Equilibrium characteristics of the secondary convection in a vertical fluid layer between two flat plates 1

The nonlinear stability of the natural convection in a vertical fluid layer between two flat plates with different temperatures is investigated by a direct method to find the equilibrium states of the secondary convection. We confine ourselves to two-dimensional flows and assume that the aspect ratio of the fluid layer is very large. Since the Prantl number is assumed to be very small, the buoyancy effect caused by temperature disturbances is negligible. As a result we obtained a neutral surface of the energy of the fundamental mode of the secondary convection. It is concluded that there is no finite amplitude instability below the critical Grashof number derived from linear stability theory, and that both the unstable equilibrium solution (threshold amplitude solution) and the stable equilibrium solution (finite amplitude solution) are found outside the neutral curve of the linear stability. Our results are almost consistent with those of Nagata and Busse (1983), but are more accurate and more thorough.     

An experimental research on the instability of natural convection boundary layer around a vertical heated flat plate

Experimental results on the instability of the isothermal naturalconvection boundary layer around a vertical heated flat plate are presented. It is demonstrated that the characteristics of the instability wave in the outer layer is consistent with the calculation of Brewster & Gebhart. After an initial growth of its low frequency components at the downstream side of the turning point of the neutral curve (Gr≈120) its comparatively higher frequency components develop and become turbulent subsequently with a buoyancy subrange in its power spectra. Simultaneously, in the measurement at the inner layer near the wall a viscous instability signal the same as the Tollmien-Schlichting waves in ordinary boundary layer and its subharmonics in a much higher frequency domain is discovered and an inertial subrange can be observed in the spectra atGr≈378.6. The project supported by the National Natural Science Foundation of China (19572004)     

Global instability of Stokes layer for whole wave numbers

The study on the global instability of a Stokes layer,which is a typical unsteady flow,is usually a paradigm for understanding the instability and transition of unsteady flows.Previous studies suggest that the neutral curve of the global instability obtained by the Floquet theory is only mapped out in a limited range of wave numbers(0.2 α 0.5).In this paper,the global instability is investigated with numerical simulations for all wave numbers.It is revealed that the peak of the disturbances displays irregularity rather than the periodic evolution while the wave number is beyond the above range.A "neutral point" is redefined,and a neutral curve of the global instability is presented for the whole wave numbers with this new definition.This work provides a deeper understanding of the global instability of unsteady flows.     

Asymptotic structure of inviscid disturbances in a thin shock layer

The WKB method, used in [4] to analyze the short-wave instability of a supersonic mixing layer, is employed to investigate various types of inviscid three-dimensional short-wave disturbances in a thin shock layer of perfect gas with arbitrary velocity and temperature distributions across the layer. Simple analytic expressions for the dispersion relations are obtained for neutral disturbances. The results of an asymptotic analysis are compared with direct numerical calculations for a simple model of the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 72–79, November–December, 1988.     

Forced and mixed convection boundary layer flow along a flat plate with variable viscosity and variable Prandtl number: new results

The steady laminar boundary layer flow along a flat plate is studied taking into account the variation of fluid viscosity and fluid Prandtl number with temperature. In the forced convection case the plate moves with constant velocity and its temperature varies in power law with x. In the mixed convection case the plate temperature is constant and the fluid moves upwards due to an external free stream and due to buoyancy forces. The results are obtained with the direct numerical solution of the boundary layer equations. The study concerns the wall heat transfer, the wall shear stress and velocity and temperature profiles across the boundary layer. The results of the present work are different from those existing in the literature, which have been obtained with the assumption of constant Pr number.     

Thermocapillary Instability of a Cylindrical Layer in the Presence of a Radial Temperature Gradient

Within a linear formulation, the thermocapillary instability of equilibrium of a cylindrical layer of heat-conducting viscous fluid in the presence of a radial temperature gradient is investigated with respect to arbitrary disturbances. It is shown that the Rayleigh instability mechanism results in the appearance of monotonous disturbances of a new type. For steady disturbances, the neutral curve is split into two separate segments, each corresponding to its own type of disturbances. For a deformable free boundary, new oscillating disturbances in the form of surface waves develop. It is found that, in the case of axial symmetry, the behavior of these disturbances completely coincides with the oscillating disturbance behavior in a plane layer.     

