Direct numerical simulation of disturbances generated by periodic suction-blowing in a hypersonic boundary layer

A numerical algorithm and code are developed and applied to direct numerical simulation (DNS) of unsteady two-dimensional flow fields relevant to stability of the hypersonic boundary layer. An implicit second-order finite-volume technique is used for solving the compressible Navier–Stokes equations. Numerical simulation of disturbances generated by a periodic suction-blowing on a flat plate is performed at free-stream Mach number 6. For small forcing amplitudes, the second-mode growth rates predicted by DNS agree well with the growth rates resulted from the linear stability theory (LST) including nonparallel effects. This shows that numerical method allows for simulation of unstable processes despite its dissipative features. Calculations at large forcing amplitudes illustrate nonlinear dynamics of the disturbance flow field. DNS predicts a nonlinear saturation of fundamental harmonic and rapid growth of higher harmonics. These results are consistent with the experimental data of Stetson and Kimmel obtained on a sharp cone at the free-stream Mach number 8.     

A three-dimensional PSME model for rotating flows in an annular cavity

A pseudospectral matrix-element (PSME) numerical model is described for the simulation of rotating flows in a three-dimensional annular cavity. Temporal discretisation is implemented using a second-order semi-implicit scheme. Modified compressibility is invoked to handle the coupling between velocity and pressure while maintaining the incompressibility constraint. The governing continuity and Navier–Stokes momentum equations and boundary conditions are discretised using Chebyshev and Fourier collocation formulae. The model is validated against numerical results from alternative schemes and experimental data on rotating flows in an annular cavity. A base flow regime and instability patterns are observed, in accordance with other previously published investigations. It is demonstrated that the PSME model provides an accurate representation of rotating flows in an annular cavity.     

Two-way coupling of Eulerian–Lagrangian model for dispersed multiphase flows using filtering functions

Eulerian–Lagrangian approaches for dispersed multiphase flows can simulate detailed flow structures with a much higher spatial resolution than the Eulerian–Eulerian approaches. However, there are still unsolved problems regarding the calculation method for accurate two-way interaction, especially on the numerical instability due to the dispersion migration through discrete computational grids. Inadequate solvers sometimes produce false velocity fluctuation which makes the simulation unstable. In this paper, a new calculation method for dispersion-to-continuous phase interaction, which is accompanied by spherical dispersion migration, is proposed. The basic principle of the method is the introduction of Lagrangian filtering functions which convert discrete dispersion volume fractions to a spatially differentiable distribution. The performance of linear, Gaussian and sinewave filtering functions is examined by simple benchmark tests and applied to the simulation of dispersion-generated fluctuation. Using the present method, three-dimensional continuous phase flow structures induced by rising spherical bubbles and/or settling solid particles are demonstrated.     

Inviscid instabilities in two-dimensional spatially periodic flows

The instability of two-dimensional vortex arrays with hexagonal symmetry is investigated with respect to inviscid perturbations. A numerical treatment in the framework of Floquet theory provides critical parameters for instability onset and the spatial structure of unstable modes which are in agreement with experiments in electromagnetically driven flows conducting fluids. The stability of point vortex lattices is briefly discussed.     

Experimental studies of interfacial instabilities in multilayer pressure-driven flow of polymeric melts

The interfacial deformation and stability of two-(A-B) as well as three-layer symmetric (A-B-A) and asymmetric (A-B-C) pressure-driven flow of viscoelastic fluids has been investigated. Flow visualization in conjunction with digital image processing has been used to observe and measure the rate of encapsulation and interfacial stability/instability of the flow. Specifically, the encapsulation behavior as well as stability/instability of the interface and the corresponding growth or decay rate of disturbances as a function of various important parameters, namely, number of layers and their arrangement, layer depth ratio, viscosity and elasticity ratio as well as disturbance frequency, have been investigated. Based on these experiments, we have shown that the encapsulation phenomena occurs irrespective of the stability/instability of the interface and in cases when both encapsulation and instability occur simultaneously their coupling leads to highly complex and three-dimensional interfacial wave patterns. Moreover, it has been shown that the simple notion that less viscous fluids encapsulate more viscous fluids is incorrect and depending on the wetting properties of the fluid as well as their first and second normal stresses the reverse could occur. Additionally, in two- and three-layer flows it has been shown that by placing a thin, less viscous layer adjacent to the wall longwave disturbances can be stabilized while short and intermediate wavelength disturbances are stabilized when the more elastic fluid is the majority component. Furthermore, in three-layer flows it has been demonstrated that in the linear instability regime no dynamic interaction between the two interfaces is possible for short and intermediate wavenumber disturbances. However, in the nonlinear stability regime dynamic interactions between interfaces have been observed in this range of disturbance wavenumbers leading to highly chaotic flows. Finally, in the parameter space of this study no subcritical bifurcations were observed while supercritical bifurcations resulting in waves with a pointed front and a gradual tail were observed.     

