Vortical structures in a turbulent far-wake: effect of Reynolds number

The effect of the Reynolds number on vortical structures in a turbulent far-wake has been investigated for Re_d (based on the free stream velocity and the cylinder diameter) =2800 and 9750. Velocity data were obtained using two orthogonal arrays of 16 X-wires, eight in the (x,y)-plane and eight in the (x,z)-plane. Structures were detected in both planes using a technique based on vorticity concentration and circulation. Conditional streamlines and contours of vorticity based on spanwise structures, i.e. detections in the (x,y)-plane, reveal that the streamwise size of spanwise structures increases as Re_d increases. The interrelationship is investigated between detections simultaneously identified in the two planes. Transverse structures, i.e. detections in the (x,z)-plane, correspond, with a relatively high probability, to spanwise structures, in conformity with a distortion in the (y,z)-plane of spanwise structures. Those that correspond, with relatively high probability, to the saddle between consecutive spanwise structures are interpreted in terms of ribs, whose signatures are detectable in instantaneous data. The probability is also high for transverse structures to occur between the focus of a spanwise structure and its associated saddle when Re_d=9750, but not when Re_d=2800. This is consistent with an increased vortex pairing frequency at the higher Re_d, as observed in instantaneous sectional streamlines.     

Uniformly valid approximations for non-linear oscillations with small damping

A uniformly valid zeroth-order approximation is obtained for the general equation y + εH(y)y + M(y)y = 0, where ε is a small parameter. The notion of multiple scaling is utilized to set up a systematic approximation scheme. Examples are given for simple polynomials for H(y) and M(y), which lead to results involving elliptic integrals. Further restrictions allow progress to be made in terms of gamma functions.     

Stress state of compound polygonal plate

The constructions made of bars and plates with holes, openings and bulges of various forms are widely used in modern industry. By loading these structural elements with different efforts, there appears concentration (accumulation) of stress whose values sometimes exceeds the admissible one. The durability of the given element is defined according to the quantity of these stresses. Since the failure of details and construction itself begins from the place where the stress concentration has the greatest value.

Therefore the exact determination of stress distribution in details (bars, plates, beams) is of great scientific and practical interest and is one of the important problems of the solid fracture.

Compound details (when the nucleus of different material is soldered to the hole) are often used to decrease the stress concentration.

In the present paper, we study a stress–strain state of polygonal plate weakened by a central elliptic hole with two linear cracks info which a rigid nucleus (elliptic cylinder with two linear bulges) of different material was put in (soldered) without preload.

The problem is solved by a complex variable functions theory stated in papers [Theory of Elasticity, Higher School, Moscow, 1976, p. 276; Plane Problem of Elasticity Theory of Plates with Holes, Cuts and Inclusions, Publishing House Highest School, Kiev, 1975, p. 228; Bidimensional Problem of Elasticity Theory, Stroyizdat, Moscow, 1991, p. 352; Science, Moscow (1996) 708; MSB AH USSR OTH 9 (1948) 1371].

Kolosov–Mushkelishvili complex potential (z) and ψ(z) satisfying the definite boundary conditions are sought in the form of sums of functional series.

After making several strict mathematical transformations, the problem is reduced to the solution of a system of linear algebraic equations with respect to the coefficients of expansions of functions (z) and ψ(z).

Determining the values of (z) and ψ(z), we can find the stress components σ_r, σ_θ and τ_rθ at any point of cross-section of the plate and nucleus on the basis of the known formulae. The obtained solution is illustrated by numerical example.

Changing the parameters A₁, m₁, e, A₂, and m₂ we can get the various contour plates.

For example, if we assume m₁=0, A₁=r, then the internal contour of L₁ becomes the circle of radius r with two rectilinear cracks (for the nucleus––a rectilinear bulges).

Further, if we assume a small semi-axis of the ellipse b₁ to be equal to zero (b₁=0), then a linear crack becomes the internal contour of L₁ (and the nucleus becomes the linear rigid inclusion made of other material). For m₂=0; A₂=R, the external contour L₂ turns into the circle of radius R.

