Transient growth in the asymptotic suction boundary layer

In the present experimental setup, the transient disturbance growth in a spatially invariant boundary layer flow, i.e., the asymptotic suction boundary layer (ASBL), has been investigated. The choice of the ASBL brings along several advantages compared with an ordinary spatially growing boundary layer. A unique feature of the ASBL is that the Reynolds number (Re) can be varied without changing the boundary layer thickness, which in turn allows for parameter variations not possible to carry out in traditional boundary layer flows. A spanwise array of discrete surface roughness elements was mounted on the surface to trigger modes with different spanwise wavenumbers (β). It is concluded that for each mode there exists a threshold roughness Reynolds number (Re _k ), below which no significant transient growth is present. The experimental data suggests that this threshold Re _k is both a function of β and Re. An interesting result is that the energy growth curves respond differently to a change in Re _k when caused by a change in roughness height k, implying that Re remains constant, compared with a change in the free-stream velocity U_￥U_\infty, which also affects the Re. The scaling of the energy growth curves both in level and the downstream direction is treated and appropriate scalings are found. The result shows a complex non-linear receptivity mechanism. Optimal perturbation theory, which has failed to predict the energy evolution in growing boundary layers, is tested for the ASBL and shows that it may satisfactorily predict the evolution of all transiently growing modes that are triggered by the roughness elements.     

Numerical modeling of turbulent boundary layer suction

For the problem of gas suction from the turbulent flow over a plate, the results of numerically solving the Navier-Stokes equations complemented by a differential model of turbulence are presented. On the range of Mach numbers from 0.8 to 1, the effect of suction of various intensities on the flow parameters in the neighborhood of the suction region and downstream is considered.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 45–49, November–December, 1996.     

Stability of the asymptotic boundary layer with suction against finite-amplitude perturbations

A single-harmonic analysis is made of the nonlinear stability of the asymptotic boundary layer with suction. The critical values of the parameters are found, and an analysis is made of the shape of the neutral surface and the profiles of the average and the pulsation velocities as compared with experimental results.Translated from Izvestiya Akadeiaii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 140–143, May–June, 1980.I thank M. A. Gol'.dshtik and V. N. Shtern for interest in the work and for discussing the results.     

The restoration coefficient and Reynolds analogy in a boundary layer with injection and suction over the entire Prandtl number range

The restoration and Reynolds analogy coefficients are calculated for a laminar self-similar boundary layer on a permeable plate over the entire possible range of variation in the Prandtl number and the injection and suction parameter.     

Combined influence of the Reynolds number and localised wall suction on a turbulent boundary layer

This paper considers the effect the Reynolds number has on a turbulent boundary layer that is subjected to concentrated suction, applied through a short porous wall strip. The response of the skin friction coefficient to suction is strongly modulated by the momentum thickness Reynolds number R ₀. The magnitude and wavelength of the variation of the skin friction decrease as R ₀ increases. Measurements clearly show that it is the combination of R ₀ and the suction rate that controls the boundary layer response. Relaminarisation of the near-wall flow, which occurs just downstream of the suction strip when =5.5 and R ₀=660, could not be achieved at higher Reynolds numbers. It is suggested that the ratio R ₀/ should not exceed a (as yet undetermined) critical value if pseudo-relaminarisation is to occur. The mean velocity profiles differ from the undisturbed profile for all the values of R ₀ and considered here. Although the redistribution of the turbulent kinetic energy among the normal Reynolds stresses is affected by , a variation in R ₀ does not appear to alter the effect of on this redistribution.     

Influence of localised double suction on a turbulent boundary layer

The effects of localised suction applied through a pair of porous wall strips on a turbulent boundary layer have been quantified through the measurements of mean velocity and Reynolds stresses. The results indicate that the use of second strip extends the pseudo-relaminarisation zone but also reduces the overshoot in the longitudinal and normal r.m.s. velocities. While the minimum r.m.s. occurs at x/δ_o=3.0 (one strip) and x/δ_o=12 (two strips), the reduction observed for the latter case is larger. Relative to no suction, the turbulence level is modified by suction and the effect is enhanced with double suction. This increased effectiveness reflects the fact that the second strip acts on a boundary layer whose near-wall active motion has been seriously weakened by the first strip.     

LDA measurements in low Reynolds number turbulent boundary layer

LDA measurements of the mean velocity in a low Reynolds number turbulent boundary layer allow a direct estimate of the friction velocity U from the value of /y at the wall. The trend of the Reynolds number dependence of / is similar to the direct numerical simulations of Spalart (1988).     

