外形任意的多孔介质轴对称物体中充满非Newton幂律流体时的自然对流

在一个轴对称、外形任意的多孔介质二维体中,充满了有屈服应力的非Newton幂律流体时,数值分析其自由对流及其传热/传质问题．利用相似变换,将边界层控制方程及其边界条件变换为无量纲形式,然后用有限差分法求解该方程组．所研究的参数为流变常数、浮力比和Lewis数．给出并讨论了典型的速度、温度及浓度曲线．发现屈服应力参数值和非Newton流体的幂律指数对结果有着显著的影响．     

T型微通道内液滴在幂律流体中运动机理的格子Boltzmann方法研究北大核心CSCD

采用非Newton不可压两相流格子Boltzmann模型研究了T型微通道内Newton液滴在非Newton幂律流体中的运动过程.研究了非Newton流体幂律指数n、主管道毛细数Ca、两相流量比Q、两相黏度比M以及主管道壁面润湿性θ对液滴在T型微通道内的形成尺寸、形成时间和变形参数(DI)的影响.研究结果表明:首先,主管道流体幂律指数n从0.4增加到1.6时,液滴的形成尺寸近似呈线性减小,而液滴的形成时间和变形参数先快速减小,然后缓慢减小;其次,黏度比对液滴形成尺寸、液滴形成以及变形参数的影响与幂律指数的影响基本一致;再者,随着Ca和主管道壁面润湿性的增加,形成液滴的尺寸近似呈线性减小,形成液滴的时间和变形参数先快速减小然后缓慢减小,且减小趋势随幂律指数的增加而减缓;最后,研究结果还表明主管道和子管道的流量比Q越大,液滴形成时间越长,液滴形成尺寸和变形参数越小.     

水平来流对扰动成长和对流周期性的影响

对Pr=0.0272的纯流体在矩形腔体外加水平来流时,进行二维流体力学基本方程组的数值模拟.研究了该纯流体Rayleigh-Benard对流的一维行波斑图的成长及时空的演化.发现对流成长过程可以划分为3个阶段,即对流发展、对流指数成长和周期变化。在对流指数成长阶段对不同相对Rayleigh(瑞利)数Ra_r的最大垂直流速场随时间变化的情况进行分析,获得了最大垂直流速场指数成长阶段的线性成长率γ_m和相对Rayleigh数Ra_r的关系公式.研究了行波周期受水平来流Reynolds(雷诺)数的影响,揭示了行波对流周期性及其对水平来流Reynolds数的依赖性.     

微通道内电渗压力混合驱动幂律流体流动模拟

为了研究微通道内电渗压力混合驱动幂律流体的流动特性,建立了微通道内电渗压力混合驱动幂律流体的计算模型,其双电层电势、流体的流场分布分别由Poisson-Boltzmann(P-B)方程和Navier-Stokes(N-S)方程描述.讨论了无量纲Debye(德拜)参数K、壁面ζ*电势和幂律指数n对流体流动特性和Poiseuille数的影响.结果表明,当压力梯度与外加电场方向一致(Γ0)时,剪切变稀流体的速度大于剪切变稠流体;压力梯度与外加电场方向相反(Γ0)时,结果相反.Poiseuille数是无量纲Debye常数K、壁面ζ*电势和幂律指数n的增函数.     

饱和纳米流体多孔介质中竖直嵌入板上边界层的非Newton流

在层流条件下,对饱和多孔介质中的竖直板,研究幂指数型非Newton流的自由对流热交换.非Newton纳米流体服从幂指数型的数学模型,模型综合考虑了Brown运动和热泳的影响.通过相似变换,将问题的偏微分控制方程组,转化为常微分方程组,得到了常微分方程组的数值解.数值解依赖于幂指数n,Lewis数Le,浮力比Nr,Brown运动参数Nb,以及热泳参数Nt.在n和Le的不同取值下,研究并讨论了对相关流体性质参数的影响和简化的Nusselt数.     

转动与摆动复合运动下脂润滑关节轴承的数值分析

建立了球面轴承的三维润滑模型,该模型将内圈的转动运动、轴颈倾斜引起的内圈倾斜和内圈的摆动运动等因素纳入考虑,推导出球坐标下适用于非Newton(牛顿)流体润滑的Reynolds(雷诺)方程.应用该模型,并考虑使用润滑脂的Ostwald流变模型,对向心关节轴承的润滑问题进行了数值计算,研究了在不同的幂律指数、内圈倾斜角度和摆动角速度下,脂润滑膜的压力分布、最大压力、承载力和流量.结果表明:在合适的操作条件下,脂润滑能产生明显的流体动压效应;在其它参数不变时,幂律指数对脂润滑膜的最大压力和承载能力影响显著,相对于Newton流体,剪切稠化流体可提高润滑膜的最大压力和承载能力,并增加周向流量,而剪切稀化流体的影响效果则相反;内圈倾斜角度对脂润滑膜最大压力和承载能力的影响较小,内圈摆动角速度的影响则较为明显.     