The obtained method of solution may be applied and in other similar problems of elasticity theory; tension of compound polygonal plate, torsion and bending of compound prismatic beams, etc.     

Flow measurements inside a heated multiple rotating cavity with axial throughflow

This paper discusses experimental results from a multiple cavity test rig representative of a high pressure compressor internal air system. Measurements of the axial, tangential and radial velocity components are presented. These were made using a two component, laser doppler anemometry (LDA) system for a range of non-dimensional parameters representative of engine conditions (Re up to 4 × 10⁶ and Re_z up to 1.8 × 10⁵). Tests were carried out for two different sizes of annular gap between the (non-rotating) drive shaft and the disc bores.

The axial and radial velocities inside the cavities are virtually zero. The size of the annular gap between disc bore and shaft has a significant effect on the radial distribution of tangential velocity. For the narrow annular gap (d_h/b = 0.092), there is an increase of non-dimensional tangential velocity V/Ωr with radial location from V/Ωr < 1 at the lower radii to solid body rotation V/Ωr = 1 further into the cavity. For the wider annular gap (d_h/b = 0.164), there is a decrease from V/Ωr > 1 at the lower radii to solid body rotation further into the cavity. An analysis of the frequency spectrum obtained from the tangential velocity measurements is consistent with a flow structure in the r– plane consisting of pairs of contra rotating vortices.     

The effect of axial stretch on cavitation in an elastic cylinder

The phenomenon of cavitation in an elastic cylinder subjected to a combined axial stretch λ_z and radial traction P is examined. One possible response of the cylinder to this loading, for all λ_z; and P, is a pure homogeneous deformation. However, for some materials, the homogeneous deformation becomes unstable at certain critical values of (λ_z, P), and a second deformation bifurcates from the homogeneous one; this latter deformation involves a cylindrical cavity co-axial with the elastic cylinder. We determine the values of (λ_z, P) at which this happens. The results are displayed by constructing a curve in the (λ_z, P)-plane which divides this plane into regions where the homogeneous deformation is stable and unstable.     

Can a single-wall carbon nanotube be modeled as a thin shell?

Single-wall carbon nanotubes (SWCNT) have been frequently modeled as thin shells, but the shell thickness and Young's modulus reported in literatures display large scattering. The order of error to approximate SWCNTs as thin shells is studied in this paper via an atomistic-based finite-deformation shell theory, which avoids the shell thickness and Young's modulus, but links the tension and bending rigidities directly to the interatomic potential. The ratio of atomic spacing (Δ≈0.14 nm) to the radius of SWCNT, Δ/R, which ranges from zero (for graphene) to 40% [for a small (5,5) armchair SWCNT (R=0.35 nm)], is used to estimate the order of error. For the order of error O[(Δ/R)³], SWCNTs cannot be represented by a conventional thin shell because their constitutive relation involves the coupling between tension and curvature and between bending and strain. For the order of error O[(Δ/R)²], the tension and bending (shear and torsion) rigidities of SWCNTs can be represented by an elastic orthotropic thin shell, but the thickness and elastic modulus cannot. Only for the order of error O(Δ/R), a universal constant shell thickness can be defined and SWCNTs can be modeled as an elastic isotropic thin shell.     

Solutions of some classes of second order non-linear ordinary differential equations

A second order non-linear ordinary differential equation satisfied by a homogeneous function of u and v where u is a solution of the linear equation ÿ + p(t)ÿ + r(t)y = 0 and v = ωu, ω being an arbitrary function of t, is obtained. Defining ω suitably in two specific cases, solutions are obtained for a non-linear equation of the form ÿ + p(t)ÿ + q(t)y = μÿ²y^{−1 +} f(t)yⁿ where μ ≠ 1, n≠ 1. Applying our results, some classes of equations of the above type possessing solutions involving two or one or no arbitrary constants are derived. Some illustrative examples are also discussed.     

