Simulation of a Large-Eddy-Break-up Device (LEBU) in a Moderate Reynolds Number Turbulent Boundary Layer

A well-resolved large eddy simulation (LES) of a large-eddy break-up (LEBU) device in a spatially evolving turbulent boundary layer is performed with, Reynolds number, based on free-stream velocity and momentum-loss thickness, of R e _θ ≈ 4300. The implementation of the LEBU is via an immersed boundary method. The LEBU is positioned at a wall-normal distance of 0.8 δ (δ denoting the local boundary layer thickness at the location of the LEBU) from the wall. The LEBU acts to delay the growth of the turbulent boundary layer and produces global skin friction reduction beyond 180δ downstream of the LEBU, with a peak local skin friction reduction of approximately 12 %. However, no net drag reduction is found when accounting for the device drag of the LEBU in accordance with the towing tank experiments by Sahlin et al. (Phys. Fluids 31, 2814, 1988). Further investigation is performed on the interactions of high and low momentum bulges with the LEBU and the corresponding output is analysed, showing a ‘break-up’ of these large momentum bulges downstream of the LEBU. In addition, results from the spanwise energy spectra show consistent reduction in energy at spanwise length scales for \(\lambda _{z}^{+} > 1000\) independent of streamwise and wall-normal location when compared to the corresponding turbulent boundary layer without LEBU.     

Perspectives on the Phenomenology and Modeling of Boundary Layer Transition

The characteristics of the coherent structures in a strongly decelerated large-velocity-defect boundary layer are analysed by direct numerical simulation. The simulated boundary layer starts as a zero-pressure-gradient boundary layer, decelerates under a strong adverse pressure gradient, and separates near the end of the domain, in the form of a very thin separation bubble. The Reynolds number at separation is R e _?? =3912 and the shape factor H=3.43. The three-dimensional spatial correlations of (u, u) and (u, v) are investigated and compared to those of a zero-pressure-gradient boundary layer and another strongly decelerated boundary layer. These velocity pairs lose coherence in the streamwise and spanwise directions as the velocity defect increases. In the outer region, the shape of the correlations suggest that large-scale u structures are less streamwise elongated and more inclined with respect to the wall in large-defect boundary layers. The three-dimensional properties of sweeps and ejections are characterized for the first time in both the zero-pressure-gradient and adverse-pressure-gradient boundary layers, following the method of Lozano-Durán et al. (J. Fluid Mech. 694, 100–130, [2012]). Although longer sweeps and ejections are found in the zero-pressure-gradient boundary layer, with ejections reaching streamwise lengths of 5 boundary layer thicknesses, the sweeps and ejections tend to be bigger in the adverse-pressure-gradient boundary layer. Moreover, small near-wall sweeps and ejections are much less numerous in the large-defect boundary layer. Large sweeps and ejections that reach the wall region (wall-attached) are also less numerous, less streamwise elongated and they occupy less space than in the zero-pressure-gradient boundary layer.     

Streamwise Vortices and Velocity Streaks in a Locally Drag-Reduced Turbulent Boundary Layer

This work aims to understand the changes associated with the near-wall streaky structures in a turbulent boundary layer (TBL) where the local skin-friction drag is substantially reduced. The Reynolds number is R e _?? = 1000 based on the momentum thickness or R e _τ = 440 based on the friction velocity of the uncontrolled flow. The TBL is perturbed via a local surface oscillation produced by an array of spanwise-aligned piezo-ceramic (PZT) actuators and measurements are made in two orthogonal planes using particle image velocimetry (PIV). Data analyses are conducted using the vortex detection, streaky structure identification, spatial correlation and proper orthogonal decomposition (POD) techniques. It is found that the streaky structures are greatly modified in the near-wall region. Firstly, the near-wall streamwise vortices are increased in number and swirling strength but decreased in size, and are associated with greatly altered velocity correlations. Secondly, the velocity streaks grow in number and strength but contract in width and spacing, exhibiting a regular spatial arrangement. Other aspects of the streaky structures are also characterized; they include the spanwise gradient of the longitudinal fluctuating velocity and both streamwise and spanwise integral length scales. The POD analysis indicates that the turbulent kinetic energy of the streaky structures is reduced. When possible, our results are compared with those obtained by other control techniques such as a spanwise-wall oscillation, a spanwise oscillatory Lorentz force and a transverse traveling wave.     

