Heat exchange and drag in a turbulent boundary layer with pressure gradient

On the basis of a semiempirical Prandtl model of turbulence, the heat transfer and drag coefficients are determined in a turbulent boundary layer with longitudinal pressure gradient.     

Influence of a positive pressure gradient on the characteristics of a turbulent boundary layer

Based on a systematic analysis of present day experimental data published in the literature, a modified Prandtl—Clauser turbulence model is presented which makes it possible to take into account the effect of a positive pressure gradient on the average characteristics of a turbulent boundary layer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 2, pp. 232–239, August, 1988.     

A turbulent boundary layer with injection into a compressible fluid with a pressure gradient

We use the semiempirical theory of turbulence to study the effect exerted by the input of a homogeneous material through the main flow on the friction and on the heat transfer in the turbulent boundary layer, in a compressible fluid with a pressure gradient.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 6, pp. 989–1001, June, 1969.     

Experimental determination of skin friction coefficient in a turbulent boundary layer with a longitudinal pressure gradient

A study is made of the applicability of indirect methods for the determination of the local skin friction coefficient in a turbulent boundary layer with a longitudinal pressure gradient.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 5, pp. 793–802, May, 1976.     

Conditional analysis in a turbulent boundary layer with strong density differences

Summary A study of the fine structure of wall turbulence in the presence of strong density variations through a conditional analysis of experimental data obtained in a wind tunnel is presented in this paper. Density variations within the boundary layer are produced by injection of air or helium into a mixture of these two components. The conditional analysis carried out in this study shows that the injection of helium into the boundary layer generates more violent ejections than in the case of an injection of air. This result is confirmed by the significant contribution of the ejections to the turbulent mass flux. The results obtained show that in the fully turbulent zone the ejections are associated with strong velocity fluctuations for the two injected gases. This is even more so for the fluctuations of density when an injection of helium is considered. At two locations of the flow (x/e = 8.3 and x/e = 33.3, where e = 3 mm is the slot width) we show that the contributions of a large excursion in the two quadrants of the u' – ρ' plane, corresponding to the two events of the fluid movement, the ejection and sweeping, are very intermittent owing to the fact that they are associated only to a very low number of measurement points. The ejections at y⁺ > 50 are more significant and much more energetic in the case of helium.     

MHD compressible turbulent boundary-layer flow with adverse pressure gradient

Summary The effects of the magnetic field and localized suction on the steady turbulent compressible boundary-layer flow with adverse pressure gradient are numerically studied. The magnetic field is constant and applied transversely to the direction of the flow (global or local). The fluid flow is subjected to a constant velocity of localized suction, and there is no heat transfer between the fluid and the plate (adiabatic plate). The Reynolds-Averaged Boundary-Layer (RABL) equations and their boundary conditions are transformed using the compressible Falkner-Skan transformation. The resulting coupled and nonlinear system of PDEs is solved using the Keller’s box method. For the eddy-kinematic viscosity the turbulent models of Cebeci-Smith and Baldwin-Lomax are employed. For the turbulent Prandtl number the extended Kays-Crawford’s model is used. The flow is subjected to an adverse pressure gradient. The obtained results show that the flow field can be controlled by the applied magnetic field as well as by localized suction.     

Comparison of experimental data and semi-empirical calculation for an incompressible turbulent boundary layer with pressure gradient

A comparison is made of the velocity profiles obtained by semiempirical methods of calculation and those from universal empirical relations. A method of simplifying the semiempirical calculation is proposed.     

Micro-slot injection into a boundary layer driven by a favourable pressure gradient

This study aims to investigate the nonlinear forced vibration of functionally graded (FG) nanobeams. It is assumed that material properties are gradually graded in the direction of thickness. Nonlocal nonlinear Euler–Bernoulli beam theory is used to derive nonlocal governing equations of motion. The linear eigenmodes of FG nanobeams are used to transform a partial differential equation of motion into a system of ordinary differential equations via the Galerkin method. The multiple scale method is used to find the governing equations of the steady-state responses of FG nanobeams excited by a distributed harmonic force with constant intensity. It is also assumed that the working frequency is close to three times greater than the lowest natural frequency. Based on the equation governing the linear natural frequencies of FG nanobeams, the influence of the small scale parameter, material composition, and stiffness of the foundation on the linear relationship among natural frequencies is studied. Results show that superharmonic response or a combination of resonances may occur as well as a subharmonic response depending on the power-law index and stiffness of the foundation. Then the governing equations of a steady-state response of FG nanobeams for four possible solutions are obtained depending on the value of the small scale parameter. It is shown that the simplest response of FG nanobeams is a subharmonic response or superharmonic response. The equations governing the frequency–response curves are obtained and the effects of the power-law index and small scale parameter on them are discussed.     

