Exact solutions to the Korteweg-de Vries-Burgers equation

We introduce a transormation which reduces the Korteweg-de Vries-Burgers (KdVB) equation, u_t + 2auu_x + 5bu_xx + cu_xxx = 0, to a quadratic form involving a new dependent variable and its partial derivatives. Exact solutions of the KdVB equation can be obtained by solving this equation. The exact form of the travelling wave solution to the KdVB equation is obtained in this paper, and its nature depends on the direction of propagation of the wave.     

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.     

Experimental study of turbulence in isothermal and stably stratified homogeneous shear flows: Mean flow measurements

The evolution of freestream turbulence under the combined action of linear shear and stable linear temperature profile is investigated. The experiment is carried out in a small, open circuit, low-speed test cell that uses air as working fluid. The temperature gradient formed at the entrance to the test section by means of an array of 24 horizontal, differentially heated elements is varied to get a maximum Brunt-Vaisala frequency N_o[=({g/T_m}{∂T/∂y})^1/2] of 3.1⁻¹. Linear velocity profiles are produced using screens of variable mesh size. The Reynolds number Re_M based on centre-line velocity and mesh size is varied from 80 to 175. Isothermal studies are carried out in four different experiments with varying velocity gradients. The effect of inlet turbulence level on growth of turbulence is studied in these flows by keeping the shear parameter Sh (=(x/u)(∂u/∂y)) constant. The range of shear parameters considered is 2.5–7.0. Shear and stratification combined produce a maximum gradient Richardson number Ri_g (= N_o²/(∂u/∂y)²) of 0.0145. Results have been presented in terms of evolution of variance of velocity fluctuations, Reynolds shear stress and temperature fluctuations. Measurements show the following: In isothermal flows the growth rate of turbulence quantities depends on both shear parameter and inlet turbulence level. There are distinct stages in the evolution of the flow and that can be identified by the power-law exponent of growth of turbulence. Shear is seen to promote the growth of turbulence and accelerate it towards a fully developed equilibrium state. Stratification initially suppresses the growth of turbulence and, hence, enhances the degree of underdevelopment. Under these conditions shear becomes active and subsequently enhances the growth rate of turbulence quantities.     

Coherent fine scale eddies in turbulence transition of spatially-developing mixing layer

To investigate the relationship between characteristics of the coherent fine scale eddy and a laminar–turbulent transition, a direct numerical simulation (DNS) of a spatially-developing turbulent mixing layer with Re_ω,0 = 700 was conducted. On the onset of the transition, strong coherent fine scale eddies appears in the mixing layer. The most expected value of maximum azimuthal velocity of the eddy is 2.0 times Kolmogorov velocity (u_k), and decreases to 1.2u_k, which is an asymptotic value in the fully-developed state, through the transition. The energy dissipation rate around the eddy is twice as high compared with that in the fully-developed state. However, the most expected diameter and eigenvalues ratio of strain rate acting on the coherent fine scale eddy are maintained to be 8 times Kolmogorov length (η) and :β:γ = −5:1:4 in the transition process. In addition to Kelvin–Helmholtz rollers, rib structures do not disappear in the transition process and are composed of lots of coherent fine scale eddies in the fully-developed state instead of a single eddy observed in early stage of the transition or in laminar flow.     

A study of properties of vortex stretching and enstrophy generation in numerical and laboratory turbulence

Dynamically relevant alignments are used in order to show that regions with weak vorticity are not structureless, non-Gaussian and dynamically not passive. for example, the structure of vorticity in quasi-homogeneous/isotropic turbulent flows is associated with strong alignment between vorticity ω and the eigenvectors of the rate of strain tensor λ_i (especially — but not only — between ω and λ₂) rather than with intense vorticity only. Consequently, much larger regions of turbulent flow than just those with intense vorticity are spatially structured. The whole flow field — even with the weakest measurable enstrophy — is strongly non-Gaussian, which among other things is manifested in strong alignment between vorticity and the vortex stretching vector W_i ≡ ω_jS_ij. It is shown that the quasi-two-dimensional regions corresponding to large cos(ω, λ₂) are qualitatively different from purely two-dimensional ones, e.g. in that they possess essentially nonvanishing enstrophy generation, which is larger than its mean for the whole field.     