Similarity solutions of Prandtl mixing length modelled two dimensional turbulent boundary layer equations

The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, for two dimensional turbulent boundary layers, no Blasius type similarity solutions (special exact solutions) have ever been found. In the light of Blasius’ pioneer works, we extend Blasius similarity transformation to the two dimensional turbulent boundary layers, and for a special case of flow modelled by Prandtl mixing-length, we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation. The ordinary differential equation is numerically solved and some useful quantities are produced. For numerical calculations, a complete Maple code is provided.     

High Reynolds number thick axisymmetric turbulent boundary layer measurements

Experimental measurements of the wall shear stress and momentum thickness for thick axisymmetric turbulent boundary layers are presented. The use of a full-scale towing tank allowed zero pressure gradient turbulent boundary layers to be developed on cylinders with diameters of 0.61, 0.89, and 2.5 mm and lengths ranging from 30 m to 150 m. Moderate to high Reynolds numbers (10⁴<Re <10⁵, 10⁸<Re _L<10⁹) are considered. The relationship between the mean wall shear stress, cylinder diameter, cylinder length, and speed was investigated, and the spatial growth of the momentum thickness was determined. The wall shear stress is significantly higher, and the spatial growth of the boundary layers is shown to be lower than for a comparable flat-plate case. The mean wall shear stress exhibits variations with length that are not seen in zero pressure gradient flat plate turbulent boundary layers. The ratio of outer to inner boundary layer length scales is found to vary linearly with Re , which is qualitatively similar to a flat plate turbulent boundary layer. The quantitative effect of a riblet cylindrical cross-sectional geometry scaled for drag reduction based on flat plate criteria was also measured. The flat plate criteria do not lead to drag reduction for this class of boundary layer shear flows.List of symbols a cylinder radius, mm - A _s total cylindrical surface area, m² - C _d tangential drag coefficient - D drag force, Newtons - boundary layer thickness, mm - * displacement thickness, mm - h riblet height, mm - L cylinder length, m - kinematic viscosity, m²/s - momentum thickness, mm - fluid density, kg/m³ - r radial coordinate, mm - Re _L Reynolds number based on length= - Re Reynolds number based on momentum thickness= - s riblet spacing, mm - _w mean wall shear stress, N/m² - u(r) mean streamwise velocity, m/s - u friction velocity= - U _o tow speed, m/s - x streamwise coordinate, m     

Influence of the distribution of suction on the structure of the turbulent boundary layer

In this paper we present the results of an investigation of the influence of distributed suction on the structure of a turbulent boundary layer in an aqueous medium. It is shown that with increasing suction rate, the completeness of the profile increases while the pulsation intensity of the longitudinal velocity component decreases.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 127–129, May–June, 1969.     

Low Reynolds number axisymmetric turbulent boundary layer on a cylinder

In the present study, an axisymmetric turbulent boundary layer growing on a cylinder is investigated experimentally using hot wire anemometry. The combined effects of transverse curvature as well as low Reynolds number on the mean and turbulent flow quantities are studied. The measurements include the mean velocity, turbulence intensity, skewness and flatness factors in addition to wall shear stress. The results are presented separately for the near wall region and the outer region using dimensionless parameters suitable for each case. They are also compared with the results available in the open literature.The present investigation revealed that the mean velocity in near wall region is similar to other simple turbulent flows (flat plate boundary layer, pipe and channel flows); but it differs in the logarithmic and outer regions. Further, for dimensionless moments of higher orders, such as skewness and flatness factors, the main effects of the low Reynolds number and the transverse curvature are present in the near wall region as well as the outer region.     

Interaction of an oscillating vortex with a turbulent boundary layer

An oscillating vortex embedded within a turbulent boundary layer was generated experimentally by forcing a periodic lateral translation of a half-delta wing vortex generator. The objective of the experiment was to investigate the possibility that a natural oscillation, or meander, might be responsible for flattened vortex cores observed in previous work, which could also have contaminated previous turbulence measurements. The effect of this forced oscillation was characterized by comparison of measurements of the mean velocities and Reynolds stresses at two streamwise stations, for cases with and without forcing. The Reynolds stresses, especially w, were affected significantly by the forced oscillation, mainly through contributions from the individual production terms, provided the vortex was not too diffuse.List of Symbols a amplitude of forced vortex motion - f frequency of forced vortex generator motion - l vortex generator root chord - L flow length scale - R _Y , R _Z vortex core radial dimensions in vertical and spanwise directions, respectively - R_r vortex circulation Reynolds number R = / - u, v, w instantaneous velocity components in X, Y, Z directions - U, V, W mean velocities; shorthand notation for u, , w - X, Y, Z right-hand Cartesian streamwise, vertical, and spanwise coordinate directions - boundary-layer thickness - overall circulation - air kinematic viscosity - _x streamwise vorticity, _X = W/Y–V/d+t6Z - ( )₀ reference value (measured at X = 10 cm) - ( )c refers to vortex center - ( ) _max maximum value for a particular crossflow plane - ( ) (overbar) time average - ( ) (prime) fluctuating component, e.g., u=U+u     