Effect of Free-Stream Turbulence on the Reduction of Surface Friction in a Turbulent Boundary Layer Behind LEBU-Devices

The effect of increased free-stream turbulence on the reduction of the surface friction coefficient c _f in a turbulent boundary layer behind large-eddy break-up (LEBU) devices is investigated using a gravimetric method. The turbulence level was ε ≈ 1.9–4.9 % and the turbulence scale L _e ≈ 40–110 mm. The boundary layer Reynolds number Re** was varied from 2300 to 7500, with the boundary layer thickness being varied on the range δ = 33–44 mm. It is shown that an increase in the turbulence level ε has almost no impact on the relative reduction of friction behind LEBU-devices, whereas, under similar conditions of elevated free-stream turbulence, for another method, namely, the use of surface riblets, the friction reduction may be more strongly expressed.     

Experimental study on flow control of the turbulent boundary layer with micro-bubbles

The effect of micro-bubbles on the turbulent boundary layer in the channel flow with Reynolds numbers (Re) ranging from \(0.87\times 10 ^{5}\) to \(1.23\times 10^{5}\) is experimentally studied by using particle image velocimetry (PIV) measurements. The micro-bubbles are produced by water electrolysis. The velocity profiles, Reynolds stress and instantaneous structures of the boundary layer, with and without micro-bubbles, are measured and analyzed. The presence of micro-bubbles changes the streamwise mean velocity of the fluid and increases the wall shear stress. The results show that micro-bubbles have two effects, buoyancy and extrusion, which dominate the flow behavior of the mixed fluid in the turbulent boundary layer. The buoyancy effect leads to upward motion that drives the fluid motion in the same direction and, therefore, enhances the turbulence intense of the boundary layer. While for the extrusion effect, the presence of accumulated micro-bubbles pushes the flow structures in the turbulent boundary layer away from the near-wall region. The interaction between these two effects causes the vorticity structures and turbulence activity to be in the region far away from the wall. The buoyancy effect is dominant when the Re is relatively small, while the extrusion effect plays a more important role when Re rises.     

Revisiting History Effects in Adverse-Pressure-Gradient Turbulent Boundary Layers

The goal of this study is to present a first step towards establishing criteria aimed at assessing whether a particular adverse-pressure-gradient (APG) turbulent boundary layer (TBL) can be considered well-behaved, i.e., whether it is independent of the inflow conditions and is exempt of numerical or experimental artifacts. To this end, we analyzed several high-quality datasets, including in-house numerical databases of APG TBLs developing over flat-plates and the suction side of a wing section, and five studies available in the literature. Due to the impact of the flow history on the particular state of the boundary layer, we developed three criteria of convergence to well-behaved conditions, to be used depending on the particular case under study. (i) In the first criterion, we develop empirical correlations defining the R e _?? -evolution of the skin-friction coefficient and the shape factor in APG TBLs with constant values of the Clauser pressure-gradient parameter β = 1 and 2 (note that β = δ ^?/τ _w dP _e /dx, where δ ^? is the displacement thickness, τ _w the wall-shear stress and dP _e /dx the streamwise pressure gradient). (ii) In the second one, we propose a predictive method to obtain the skin-friction curve corresponding to an APG TBL subjected to any streamwise evolution of β, based only on data from zero-pressure-gradient TBLs. (iii) The third method relies on the diagnostic-plot concept modified with the shape factor, which scales APG TBLs subjected to a wide range of pressure-gradient conditions. These three criteria allow to ensure the correct flow development of a particular TBL, and thus to separate history and pressure-gradient effects in the analysis.     

LES-based Study of the Roughness Effects on the Wake of a Circular Cylinder from Subcritical to Transcritical Reynolds Numbers

This paper investigates the effects of surface roughness on the flow past a circular cylinder at subcritical to transcritical Reynolds numbers. Large eddy simulations of the flow for sand grain roughness of size k/D = 0.02 are performed (D is the cylinder diameter). Results show that surface roughness triggers the transition to turbulence in the boundary layer at all Reynolds numbers, thus leading to an early separation caused by the increased momentum deficit, especially at transcritical Reynolds numbers. Even at subcritical Reynolds numbers, boundary layer instabilities are triggered in the roughness sublayer and eventually lead to the transition to turbulence. The early separation at transcritical Reynolds numbers leads to a wake topology similar to that of the subcritical regime, resulting in an increased drag coefficient and lower Strouhal number. Turbulent statistics in the wake are also affected by roughness; the Reynolds stresses are larger due to the increased turbulent kinetic energy production in the boundary layer and separated shear layers close to the cylinder shoulders.     

