An experimental study on boundary layer transition detection over a pitching supercritical airfoil using hot-film sensors

In the present work, experimental tests are conducted to study boundary layer transition over a supercritical airfoil undergoing pitch oscillations using hot-film sensors. Tests have been undertaken at an incompressible flow. Three reduced frequencies of oscillations and two mean angles of attack are studied and the influences of those parameters on transition location are discussed. Different algorithms are examined on the hot-film signals to detect the transition point. Results show the formation of a laminar separation bubble near the leading edge and at relatively higher angles of attack which leads to the transition of the boundary layer. However, at lower angles of attack, the amplification of the peaks in voltage signal indicate the emergence of the vortical structures within the boundary layer, introducing a different transition mechanism. Moreover, an increase in reduced frequency leads to a delay in transition onset, postponing it to a higher angle of attack, which widens the hysteresis between the upstroke and downstroke motions. Rising the reduced frequency yields in weakening or omission of vortical disturbances ensuing the removal of spikes in the signals. Of the other important results observed, is faster movement of the relaminarization point in the higher mean angle of attack. Finally, a time–frequency analysis of the hot-film signals is performed to investigate evolution of spectral features of the transition due to the pitching motion. An asymmetry is clearly observed in frequency pattern of the signals far from the bubble zone towards the trailing edge; this may reflect the difference between the transition and relaminarization physics. Also, various ranges of frequency were obtained for different transition mechanisms.     

Dynamics of low-speed streak evolution and interaction in laminar boundary layer

The present paper presents an experimental effort on the regeneration process of two low-speed laminar streaks in a zero-pressure-gradient laminar boundary layer. Two vertical thin wires separated by a spanwise distance of 30 mm are used to introduce disturbances of two rolls of transitional Karmain vortex street to the downstream boundary layer. Both hydrogen bubble visualization and particle image velocimetry （PIV） measurement show that two lowspeed streaks are induced through leading-edge receptivity process. As these streaks develop in the downstream, two additional low-speed streaks begin to appear outboard of the flank of the original two, together with complex dynamics of streak splitting and merging. A flow pattern of four streaks aligned along the spanwise direction occurs finally in the far downstream. It is found that besides the mechanisms of streak breakdown, the streak interaction is also an important factor characterizing the instability of low speed streaks and their regeneration process.     

On the numerical computation of laminar boundary layers at a phase-changing,gas-liquid interface

The two-dimensional, laminar boundary-layer equations of heat, mass and momentum at a smooth, phase-changing, gas-liquid interface are solved numerically by the Keller Box method. The gas and liquid regimes are embedded in a single marching scheme which computes interfacial parameters implicitly. Results of both self-similar and non-similar boundary-layer computations are presented and effects of mild pressure gradient, a mean current in the liquid, and free-stream vapour concentration on the interfacial parameters are analysed. In order to assess the accuracy of the method, several self-similar problems are solved by Runge-Kutta integration and results are compared to those obtained by the finite-difference scheme. Agreement is excellent in all cases.     

A parametric study of LES on laminar-turbulent transitional flows past an airfoil

Low-Reynolds-number aerodynamic performance of small-sized air vehicles is an area of increasing interest. In this study, low-Reynolds-number flows past an SD7003 airfoil are investigated to understand important viscous features of laminar separation and transitional flow followed by the complicated behavior of the flow reattachment process. In order to satisfy the three-dimensional (3D) requirement of the code, a simple “3D wing” is constructed from a two-dimensional (2D) airfoil. A parametric study of large eddy simulation (LES) on the airfoil flows at Re = 60,000 is performed. Effects of grid resolution and sub-grid scale (SGS) models are investigated. Although 3D effects cannot be accurately captured owing to the limitation of the grid resolution in the spanwise direction, the preliminary LES calculations do reveal some important flow characteristics such as leading-edge laminar separation and vortex shedding from the primary laminar separation bubble on the low-Reynolds-number airfoil.     

