotropic turbulence. All results show a shear-layer structure consisting of aligned vortical motions, separating two larger-scale regions of relatively uniform flow. Because the directions of maximum and minimum strain in a shear layer are in the plane normal to the vorticity vector, this vector aligns with the remaining strain direction, i.e. the intermediate eigenvector of the strain rate tensor. Further, the QR joint p.d.f. for these average flow patterns reveals a shape reminiscent of the teardrop, as seen in many turbulent flows. The above-mentioned organization of the small-scale motions is not only found in the average patterns, but is also frequently observed in the instantaneous velocity fields of the different turbulent flows. It may, therefore, be considered relevant and universal.
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Wei, Dapeng, Bilong Liu, and Ludi Kang. "Numerical Investigation of Distributed Speed Feedback Control of Turbulent Boundary Layer Excitation Curved Plates Radiation Noise." Acoustics 5, no. 2 (April 19, 2023): 414–28. http://dx.doi.org/10.3390/acoustics5020024.
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The control of decentralized velocity feedback on curved aircraft plates under turbulent boundary layer excitations is numerically investigated in this paper. Sixteen active control units are set on the plate to reduce the vibration and sound radiation of the plate. The computational results from the two methods are compared to verify the accuracy of the numerical model. The plate kinetic energy and the radiated sound power under turbulent boundary layer and control unit excitations are analyzed. The influences of control unit distribution, plate thickness and curvature on radiated sound are discussed. Unlike a flat plate, the control of the lower-order high radiation modes of a curved plate under TBL excitations is critical since these modes predominate the sound radiations. The control of these modes, however, is sensitive to the ratio of the stiffness associated with the membrane tensions to the stiffness associated with the bending forces. This ratio implies that the plate curvature and the thickness play an important role in the control effect. When the plate is thinner and the radius is smaller, the control is less effective.
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Rocha, Joana, Afzal Suleman, and Fernando Lau. "Prediction of Turbulent Boundary Layer Induced Noise in the Cabin of a BWB Aircraft." Shock and Vibration 19, no. 4 (2012): 693–705. http://dx.doi.org/10.1155/2012/153204.
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This paper discusses the development of analytical models for the prediction of aircraft cabin noise induced by the external turbulent boundary layer (TBL). While, in previous works, the contribution of an individual panel to the cabin interior noise was considered, here, the simultaneous contribution of multiple flow-excited panels is analyzed. Analytical predictions are presented for the interior sound pressure level (SPL) at different locations inside the cabin of a Blended Wing Body (BWB) aircraft, for the frequency range 0–1000 Hz. The results show that the number of vibrating panels significantly affects the interior noise levels. It is shown that the average SPL, over the cabin volume, increases with the number of vibrating panels. Additionally, the model is able to predict local SPL values, at specific locations in the cabin, which are also affected with by number of vibrating panels, and are different from the average values.
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Polivanov P. A. "Numerical and experimental study of the effect of gas blowing/suction through a perforated surface on the boundary layer at a supersonic Mach number." Technical Physics Letters 48, no. 14 (2022): 15. http://dx.doi.org/10.21883/tpl.2022.14.52056.18862.
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In this paper a numerical and experimental study of the effect of blowing/suction through a perforated surface on a turbulent boundary layer at a Mach number M=1.4 was carried out. Most of the calculations were performed by Reynolds-averaged Navier-Stokes equations with the kappa-ω SST turbulence model. The calculated geometry completely repeated the experimental one including the perforated surface. The numerical data were compared with experimental measurements obtained by the PIV method. Analysis of the data made it possible to find the limits of applicability of the numerical method for the flow under study. Keywords: supersonic flow, gas blowing/suction through a perforated surface, boundary layer, turbulence model kappa-ω SST, PIV method.
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Li, Biaohui, Jinhao Zhang, and Nan Jiang. "Influence of Synthetic Jets on Multiscale Features in Wall-Bounded Turbulence." Actuators 11, no. 7 (July 18, 2022): 199. http://dx.doi.org/10.3390/act11070199.