The Prandtl number effect in porous layer convection

A Prandtl number effect for natural convection in a horizontal porous layer is demonstrated to be an explanation for the difference in heat transfer between different porous systems. A Prandtl number trend in experimental data is identified and arguments are presented to substantiate a Prandtl number dependence. Finally, Nusselt number correlations of experimental data at different Prandtl numbers have been developed.     

Transport of particles in an atmospheric turbulent boundary layer

A program incorporating the parallel code of large eddy simulation (LES) and particle transportation model is developed to simulate the motion of particles in an atmospheric turbulent boundary layer (ATBL). A model of particles of 100-micrometer order coupling with large scale ATBL is proposed. Two typical cases are studied, one focuses on the evolution of particle profile in the ATBL and the landing displacement of particles, whereas the other on the motion of particle stream.The English text was polished by Yunming Chen.     

Interaction of an elastic boundary with a viscous sublayer of a turbulent boundary layer

The boundary region of a turbulent boundary layer contributes greatly to the drag. Intense turbulence is generated in this region. Below we investigate the interaction of an elastic boundary with a viscous sublayer for a decrease in the Reynolds stresses, and for a corresponding decrease in the drag. It does not seem possible to investigate the general case. Therefore, the problem is solved within the framework of the limitations made by Sternberg [1] for the theory of a viscous sublayer in a turbulent flow near a solid smooth wall.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 58–62, May–June, 1971.The authors thanks G. S. Migirenko for advice and remarks given during a discussion of the work.     

The unsteady hydromagnetic thermal boundary layer with suction

The unsteady two-dimensional laminar flow of a viscous incompressible and electrically conducting fluid near an oscillating porous plate in the presence of uniform suction, is investigated. The solutions for the velocity, magnetic field, electric current density, temperature and Nusselt number are given in a closed form for the case of the magnetic Prandtl number being equal to unity. The other significant constants are the Eckert number, the fluid Prandtl number and the frequency of oscillation. The influence of these parametres on the solutions is given in both tabulated and graphical forms.     

The turbulent/non-turbulent interface in an adverse pressure gradient turbulent boundary layer

The turbulent/non-turbulent interface (TNTI) in an adverse pressure gradient (APG, β = 1.45) turbulent boundary layer (TBL) is explored here by using direct numerical simulation (DNS) data; β is the Clauser pressure gradient parameter. For comparison, the DNS data for a zero pressure gradient (ZPG) TBL is included. The interface is extracted with an approach based on enstrophy criteria. Depending on the enstrophy, the outer boundary layer flow can be classified into the free stream, boundary layer wake, and intermittent flow regimes. The fractal dimension of the interface is obtained by using the box-counting algorithm, and was found to be constant over a long range of box sizes. The TNTI shows a monofractal behavior. The geometric complexity of a TNTI can be determined in terms of the genus, which is defined as the number of handles in a geometric object. We examine the volume and projection area of the genus of the TNTI to analyze the entrainment process. The geometric complexity of the APG TBL interface and the local entrainment are greater than those of the ZPG TBL, as is evident in the increases in the genus near the interface. The local entrainment velocity is dominantly affected by the viscous diffusion at the interface.     

Double large field stereoscopic PIV in a high Reynolds number turbulent boundary layer

An experiment on a flat plate turbulent boundary layer at high Reynolds number has been carried out in the Laboratoire de Mecanique de Lille (LML, UMR CNRS 8107) wind tunnel. This experiment was performed jointly with LEA (UMR CNRS 6609) in Poitiers (France) and Chalmers University of Technology (Sweden), in the frame of the WALLTURB European project. The simultaneous recording of 143 hot wires in one transverse plane and of two perpendicular stereoscopic PIV fields was performed successfully. The first SPIV plane is 1?cm upstream of the hot wire rake and the second is both orthogonal to the first one and to the wall. The first PIV results show a blockage effect which based on both statistical results (i.e. mean, RMS and spatial correlation) and a potential model does not seem to affect the turbulence organization.