Rayleigh-Benard convection: experimental study of time-dependent instabilities

The transition from steady thermal convection to turbulent thermal convection in a horizontal layer of water (Prandtl number=5.8) contained by a square cavity of large aspect ratio (48.5) has been studied using laser Doppler velocimetry. Power spectra of the horizontal velocity fluctuations were measured in the Rayleigh number range from 30,000 and 99,000, wherein periodic, quasi-periodic, and broad-band time-dependent instabilities coexist. At Rayleigh numbers greater than 32,000 a narrow-band spectrum emerges. The frequency of this motion scales with x/d ² modified by a Prandtl number factor for intermediate values of the Prandtl number. Between 10 Ra _c and 30 Ra _i the frequency undergoes three abrupt jumps while increasing along an Ra ^2/3 power law. A different frequency mode that occurs above 30 Ra _c appears to be associated with fully turbulent convection.List of symbols c heat capacity - d depth of fluid layer - f frequency - g gravitational acceleration - H heat flux - k thermal conductivity - Nu Nusselt number=Hd/k T - Pr Prandtl number=v/x - Ra Rayleigh number - Ra _c critical Rayleigh number=1708 - T temperature difference across the fluid layer - thermal coefficient of expansion - _v aspect ratio=width/depth - x thermometric conductivity=k/ - kinematic viscosity - density A version of this paper was presented at the Tenth Symposium of Turbulence, University of Missouri-Rolla, September 22–24, 1986     

Wetting front instabilities: a three-dimensional experimental investigation

Wetting front instability or fingering experiments were conducted in three-dimensional infiltration columns, featuring stratified fine-over-coarse texture porous media, to investigate the influences of various soil and wetting phase properties on finger diameter and propagation velocity. The system parameter varied in this study included permeability, system flux rate, media size and gradation uniformity, initial moisture content, viscosity, density, and surface tension. The influence of each parameter is discussed and compared, where applicable, to the finding of previous studies. Finger diameter and velocity data were acquired using a neutron radioscopy based, real-time imaging system. Through the use of the imaging system, a very accurate and reliable experimental data set was produced for three-dimensional fingering events.     

Analytical and numerical solutions for vacuum preloading considering a radius related strain distribution

A system of PVDs combined with other preloading methods such as vacuum preloading and surcharge preloading is an effective and economical method which is widely used in the ground treatment. The consolidation theories for drain wells under equal strain condition are often used in the design of ground treatment by PVDs. A radius related strain distribution is proposed to get analytical solutions for the excess pore water pressure and settlement. A linear distributed vacuum pressure along the drain depth and the smear zone as well as well resistance are considered. The numerical results for vacuum loading process are obtained by developed FEM model to compare with the analytical solutions. The results indicate that the influence of the equal strain hypothesis cannot be neglected when n is larger than 10, where n denotes the ratio of diameter of the model to diameter of the drain. The analytical solutions proposed in this paper are more consistent with the numerical results than the analytical results obtained employing the equal strain condition.     

Hybrid theoretical,experimental and numerical study of vibration and buckling of composite shells with scatter in elastic moduli

Hybrid theoretical, experimental and numerical method is proposed for free vibration and buckling of composite shell with unavoidable scatter in elastic moduli. Based on the Goggin’s measurement techniques, the elastic moduli for material T300-QY8911 are measured, and a set of experimental points are obtained. The measurements of elastic moduli are quantified by either (1) the smallest ellipsoid and (2) the smallest four-dimensional uncertainty hyper-rectangle. Then uncertainty propagation in vibration and buckling problems of composite shell by ellipsoidal analysis and interval analysis are, respectively, studied from the theoretical standpoint. Comparison between these analyses is performed numerically.     

Dynamic analysis of piezoelectric energy harvester under combination parametric and internal resonance: a theoretical and experimental study

In this work, theoretical and experimental analysis of a piezoelectric energy harvester with parametric base excitation is presented under combination parametric resonance condition. The harvester consists of a cantilever beam with a piezoelectric patch and an attached mass, which is positioned in such a way that the system exhibits 1:3 internal resonance. The generalized Galerkin’s method up to two modes is used to obtain the temporal form of the nonlinear electromechanical governing equation of motion. The method of multiple scales is used to reduce the equations of motion into a set of first-order differential equations. The fixed-point response and the stability of the system under combination parametric resonance are studied. The multi-branched non-trivial response exhibits bifurcations such as turning point and Hopf bifurcations. Experiments are performed under various resonance conditions. This study on the parametric excitation along with combination and internal resonances will help to harvest energy for a wider frequency range from ambient vibrations.

