Dual leading-edge vortex structure for flow over a simplified butterfly model

The dye visualization experiments show that a dual leading-edge vortex (LEV) structure exists on the suction side of a simplified butterfly model of Papilio ulysses at α = 8°−12°. Furthermore, the results of particle image velocimetry (PIV) measurement indicate that the axial velocity of the primary (outer) vortex core reaches the lower extreme value while a transition from a “wake-like” to a “jet-like” axial velocity profile occurs. The work reveals for the first time the existence of dual LEV structure on the butterfly-like forward-sweep wing configuration.     

Development of an Intermittency Equation for the Modeling of the Supersonic/Hypersonic Boundary Layer Flow Transition

An intermittency transport equation is developed in this study to model the laminar-turbulence boundary layer transition at supersonic and hypersonic conditions. The model takes into account the effects of different instability modes associated with the variations in Mach numbers. The model equation is based on the intermittency factor γ concept and couples with the well-known SST k–ω eddy-viscosity model in the solution procedures. The particular features of the present model approach are that: (1) the fluctuating kinetic energy k includes the non-turbulent, as well as turbulent fluctuations; (2) the proposed transport equation for the intermittency factor γ triggers the transition onset through a source term; (3) through the introduction of a new length scale normal to wall, the present model employs the local variables only avoiding the use of the integral parameters, like the boundary layer thickness δ, which are often cost-ineffective with the modern CFD methods; (4) in the fully turbulent region, the model retreats to SST model. This model is validated with a number of available experiments on boundary layer transition including the incompressible, supersonic and hypersonic flows past flat plates, straight/flared cones at zero incidences, etc. It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition with a reasonably wide range of Mach numbers.     

Three-dimensional visualization of large structures in the turbulent boundary layer

 A new method of visualizing the coherent structures in the boundary layer is used to develop insight into how these structures form and to provide information on the relative frequency of typical shapes noticed in the near-wall flow. These results were achieved in a water channel using a recently developed tracer which remains as a moving dye streak while conforming to the convoluted motions in the boundary layer. The tracer is formulated from a surfactant–polymer–emulsion mixture which retains its capabilities as a marker of evolving flow motions in the boundary layer for a meter or more before eventually dispersing. Three-dimensional, continuous visualization of the structures can be obtained as they move along a flat plate. Photos and video frames demonstrate the evolution and properties of the most widely discussed boundary-layer structure, the Theodorsen (horseshoe) vortex. Received: 16 November 1999/Accepted: 24 May 2000     

Three-dimensional Turbulent Boundary Layer in a Shrouded Rotating System

A thre-dimensional direct numerical simulation is combined with a laboratory study to describe the turbulent flow in an enclosed annular rotor-stator cavity characterized by a large aspect ratio G = (b − a)/h = 18.32 and a small radius ratio a/b = 0.152, where a and b are the inner and outer radii of the rotating disk and h is the interdisk spacing. The rotation rate Ω considered is equivalent to the rotational Reynolds number Re = Ωb ²/ν= 9 .5 × 10⁴ (ν the kinematic viscosity of water). This corresponds to a value at which experiment has revealed that the stator boundary layer is turbulent, whereas the rotor boundary layer is still laminar. Comparisons of the computed solution with velocity measurements have given good agreement for the mean and turbulent fields. The results enhance evidence of weak turbulence by comparing the turbulence properties with available data in the literature (Lygren and Andersson, J Fluid Mech 426:297–326, 2001). An approximately self-similar boundary layer behavior is observed along the stator. The wall-normal variations of the structural parameter and of characteristic angles confirm that this boundary layer is three-dimensional. A quadrant analysis (Kang et al., Phys Fluids 10:2315–2322, 1998) of conditionally averaged velocities shows that the asymmetries obtained are dominated by Reynolds stress-producing events in the stator boundary layer. Moreover, Case 1 vortices (with a positive wall induced velocity) are found to be the major source of generation of special strong events, in agreement with the conclusions of Lygren and Andersson (J Fluid Mech 426:297–326, 2001).     

