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The turbulent boundary layer in a viscous incompressible fluid developing longitudinally past the surface of a thin cone or cylinder at a finite distance from the laminar–turbulent transition zone is studied. The characteristic Reynolds number, determined from the external flow velocity and the length of the body, is assumed to be large, and the thickness of the boundary layer is small and comparable to the radius of the body. The asymptotic method of multiple scales is used to find solutions to the Navier–Stokes equations. Instead of the traditional decomposition of the solution into time-averaged values and their fluctuations, the velocities and pressure are expressed as an asymptotic series consisting of steady and perturbed terms. As a result, the viscous steady flow (‘secondary’) that arises in the boundary layer as a mandatory component of fast turbulent fluctuations was described. Analytical and numerical solutions for the radial steady velocity are presented, describing the self-induced suction of fluid from the external flow into the boundary layer. Further analytical solutions are obtained for the longitudinal and circumferential velocities, which differ markedly from the laminar regime. The solutions found are somewhat similar to the degenerate (one-dimensional) case of self-sustaining longitudinal thin structures in turbulent shear flows. A qualitative comparison with direct numerical simulations is presented. [ABSTRACT FROM AUTHOR]

This paper reports on the recent NATO Advanced Vehicle Technology (AVT) effort associated with smooth-wall two-dimensional turbulent boundary layer flows subjected to streamwise pressure gradients. The effort considered experiments, Reynolds Averaged Navier-Stokes (RANS) simulations, modelling, scaling and flow physics relative to the subject flows. Special attention is given to the current predictive capabilities and deficiencies of RANS simulations, and the interplay between experiments and RANS validation and development. In addition, the efficacy of the prediction of velocity field response and wall pressure statistics are respectively demonstrated via Resolvent and Gene Expression Programming based models. The persistence of a logarithmic mean velocity profile is evaluated and measures of non-equilibrium are described and discussed. A number of open issues are described and recommendations for future research are suggested. [ABSTRACT FROM AUTHOR]

The characteristics of uniform momentum zones (UMZs) and UMZ interfaces in turbulent channel flow (TCF) at friction Reynolds number ranging from 600 to 2000 are investigated. The focus is on the Reynolds number effect and the difference among the turbulent channel flow, turbulent pipe flow (TPF), and turbulent boundary layer (TBL). The UMZ is identified using the approach of probability density histograms, a discrete approximation of the probability density function. We find that the average number of UMZs increases with the Reynolds number, similar to the findings in the TBL. The first group of UMZ in the TCF, namely the quiescent core, has a thicker thickness at a higher Reynolds number. Therefore, the UMZ closer to the channel centre significantly influences high Reynolds number wall turbulence by occupying a large portion of the channel. With increasing Reynolds number, the intensity of spanwise vorticity at the UMZ interface increases, while the thickness of the local maximum decreases. The dominance of prograde vorticity at the interface also increases with the Reynolds number. Moreover, the contortion of the UMZ interface is significantly enhanced at high Reynolds numbers than at low Reynolds numbers in both the streamwise and spanwise directions. Furthermore, the number of UMZ for a given snapshot is related to the overall velocity fluctuations in the subregion, increasing with large-scale Q2 events and decreasing with large-scale Q4 events. Comparing the three flow configurations, UMZs show similarities in their trends, along with two notable differences. First, the TPF has more UMZs compared to the TCF and TBL. Second, the innermost group in the TPF is considerably thicker than that of the higher ranks, a pattern absent in the TCF and TBL. The present findings advance the understanding of UMZs in TCF and demonstrate the similarities and differences between the cases of TCF and TBL. [ABSTRACT FROM AUTHOR]

This document is a letter from the guest editors of the Journal of Turbulence, summarizing the outcomes of a four-year NATO Science and Technology Organization (STO) effort on non-equilibrium high-Reynolds number turbulent boundary layers. The goal of the project was to improve prediction models for high Reynolds number non-equilibrium boundary layers at incompressible conditions. The project involved experimental studies, computational teams, and collaboration between government, academia, and industry. The letter highlights the findings from experiments on non-equilibrium boundary layers generated from exposure to pressure gradients, boundary layers developing over rough surfaces, and the effects of three-dimensional surface geometries. The articles in this special issue provide new insights into flow simulation problems and demonstrate the effectiveness of collaborative efforts in advancing scientific consensus. [Extracted from the article]

We perform direct numerical simulations to investigate the characteristics of wall heat flux (WHF) in the interaction of an oblique shock wave at an angle of 33.2° and free-stream Mach number M∞ = 2.25 impinging on supersonic turbulent expansion corners with deflection angles of 0o (flat plate), 6o and 12o. The effect of the expansion on the WHF characteristics is analysed by comparing it to the interaction with the flat plate under the same flow conditions and a fixed shock impingement point. In the post-expansion region, the decreased mean WHF is found to collapse onto the flat plate case when scaled with the mean wall pressure. The statistical properties of the WHF fluctuations, including probability density function, frequency spectra, and space–time correlations, are comparatively analysed. The expansion causes an increase in the occurrence probability of negative extreme events, an enhancement of high-frequency energy, and an inhibition of intermediate-frequency energy. The increased expansion angle also results in a faster recovery of characteristic spanwise length scales and an increase in convection velocity. We use the mean WHF decomposition method in conjunction with bidimensional empirical mode decomposition to quantitatively analyse the impact of expansion on scale contributions. It is demonstrated that the presence of the expansion corner has no significant impact on the decomposed results, but it significantly reduces the contribution associated with outer large-scale structures. [ABSTRACT FROM AUTHOR]

The effect of a permanent, localised and non-uniform magnetic field on the near-wall turbulence in a fully developed channel flow is analysed through direct numerical simulations. The magnetic field distribution is obtained by an arrangement of magnets placed on the upper and lower channel walls, producing preferentially either a streamwise (i.e. in the main flow direction) or a spanwise magnetic field component. The wall shear stress is drastically reduced under the effect of the streamwise arrangement of the wall magnets wherein both streamwise and wall-normal magnetic fields are involved. The magnetic braking effect leads to an important increase of the body force. Paradoxically enough, the small-scale turbulent activity is significantly increased above the low buffer layer in this case. On the opposite, imposing a magnetic field with a predominant spanwise component reduces tremendously the population of the turbulent shear stress producing eddies by directly affecting the regeneration of the buffer layer quasi-streamwise vortices. The flow is quasi-relaminarised between the magnets in the low-buffer and viscous sublayers. The wall shear increases in a predictable and deterministic way over the magnets, wherein the wall normal magnetic field component induces electric current loops. [ABSTRACT FROM AUTHOR]