     

Experimental and numerical investigations on flashing-induced instabilities in a single channel

During the start-up phase, natural circulation BWRs (NC-BWRs) need to be operated at low pressure conditions. Such conditions favor flashing-induced instabilities due to the large hydrostatic pressure drop induced by the tall chimney. Moreover, in novel NC-BWR designs the steam separation is performed in the steam separators which create large pressure drops at the chimney outlet, which effect on stability has not been investigated yet.In this work, flashing-induced oscillations occurring in a tall, bottom heated channel are numerically investigated by using a simple linear model with three regions and an accurate implementation for estimating the water properties. The model is used to investigate flashing-induced instabilities in a channel for different values of the core inlet friction value. The results are compared with experiments obtained by using the CIRCUS facility at the same conditions, showing a good agreement. In addition, the experiments on flashing-induced instabilities are presented in a novel manner allowing visualizing new details of the phenomenon numerical stability investigations on the effect of the friction distribution are also done. It is found that by increasing the total restriction in the channel the system is destabilized. In addition, the chimney outlet restriction has a stronger destabilizing effect than the core inlet restriction. A stable two-phase region is observed prior to the instabilities in the experiments and the numerical simulations which may help to pressurize the vessel of NC-BWRs and thus reducing the effects of flashing instabilities during start-up.     

Dynamic force-penetration curves in rock by matching theoretical to experimental wave propagation response

A methodology to obtain the dynamic force-penetration curve of a rock specimen is presented. For this, a simple portable experimental setup is used. On one end, a hand-held hammer strikes a slender chisel. On the other end the chisel is in contact with the rock specimen into which the generated stress wave propagates. Strain gages installed at a selected section of the chisel are recorded throughout the impact duration. The theoretical signal at the same section is simulated using a numerical method based on the impulsemomentum principle previously developed by the author. Essentially the shape of the simulated theoretical response at the strain gage section depends on the impact velocity of the hammer and the slope of the assumed force-penetration curve. These two parameters are adjusted until the shape of the theoretical signal at the strain gage closely matches the experimental signal. Due to its simplicity, the proposed methodology has the potential of becoming a standard dynamic test for obtaining the force-penetration curvs in rocks.     

Poroelastic toughening in polymer gels: A theoretical and numerical study

We explore the Mode I fracture toughness of a polymer gel containing a semi-infinite, growing crack. First, an expression is derived for the energy release rate within the linearized, small-strain setting. This expression reveals a crack tip velocity-independent toughening that stems from the poroelastic nature of polymer gels. Then, we establish a poroelastic cohesive zone model that allows us to describe the micromechanics of fracture in gels by identifying the role of solvent pressure in promoting poroelastic toughening. We evaluate the enhancement in the effective fracture toughness through asymptotic analysis. We confirm our theoretical findings by means of numerical simulations concerning the case of a steadily propagating crack. In broad terms, our results explain the role of poroelasticity and of the processes occurring in the fracturing region in promoting toughening of polymer gels.     

Experimental and theoretical observations of elastic instabilities in eccentric cylinder flows: local versus global instability

A theoretical and experimental investigation of the stability of the viscoelastic flow of a Boger fluid between eccentric cylinders is presented. In our theoretical study, a local linear stability analysis for the flow of an Oldroyd-B fluid suggests that the flow is elastically unstable for all eccentricities. A global solution to the stability problem is obtained by a perturbation eigenvalue analysis, incorporating the azimuthal variation of the base state flow at the same order as the streamwise variation of the stability function. A comparison between the local and global stability predictions is made. Flow visualization experiments with a solution of high molecular weight polyisobutylene dissolved in a viscous solvent clearly show the transition from a purely azimuthal flow to a secondary toroidal flow. Comparison of these experimental results with the local linear stability theory shows good agreement between the measured and predicted critical conditions for the onset of the non-inertial cellular instability at small δ, where δ is the eccentricity made dimensionless with the average gap thickness. At higher eccentricities, experiment and local linear stability theory cease to agree. Evidence will be given that this disagreement is due to a global affect, i.e. the convection of stress not included the local theory. Specifically, it is suggested that convection of polymeric stresses in the base flow as well as in the disturbance flow can stabilize the instabilities found in this geometry. Finally, the discovery of a new localized purely elastic instability associated with the recirculation flow in the co-rotating eccentric cylinder geometry is presented.     

Dynamic vorticity condition: Theoretical analysis and numerical implementation

The dynamic boundary conditions for vorticity, derived from the incompressible Navier-Stokes equations, are examined from both theoretical and computational points of view. It is found that these conditions can be either local (Neumann type) or global (Dirichlet type), both containing coupling with the boundary pressure, which is the main difficulty in applying vorticity-based methods. An integral formulation is presented to analyse the structure of vorticity and pressure solutions, especially the strength of the coupling. We find that for high-Reynolds-number flows the coupling is weak and, if necessary, can be effectively bypassed by simple iteration. In fact, even a fully decoupled approximation is well applicable for most Reynolds numbers of practical interest. The fractional step method turns out to be especially appropriate for implementing the decoupled approximation. Both integral and finite difference methods are tested for some simple cases with known exact solutions. In the integral approach smoothed heat kernels are used to increase the accuracy of numerical quadrature. For the more complicated problem of impulsively started flow over a circular cylinder at Re = 9500 the finite difference method is used. The results are compared against numerical solutions and fine experiments with good agreement. These numerical experiments confirm our thoeretical analysis and show the advantages of the dynamic condition in computing high-Reynolds-number flows.     