Effect of local forcing on a turbulent boundary layer

An experimental study is performed to analyze flow structures behind local suction and blowing in a flat-plate turbulent boundary layer. The local forcing is given to the boundary layer flow by means of a sinusoidally oscillating jet issuing from a thin spanwise slot at the wall. The Reynolds number based on the momentum thickness is about Re _θ =1700. The effects of local forcing are scrutinized by altering the forcing frequency (0.011 ≤ f ⁺≤ 0.044). The forcing amplitude is fixed at A ₀=0.4. It is found that a small local forcing reduces the skin friction and the skin friction reduction increases with the forcing frequency. A phase-averaging technique is employed to capture the large-scale vortex evolution. An organized spanwise vortical structure is generated by the local forcing. The cross-sectional area of vortex and the time fraction of vortex are examined by changing the forcing frequency. An investigation of the random fluctuation components reveals that turbulent energy is concentrated near the center of vortical structures. Received: 17 March 2000/Accepted: 3 April 2001     

On displacements and stresses in a semi-infinite laminated layer: comparative results

This paper deals with some comparison results for displacements and stresses in a periodically stratified elastic semi-infinite layer determined within the framework of two approaches: (1) based on the homogenized model with microlocal parameters [Woźniak (1987) Int J Eng Sci 25: 483–499; Woźniak (1987) Bull Ac Pol Tech Sci 35: 143–151]; (2) obtained directly from the theory of elasticity. A body is assumed to be composed of n elastic two-component periodically repeated laminae. The perfect mechanical bonding between the layers is assumed. The normal displacements and zero shear stresses on the boundary being a cross-section of the composite component are taken into account. The lateral boundary surfaces are assumed to be rigid fixed. The obtained results from the two approaches are compared and presented in the form of figures.     

Influence of roughness on attachment line boundary layer transition in hypersonic flow

 Attachment line boundary layer transition on swept cylinders is studied in a low enthalpy hypersonic wind tunnel at M _∞=7.14. Sweep angles of 60° and 70° are used and transition is detected by means of heat flux measurements. The influence on attachment line transition of single 2D-roughness elements, in the form of tripwires or slots, as well as 3D obstacles is determined and the results are analyzed with respect to Poll’s criterion. Received: 16 January 1996 / Accepted: 12 July 1996     

A study of a turbulent boundary layer in stalled-airfoil-type flow conditions

The experimental study of the turbulent boundary layer under external flow conditions similar to those found on the suction side of airfoils in trailing-edge post-stall conditions has been performed. Detailed boundary layer measurements were carried out with a PIV system and a two-sensor wall probe. They cover the region downstream of the suction peak where the boundary layer is subjected to a very strong adverse pressure gradient and has suffered from an abrupt transition from strong favorable to strong adverse pressure gradients. The experiments show that in spite of these severe conditions, the boundary layer is surprisingly able to recover a state of near-equilibrium before separating. In this near-equilibrium zone, the mean velocity defect and all the measured Reynolds stresses are self-similar (in the outer region) with respect to the outer scales δ and U _e δ*/δ. The mean momentum balance indicates that for the upper half of the outer region, the advection terms dominate all the stress-gradient terms in the zone prior to separation. A large portion of the outer region has therefore become essentially an inertial flow zone where an approach toward equilibrium is expected.An erratum to this article can be found at     