Many turbulence theories in use today are based on two-dimensional equilibrium flows and have limitations when applied to three-dimensional flows. A three-dimensional law of the wall would help to improve simulation fidelity, but while several versions have been proposed, none have been widely accepted. In this study, the three-dimensional attached boundary layer flow over the windward side of the BeVERLI (Benchmark Validation Experiments for RANS/LES Investigations) Hill bump model was measured using near-wall laser Doppler velocimetry in the Virginia Tech Stability Wind Tunnel to study the mean flow and turbulence structure. These mean velocity measurements are compared with the predictions of the proposed three-dimensional (3D) law of the wall of van den Berg [A three-dimensional law of the wall for turbulent shear flows. J Fluid Mech. 1975;70(1):149–160.], which incorporates pressure gradients and inertial effects but assumes alignment of the mean flow gradient and shear-stress angles, and to the sublayer momentum equations, which are exact in the limit of wall-normal x 2 + → 0. In regions with mild stress/strain misalignment, the van den Berg model compares favourably with the experimental data up to a maximum of x 2 + ≈ 800 , and the sublayer momentum relationship compares favourably with the experimental data in the linear sublayer. [ABSTRACT FROM AUTHOR]

The discrete element method was recently revisited using a double averaged Navier-Stokes formulation [Chedevergne F. A double-averaged navier-stokes k − ω turbulence model for wall flows over rough surfaces with heat transfer. J Turbul. 2021 Sep;22(11):713–734. doi:] and a new closure relation for the drag coefficient [Chedevergne F, Forooghi P. On the importance of the drag coefficient modelling in the double averaged navier-stokes equations for prediction of the roughness effects. J Turbul. 2020 Aug;21(8):463–482. doi:]. The developed model lies on the notion of representative elementary roughness whose characterisation needs to be generalised to provide a rigorous definition for randomly distributed rough configurations. From 3D scans of rough surfaces and simple image processing, a procedure was proposed to compute the blockage factor and the elementary diameter, the two main parameters of the representative elementary roughness. The procedure was successfully applied to two experimental configurations [Squire D, Morrill-Winter C, Hutchins N, et al. Comparison of turbulent boundary layers over smooth and rough surfaces up to high reynolds numbers. J Fluid Mech. 2016;795:210–240; Croner E, Léon O, Chedevergne F. Industrial use of equivalent sand grain height models for roughness modelling in turbomachinery. In: 55th 3AF International Conference on Applied Conference; Poitiers, France; Apr 2021. ]. Computed velocity profiles match experimental ones when the Reynolds number is varied, showing at the same time the relevance of the procedure and the validity of the double averaged Navier-Stokes model across the different rough regimes. [ABSTRACT FROM AUTHOR]

There is a widely accepted conclusion that the wall roughness do not always enhance the heat transport of the turbulent thermal convection. In this paper, the heat transfer efficiency is statistically investigated from the perspective of turbulent structure. The effect of turbulent structure on the heat transfer of Rayleigh–Bénard convection with triangular rough element on the top and bottom plates is numerically simulated by a lattice Boltzmann method. We use a clustering method to identify complex turbulent structures associated with intense events. The reduction of the Nusselt number is obtained for small roughness height H/L, while the enhancement of heat transport appears for large H/L. For the large H/L case, the positive temperature structures T c p occupying the negative heat transfer events ⟨ T v ⟩ n reduce the efficiency of the heat transfer. On the contrary, the negative temperature turbulent structures T c n boost the heat transfer. By analyzing the conditional average field, we found that the enhancement of the heat transfer for large H/L cases is due to that the negative temperature structures play a dominant role. For small H/L cases, the positive temperature structures T c p inhibit the heat transfer. Furthermore, the more positive and negative temperature structures for large H/L cases are generated near the solid wall and the corner of the box. The physical explanation for the Nu enhancement is that the more secondary vortices are generated by the interaction of these turbulent structures and the rough wall, leading to more plumes ejected from the boundary layers to the bulk. [ABSTRACT FROM AUTHOR]

Direct numerical simulation (DNS) is performed to study high-enthalpy effects on a turbulent boundary layer (TBL) over a curved compression corner. The post-shock flow state behind a wedge flying at Mach 20 and at an altitude of 30 km are chosen for the present simulation. The post-shock temperature is 3400 K, which is high enough to trigger chemical non-equilibrium of the air. A low-enthalpy case is used for comparison. The influences on the instantaneous structures of the streamwise velocity, temperature, and oxygen atoms are examined. The results show that the flow structures are similar on an upstream flat plate in both cases, while on a ramp, streaks of streamwise velocity fluctuations in the high-enthalpy case experience stronger shrink compared with that in the low-enthalpy case. Furthermore, streaks of temperature break into smaller ones when dissociation reactions are introduced. Qualitative and quantitative comparisons are made with the low-enthalpy case; performed using two-point streamwise wall-normal correlation, space–time correlation, and by comparing the propagation velocities of the fluctuations. The results of these analyses validate the observations about the instantaneous fluctuations and show that the differences in the propagation velocity are affected by convection effects and chemical reactions, and that the dissociation reactions accelerate the propagation of temperature fluctuations. [ABSTRACT FROM AUTHOR]

The prediction of turbulent flows over rough surfaces is important for many applications in engineering and in the natural sciences. Since the resolution of the roughness requires significant computational resources, most modelling approaches rely on the related concepts of 'equivalent sand-grain roughness' and 'wall similarity'. While the validity of these concepts is well established for zero-pressure-gradient boundary-layers and for channel flows, such is not the case for non-equilibrium conditions. This raises a number of important questions, some of which are discussed in this paper. We also suggest some possible paths to answering these questions. [ABSTRACT FROM AUTHOR]

Uniform blowing through a permeable surface acts as an active flow control method in wall bounded flows. Such control technique was investigated in a zero pressure gradient turbulent boundary layer over a flat plate. Measurement data were obtained with the help of Laser Doppler Anemometry technique. Besides the drag reduction characteristics of such flow control method, time averaged measurement of stream-wise and wall-normal velocity components was taken at Reynolds number based on momentum thickness ( R e θ , S B L = U ∞ θ / ν) of 1100–3670. Due to the difference in surface condition with and without blowing, mean properties of the boundary condition at wall influence the flow properties when scaled with outer scaling properties. Enhanced turbulence is observed in Reynolds stresses using statistical analysis including the thickening of the boundary layer. [ABSTRACT FROM AUTHOR]

