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.     

Turbulence Modeling for the Stable Atmospheric Boundary Layer and Implications for Wind Energy

The near-surface structure of atmospheric turbulence affects the design and operation of wind turbines and is especially difficult to predict under stably-stratified conditions. This study uses large-eddy simulation (LES) to explore properties of the stable boundary layer (SBL) using an explicit filtering and reconstruction turbulence modeling approach. Simulations of the atmospheric boundary layer over flat terrain, under both moderately and strongly stable conditions are performed. Results from high-resolution simulations are used to investigate SBL flow structures including mean profiles and turbulence statistics, which are relevant to wind energy applications. The applicability of power-law relations and empirical similarity formulations for predicting wind speed depend on the strength of stratification and are shown to be inadequate. Low-level jets form in the simulations. Under strong stability, vertical wind shear below the jet triggers intermittent turbulence. The associated sporadic “bursting” events are extremely energetic and last longer than the time scale of the largest eddies. Such phenomena can have adverse effects on turbine lifetime and performance.     

Modeling the Effect of Freestream Turbulence on Unsteady Boundary Layer Flow

We present a new version of the two-equation turbulence model, which makes it possible to calculate continuously the entire flow range from laminar to turbulent, including transition, in the case of a time-periodic, high-turbulence-level freestream. The influence of the parameters characterizing the harmonic fluctuations of the external velocity and the freestream turbulence intensity and scale on the parameters of the flat-plate flow are analyzed. A comparison of the numerical solutions with the experimental and theoretical data indicates the possibility of describing the wall flow properties on the basis of a quasi-stationary turbulence model, as the Reynolds number varies from low to high values.     

Effect of Strong External Turbulence on a Wall Jet Boundary Layer

The initial stage of the development of a wall jet under the influence of strong external turbulence has been studied in a novel shear-flow mixing-box experiment. A fully developed channel flow of depth h (40 mm) enters along the top wall of a cuboidal box of height 11 h in which a combination of oscillatory and turbulent velocity fluctuations are generated by a vertical oscillating grid at the midplane 5 h below the wall. When the ratio of the rms grid-generated velocity fluctuations, , to the local mean velocity inside the wall jet layer, u, is greater than about 0.1, significant changes are observed in the mean shear profile and in the eddy structure of the wall jet. The wall jet thickness increases by approximately 25% but the maximum velocity decreases by less than 10% compared to the case without the external turbulence. Fluctuations of the streamwise velocity component increase as expected in the outer part of the wall jet, but the most significant result is the increase by 70% of the fluctuations in the boundary layer close to the wall. CFD simulations using the k-ɛ RNG of the FLUENT CFD Code do not properly model the effect of the large scale external turbulence in this experiment. However, an artificial method, which introduces a series of small inlet/outlet jets to represent external turbulence, approximately simulates the overall effects of the oscillating grid on the wall jet, but does not simulate the amplification of the near wall turbulence. F. T. M. Nieuwstadt: Rest in peace (1946–2005).     

Simulation of the Effect of the Freestream Turbulence Parameters on the Boundary Layer of a Curvilinear Airfoil

Modified variants of differential turbulence models which make it possible continuously to calculate both the entire flow region with laminar, transition and turbulent regimes and local low Reynolds number zones are proposed for investigating the flow and heat transfer in the boundary layers developing in compressible gas flow past curvilinear airfoils. The effect of the intensity and scale of free-stream turbulence and their variability along the outer boundary layer edge, as well as the combined action of the turbulence intensity and the streamwise pressure gradient in flow past blade profiles, on the heat transfer and near-wall turbulence characteristics is analyzed. The numerical results are compared with experimental and theoretical data.     

Emergence of Fluid Rotation in the Marangoni Boundary Layer in the Region of Local Cooling of the Free Boundary

Rotation bifurcation in a steady axisymmetric thermocapillary flow of an incompressible fluid filling a semi-infinite space bounded by the free surface with a nonuniform distribution of temperature is studied. The fluid flow is calculated on the basis of Navier–Stokes equations under the assumption of small diffusion coefficients. It is shown that the bifurcation triggers rotational motion in a thin Marangoni boundary layer in the case of local cooling of the free boundary near the axis of symmetry and in the presence of an external flow; there is no rotation outside this layer. In the case of local heating of the free boundary, rotation is not observed.     

Simulation of the Effect of the Freestream Turbulence Parameters on Heat Transfer in an Unsteady Boundary Layer

A variant of the two-parameter turbulence model which makes it possible continuously to calculate a flow region with laminar, transition and turbulent regimes is proposed for investigating the flow under conditions of high freestream turbulence intensity. It is shown that the properties of the thermal transition can be theoretically described using the quasi-steady turbulence model in the case of periodic freestream velocity distribution. The numerical results are compared with theoretical and experimental data. The approach proposed is developed for determining the combined effect of the parameters of harmonic fluctuations of the external velocity and freestream turbulence on the heat transfer characteristics on a flat plate with different boundary conditions for the enthalpy.     

