An Iteration Method to Solve the Boundary Layer Flow past a Flat Plate

An iteration method similar to the thin-wing-expansion method for the compressible flow has been proposed to solve the boundary layer flow past a flat plate. Using such an iteration, the first step of which is Oseen’s approximation, the boundary layer past a flat plate is studied. As proceeding from the first approximation to the second and third approximations, it is realized that our solution approaches to a well known Howarth’s bench mark one gradually. Hence, it is concluded that the usefulness of the present method has been confirmed.

Series Solution of Non-Similarity Boundary-Layer Flow in Porous Medium

This paper aims to present complete series solution of non-similarity boundary-layer flow of an incompressible viscous fluid over a porous wedge. The corresponding nonlinear partial differential equations are solved analytically by means of the homotopy analysis method (HAM). An auxiliary parameter is introduced to ensure the convergence of solution series. As a result, series solutions valid for all physical parameters in the whole domain are given. Then, the effects of physical parameters γ and Prandtl number Pr on the local Nusselt number and momentum thickness are investigated. To the best of our knowledge, it is the first time that the series solutions of this kind of non-similarity boundary-layer flows are reported.

Optimization of heat transfer in the thermal Marangoni convective flow of a hybrid nanomaterial with sensitivity analysis

The heat transfer rate of the thermal Marangoni convective flow of a hybrid nanomaterial is optimized by using the response surface methodology(RSM).The thermal phenomenon is modeled in the presence of a variable inclined magnetic field,thermal radiation,and an exponential heat source.Experimentally estimated values of the thermal conductivity and viscosity of the hybrid nanomaterial are utilized in the calculation.The governing intricate nonlinear problem is treated numerically,and a parametric analysis is carried out by using graphical visualizations.A finite difference-based numerical scheme is utilized in conjunction with the 4-stage Lobatto IIIa formula to solve the nonlinear governing problem.The interactive effects of the pertinent parameters on the heat transfer rate are presented by plotting the response surfaces and the contours obtained from the RSM.The mono and hybrid nanomaterial flow fields are compared.The hybrid nanomaterial possesses enhanced thermal fields for nanoparticle volume fractions less than 2%.The irregular heat source and the thermal radiation enhance the temperature profiles.The high level of the thermal radiation and the low levels of the exponential heat source and the angle of inclination(of the magnetic field)lead to the optimized heat transfer rate(Nux=7.46275).

MATHEMATICAL MODELING OF NEAR-WALL FLOWS OF TWO- PHASE MIXTURE WITH EVAPORATING DROPLETS

In the framework of the two-continuum approach, using the matched asymptotic expansion method, the equations of a laminar boundary layer in mist flows with evaporating droplets were derived and solved. The similarity criteria controlling the mist flows were determined. For the flow along a curvilinear surface, the forms of the boundary layer equations differ from the regimes of presence and absence of the droplet inertia deposition. The numerical results were presented for the vapor-droplet boundary layer in the neighborhood of a stagnation point of a hot blunt body. It is demonstrated that, due to evaporation, a droplet-free region develops near the wall inside the boundary layer. On the upper edge of this region, the droplet radius tends to zero and the droplet number density becomes much higher than that in the free stream. The combined effect of the droplet evaporation and accumulation results in a significant enhancement of the heat transfer on the surface even for small mass concentration of the droplets in the free stream.

THE EFFECT OF PARTICLES ON FLUID TURBULENCE IN A TURBULENT BOUNDARY LAYER OVER A CYLINDER

The turbulent fluid and particle interaction in the turbulent boundary layer for cross how over a cylinder has been experimentally studied. A phase-Doppler anemometer was used to measure the mean and fluctuating velocities of both phases. Two size ranges of particles (30 mu m similar to 60 mu m and 80 mu m similar to 150 mu m) at certain concentrations were used for considering the effects of particle sizes on the mean velocity profiles and on the turbulent intensity levels. The measurements clearly demonstrated that the larger particles damped fluid turbulence. For the smaller particles, this damping effect was less noticeable. The measurements further showed a delay in the separation point for two phase turbulent cross how over a cylinder.