The wall-shear stress (WSS) fluctuations in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer are investigated by means of direct numerical simulation (DNS) at Mach 2.25. The numerical results agree very well with previous experiments and DNS data in terms of turbulence statistics, wall pressure, and skin friction. The fluctuating WSS characteristics, including probability density function (PDF), frequency spectrum, space–time correlation, and convection velocity, are analysed systematically. It is found that the positively skewed PDF shape of the streamwise WSS fluctuations is significantly changed due to the presence of a separation bubble, while the PDF shape of the spanwise component is slightly affected, exhibiting a symmetric behaviour across the interaction. The weighted power-spectrum density map indicates that the low-frequency unsteadiness associated with the separated shock - exhibits little influence on the spectrum for either component, and no enhancement of the low-frequency energy is observed. A significant reduction in the spatial extent of the two-point correlation is observed, causing spanwise elongated coherence for the streamwise WSS fluctuations in the separation region. Moreover, the elliptic behaviour of the space–time correlations is essentially preserved throughout the interaction, and this is accompanied by a sudden reduction of the convection velocity in the separation bubble. [ABSTRACT FROM AUTHOR]

We performed large-eddy simulations of the flow over an aerofoil to understand the effects of leading-edge roughness designed to mimic ice accretion. The roughness elements protrude outside the boundary layer, which, near the leading edge, is very thin; thus, the configuration does not represent a classical rough-wall boundary layer, but rather the flow over macroscopic obstacles. A grid convergence study is conducted and results are validated by comparison to numerical and experimental studies in the literature. The main effect of the obstacles is to accelerate transition to turbulence. Significant variations in structure generation are observed for different roughness shapes. The three-dimensionality of the irregularities has a strong impact on the flow: it creates alternating regions of high-speed ('peaks') and low-speed ('valleys') regions, a phenomenon termed 'channelling'. The valley regions resemble a decelerating boundary layer: they exhibit considerable wake and higher levels of Reynolds stresses. The peak regions, on the other hand, are more similar to an accelerating one. Implications of the channelling phenomenon on turbulence modelling are discussed. [ABSTRACT FROM AUTHOR]

We present a systematic approach to extract the characteristic vortex region that contains the essential features of a complex flow field. The process involves the analysis of the complex eigenvalues of the velocity gradient tensor. In particular, we propose the analysis using the joint and marginal probability distributions of the complex eigenvalues of the velocity gradient tensor that preserves the sufficient swirling strength and the required orbital compactness of the swirling orbits defining the vortex region. We consider three complex flow scenarios for the application and the assessment of the proposed approach: (i) rotating Rayleigh–Benard convection, (ii) turbulent channel flow, (iii) turbulent flow field in a cylindrical cyclonic separator. While problem (i) is considered for the extraction of subsumed cyclonic structure, problems (ii) and (iii) are reminiscent of wall-bounded turbulent flows, relevant for different industrial applications. [ABSTRACT FROM AUTHOR]

Direct numerical simulations of turbulent boundary layers with roughness elements on a wall were performed to investigate the spatial characteristics of rough-wall turbulence and establish a corresponding prediction method. When the roughness height was larger than the buffer layer, the rough-wall turbulence exhibited different spatial characteristics of the turbulence structures from those pertaining to a smooth wall. A novel spatial scaling method was established to examine the universal spatial characteristics of turbulence structures in the presence and absence of wall roughness. Specifically, the viscous length was determined by modifying the definition of the friction velocity in the region in which the roughness influenced the flow. The rough-wall turbulence could be accurately predicted by performing large eddy simulations using the subgrid scale model with the filter width, which was modified using the proposed spatial scaling method. The proposed model can be used to design more efficient fluid machinery in engineering applications. [ABSTRACT FROM AUTHOR]

This paper explores the use of a small-span direct numerical simulation for a transient, smooth-wall turbulent channel flow and then applies the small-span simulation to a transient channel flow with riblets. A flow configuration similar to that of S. He and M. Seddighi (J Fluid Mech. 2013;715:60–102) is used to study the impulse response of a half-height channel flow to an abrupt increase in bulk velocity (with a friction Reynolds number increasing from 180 to 418). A minimal domain span sufficient to include the near-wall quasi-streamwise vortices in the 'healthy turbulence' region is used. The turbulent flow undergoes reverse transition toward a quasi-laminar state, followed by a retransition phase to the new equilibrium state. On a smooth wall, detailed comparisons with a full-span case show that the small-span test case captures satisfactorily the essential dynamics during the entire transition process, although it yields a slight delay in recovery to the new equilibrium. This difference is attributed to a slower streak transient growth due to an underestimation of near-wall spanwise fluctuations. This underestimation is associated with the missing large attached eddies that are not contained in the small span of the simulation domain. These comparisons justify the use of small-span simulations for identifying the main flow physics in a non-equilibrium accelerating wall turbulence. The application to the riblet flow shows that riblets do not fundamentally affect the flow dynamics, but delay the retransition as a result of significantly milder streak meandering. The streak-stabilisation effect of riblets is still active in a strongly accelerating turbulence and tends to prolong the flow recovery. [ABSTRACT FROM AUTHOR]

An experimental investigation of near-wall scale interactions in the presence of a deterministic forcing input is presented in this work. The external forcing input was generated by a wall-mounted piezoelectric (PZT) actuator, which directly introduces a dynamic perturbation into the near-wall cycle of turbulent boundary layer flow. The spectra of velocity fluctuations indicated that the fundamental forcing mode can be observed in all the perturbed cases and that the occurrence of high-order harmonics is dependent on the PZT perturbation amplitude. Under the strong forcing input, the fundamental forcing mode is influenced by large-scale structures through a high-degree amplitude modulation (AM) effect. More importantly, the phase-switching process was found for the high-order harmonics and small-scale turbulence, both of which are in phase with the forcing mode in y + ∼ x < 10 and are switched to be out of phase in 20 ∼ x < y + ∼ x < 50. It was demonstrated that the forcing mode rearranges both the harmonics and small-scale turbulence in the near-wall region, as evidenced by the AM effect and phase relationship. In addition, the near-wall scale rearrangements were confirmed by the skewness cross-term distribution. [ABSTRACT FROM AUTHOR]

Aero-optical reduction in flat-plate turbulent boundary layer has been widely concerned due to critical application for high-speed target-seeking vehicles. From the perspective of disciplinary intersection between aerodynamic and optical engineering, the turbulence-aberrated optical behaviour, in high-Reynolds-number supersonic freestream, is numerically investigated using the in-house code High-Order SimulaTor for Aerodynamics (HOSTA) and ray-tracing scheme. To evaluate the efficiency of wall cooling strategy to reduce the detrimental aero-optical distortions, the authors leverage the theoretical equation deduced from Sutton statistic model for mutual verification with the simulative results. Additionally, based on the beneficial wall cooling effects on turbulent aero-optical reduction, comparison suggests that refrigeration directly towards the turbulence section is the most effective rather than cooling the laminar or transitional region. In further discussion, wall blowing, suction and combinational blowing and suction schemes are issued. Results reveal the rationality of employing proper suction amplitude to modify the flow into laminar state, and sufficiently high suction intensity is also promising in turbulent aero-optical reduction despite the fact of low efficiency currently. The current study puts an eye on the simulation concerning three-dimensional supersonic turbulent flow in high-Reynolds-number freestream and the application of statistic model, and future investigation is suggested for higher effectiveness of aero-optical suppression. [ABSTRACT FROM AUTHOR]

