Vibration of continuous systems with compliant boundaries

A theoretical study of two types of continuous systems with a general form of compliant boundary conditions is presented. The systems considered are elastic beams and circular plates with elastic damped edge constraints. Beam studies are restricted to those with identical boundary conditions at each end. The method of solution consists of formulating the edge condition of the system in terms of the impedance of the compliant boundary material and of using classical solution techniques to solve the equations of motion. The result of matching the boundary conditions of the system with constraining conditions is the system frequency equation in terms of the constraint impedances.A discussion is presented giving the influence of the compliant material on the vibration of the structure. The models give numerically the effect of elasticity and damping of the supports on the resonant frequencies of the systems. Parameters are obtained which indicate when one may assume simply supported or clamped boundaries for the actual case of elastic damped constraints without introducing large errors in the natural frequencies.     

Interference action of weakly compliant boundaries in the gradient flows

The conditions for possible reduction of hydrodynamic resistance by the compliant coatings are considered from two points of view: pulling the laminar flow and alteration of turbulence generation in the near-wall zone. A strong effect of the longitudinal pressure gradient and reasonability of the search for the laminarized bypass flows in the presence of compliant coatings are distinguished.     

New aspects of unsteady couette flow

A recent extension of the recurrence-rate correlation technique of Erdmann and Gellert has been used to measure fluctuating cellular flows between concentric cylinders with the inner cylinder rotating. The length of the fluid-filled annulus was smaller than in most previous experiments of this kind. Direct velocity correlation measurements have revealed unexpected features in the development of these flows with increasing Reynolds number. The transition process was found to retain temporal order to a greater extent than indicated by many previous observations.     

Balancing energy to estimate damping in a forced oscillator with compliant contact

This work identifies damping parameters from compliant-contact vibration systems using an energy balance. To develop the identification algorithms, the energy loss as registered in the force-displacement relationship of the real system is expressed in terms of a theoretical model incorporating an ideal compliant contact. Two approaches, one based on the harmonic response assumption and the other directly integrating the system responses, are developed. Numerical and experimental investigations are performed to illustrate the reliability of the identification algorithms. The method is applied to an experimental industrial linear-bearing system.     

Boundary conditions on a compliant wall in the turbulent flow

It is shown that with an increase in elasticity modulus of the coating material from 0.01 MPa to 100 MPa the pulsation velocity of coating surface changes not more than by 30 % and equals 0.17–0.24 of the value of dynamic flow velocity, and this can change significantly Reynolds stresses in the near-wall area. According to performed analysis, it was found out that the deformation value of the compliant coatings within the velocity range, optimal for their interaction with the turbulent flow, is only several units of the viscous scale. Moreover, these deformations are very gentle: the ratio of amplitude of deformation to wavelength is less than 10^?3. It is assumed that while modeling the interaction between the compliant coating and turbulent flow it is not necessary to transfer the boundary conditions to the moving coating surface. Perhaps, it will be sufficient to determine the velocity of wall motion over the undisturbed coating surface.     

Heat transfer in unsteady MHD oscillatory flow

Heat transfer in unsteady MHD channel flow (of an incompressible viscous and electrically conducting fluid) under oscillatory pressure gradient when the channel surfaces are conducting and moving with time-dependent velocities has been analysed. The velocity, magnetic field and temperature distributions have been obtained and their numerical results are shown graphically.Symbols u velocity - H _o applied magnetic field - H _x induced magnetic field - T temperature - T ₁ ^* ,T ₂ ^* temperatures of the upper and lower planes - density - p pressure - kinematic viscosity - magnetic diffusivity - electrical conductivity of the fluid - A ^* characteristic velocity - L characteristic length - _e magnetic permeability of the fluid - C _p specific heat - coefficient of viscosity - k thermal conductivity - ₁, ₂ permeabilities of the planes - ₁, ₂ conductivities of the planes - ₁, ₂ conductance ratios of the planes - Pr Prandtl number (=C _p /k) - E Eckert number - M Hartmann number (= _e H _o L/) - R _e Reynolds number (=LA ^*/) - R _m magnetic Reynolds number (= _e LA ^*) - S Pr.E(=S)     

Sound generation in a flow near a compliant wall

The generation of sound near an infinite compliant wall is studied, with account taken of a uniform mean flow. Stable and unstable configurations are looked at. It is shown that a possible influence of the wall on the sound generation occurs only via a modification of the turbulence if hydrodynamic non-linearities are responsible for the levelling-off of the instabilities. Then no fundamentally more efficient sound sources are found. An increase of the radiated sound may be possible because of the mirror sources and because of their possibly reduced compactness.     

