Effect of the freestream turbulence scale and the leading edge shape on boundary layer laminar-turbulent transition

The effect of the leading edge shape and the turbulence scale on laminar-turbulent transition in the flat-plate boundary layer due to grid turbulence is investigated. In the experiments, the turbulence scale was changed by a factor of three and the bluntness radius of the edge by a factor of four, all other factors being fixed. It is shown that on the plate with a sharp edge the fluctuation growth rate and the laminar-turbulent transition point depend nonmonotonically on the turbulence scale. On the blunt plate transition occurs considerably earlier than on the sharp plate.     

Numerical Modeling of the Development of a Streaky Structure in a Boundary Layer at a High Freestream Turbulence Level

The disturbances generated by external turbulence in the boundary layer on a flat plate set suddenly in motion are determined. A turbulent flow calculated by direct numerical simulation is taken as the initial conditions. The solution obtained simulates the initial stage of laminar-turbulent transition in the flat-plate boundary layer at a high turbulence level in the oncoming flow. The solution makes it possible to estimate the effects of different factors, such as nonstationarity, nonlinearity, and the parameters of the freestream velocity fluctuation spectrum, on disturbance enhancement in the boundary layer.     

Statistical description of laminar-turbulent transition in a boundary layer at high freestream turbulence degree

The statistical approach is applied to calculate the intermittence coefficient in boundarylayer laminar-turbulent transition due to external turbulence. It is assumed that turbulent regions in the boundary layer are associated with the appearance of turbulent spots generated by the secondary instability of streaky structures that have reached a threshold amplitude. An universal dependence of the intermittence coefficient in the transition region on the velocity fluctuation amplitude and the Reynolds number is obtained. It describes well the experimental results.     

Receptivity of the inclined-cylinder attachment-line boundary layer to vortex perturbations

The receptivity of the boundary layer in the neighborhood of the attachment line of a cylinder inclined to the flow with respect to periodic vortex perturbations frozen into the stream is investigated. The problem considered simulates the interaction between external turbulence and the leading-edge swept wing boundary layer. It is shown that if the direction of the external perturbation vector is almost parallel to the leading edge, then the external perturbations are considerably strengthened at the outer boundary layer edge. This effect can cause laminar-turbulent transition on the attachment line at subcritical Reynolds numbers.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 72–85. Original Russian Text Copyright © 2004 by Ustinov.     

NUMERICAL STUDY OF LOCAL BOUNDARY LAYER RECEPTIVITY TO FREESTREAM VORTICAL DISTURBANCES

IntroductionTheproblemofhowthedisturbancesinthefreestream ,suchassoundwaveandvorticesetc .,excitethedisturbancewavesintheboundarylayeriscalledreceptivityproblem[1,2 ].Throughthiscoursetheinitialconditionsofdisturbance,suchasitsamplitude,frequency ,andphasearedetermined .ThedispersionrelationsoffreestreamdisturbancesaredifferentfromthoseofT_Swaves.Asaresult,suchdisturbancesaloneinthefreestreamdonotexciteT_Swavesinboundarylayer.But,whentheperiodicdisturbancesinboundarylayerforcedbyfreestreamdi…     

Receptivity of the Flat-Plate Boundary Layer to Free-Stream Turbulence

The linear problem of generation of perturbations of a flat-plate boundary layer by external turbulence is solved. The turbulence is represented in the form of a set of space- and time-periodic vortex modes. It is shown that the boundary layer is most receptive to low-frequency longitudinal vorticity modes. The mean-square velocity fluctuations in the boundary layer and their spectrum are found for isotropic turbulence with a spectrum satisfying the Kolmogorov-Obukhov law.     

STUDY OF MECHANISM OF BREAKDOWN IN LAMINARTURBULENT TRANSITION OF SUPERSONIC BOUNDARY LAYER ON FLAT PLATE

Spatial mode direct numerical simulation has been applied to study the mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate with Mach number 4.5. Analysis of the result showed that, during the breakdown process in laminar-turbulent transition, the mechanism causing the mean flow profile to evolve swiftly from laminar to turbulent was that the modification of mean flow profile by the disturbance, when they became larger, leads to remarkable change of its stability characteristics. Though the most unstable T-S wave was of second mode for laminar flow, the first mode waves played the key role in the breakdown process in laminar-turbulent transition.     

