Region Of Turbulent Boundary Layer Research Articles

Consistent outer scaling and analysis of adverse pressure gradient turbulent boundary layers

Under adverse pressure gradient (APG) conditions, the outer regions of turbulent boundary layers (TBLs) are characterized by an increased velocity defect $U_{e}-U$ , an outwards shift of the peak value of the Reynolds shear stress $-\langle uv\rangle$ and an appearance of the outer peak value of the Reynolds normal stress $\langle uu\rangle$ . Here $U_{e}$ is the TBL edge velocity. Scaling APG TBLs is challenging due to the non-equilibrium effects caused by changes in the APG. To address this, the response distance of TBLs to non-equilibrium conditions is utilized to extend the Zagarola–Smits scaling $U_{zs} = U_{e}({\delta ^{*} }/{\delta })$ and ensure that the original properties of the Zagarola–Smits scaling are maintained as $Re \to \infty$ . Here $\delta ^{*}$ is the displacement thickness and $\delta$ is the boundary layer thickness. Based on the established correlation between $U_{e}-U$ and $-\langle uv\rangle$ , the scaling is extended to $-\langle uv\rangle$ . Furthermore, considering the coupling relationship between Reynolds stress components, the scaling is extended to encompass each Reynolds stress component. The proposed consistent scaling is verified using five non-equilibrium databases and five near-equilibrium databases, successfully collapsing the data of the TBL outer region. The pressure gradient parameter $\beta =({\delta ^{*} }/{\rho u_{\tau }^{2} }) ({\mathrm {d} P_{e} }/{\mathrm {d}\kern0.7pt x})$ of these databases spans two orders of magnitude. Here $P_{e}$ is the boundary layer edge pressure, $u_{\tau }$ is the friction velocity and $\rho$ is the density. Finally, the influence of the APG on the inner and outer regions of TBLs is analysed using the mean momentum balance equation. The analysis suggests that the shift of the $-\langle uv\rangle$ peak to the outer region under APG conditions is due to an insufficient inertia term near the inner region to balance the APG. It is observed that the APG promotes interaction between the inner and outer regions of TBLs, but the inner and outer regions still retain distinctive properties.

Research on time series prediction of the flow field in supersonic combustor based on deep learning

The detection of supersonic combustion flow field provides valuable reference information for the efficient combustion of hypersonic vehicles. From the perspectives of scramjet operation during flight as well as experiment where the measured information is limited, flow field prediction using deep learning technology is a promising method that can provide future flow field evolution in scramjet combustors. This study proposes a convolutional neural network model of multi-temporal pressure information fusion to predict combustion flow field based on wall pressure. In addition, it analyzes the effect of various wall pressures on the flow field prediction. An experimental dataset of supersonic ground-pulse wind tunnel tests with different injection pressures is built through the combustion chamber wall under self-ignition conditions of a hydrogen-fueled scramjet. The results showed that the predicted flow field of the combustor agrees with the ground test, average correlation coefficient reached more than 90% and when the wall pressure number is 32, the average peak signal to noise ratio reaches about 23. and the main wave structure and turbulent boundary layer region are restored even if there is a shock boundary layer interaction.

An experimental investigation on the isoenergetic supersonic cooling films subjected to different ratios of static pressure

Ratio of static pressure (RSP) is a critical factor affecting the development of supersonic cooling film flow field. To give a good account of flow characteristics and physical mechanisms on the influences of RSPs, experiments are conducted employing the nanoparticle planar laser scattering (NPLS) and particle-image velocimetry (PIV) techniques. A supersonic cooling film is tangentially injected at a Mach number of Maj=2 into a laminar boundary layer at a mainstream Mach number of Ma∞=3 with different RSP cases. The flow field is divided into four sections: the wake region, the potential core region, the wall-jet region, and the fully developed turbulent boundary layer region. The velocity profile extracted at the fully developed turbulent boundary layer region is proved to be consistent with the theoretical composite profile. Moreover, a new criterion that distinguishes the specific position of the impingement point where the mixing layer approaches the bottom boundary layer is proposed based on the distribution of principal strain rate of the mean velocity field. The analysis of turbulent structures finds that the K–H vortex structures are sensitive to RSPs, and more broken vortices generated when the two fluids mix. The intensity of wave structures is depicted in the synthetic schlieren images when subjected to different RSPs. In addition, the turbulent characteristics show a weaker mixing process with increased RSP, indicating a prolonging in the effective cooling length. Furthermore, the disturbance at the slot and variations of velocity gradient downstream are addressed and analyzed to reveal the physical mechanisms for the mixing process on RSP differences.