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This experimental research focuses on the impacts of submerged synthetic jets on a fully-developed turbulent boundary layer (TBL) under a drag reduction working case. Two-dimensional velocity vectors in the flow field are captured with the aid of a particle image velocimetry (PIV) system. Proper orthogonal decomposition (POD) analyses provide evidence that synthetic jets notably attenuate the induction effect of prograde vortex on the low-speed fluid in large-scale fluctuation velocity field, thereby weakening the bursting process of near-wall turbulent events. Furthermore, the introduced perturbance redistributes the turbulent kinetic energy (TKE) and concentrates the TKE onto small-scale coherent structures. Modal time coefficients in various orders of POD are divided into components of multiple frequency bands by virtue of complementary ensemble empirical mode decomposition (CEEMD). It is found that the turbulence signals are shifted from low-frequency to high-frequency bands thanks to synthetic jets, thus revealing the relationship between scales and frequency bands. One further method of scale decomposition is proposed, that is, the large-scale fluctuating flow field will be obtained after removing the high-frequency noise data with the help of continuous mean square error (CMSE) criterion.
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Park, Hyungmin, Guangyi Sun, and Chang-Jin “CJ” Kim. "Superhydrophobic turbulent drag reduction as a function of surface grating parameters." Journal of Fluid Mechanics 747 (April 23, 2014): 722–34. http://dx.doi.org/10.1017/jfm.2014.151.
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AbstractDespite the confirmation of slip flows and successful drag reduction (DR) in small-scaled laminar flows, the full impact of superhydrophobic (SHPo) DR remained questionable because of the sporadic and inconsistent experimental results in turbulent flows. Here we report a systematic set of bias-free reduction data obtained by measuring the skin-friction drags on a SHPo surface and a smooth surface at the same time and location in a turbulent boundary layer (TBL) flow. Each monolithic sample consists of a SHPo surface and a smooth surface suspended by flexure springs, all carved out from a $2.7 \times 2.7 {\mathrm{mm}}^{2}$ silicon chip by photolithographic microfabrication. The flow tests allow continuous monitoring of the plastron on the SHPo surfaces, so that the DR data are genuine and consistent. A family of SHPo samples with precise profiles reveals the effects of grating parameters on turbulent DR, which was measured to be as much as ${\sim }75\, \%$.
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Kappagantu, Ramana, Manuel Etchessahar, Edgar Matas, and Koen Vansant. "Aircraft interior acoustics - background noise contamination." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 5 (August 1, 2021): 1606–19. http://dx.doi.org/10.3397/in-2021-1882.
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Aircraft interior noise is an important factor to be considered for cabin comfort. In a cruising condition this noise source is mostly broadband in nature and is coming from the exterior, primarily the turbulent boundary layer (TBL) of the flow around the moving aircraft. Capturing this noise to a high frequency is critical for designing the sound packaging. Also, this becomes important in the design of public announcement (PA) system for the aircraft cabin, i.e. the correct placement of speakers. One of the metrics used for this acoustic design is speech transmission index. Deterministic techniques like finite or boundary element techniques for low frequencies and ray tracing method to reach higher frequencies are better suited for getting the narrow band responses. On the other hand, to characterize the background noise due to the TBL loads, statistical energy analysis (SEA) route is pursued. In this paper the authors combine different techniques to capture the background noise and use them with PA sources and eventually capture the sound perceived at points of interest. The articulation metrics are compared for different operating conditions of the aircraft. In the presentation attempts will be made to play the auralized sounds.
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Huang, Chunlong, Hui Li, and Nansong Li. "Flow Noise Spectrum Analysis for Vertical Line Array During Descent in Deep Water." Journal of Theoretical and Computational Acoustics 28, no. 04 (October 19, 2020): 2050022. http://dx.doi.org/10.1142/s259172852050022x.
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Reliable acoustic path (RAP) is a direct path used for sound propagation between a shallow source and a deep receiver in deep water. The RAP environment can provide a high signal-to-noise ratio (SNR) environment for source localization, so it has been widely studied for underwater passive detection. Active detection can be used for source localization during the descent of a vertical line array (VLA). However, the flow noise originating from the pressure fluctuations in the turbulent boundary layer (TBL) during the descent degrades the detection performance of the VLA. This paper presents a calculation of the response of the cylindrical hydrophones to axisymmetric turbulent wall pressure and the physical properties of flow noise. The flow noise was calculated using the wavenumber-frequency spectrum analysis method, which is based on Carpenter’s TBL pressure spectrum. The results show that the energy of the flow noise is concentrated mainly in low frequencies and it increases and spreads toward high frequencies with increasing stream velocity. The conclusions have been verified with experimental data. In addition, the noise correlation between two hydrophones will undergo oscillatory decay as the hydrophone spacing increases. The above findings will be beneficial for signal processing of an active sonar array.