Improvement for expansion of parabolized stability equation method in boundary layer stability analysis

An improved expansion of the parabolized stability equation(iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber α and its streamwise gradient dα/dx are unknown variables. This eigenvalue problem is solved for the eigenvalue dα/dx with an initial α, and the correction of α is performed with the conservation relation used in the PSE. The i EPSE is validated in several compressible and incompressible boundary layers. The computational results show that the prediction accuracy of the i EPSE is significantly higher than that of the ESPE, and it is in excellent agreement with the PSE which is regarded as the baseline for comparison. In addition, the unphysical multiple eigenmode problem in the EPSE is solved by using the i EPSE. As a local non-parallel stability analysis tool, the i EPSE has great potential application in the eNtransition prediction in general three-dimensional boundary layers.     

Consequences of the Translation Invariance on the Darcy Free Convection Flow Past a Vertical Surface

It is shown that the governing equation for the stream function of the Darcy free convection boundary layer flows past a vertical surface is invariant under arbitrary translations of the transverse coordinate y. The consequences of this basic symmetry property on the solutions corresponding to a prescribed surface temperature distribution T _w (x) are investigated. It is found that starting with a “primary solution” which describes the temperature boundary layer on an impermeable surface, infinitely many “translated solutions” can be generated which form a continuous group, the “translation group” of the given primary solution. The elements of this group describe free convection boundary layer flows from permeable counterparts of the original surface with a transformed temperature distribution \({\tilde {T}_w \left( x \right)}\), when simultaneously a suitable lateral suction/injection of the fluid is applied. It turns out in this way that several exact solutions discovered during the latter few decades are in fact not basically new solutions, but translated counterparts of some formerly reported primary solutions. A few specific examples are discussed in detail.     

Predicting Turbulent Spectra in Drag-reduced Flows

In the present work we describe how turbulent skin-friction drag reduction obtained through near-wall turbulence manipulation modifies the spectral content of turbulent fluctuations and Reynolds shear stress with focus on the largest scales. Direct Numerical Simulations (DNS) of turbulent channels up to Re _τ = 1000 are performed in which drag reduction is achieved either via artificially removing wall-normal turbulent fluctuations in the vicinity of the wall or via streamwise-travelling waves of spanwise wall velocity. This near-wall turbulence manipulation is shown to modify turbulent spectra in a broad range of scales throughout the whole channel. Above the buffer layer, the observed changes can be predicted, exploiting the vertical shift of the logarithmic portion of the mean streamwise velocity profile, which is a classic performance measure for wall roughness or drag-reducing riblets. A simple model is developed for predicting the large-scale contribution to turbulent fluctuation and Reynolds shear stress spectra in drag-reduced turbulent channels in which a flow control acts at the wall. Any drag-reducing control that successfully interacts with large scales should deviate from the predictions of the present model, making it a useful benchmark for assessing the capability of a control to affect large scales directly.     

Effect of the mode of gas-surface interaction on intensive monatomic gas evaporation

The direct Monte Carlo simulation method is used for investigating the effect of the thermal accommodation coefficient α _E on the relations on the Knudsen layer boundary in the presence of intensive evaporation. The model of mirror reflection of molecules from the surface is considered. It is shown that diffuse reflection with α _E = 0 leads to almost the same relations on the Knudsen layer boundary as mirror reflection. The accuracy of the moment method is estimated in application to the problems of intensive evaporation with diffuse and mirror reflection from the surface.     

Effect of Inflow Turbulence on an Airfoil Flow with Laminar Separation Bubble: An LES Study

The present paper is concerned with numerical investigations on the effect of inflow turbulence on the flow around a SD7003 airfoil. At a Reynolds number Re_c =?60,000, an angle of attack α =?4^° and a low or zero turbulence intensity of the oncoming flow, the flow past the airfoil is known to be dominated by early separation, subsequent transition and reattachment leading to a laminar separation bubble with a distinctive pressure plateau. The objective of the study is to investigate the effect of inflow turbulence on the flow behavior. For this purpose, a numerical methodology relying on a wall-resolved large-eddy simulation, a synthetic turbulence inflow generator and a specific source term concept for introducing the turbulence fluctuations within the computational domain is used. The numerical technique applied allows the variation of the free-stream turbulence intensity (TI) in a wide range. In order to analyze the influence of TI on the arising instantaneous and time-averaged flow field past the airfoil, the present study evaluates the range 0% ≤ TI ≤?11.2%, which covers typical values found in atmospheric boundary layers. In accordance with experimental studies it is shown that the laminar separation bubble first shrinks and finally completely vanishes for increasing inflow turbulence. Consequently, the aerodynamic performance in terms of the lift-to-drag ratio increases. Furthermore, the effect of the time and length scales of the isotropic inflow turbulence on the development of the flow field around the airfoil is analyzed and a perceptible influence is found. Within the range of inflow scales studied decreasing scales augment the receptivity of the boundary layer promoting an earlier transition.     