Incompressible laminar 2D steady thermal boundary layers with temperature-dependent kinematic viscosity and thermal diffusivity

We prove that the incompressible 2D steady thermal boundary layer equations with temperature-dependent kinematic viscosity ν and thermal diffusivity α is maximally symmetric provided the Prantl number Pr=ν/α is constant and or ν=K₂(AT+B)^K₁ if we neglect energy dissipation and if we take into account dissipation. This result corroborates assumptions often made in applications. When we disregard dissipation, the symmetry Lie algebra assumes the forms L^r⊕L^∞, where L^∞ is an infinite-dimensional Lie algebra and L^r is an r-dimensional Lie algebra with r∈{3,4,5,6}. If we include dissipation, r∈{2,3}. We notice that dissipation has a symmetry breaking effect.We also show how the symmetries can be employed for the calculation of invariant solutions.     

Active compliant wall for skin friction reduction

In order to reduce skin friction drag, an active laminarisation method is developed. Laminar-turbulent boundary layer transition caused by Tollmien–Schlichting (TS) waves is delayed by attenuation of these convective instabilities. An actively driven compliant wall is integrated as part of a wing’s surface. Different configurations of piezo-based actuators are combined with an array of sensitive surface flow sensors. Wall-normal actuation as well as inclined wall displacement are investigated. Together with a realtime-control strategy, transition onset is shifted downstream by six average TS-wave lengths. Using the example of flow velocity, the influence of variable flow conditions on TS-damping rates was investigated. Besides, the boundary layer flow downstream of the active wall area as well as required wall deflections and the global damping effect on skin friction are presented in this paper.     

Viscous boundary layers in flows through a domain with permeable boundary

The effect of small viscosity on nearly inviscid flows of an incompressible fluid through a given domain with permeable boundary is studied. The Vishik–Lyusternik method is applied to construct a boundary layer asymptotic at the outlet in the limit of vanishing viscosity. Mathematical problems with both consistent and inconsistent initial and boundary conditions at the outlet are considered. It is shown that in the former case, the viscosity leads to a boundary layer only at the outlet. In the latter case, in the leading term of the expansion there is a boundary layer at the outlet and there is no boundary layer at the inlet, but in higher order terms another boundary layer appears at the inlet. To verify the validity of the expansion, a number of simple examples are presented. The examples demonstrate that asymptotic solutions are in quite good agreement with exact or numerical solutions.     

Group theoretical analysis and similarity solutions for stress boundary layers in viscoelastic flows

Lie group theory is used to obtain point symmetries of the boundary layer equations derived in the literature for the high Weissenberg number flow of upper convected Maxwell (UCM) and Phan-Tien-Tanner (PTT) type of viscoelastic fluids. The equations are reduced to ordinary differential equation systems with the use of scaling and spiral transformation groups. Similarity solutions are obtained and discussed for different cases such as flow around corners, flow over moving and stretching walls, and exponential shear flows.     

A spectral collocation method for compressible,non-similar boundary layers

An efficient and highly accurate algorithm based on a spectral collocation method is developed for numerical solution of the compressible, two-dimensional and axisymmetric boundary layer equations. The numerical method incorporates a fifth-order, fully implicit marching scheme in the streamwise (timelike) dimension and a spectral collocation method based on Chebyshev polynomial expansions in the wall-normal (spacelike) dimension. The discrete governing equations are cast in residual form and the residuals are minimized at each marching step by a preconditioned Richardson iteration scheme which fully couples energy, momentum and continuity equations. Preconditioning on the basis of the finite difference analogues of the governing equations results in a computationally efficient iteration with acceptable convergence properties. A practical application of the algorithm arises in the area of compressible linear stability theory, in the investigation of the effects of transverse curvature on the stability of flows over axisymmetric bodies. The spectral collocation algorithm is used to derive the non-similar mean velocity and temperature profiles in the boundary layer of a ‘fuselage’ (cylinder) in a high-speed (Mach 5) flow parallel to its axis. The stability of the flow is shown to be sensitive to the gradual streamwise evolution of the mean flow and it is concluded that the effects of transverse curvature on stability should not be ignored routinely.     