Turbulence in rough-wall boundary layers: universality issues

Wind tunnel measurements of turbulent boundary layers over three-dimensional rough surfaces have been carried out to determine the critical roughness height beyond which the roughness affects the turbulence characteristics of the entire boundary layer. Experiments were performed on three types of surfaces, consisting of an urban type surface with square random height elements, a diamond-pattern wire mesh and a sand-paper type grit. The measurements were carried out over a momentum thickness Reynolds number (Re _θ) range of 1,300–28,000 using two-component Laser Doppler anemometry (LDA) and hot-wire anemometry (HWA). A wide range of the ratio of roughness element height h to boundary layer thickness δ was covered (0.04 ￡ h/d ￡ 0.400.04 \leq h/\delta \leq 0.40). The results confirm that the mean profiles for all the surfaces collapse well in velocity defect form up to surprisingly large values of h/δ, perhaps as large as 0.2, but with a somewhat larger outer layer wake strength than for smooth-wall flows, as previously found. At lower h/δ, at least up to 0.15, the Reynolds stresses for all surfaces show good agreement throughout the boundary layer, collapsing with smooth-wall results outside the near-wall region. With increasing h/δ, however, the turbulence above the near-wall region is gradually modified until the entire flow is affected. Quadrant analysis confirms that changes in the rough-wall boundary layers certainly exist but are confined to the near-wall region at low h/δ; for h/δ beyond about 0.2 the quadrant events show that the structural changes extend throughout much of the boundary layer. Taken together, the data suggest that above h/δ ≈ 0.15, the details of the roughness have a weak effect on how quickly (with rising h/δ) the turbulence structure in the outer flow ceases to conform to the classical boundary layer behaviour. The present results provide support for Townsend’s wall similarity hypothesis at low h/δ and also suggest that a single critical roughness height beyond which it fails does not exist. For fully rough flows, the data also confirm that mean flow and turbulence quantities are essentially independent of Re _θ; all the Reynolds stresses match those of smooth-wall flows at very high Re _θ. Nonetheless, there is a noticeable increase in stress contributions from strong sweep events in the near-wall region, even at quite low h/δ.     

Scanning PIV investigation of the laminar separation bubble on a SD7003 airfoil

A laminar separation bubble occurs on the suction side of the SD7003 airfoil at an angle of attack α =  4–8° and a low Reynolds number less than 100,000, which brings about a significant adverse aerodynamic effect. The spatial and temporal structure of the laminar separation bubble was studied using the scanning PIV method at α =  4° and Re = 60,000 and 20,000. Of particular interest are the dynamic vortex behavior in transition process and the subsequent vortex evolution in the turbulent boundary layer. The flow was continuously sampled in a stack of parallel illuminated planes from two orthogonal views with a frequency of hundreds Hz, and PIV cross-correlation was performed to obtain the 2D velocity field in each plane. Results of both the single-sliced and the volumetric presentations of the laminar separation bubble reveal vortex shedding in transition near the reattachment region at Re = 60,000. In a relatively long distance vortices characterized by paired wall-normal vorticity packets retain their identities in the reattached turbulent boundary layer, though vortices interact through tearing, stretching and tilting. Compared with the restricted LSB at Re = 60,000, the flow at Re = 20,000 presents an earlier separation and a significantly increased reversed flow region followed by “huge” vortical structures.     

Direct and large-eddy simulations of transition in the compressible boundary layer

The transition to turbulence in the three-dimensional compressible boundary layer over a semi-infinite insulated flat plate is studied by means of direct and large-eddy simulations. Results are presented in the quasi-incompressible (Mach number equal to 0.5) and high supersonic (Mach number equal to 5) cases, both in temporal and spatial configurations. Simulations of controlled transition, in which a two-dimensional wave corresponding to the primary instability is introduced at the initial stage, allows us to study the secondary instability of the flow. The latter is triggered with the aid of a three-dimensional white-noise perturbation of small amplitude superposed upon the wave. At a low Mach number, a direct-numerical simulation shows that the fundamental mode is selected, leading to the peak-valley structure found by Klebanoff et al. (1962). The complete transition process is then studied, with emphasis on vortex-filament dynamics. It is shown that the development to turbulence is well simulated, at least for the prediction of average quantities of the flow. In the high Mach number case, no direct-numerical simulation is possible, and we use a subgrid-scale model, the structure-function model, in order to perform a large-eddy simulation of the transition. In this case, the subharmonic mode appears, giving rise to a staggered pattern of vortices. These vortices, which affect the whole thickness of the boundary layer, are more elongated than in the incompressible case.This work was supported by CNES-Avions Marcel Dassault in the frame of the Hermès program (Contract No. RDMF3/86), by DRET (Contract Nos. 87/808/11 and 88/150), and by CNRS (GDR Mécanique des Fluides Numérique and GDR Hypersonique).Unité associée CNRS.     