Effects of slip condition on MHD stagnation-point flow over a power-law stretching sheet

The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group transformation is used to get the invariants. Using the invariants, a third-order ordinary differential equation corresponding to the momentum is obtained. An analytical solution is obtained in a series form using a homotopy analysis method. Reliability and efficiency of series solutions are shown by the good agreement with numerical results presented in the literature. The effects of the slip parameter, the magnetic field parameter, the velocity ratio parameter, the suction velocity parameter, and the power law exponent on the flow are investigated. The results show that the velocity and shear stress profiles are greatly influenced by these parameters.

A Mathematical Model for Magnetohydrodynamic Convection Flow in a Rotating Horizontal Channel with Inclined Magnetic Field, Magnetic Induction and Hall Current Effects

Closed-form and asymptotic solutions are derived for the steady, fully-developed hydromagnetic free and forced convection flow in a rotating horizontal parallel-plate channel under the action of an inclined magnetic field and constant pressure gradient along the longitudinal axis of the channel. The magnetic field is strong enough to generate Hall current effects and the magnetic Reynolds number of sufficient magnitude that induced magnetic field effects are also present. Secondary flow is present owing to the Hall current effect. The channel plates are also taken to be electrically-conducting. The conservation equations are formulated in an (x, y, z) coordinate system and non-dimensionalized using appropriate transformations. The resulting non-dimensional coupled ordinary differential equations for primary and secondary velocity components and primary and secondary induced magnetic field components and transformed boundary conditions are shown to be controlled by the dimensionless pressure gradient parameter (px), Hartmann number (M2), Grashof number (G), Hall current parameter (m), rotational parameter (K2), magnetic field inclination (&#920), and the electrical conductance ratios of the upper (&#9201) and lower (&#9202) plates. Solutions are derived using the method of complex variables. Asymptotic solutions are also presented for very high rotation parameter and Hartmann number of order equal to unity, for which Ekman-Hartmann boundary layers are identified at the plates. A parametric study of the evolution of velocity and induced magnetic field distributions is undertaken. It is shown that generally increasing Hall current effect (m) serves to accentuate the secondary (cross) flow but oppose the primary flow. An increase in rotational parameter (K2) is also found to counteract primary flow intensity. An elevation in the Grashof number i.e. free convection parameter (G) is shown to aid the secondary induced magnetic field component (Hz);however there is a decrease in magnitudes of the primary induced magnetic field component (Hx) with increasing Grashof number. Increasing inclination of the applied magnetic field (&#920, is also found to oppose the primary flow (u1) but conversely to strongly assist the secondary flow (w1). Both critical primary (Gcx) and secondary (Gcz)Grashof numbers are shown to be reduced with increasing inclination of the magnetic field (&#920), increasing Hall parameter (m) and rotational parameter (K2). Applications of the study arise in rotating MHD induction power generators and also astrophysical flows.

THE FLOW STRUCTURE OF DILUTE GAS-PARTICLE SUSPENSIONS BEHIND A SHOCK WAVE MOVING ALONG A FLAT SURFACE

The asymptotic and numerical investigations of shock-induced boundary layers in gas-particle mixtures are presented. The Saffman lift force acting on a particle in a shear flow is taken into account. It is shown that particle migration across the boundary layer leads to intersections of particle trajectories. The corresponding modification of dusty gas model is proposed in this paper.The equations of two-phase sidewall boundary layer behind a shock wave moving at a constant speed are obtained by using the method of matched asymptotic expansions. The method of the calculation of particle phase parameters in Lagrangian coordinates is described in detail. Some numerical results for the case of small particle concentration are given.

QUADRANT ANALYSIS OF BUBBLE INDUCED VELOCITY FLUCTUATIONS IN A TRANSITIONAL BOUNDARY LAYER

Our previous study showed that the frictional drag decreases with increasing void fraction at Re〉1300, while it increases at Re 〈 1000. Decomposition of the Reynolds shear stress also implied that bubbles induce isotropy of turbulence. In order to confirm our previous analysis and to further investigate flow fields in the vicinity of bubbles, we analyze velocity fluctuations on the quadrant space in the streamwise and transverse directions （u′-v′ plane）. Here, we focus on two specific Reynolds numbers （at Re≈900 and ≈1410, which are close to the laminar-to-turbulent transition regime） and discuss bubble effects on sweep （u′〉 0, v′〈 0 ） and ejection （u′〈 0, v′〉 0） events as a function of the Reynolds number. We also illustrate velocity fluctuations in the vicinity of an individual bubble and a swarm of bubbles on the u′- v′ coordinates. The results show that a bubble swarm suppresses the velocity fluctuations at Re≈1410.