Applications of parabolized stability equation for predicting transition position in boundary layers

The phenomenon of laminar-turbulent transition exists universally in nature and various engineering practice.The prediction of transition position is one of crucial theories and practical problems in fluid mechanics due to the different characteristics of laminar flow and turbulent flow.Two types of disturbances are imposed at the entrance,i.e.,identical amplitude and wavepacket disturbances,along the spanwise direction in the incompressible boundary layers.The disturbances of identical amplitude are consisted of one two-dimensional(2D) wave and two three-dimensional(3D) waves.The parabolized stability equation(PSE) is used to research the evolution of disturbances and to predict the transition position.The results are compared with those obtained by the numerical simulation.The results show that the PSE method can investigate the evolution of disturbances and predict the transition position.At the same time,the calculation speed is much faster than that of the numerical simulation.     

Non-equilibrium,nonlinear critical layers in laminar-turbulent transition

We describe some recent developments of high-Reynolds-number asymptotic theory for the nonlinear stage of laminar-turbulent transition in nearly parallel flows. The classic weakly nonlinear theory of Landau and Stuart is briefly revisited with the dual purposes of highlighting its fundamental ideas, which continue to underlie much of current theoretical thinking, as well as its difficulty in dealing with unbounded flows. We show that resolving such a difficulty requires an asymptotic approach based on the high-Reynolds-number assumption, which leads to a nonlinear critical-layer theory. Major recent results are reviewed with emphasis on the non-equilibrium effect. Future directions of investigation are indicated.     

Effects of T-S wave amplitude on the control of boundary layer transition bystreaks

The effects of streaks on boundary layer transition depend on the initial amplitude of T-S waves introducedto excite the transition. This problem was studied in a flat-plate boundary layer in water tunnel byusing hydrogen bubble method. Three T-S wave initial amplitudes were tested. The results show thatboth narrow and wide-spacing streaks depress the transition excited by T-S waves with lower initialamplitude. However, when transition is excited by T-S waves of higher initial amplitude, thenarrow-spacing streaks depress the transition, while the wide-spacing streaks promote thetransition. Further the underlying mechanisms were also analyzed.     

Turbulent spots in boundary layers in a free-piston shock-tunnel flow

In this paper, experiments to detect turbulent spots in the transitional boundary layers, formed on a flat plate in a free-piston shock tunnel flow, are reported. Experiments indicate that thin-film heat-transfer gauges are suitable for identifying turbulent-spot activity and can be used to identify parameters such as the convection rate of spots and the intermittency of turbulence.     

Turbulence structure in non-equilibrium boundary layers with favorable and adverse pressure gradients

An experimental study was conducted to document the turbulence in boundary layers on smooth walls subject to a favorable pressure gradient followed by a zero pressure gradient recovery and an adverse pressure gradient. Two component velocity profiles were acquired along the spanwise centerline of the test section, and velocity fields were obtained at the same locations in streamwise wall-normal and streamwise–spanwise planes using PIV. The FPG was shown to reduce the turbulence in the outer part of the boundary layer, reducing the transport of this turbulence and the effect of sweeps toward the wall. This reduced the inclination angle of the large structures and increased their length scale, particularly in the streamwise and spanwise directions. Recovery from the FPG to a ZPG was rapid. The APG reduced the near wall shear, resulting in a reduced effect of ejections relative to sweeps. The APG had an opposite but smaller effect on the shape and size of structures compared to the FPG.     