激波诱导下的气体界面不稳定性实验研究

界面不稳定性, 特别是Richtmyer–Meshkov (RM) 不稳定性, 是流体
力学中一项重要的研究内容, 无论在学术研究领域还是工程应用领域都有着
重要的研究价值和应用背景. RM 不稳定性问题自提出以来, 得到了学术界
广泛的关注, 其研究无论是在实验方法、数值模拟还是在理论分析方面都取
得了很大的进展. 在激波管中开展激波与界面相互作用的实验研究, 即研究
界面初始扰动在激波诱导下的演化规律, 是目前研究RM 不稳定性的重要手
段. RM 不稳定性实验研究包括3 个部分, 分别是激波的产生、界面的形成
以及流场的观测. 综述了RM 不稳定性的实验研究进展, 并针对目前研究的
局限性提出了RM 不稳定性今后实验研究的重点和方向: 汇聚激波作用下界
面不稳定性的发展规律; 激波冲击下多种形状及大振幅界面的演化机理; 三
维界面的RM 不稳定性发展规律; 可压缩湍流的形成与混合机理.      

Pressure spectra in homogeneous low Reynolds number turbulent shear flow subjected to weak rotation

In this paper, pressure spectra have been derived from the authors’ model (Eur. J. Mech., B/Fluids 12 (1) (1993) 31–42) developed by means of rapid distortion theory (RDT) of homogeneous low Reynolds number turbulent shear flow subjected to weak rotation. The combined effects of uniform shear dU₁/dx₂ and weak rotation Ω₃ on the evolution of pressure spectra have been examined in terms of the rotation number 2Ω₃/(dU₁/dx₂). It is found that the system rotation exhibits the opposite effect on the pressure field as compared with the influence of rotation on the velocity fluctuations.     

镁合金表面磁控溅射CNx/SiC/Ti多层膜的摩擦磨损性能

采用室温磁控溅射技术在镁合金(AZ91D)表面制备了CNx/SiC/Ti(氮化碳/碳化硅/钛)多层膜(SiC、Ti为中间层),研究了CNx薄膜的纳米压痕行为和摩擦磨损性能.结果表明:CNx薄膜具有低的纳米硬度(6.67GPa)、低的弹性模量(54.68GPa)和高的硬度与弹性模量比值(0.122);在以氮化硅球为对摩副的室温干摩擦条件下摩擦系数约为0.162,磨损率在10-6mm3/(m.N)级,薄膜经长时间(3.5h)磨损后未出现裂纹和剥落.分析表明,摩擦化学和硬度与弹性模量比值对摩擦系数和磨损率有重要影响.     

Shear-free turbulent diffusion—classical and new scaling laws

We consider the problem of turbulence generation at a vibrating grid in the x₂–x₃ plane. Turbulence diffuses in the x₁-direction. Analyzing the multi-point correlation equation using Lie-group analysis, we find three different invariant solutions (scaling laws): classical diffusion-like solution (heat equation like), decelerating diffusion-wave solution and finite domain diffusion due to rotation. All solutions have been obtained using Lie-group (symmetry) methods. It is shown that if only one spatial dimension is considered, models based on Reynolds averaging are only capable to model either the diffusion-like solution or the decelerating diffusion-wave solution. The latter solution is only admitted under certain algebraic constraints on the model constants; e.g. in case of the K– model the model constants need to obey the relation c₂σ/σ_K=2. Turbulent diffusion on a finite domain induced by rotation is not admitted by any of the classical models. Finally, in the appendix it is shown that Lele's transformation (Phys. Fluids 28(1) (1985) 64) leads to a complete analytic solution of the steady diffusion problem modelled by the K– equation.     

Convection regimes and heat transfer characteristics along a continuously moving heated vertical plate

The steady laminar flow and thermal characteristics of a continuously moving vertical sheet of extruded material are studied close to and far downstream from the extrusion slot. The velocity and temperature variations, obtained by a finite volume method, are used to map out the entire forced, mixed and natural convection regimes. The effects of the Prandtl number (Pr) and the buoyancy force parameter (B) on the friction and heat transfer coefficients are investigated. Comparisons with experimental measurements and solutions by others in the pure forced and pure natural convection regions are made. In the mixed convection region, the results are compared with available finite-difference solutions of the boundary layer equations showing excellent agreement. The region close to the extrusion slot is characterized as a non-similar forced-convection dominated region in which Nu_xRe_x^−1/2 drops sharply with increasing Richardson number (Ri_x). This is followed by a self-similar forced-convection dominated region in which Nu_xRe_x^−1/2 levels off with increasing Ri_x until the buoyancy effect sets in. The existence and extent of the latter region depend upon the value of B. A non-similar mixed convection region where increasing buoyancy effect enhances the heat transfer rate follows. Finally, this region is followed downstream by a self-similar natural-convection dominated region in which Nu_xRe_x^−1/2 approaches the pure natural convection asymptote at large Ri_x. Critical values of Ri_x to distinguish the various convection regimes are determined for different Pr and B.     

