DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.     

On numerical solution of dynamic problems in the theory of reinforced shells

Dynamic problems for cylindrical shells reinforced with discrete ribs are examined. A numerical algorithm based on Richardson extrapolation is developed. Specific problems are solved, and the results are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 50–56, May 2006.     

Gyromat 2000陀螺经纬仪强制对中装置的研制

Gyromat2000陀螺经纬仪是目前自动化程度和精度最高的电子陀螺经纬仪，为了保证其在强制对中方位边上高精度的测量，必须对仪器的强制对中装置进行研制，该文结合作者实践过程，对该装置的研制和测试工作进行阐述。     

钝体射流火焰及其点火过程的大涡模拟

钝体燃烧器广泛应用于航空发动机、燃气轮机、锅炉等设备的燃烧室中.对其点火过程的了解和控制直接关系到设备的安全运行和污染物排放等重要问题.我们采用基于火焰面/过程变量燃烧模型的大涡模拟方法对湍流非预混钝体射流火焰及其点火过程进行了详细的数值模拟.以Sydney钝体燃烧器的无反应射流和有反应甲烷/氢气(CH_4/H_2)火焰为研究对象,首先通过统计平均的数值结果与实验测量及文献数据的对比,全面检验了所用数值方法和燃烧模型;随后,详细展示了钝体燃烧器点火和火焰发展的瞬态过程;最后,对钝体射流的点火过程进行了细致的分析和表征.根据温度峰值、羟基(OH)质量分数和甲醛(CH_2O)质量分数峰值随时间的变化表征了强制点火过程的4个阶段:点火源衰减、点火触发、点火核生成和点火成功.其中,点火核驻留的空间位置位于钝体燃烧器冷态流场外侧涡的尾部回流区域附近.     

Darcy-Forchheimer natural,forced and mixed convection heat transfer in non-Newtonian power-law fluid-saturated porous media

The governing equation for Darcy-Forchheimer flow of non-Newtonian inelastic power-law fluid through porous media has been derived from first principles. Using this equation, the problem of Darcy-Forchheimer natural, forced, and mixed convection within the porous media saturated with a power-law fluid has been solved using the approximate integral method. It is observed that a similarity solution exists specifically for only the case of an isothermal vertical flat plate embedded in the porous media. The results based on the approximate method, when compared with existing exact solutions show an agreement of within a maximum error bound of 2.5%.Nomenclature A cross-sectional area - b _i coefficient in the chosen temperature profile - B ₁ coefficient in the profile for the dimensionless boundary layer thickness - C coefficient in the modified Forchheimer term for power-law fluids - C ₁ coefficient in the Oseen approximation which depends essentially on pore geometry - C _i coefficient depending essentially on pore geometry - C _D drag coefficient - C _t coefficient in the expression forK ^* - d particle diameter (for irregular shaped particles, it is characteristic length for average-size particle) - f _p resistance or drag on a single particle - F _R total resistance to flow offered byN particles in the porous media - g acceleration due to gravity - g _x component of the acceleration due to gravity in thex-direction - Grashof number based on permeability for power-law fluids - K intrinsic permeability of the porous media - K ^* modified permeability of the porous media for flow of power-law fluids - l _c characteristic length - m exponent in the gravity field - n power-law index of the inelastic non-Newtonian fluid - N total number of particles - Nux,_D,F local Nusselt number for Darcy forced convection flow - Nux,_D-F,F local Nusselt number for Darcy-Forchheimer forced convection flow - Nux,_D,M local Nusselt number for Darcy mixed convection flow - Nux,_D-F,M local Nusselt number for Darcy-Forchheimer mixed convection flow - Nux,_D,N local Nusselt number for Darcy natural convection flow - Nux,_D-F,N local Nusselt number for Darcy-Forchheimer natural convection flow - pressure - p exponent in the wall temperature variation - _Pe c characteristic Péclet number - _Pe x local Péclet number for forced convection flow - _Pe x modified local Péclet number for mixed convection flow - _Ra c characteristic Rayleigh number - _Ra x local Rayleigh number for Darcy natural convection flow - _Ra x local Rayleigh number for Darcy-Forchheimer natural convection flow - Re convectional Reynolds number for power-law fluids - Reynolds number based on permeability for power-law fluids - T temperature - T _e ambient constant temperature - T w,_ref constant reference wall surface temperature - T _w(X) variable wall surface temperature - T _w temperature difference equal toT w,_ref–T _e - T ₁ term in the Darcy-Forchheimer natural convection regime for Newtonian fluids - T ₂ term in the Darcy-Forchheimer natural convection regime for non-Newtonian fluids (first approximation) - T _N term in the Darcy/Forchheimer natural convection regime for non-Newtonian fluids (second approximation) - u Darcian or superficial velocity - u ₁ dimensionless velocity profile - u _e external forced convection flow velocity - u _s seepage velocity (local average velocity of flow around the particle) - u _w wall slip velocity - U c _M characteristic velocity for mixed convection - U c _N characteristic velocity for natural convection - x, y boundary-layer coordinates - x ₁,y ₁ dimensionless boundary layer coordinates - X coefficient which is a function of flow behaviour indexn for power-law fluids - effective thermal diffusivity of the porous medium - shape factor which takes a value of/4 for spheres - shape factor which takes a value of/6 for spheres - ₀ expansion coefficient of the fluid - _T boundary-layer thickness - T ₁ dimensionless boundary layer thickness - porosity of the medium - similarity variable - dimensionless temperature difference - coefficient which is a function of the geometry of the porous media (it takes a value of 3 for a single sphere in an infinite fluid) - ₀ viscosity of Newtonian fluid - ^* fluid consistency of the inelastic non-Newtonian power-law fluid - constant equal toX(2 ^2–n )/ - density of the fluid - dimensionless wall temperature difference     