Near-wall flow in a three-dimensional boundary layer on the endwall of a 30° bend

 Turbulence measurements are reported on the three-dimensional turbulent boundary layer along the centerline of the flat endwall in a 30° bend. Profiles of mean velocities and Reynolds stresses were obtained down to y ⁺≈2 for the mean flow and y ⁺≈8 for the turbulent stresses. Mean velocity data collapsed well on a simple law-of-the-wall based on the magnitude of the resultant velocity. The turbulence intensity and turbulent shear stress magnitude both increased with increased three-dimensionality. The ratio of these two quantities, the a ₁ structure parameter, decreased in the central regions of the boundary layer and showed profile similarity for y ⁺<50. The shear stress vector angle lagged behind the velocity gradient vector angle in the outer region of the boundary layer, however there was an indication that the shear stress vector tends to lead the velocity gradient vector close to the wall. Received: 16 July 1996/Accepted: 14 July 1997     

The method of composite expansions applied to boundary layer problems in symmetric bending of the spherical shells

In this paper,the method of composite expansions which was proposed by W. Z. Chien (1948)[5]is extended to investigate two-parameter boundary layer problems.For the problems of symmetric deformations of the spherical shells under the action of uniformly distribution load q, its nonlinear equilibrium equations can be written as follows: where ε and δ are undetermined parameters.If δ=1 and ε is a small parameter, the above-mentioned problem is called first boundary layer problem; if ε is a small parameter, and δ is a small parameter, too, the above-mentioned problem is called second boundary layer problem.For the above-mentioned problems, however, we assume that the constants ε, δ and p satisfy the following equation: εp=1-ε In defining this condition by using the extended method of composite expansions, we find the asymptotic solution of the above-mentioned problems with the clamped boundary conditions.     

Numerical Simulation of Riblet Controlled Spatial Transition in a Zero-Pressure-Gradient Boundary Layer

To analyze the fundamental physical mechanism which determines the damping effect of a riblet surface on three-dimensional transition several numerical simulations of spatial transition in a flat plate zero-pressure-gradient boundary layer above a riblet wall are performed in this study. Two types of forced transition scenarios are investigated. The first type of transition is defined by K-type transition induced by a dominant two-dimensional Tollmien–Schlichting (TS) wave and a weak spanwise disturbance. The second type of transition is purely excited by two oblique waves. By a qualitative analysis of the occurring maximum wall-normal and spanwise velocity components and the Fourier modes of the disturbances the two-dimensional TS waves are found to be amplified by riblets, whereas three-dimensional structures, i.e., Λ-, hairpin, and streamwisely aligned vortices, are damped. At oblique transition the breakdown to turbulence is delayed by the riblets compared to transition on a clean surface. The investigation of the near wall flow structure reveals secondary flows induced by the riblets and reduced wall normal ejections as well as a reduced downwash.     

Vortex Shedding from a Hemisphere in a Turbulent Boundary Layer

Supercritical turbulent boundary layer flow over a hemisphere with a rough surface (Re= 150000) has been simulated using Large Eddy Simulation (LES) and analyzed using the Karhunen--Loève expansion (“Proper Orthogonal Decomposition,” POD). The time-dependent inflow condition is provided from a separate LES of a boundary layer developing behind a barrier fence and a set of vorticity generators. LES results using significantly different grid resolutions are compared with a corresponding wind tunnel experiment to demonstrate the reliability of the simulation. The separation processes are analyzed by inspecting second-order moments, time spectra, and instantaneous velocity distributions. Applying POD, a detailed study of the spatiotemporal structure of the separation processes has been carried out. From this analysis it can be concluded that the major event in the separated flow behind the obstacle is the shedding of “von Kármán”-type vortices, which can be represented by the first three energetically dominant modes. Received 23 January 1997 and accepted 19 February 1998     