Accumulating particles at the boundaries of a laminar flow

The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a Fokker-Planck equation for the particle density. It is shown that for extended spherical particles the shape of the fluid domain gives rise to inhomogeneous particle densities, thereby leading to particle accumulation and corresponding depletion. For extended spherical particles, conditions are specified that lead to inhomogeneous densities and consequently to regions with particle accumulation and depletion.     

Preprocessed visualization of large scale unsteady flow simulations

In some cases, conventional CFD visualization techniques do not give us sufficient information of the flowfield, especially when the flowfield is unsteady, and there is a need for a new postprocessing technique. In the present paper, one of such new post-processing techniques is proposed. In the present technique, raw result of CFD simulation is pre-processed by frequency filters, and then processed secondary data set is visualized. The idea is applied to two examples. The examples show that the present method visualizes each frequency mode separately, and gives clear view of the temporal variation of the whole flowfield. The results indicate that the present method improves the understandings of the flow mechanism.     

On the problem of damping of ferromagnetic spin waves by conduction electrons

The life time of a resonance spin wave has been studied in ferromagnetic transition metals utilizing the theory of generalized Brown's motion. A basic assumption is the exchange interaction of 3d electrons with the damped excitations of 4s electron spins. It is shown, that a result can be obtained in a form, which is simpler and physically more evident than the one derived using Green's functions.Na Slovance 2, Praha 8, Czechoslovakia.The authors wish to express their thanks to Z. Frait, V. Kamberský and L. Murtinová for valuable discussions and comments on the paper.     

On the design of optimal compliant walls for turbulence control

This paper employs the resolvent framework to consider the design of compliant walls for turbulent skin friction reduction. Specifically, the effects of simple spring–damper walls are contrasted with the effects of more complex walls incorporating tension, stiffness and anisotropy. In addition, varying mass ratios are tested to provide insight into differences between aerodynamic and hydrodynamic applications. Despite the differing physical responses, all the walls tested exhibit some important common features. First, the effect of the walls (positive or negative) is the greatest at conditions close to resonance, with sharp transitions in performance across the resonant frequency or phase speed. Second, compliant walls are predicted to have a more pronounced effect on slower moving structures because such structures generally have larger wall-pressure signatures. Third, two-dimensional (spanwise constant) structures are particularly susceptible to further amplification. These features are consistent with many previous experiments and simulations, suggesting that mitigating the rise of such two-dimensional structures is essential to designing performance-improving walls. For instance, it is shown that further amplification of such large-scale two-dimensional structures explains why the optimal anisotropic walls identified in previous direct numerical simulations only led to drag reduction in very small domains. The above observations are used to develop design and methodology guidelines for future research on compliant walls.     

Modelling the unsteady melt flow under a pulsed magnetic field

A numerical model for the unsteady flow under a pulsed magnetic field of a solenoid is developed, in which magnetohydrodynamic flow equations decouple into a transient magnetic diffusion equation and unsteady Navier–Stokes equations in conjunction with two equations of the k–ε turbulent model. A Fourier series method is used to implement the boundary condition of magnetic flux density under multiple periods of a pulsed magnetic field （PMF）. The numerical results are compared with the theoretical or experimental results to validate the model under a time-harmonic magnetic field; it is found that the toroidal vortex pair is the dominating structure within the melt flow under a PMF. The velocity field of a molten melt is in a quasi-steady state after several periods; changing the direction of the electromagnetic force causes the vibration of the melt surface under a PMF.     

An unsteady pseudoshock model for barotropic gas flow

A mathematical unsteady pseudoshock model describing the continuous transition from supersonic to subsonic flow is constructed for a barotropic gas flow in a long flat channel or a nozzle. The model is based on a two-layer scheme of flow with mass transfer including a potential supersonic core and a turbulent boundary layer.     

直拉法晶体生长过程非稳态流体热流耦合

为了改善复杂对流形态下的晶体生长品质, 提出了一种改进的格子Boltzmann方法研究非稳态熔体流动和传热的耦合性质. 该方法基于不可压缩轴对称D2Q9模型, 构建了包含旋转惯性力和热浮力等外力项的演化关系, 实现了对轴对称旋转流体的速度、温度和旋转角速度的计算与分析. 结果表明, 非稳态熔体中的流、热耦合性质与格拉斯霍夫数和雷诺数的相互作用有关; 通过调节高雷诺数, 可有效抑制熔体中的自然对流, 改善温度分布, 有助于提高单晶的品质. 数值计算结果与实际硅单晶生长试验均证明了所提方法的正确性及有效性.