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Araya, Guillermo, Luciano Castillo, and Fazle Hussain. "The log behaviour of the Reynolds shear stress in accelerating turbulent boundary layers." Journal of Fluid Mechanics 775 (June 19, 2015): 189–200. http://dx.doi.org/10.1017/jfm.2015.296.
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Direct numerical simulation of highly accelerated turbulent boundary layers (TBLs) reveals that the Reynolds shear stress,$\overline{u^{\prime }v^{\prime }}^{+}$, monotonically decreases downstream and exhibits a logarithmic behaviour (e.g. $-\overline{u^{\prime }v^{\prime }}^{+}=-(1/A_{uv})\ln y^{+}+B_{uv}$) in the mesolayer region (e.g. $50\leqslant y^{+}\leqslant 170$). The thickness of the log layer of$\overline{u^{\prime }v^{\prime }}^{+}$increases with the streamwise distance and with the pressure gradient strength, extending over a large portion of the TBL thickness (up to 55 %). Simulations reveal that$V^{+}\,\partial U^{+}/\partial y^{+}\sim 1/y^{+}\sim \partial \overline{u^{\prime }v^{\prime }}^{+}/\partial y^{+}$, resulting in a logarithmic$\overline{u^{\prime }v^{\prime }}^{+}$profile. Also,$V^{+}\sim -y^{+}$is no longer negligible as in zero-pressure-gradient (ZPG) flows. Other experimental/numerical data at similar favourable-pressure-gradient (FPG) strengths also show the presence of a log region in$\overline{u^{\prime }v^{\prime }}^{+}$. This log region in$\overline{u^{\prime }v^{\prime }}^{+}$is larger in sink flows than in other spatially developing FPG flows. The latter flows exhibit the presence of a small power-law region in$\overline{u^{\prime }v^{\prime }}^{+}$, which is non-existent in sink flows.
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Yoon, Min, Jinyul Hwang, and Hyung Jin Sung. "Contribution of large-scale motions to the skin friction in a moderate adverse pressure gradient turbulent boundary layer." Journal of Fluid Mechanics 848 (June 1, 2018): 288–311. http://dx.doi.org/10.1017/jfm.2018.347.
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Direct numerical simulation of a turbulent boundary layer (TBL) subjected to a moderate adverse pressure gradient (APG,$\unicode[STIX]{x1D6FD}=1.45$) is performed to explore the contribution of large scales to the skin friction, where$\unicode[STIX]{x1D6FD}$is the Clauser pressure gradient parameter. The Reynolds number based on the momentum thickness develops from$Re_{\unicode[STIX]{x1D703}}\approx 110$to 6000 with an equilibrium region in$Re_{\unicode[STIX]{x1D703}}=4000$–5500. The spanwise wavelength ($\unicode[STIX]{x1D706}_{z}$) spectra of the streamwise and spanwise velocity fluctuations show that the large-scale energy is significantly enhanced throughout the boundary layer. We quantify the superposition and amplitude modulation effects of these enhanced large scales on the skin friction coefficient ($C_{f}$) by employing two approaches: (i) spanwise co-spectra of$\langle v\unicode[STIX]{x1D714}_{z}\rangle$and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$; (ii) conditionally averaged$\langle v\unicode[STIX]{x1D714}_{z}\rangle$and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$. The velocity–vorticity correlations$\langle v\unicode[STIX]{x1D714}_{z}\rangle$and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$are related to the advective transport and the vortex stretching, respectively. Although$\langle v\unicode[STIX]{x1D714}_{z}\rangle$negatively contributes to$C_{f}$, the positive contribution of the large scales ($\unicode[STIX]{x1D706}_{z}>0.5\unicode[STIX]{x1D6FF}$) is observed in the co-spectra of weighted$\langle v\unicode[STIX]{x1D714}_{z}\rangle$. For the co-spectra of weighted$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$, we observe an outer peak at$\unicode[STIX]{x1D706}_{z}\approx 0.75\unicode[STIX]{x1D6FF}$and the superposition of the large scales in the buffer region, leading to the enhancement of$C_{f}$. The magnitude of$\langle v\unicode[STIX]{x1D714}_{z}\rangle$and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$depends on the large-scale streamwise velocity fluctuations ($u_{L}$). In particular, the negative-$u_{L}$events amplify$\langle v\unicode[STIX]{x1D714}_{z}\rangle$in the outer region, and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$is enhanced by the positive-$u_{L}$events. As a result, the skin friction induced by$\langle v\unicode[STIX]{x1D714}_{z}\rangle$and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$increases in the present APG TBL.