Series solution of non-similarity natural convection boundary-layer flows over permeable vertical surface

The non-similarity solution for natural convection from a permeable isothermal vertical wall is considered. The governing boundary-layer equations for non-similarity flow and temperature fields are solved using the homotopy analysis method. The homotopy-Pade’ technique is applied to accelerate the convergence of the homotopy-series solution. The influence of physical parameters on the non-similarity flows is investigated in detail. Different from the previous analytic results,the homotopy-series solutions are convergent and valid for all physical parameters in the whole domain 0 x 【 ∞ and 0 y 【 ∞.

沟槽对液固两相湍流中展向涡结构影响的实验研究

采用粒子图像测速技术(particlesimage velocimetry,PIV)研究沟槽对含有355μm聚苯乙烯颗粒的液固两相湍流边界层的影响规律,通过对比流过沟槽壁面与光滑平板含颗粒流的平均速度剖面、湍流度及雷诺切应力等湍流统计量,分析沟槽对两相湍流边界层特性的影响。采用空间多尺度、局部平均结构函数和λci涡量识别准则准确识别发卡涡展向涡的涡心,并提取周围脉动速度及流线的空间拓扑结构,对不同法向高度处顺向涡的数量规律进行统计分析。结果发现:与光滑平板相比,沟槽壁面平均速度剖面缓冲层部分抬升,对数区外移,壁面摩擦速度和摩擦切应力变小,表现出4.86%的减阻效果;在同一法向高度,相较于光滑壁面,沟槽壁面下检测到的顺向涡结构倾角较小,数量也较少,周围流向脉动速度较弱,说明在两相流中沟槽壁面能够削弱发卡涡的强度和发生可能,达到减阻的效果。

致密气藏多层砂体合采井产量递减分析方法

致密气藏主力产层多为多层叠置河道砂体,合采时普遍存在各产层贡献不明及砂体动用边界不清的问题。首先,考虑各层河道砂体形态特征和边界尺寸差异,根据等效渗流体积原则,建立了致密气藏多层河道砂体合采井生产模型。其次,基于现代产量递减分析理论,形成了致密气藏多层河道砂体的边界确定方法和合采井产量递减分析图版。最后,讨论不同河道砂体边界距离、砂体数量和砂体位置下的产量递减特征,明确了多层河道砂体对产量递减的影响。研究表明:致密气藏多层河道砂体合采井产量具有5个递减阶段,不稳定流中期阶段可诊断各层砂体边界距离是否相等;河道砂体范围越小,宽砂体数量越少,宽砂体占比越小,储集层稳产能力越差,不稳定流早期阶段和不稳定流中期阶段易出现产量递减速率增大现象。建立的产量递减分析方法可为产层动用程度评价和增产措施制定提供依据。

Investigation of influence of local cooling/heating on nonlinear instability of high-speed boundary layer with direct numerical simulations

The influence of local cooling/heating on two types of nonlinear instabilities of the high-speed boundary layer,namely,the First and Second Mode Oblique Breakdown(FMOB and SMOB),is studied using direct numerical simulations.Local cooling and heating are performed at the weak and strong nonlinear stages of the two types of nonlinear instabilities.It is found that for the FMOB,local cooling at the weak nonlinear region will suppress the increase of the fundamental mode,leading to transition delay.Opposite to local cooling,local heating at the weak nonlinear region of the FMOB will promote the growth of the fundamental mode,resulting in the occurrence of more upstream transition onset.However,if local cooling and heating are performed at the strong nonlinear region,the influence of both local cooling and heating on the FMOB can be neglected.Remarkably,both local heating and cooling can delay the SMOB for different mechanisms.Performing local cooling at the weak nonlinear region of the SMOB,the low amplitude of higher spanwise wavenumber steady mode caused by local cooling lies behind transition delay.When local cooling is set at the strong nonlinear region,the low amplitude of harmonic modes around the cooling area can cause transition delay.Additionally,local heating will suppress the SMOB for the slowing amplification rate of various modes caused by the local heating at both the weak and strong nonlinear stages of the SMOB.