Effect of surface steps on boundary layer transition

An experimental study has been carried out to examine the effect of a sharp-edged step on boundary layer transition. The transition position and disturbance spectra in the boundary layer for different step heights and free-stream velocities were measured by hot-wire anemometry. A correlation between the transition Reynolds number and the relative step height has been established for both backward-facing and forward-facing steps. The transition position is associated with the “N-factor” that defines the integrated growth of instability waves at transition. The boundary layer over a step has an earlier transition position than that on a smooth plate, since the instability waves amplify more rapidly than those on a smooth surface. The transition N-factor for the flow containing a step, calculated using the amplification rates on a smooth plate, will, therefore, be smaller than that on surfaces without a step. The observed reduction of the N-factor occurring with a step has been shown to correlate with the height of the step, thus, providing an empirical tool that can be used to estimate the transition position when steps occur. An appropriate value of N can be determined from knowledge of the step height.     

Near-wake flow structure downwind of a wind turbine in a turbulent boundary layer

Wind turbines operate in the surface layer of the atmospheric boundary layer, where they are subjected to strong wind shear and relatively high turbulence levels. These incoming boundary layer flow characteristics are expected to affect the structure of wind turbine wakes. The near-wake region is characterized by a complex coupled vortex system (including helicoidal tip vortices), unsteadiness and strong turbulence heterogeneity. Limited information about the spatial distribution of turbulence in the near wake, the vortex behavior and their influence on the downwind development of the far wake hinders our capability to predict wind turbine power production and fatigue loads in wind farms. This calls for a better understanding of the spatial distribution of the 3D flow and coherent turbulence structures in the near wake. Systematic wind-tunnel experiments were designed and carried out to characterize the structure of the near-wake flow downwind of a model wind turbine placed in a neutral boundary layer flow. A horizontal-axis, three-blade wind turbine model, with a rotor diameter of 13 cm and the hub height at 10.5 cm, occupied the lowest one-third of the boundary layer. High-resolution particle image velocimetry (PIV) was used to measure velocities in multiple vertical stream-wise planes (x–z) and vertical span-wise planes (y–z). In particular, we identified localized regions of strong vorticity and swirling strength, which are the signature of helicoidal tip vortices. These vortices are most pronounced at the top-tip level and persist up to a distance of two to three rotor diameters downwind. The measurements also reveal strong flow rotation and a highly non-axisymmetric distribution of the mean flow and turbulence structure in the near wake. The results provide new insight into the physical mechanisms that govern the development of the near wake of a wind turbine immersed in a neutral boundary layer. They also serve as important data for the development and validation of numerical models.     

Heat transfer characteristics of the algebraically decaying Glauert jet

The classical exponentially decaying wall jet considered independently by Tetervin (NACA TN 1644 40 pp, 1948), Akatnov (Leningrad Politek Inst Trudy 5:24–31, 1953) and Glauert (J Fluid Mech 1:625–643, 1956) as well as its algebraically decaying counterpart (which will be referred to hereafter as “algebraic Glauert Jet”, or AG-jet for short) belong to the same similarity class of solutions of the boundary layer equations. We investigate in this paper the thermal characteristics of a nonpreheated AG-jet over a permeable wall for prescribed constant wall temperature and prescribed constant heat flux. Their scaling behavior for small and large values of the Prandtl number is discussed in detail and compared to that of the classical Tetervin–Akatnov–Glauert wall jet.     

Experimental investigations of controlled transition of a laminar separation bubble in an axisymmetric diffuser

The instability of a pressure-induced laminar separation bubble is examined experimentally on an axisymmetric diffuser for a Reynolds number range 7,800 ≤ ≤ 11,400 for an inlet pipe diameter D ₁ (50 mm) and as mean input flow velocity 4.2 m/s ≤ u _m ≤ 6.1 m/s. A characterization of the base flow shows a wide-spread separation at the smooth diverging contour which gives rise to a massive amplification of instabilities. Controlled disturbances are introduced by means of a slot and a membrane actuator to trigger the transition, and the receptivity of the perturbations to the laminar boundary layer is evaluated. Different axisymmetric and azimuthal disturbances are applied in order to study their influence on the laminar–turbulent transition. The measurements show a clear dependence of the transition scenario and the reattachment length on the actuation mode.