仿生波纹夹层结构耐撞性分析及优化

为提高薄壁夹层结构耐撞性,以虾螯为仿生原型,设计梯度分布的仿生波纹形夹层结构,包括单层、双层和三层波纹结构。以初始峰值载荷F_p、比吸能E_s为耐撞性指标,利用有限元法分析了单元高宽比γ（γ₁、γ₂和γ₃分别为单元第1层、第2层和第3层的高宽比）对波纹夹层结构耐撞性的影响,采用多目标粒子群优化方法得到了夹层结构最优参数。结果表明,单层波纹结构耐撞性随单元高宽比γ的增大逐渐变差,双层波纹结构下层结构单元高宽比γ对耐撞性的影响大于上层结构单元高宽比γ对耐撞性的影响,较小的γ值有利于提高三层波纹结构的比吸能。结构优化结果表明:单层结构最优尺寸γ₁为0.8;双层结构最优尺寸为γ₁ = 0.5和γ₂ = 1.2;三层结构最优组合为γ₁ = 0.6,γ₂ = 0.6和γ₃ = 0.9。上述结果可为薄壁夹层结构轻量化设计提供新思路。     

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.     

Asymptotic soliton train solutions of Kaup–Boussinesq equations

Asymptotic soliton trains arising from a ‘large and smooth’ enough initial pulse are investigated by the use of the quasiclassical quantization method for the case of Kaup–Boussinesq shallow water equations. The parameter varying along the soliton train is determined by the Bohr–Sommerfeld quantization rule which generalizes the usual rule to the case of ‘two potentials’ h₀(x) and u₀(x) representing initial distributions of height and velocity, respectively. The influence of the initial velocity u₀(x) on the asymptotic stage of the evolution is determined. Excellent agreement of numerical solutions of the Kaup–Boussinesq equations with predictions of the asymptotic theory is found.     

An application of Nagumo''s lemma to some singularly perturbed systems

The existence and asymptotic behavior as ε → 0⁺ of periodic, almost periodic, and bounded solutions of the differential system x = f(t, x, y, ε), Ωy′ = g(t, x, y, ε), are considered where x, f; are n-vectors, y, g are m-vectors and Ω = diag{ε^h₁}…, ε^h_m for integral h_i, h₁ h₂ …, h_m. The principal tools are a lemma of Nagumo which allows the construction of appropriate upper and lower solutions and the asymptotic theory of singularly perturbed linear differential systems.     

Further consideration of the shape-factor relationship for turbulent boundary layers

The lag-entrainment predictive scheme developed by Green et al. has been modified to include the pressure-gradient parameter Π₁. In the original model suggested by Green et al. the mass-flow shape factor H₁ is related to the common shape factor H, H₁ = f(H). In the present model H₁ is related to H, Reynolds number based on the local momentum thickness θ, and Π₁; thus H₁ = f(H, R_eθ, Π₁). The modified formula for H₁, is introduced into the original lag-entrainment integral model. Calculations are made to examine the present model for the predictions of the development of boundary layers approaching separation studied experimentally by the authors. Slightly improved predictions are obtained using the model developed by El Telbany et al. However, the present model proved to give an improved representation of the development of wall shear stress in cases the two-equation turbulence model proved to be unsuccessful.     

Electromagnetic propagation in periodic porous structures

A variational technique is employed to compute approximate propagation constants for electromagnetic waves in a dielectric structure which is periodic in the X−Y plane and translationally invariant in the Z-direction. The fundamental cell, in the periodic structure, is composed of a pore and the surrounding host media. The pore is a circle of radius R₀ filled with a dielectric ε₁ and the host dielectric characterized by ε₂. The size of the cell is characterized by the length A which is R₀.

Two limiting cases are considered. In the first, the pore size is assumed to be much smaller than the wavelength; this limit is motivated by microwave heating of porous material. The approximate propagation constants are explicitly computed for this case and are shown to depend upon the two dielectric constants, the relative areas of the two regions in the cell, and on a modal number. They are not given by a simple mixture formula.

In the second limit, the pore size is taken to be of the same order as the wavelength; this limit is motivated by the propagation of light in a holey fiber. In this case our argument directly yields the dispersion relationship recently derived by Ferrando et al. [Opt. Lett. 24 (1999) 276], using intuitive and physical reasoning. Thus, our method puts theirs into a mathematical framework from which other approximations might be deduced.     

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.     

Al(OH)3对聚丙烯腈粉火焰传播特性影响研究

为研究Al(OH)₃粉体抑爆剂对聚丙烯腈（polyacrylonitrile, PAN）粉尘爆炸的抑制作用,利用透明管道爆炸传播测试系统,研究不同含量的Al(OH)₃对PAN粉尘爆炸火焰传播形态、温度等参数的影响,并采用扫描电镜、热重分析仪、傅里叶红外光谱仪研究Al(OH)₃抑制PAN粉尘爆炸的微观特征,总结出Al(OH)₃对PAN粉尘爆炸的抑制机理。测试结果表明,随着Al(OH)₃质量分数的增加,PAN粉尘爆燃的最大火焰传播距离和传播速度逐渐减小。同时压力监控及温度监控结果显示,随着Al(OH)₃质量分数的增加,PAN粉尘的最大爆炸压力及最大温度均逐渐减小,由此验证了Al(OH)₃对PAN粉尘爆炸的抑制作用,且60%质量比的Al(OH)₃的抑制效果最好。通过对PAN粉尘爆炸固态产物表征及热分析的研究,从物理和化学两个方面分析了Al(OH)₃对PAN粉尘火焰的抑制机理,物理抑制包括包覆、吸热降温、气体惰化3种方式,化学抑制主要通过消耗维持燃烧爆炸连锁反应的关键自由基?O和?OH减少了自由基?H、?OH与?O之间的放热反应。     

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.     