From Streaks to Spots and on to Turbulence: Exploring the Dynamics of Boundary Layer Transition

“...an eerie type of chaos can lurk just behind a facade of order, and yet deep inside the chaos lurks an even eerier type of order.” Douglas Hofstadter Bypass transition to turbulence in boundary layers is examined using linear theory and direct numerical simulations (DNS). First, the penetration of low-frequency free-stream disturbances into the boundary layer is explained using a model problem with two time scales, namely the shear and wall-normal diffusion. The simple model provides a physical understanding of the phenomenon of shear sheltering. The second stage in bypass transition is the amplification of streaks. Streak detection and tracking algorithms were applied to examine the characteristics of the streak population inside the boundary layer, beneath free-stream turbulence. It is demonstrated that simple statistical averaging masks the wealth of streak amplitudes in transitional flows, and in particular the high-amplitude, relatively rare events that precede the onset of turbulence. The third stage of the transition process, namely the secondary instability of streaks, is examined using secondary instability analysis. It is demonstrated that two types of instability are possible: An outer instability arises near the edge of the boundary layer on the lifted, low-speed streaks. An inner instability also exists, and has the appearance of a near-wall wavepacket. The stability theory is robust, and can predict the particular streaks which are likely to undergo secondary instability and break down in transitional boundary layers beneath free-stream turbulence. Beyond the secondary instability, turbulent spots are tracked in DNS in order to examine their characteristics in the subsequent non-linear stages of transition. At every stage, we compare the findings from linear theory to the empirical observations from direct solutions of the Navier-Stokes equations. The complementarity between the theoretical predictions and the computational experiments is highlighted, and it leads to a detailed view of the mechanics of transition.     

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.     

Steady Streamwise Structures in the Boundary Layer on a Swept Wing with Elevated Turbulence of the Incoming Flow

Results for a turbulized flow past the windward side of a swept wing model are presented. Origination of steady disturbances in the form of streamwise structures is found. The greatest effect on the formation of these disturbances is exerted by the curvature of the external flow streamlines. The secondary flow in the boundary layer leads to an increase in the characteristic scale of disturbances in the transverse direction, as compared to the flow around the model at a zero yaw angle.     

Boundary Element Analysis of Vibro-Acoustic Interaction between Vibrating Membrane and Thin Fluid Layer

This paper presents a variational formulation for the study of the acoustic propagation and radiation of a vibrating membrane coupled to a cavity filled with a visco-thermal fluid. This formulation is obtained by combining a variational formulation by integral equations of both internal and external fluids, which takes account of acoustic and entropic waves coupling, with a classical variational formulation of the membrane. Numerical results obtained by this new formulation are compared to those obtained when the viscous and thermal effects are not considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

Turbulence Energy Distribution in the Stokes Layer

Using the method of matched asymptotic expansions, an analytical solution of the balance equation for turbulence energy is constructed for a shallow basin (sea) in which the fluid depth does not exceed the Stokes layer thickness. In this case, a gradient-viscous balance is established with the turbulent viscosity being balanced mainly by the pressure gradient. It is shown that nonlinear boundary layers attributable to turbulence energy diffusion are formed near the bottom and the free surface (or ice). In the neighborhood of the point of maximum flow velocity (if this maximum is attained inside the flow), a nonlinear internal boundary layer also develops. Outside these layers, the turbulence energy generation is in the first approximation balanced by the energy dissipation. Asymptotic solutions for the boundary layers are constructed.     

Transition to Turbulence in the Boundary Layer on a Plate in the Presence of a Negative Free-Stream Pressure Gradient

Transition to turbulence in the boundary layer on a flat plate is investigated numerically for an incompressible fluid flow with a given negative free-stream pressure gradient. The transition is investigated using the three-parameter turbulence model developed by the authors. The calculation results are compared with the available experimental data.     

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.     

Unsteady Free Convection Boundary Layer Flows of a Bingham Fluid in Cylindrical Porous Cavities

Transport in Porous Media - We consider two unsteady free convection flows of a Bingham fluid when it saturates a porous medium contained within a vertical circular cylinder. The cylinder is...     

The Onset of Fluid Rotation in a Thermogravitational Boundary Layer with Local Cooling of the Free Surface

Axisymmetric regimes of flows of an inhomogeneous fluid in the boundary layer near a free surface are calculated for a nonuniform temperature distribution on this surface. For the fluid motion equations written in the Oberbeck-Boussinesq approximation, the leading terms of asymptotic expansions of solutions of a steady-state problem are constructed. It is shown that in the presence of local cooling of the free surface and a rising outer fluid stream, as a result of a bifurcation, a pair of rotational regimes may develop in a thin boundary layer near the free surface, with no rotation observed outside this layer. No bifurcation of rotation was detected in the case of local heating of the free surface.     

Universal Velocity Defect Law for the Turbulent Boundary Layer

Turbulent plane boundary layer flows of an incompressible fluid are considered. A refinement of the known Coles wake law is proposed. This refinement makes it possible to ensure the smooth matching of the turbulent boundary layer velocity profile with the outer flow and to extend the range of validity of the law to the case of large positive pressure gradients. The accuracy of the analytical approximation obtained is verified by comparison with the known experimental equilibrium velocity profiles. Using the approximation proposed, a relation for calculating the cross-sectional distribution of the Reynolds stress in the equilibrium boundary layer is derived. The pressure distributions for which the equilibrium turbulent boundary layer flows are single- and two-valued are distinguished.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 89–101.Original Russian Text Copyright © 2005 by Mikhailov.     

Almost Global Existence for the Prandtl Boundary Layer Equations

We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H¹ space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within \({\varepsilon}\) of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time \({T_{\varepsilon} \geqq {\rm exp}(\varepsilon^{-1} / {\rm log}(\varepsilon^{-1}))}\).