热传导率对不同传导参数下幂律非Newton流体流经连续伸展表面时热传导的影响

在一个具有吸入/吹出功能、幂律变化的伸展表面上,分析了二维稳定非Newton流体的流动.假定热传导率按温度的线性函数变化.将控制方程无量纲化后,用Runge-Kutta法进行数值求解.将该问题的一个特例所得到的一些结果,与以前发表的结果相比较,发现两者有着很好的一致性.考虑两种情况,一种对应着致冷的表面温度,另一种对应着均匀的表面温度.数值结果显示,对上述两种情况,可变热传导参数β,传质参数d和幂律指数n,对温度分布和Nusselt数有着重大的影响.     

非Newton流体的物质点法模拟研究

准确模拟非Newton流体的运动特性具有重要的工程意义.物质点法作为一种相对新兴的粒子型算法,其结合了Lagrange算法和Euler算法的双重优势,已广泛有效地应用于各个工程领域.基于物质点法,结合人工状态方程,分析了两种非Newton流体(cross流体和幂律流体)在平板Poiseuille流和Couette流情况下的流动特性.结果表明:对Newton流体,物质点模拟结果与理论值一致;对非Newton流体,物质点法可准确模拟其剪切稀化和剪切稠化现象.表明了物质点法在模拟非Newton流体流动问题时的适用性,拓展了物质点法的应用范围.     

不对称柔性壁管道内幂律流体蠕动传输的精确解

在不对称管道内,研究了壁面柔曲性对非Newton流体蠕动流的影响.流变学性质由幂律流体本构方程表征.在数学表达中,采用了长波和低Reynolds数近似.得到了流函数和速度的精确解.给出了流线图及其俘获现象.对所讨论的流动,陈列了关键参数的显著特征,并最后给出了主要结论.     

非Newton流体在多孔介质中沿竖直面作自由对流时应力屈服和Soret效应对其传热/传质的影响

对饱和的非Newton幂律流体,流经多孔介质中竖直平板时的自由对流,在出现应力屈服和Soret效应时,研究化学反映对传热/传质的影响.用相似变换,将边界层控制方程及其边界条件转换为无量纲的形式,然后通过有限差分法求解该方程.给出并讨论了浓度曲线,以及本问题各种参数值时的Nusselt数和Sherwood数.发现化学反应参数γ、化学反应级m、Soret数Sr、浮力比N、Lewis数Le及无量纲流变参数Ω对流场有着显著的影响.     

Stability of an infinite horizontal layer of fluid with a spatial heat source in the presence of a magnetic field

The stability of an electrically conducting infinite layer of a viscous fluid which loses heat throughout its volume at a constant rate in the presence of a magnetic field is discussed. The value of the critical Rayleigh number R is found to decrease as the rate of heat loss increases which implies that the layer becomes more unstable. It is observed that the destabilizing effect of the heat source term Q is more prominent when the strength of the magnetic field is low. The aspect ratio ‘a’ increases with increasing Q showing that the horizontal dimension of the cells decreases with increasing Q.     

Hydromagnetic instability of a power-law liquid film flowing down a vertical cylinder using numerical approximation approach techniques

The long-wave perturbation method is employed to investigate the hydromagnetic stability of a thin electrically-conductive power-law liquid film flowing down the external surface of a vertical cylinder in a magnetic field. The validity of the numerical results is improved through the introduction of the flow index and the magnetic force into the governing equation. In contrast to most previous studies presented in the literature, the solution scheme employed in this study is based on a numerical approximation approach rather than an analytical method. The normal mode approach is used to analyze the stability of the film flow. The modeling results reveal that the stability of the film flow system is weakened as the radius of the cylinder is reduced. However, the flow stability can be enhanced by increasing the intensity of the magnetic field and the flow index, respectively. In general, the optimum conditions can be found through the use of a system to alter stability of the film flow by controlling the applied magnetic field.     

A nonlinear stability analysis of a rotating double-diffusive magnetized ferrofluid

A nonlinear stability result for a double-diffusive magnetized ferrofluid layer rotating about a vertical axis for stress-free boundaries is derived via generalized energy method. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. The result is compared with the result obtained by linear instability theory. The critical magnetic thermal Rayleigh number given by energy theory is slightly less than those given by linear theory and thus indicates the existence of subcritical instability for ferrofluids. For non-ferrofluids, it is observed that the nonlinear critical stability thermal Rayleigh number coincides with that of linear critical stability thermal Rayleigh number. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of magnetic parameter, M₃, solute gradient, S₁, and Taylor number, T_A1, on subcritical instability region have been analyzed. We also demonstrate coupling between the buoyancy and magnetic forces in the nonlinear stability analysis.     