Motivated by the needs of wall modelled Large Eddy Simulation (LES), we introduce fits to numerical solutions of the Reynolds Averaged Navier–Stokes equations in their simplest near-wall, boundary layer approximation including a mixing-length model. We formulate the problem such that independent dimensionless variables are those directly available in LES. We provide practical fits for the dependent variable, fits that encompass a smooth transition between the viscous sublayer and inertial logarithmic layer, and then progress first considering moderate pressure gradients as well as roughness effects under the assumption that the mixing-length is not affected by the pressure gradient. An alternative fit based on the empirical wall model of Nickels (Inner scaling for wall-bounded flows subject to large pressure gradients. J Fluid Mech. 2004;521:217–239) is also provided, taking into account possible effects of pressure gradient on turbulence near-wall structure. We then consider the case of general pressure gradients, both favourable and adverse, up to conditions of separation, for both smooth and rough surfaces. The proposed fitting functions constitute a generalised Moody chart, comply with analytical solutions valid in various asymptotic regimes, and obviate the need for numerical iterative solution methods or near-wall numerical integration of ordinary differential equations during LES. [ABSTRACT FROM AUTHOR]

The effect of wall expansion on the structural and statistical characteristics of wall-shear stress (WSS) fluctuations was investigated by direct numerical simulations of a supersonic turbulent boundary layer over a sharp expansion corner with various deflection angles (β = 00, 20, 50 and 100). It is found that the two-dimensional fields of WSS are characterised as streamwise-elongated streaky structures being aligned in the spanwise direction, resembling low- and high-speed streaks in the buffer region of the flow. Due to the relaminarization effect, these WSS steaks experience a sudden weakening shortly after the expansion corner, but present gradual regrowth with their length scales even exceeding those of the flat-plate case in the far downstream. A strong streamwise-alignment of the instantaneous WSS vector is evident in the case of the largest deflection angle, suggesting a distinct reduction of the intermittency in the relaminarization process. Furthermore, the characteristic time scale of the spanwise component of WSS is quasi-invariant to the expansion effect, while the peak frequency of the streamwise component increases with the increase of the deflection angle. [ABSTRACT FROM AUTHOR]

Temporally developing direct numerical simulations (T-DNS) are performed for free-stream turbulence induced bypass transition flow over a flat-plate under zero-pressure gradient, and results are validated using experimental data and spatially developing DNS (S-DNS) results. The temporal simulations predict the growth of near-wall Klebanoff modes in the pre-transition regime and their subsequent breakdown due to the sinuous-like instability, where the increase in free-stream turbulence intensity and length scale enhanced the instability. A formulation for the domain translation velocity is developed using the momentum integral boundary layer equation, to estimate the translation of the domain along the plate. The formulation was found to be robust for a range of free-stream turbulence intensities, and both the boundary layer growth and free-stream decay compared well with spatial simulations, confirming that the same translation velocity can be used for the entire domain. The optimal domain size for a temporal simulation is dictated by the length scale of the turbulent spots and errors due to streamwise periodicity, and is estimated to be ∼ 8 to 10 δ onset , where δ onset is the boundary layer thickness at the transition onset. The T-DNS prediction of the integral boundary layer parameters, mean flow, second and higher-order statistics, stress budgets, and free-stream decay were comparable to those of S-DNS, even though they were obtained on ten times smaller streamwise domain and numerical grid. However, T-DNS are limited for bypass transtion flows for which leading-edge effects are unimportant, and may have limitations for the accurate predictions of the near-wall Klebanoff modes that extend up to breakdown. Nonetheless, temporal approach is identified to be a viable inexpensive alternative to the spatial approach for canonical test cases for transition flow physics analysis. [ABSTRACT FROM AUTHOR]

Uniform blowing in wall bounded shear flows is well known for its drag reducing effects and has long been investigated ever since. However, many contemporary and former research on this topic has confirmed the drag reducing effect but very less is known regarding how blowing is effecting the Reynolds stresses at high Reynolds number. Therefore, effect of uniform blowing has been experimentally investigated using Stereo Particle Image Velocimetry (SPIV) measurements in a zero pressure gradient turbulent boundary layer (TBL). The data presented in this literature covers a large range of high Reynolds number flow e.g. Reθ = 7500∼19763 where Reynolds number is based on the momentum thickness. Upstream blowing was varied from 1%∼6% of free stream velocity and measurements were taken downstream after a short interval. Logarithmic and outer region of the TBL was given special attention in terms of investigating statistics and turbulence properties. [ABSTRACT FROM AUTHOR]

Transpired boundary layers are of major interest for many industrial applications. Although well described, there is no turbulence model specifically dedicated to the prediction of boundary layers for both blowing and suction configurations. Revisiting closure relations of turbulence models, a general strategy was established to recover Stevenson's law of the wall that described the behaviour of transpired boundary layers in the wall region. The methodology is applied to the k − ω SST turbulence model and compared to Wilcox's correction, only applicable to blowing cases. A version of the proposed correction, more suited to RANS solvers, was also derived. Several experimental boundary layer configurations with blowing or suction were computed using both versions of the correction. The good agreements observed on all cases prove the relevance and the efficiency of the present strategy. Abbreviations:l: mixing length; u: longitudinal velocity component; v: wall-normalvelocity component; u ′ : longitudinal velocity fluctuation; v ′ : wall-normal velocityfluctuation; x: longitudinal direction; y: wall-normal direction; k: turbulent kineticenergy; ω: specific dissipation; δ 1 : displacement thickness; τ: shear stress; ρ: density; ν: kinematic viscosity; ν t : eddy viscosity; μ: dynamic viscosity; κ: Kàrmàn constant; + :superscript for dimensionless wall quantities; w : subscript for quantities at the wall; ⟨ ⟩ :Reynolds average [ABSTRACT FROM AUTHOR]

Spalart-Allmaras (SA) model is a low Reynolds number (Re) model, which means that the first off-wall grid point should be placed in the viscous sub-layer with y + ≃ 1. This restriction of placing the first off-wall grid point so close to the wall leads to an increase in the mesh size, and thus the computation. The wall function approach is an alternative to this problem. The standard wall function method usually employed has a limitation for cases that involve high adverse pressure gradient and compressibility. This limits its use to the non-separated flows only. The present work focuses on the formulation of the generalised wall function given by Shih et al. [A generalized wall function; 1999] and applies it to the SA turbulence model, with some modification. The proposed modification was found to remove the oscillation and inaccuracy found in the result when directly using the Shih et al. model. Several flows, with zero pressure gradient to those with adverse pressure gradient leading to flow separation, are solved with the proposed wall treatment, with relatively coarse grids involving y + beyond 50 and up to 100 for certain cases. It is concluded that the results in each case are close to those obtained by the low-Re SA model, despite the use of much coarser meshes. [ABSTRACT FROM AUTHOR]