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Liefvendahl, Mattias, and Mattias Johansson. "Wall-Modeled LES for Ship Hydrodynamics in Model Scale." Journal of Ship Research 65, no. 01 (March 17, 2021): 41–54. http://dx.doi.org/10.5957/josr.09180065.
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A complete approach for wall-modeled large-eddy simulation (WMLES) is demonstrated for the simulation of the flow around a bulk carrier in the model scale. Essential components of the method are an a-priori estimate of the thickness of the turbulent boundary layer (TBL) over the hull and to use an unstructured grid with the appropriate resolution relative to this thickness. Expressions from the literature for the scaling of the computational cost, in terms of the grid size, with Reynolds number, are adapted in this application. It is shown that WMLES is possible for model scale ship hydrodynamics, with ∼108 grid cells, which is a gain of at least one order of magnitude as compared with wall-resolving LES. For the canonical case of a flat-plate TBL, the effects of wall model parameters and grid cell topology on the predictive accuracy of the method are investigated. For the flat-plate case, WMLES results are compared with results from direct numerical simulation, RANS (Reynolds-averaged Navier-Stokes), and semi-empirical formulas. For the bulk carrier flow, WMLES and RANS are compared, but further validation is needed to assess the predictive accuracy of the approach.
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Foroozan, F., A. Güemes, M. Raiola, R. Castellanos, S. Discetti, and A. Ianiro. "Synchronized measurement of instantaneous convective heat flux and velocity fields in wall-bounded flows." Measurement Science and Technology 34, no. 12 (August 10, 2023): 125301. http://dx.doi.org/10.1088/1361-6501/ace8ad.
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Abstract This work presents an experimental setup for acquiring synchronized wall and flow field measurements in a turbulent boundary layer (TBL). Instantaneous measurements of the convective heat transfer distribution at the wall and of the flow field are carried out simultaneously, using synchronized wall-parallel planar particle image velocimetry and infrared thermography. A low-thermal-inertia heated-thin-foil sensor is embedded in the wall beneath the TBL to measure the wall temperature maps with enough temporal resolution. The unsteady energy balance of the heated foil can be solved to restore the instantaneous value of the convective heat transfer coefficient on the wall. A detailed description of the sensor design is included. Furthermore, owing to the relatively low signal-to-noise ratio of instantaneous temperature fluctuation measurements, a recipe for data processing is proposed. A study to characterize the uncertainty of the experimental setup design is also performed. The overall agreement in the correlation between wall heat transfer and velocity fields with the literature supports the validity of the proposed approach. This solution is potentially interesting for flow control purposes, where sensing is performed at the wall.
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Redford, John A., and Mark W. Johnson. "Predicting Transitional Separation Bubbles." Journal of Turbomachinery 127, no. 3 (March 1, 2004): 497–501. http://dx.doi.org/10.1115/1.1860573.
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This paper describes the modifications made to a successful attached flow transition model to produce a model capable of predicting both attached and separated flow transition. This transition model is used in combination with the Fluent CFD software, which is used to compute the flow around the blade assuming that it remains entirely laminar. The transition model then determines the start of transition location and the development of the intermittency. These intermittency values weight the laminar and turbulent boundary layer profiles to obtain the resulting transitional boundary layer parameters. The ERCOFTAC T3L test cases are used to validate the predictions. The T3L blade is a flat plate with a semi-circular leading edge, which results in the formation of a separation bubble the length of which is strongly dependent on the transition process. Predictions were performed for five T3L test cases for differing free-stream turbulence levels and Reynolds numbers. For the majority of these test cases the measurements were accurately predicted.
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SAKAMOTO, KEI, and KAZUNORI AKITOMO. "The tidally induced bottom boundary layer in a rotating frame: similarity of turbulence." Journal of Fluid Mechanics 615 (November 25, 2008): 1–25. http://dx.doi.org/10.1017/s0022112008003340.