Effects of polymer additives on the large scale structure of a two-dimensional submerged jet

The large structures on the boundary of a two-dimensional submerged jet were examined. In the first experiment, a jet of a 100 ppm aqueous polyacrylamid solution was fed into pure water (P/W). In the second experiment, the jet as well as the ambient fluid were pure water (W/W), whereas in the third experiment, polymer solution (W/P) was in the ambient only.The large structures were found to be of the same size for all three experiments. The spread-angle was lowest for P/W and highest for W/P. These effects are attributed to a strong flow which stretches the polymer molecules in the mixing layer.     

Conjugate natural convection from an array of discrete heat sources: part 2 — a numerical parametric study

Coupled conduction and natural convection transport within a discretely heated cavity have been investigated numerically. One vertical wall of the cavity is composed of discrete, isoflux heat sources mounted in a substrate of finite thermal conductivity. The opposite vertical wall and the horizontal walls are assumed to be isothermal and adiabatic, respectively. The governing steady-state partial differential equations for the fluid and solid region are solved simultaneously using a control volume formulation, coupled with an additive correction multigrid procedure that increases the convergence rate of the solution. The fluid Prandtl number and heater/fluid thermal conductivity ratio are fixed at 25 and 2350, respectively, corresponding to a dielectric fluid (FC-77) and heaters manufactured from silicon. With increasing modified Rayleigh number (10⁴ < Ra_Lz^* < 109), the cavity flow becomes more boundary layer-like along the vertical walls, and multiple fluid cells develop in the central region. Thermal spreading in the substrate increases with decreasing modified Rayleigh number and with increasing values of the substrate/fluid thermal conductivity ratio (10⁻¹ <- R_s ≤ 10³). For large R_s, the discrete heat sources lose their thermal identity, and the streamlines and isotherms resemble those associated with a differentially heated cavity. Thermal spreading in the substrate also has a significant effect on circulation in the cavity and on maximum surface temperatures.     

Theoretical analysis of a wheel driven root crop harvester

A prototype of a wheel driven trailer was developed to simulate a wheel driven trailed root crop harvester. The mobility of the prototype tractor-trailer system was improved by driving the trailer wheels by a mounted engine. A mathematical model to predict the mobility and the stability of the system was developed. The model was validated by field experiments conducted in plowed, rotary tilled and untilled fields. The model was found to predict performance with a high accuracy. Parameter studies were conducted to investigate the effects of several design parameters, such as the peripheral velocity ratio (R_s), the weight of the trailer (m₁), the trailer's C.G. location (L_L) and the height of a hitch point (h), on the mobility and the stability of the system.     

Hole diameter effect on flow characteristics of wake behind porous fences having the same porosity

The hole diameter effect on the flow characteristics of wake behind porous fences has been investigated experimentally in a circulating water channel having a test section of 300^w×200^h×1200^l (mm). Three porous fences having different hole diameters of d=1.4,2.1,2.8 mm were tested in this study, but they have the same =38.5% geometric porosity. One thousand instantaneous velocity fields for each fence were measured consecutively by the hybrid PTV system employing a high-speed CCD camera. Free stream velocity was fixed at 10 cm/sec and the corresponding Reynolds number based on the fence height was Re=2,985. Consequently, the fence with the smallest hole diameter d=1.4 mm (d_1.4) decreases the streamwise velocity component and increases the vertical velocity component. Among the three hole diameters tested in this study, the d_1.4 fence has the largest turbulence intensity in the shear layer developed from the fence top. Regardless of the hole diameter, however, all three fences having the same porosity reduce the reduction of turbulent intensity in the lower region below the fence height (y/H<1).     