Measurement of local forcing on a turbulent boundary layer using PIV

An experimental study was carried out to investigate the effect of periodic blowing and suction on a turbulent boundary layer. Particle image velocimetry (PIV) was used to probe the characteristics of the flow. Local forcing was introduced to the boundary layer via a sinusoidally-oscillating jet issuing from a thin spanwise slot. Three forcing frequencies (f⁺=0.44, 0.66 and 0.88) with a fixed forcing amplitude (A⁺=0.6) were employed at Re _θ =690. The effect of three different forcing angles (α=60°, 90° and l20°) was investigated under a fixed forcing frequency (f⁺=0.088). The PIV results showed that the wall-region velocity decreases on imposition of the local forcing. Inspection of the phase-averaged velocity profiles revealed that spanwise large-scale vortices are generated downstream of the slot and persist farther downstream. The highest reduction in skin friction was achieved at the highest forcing frequency (f⁺=0.088) and a forcing angle of α=120°. The spatial fraction of the vortices was examined to analyze the skin friction reduction.     

Pressure-Gradient Turbulent Boundary Layers Developing Around a Wing Section

A direct numerical simulation database of the flow around a NACA4412 wing section at R e _c = 400,000 and 5^° angle of attack (Hosseini et al. Int. J. Heat Fluid Flow 61, 117–128, 2016), obtained with the spectral-element code Nek5000, is analyzed. The Clauser pressure-gradient parameter β ranges from ? 0 and 85 on the suction side, and from 0 to ? 0.25 on the pressure side of the wing. The maximum R e _?? and R e _τ values are around 2,800 and 373 on the suction side, respectively, whereas on the pressure side these values are 818 and 346. Comparisons between the suction side with zero-pressure-gradient turbulent boundary layer data show larger values of the shape factor and a lower skin friction, both connected with the fact that the adverse pressure gradient present on the suction side of the wing increases the wall-normal convection. The adverse-pressure-gradient boundary layer also exhibits a more prominent wake region, the development of an outer peak in the Reynolds-stress tensor components, and increased production and dissipation across the boundary layer. All these effects are connected with the fact that the large-scale motions of the flow become relatively more intense due to the adverse pressure gradient, as apparent from spanwise premultiplied power-spectral density maps. The emergence of an outer spectral peak is observed at β values of around 4 for λ _z ? 0.65δ ₉₉, closer to the wall than the spectral outer peak observed in zero-pressure-gradient turbulent boundary layers at higher R e _?? . The effect of the slight favorable pressure gradient present on the pressure side of the wing is opposite the one of the adverse pressure gradient, leading to less energetic outer-layer structures.     

Effect of tube diameter and capillary number on platelet margination and near-wall dynamics

I investigate the effect of tube diameter D and red blood cell capillary number Ca (i.e. the ratio of viscous to elastic forces) on platelet margination in blood flow at ≈37 % tube haematocrit. The system is modelled as three-dimensional suspension of deformable red blood cells and nearly rigid platelets using a combination of the lattice-Boltzmann, immersed boundary and finite element methods. Results of simulations during the dynamics before the steady state has been reached show that a non-diffusive radial platelet transport facilitates margination. This non-diffusive effect is important near the edge of the cell-free layer, but only for Ca > 0.2, when red blood cells are tank-treading. I also show that platelet trapping in the cell-free layer is reversible for Ca ≤ 0.2. Margination is essentially independent of Ca only for the smallest investigated tube diameter (D = 10 μm). Once platelets have reached the cell-free layer, they tend to slide rather than tumble. The tumbling rate is essentially independent of Ca but increases with D. Strong confinement suppresses tumbling due to the relatively small cell-free layer thickness at ≈ 37 % tube haematocrit.     

The linearized pressure Poisson equation for global instability analysis of incompressible flows

The linearized pressure Poisson equation (LPPE) is used in two and three spatial dimensions in the respective matrix-forming solution of the BiGlobal and TriGlobal eigenvalue problem in primitive variables on collocated grids. It provides a disturbance pressure boundary condition which is compatible with the recovery of perturbation velocity components that satisfy exactly the linearized continuity equation. The LPPE is employed to analyze instability in wall-bounded flows and in the prototype open Blasius boundary layer flow. In the closed flows, excellent agreement is shown between results of the LPPE and those of global linear instability analyses based on the time-stepping nektar++, Semtex and nek5000 codes, as well as with those obtained from the FreeFEM++ matrix-forming code. In the flat plate boundary layer, solutions extracted from the two-dimensional LPPE eigenvector at constant streamwise locations are found to be in very good agreement with profiles delivered by the NOLOT/PSE space marching code. Benchmark eigenvalue data are provided in all flows analyzed. The performance of the LPPE is seen to be superior to that of the commonly used pressure compatibility (PC) boundary condition: at any given resolution, the discrete part of the LPPE eigenspectrum contains converged and not converged, but physically correct, eigenvalues. By contrast, the PC boundary closure delivers some of the LPPE eigenvalues and, in addition, physically wrong eigenmodes. It is concluded that the LPPE should be used in place of the PC pressure boundary closure, when BiGlobal or TriGlobal eigenvalue problems are solved in primitive variables by the matrix-forming approach on collocated grids.     