Effects of inertia and surface tension on a power-law fluid flowing down a wavy incline

We consider a thin film of a power-law liquid flowing down an inclined wall with sinusoidal topography. Based on the von Kármán–Pohlhausen method an integral boundary-layer model for the film thickness and the flow rate is derived. This allows us to study the influence of the non-Newtonian properties on the steady free surface deformation. For weakly undulated walls we solve the governing equation analytically by a perturbation approach and find a resonant interaction of the free surface with the wavy bottom. Furthermore, the analytical approximation is validated by numerical simulations. Increasing the steepness of the wall reveals that nonlinear effects like the resonance of higher harmonics grow in importance. We find that shear-thickening flows lead to a decrease while shear thinning flows lead to an amplification of the steady free surface. A linear stability analysis of the steady state shows that the bottom undulation has in most cases a stabilizing influence on the free surface. Shear thickening fluids enhance this effect. The open questions which occurred in the linear analysis are then clarified by a nonlinear stability analysis. Finally, we show the important role of capillarity and discuss its influence on the steady solution and on the stability.     

高超声速尾迹流场稳定性数值研究

通过数值模拟, 对高超声速尾迹流场进行了研究, 对其尾迹流动的失稳过程进行了分析.选取计算模型为圆球,Ma= 6.0, Re = 1.71\times 10^6(Re以球头半径为参考长度). 通过数值模拟,首先得到的流动是稳定解,在底部发展出一个主分离区和一个二次分离区,流动是轴对称状态. 不添加任何扰动继续进行计算,发现底部流场缓慢发展出微弱的非定常流动. 随后,该现象继续发展,出现明显的结构失稳,得到了无量纲周期为12.0的周期解. 给出了高超声速圆球绕流尾迹结构的周期性演化过程,对其涡系结构的演化及奇点特征进行了分析. 研究表明该数值模拟方法可用于底部流动稳定性问题的研究,同时证实了高超声速底部流动也存在流动不稳定性.      

Pressure-based method for combustion instability analysis

An improved pressure-based method has been applied to predict the two-dimensional instability analysis of liquid-fuelled rocket engines. This method is non-iterative for transient flow calculations and applicable to all-speed flows. Validation cases include the shock-tube problem, the blast flow field and unsteady spraycombusting flows. Computations for the combustion instability analysis were carried out for various combustion parameters such as spray initial conditions and combustor geometries. Unsteady behaviours of the stable and unstable spray flame fields and effects of acoustic oscillations on the fuel droplet vaporization and combustion process are studied in detail. The present numerical model successfully demonstrates the capability of predicting combustion instability as well as fast transient compressible flows at all speeds.     

Linear stability and dynamics of viscoelastic flows using time-dependent numerical simulations