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To investigate turbulent properties of the tidally induced bottom boundary layer (TBBL) in a rotating frame, we performed three-dimensional numerical experiments under unstratified conditions, varying the temporal Rossby number Rot = |σ*/f*|, where σ* and f* are the tidal frequency and the Coriolis parameter, respectively. The vertical profiles of the time-averaged currents and stresses showed good similarity and coincided well with the turbulent Ekman layer, when they were normalized by the modified ‘outer’ scales, the frictional velocity u*τ, T* = 1/|f* + σ*| and δ* = u*τ/|f* + σ*| for the velocity, time and length scales (σ* is positive when the tidal ellipse rotates anticlockwise). This means that the similarity in turbulent statistics is universally applicable to the TBBL in the world's ocean except near the equator. Although strong inertial waves contaminated the perturbation field when Rot ~ 1 and masked the similarity, the apparent diffusivity κ*ap estimated by tracer experiments again showed similarity, since the inertial waves did not affect the mixing process in the present experiments. Thus, κ*ap can be represented in terms of the three external parameters: the latitude (f*), the tidal frequency (σ*) and the tidal amplitude (u*τ). The obtained scaling of u*τ δ* = u*τ2/|f*+σ*| for κ*ap suggests that effective mixing may occur when Rot ~ 1, i.e. near the critical latitude.
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Sun, B., M. Shehzad, C. Willert, J. M. Foucaut, C. Cuvier, Y. Ostovan, C. Atkinson, and J. Soria. "High Spatial Resolution 2C-2D PIV Measurements Using A 47 MPx Sensor Of High Reynolds Number Turbulent Boundary Layer Flow." Proceedings of the International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics 20 (July 11, 2022): 1–8. http://dx.doi.org/10.55037/lxlaser.20th.66.
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In the past decade, advances in electronics technology have made larger imaging sensors available to the experimental fluid mechanics community. These advancements have enabled the measurement of 2-component 2-dimensional (2C-2D) velocity fields using particle image velocimetry (PIV) with much higher spatial resolution than previously possible using a single camera. Although previously reported experiments have incorporated multiple-camera arrays to acquire high spatial resolution PIV, using a single large camera can greatly reduce the complexity of the experimental setup as well as the error introduced by the calibration between the cameras. In this paper, the ability of a single large sensor for high spatial resolution PIV is demonstrated by performing the measurement of a zero-pressure-gradient turbulent boundary layer (ZPG-TBL). In post-processing the PIV images, the lens distortion error is of particular importance, as the lens distortion error increases with the size of the imaging sensor. The third-order polynomial functions are used to model the lens distortion in this study, and the correction is performed on the PIV vectors to save computational cost. The first- and second-order statistics are calculated and compared with the profiles captured by small camera arrays, and the result shows that the corrected profiles agree well with the previously acquired data, therefore, the lens distortion error can be corrected.
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"Inflow turbulence generation using an equivalent boundary layer model." Physics of Fluids 35, no. 7 (July 1, 2023). http://dx.doi.org/10.1063/5.0157360.
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Eddy-resolved simulation of external flow usually requires inflow boundary conditions representing a turbulent boundary layer (TBL) flow, and the quality of the inflow turbulent fluctuation directly impact the accuracy and the cost of the simulation. The present study proposes a new method to generate TBL inflow turbulence, i.e., the equivalent boundary layer (EBL) model. Based on the open-channel model, EBL approximates TBL flow at a given Reynolds number by recovering the mean momentum balance with driving force. It simulates streamwise homogeneous turbulence, applying periodic boundary conditions and, thus, overcomes the complexity and artificiality incurred by the classic recycling–rescaling methods. The current paper discusses the difference between turbulent channel and boundary layer flows from the equation point of view and designs the driving force corresponding to the mean inertial force of boundary layer. Also, the total shear stress models for obtaining the driving force are validated both a priori and a posteriori. Direct numerical simulations (DNS) are carried out for EBLs at Reθ=1000,1420, and 2000 (where Reθ is the Reynolds number based on the momentum thickness), showing that the EBL model well reflects the statistical characteristics of TBL at corresponding Reynolds numbers. The application of the EBL model for the generation of inflow turbulence is also demonstrated by DNS of turbulent boundary layers with inlet Reθ=1000,1420, and 2000. The computational results agree well with generally acknowledged DNS data published in the literature, in terms of streamwise developing statistics, and profiles and energy spectra at characteristic cross sections. Judging from the mean velocity, the adjustment section is shorter than one boundary layer thickness.