On attenuation of free and forced waves in an infinitely long visco-elastic layer of a constant thickness

The conventional concepts of a loss factor and a complex-valued elastic module are used to study wave attenuation in a visco-elastic layer. The hierarchy of reduced order models is employed to assess attenuation levels of free and forced waves in various situations. First, the free waves are considered. In the low frequency limit, the attenuation of these waves is found to be in the excellent agreement with the existing knowledge. At high frequencies, predictions of the reduced order models fully agree with the solutions of exact Rayleigh–Lamb problem. Alternative excitation cases are considered for the forcing problem and a measure of the attenuation level is proposed and validated. The differences between two regimes, the low frequency one, when a waveguide supports only one propagating wave, and the high frequency one, when several waves are supported, are demonstrated and explained.     

垂直激励圆柱形容器中的表面波特性研究

利用奇异摄动理论的两时间变量展开法，研究了垂直强迫激励圆柱形容器中的单一水表面驻波模式。假设流体是无粘、不可压且运动是无旋的，在忽略了表面张力的影响下，得到一个具有立方项以及底部驱动项影响的非线性振幅方程。对上述方程进行了数值计算，并研究了特定(3，4)模式的表面驻波结构和特性，如驻波的节点分布及随某些参数的变化规律等，从计算的等高线的图象来看，和以往的实验结果相当吻合。     

Resonance Vibrations and Dissipative Heating of Thin-Walled Laminated Elements Made of Physically Nonlinear Materials

The dynamic thermomechanical problem for thin-walled laminated elements is formulated based on the geometrically linear theory and Kirchhoff–Love hypotheses. A simplified model of vibrations and dissipative heating of structurally inhomogeneous inelastic bodies under harmonic loading is used. The mechanical properties of materials are described using strain-dependent complex moduli. A nonstationary vibration-heating problem is solved. The dissipative function, derived from the stationary solution, is used to specify internal heat sources. The amplitude–frequency characteristics and spatial distributions of the main field variables are studied for a sandwich beam subjected to forced vibrations     

Numerical simulation of forced convection over a periodic series of rectangular cavities at low Prandtl number

Convective heat transfer in laminar conditions is studied numerically for a Prandtl number Pr = 0.025, representative of liquid lead–bismuth eutectic (LBE). The geometry investigated is a channel with a periodic series of shallow cavities. Finite-volume simulations are carried out on structured orthogonal curvilinear grids, for ten values of the Reynolds number based on the hydraulic diameter between Re_m = 24.9 and Re_m = 2260. Flow separation and reattachment are observed also at very low Reynolds numbers and wall friction is found to be remarkably unequal at the two walls. In almost all cases investigated, heat transfer rates are smaller than the corresponding flat channel values. Low-Prandtl number heat transfer rates, investigated by comparison with Pr = 0.71 results, are large only for uniform wall temperature and very low Re. Influence of flow separation on local heat transfer rates is discussed, together with the effect of different thermal boundary conditions. Dependency of heat transfer performance on the cavity geometry is also considered.     

窄长方形贮箱中液体的强迫晃动

本文求解了窄长方形贮箱中液体的强迫晃动，给出激励中含恒定分量时的几种液面波高修正方法，并对它们作了比较．