Universal threshold of the transition to localized turbulence in shear flows

Experimental and numerical studies have shown similarities between localized turbulence in channel and pipe flows. By scaling analysis of a disturbed-flow model, this paper proposes a local Reynolds number Re_M to characterize the threshold of transition triggered by finite-amplitude disturbances. The Re_M represents the maximum contribution of the basic flow to the momentum ratio between the nonlinear convection and the viscous diffusion. The lower critical Re_M observed in experiments of plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow are all close to 323, indicating the uniformity of mechanism governing the transition to localized turbulence.     

Response of the boundary layer developing over a blunt-nosed flat plate to free-stream non-uniformities

The response of the boundary layer on a flat plate with blunt nose to infinitesimally small non-uniformity in the freestream velocity along the span has been studied. The non-uniformity was shown to excite boundary-layer disturbances similar to streaks or Klebanoff modes generally observed in experiments conducted with a high level of free-stream turbulence. The boundary layer disturbances have a predominantly streamwise velocity component and exhibit transient growth. In contrast to streaks generated by streamwise vortices impinging on the sharp nose of a plate, the disturbances produced by free-stream non-uniformity interaction with a blunt nose have a different level of growth. Their maximal amplification scales with the Reynolds number, based on the size of nose bluntness and is almost independent of the spanwise period of disturbances. This difference was shown to be caused by additional amplification of disturbances via vortex lines stretching around the leading edge.     

Particle-turbulence interaction in a boundary layer

Particle-turbulence interaction in wall turbulent flows has been studied. A series of experiments varying particle size, particle density, particle loading and flow Re has been conducted. The results show that the larger polystyrene particles (1100 μm) cause an increase in the number of wall ejections, giving rise to an increase in the measured values of the turbulence intensities and Reynolds stresses. On the other hand, the smaller polystyrene particles (120 μm) bring about a decrease in the number of wall ejections, causing a decrease in the measured intensities and Reynolds stresses. These effects are enhanced as the particle loading is increased. It was also found that the heavier glass particles (88 μm) do not bring about any significant modulation of turbulence. In addition, measurements of the burst frequency and the mean streak-spacing show no significant change with increase in particle loading. Based on these observations, a mechanism of particle transport in wall turbulent flows has been proposed, in which the particles are transported (depending on their size, density and flow Re) by the bursting events of the wall regions.     

Laminar-turbulent transition in the boundary layer on cones in a hypersonic flow at high Reynolds numbers per meter

The laminar-turbulent transition is experimentally studied in boundary-layer flows on cones with a rectangular axisymmetric step in the base part of the cone and without the step. The experiments are performed in an A-1 two-step piston-driven gas-dynamic facility with adiabatic compression of the working gas with Mach numbers at the nozzle exit M _∞ = 12–14 and pressures in the settling chamber P₀ = 60–600 MPa. These values of parameters allow obtaining Reynolds numbers per meter near the cone surface equal to Re _1e = (53–200) · 10⁶ m ⁻¹. The transition occurs at Reynolds numbers Re _tr = (2.3–5.7) · 10⁶. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 76–83, May–June, 2007.     

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.     

Investigation of the heat transfer and Reynolds analogy in a turbulent boundary layer at a high freestream turbulence level

The results of a systematic experimental study of the flow turbulence level effect on the heat transfer and Reynolds analogy coefficients over a wide range of the relevant parameters (the turbulence intensity and scale and the Reynolds number) are presented. The notion of the equivalent flow turbulence, which unifies the above-mentioned parameters, is introduced. It is established that the skin friction and heat transfer coefficients increase with the equivalent turbulence, while the Reynolds analogy coefficient remains unchanged. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 61–71, January–February, 2000.     

