On The Atmospheric Boundary Layer Flow Modelling

The paper presents a mathematical and numerical investigation of the flow in the atmospheric boundary layer (ABL) over complex topography. The flow is supposed to be viscous, incompressible, turbulent and stationary. Two different mathematical–numerical approaches are briefly mentioned. Both models have been used to simulate a flow and pollution dispersion over a complex surface coal field in the North Bohemia which is supposed to be partially covered by a high forest stand. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Two-Phase Flow in a Rotating Boundary Layer

The two-phase flow induced by a rotating disk in a stationary unbounded mixture is considered. The generalized similarity assumption of von Karman reduces the averaged equations of motion with a linear drag between the phases to a system of ordinary differential equations. These are investigated by asymptotic and numerical techniques. The equations display a nontrivial behavior in a sublayer near the boundary, whose thickness is of the order of the particle size. The volume fraction of the dispersed phase is singular unless a small suction is applied on the disk or a small diffusion term is added to the continuity equations. Outside this sublayer, the velocity field is quite similar to a rescaled classical von Karman flow. Good agreement between asymptotic and numerical solution is obtained, although there is considerable stiffness in the equations. The motion of a solid particle in a von Karman flow is also discussed, but the present investigation is restricted to small radii because the shear-lift force is neglected.     

关于边界层方法

本文指出传统的边界层方法(包括匹配法和Vi?ik—Lyusternik方法)的不足:不能作出边界层项的渐近展开式.提出多重尺度构造边界层项的方法,得到符合实情的结果.又与Levinson所用的方法比较,本方法能更简单地导出后一方法给出的边界层项的渐近展开式.又应用此方法研究现有的关于奇异摄动的某些成果,指出这些成果的局限性,并在一般情况下作出解的渐近展开式.     

On the Production of Sound by Turbulent Boundary Layer Flow over a Compliant Coating

A theory is proposed of the generation of sound by turbulentboundary layer flow over a nominally plane, compliant wall coating.It is argued that, at sufficiently low mean flow Mach numbers,the principal noise production mechanism involves the scatteringof energy into sound from the hydrodynamic region of the wallpressure fluctuations by time dependent irregularities in thefree surface of the coating induced by the turbulent flow. Theeffective noise sources are equivalent to a distribution ofaerodynamic dipoles over the surface of the coating whose axesare parallel to the wall. The far field acoustic pressure spectrum,and the wavenumber-frequency wall pressure spectrum in the acousticdomain are expressed in terms of the behaviour of the wall pressurespectrum in the hydrodynamic domain. A simple empirical modelof the hydrodynamic region, defined in terms of measurable parameters,is used to obtain explicit representations of the acoustic spectra.     

On a Boundary Layer Problem

This is a continuation of our earlier article concerning the boundary-value problem     where A , B are prescribed constants, and 0 < ε ≪ 1 is a small positive parameter. In that article, we assumed the coefficients a ( x ) and b ( x ) are sufficiently smooth functions with the behavior given by a ( x ) ∼ αx and b ( x ) ∼ β as x → 0, where α > 0 and β / α ≠ 1, 2, 3,…. In the present article, we are concerned with the case α < 0 and β / α ≠ 0, −1, −2,…. An asymptotic solution is obtained for the problem, which holds uniformly for all x in [ x ₋, x ₊]. Our result is proved rigorously, and shows that a previous result in the literature is incorrect.     

Physical Modelling of Point Source Dispersion Inside Atmospheric Boundary Layer

One of the most important problems in the turbulence theory is the process of turbulent mixing. Although many theoretical and experimental studies on the structure functions of a passive scalar as well as the probability density functions of its increment and gradient in a turbulent fluid have been published so far, the instantaneous feature of an advected scalar has not been explored very well. There are only a few experimental studies on a scalar concentration fluctuation analysis in turbulent flows. In this study the time‐series of both longitudinal velocity component and concentration analysis are to be presented. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundary Layer Flow near a Discontinuity in Wall Conditions

A numerical method for integration of the laminar boundary layerequations past a discontinuous chage in the boundary conditionsalong a flat palte is presented, together with some resultscomputed for slot-injection of fluid from the plate. The method,which is discussed in detail, is a two-region matching procedurethat follows very closely the mathematical development of thesolution near the singularity and seems capable of being adaptedto more general non-linear parabolic problems.     

Asymptotic Approach to the Problem of Boundary Layer Instability in Transonic Flow

Tollmien–Schlichting waves can be analyzed using the Prandtl equations involving selfinduced pressure. This circumstance was used as a starting point to examine the properties of the dispersion relation and the eigenmode spectrum, which includes modes with amplitudes increasing with time. The fact that the asymptotic equations for a nonclassical boundary layer (near the lower branch of the neutral curve) have unstable fluctuation solutions is well known in the case of subsonic and transonic flows. At the same time, similar solutions for supersonic external flows do not contain unstable modes. The bifurcation pattern of the behavior of dispersion curves in complex domains gives a mathematical explanation of the sharp change in the stability properties occurring in the transonic range.     