Outer scaling of the mean momentum equation for turbulent boundary layers under adverse pressure gradient

A new scaling of the mean momentum equation is developed for the outer region of turbulent boundary layers (TBLs) under adverse pressure gradient (APG). The maximum Reynolds shear stress location, denoted as $y_{m}$ , is employed to determine the proper scales for the outer region of an APG TBL. An outer length scale is proposed as $\delta _e - y_{m}$ , where $\delta _e$ is the boundary layer thickness. An outer velocity scale for the mean streamwise velocity deficit is proposed as $U_e - U_{m}$ , where $U_e$ and $U_m$ are the mean streamwise velocities at the boundary layer edge and $y_{m}$ , respectively. An outer velocity scale for the mean wall-normal velocity deficit is proposed as $V_e - V_{m}$ , where $V_e$ and $V_{m}$ are the wall-normal velocities at $\delta _e$ and $y_{m}$ , respectively. The maximum Reynolds shear stress is found to scale as $(\delta _e - y_{m}) U_e \,{\rm d}U_e/{{\rm d}x}$ . The new outer scaling collapses well the experimental and numerical data on APG TBLs over a wide range of Reynolds numbers and strengths of pressure gradient. Approximations of the new scaling are developed for TBLs under strong APG and at high Reynolds numbers. The relationships between the new scales and previously proposed scales are discussed.

An immersed boundary method for wall-modeled large-eddy simulation of turbulent high-Mach-number flows

The excessive computational resource requirements for direct numerical simulation (DNS) and wall-resolved large eddy simulation (LES) make these methods intractable for simulations concerning turbulent flows over complex, real-world geometries. Wall-modeled LES (WMLES) approaches seek to reduce this cost by applying wall-layer models to the inner-most region of turbulent boundary layers. Immersed boundary methods (IBMs) have grown in popularity over the past few decades since the mesh can be automatically generated for any complex geometry - a potentially major advancement for common industrial CFD simulations. However, immersed boundary approaches suffer from reduced numerical accuracy and, possibly, stability at the wall, primarily attributable to irregular discretization of boundary operators. This is a problem that is especially significant for WMLES of high Mach number flows, where numerical schemes have the conflicting requirements to be both stable at high wavenumbers and non-dissipative. This presentation introduces a coupled IBM-WMLES approach that is tailored to the simulation of high-speed turbulent flows. The basis of this method is to carefully address numerical dissipation and stability away from and close to the wall. This is achieved by using a hybrid central-upwind flux reconstruction scheme and careful application of smooth boundary conditions. The presented test cases evaluate the current scheme for a wide range of physical flow phenomena, and include a turbulent channel for basic validation, a hypersonic transitional boundary layer to investigate high-speed zero-pressure-gradient flows, a hypersonic shock wave boundary layer interaction to investigate adverse pressure gradients, separation, and turbulent heating, and a hypersonic compression ramp which is significantly challenging as it combines all of the features from the aforementioned high-speed flow problems.

Large-scale characteristics of a stably stratified turbulent shear layer

Implicit large eddy simulation is performed to investigate large-scale characteristics of a temporally evolving, stably stratified turbulent shear layer arising from the Kelvin–Helmholtz instability. The shear layer at late time has two energy-containing length scales: the scale of the shear layer thickness, which characterizes large-scale motions (LSM) of the shear layer; and the larger streamwise scale of elongated large-scale structures (ELSS), which increases with time. The ELSS forms in the middle of the shear layer when the Richardson number is sufficiently large. The contribution of the ELSS to velocity and density variances becomes relatively important with time although the LSM dominate the momentum and density transport. The ELSS have a highly anisotropic Reynolds stress, to a degree similar to the near-wall region of turbulent boundary layers, while the Reynolds stress of the LSM is as anisotropic as in the outer region. Peaks in the spectral energy density associated with the ELSS emerge because of the slow decay of turbulence at very large scales. A forward interscale energy transfer from large to small scales occurs even at a small buoyancy Reynolds number. However, an inverse transfer also occurs for the energy of spanwise velocity. Negative production of streamwise velocity and density spectra, i.e. counter-gradient transport of momentum and density, is found at small scales. These behaviours are consistent with channel flows, indicating similar flow dynamics in the stratified shear layer and wall-bounded shear flows. The structure function exhibits a logarithmic law at large scales, implying a $k^{-1}$ scaling of energy spectra.