Effect of incomplete thermal accommodation on intensive subsonic gas condensation

The direct Monte Carlo simulation method is used for investigating the effect of the thermal accommodation coefficient α _E on the relation for the Knudsen layer in the presence of intensive subsonic condensation. It is shown that the deviation of α _E from unity may significantly affect the flow parameters, in particular, M_lim, the Mach number value limiting for subsonic condensation. It is shown that a decrease in α _E leads to an increase in M_lim (M_lim < 1) if the relative flow temperature (ratio of the outer Knudsen layer boundary to the surface temperature) T < 1 and to a decrease in M_lim if T > 1. It is shown that for mirror reflection of molecules from the surface this effect may intensify.     

Numerical Study of Turbulent Channel Flow over Surfaces with Variable Spanwise Heterogeneities: Topographically-driven Secondary Flows Affect Outer-layer Similarity of Turbulent Length Scales

Wall-bounded turbulent flows over surfaces with spanwise heterogeneous surface roughness – that is, spanwise-adjacent patches of relatively high and low roughness – exhibit mean flow phenomena entirely different to what would otherwise exist in the absence of spanwise heterogeneity. In the outer layer, mean counter-rotating rolls occupy the depth of the flow, and are positioned such that “upwelling” and “downwelling” occurs above the low and high roughness, respectively. It has been comprehensively shown that these secondary flows are Prandtl’s secondary flow of the second kind (Anderson et al., J. Fluid Mech. 768, 316–347 2015). This behaviour indicates that spanwise spacing, s _y , between adjacent patches of high and low roughness is, itself, a problem parameter; in this study, we have systematically assessed how s _y affects turbulence structure in high Reynolds number channel flows via two-point correlations. “High roughness” is imposed with streamwise-aligned pyramid elements with height, h, selected to be ≈ 5% of the channel half height, H. For \(s_{y}/H \gtrsim 1\), we find that the aforementioned domain-scale mean circulations exist and the surface may be regarded as a topography. For s _y /H ? 0.2, turbulence statistics show characteristics very similar to a homogeneous roughness and thus the surface may be regarded as a roughness. For 0.2 ? s _y /H ? 2, the spatial extent of the counter-rotating rolls is controlled by proximity to adjacent rows, and we define such surfaces as being intermediate. We refer to such surfaces as intermediate state.     

Time-dependent drag reduction and ageing in aqueous solutions of a cationic surfactant

The turbulent pipe flow of a highly dilute aqueous cationic surfactant solution is investigated by means of a pulsed ultrasound Doppler method with special emphasis on the wall boundary layer. The velocity profiles are recorded for several Reynolds numbers at varying ages of the solution. The wall shear stress velocities u _τ used for the normalization of the velocity profiles are determined by fitting the measured profiles to the universal linear velocity profile in the viscous sublayer. The theoretical pressure loss is then calculated from the numerical values of u _τ and compared to the experimental values. Two different scaling methods are discussed for the velocity fluctuations concerning the correlation of the root-mean square values with the effect and the amount of drag reduction. It is shown that outer scaling with the mean velocity is appropriate for the detection of drag reduction in surfactant solutions, rather than inner scaling with the wall shear stress velocity, which is common practice in investigations of 'usual' turbulent flows.     

Mach Wave Effect on Laminar-Turbulent Transition in Supersonic Flow over a Flat Plate

The effect of a Mach wave (N wave) on laminar-turbulent transition induced by the first instability mode (Tollmien–Schlichting wave) in the flat-plate boundary layer is investigated on the basis of the numerical solution of Navier–Stokes equations at the freestream Mach number of 2.5. In accordance with the experiment, the N wave is generated by a two-dimensional roughness at the computation domain boundary corresponding to the side wall of the test section of a wind tunnel. It is shown that the disturbance induced by the backward front of the N wave in the boundary layer has no effect on the beginning of transition but displaces downstream the nonlinear stage of the first mode development. The disturbance induced by the forward front of the N wave displaces the beginning of transition upstream.