Ultimately, numerical simulation of viscoelastic flows will prove most useful if the calculations can predict the details of steady-state processing conditions as well as the linear stability and non-linear dynamics of these states. We use finite element spatial discretization coupled with a semi-implicit θ-method for time integration to explore the linear and non-linear dynamics of two, two-dimensional viscoelastic flows: plane Couette flow and pressure-driven flow past a linear, periodic array of cylinders in a channel. For the upper convected Maxwell (UCM) fluid, the linear stability analysis for the plane Couette flow can be performed in closed form and the two most dangerous, although always stable, eigenvalues and eigenfunctions are known in closed form. The eigenfunctions are non-orthogonal in the usual inner product and hence, the linear dynamics are expected to exhibit non-normal (non-exponential) behavior at intermediate times. This is demonstrated by numerical integration and by the definition of a suitable growth function based on the eigenvalues and the eigenvectors. Transient growth of the disturbances at intermediate times is predicted by the analysis for the UCM fluid and is demonstrated in linear dynamical simulations for the Oldroyd-B model. Simulations for the fully non-linear equations show the amplification of this transient growth that is caused by non-linear coupling between the non-orthogonal eigenvectors. The finite element analysis of linear stability to two-dimensional disturbances is extended to the two-dimensional flow past a linear, periodic array of cylinders in a channel, where the steady-state motion itself is known only from numerical calculations. For a single cylinder or widely separated cylinders, the flow is stable for the range of Deborah number (De) accessible in the calculations. Moreover, the dependence of the most dangerous eigenvalue on De≡λV/R resembles its behavior in simple shear flow, as does the spatial structure of the associated eigenfunction. However, for closely spaced cylinders, an instability is predicted with the critical Deborah number De_c scaling linearly with the dimensionless separation distance L between the cylinders, that is, the critical Deborah number De_Lc≡λV/L is shown to be an O(1) constant. The unstable eigenfunction appears as a family of two-dimensional vortices close to the channel wall which travel downstream. This instability is possibly caused by the interaction between a shear mode which approaches neutral stability for De ≫ 1 and the periodic modulation caused by the presence of the cylinders. Nonlinear time-dependent simulations show that this secondary flow eventually evolves into a stable limit cycle, indicative of a supercritical Hopf bifurcation from the steady base state.     

离散型湍流多相流动的研究进展和需求

离散型多相流动,指气体-颗粒(气-固)、液体-颗粒(液-固)、液体-气泡、气体-液雾以及气泡-液体-颗粒等两相或三相流动.这种类型的多相流动广泛存在于能源, 航天和航空, 化工和冶金,交通运输, 水利, 核能等领域.本文阐述了离散型多相流动的国内外基础研究,包括颗粒/液滴/气泡在流场中受流体动力作用力的研究, 颗粒-颗粒,液滴-液滴,气泡-气泡之间以及颗粒/液滴和壁面之间碰撞和聚集规律的研究,颗粒-气体和气泡-液体湍流相互作用的研究, 和数值模拟的研究,包括多相流动的雷诺平均模拟、大涡模拟和直接数值模拟的研究进展.最后, 归纳了目前尚待研究的需求.      

平面可压基频涡卷非线性演化行为数值研究

采用高精度迎风/对称紧致混合差分算法,对可压自由剪切层转捩区中的几种典型展向大尺度涡作用型态进行了直接数值模拟,通过施加给定来流条件下的线性最不稳定黏性基频扰动及其亚谐扰动,以被动守恒标量技术给出了基频涡卷的饱和、撕裂、融合以及三涡对并等细节结构。分析显示,亚谐振动相差是促生基频涡卷不同非线性演化过程的重要因素之一,可对扰动量的发展变化,以及剪切层厚度和混合效率产生直接影响,计算结果同实验流动显示图像十分相似,表明了主导线性扰动的非线性耦合效应与一些实际涡作用行为间的内联系。     

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL (Ⅰ) -THE UPPER BOUND ON THE EVOLUTION OF DISTURBANCE TO THE NONLINEARLY UNSTABLE BASIC FLOW

ＩｎｔｒｏｄｕｃｔｉｏｎＥｖｅｒｓｉｎｃｅＳｈｅｐｈｅｒｄｈａｓｓｕｇｇｅｓｔｅｄａｎｏｖｅｌｍｅｔｈｏｄｔｏｓｔｕｄｙｎｏｎｌｉｎｅａｒｓａｔｕｒａｔｉｏｎｏｆｂａｒｏｔｒｏｐｉｃａｎｄｂａｒｏｃｌｉｎｉｃｉｎｓｔａｂｉｌｉｔｙ[1- 3],ｍａｎｙａｕｔｈｏｒｓｈａｖｅｍａｄｅｆｕｒｔｈｅｒｒｅｓｅａｒｃｈｏｎｔｈｅｐｒｏｂｌｅｍ .Ｓｈｅｐｈｅｒｄ’ｓｍｅｔｈｏｄｉｓａｓｆｏｌｌｏｗｓ:Ｆｉｒｓｔ,ｃｈｏｏｓｅａｃｌａｓｓｏｆｓｔａｂｌｅｂａｓｉｃｆｌｏｗｓ;ｔｈｅｎ ,ｄｅｃｏｍｐｏｓｅｔｈｅｄｉｓｔ…     