柱状固粒两相边界层流场稳定性研究

从运动方程和本构方程出发,推导得到了含柱状粒子两相流场的修正Orr-Sommerfeld方程,然后在边界层流场中,采用数值计算方法,得到了含柱状粒子流场的稳定性中性曲线,给出了流场失稳的临界雷诺数.结果表明在所述情况下,柱状粒子对流场起着抑制失稳的作用,而且抑制的程度随着柱状粒子体积分数和长径比的增加而提高.     

圆锥形血管中的振荡发展流动

本文在小锥度角的假设下,研究了圆锥形血管的非定常振荡的发展流动问题.导得了相应的速度分布公式.分析表明,所有收缩的圆锥形血管的流动都是发展流动,而且锥度角对发展流动的影响随着锥度角的增大而增大.     

Lower Branch Modes of the Compressible Boundary Layer Flow Due to a Rotating-Disk

In this article, a theoretical study is pursued to investigate the structure of the lower branch neutral stability modes of three-dimensional small disturbances imposed on the compressible boundary layer flow due to a rotating-disk. Special attention is focused on to the short-wavelength stationary/nonstationary compressible crossflow vortex modes at sufficiently high Reynolds numbers with reasonably small scaled frequencies. Following closely the asymptotic framework introduced in [ 1 ] for the incompressible stationary modes, it is demonstrated here that the compressible modes having sufficiently long time scale can also be described by an asymptotic expansion procedure based on the triple-deck approach. Making use of this rational asymptotic technique, which rigorously takes into account the nonparallel effects, the asymptotic structure of the nonstationary modes is shown to be adjusted by a balance between viscous and Coriolis forces, and resulted from the fact of vanishing shear stress at the disk surface, as in the incompressible Von Karman's flow. As a consequence of matching successive regions in the asymptotic procedure, it is found that the wavenumber and the orientation of the compressible lower branch modes are governed by an eigenrelation, which is akin to the one obtained previously in [ 1 ] for the incompressible stationary mode and in [ 2 ] for the compressible stationary modes. The nonparallel influences are toward destabilizing all the modes, though the wall insulation and heating are relatively stabilizing for the modes in the vicinity of the stationary mode, unlike the wall cooling. The asymptotic compressible data obtained at high Reynolds number limit compares fairly well with the numerical results generated directly solving the linearized compressible system with usual parallel flow approximation.     

可渗透收缩薄膜引起的三维

研究可渗透收缩薄膜上的不稳定粘性流动.通过相似变换得到相似方程.在不同的不稳定参数、质量吸入参数、收缩参数、Prandtl数下,数值地求解相似方程,得到速度和温度的分布,以及表面摩擦因数和Nusselt数等.结果发现,与不稳定的伸展薄膜不同,在质量吸入参数和不稳定参数的某一范围内,可渗透收缩薄膜上的不稳定流动存在双重解.     

可渗透收缩薄膜引起的三维不稳定边界层流动

研究可渗透收缩薄膜上的不稳定粘性流动．通过相似变换得到相似方程．在不同的不稳定参数、质量吸入参数、收缩参数、Prandtl数下,数值地求解相似方程,得到速度和温度的分布,以及表面摩擦因数和Nusselt数等．结果发现,与不稳定的伸展薄膜不同,在质量吸入参数和不稳定参数的某一范围内,可渗透收缩薄膜上的不稳定流动存在双重解．     

On Boundary Layer Control Using Suction in the Wind Tunnels

In this paper a closed-form analysis of flow in a two-dimensional transonic wind tunnel that uses sidewall distributed suction around the model to reduce sidewall boundary-layer effects is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Non-Linear Ordinary Differential Equations of Boundary Layer Type

A numerical method previously applied to linear two-point boundary value problems of boundary layer type is extended to some non-linear problems. Discretization of the differential equation leads to a set of non-linear algebraic equations, which is solved by a modified Newton's method; both the mesh spacing and the boundary layer parameter are iteratively adjusted during the solution process. Several examples are discussed; one of these concerns the problem of shock wave formation in a supersonic nozzle.     

On the Prandtl Boundary Layer Equations in Presence of Corner Singularities

In this paper we prove the well-posedness of the Prandtl boundary layer equations on a periodic strip when the initial and the boundary data are not assigned to be compatible.     

自由来流湍流与三维壁面局部粗糙诱导平板边界层不稳定T-S波的数值研究

采用直接数值模拟（DNS）方法,研究了在自由来流湍流与三维壁面局部粗糙作用下平板边界层内诱导产生不稳定T-S波的物理问题.数值结果可知,在平板边界层内发现了二维和三维T-S波组成的波包空间序列以及求得了波包向前传播的群速度大小,从而证明了自由来流湍流与三维壁面局部粗糙作用是激励平板边界层内诱导产生不稳定T-S波的一种机制.随后,建立了平板边界层内被激发的二维和三维T S波的初始幅值与自由来流湍流度,三维壁面局部粗糙的流向长度、展向宽度及法向高度之间的关系.这一问题的深入研究,进一步完善了流动稳定性与湍流理论.