A visual study on complex flow structures and flow breakdown in a boundary layer transition

A visualization study is conducted on the excited laminar-turbulent transition within a flat plate boundary layer flow in a water tunnel. The hydrogen bubble technique is employed to investigate the complex characteristics of the flow structure and its breakdown in the later stages of the transition. A new flow structure is observed, which involves two secondary hairpin vortices outboard of both legs of a primary hairpin vortex. This complex structure is argued to be a precursor of a turbulent spot in this K-type transition. Also reported in the paper is the evolution of the flow structure and its subsequent breakdown, manifested by the emergence of dark spots, low-speed fluid bumps, and near-wall hairpin vortex groups. The results indicate that the near-wall flow breakdown is the result of instability of a local three-dimensional high-shear layer between the low-speed fluid bump and the outer higher-speed region.     

Transient flow rate behaviour in an external natural convection boundary layer

A theoretical approach is proposed to investigate the transient dynamic behaviour of a free convection boundary layer-type flow. The set of continuity, momentum and energy equations are solved with the classical Boussinesq approximation using the Karman–Pohlhausen integral method. Applying a step variation of the uniform heat flux on a vertical wall, the boundary layer thickness and velocity profiles within the viscous layer, streamline patterns and volumetric flow rate are evaluated as a function of time. In addition, corresponding fully analytical asymptotic solutions are derived to be readily used in engineering applications.     

Elementary solutions for streaky structures in boundary layers with and without suction

The temporal evolutions of small, streamwise elongated disturbances in the asymptotic suction boundary layer (ASBL) and the Blasius boundary layer (BBL) are compared. In particular, initial perturbations localized (δ-functions) in the wall-normal direction are studied, corresponding to an axi-symmetric jet coming out of a plane parallel to the flat plate. Analytical solutions are presented for the wall-normal and streamwise velocities in the ASBL case whereas both analytical and numerical methods are used for the BBL case. The initial position of the perturbation and its spanwise wave number are varied in a parameter study. We present results of maximum amplitudes obtained, the time to reach them, their position and optimal spanwise scales. Free-stream disturbances are shown to migrate towards the wall and reach their (negative) optimum inside the boundary layer. The migration is faster for the ASBL case and a larger amplitude is reached than for the BBL. For perturbations originating inside the boundary layer the amplitudes are overall larger and show the phenomenon of overshoot, i.e. positive amplitudes moving out of the boundary layer. The overall largest amplitudes are obtained for the BBL case, as in other studies, but it is shown that for free-stream disturbances initiated somewhere downstream the leading edge streak growth may be amplified due to suction since in the BBL the disturbance mainly advects above the boundary layer.     

The numbers of jump layers of boundary value problems in quasilinear differential equations

This paper discusses the numbers of jump layers of boundary value problems in quasilinear differential equations. In addition, the paper gives several examples to explain why the original equation must be rediscussed when the determinate function in reference [1] is always equal to zero.     

The structures of turbulent boundary layer in the vicinity of separation

Large coherent structures of turbulent boundary layer in the vicinity of separation were observed in a water channel by the hydrogen bubble method. Motion pictures of the de views were taken. The features of the instantaneous velocity profiles, the large transverse and streamwise vortices were discussed.     

Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet

An analysis is made for the steady mixed convection boundary layer flow near the two-dimensional stagnation-point flow of an incompressible viscous fluid over a stretching vertical sheet in its own plane. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the stagnation-point. Two equal and opposite forces are impulsively applied along the x-axis so that the wall is stretched, keeping the origin fixed in a viscous fluid of constant ambient temperature. The transformed ordinary differential equations are solved numerically for some values of the parameters involved using a very efficient numerical scheme known as the Keller-box method. The features of the flow and heat transfer characteristics are analyzed and discussed in detail. Both cases of assisting and opposing flows are considered. It is observed that, for assisting flow, both the skin friction coefficient and the local Nusselt number increase as the buoyancy parameter increases, while only the local Nusselt number increases but the skin friction coefficient decreases as the Prandtl number increases. For opposing flow, both the skin friction coefficient and the local Nusselt number decrease as the buoyancy parameter increases, but both increase as Pr increases. Comparison with known results is excellent.