Adverse-pressure-gradient turbulent boundary layer flow was inspected at Reynolds number based on momentum thickness, R e θ ≈ 1200 , using particle image velocimetry in a refractive-index-matching flume. Proper orthogonal decomposition was used to quantify the effect of large-scale motions on the Reynolds stresses at the onset of separation and within the separated flow. Results show that approximately 90 % of the Reynolds shear stress, u v ¯ , is due to large-scale motions containing 65 % of the turbulence kinetic energy at the tested Reynolds number. The decomposed velocity field revealed that only the first ∼ 10 % of the modes is sufficient to recover 65 % of the turbulence kinetic energy. In this partition, the large-scale motion contribution to the streamwise component of the Reynolds normal stress, u 2 ¯ , is about 70 % and continues to grow with flow separation. In addition, the large- and small-scale motions equally contributed to the vertical component of the Reynolds normal stress, v 2 ¯ , and the contribution of the large-scale motions increased as the flow separated. Overall, results emphasise the significant impact of the large-scale motions on the Reynolds stresses in the separated flow, which may impact flow control strategies. [ABSTRACT FROM AUTHOR]

The incompressible temporally developing turbulent boundary layer (TBL) is analysed using the map-based stochastic one-dimensional turbulence (ODT) model. The TBL is a canonical flow problem, which is, in the present study, formed by a planar moving wall and a free stream at rest. An understanding of this idealised flow is of fundamental relevance for the numerical analysis of turbulent boundary-layer-type flows. In the present ODT simulations, the flow variables are resolved on all scales along a wall-normal, one-dimensional domain. These variables are evolved by a deterministic and a stochastic process. The latter models the effect of turbulent advection and pressure fluctuations, whereas the former represents molecular diffusion. The model is appropriate for high Reynolds numbers for which the turbulence field exhibits a broad range of scales and is notionally featureless. We show that ODT is able to capture salient features of the TBL by comparing the various statistics with available reference direct numerical simulation (DNS) results for different bulk Reynolds numbers in the range 250 ≤ R e b ≤ 2000 using fixed model parameters. The influence of the model parameters is analysed for R e b = 1000 and optimal parameter values are provided. The results discussed in this paper suggest that ODT is an economical and reasonably accurate approach for the simulation of transient turbulent boundary-layer-type flows. [ABSTRACT FROM AUTHOR]

The structural attributes of turbulent flow over a complex roughness topography are explored using high-frame-rate stereo particle-image velocimetry measurements in the wall-normal-spanwise plane. The roughness under consideration was replicated from a turbine blade damaged by deposition of foreign materials and contains a broad range of topographical scales arranged in a highly irregular manner. Previous results from Barros and Christensen [Observations of turbulent secondary flows in a rough-wall boundary layer. J Fluid Mech. 2014;748] revealed strong spanwise heterogeneity in the flow attributed to the formation of roughness-induced turbulent secondary flows identified by spanwise-alternating low- and high-momentum flow pathways (HMP & LMP, respectively) in the mean flow marked by enhanced Reynolds stresses and turbulent kinetic energy. Frequency spectra of streamwise velocity at fixed wall-normal location presented herein also display strong dependence on spanwise position. In particular, the roughness promotes enhanced energy content of the large-scale and smaller-scale motions (as opposed to very-large-scale ones). Depending on spanwise position, pre-multiplied spectra highlight significant modification of the energy content of the very large-scale motions (superstructures) due to roughness compared to smooth-wall flow. Of note, a shift in both TKE and RSS content to shorter streamwise scales at an LMP was noted, while less of an impact was found coincident with an HMP. [ABSTRACT FROM AUTHOR]

Understanding of the structure of turbulent flows at extreme Reynolds numbers (Re) is relevant because of several reasons: almost all turbulence theories are only valid in the high Re limit, and most turbulent flows of practical relevance are characterized by very high Re. Specific questions about wall-bounded turbulent flows at extreme Re concern the asymptotic laws of the mean velocity and turbulence statistics, their universality, the convergence of statistics towards their asymptotic profiles, and the overall physical flow organization. In extension of recent studies focusing on the mean flow at moderate and relatively high Re, the latter questions are addressed with respect to three canonical wall-bounded flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Main results reported here are the asymptotic logarithmic law for the mean velocity and corresponding scale-separation laws for bulk flow properties, the Reynolds shear stress, the turbulence production and turbulent viscosity. A scaling analysis indicates that the establishment of a self-similar turbulence state is the condition for the development of a strict logarithmic velocity profile. The resulting overall physical flow structure at extreme Re is discussed. [ABSTRACT FROM AUTHOR]

The universality and mathematical physical structure of wall-bounded turbulent flows is a topic of discussions over many decades. There is no agreement about questions like what is the physical mean flow structure, how universal is it, and how universal are theoretical concepts for local and global flow variations. These questions are addressed by using latest direct numerical simulation (DNS) data at moderate Reynolds numbers Re and experimental data up to extreme Re. The mean flow structure is explained by analytical models for three canonical wall-bounded turbulent flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Thorough comparisons with DNS and experimental data provide support for the validity of models. Criteria for veritable physics derived from observations are suggested. It is shown that the models presented satisfy these criteria. A probabilistic interpretation of the mean flow structure shows that the physical constraints of equal entropies and equally likely mean velocity values in a region unaffected by boundary effects impose a universal log-law structure. The structure of wall-bounded turbulent flows is much more universal than previously expected. There is no discrepancy between local logarithmic velocity variations and global friction law and bulk velocity variations. Flow effects are limited to the minimum: the difference of having a bounded or unbounded domain, and the variation range of mean velocity values allowed by the geometry. [ABSTRACT FROM AUTHOR]

In this paper, hot-wire anemometry (HWA) is used to experimentally investigate interactions between a fully developed turbulent boundary layer and wake of an elliptic cylinder where axis ratio (AR) of the cylinder is 2. The elliptic cylinder was located inside and outside a turbulent boundary layer with a thickness (δ) of 0.38B. Furthermore, experiments were conducted at different Reynolds numbers (13,250 and 26,500) based upon the smallest cylinder diameter (B). Mean velocity, turbulence intensity and higher-order central moments of velocity signals (i.e. skewness and flatness) measurements were performed using HWA upon wake-boundary layer interactions on a flat plate. Results showed that profiles of stream-wise mean velocity and turbulence intensity were greatly dependent on gap ratio (G/B) and Reynolds number (Re) in near-wake region. It was also observed that, except for G/B = 0.1, the wake-boundary layer interactions were faster at Reynolds number of 26,500 rather than 13,250. The interactions occurred earlier upon fluctuating the velocity rather than the case where a fixed mean velocity was considered. The results further show that an increase in the gap ratio increases Strouhal number almost independent of δ/B. Behind the cylinder, relatively smaller wake region was obtained at Re = 26,500 rather than Re = 13,250, where the velocity profiles quickly converged to the flat plate boundary layer velocity profiles. [ABSTRACT FROM AUTHOR]