Wavelet-based adaptive wall-modeled large eddy simulation method for compressible turbulent flows

We develop a wavelet-based adaptive wall-modeled large eddy simulation (WA-WMLES) method to overcome the stringent restriction on step size for time integration, caused by mesh resolution requirement to resolve inner viscous sublayer, which becomes computationally expensive as the Reynolds number increases. This approach uses a wavelet-based adaptive large eddy simulation, incorporated into the anisotropic-adaptive wavelet collocation framework, to resolve the outer region of turbulent boundary layer, while the inner part is approximated by the wall-shear-stress model, and extends the application of the wavelet-based adaptive methods to a realistic wall-bounded turbulent flow configuration at a relatively high (order of a million) Reynolds number.

Ratio-cut background removal method and its application in near-wall PTV measurement of a turbulent boundary layer

Optical contamination due to wall reflection creates limitations for near-wall velocity field measurement via either particle image velocimetry (PIV) or particle tracking velocimetry (PTV). In this paper, a simple image pre-processing method, i.e. the ratio cut method, is proposed to deal with this problem. It is based on the ratio between the grayscale intensities of tracer particles and those of the laser-illuminated background, on which a direct minimum cut is applied on the basis of a non-dimensional threshold for background removal. To evaluate its performance in near-wall measurement, this ratio cut method, along with two other typical pre-processing methods, i.e. the minimum removal method and the proper orthogonal decomposition (POD) filtering method, are applied to particle images in the near-wall region of turbulent boundary layers over an opaque roughness wall (ORW), whose characteristic roughness height is small enough to be regarded as hydraulically smooth, but still gives rise to severe wall reflection. Results for a case involving a transparent smooth wall, which suffers less from wall reflection issues, and direct numerical simulation (DNS) data at a similar Reynolds number are employed as reference baselines for performance evaluation. The examination of pre-processed particle images, as well as the probability density function (PDF) of grayscale intensities, indicates that the ratio cut method is capable of eliminating time-dependent flare, reducing noise level, and retaining low-intensity particles in the ORW case. These features are almost completely absent in both the minimum removal method and the POD filtering method. In addition, PTV-obtained velocity statistics for an ORW, pre-processed by the ratio cut method, including data relating to fluctuating intensity and the PDF distribution of fluctuating velocity, are shown to be more consistent with those relating to baseline cases than data obtained by either of the the other two methods used for comparison. Moreover, evidence is also provided regarding the superiority and robustness of this approach, in terms of estimating the mean skin friction from the near-all mean velocity profile.

Spectral-scaling-based extension to the attached eddy model of wall turbulence

Two-dimensional (2-D) spectra of the streamwise velocity component, measured at friction Reynolds numbers ranging from 2400 to 26000, are used to refine a model for the logarithmic region of turbulent boundary layers. Here, we focus on the attached eddy model (AEM). The conventional AEM assumes the boundary layer to be populated with hierarchies of self-similar wall-attached ($Type\,A$) eddies alone. While $Type\,A$ eddies represent the dominant energetic large-scale motions at high Reynolds numbers, the scales that are not represented by such eddies are observed to carry a significant proportion of the total kinetic energy. Therefore, in the present study, we propose an extended AEM that incorporates two additional representative eddies. These eddies, named $Type\,C_A$ and $Type\,SS$, represent the self-similar but wall-incoherent low-Reynolds number features, and the non-self-similar wall-coherent superstructures, respectively. The extended AEM is shown to better predict a greater range of energetic length scales and capture the low- and high-Reynolds number scaling trends in the 2-D spectra of all three velocity components. A discussion on spectral self-similarity and the associated $k^{-1}$ scaling law is also presented.

Experimental study on dominant vortex structures in near-wall region of turbulent boundary layer based on tomographic particle image velocimetry

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.