Linear stability of three-dimensional boundary layers

Stability of compressible three-dimensional boundary layers on a swept wing model is studied within the framework of the linear theory. The analysis based on the approximation of local self-similarity of the mean flow was performed within the Falkner-Skan-Cooke solution extended to compressible flows. The calculated characteristics of stability for a subsonic boundary layer are found to agree well with the measured results. In the case of a supersonic boundary layer, the results calculated for a Mach number M = 2 are also in good agreement with the measured spanwise scales of nonstationary vortices of the secondary flow. The calculated growth rates of disturbances, however, are substantially different from the measured values. This difference can be attributed to a high initial amplitude of disturbances generated in the experiment, which does not allow the linear stability theory to be applied. The evolution of natural disturbances with moderate amplitudes is fairly well predicted by the theory. The effect of compressibility on crossflow instability modes is demonstrated to be insignificant. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 3–14, March–April, 2008.     

Numerical modeling of perturbation propagation in a supersonic boundary layer

The growth of two-dimensional disturbances generated in a supersonic (M = 6) boundary layer on a flat plate by a periodic perturbation of the injection/suction type is investigated on the basis of a numerical solution of the Navier-Stokes equations. For small initial perturbation amplitudes, the second-mode growth rate obtained from the numerical modeling coincides with the growth rate calculated using linear theory with account for the non-parallelism of the main flow. Calculations performed for large initial perturbation amplitudes reveal the nonlinear dynamics of the perturbation growth downstream, with rapid growth of the higher multiple harmonics.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 33–44. Original Russian Text Copyright © 2004 by Egorov, Sudakov, Fedorov.     

Dynamical characteristics of coherent structure in the outer region of turbulence boundary layer

In the present paper the coherent structures in the outer region of turbulent boundary layer were investigated experimentally and analytically. From the observation of the flow field over smooth wall, rough wall and sand wave wall, it was found that the direct effect of wall on the flow structure can reachy ⁺¹≈100, and both lateral and vertical vortices exist in the outer region, but the coherent structures in the outer region are mainly the formation, development and decay of the large-scale lateral vortices. By experimental and dynamical analysis, some influence factors and their relations associated with the dynamical process of lateral vortices were deduced. The project supported by the National Natural Science Foundation of China     

Traveling disturbance appearing in boundary layer transition in a Yawed cylinder

Boundary layers that develop over a body in fluid flow are in most cases three-dimensional owing to the spin, yaw, or surface curvature of the body. Therefore, the study of three-dimensional (3D) boundary-layer transition is essential to work in practical aerodynamics. The present investigation is concerned with the problem of 3D boundary layers over a yawed body. A yawed cylinder model that represents the leading edge portion of a swept wing and the mechanism of crossflow instability are investigated in detail using hot-wire velocimetry and a flow visualization technique. As a result, traveling disturbances having frequencies f₁ and f₂, which differ by about one order of magnitude, are detected in the transition region. The phase velocities and directions of travel of those disturbances are measured. Results for the low-frequency disturbance f₁ show qualitative coincidence with results numerically predicted for a crossflow unsteady disturbance. Nameley, F₁ travels nearly spanwise to the yawed cylinder and very close to the cylinder wall. The results for the high-frequency disturbance f₂ good agreement with the existing experimental results. The ₂ disturbance is found to be the high-frequency inflectional secondary instability that appears in 3D boundary layer transition in general. A two-stage transition process, where stationary crossflow vortices appear as the primary instability and a traveling inflectional disturbance is generated as a secondary instability, was observed. Secondary instability seems to play a major role in turbulent transition.     

Investigating flow topologies in boundary layer transition using direct numerical simulation

A numerical method developed for simulating three-dimensional incompressible boundary layer flow is presented. K-type transition up to the two-spike stage is simulated, and flow topologies at various stages of transition are determined. Comparison with flow topologies from other simulations of turbulent and transitioning flows is made. Financial support provided by Air Operations Division, Aeronautical and Maritime Research Laboratory, Defence Science and Technology Organisation, Australia.