The phase-relationship between large-scale motions and small-scale fluctuations in a non-equilibrium turbulent boundary layer was investigated. A zero-pressure-gradient flat plate turbulent boundary layer was perturbed by a short array of two-dimensional roughness elements, both statically, and under dynamic actuation. Within the compound, dynamic perturbation, the forcing generated a synthetic very-large-scale motion (VLSM) within the flow. The flow was decomposed by phase-locking the flow measurements to the roughness forcing, and the phase-relationship between the synthetic VLSM and remaining fluctuating scales was explored by correlation techniques. The general relationship between large- and small-scale motions in the perturbed flow, without phase-locking, was also examined. The synthetic large scale cohered with smaller scales in the flow via a phase-relationship that is similar to that of natural large scales in an unperturbed flow, but with a much stronger organizing effect. Cospectral techniques were employed to describe the physical implications of the perturbation on the relative orientation of large- and small-scale structures in the flow. The correlation and cospectral techniques provide tools for designing more efficient control strategies that can indirectly control small-scale motions via the large scales. [ABSTRACT FROM AUTHOR]

An analysis is presented describing the characteristics of mean velocity profile in the axisymmetric turbulent inner near-wake flow behind a body of revolution. The near wake is developing under zero streamwise pressure gradient and the upstream turbulent boundary layer is fully developed. It is shown that the boundary layer condition that exists at the trailing edge can be used to describe the mean velocity profiles in the inner near wake. It is shown that the logarithmic layer of the upstream turbulent boundary layer continues to be valid for some more distance in the near wake, and as the streamwise distance is increased, the logarithmic layer is slowly getting destroyed. It is also shown that the central line velocity exhibits a logarithmic behaviour for large streamwise distance. Results of the analysis have been validated using available experimental data. [ABSTRACT FROM AUTHOR]

A supersonic turbulent boundary layer over a compression ramp is numerically investigated using the constrained large-eddy simulation (CLES) method. The compression corner is characterised by a deflection angle of 24°. The free-stream Mach number isMa∞= 2.9, and the Reynolds number based on the momentum thickness of inlet boundary layer isReθ= 2300. The mean and statistical quantities, such as mean velocity, wall pressure and Reynolds stresses, are thoroughly analysed and compared with those from traditional large-eddy simulation (LES), experimental measurement and direct numerical simulation (DNS). It turns out that CLES can predict the friction coefficient, wall-pressure distribution, size of separation bubble, Reynolds stresses, etc. more accurately than traditional LES, and the results are in reasonable agreement with the experimental and/or DNS data. Also discussed are the effects of specific parameterisations of the Reynolds constraint and interfacial positions separating the constrained and unconstrained regions on the performance of the CLES method. [ABSTRACT FROM AUTHOR]

Direct numerical simulations of shock wave and supersonic turbulent boundary layer interaction in a 24° compression ramp with adiabatic and cold-wall temperatures are conducted. The wall temperature effects on turbulence structures and shock motions are investigated. The results are validated against previous experimental and numerical data. The effects of wall cooling on boundary layer characteristics are analysed. Statistical data show that wall cooling has a significant effect on the logarithmic region of mean velocity profile downstream the interaction region. Moreover, the influence of wall temperature on Reynolds stress anisotropy is mainly limited in the near-wall region and has little change on the outer layer. As the wall temperature decreases, the streamwise coherency of streaks increases. Based on the analysis of instantaneous Lamb vector divergence, the momentum transport between small-scale vortices on cold-wall condition is significantly enhanced. In addition, spectral analysis of wall pressure signals indicates that the location of peak of low-frequency energy shifts toward higher frequencies in cold case. Furthermore, the dynamic mode decomposition results reveal two characteristic modes, namely a low-frequency mode exhibiting the breathing motion of separation bubble and a high-frequency mode associated with the propagation of instability waves above separation bubble. The shape of dynamic modes is not sensitive to wall temperature. [ABSTRACT FROM PUBLISHER]

We conduct a series of large eddy simulations (LES) of turbulent boundary layers over arrays of cuboidal roughness elements at arbitrary orientation angles (non-frontal orientations with the incident flow). Flow response to changing roughness orientation is systematically studied at two ground coverage densities, λp= 0.06 and 0.11. As expected, the effective roughness heightszomeasured from LES are higher for λp= 0.11 than for λp= 0.06, although appreciable changes both inzoand wall shear stress (friction velocity) are observed at both ground coverage densities as the roughness orientation angle changes. This suggests the necessity of accounting for detailed rough wall topology (including more information than just λp, λf) when relating rough wall morphology to its aerodynamic properties. To this end, a recently developed analytical rough wall parameterisation is used to predict the aerodynamic properties of the simulated rough surfaces. In this rough wall model, wake interactions among roughness elements are explicitly modelled using the concept of sheltering height and exponential attenuation coefficient. As a result, the parameterisation is responsive to detailed ground roughness arrangements and flow conditions, including roughness height variations, element orientation, incident flow direction, transverse displacements, etc. Model-predicted effective roughness heights, wall stress, mean velocity at the height of the roughness, and in some cases displacement height, are compared against the LES measurements from this study as well as numerical/experiment measurements from other authors. The predictions from the model are found to agree well with the measurements both in trends and in absolute values, thus extending the applicability of the analytical rough wall model to more general surfaces than those previously tested. [ABSTRACT FROM PUBLISHER]

A series of large-eddy simulations of spatially developing turbulent boundary layers with uniform blowing at moderate Reynolds numbers (based on free-stream velocity,U∞, and momentum thickness, θ) up toReθ≈ 2500 were performed with the special focus on the effect of intermittent (separated in streamwise direction) blowing sections. The number of blowing sections,N, investigated is set to be 3, 6, 20, 30 and compared toN= 1, which constitutes the reference case, while the total wall-mass flux is constrained to be the same for all considered cases, corresponding to a blowing amplitude of 0.1% ofU∞for the reference case. Results indicate that the reference case provides a net-energy saving rate of around 18%, which initially decreases at most 2% points forN= 3 but recovers with increasingN, where the initial reduction of the drag reduction is found to be related to the shorter streamwise length of the intermittent blowing sections. The physical decomposition of the skin friction drag through the Fukagata-Iwamoto-Kasagi (FIK) identity shows that the distribution of all components over each blowing section has similar trends, resulting in similar averaged values over the whole control region. [ABSTRACT FROM PUBLISHER]