Characterization of near-wall structures in the log-region of a turbulent boundary layer by means of conditional statistics of tomographic PIV data

The random-in-appearance turbulent flow of boundary layers seem to display packages of organized coherent structures near the wall. The understanding of the generation and interaction of these structures and their contribution to the production and dissipation of turbulence is of great relevance to the modelling and control of wall-bounded flows. The present work is a contribution to the knowledge about organized coherent structures at the logarithmic region of turbulent boundary layers at relatively high Reynolds number. From a six-camera tomo-PIV experiment, conducted in a wind tunnel with a Reynolds number based on the momentum thickness of 8500, conditional statistics were obtained that allowed the characterization of low- and high-speed regions, ejections, sweeps and vortices. The analyses confirmed findings from previous works in the literature regarding ejection and sweep structures as being major contributors to the turbulent production, while vortices are responsible for dissipating this energy in the self-sustaining turbulent process. The vortical structures were found to be close to low-speed regions, being responsible to maintain these regions and to induce ejection and sweep events. The conditional statistics on the coherent structures at the log-region obtained in the present work were in good agreement with the literature, including statistics at the inner and outer regions of the canonical flow of a flat plate boundary layer, which suggest some possible general structure organization.

A library for wall-modelled large-eddy simulation based on OpenFOAM technology

This work presents a feature-rich open-source library for wall-modelled large-eddy simulation (WMLES), which is a turbulence modelling approach that reduces the computational cost of standard (wall-resolved) LES by introducing special treatment of the inner region of turbulent boundary layers (TBLs). The library is based on OpenFOAM and enhances the general-purpose LES solvers provided by this software with state-of-the-art wall modelling capability. The included wall models belong to the class of wall-stress models that account for the under-resolved turbulent structures by predicting and enforcing the correct local value of the wall shear stress. A review of this approach is given, followed by a detailed description of the library, discussing its functionality and extensible design. The included wall-stress models are presented, based on both algebraic and ordinary differential equations. To demonstrate the capabilities of the library, it was used for WMLES of turbulent channel flow and the flow over a backward-facing step (BFS). For each flow, a systematic simulation campaign was performed, in order to find a combination of numerical schemes, grid resolution and wall model type that would yield a good predictive accuracy for both the mean velocity field in the outer layer of the TBLs and the mean wall shear stress. The best result, ≈1% error in the above quantities, was achieved for channel flow using a mildly dissipative second-order accurate scheme for the convective fluxes applied on an isotropic grid with 27000 cells per δ3-cube, where δ is the channel half-height. In the case of flow over a BFS, this combination led to the best agreement with experimental data. An algebraic model based on Spalding’s law of the wall was found to perform well for both flows. On the other hand, the tested more complicated models, which incorporate the pressure gradient in the wall shear stress prediction, led to less accurate results. Program SummaryProgram Title: libWallModelledLESProgram Files doi:http://dx.doi.org/10.17632/m8dnsnp4nd.1Licensing provisions: GPLv3Programming language: C++Nature of problem: Large-eddy simulation (LES) is a scale-resolving turbulence modelling approach providing a high level of predictive accuracy. However, LES of high Reynolds number wall-bounded flows is prohibitively computationally expensive due to the need for resolving the inner region of turbulent boundary layers (TBLs) [1]. This inhibits the application of LES to many industrially relevant flows [2] and prompts for the development of novel modelling techniques that would modify the LES approach in a way that allows it to retain its accuracy (at least away from walls) yet significantly lower its computational cost. Solution method: Wall-modelled LES (WMLES) is an approach that is based on complementing LES with special near-wall modelling that allows to leave the inner layer of TBLs unresolved by the computational grid. Many types of wall models have been proposed [1,3], commonly tested within the framework of in-house research codes. Here, an open-source library implementing several wall models is presented. The library is based on OpenFOAM, which is currently the most widely used general-purpose open-source software for computational fluid dynamics. The developed library can be directly applied to both academic and industrial flow cases, leading to a wider adoption of wall modelling and better understanding of its strengths and limitations.[1] J. Larsson, S. Kawai, J. Bodart, and I. Bermejo-Moreno. Large eddy simulation with modeled wall-stress: recent progress and future directions. Mechanical Engineering Reviews, 3(1):1-23, 2016.[2] J. Slotnick, A. Khodadoust, J. Alonso, D. Darmofal, W. Gropp, E. Lurie, D. Mavriplis. CFD vision 2030 study: A path to revolutionary computational aerosciences, Tech. rep., NASA, 2014.[3] S. T. Bose and G. I. Park. Wall-modeled large-eddy simulation for complex turbulent flows. Annual Review of Fluid Mechanics, 50(1):535–561, 2018.

The modulation of particles on coherent structure of turbulent boundary layer in dilute liquid-solid two-phase flow with PIV

Liquid-solidtwo-phase wall turbulent flow is an important flow pattern in engineering field. Studying the modulation of particles on fluid plays a significant role in revealing the mechanism of momentum, heat and mass transfer, improving production efficiency and decreasing energy consumption. The statistical characteristics and coherent structure in the flat plate turbulent boundary layer in clean water condition and near-neutrally liquid-solid two-phase flow with 200 um polystyrene particles (dp+=2.29,dp+=duτv) measured by means of PIV technique were compared and analyzed. The variation rule of turbulent statistic characteristics such as mean velocity profile, turbulence intensity and Reynolds shear stress of fluid with polystyrene particles and clean water under the same free flow velocity was investigated. Based on the locally-average velocity structure function and condition sampling technique, the coherent structure was detected, and the two-dimensional spatial topologies such as the fluctuation velocity, Reynolds shear stress and spanwise vorticity in ejection and sweep events at different wall heights under two working conditions were extracted with phase-average method. It was found that in the buffer layer the flow velocity with particles was greater than that of clean water, while there was little difference between them in the logarithmic law region. Compared with the clean water, the streamwise turbulent intensity was decreased in particle-laden flow, whereas the normal turbulent intensity, the comprehensive turbulence intensity and the Reynolds shear stress were all increased, with the expense of a slightly increase of the friction drag in the fluid with particles by 3.57%. In the bursting of coherent structure, the addition of polystyrene particles suppressed the fluid streamwise fluctuation in a turbulent boundary layer, gave a rise to the normal fluctuation and Reynolds shear stress, while inhibited the streamwise development of the spanwise vortex and promoted its normal development. The addition of particles facilitated the fluctuation of the fluid microcluster, and as well as the transverse momentum transfer in the log law region of turbulent boundary layer. The particles could increase the probability of the coherent structure ejection events and had less influence on the sweep events. The number and intensity of the ejection event was the key to improve the flow normal turbulence intensity and even to improve the energy exchange near the wall. The presence of appropriate scale particles in wall turbulence could play an important role in strengthening the transfer of momentum, heat and mass, and promoting mixing and reaction in the engineering, only by slightly increasing the fraction resistance.

Effectiveness of blowing for improving the high-speed trains aerodynamics

The promising method of drag reduction with the use of micro-blowing through the streamlined surface has been proposed for its use to the external surface of high-speed train. The advantages of high-speed train as an object of micro-blowing application are introduced. The corresponding RANS-based mathematical model is elaborated, and the computations of the external flow around a long train body are performed. Predictions of the turbulent boundary layer over penetrable surface with different modes of micro-blowing have been presented and analyzed. The developed modifications of mathematical model of turbulence have been used to take into account the micro-blowing influence in the inner region of turbulent boundary layer. The obtained results of parametric analysis of drag reduction depending on the area of permeable sections, intensity of micro-blowing, and high-speed train length have been analyzed. In particular, the dependence between drag reduction effect and length of train body with realized micro-blowing as well as its intensity is established. Realization of micro-blowing with blowing velocity just 0.25 % of train speed (V = 100 m/s) on the 70 % of the streamlined surface area for just one train carriage (L = 25 m) allows one to reduce the aerodynamic drag (including the most actual friction and head-tail pressure components) of the whole train (L = 200 m) by about 5.25 %, so in case of micro-blowing realization on all its 8 carriages, the train’s aerodynamic drag can be reduced approximately by 42 %.