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL(Ⅱ)- THE LOWER BOUND ON THE DISTURBANCE ENERGY AND POTENTIAL ENSTROPHY TO THE NONLINEARLY UNSTABLE BASIC FLOW

ＩｎｔｒｏｄｕｃｔｉｏｎＳｉｎｃｅｔｈｅｐｉｏｎｅｅｒｉｎｇｗｏｒｋｏｎｎｏｎｌｉｎｅａｒｓｔａｂｉｌｉｔｙｏｆｐｌａｎａｒｉｎｃｏｍｐｒｅｓｓｉｂｌｅｓｔｅａｄｙｆｌｏｗｂｙＡｒｎｏｌ’ｄ ,ａｇｒｅａｔｄｅａｌｏｆａｔｔｅｎｔｉｏｎｈａｓｂｅｅｎｐａｉｄｔｏｎｏｎｌｉｎｅａｒｓｔａｂｉｌｉｔｙｏｆｆｌｕｉｄ (ｅｓｐｅｃｉａｌｌｙｇｅｏｐｈｙｓｉｃａｌｆｌｕｉｄ)ｍｏｔｉｏｎ ,ａｎｄｍｕｃｈｐｒｏｇｒｅｓｓｈａｓｂｅｅｎｍａｄｅ.ＡｓｍｅｎｔｉｏｎｅｄｉｎＲｅｆ.[1 ] ,ｉｎｔｈｅｒｅａｌａｔｍｏｓ…     

聚苯胺体系电流变流体的阻尼机理及阻尼模型研究

对聚苯胺体系电流变流体在正弦信号作用下的阻尼力响应及其频谱特性进行了理论和实验研究。提出电流变流体的非线性阻尼力的频谱是由基频和频率为基频奇数倍的高次谐波分量组成。建立了由粘性阻尼和迟滞阻尼组成的电流变流体阻尼模型，通过对模型的傅立叶变换及数值仿真，验证了理论分析及阻尼模型的正确性。     

On the stability of the shear flow of a viscoelastic fluid with slip along the fixed wall

In this paper we solve the time-dependent shear flow of an Oldroyd-B fluid with slip along the fixed wall. We use a non-linear slip model relating the shear stress to the velocity at the wall and exhibiting a maximum and a minimum. We assume that the material parameters in the slip equation are such that multiple steady-state solutions do not exist. The stability of the steady-state solutions is investigated by means of a one-dimensional linear stability analysis and by numerical calculations. The instability regimes are always within or coincide with the negative-slope regime of the slip equation. As expected, the numerical results show that the instability regimes are much broader than those predicted by the linear stability analysis. Under our assumptions for the slip equation, the Newtonian solutions are stable everywhere. The interval of instability grows as one moves from the Newtonian to the upper-convected Maxwell model. Perturbing an unstable steady-state solution leads to periodic solutions. The amplitude and the period of the oscillations increase with elasticity.     

Centrifugal instability and the rib vortices in the cylinder wake

The physical mechanism for generation of streamwise vortices (or rib vortices) in the cylinder wake is numerically investigated with a finite-difference scheme. Rayleigh's theory of centrifugal instability for inviscid axisymmetric flow is extended to analyze the 2-D primary flows. Accordingly, an analytical dimensionless groupRay=−(r/v _θ)∂v _θ/∂r−1 is derived, wherev _θ represents the velocity of a fluid element relative to the oncoming flow,r is the local curvature radius of the element pathline. Centrifugal instability occurs whenRay>0. Stability analyses are carried out with this discriminant for primary flows at different time levels in a half shedding period of the von Kármán (or vK) vortices. Unstable areas are identified and the locations of rib vortices are coincident well with the unstable areas within the first wavelength of vK vortices behind the cylinder. The numerical results also show that rib vortices experience amplification in this region. It is apparent that centrifugal instability plays an important role in the generation of rib vortices in the cylinder wake. The project spported by the National Natural Science Foundation of China     