Tensorial decompositions and projections are used to study the performance of algebraic non-linear models and predict the anisotropy of the Reynolds stresses. Direct numerical simulation (DNS) data for plane channel flows at friction Reynolds number (Reτ= 180, 395, 590, 1000), and for the boundary layer using both DNS (Reτ= 359, 830, 1271) and experimental data (Reτ= 2680, 3891, 4941, 7164) are used to build and evaluate the models. These data are projected into tensorial basis formed from the symmetric part of mean velocity gradient and non-persistence-of-straining tensor. Six models are proposed and their performances are investigated. The scalar coefficients for these six different levels of approximations of the Reynolds stress tensor are derived, and made dimensionless using the classical turbulent scales, the kinetic turbulent energy (κ) and its dissipation rate (ε). The dimensionless coefficients are then coupled with classical wall functions. One model is selected by comparing the predicted Reynolds stress components with experimental and DNS data, presenting a good prediction for the shear and normal Reynolds stresses. [ABSTRACT FROM PUBLISHER]

Vortex identification techniques are used to analyse the wake of a 4 × 3 array of model wind turbines. The Q-criterion, Δ-criterion, and λ2-criterion are applied to particle image velocimetry data gathered fore and aft of the last row centerline turbine. The Q-criterion and λ2-criterion provide a clear indication of regions where vortical activity exists, while the Δ-criterion is not successful. Galilean decomposition, Reynolds decomposition, vorticity, and swirling strength are used to further understand the location and behaviour of the vortices. The techniques identify and display the high-magnitude vortices in high-shear zones resulting from the blade tips. Using Galilean and Reynolds decomposition, swirling motions are shown encapsuling vortex regions in agreement with the identification criteria. The Galilean decompositions selected are 20% and 50% of a convective velocity of 7 m/s. As the vortices convect downstream, the strength of the vortices decreases in magnitude, particularly in the far wake of the array, to approximately 25% of those present in the near wake. A high level of vortex activity is visualised as a result of the top tip of the wind turbine blade -- the location where the highest vertical entrainment is present. Analysing the full frame set, the Q-criterion, λ2-criterion, and swirling strength prove comparable, while the Δ-criterion under-performs in regions of high turbulence activity, namely in the back of the turbine. Entraining flow into the turbine canopy interacting with the turbine generates high-magnitude vortices concentrated at the blade tips. The count of vortices decreases when moving from the top tip down to the wall, as well as their strength for each Galilean technique when a non-zero threshold is applied. Vortex sizes in the near wake are found comparable to turbine blade, hub, and mast dimensions. In the far wake, the resulting size of the vortices is approximately 30% of those in the near wake. These vortices increase in velocity as they convect downstream, following the mean velocity behaviour. The lowest magnitude vortices reside at the hub height in the near-wake region, where they convect at nearly half the speed of those at the blade tips. [ABSTRACT FROM PUBLISHER]

A series of large-eddy simulations of a turbulent asymptotic suction boundary layer (TASBL) was performed in a periodic domain, on which uniform suction was applied over a flat plate. Three Reynolds numbers (defined as ratio of free-stream and suction velocity) ofRe= 333, 400 and 500 and a variety of domain sizes were considered in temporal simulations in order to investigate the turbulence statistics, the importance of the computational domain size, the arising flow structures as well as temporal development length required to achieve the asymptotic state. The effect of these two important parameters was assessed in terms of their influence on integral quantities, mean velocity, Reynolds stresses, higher order statistics, amplitude modulation and spectral maps. While the near-wall region up to the buffer region appears to scale irrespective ofReand domain size, the parameters of the logarithmic law (i.e. von Kármán and additive coefficient) decrease with increasingRe, while the wake strength decreases with increasing spanwise domain size and vanishes entirely once the spanwise domain size exceeds approximately two boundary-layer thicknesses irrespective ofRe. The wake strength also reduces with increasing simulation time. The asymptotic state of the TASBL is characterised by surprisingly large friction Reynolds numbers and inherits features of wall turbulence at numerically highRe. Compared to a turbulent boundary layer (TBL) or a channel flow without suction, the components of the Reynolds-stress tensor are overall reduced, but exhibit a logarithmic increase with decreasing suction rates, i.e. increasingRe. At the same time, the anisotropy is increased compared to canonical wall-bounded flows without suction. The reduced amplitudes in turbulence quantities are discussed in light of the amplitude modulation due to the weakened larger outer structures. The inner peak in the spectral maps is shifted to higher wavelength and the strength of the outer peak is much less than for TBLs. An additional spatial simulation was performed, in order to relate the simulation results to wind tunnel experiments, which – in accordance with the results from the temporal simulation – indicate that a truly TASBL is practically impossible to realise in a wind tunnel. Our unique data set agrees qualitatively with existing literature results for both numerical and experimental studies, and at the same time sheds light on the fact why the asymptotic state could not be established in a wind tunnel experiment, viz. because experimental studies resemble our simulation results from too small simulation boxes or insufficient development times. [ABSTRACT FROM PUBLISHER]

This study assesses the hypothesis of incomplete similarity for a plane turbulent wall jet on smooth and transitionally rough surfaces. Typically, a wall jet is considered to consist of two regions: an inner layer and an outer layer. The degree to which these two regions reach equilibrium with each other and interact to produce the property of self-similarity remains an open question. In this study, the analysis of the outer and inner regions indicates that each region is characterised by a half-width which exhibits its own distinct dependence on the streamwise distancexfrom the slot, and a single self-similar structure for both regions does not exist. More specifically, the inner and outer layers of the wall jet exhibit different scaling laws, which results in two self-similar mean velocity profiles, both of which retain a dependence on the slot heightH. As such, incomplete similarity of the wall jet on smooth and transitionally rough surfaces is confirmed by this study. In addition, comparison of the experimental results for the transitionally rough surface with the smooth wall case indicates that the surface roughness modifies the development of the mean velocity profile in both the inner and outer regions, although the effect on the outer region is relatively small and close to the experimental uncertainty. [ABSTRACT FROM AUTHOR]