Strain-gage stability measurements for three years at 150°C in air

The zero shifts of nickel-chromium foil strain gages (modified Karma) were measured over a period of three years at a constant temperature of 150°C in air. Three gage lengths were included—1.585 mm (1/16 in.), 3.170 mm (1/8 in.), and 6.340 mm (1/4 in.). The strain gages were bonded to constant-stress cantilever beams which were subjected to nomial mechanical strain levels of 0, ±780 μm/m, and ± 1350 μm/m. Each strian gage was connected by threewire leads to a Wheatstone-bridge circuit for the test duration. The data support two general observations: (1) short gage lengths suffer larger zero shifts than longer gage lengths, and (2) gages in compression suffer large zero shifts than gages in tension. On the assumption that the major cause of the zero shifts is a combination of corrosion of the foil and creep of the gage/epoxy/beam system, the author suggests a possible way to correct for the zero shift by experimentally determining the combined corrosion/creep effect and substracting it from the strain-gage readings. Some of the data appear to be consistent with this assumption, but some of the data do not.     

On rubber disks under rotation or axisymmetric stretching

The governing equations for a class of axisymmetric problems under large elastic deformation, concerned with a circular rubber disk with body force as well as non-uniform initial thickness, are formulated in terms of two coupled first-order ordinary differential equations with explicit derivatives. The following two problems subjected to different boundary conditions are solved: (a) Rotating disks with uniform initial thickness (b) Circular disks with non-uniform initial thickness under axisymmetric stretching at the outer boundary. In problem (b), the rubber disk whose initial thickness contour is h₀ = crⁿ (where c and n are any constants), or whose final thickness is a constant, is considered. Highly elastic materials with a Mooney strain-energy function are used for numerical calculations.     

Large-scale structure of a leading-edge separation bubble with local forcing

The Karhunen-Loeve (K-L) expansion is used to extract coherent structures from a leading-edge separation bubble with local forcing. A leading-edge separation bubble is simulated using the discrete vortex method, where a time-dependent source forcing is perturbed near the separation point. Based on the wealth of numerical data, the K-L procedure is applied in a range of the forcing amplitude (A₀ = 0, 0.5, 1.0 and 1.5) and forcing frequency (0 f_FH/U_∞ 0.3). Application of K-L procedure reveals that the eigenstructures are changed noticeably by local forcings. In an effort to investigate the mechanism of decreasing reattachment length (x_R), dynamic behaviors of the expansion coefficients and contributions of the eigenfunctions are scrutinized. As the forcing amplitude increases, large-scale vortex structures are formed near the separation point. Furthermore, the flow becomes more organized, which results in the reduction of x_R. Two distinctive regimes are classified: the regime of decreaing x_R and the regime of increasing x_R. The K-L global entropy indicates that x_R is closely linked to the organization of the flow structure.     

Microwave-hydrothermal preparation of a graphene/hierarchy structure MnO2 composite for a supercapacitor

Graphene/hierarchy structure manganese dioxide （GN/MnO2） composites were synthesized using a simple microwave-hydrothermal method. The properties of the prepared composites were analyzed using field emission scanning electron microscopy （FE-SEM）, X-ray diffraction （XRD）, transmission electron microscopy （TEM）, and X-ray photoelectron spectroscopy （XPS） measurements. The electrochemical performances of the composites were analyzed using cyclic voltammetry, electrochemical impedance spectrometry （EIS）, and chronopotentiometry. The results showed that GN/MnO2 （10 wt% graphene） displayed a specific capacitance of 244 F/g at a current density of 100 mA/g. An excellent cyclic stability was obtained with a capacity retention of approximately 94.3% after 500 cycles in a 1 mol/L Li2SO4 solution. The improved electrochemical performance is attributed to the hierarchy structure of the manganese dioxide, which can enlarge the interface between the active materials and the electrolyte. The prepa- ration route provides a new approach for hierarchy structure graphene composites; this work could be readily extended to the preparation of other graphene-based composites with different structures for use in energy storage devices.