Spectral methods for the simulation of incompressible flows in spherical shells

A spatial discretization of the incompressible Navier–Stokes equation is presented in which the velocity is decomposed using poloidal and toroidal scalars whose spatial dependence is given in terms of spherical harmonics and Chebychev polynomials. The radial resolution needs to be large enough at any given angular resolution in order to avoid instability in the simulation of rotating flows. Several semi‐implicit time steps are discussed. The most accurate scheme is an integrating factor technique. Copyright © 1999 John Wiley & Sons, Ltd.     

Linear instability in the wake of an elliptic wing

Linear global instability analysis has been performed in the wake of a low aspect ratio three-dimensional wing of elliptic cross section, constructed with appropriately scaled Eppler E387 airfoils. The flow field over the airfoil and in its wake has been computed by full three-dimensional direct numerical simulation at a chord Reynolds number of \(Re_{c}=1750\) and two angles of attack, \(\mathrm{{AoA}}=0^\circ \) and \(5^\circ \). Point-vortex methods have been employed to predict the inviscid counterpart of this flow. The spatial BiGlobal eigenvalue problem governing linear small-amplitude perturbations superposed upon the viscous three-dimensional wake has been solved at several axial locations, and results were used to initialize linear PSE-3D analyses without any simplifying assumptions regarding the form of the trailing vortex system, other than weak dependence of all flow quantities on the axial spatial direction. Two classes of linearly unstable perturbations were identified, namely stronger-amplified symmetric modes and weaker-amplified antisymmetric disturbances, both peaking at the vortex sheet which connects the trailing vortices. The amplitude functions of both classes of modes were documented, and their characteristics were compared with those delivered by local linear stability analysis in the wake near the symmetry plane and in the vicinity of the vortex core. While all linear instability analysis approaches employed have delivered qualitatively consistent predictions, only PSE-3D is free from assumptions regarding the underlying base flow and should thus be employed to obtain quantitative information on amplification rates and amplitude functions in this class of configurations.     

Direct numerical simulation of turbulent Taylor–Couette flow

The direct numerical simulation (DNS) of the Taylor–Couette flow in the fully turbulent regime is described. The numerical method extends the work by Quadrio and Luchini [M. Quadrio, P. Luchini, Eur. J. Mech. B/Fluids 21 (2002) 413–427], and is based on a parallel computer code which uses mixed spatial discretization (spectral schemes in the homogeneous directions, and fourth-order, compact explicit finite-difference schemes in the radial direction). A DNS is carried out to simulate for the first time the turbulent Taylor–Couette flow in the turbulent regime. Statistical quantities are computed to complement the existing experimental information, with a view to compare it to planar, pressure-driven turbulent flow at the same value of the Reynolds number. The main source for differences in flow statistics between plane and curved-wall flows is attributed to the presence of large-scale rotating structures generated by curvature effects.     

金属切屑塑性流动的稳定性

对金属正交切削过程中切屑形成机制和材料塑性流动行为进行实验研究和理论分析. 通过对4 种常用金属材料正交切削过程的实验研究和切屑形貌的微观观察,确定了连续切屑转变成锯齿切屑的临界速度. 结果表明该临界速度与材料性能相关. 在实验观察基础上,提出描述材料正交切削过程的二维分析模型. 该模型假设切屑形成区为包括主剪切区和次剪切区的一个平行四边形. 载荷有主剪切区中的剪应力和次剪切区中的正压力;通过量纲分析得到描述材料正交切削过程的无量纲主控参数和无量纲形式的基本控制方程;应用线性稳定性分析方法建立平面应变状态下评价材料塑性流动稳定性的普遍准则;求得切屑形成区内材料塑性变形的速度和应力近似解. 讨论切屑形成、形貌转变以及相关的塑性失稳机制. 分析结果表明, 表征材料惯性与阻尼之比的无量纲参数— 雷诺数可以作为主控参数描述金属切削过程以及切屑材料塑性流动的稳定性.