Numerical study of the transition to chaos of a buoyant plume from a two-dimensional open cavity heated from below

The transition to a chaotic plume from a two-dimensional (2D) open cavity heated from below has been investigated using numerical simulation. A large range of Rayleigh numbers (Ra) pertaining to an aspect ratio of A = 1, and Prandtl number (Pr) of Pr = 0.71 (air) is numerically investigated. It is shown that there exists a complex transition of the plume from a steady reflection symmetry to a chaotic flow with a sequence of bifurcations. As the Rayleigh number increases, the plume from the open cavity undergoes a supercritical pitchfork bifurcation from a steady reflection symmetry to a steady reflection asymmetry flow. Once the Rayleigh number exceeds 7 × 10³, the plume appears as a distinct flapping namely, a Hopf bifurcation, and then as a distinct puffing. The chaotic plume has the possibility to exhibit an alternate appearance of flapping and puffing in the event the Rayleigh number exceeds 8 × 10⁴. Moreover, the dynamics of the plume from the open cavity is discussed, and the dependence on the Rayleigh number of heat and mass transfer of the plume from the open cavity is quantified.     

Lattice Boltzmann simulation of convective heat transfer of non-Newtonian fluids in impeller stirred tank

Lattice Boltzmann simulation of convective heat transfer of non-Newtonian fluids in an impeller stirred tank is performed. The curved and moving boundary methods combined with the unknown-index algorithm are used to solve the flow and thermal fields induced in a cold tank by an oscillating hot impeller. For a given maximum radius of the blades, the simulation results show that a rectangular impeller of large aspect ratio induces stronger heat transfer effect on the tank walls than the small aspect ratio. This is because the latter would cause worse field synergy than the former, i.e. the induced local velocities of fluid are mostly perpendicular to the temperature gradients. The convection effects on the tank walls are also improved as the oscillation amplitude of impeller increases until the swept areas of impeller are close to whole azimuth of the tank, i.e., oscillation amplitude of 90°. The maximum Nusselt number on the tank walls for power-law fluid flows of n = 0.7, 1 and 1.5 occurs at oscillation amplitude of 75°. Finally, it is found that the heat transfer effect on the tank walls is reduced as the power-law index of fluid increases.     

Effect of rotation on the onset of double diffusive convection in a Darcy porous medium saturated with a couple stress fluid

The effect of rotation on the onset of double diffusive convection in a horizontal couple stress fluid-saturated porous layer, which is heated and salted from below, is studied analytically using both linear and weak nonlinear stability analyses. The extended Darcy model, which includes the time derivative and Coriolis terms, has been employed in the momentum equation. The onset criterion for stationary, oscillatory and finite amplitude convection is derived analytically. The effect of Taylor number, couple stress parameter, solute Rayleigh number, Lewis number, Darcy–Prandtl number, and normalized porosity on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the rotation, couple stress parameter and solute Rayleigh number have stabilizing effect on the stationary, oscillatory, and finite amplitude convection. The Lewis number has a stabilizing effect in the case of stationary and finite amplitude modes, with a destabilizing effect in the case of oscillatory convection. The Darcy–Prandtl number and normalized porosity advances the onset of oscillatory convection. A weak nonlinear theory based on the truncated representation of Fourier series method is used to find the finite amplitude Rayleigh number and heat and mass transfer. The transient behavior of the Nusselt number and Sherwood number is investigated by solving the finite amplitude equations using Runge–Kutta method.     

Linear and non-linear magnetoconvection in a porous medium

Linear and non-linear magnetoconvection in a sparsely packed porous medium with an imposed vertical magnetic field is studied. In the case of linear theory the conditions for direct and oscillatory modes are obtained using the normal modes. Conditions for simple and Hopf-bifurcations are also given. Using the theory of self-adjoint operator the variation of critical eigenvalue with physical parameters and boundary conditions is studied. In the case of non-linear theory the subcritical instabilities for disturbances of finite amplitude is discussed in detail using a truncated representation of the Fourier expansion. The formal eigenfunction expansion procedure in the Fourier expansion based on the eigenfunctions of the corresponding linear stability problem is justified by proving a completeness theorem for a general class of non-self-adjoint eigenvalue problems. It is found that heat transport increases with an increase in Rayleigh number, ratio of thermal diffusivity to magnetic diffusivity and porous parameter but decreases with an increase in Chandrasekhar number.     

Unsteady flow and heat transfer in a thin film of Ostwald–de Waele liquid over a stretching surface

In this paper, the effects of viscous dissipation and the temperature-dependent thermal conductivity on an unsteady flow and heat transfer in a thin liquid film of a non-Newtonian Ostwald–de Waele fluid over a horizontal porous stretching surface is studied. Using a similarity transformation, the time-dependent boundary-layer equations are reduced to a set of non-linear ordinary differential equations. The resulting five parameter problem is solved by the Keller–Box method. The effects of the unsteady parameter on the film thickness are explored numerically for different values of the power-law index parameter and the injection parameter. Numerical results for the velocity, the temperature, the skin friction and the wall-temperature gradient are presented through graphs and tables for different values of the pertinent parameter. One of the important findings of the study is that the film thickness increases with an increase in the power-law index parameter (as well as the injection parameter). Quite the opposite is true with the unsteady parameter. Furthermore, the wall-temperature gradient decreases with an increase in the Eckert number or the variable thermal conductivity parameter. Furthermore, the surface temperature of a shear thinning fluid is larger compared to the Newtonian and shear thickening fluids. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena.