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.     

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.     

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.     

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.     

Magnetohydrodynamic stability of boundary layers along a flat plate with pressure gradient

Summary The purpose of the paper is to consider theoretically the characteristics of steady two-dimensional magnetohydrodynamic boundary layer flow past a flat plate with pressure gradient in the presence of transverse magnetic field and its stability problem. The boundary layer equation is transformed into a non-similar one and numerical solutions are obtained by the difference-differential method. The neutral stability curves for wavelike disturbances of Tollmien-Schlichting type are then presented for the velocity profiles obtained above. Numerical results for the magnetic parameter and pressure gradient parameter are given for the velocity profiles, coefficient of skin friction, displacement thickness and the critical Reynolds number.With 10 Figures     

Analysis of a turbulent boundary layer subjected to a strong adverse pressure gradient

We define two non-dimensional parameters $\text{Λ =}\text{τ}{}_{\mathrm{w}}\text{p}{}_{\mathrm{x}}\text{δ}$ and $\text{R}{}_{\mathrm{p}}\text{=}\text{U}{}_{\mathrm{p}}\text{δ}\text{ν}$ where τ_w is the wall stress, p_x(?0) is the pressure gradient to which the turbulent boundary layer (of thickness δ) is subjected, ν is the kinematic viscosity, $\text{U}{}_{\mathrm{p}}\text{= (}\text{νp}{}_{\mathrm{x}}\text{p}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ is a characteristic velocity and p is the density. The limit corresponding to the strong adverse pressure gradient is formulated as Λ → 0, R_p → ∞, ΛR_p finite. Using appropriate inner and outer asympcotic expansions, both above a wall layer possibly scaling with τ_w and ν, it is found by an application of Millikan's argument that there is an inertial sublayer where the streamwise velocity distribution obeys a half-power law, whose slope depends on Λ, and intercept on ΛR_p. Indeed comparison with available experimental data shows the inner law to be well represented by $\text{u}\text{Up}\text{= (3.5 + 19Λ)(}\text{yU}{}_{\mathrm{p}}\text{ν}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{+ 2.5ΛR}{}_{\mathrm{p}}$. The outer flow obeys a generalized defect law; use of constant eddy viscosity closure yields results in good agreement with experiment.     

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.     

Turbulent to laminar transition of a boundary layer under large negative pressure gradients

Results are shown of an experimental study concerning the development of a laminar sub-layer in a turbulent boundary layer under large negative longitudinal pressure gradients.Translated from Inzhenerno-Fizicheskii Zharnal, Vol. 24, No. 2, pp. 276–281, February, 1973.     

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.     

Effect of a pressure gradient and of external flow turbulence on flow in a boundary layer

The effect of a pressure gradient and of external flow turbulence on the nature of flow in the laminar, transition, and turbulent regions is investigated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 6, pp. 1100–1109, June, 1978.     

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.     

Global stability of the rotating-disk boundary layer

The global stability of the von Kármán boundary layer on the rotating disk is reviewed. For the genuine, radially inhomogeneous base flow, linearized numerical simulations indicate that convectively propagating forms of disturbance are predominant at all radii. The presence of absolute instability does not lead to the formation of any unstable linear global mode, even though the temporal growth rate of the absolute instability increases along the radial direction. Analogous behaviour can be found in the impulse solutions of a model amplitude equation, namely the linearized complex Ginzburg–Landau equation. These solutions show that, depending on the precise balance between spatial variations in the temporal growth rate and the corresponding shifts in the temporal frequency, globally stable behaviour can be obtained even in the presence of a strengthening absolute instability. The radial dependency of the absolute temporal frequency is sufficient to detune the disturbance oscillations at different radial positions, thus overcoming the radially increasing absolute growth, thereby giving rise to a stable global response. The origin of this form of behaviour can be traced to the fact that the cylindrical geometry of the rotating-disk flow dictates a choice of a globally valid time non-dimensionalization that, when properly employed, leads to a significant radial variation in the frequency for the absolute instability.     

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.     

Application of a two-layer model of turbulence in calculation of a boundary layer with a pressure gradient

The characteristic features of the formulation of a two-layer turbulence model and its application in calculation of near-wall turbulent flows are considered. Factors that influence the effectiveness of implementation of the model and ways of expanding the limits of its applicability are discussed. The possibilities of the two-layer model are demonstrated by calculating a boundary layer on a flat plate with a longitudinal pressure gradient. A comparison of the results of calculation of the heat-transfer characteristics by the two-layer model, two-parameter dissipation model, and Spalart-Allmaras model with the data of a physical experiment and available correlations is made. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 1, pp. 90–99, January–February, 2007.     

Effect of temperature factor and turbulence of the impinging stream on the transition in the boundary layer with gradient flow

An experimental study is made of the start of the transition and the extent of the transition zone in flow over a cooled wing profiled by a stream with an increased degree of turbulence in a wide range of Reynolds numbers.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 3, pp. 393–398, March, 1977.     

Study on boundary layer transition of a rotating disk

Summary Behaviour of spiral vortices being generated in transition regime of a disk rotating in otherwise undisturbed fluid is experimentally studied in detail. Through visualizations of the transition regime by using close-up camera, new striped flow patterns originating along the axis of spital vortices are found to be ring-like vortices which occur on the surfaces of each spiral vortices. Mechanism of the spiral vortex is clarified by cutting the vortices by strobo slit light. It is also found out experimentally that the phase velocity of the vortices is zero.     

使用梯度过渡层的掺Cr碳膜的显微组织特征

为了探究C、Cr两种主要成膜元素在非晶碳膜中的存在和分布状态,采用非平衡磁控溅射离子镀技术制备出了具有梯度过渡层的掺Cr碳膜,利用高分辨透射电子显微术(HRTEM)分析了薄膜的显微组织.结果表明,沉积在硅晶片上的纯Cr底层具有典型的柱状晶结构,其上的梯度过渡层则由各种形态的Cr纳米晶和富碳非晶基质构成.沿薄膜生长方向,随着Cr含量逐渐降低,过渡层中的Cr纳米晶依次形成层片晶、岛状晶和微晶.掺Cr碳膜的工作层则是一种非晶的纳米多层膜.膜中的C始终以非晶态存在,所观察到的结晶相均属金属Cr,同时纯Cr层柱状晶和过渡层中的各种Cr纳米晶都不同程度地具有(110)晶面的择优取向.     

A parametric method of solving laminar boundary layer equations with a longitudinal pressure gradient in an equilibrium-dissociated gas

The possibility is examined of reducing the equations of a laminar boundary layer with longitudinal pressure gradient in the presence of an equilibrium-dissociated gas to some universal system of equations.     

Effect of uniform suction or injection on a magnetohydrodynamic boundary layer flow along a flat plate with pressure gradient

Summary The effect of uniform suction or injection on the flow of an incompressible electrically conducting fluid past a flat plate with pressure gradient in the presence of a transverse magnetic field was theoretically investigated. The boundary layer equations were transformed into non-similar ones, and the numerical calculations of the resulting equations were performed by the difference differential method. The velocity profiles, the coefficient of skin friction, and the displacement thickness were given for various values of the pressure gradient, the magnetic and suction/injection parameters. The neutral stability curves for wavelike disturbances of Tollmien-Schlichting type and the critical Reynolds numbers were then presented for the velocity profiles obtained above.With 13 Figures