Non-linear oscillations with multiple forcing terms

The problem of determining the transient response of a non-linear oscillator of the form ü + u = εƒ(u,u) + E(t) is studied by the method of multiple time scales, using the symbolic computation system MACSYMA. when the excitation E(t) consists of a finite number of harmonic forcing terms. Here ε is a small parameter and ƒ(u,u) is a non-linear function of its arguments. In particular, the Van der Pol and Duffing oscillators are studied in detail. It is found that when the forcing frequencies are not close to each other or close to the primary resonance of the system, then the response of the system is analogous to the behavior when only one forcing term is present. However, when the forcing frequencies are close to each other or close to the primary resonance, then the behavior is quite different, exhibiting certain oscillations not observed in the case of one forcing term.     

(CuMnNi)100-xAlx高熵铜合金的显微组织、力学与摩擦学性能研究

针对工业领域对新型高强高耐磨金属材料的需求,制备了(CuMnNi)_100-xAl_x (x＝0, 5, 10, 15)系列高熵铜合金,研究了Al含量对高熵铜合金的物相组成、显微组织、力学性能和摩擦磨损性能的影响. 结果表明:CuMnNi高熵合金仅由面心立方结构(FCC)的高熵固溶体相组成,Al元素的添加对合金基体FCC相产生了强烈的固溶强化作用,并促进了体心立方(BCC)相形成. FCC相具有良好的塑性和韧性,而BCC相具有高强度和高硬度,两者共同作用使(CuMnNi)_100-xAl_x系列高熵铜合金的强度随Al含量增加而提高,而塑性和韧性不断降低. 其中,(CuMnNi)₉₀Al₁₀高熵铜合金中FCC相和BCC相的含量达到最佳匹配,使其具有优异的综合力学性能. 室温下,得益于优异的力学性能和硬质BCC相良好的抗磨作用,(CuMnNi)₉₀Al₁₀高熵铜合金的耐磨性优于常规耐磨铝青铜C6161,磨粒磨损为其主要磨损机制.      

电解质吸附对水基带电表面黏着的影响

为研究界面黏着,利用表面力仪在高离子强度电解质水溶液中测量负电云母表面之间的法向力.在纯水中,因范德华吸引,两表面跳跃至直接接触(间距0?),分离两表面时测得界面黏着力为-46.7 m N/m.在0.1 mol/L K₂SO₄中,因K₊离子牢固吸附于云母,表面间距稳定于5?,黏着力仅-2.9 m N/m;在0.1 mol/L Ca(NO₃)₂中,云母表面吸附的Ca₂⁺离子产生显著短程水合排斥,但在较低载荷下解吸附,导致两表面直接接触,黏着力高达-40.7 m N/m.加入Ca(OH)₂于0.1 mol/L K₂SO₄仅产生微弱短程排斥,黏着状态几乎与纯K₂SO₄水溶液中相同.聚电解质PCE从0.1 mol/L K₂SO₄中吸附于云母表面且诱导远程空间位阻排斥,但在中等载荷下解吸附,导...     

爆轰法合成纳米CeO粉末*2

爆轰合成过程中采用Ce(NO₃)₃·6H₂O制备的可爆药剂,并利用X射线衍射仪(XRD)和透射电子显微镜(TEM)对合成的纳米CeO₂粉末进行了检测,研究了起爆方式对于合成产物结晶化度、粒径和形貌的影响。结果表明,采用Ce(NO₃)₃·6H₂O制备的可爆药剂,可以合成立方晶系的球形纳米CeO₂; 提高可爆药剂的爆速,可有效降低纳米CeO₂的粒径,得到球形化更好的纳米粒子。     

Stability of flows in a peristaltic transport

The stability problem related to the basic flows induced by the peristaltic waves propagating along the deformable walls is investigated numerically. The neutral stability boundary is obtained by solving the relevant Orr–Sommerfeld equation via a verified preconditioned complex-matrix solver. The critical Reynolds number becomes 577.25 when the ratio of the wave speed to the maximum speed of the basic flow (c/u_max) becomes 10.