Outer scales and parameters of adverse-pressure-gradient turbulent boundary layers

A clear and consistent framework for the analysis of the outer region of adverse-pressure-gradient turbulent boundary layers is established in this paper based on basic principles and theory, and the help of six adverse-pressure-gradient turbulent boundary layer databases and a zero-pressure-gradient one. Outer velocity and length scales for the mean velocity defect and the Reynolds stresses are discussed first. The conditions of validity of four velocity scales are determined in terms of the shape factor, since one scale is restricted to small velocity-defect boundary layers (the friction velocity $u_{\unicode[STIX]{x1D70F}}$), one to large-defect ones (the pressure-gradient velocity $U_{po}$), while the two others are proper scales for all velocity-defect conditions (the Zagarola–Smits velocity $U_{zs}$ and the mixing-layer-type velocity $U_{m}$). The turbulent boundary layer equations are then used to bring out, in a consistent manner and without assuming any self-similar behaviour, a set of non-dimensional parameters characterizing the outer region of turbulent boundary layers with arbitrary pressure gradients. In terms of a generic outer length scale $L_{o}$ and velocity scale $U_{o}$, these non-dimensional parameters are the pressure-gradient parameter $\unicode[STIX]{x1D6FD}_{o}=L_{o}/(\unicode[STIX]{x1D70C}U_{o}^{2})\,\text{d}p_{e}/\text{d}x$, the Reynolds number $Re_{o}=U_{o}L_{o}/\unicode[STIX]{x1D708}(U_{o}/U_{e})$ and the inertial parameter $\unicode[STIX]{x1D6FC}_{o}=U_{e}V_{e}/U_{o}^{2}$, where $U_{e}$ and $V_{e}$ are respectively the streamwise and wall-normal components of mean velocity at the boundary layer edge. These parameters have a clear physical meaning: they are ratios of the order of magnitude of forces, with the Reynolds shear stress gradient (apparent turbulent force) as the reference force – inertial to apparent turbulent forces for $\unicode[STIX]{x1D6FC}_{o}$, pressure to apparent turbulent forces for $\unicode[STIX]{x1D6FD}_{o}$ and apparent turbulent to viscous forces for $Re_{o}$. We discuss at length their significance and determine under what conditions they retain their meaning depending on the outer velocity scale that is considered. The seven boundary layer databases are analysed and compared using the established framework. An astonishing and impressive result is obtained: by choosing $U_{o}=U_{zs}$, the streamwise evolution of the three ratios of forces in the outer region can be accurately followed with $\unicode[STIX]{x1D6FD}_{zs}$, $\unicode[STIX]{x1D6FC}_{zs}$ and $Re_{zs}$ in all these flows – not just the order of magnitude of these ratios. This cannot be achieved with $u_{\unicode[STIX]{x1D70F}}$ and $U_{po}$, and only imperfectly with $U_{m}$. Consequently, $\unicode[STIX]{x1D6FD}_{zs}$, $\unicode[STIX]{x1D6FC}_{zs}$ and $Re_{zs}$ can be used to follow – in a global sense – the streamwise evolution of the streamwise mean momentum balance in the outer region.

A self-sustaining process model of inertial layer dynamics in high Reynolds number turbulent wall flows.

Field observations and laboratory experiments suggest that at high Reynolds numbers Re the outer region of turbulent boundary layers self-organizes into quasi-uniform momentum zones (UMZs) separated by internal shear layers termed 'vortical fissures' (VFs). Motivated by this emergent structure, a conceptual model is proposed with dynamical components that collectively have the potential to generate a self-sustaining interaction between a single VF and adjacent UMZs. A large-Re asymptotic analysis of the governing incompressible Navier-Stokes equation is performed to derive reduced equation sets for the streamwise-averaged and streamwise-fluctuating flow within the VF and UMZs. The simplified equations reveal the dominant physics within-and isolate possible coupling mechanisms among-these different regions of the flow.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'.