浮力对混合对流流动及换热特性的影响

用热线和冷线相结合的技术测量垂直圆管内逆混合对流流体的平均速度、 温度以及它们的脉动. 较详细地研究了浮力对逆混合对流的流动特性和传热特性的影响. 评 估了实验中采用的冷线测量温度补偿速度探头温度敏感的影响. 逆混合对流的传热结果用无 量纲参数Ω (Ω= Grd / Red2 )来表示，其中，基于管道直 径的雷诺数Red变化范围为900~18000, 浮力参数Ω变化范围为 0.004899~0.5047. 研究结果表明，浮力对逆混合对流的换热有强化作用. 随着葛拉晓夫数Grd的增加，温度脉动，流向雷诺正应力和流向温度通量增 大，并且在靠近壁面的流体区域尤其明显. 热线与冷线相结合的技术适合于研究非绝热的流 动测量，可以用于研究浮力对流动和换热特性的影响.     

On hot-wire diagnostics in Rayleigh–Taylor mixing layers

Two hot-wire flow diagnostics have been developed to measure a variety of turbulence statistics in the buoyancy driven, air-helium Rayleigh–Taylor mixing layer. The first diagnostic uses a multi-position, multi-overheat (MPMO) single wire technique that is based on evaluating the wire response function to variations in density, velocity and orientation, and gives time-averaged statistics inside the mixing layer. The second diagnostic utilizes the concept of temperature as a fluid marker, and employs a simultaneous three-wire/cold-wire anemometry technique (S3WCA) to measure instantaneous statistics. Both of these diagnostics have been validated in a low Atwood number (A _t  ≤ 0.04), small density difference regime, that allowed validation of the diagnostics with similar experiments done in a hot-water/cold-water water channel facility. Good agreement is found for the measured growth parameters for the mixing layer, velocity fluctuation anisotropy, velocity fluctuation p.d.f behavior, and measurements of molecular mixing. We describe in detail the MPMO and S3WCA diagnostics, and the validation measurements in the low Atwood number regime (A _t  ≤ 0.04). We also outline the advantages of each technique for measurement of turbulence statistics in fluid mixtures with large density differences.     

Effects of a.c. Electric Field and Rotation on Bénard–Marangoni Convection

The coupled buoyancy and thermocapillary instability, the Bénard–Marangoniproblem, in an electrically conducting fluid layer whose upper surface is deformed and subject to a temperature gradient is studied. Both influences of an a.c. electric field and rotation are investigated. Special attention is directed at the occurrence of convection both in the form of stationary motion and oscillatory convection. The linear stability problem is solved for different values of the relevant dimensionless numbers, namely the a.c. electric Rayleigh number, the Taylor, Rayleigh, Biot, Crispation and Prandtl numbers. For steady convection, it is found that by increasing the angular velocity, one reinforces the stability of the fluid layer whatever the values of the surface deformation and the applied a.c. electric field. We have also determined the regions of oscillatory instability and discussed the competition between both stationary and oscillatory convections. This revised version was published online in July 2006 with corrections to the Cover Date.     

An investigation of thermally stratified turbulent channel flow with temperature oscillation on the bottom wall by large eddy simulation

Thermally stratified shear turbulent channel flow with temperature oscillation on the bottom wall of the channel is calculated to investigate the behavior of turbulent flow and heat transfer by use of large eddy simulation (LES) approach coupled with dynamic subgrid-scale (SGS) models. The objective of this study is to deal with the effect of the temperature oscillation on turbulent behavior of thermally stratified turbulent channel flow and to examine the effectiveness of the LES technique for predicting statistically unsteady turbulent flow driven by time-varying buoyancy force. To validate the present calculation, thermally stratified shear turbulent channel flow is computed and compared with available data obtained by direct numerical simulation (DNS), which confirm that the present approach can be used to predict thermally stratified turbulent channel flow satisfactorily. Further, to illustrate the effect of the temperature oscillation with different Richardson numbers and periods of the oscillation on turbulence characteristics, the phase-averaged mean value and fluctuation of the resolved velocities and temperature, and instantaneous velocity fluctuation structures are analyzed.     