A model for turbulent dissipation rate in a constant pressure boundary layer

Estimation of the turbulent dissipation rate in a boundary layer is a very involved process. Experimental determination of either the dissipation rate or the Taylor microscale, even in isotropic turbulence, which may occur in a portion of the turbulent boundary layer, is known to be a difficult task. For constant pressure boundary layers, a model for the turbulent dissipation rate is proposed here in terms of the local mean flow quantities. Comparable agreement between the estimated Taylor microscale and Kolmogorov length scale with other data in the logarithmic region suggests usefulness of this model in obtaining these quantities experimentally.     

The structure of a turbulent boundary layer

According to the wave mechanism of turbulence, pulsation in the hydrodynamic parameters results from a superposition of perturbations arising at the wall and then spreading in the flow in the form of spherical wave packets. At the flow boundary, where the fluid velocity is characterized by a large gradient, the acoustic rays of these waves exhibit bending and reversal toward the wall, whereby the trajectories with various initial orientations are interweave and the wave packets are broken. The pulsation of parameters in the region of wave packet breakage results in the formation of a turbulent boundary layer. Upon the reflection of waves, the flow velocity oscillations immediately at the wall cease that corresponds to a laminar sublayer of the turbulent boundary layer.     

Effect of pressure gradient on MHD boundary layer over a flat plate

Summary The magnetohydrodynamic (MHD) boundary layer flow over a flat plate is examined here for two cases, viz. a uniform free-stream velocity and a uniform hydrostatic pressure. The nonlinear boundary layer equations are solved using a reliable finite-difference method. The boundary layer physical parameters such as skin-friction coefficient, displacement, momentum and energy thicknesses of the boundary layer are determined. It is found that the normal surface velocity gradient decreases with the local magnetic interaction parameter for the cases of a uniform hydrostatic pressure, whereas in the case of a uniform free-stream volocity it increases with the interaction parameter.     

A study of the flow pattern on the wall side of a turbulent boundary layer with injection and a positive pressure gradient

Results are shown of an experimental study dealing with the flow pattern on the wall side of a turbulent boundary layer with injection and a positive longitudinal pressure gradient.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 2, pp. 261–264, August, 1973.     

Laminar superlayer in a turbulent boundary layer

We confirm the existence of a sharp boundary between the turbulent and non-turbulent fluid at the outer region of a zero-pressure-gradient turbulent boundary layer at a low Reynolds number. For the first time, using the Tomographic Particle Image Velocimetry technique, we determine mean statistical parameters of the boundary: its thickness and relative velocity jump.     

Influence of pressure gradient upon boundary layer stability and transition

Summary The present paper deals with the effect of adverse pressure gradient on boundary layer stability and transition in an incompressible fluid qualitatively as well as quantitatively. In order to produce various kinds of pressure gradients along a flat plate located horizontally, the cross sectional area of the working chamber is varied by the vertical side walls. Changes in velocity profiles and in intensity of streamwise velocity fluctuation in a boundary layer are measured in the transition region. The distribution of dynamic pressure at 0.43 mm from the surface is correlated with that of intensity of velocity fluctuation. Moreover, transition length is correlated with a shape parameter. Further, the process of transition is shown to be different from the case of zero pressure gradient when the half included angle is 3.6 degree. Finally, mention is made of the relation between transition Reynolds number and a characteristic frequency from the standpoint of linear stability theory.With 11 Figures     

Turbulent boundary layer on a chemically active surface with a negative pressure gradient

An integral method of flow analysis is discussed for a turbulent boundary layer on an ablating surface of plane and axisymmetric bodies. The results of computations are given for ablation of the surfaces of a plate and a sphere of a material similar in composition to textolite.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 3, pp. 473–478, September, 1977.     

Critical displacement parameters of a turbulent boundary layer

The interferometer method was used for determining the critical displacement parameters of a turbulent diffusion boundary layer at a porous plate with injection of helium, nitrogen, carbon dioxide, krypton, xenon, and Freon-12. Velocity and concentration profiles were obtained for the critical flow modes.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 1, pp. 94–103, July, 1972.     

Heat transfer to a flat plate in a fully-developed turbulent boundary layer

The authors examine the results of experimental investigation of local and average heat transfer over a flat plate, with the entire plate heated, and with the initial section heated, in the Reynolds number range 2 · 10² to 5 · 10⁵.     

Adaptation of a turbulent boundary layer on a convex sufrace

The paper presents the results of numerical investigation of the adaptation of velocity profiles, turbulent shear stresses, and coefficients of friction in boundary-layer development along a convex surface and on transition of the boundary layer from a plane surface to convex one. A parameter is obtained that characterizes the completion of adaptation and its dependence on the basic flow parameters. Equations are presented for calculating coefficients of friction in the portion of boundary-layer adaptation and in the main portion. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 2, pp. 306–310, March–April, 1998.