Study of Aerodynamic and Heat-Exhaust Characteristics for a High-Altitude Long-Endurance Unmanned-Aerial-Vehicle Airfoil

This paper identifies exhaust heat characteristics depending on airfoil shapes at low Reynolds number to design a high-altitude long-endurance unmanned aerial vehicle with a wing-surface heat exchanger. In the first step, computational fluid dynamics simulations are conducted for different airfoils, each of which exhausts heat from different regions on the upper surface, at different angles of attack. This parametric study reveals that early transition near the leading edge is favorable to improve heat-exhaust characteristics, although it may increase skin friction. In addition, heat exhaust should be conducted only in the region of turbulent boundary layer behind the transition point. From these results, the airfoil shape significantly affects the Nusselt-number distribution along the upper wing surface due to the change in the location of laminar–turbulent transition and turbulent boundary-layer separation. In the next step, multi-objective optimization of an airfoil shape, which balances aerodynamic performance and heat-exhaust performance, is carried out. The obtained nondominated solutions show the tradeoffs between aerodynamic performance and heat-exhaust performance. It was confirmed that heat-exhaust performance can be controlled by the location of the laminar–turbulent transition, and improved without sacrificing aerodynamic performance at the cruising condition.

Effect of surface roughness on helicopter main rotor blade

This paper describes the effect of surface roughness when applied on helicopter main rotor blade. The aim is to prove that surface roughness can be used as a simple and inexpensive method to achieve better flight performance such as enhanced thrust and/or reduced power requirement. The research was done experimentally, using scaled model of Eurocopter AS350 Ecureuil. Smooth profile of the main rotor blade was modified by applying surface roughness on the upper and lower camber in transition and turbulent boundary layer region, starting from 25% of chord length and extending up to the trailing edge (TE). This study was conducted with the conditions of a vertical flight (particularly in hover condition) since this is a high powerconsuming flight regime for helicopter. The experiment resulted in lower power requirement but at the expense of reduced thrust at the middle collective pitch level. At upper range of the collective pitch level, surface roughness was seen to delay the stall angle as well as increase the lift in the stall region. Meanwhile, at lower pitch level, there was an increase in thrust-to-power ratio.

On the use of the Reynolds decomposition in the intermittent region of turbulent boundary layers

In the analysis of velocity fields in turbulent boundary layers, the traditional Reynolds decomposition is universally employed to calculate the fluctuating component of streamwise velocity. Here, we demonstrate the perils of such a determination of the fluctuating velocity in the context of structural analysis of turbulence when applied in the outer region where the flow is intermittently turbulent at a given wall distance. A new decomposition is postulated that ensures non-turbulent regions in the flow do not contaminate the fluctuating velocity components in the turbulent regions. Through this new decomposition, some of the typical statistics concerning the scale and structure of turbulent boundary layers are revisited.

Amplitude modulation of streamwise velocity fluctuations in the roughness sublayer: evidence from large-eddy simulations

Recent studies have demonstrated that large- and very-large-scale motions in the logarithmic region of turbulent boundary layers ‘amplitude modulate’ dynamics of the near-wall region (Marusicet al.,Science, vol. 329, 2010, pp. 193–196; Mathiset al.,J. Fluid Mech., vol. 628, 2009a, pp. 311–337). These contributions prompted development of a predictive model for near-wall dynamics (Mathiset al.,J. Fluid Mech., vol. 681, 2011, pp. 537–566) that has promising implications for large-eddy simulations of wall turbulence at high Reynolds numbers (owing to the presence of smaller scales as the wall is approached). Existing studies on the existence of amplitude modulation in wall-bounded turbulence have addressed smooth-wall flows, though high Reynolds number rough-wall flows are ubiquitous. Under such conditions, the production of element-scale vortices ablates the viscous wall region and a new near-wall layer emerges: the roughness sublayer. The roughness sublayer depth scales with aggregate roughness element height,$h$, and is typically$2h\sim 3h$. Above the roughness sublayer, Townsend’s hypothesis dictates that turbulence in the logarithmic layer is unaffected by the roughness sublayer (beyond its role in setting the friction velocity and thus inducing a deficit in the mean streamwise velocity known as the roughness function). Here, we present large-eddy simulation results of turbulent channel flow over rough walls. We follow the decoupling procedure outlined in Mathiset al.(J. Fluid Mech., vol. 628, 2009a, 311–337) and present evidence that outer-layer dynamics amplitude modulate the roughness sublayer. Below the roughness element height, we report enormous sensitivity to the streamwise–spanwise position at which flow statistics are measured, owing to spatial heterogeneities in the roughness sublayer imparted by roughness elements. For$y/h\gtrsim 1.5$(i.e. above the cubes, but within the roughness sublayer), topography dependence rapidly declines.