We present numerical studies of active flow control applied to jet flow. We focus on rectangular jets, which are more unstable than their circular counterparts. The higher level of instability is expressed mainly by an increased intensity of mixing of the main flow with its surroundings. We analyse jets with aspect ratioAr= 1,Ar= 2 andAr= 3 at Re = 10,000. It is shown that the application of control with a suitable excitation (forcing) at the jet nozzle can amplify the mixing and qualitatively alter the character of the flow. This can result in an increased spreading rate of the jet or even splitting into nearly separate streams. The excitations studied are obtained from a superposition of axial and flapping forcing terms. We consider the effect of varying parameters such as the frequency of the excitations and phase shift between forcing components. The amplitude of the forcing is 10% of the inlet centreline jet velocity and the forcing frequencies correspond to Strouhal numbers in a range St = 0.3–0.7. It is shown that qualitatively different flow regimes and a rich variety of possible flow behaviours can be achieved simply by changing aspect ratio and forcing parameters. The numerical results are obtained applying large eddy simulation in combination with a high-order compact difference code for incompressible flows. The solutions are validated based on experimental data from literature for non-excited jets forAr= 1 at Re = 1.84 × 105andAr= 2 at Re = 1.28 × 105. Both the mean velocities as well as their fluctuations are predicted with good accuracy. [ABSTRACT FROM AUTHOR]

Stochastic and deterministic subgrid parameterisations are developed for the large eddy simulation (LES) of a turbulent channel flow with friction-velocity-based Reynolds number ofReτ= 950 and centreline-based Reynolds number ofRe0= 20,580. The subgrid model coefficients (eddy viscosities) are determined from the statistics of truncated reference direct numerical simulations (DNSs). The stochastic subgrid model consists of a mean-field shift, a drain eddy viscosity acting on the resolved field and a stochastic backscatter force of variance proportional to the backscatter eddy viscosity. The deterministic variant consists of a net eddy viscosity acting on the resolved field, which represents the net effect of the drain and backscatter. LES adopting the stochastic and deterministic models is shown to reproduce the time-averaged kinetic energy spectra of the DNS within the resolved scales. [ABSTRACT FROM AUTHOR]

This study investigates the changes in the structure of a turbulent boundary layer downstream of a flow-excited Helmholtz resonator. To this end, a fully developed turbulent boundary layer over a resonator mounted flush with a flat plate was simulated by implementing a large eddy simulation (LES). To assist in understanding the effect of the resonator on the flow structure, a sensitivity study was undertaken by changing the main geometrical parameters of the resonator. The results demonstrated that when the boundary layer thickness equals the orifice length, the cross-stream component of velocity fluctuations penetrates the boundary layer, resulting in a reduction of the turbulence intensity by up to 12%. Therefore, it is concluded that a Helmholtz resonator has the potential to reduce the instabilities within the boundary layer. These investigations also assist in identifying the optimal parameters to delay turbulence events within the grazing flow using Helmholtz resonators. [ABSTRACT FROM AUTHOR]

Three-dimensional large-eddy simulations (LES) of the convective boundary layer over a domain of approximately 6 km are performed with the UCLA LES model. Simulations are forced with a constant surface heat flux and prescribed subsidence, and are run to equilibrium. Sub-grid scale fluxes are parameterised with the Smagorinsky–Lilly scheme. A range of grid spacings from 40 down to 5 m are employed. Kinetic energy spectra and the various terms in the kinetic energy spectral budget – heat flux, nonlinear transfer, pressure, and dissipation – are computed using two-dimensional discrete Fourier transforms at every vertical level. Despite the fact that isotropic grid spacings of down to 5 m (grid sizes of 11522×400) were used, an inertial range with a −5/3 spectrum is not obtained. Rather, shallower energy spectral slopes that are closer to −4/3 are found. The shallower spectra are shown to possibly result from the injection of kinetic energy over a wide range of scales via a very broad heat flux spectrum. Only with the highest resolution (Δx= 5 m) does the total heat flux begin to converge and the possibility of local isotropy emerge at small scales. Dependence on surface heat flux and domain size is considered. Preliminary sub-grid scale sensitivity results are obtained through comparison with the turbulent kinetic energy sub-grid scale model. [ABSTRACT FROM PUBLISHER]

We present an experimental investigation and data analysis of a turbulent boundary layer flow at a significant adverse pressure gradient at Reynolds number up toReθ= 10, 000. We combine large-scale particle image velocimetry (PIV) with microscopic PIV for measuring the near wall region including the viscous sublayer. We investigate scaling laws for the mean velocity and for the total shear stress in the inner part of the boundary layer. In the inner part the mean velocity can be fitted by a log-law. In the outer part of the inner layer the log-law ceases to be valid. Instead, a modified log-law provides a good fit, which is given in terms of the pressure gradient parameter and a parameter for the mean inertial effects. Finally we describe and assess a simple quantitative model for the total shear stress distribution which is local in wall-normal direction without streamwise history effects. [ABSTRACT FROM AUTHOR]

Two-point correlations of the wall fluctuating pressure and turbulent pressure and velocities in the flow field are computed in three dimensions using direct numerical simulation (DNS) databases. The mean pressure gradient in the flow has strong influence on these correlations. The DNS () in a converging/diverging channel with streamwise curvature near the lower wall is used to compute the statistics. The correlations in favourable pressure gradient and adverse pressure gradient are compared with the correlation in flat channel flow DNS (). The results show that these pressure–pressure and pressure–velocity correlations are not only sensitive to the local pressure gradient and wall curvature, but also to the pressure gradient history. [ABSTRACT FROM PUBLISHER]

Turbulent boundary layers at Mach 4.9 with the ratio of wall temperature to recovery temperature from 0.5 to 1.5 are investigated by means of direct numerical simulation. Various fundamental properties relevant to the influence of wall temperature on Morkovin’s scaling, standard and modified strong Reynolds analogies, and coherent vortical structures have been studied. It is identified that the scaling relations proposed for cool and adiabatic wall conditions, such as Morkovin’s scaling and the modified strong Reynolds analogy, are also applicable for hot wall condition. Moreover, the relation between the density and temperature fluctuations under the second-order approximation is derived and verified to provide a reliable prediction. Based on the analysis of coherent vortical structures, it is found that the orientation of vortex core can be quantitatively determined by means of the vector with its direction and modulus using the local strain direction and the imaginary part of the eigenvalue of velocity gradient tensor, respectively. As the increase of wall temperature, the spanwise distance between the two legs of hairpin vortex increases, and the mean swirling strength and the angle of vortical structure with respect to the wall plane also increase in the inner layer. The statistical properties relevant to vortical structures are nearly insensitive to the wall temperature in the outer layer. [ABSTRACT FROM PUBLISHER]

The objective of the present work is to analyse the behaviour of a turbulent decelerating boundary layer under the effect of both passive and active jets vortex generators (VGs). The stereo PIV database of Godard and Stanislas [1,2] obtained in an adverse pressure gradient boundary layer is used for this study. After presenting the effect on the mean velocity field and the turbulent kinetic energy, the line of analysis is extended with two points spatial correlations and vortex detection in instantaneous velocity fields. It is shown that the actuators concentrate the boundary layer turbulence in the region of upward motion of the flow, and segregate the near-wall streamwise vortices of the boundary layer based on their vorticity sign. [ABSTRACT FROM AUTHOR]