污秽颗粒在绝缘表面吸附前的受力和运动分析

为深入研究电力外绝缘积污规律,分析了大气污秽颗粒在绝缘表面的沉降过程,建立了污秽颗粒、空气流场简化模型;使用流体力学分析方法,分析了污秽颗粒在空气中和边界层的受力和运动过程,建立了污秽颗粒在绝缘表面吸附前的运动分析模型,并对该模型的计算结果进行了探讨.研究表明:在大气污秽颗粒较大的地区,绝缘子上表面积污速率明显偏大;而在大气污秽颗粒较小的地区以及风力较大的地区,绝缘子下表面积污速率明显偏大;控制粒径在20μm以下的大气污染颗粒的浓度,可以有效降低绝缘子的表面污秽度.

离心泵叶片压力面固液两相流的边界层分析

给出了离心泵叶片压力表面固液两相流体边界层控制方程和叶片压力面边界层分离参考点位置估算的一种方法,通过实例计算分析了相关的边界层参数,计算结果说明固液两相流的边界层厚度δ2随叶片弯曲系数Kν的减低和随质量浓度ρm的增加而减薄,并给出了对比试验的验证结果,结果是大于临界速度系数的叶片将使测试泵的性能有不同程度的下降,并且测试浓度的增加有抑制边界层分离的作用。它说明离心泵叶片压力面两相流边界层分离点的位置是随叶片形状的改变而移动的,是可以控制的。

光在超声速湍流边界层中的传输

采用数值方法分析超声速边界层流场对光传输的影响,并根据光波的变化对流场特征进行分析.用法福尔质量加权平均N-S方程及两方程湍流模型求解三维超声速平板湍流边界层流动;光在流场中的传输采用傍轴近似光波传输方程描述,用相屏法和快速傅里叶变换(FFT)技术求解.利用穿越流场的光波光强和相位的改变,直观分析光波畸变和流场的部分特征信息.

平板湍流边界层内气泡流流动实验研究

在低湍流度水槽里 ,利用片光源显示了平板气液两相湍流边界层内气泡流的流场结构 ,研究了平板安装位置、来流速度、喷气方式等参数对湍流边界层内气泡流的影响 .利用激光测速技术测量了平板水平放置时气泡流最外缘处的水平速度及厚度 .结果表明 :平板喷气减阻的原因在于喷气改变了平板湍流边界层的流动结构 。

幂律速度运动表面上磁流体在驻点附近的滑移流动

从理论上研究了具有非线性延伸表面的磁流体在滑移流区的动量传输问题.通过Lie群变换把控制方程组转化为常微分方程组,利用同伦分析方法求得了问题的近似解析解.获得的级数解与文献中的数值解吻合得较好.另外,利用级数解分析滑移参数、磁场强度、速度比率参数、吸入喷注参数和幂律指数对流动的影响.结果显示这些参数对壁剪切力和边界层内流场有较大的影响.

风沙两相流跃移层中沙粒相的速度分布

从单个跃移沙粒在气流中的运动方程出发导出了风沙两相流中沙粒相速度分布函数的Ｂｏｌｔｚｍａｎｎ方程．对风沙流研究中几种不同的分布函数及其相应的统计平均值等基本概念给出了严密的数学定义，指出了不同分布函数之间的区别和联系．在略去铅垂方向空气阻力的情况下，给出了沙粒相速度分布函数沿铅垂方向的边缘分布，作为风沙流中跃移理论的主要基础之一．利用结果对前人在风沙流研究中发现的某些重要规律和现象进行了解释．

PIM充模过程的边界层效应及机理分析

通过对注射坯进行局部密度测试及采用SEM方法观察注射坯截面上粉末-粘结剂的分布状态,揭示了PIM充模过程的边界层效应。将边界层及两相流理论应用于PIM充模过程的研究,分析表明:普通的边界层效应及粉末、粘结剂粘度和密度的差异带来的偏析现象是产生PIM边界层效应的原因。凡是影响模壁吸引熔体分子及影响熔融注射料粘度的因素均会对PIM的边界层效应产生影响。模拟结果表明:随着注射温度由430K升高到450K,PIM的边界层效应变得明显;而入口的注射料流量由60cm3/s增加到80cm3/s,这种效应反而略有减轻。