Statistical description of laminar-turbulent transition in a boundary layer at high freestream turbulence degree

The statistical approach is applied to calculate the intermittence coefficient in boundarylayer laminar-turbulent transition due to external turbulence. It is assumed that turbulent regions in the boundary layer are associated with the appearance of turbulent spots generated by the secondary instability of streaky structures that have reached a threshold amplitude. An universal dependence of the intermittence coefficient in the transition region on the velocity fluctuation amplitude and the Reynolds number is obtained. It describes well the experimental results.     

Taylor–Dean instability of yield-stress fluids at large gaps

Centrifugal instability of Bingham fluids is investigated in Taylor–Dean flow when the gap size is large compared to the cylinders radii. To determine conditions for the onset of instability, an infinitesimal axisymmetric disturbance was introduced to the basic flow and its evolution in time was monitored using a normal-mode linear stability analysis. To avoid the problem with the stress discontinuity at the location of the yield surface(s), use was made of the Papanastasiou’s regularized variation of the Bingham model in order to obtain the basic flow velocity profiles. An eigenvalue problem was obtained for the exact Bingham fluid which was solved numerically using the collocation method. A plot of the neutral instability curve at different Bingham numbers suggests that the yield stress can have a stabilizing or destabilizing effect on Taylor–Dean flow depending on the sign and magnitude of the pressure gradient, and also on the sense of rotation of the two cylinders with respect to each other.     

Self-similar solution of the unsteady mixed convection flow in the stagnation point region of a rotating sphere

An analysis is performed to present a new self-similar solution of unsteady mixed convection boundary layer flow in the forward stagnation point region of a rotating sphere where the free stream velocity and the angular velocity of the rotating sphere vary continuously with time. It is shown that a self-similar solution is possible when the free stream velocity varies inversely with time. Both constant wall temperature and constant heat flux conditions have been considered in the present study. The system of ordinary differential equations governing the flow have been solved numerically using an implicit finite difference scheme in combination with a quasilinearization technique. It is observed that the surface shear stresses and the surface heat transfer parameters increase with the acceleration and rotation parameters. For a certain value of the acceleration parameter, the surface shear stress in x-direction vanishes and due to further reduction in the value of the acceleration parameter, reverse flow occurs in the x–component of the velocity profiles. The effect of buoyancy parameter is to increase the surface heat transfer rate for buoyancy assisting flow and to decrease it for buoyancy opposing flow. For a fixed buoyancy force, heating by constant heat flux yields a higher value of surface heat transfer rate than heating by constant wall temperature.     

The onset of convection in a horizontal nanofluid layer of finite depth

This paper presents a linear stability analysis for the onset of natural convection in a horizontal nanofluid layer. The employed model incorporates the effects of Brownian motion and thermophoresis. Both monotonic and oscillatory convection for free–free, rigid–rigid, and rigid–free boundaries are investigated. The oscillatory instability is possible when nanoparticles concentrate near the bottom of the layer, so that the density gradient caused by such a bottom-heavy nanoparticle distribution competes with the density variation caused by heating from the bottom. It is established that the instability is almost purely a phenomenon due to buoyancy coupled with the conservation of nanoparticles. It is independent of the contributions of Brownian motion and thermophoresis to the thermal energy equation. Rather, the Brownian motion and thermophoresis enter to produce their effects directly into the equation expressing the conservation of nanoparticles so that the temperature and the particle density are coupled in a particular way, and that results in the thermal and concentration buoyancy effects being coupled in the same way.     

Effects of surface mass transfer on unsteady mixed convection flow over a vertical cone with chemical reaction

The unsteady mixed convection boundary layer flow over a vertical cone is considered to investigate the combined effects of the buoyancy force, thermal and mass diffusion in the presence of the first order chemical reaction and surface mass transfer. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved numerically by the combination of quasi-linearization technique and an implicit finite difference scheme. Numerical computations are performed for different values of the parameters to display the velocity, temperature and concentration profiles graphically. Both accelerating and decelerating free stream velocities are considered. Numerical results are presented for the velocity, temperature and concentration profiles as well as for the skin-friction coefficient, local Nusselt number and local Sherwood number. The obtained results are compared with previously reported ones and are found to be in excellent agreement.     