Balancing aspects of numerical dissipation,dispersion, and aliasing in time-accurate simulations

The current study looks at the selection of scheme elements that are well-suited for long-time integration of unsteady flows in the absence or under-resolution of physical diffusion. A concerted assembly of numerical components are chosen relative to a target aliasing limit, which is taken as a best-case scenario for overall spectral resolvability. High-order and optimized difference stencils are employed in order to achieve accuracy; meanwhile, quasi skew-symmetric splitting techniques for nonlinear transport terms are used in order to greatly improve robustness. Finally, tunable and scale-discriminant artificial-dissipation methods are incorporated for de-aliasing purposes and as a means of further enhancing both accuracy and stability. Central finite difference methods are considered, and spectral characterizations of the scheme components are presented. Canonical test cases (the isentropic vortex [IV] and Taylor-Green vortex problems) are chosen in order to highlight the benefits associated with the proposed approach for enhancing overall algorithm robustness and accuracy.     

Analytical,numerical and experimental investigations of architectural sandwich panels

Architectural sandwich panels with thin-walled cold-formed steel facings and rigid foamed insulating core are becoming more and more popular as enclosures for system buildings. In this paper, the structural behavior, including flexural stresses/deflections, flexural wrinkling, axial stability, thermal stresses and vibration, is presented, summarizing more than a decade of research. Methods used are analytical (boundaryvalued approaches), numerical (finite-strip, finite-layer, finite prism approaches) and experimental (full-scale testings). Key equations are formulated, and results by different methods are compared.     

Catastrophic instabilities and related results in a fluid of third grade

Thermodynamical considerations [1] have shown that the most general form for the stress constitutive relation of an incompressible fluid of grade three is T = ?p1 + μA₁ + α₁A₂ + α₂A²₁ + β(tr A²₁)A₁, where A₁ and A₂ are the first two Rivlin-Ericksen tensors. In addition, the material parameters μ, α₁, α₂ and α were shown in [1] to be restricted by certain inequalities (see (1.7), (1.8)). Here we show that the condition α₁ <0, which is compatible with the Clausius-Duhem inequality but not with the free energy being a minimum in equilibrium, leads to behavior which may not be physically acceptable. An explicit solution is presented for the second grade fluid, for which β =0 and μ, α₁ and α₂ are arbitrary, which demonstrates that if μ #62; 0 and α₁ < 0 then a rotating vortex system may increase indefinitely in amplitude.     

Dynamic stiffness characteristics of aero-engine elastic support structure and its effects on rotor systems: mechanism and numerical and experimental studies

The support structure of a rotor system is subject to vibration excitation,which results in the stiffness of the support structure varying with the excitation frequency(i.e., the dynamic stiffness). However, the dynamic stiffness and its effect mechanism have been rarely incorporated in open studies of the rotor system. Therefore, this study theoretically reveals the effect mechanism of dynamic stiffness on the rotor system. Then,the numerical study and experimental verification are conducted on...     

Correlation between theoretical and experimental solitary waves

Experimental data on surface solitary waves generated by five methods are given. These data and literature information show that at amplitudes 0.2<a/h<0.6 (h is the initial depth of the liquid), experimental solitary waves are in good agreement with their theoretical analogs obtained using the complete model of liquid potential flow. Some discrepancy is observed in the range of small amplitudes. The reasons why free solitary waves of theoretically limiting amplitude have not been realized in experiments are discussed, and an example of a forced wave of nearly limiting amplitude is given. The previously established fact that during evolution from the state of rest, undular waves break when the propagation speed of their leading front reaches the limiting speed of propagation of a solitary wave is confirmed. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 44–52, May–June, 1999.     

Experimental and theoretical aspects of the two-roll mill problem

Experiments are described in which two cylinders of the same radii-rotate with identical speeds in a bath of Newtonian or non-Newtonian liquid. The torque on one of the cylinders is measured as a function of rotational speed for various values of the cylinder separation and the flow patterns are observed by a dye-injection technique.The observed experimental results for a Newtonian liquid correlate well with the theoretical predictions but a similar correlation in the case of elastic liquids is made difficult by the strongly three-dimensional nature of the flow in this case and the difficulty in estimating the amount of liquid passing through the rollers. The possibility of flow reversal effects due to the high Trouton ratios in the case of the elastic liquids is investigated both experimentally and theoretically.     

Indentation of a compressible soft electroactive half-space: Some theoretical aspects

We theoretically study the indentation response of a compressible soft electroactive material by a rigid punch. The half-space material is assumed to be initially subjected to a finite deformation and an electric biasing field. By adopting the linearized theory for incremental fields, which is established on the basis of a general nonlinear theory for electroelasticity, the appropriate equations governing the perturbed infinitesimal elastic and electric fields are derived particularly when the material is subjected to a uniform equibiaxial stretch and a uniform electric displacement. A general solution to the governing equations is presented, which is concisely expressed in terms of four quasi-harmonic functions. By adopting the potential theory method, exact contact solutions for three common perfectly conducting rigid indenters of flat-ended circular, conical and spherical geometries can be derived, and some explicit relations that are of practical importance are outlined.