Boundary layer flow and heat transfer over an unsteady stretching vertical surface

The solution to the unsteady mixed convection boundary layer flow and heat transfer problem due to a stretching vertical surface is presented in this paper. The unsteadiness in the flow and temperature fields is caused by the time-dependent of the stretching velocity and the surface temperature. The governing partial differential equations with three independent variables are first transformed into ordinary differential equations, before they are solved numerically by a finite-difference scheme. The effects of the unsteadiness parameter, buoyancy parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. Both assisting and opposing buoyant flows are considered. It is observed that for assisting flow, the solutions exist for all values of buoyancy parameter, whereas for opposing flow, they exist only if the magnitude of the buoyancy parameter is small. Comparison with known results for steady-state flow is excellent.     

湍流边界层等动量区演化机理的实验研究

等动量区是瞬时流场中流体动量接近的局部区域,其生成和分布与相干结构密切相关. 对等动量区的研究有助于更深入认识湍流边界层相干结构,但目前对其演化过程还缺乏实验支持和机理分析. 设计并使用移动式高时间分辨率粒子图像测速技术(TRPIV)系统对光滑平板湍流边界层进行了跟踪测量,用滤波方式对数据进行降噪,结合对直接数值模拟数据的插值结果,获得脉动速度信号. 使用改进方法去掉非湍流的影响,检测边界层内的等动量区,得到其数量的时间序列,结合流向速度概率密度函数分布的变化,分析得出了等动量区的数量在大的时间尺度下从一个稳态到另一个稳态的阶梯状变化特点. 分解不同尺度的脉动速度,对大尺度和小尺度脉动信号进行条件平均,发现大尺度脉动对等动量区数量变化起主要作用,表现为不同速度流体通过发生不同猝发事件改变流向速度概率密度函数分布. 分析流向大尺度脉动空间分布的变化,发现等动量区内常含有多个大尺度脉动区域,不同区域的扩张、收缩、分裂、合并影响流向速度的集中程度,进而导致等动量区数量的变化.      

A wavelet transform analysis applied to unsteady aspects of supersonic jet screech resonance

 The multiple acoustic modes and shear layer instability waves which characterize a supersonic underexpanded rectangular jet are investigated experimentally via the Morlet wavelet transform. Because of its quasi-locality in both physical-space and Fourier space, the wavelet transformation allows one to track the time evolution of the various scales in both acoustic and velocity fluctuation signals. Using this technique it is demonstrated that multiple acoustic modes produced by the jet coexist and are not due to a mode switching mechanism. Unsteady screech tone modulation is observed and a mechanism for its occurrence is proposed. Received: 9 February 1996 / Accepted: 17 June 1996     

Steady thermocapillary-buoyant convection in a shallow annular pool. Part 2: Two immiscible fluids

This work is devoted to the study of steady thermocapillary-buoyant convection in a system of two horizontal superimposed immiscible liquid layers filling a lateral heated thin annular pool.The governing equations are solved using an asymptotic theory for the aspect ratios ε→ 0.Asymptotic solutions of the velocity and temperature fields are obtained in the core region away from the cylinder walls.In order to validate the asymptotic solutions,numerical simulations are also carried out and the results are compared to each other.It is found that the present asymptotic solutions are valid in most of the core region.And the applicability of the obtained asymptotic solutions decreases with the increase of the aspect ratio and the thickness ratio of the two layers.For a system of gallium arsenide (lower layer) and boron oxide (upper layer),the buoyancy slightly weakens the thermocapillary convection in the upper layer and strengthens it in the lower layer.     

Stratified magnetohydrodynamic flow of tangent hyperbolic nanofluid induced by inclined sheet

This paper studies stratified magnetohydrodynamic(MHD) flow of tangent hyperbolic nanofluid past an inclined exponentially stretching surface. The flow is subjected to velocity, thermal, and solutal boundary conditions. The partial differential systems are reduced to ordinary differential systems using appropriate transformations.The reduced systems are solved for convergent series solutions. The velocity, temperature,and concentration fields are discussed for different physical parameters. The results indicate that the temperature and the thermal boundary layer thickness increase noticeably for large values of Brownian motion and thermophoresis effects. It is also observed that the buoyancy parameter strengthens the velocity field, showing a decreasing behavior of temperature and nanoparticle volume fraction profiles.