On energy arguments applied to the hydrodynamic impact force

The hydrodynamic impact problem is investigated within the framework of potential-flow theory. The vertical load acting on the rigid body is derived based on either momentum or energy conservation, and using the concept of added mass together with a homogeneous Dirichlet condition for the potential on the free surface as usually done to model an impact problem. It is demonstrated that the use of this simplified dynamic free-surface condition, instead of the fully nonlinear one, has a direct influence on the computation of the loads. In particular, the equivalence of momentum and energy analysis is in general not recovered. The situation is then highlighted by performing an asymptotic analysis of the two-dimensional blunt-body asymmetric impact problem. The asymptotic solution is given explicitly and validated through comparisons with experimental results. The energy distribution is then studied. It is shown that the contradiction between momentum and energy analysis can be removed, provided that the flux of energy through the jets is taken into account in the energy balance. If the simplified free-surface condition is indeed valid in the far-field, nonlinear terms must be retained near the body, in the spray-root domains. To leading order, the energy distribution during the gravity-free inertia stage does not depend on the blunt-body shape. The general analysis based on momentum or energy conservation suggests that this result also applies for arbitrary body shape as soon as a homogeneous Dirichlet condition can be applied as a dynamical free-surface boundary condition. In this case, and for a constant vertical impact velocity, half the work performed by the body would seem to be transferred to the fluid as kinetic energy within the spray.     

Stability of Equilibria in a Four-dimensional Nonlinear Model of a Hydraulic Servomechanism

Starting from plysical laws a four-dimensional nonlinear model for mecano-hydraulic servomechanisms is deduced. The stability of its equilibria is analysed using a theorem of Lyapunov and Malkin to handle the critical case due to the presence of zero in the spectrum of the matrix of the linear part around equilibria. Stability diagrams are drawn and simulation results are presented through phase diagrams.     

Wave dynamics on a thin-liquid film falling down a heated wall

The dynamics of a thin liquid film falling down a uniformly heated wall is studied. The model introduced by Kalliadasis et al. [J. Fluid Mech. 475 (2003) 377] for the same problem is revisited and its deficiencies, namely the prediction of a critical Reynolds number with 20% error, cured. For the energy equation a high-order Galerkin projection in terms of polynomial test functions is developed. It is shown that not only does this more refined formulation correct the critical Reynolds number, but it also gives, with an appropriate expansion close to criticality, the long-wave theory. Bifurcation diagrams for permanent solitary waves are constructed and compared with the solution branches obtained from different models. It is shown that, in all cases, the long-wave theory exhibits limit points and branch multiplicity, while the other models predict the continuing existence of solitary waves. Time-dependent computations show that the free surface and interfacial temperature approach a train of coherent structures that resemble the infinite-domain stationary solitary pulses.     

SQUID NMR Studies of the Second Layer of 3He at High Density

Nuclear magnetism in the second layer of ³He films on graphite has been studied as a function of density in the zero-field limit at temperatures down to 300 µK. Total surface coverages in this study ranged from 20 atoms/nm² (the lowest coverage at which the effective exchange parameter turns ferromagnetic) through the two-phase region (ending at about 24 atoms/nm²) and into the single-phase imcommensurate solid region up to 31.2 atoms/nm². The surface layers were studied using both pulsed and cw NMR measured with our SQUID NMR system in magnetic fields of 500 µT and lower. As the surface density continues to increase in the single-phase region, the exchange constant decreases consistently with a picture of steric hindrance impeding ferromagnetic exchange. Several different observational features scale with this inferred exchange: low-field magnetization, NMR frequency shift, and the temperature of onset of significant magnetization.     

Textural Transitions in a Rotating Slab of 3He-A

The operation of a torsional oscillator for detection, of flow-driven textural transitions in, ³He-A is described. The detection technique, tracking the shift of the resonant frequency of the torsional oscillator, allows us to observe textural changes and the presence of vortices in zero magnetic field. It relies on. the anisotropic superfluid density of ³He-A and its change due to reorientation of the Î-texture caused by counterflow.     

Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency

In this paper, two brittle fracture problems are numerically simulated: the failure of a ceramic ring under centrifugal loading and crack branching in a PMMA strip. A three‐dimensional finite element package in which cohesive elements are dynamically inserted has been developed. The cohesive elements' strength is chosen to follow a modified weakest link Weibull distribution. The probability of introducing a weak cohesive element is set to increase with the cohesive element size. This reflects the physically based effect according to which larger elements are more likely to contain defects. The calculations illustrate how the area dependence of the Weibull model can be used to effectively address mesh dependency. On the other hand, regular Weibull distributions have failed to reduce mesh dependency for the examples shown in this paper. The ceramic ring calculations revealed that two distinct phenomena appear depending on the magnitude of the Weibull modulus. For low Weibull modulus, the fragmentation of the ring is dominated by heterogeneities. Whereas many cracks were generated, few of them could propagate to the outer surface. Monte Carlo simulations revealed that for highly heterogeneous rings, the number of small fragments was large and that few large fragments were generated. For high Weibull modulus, signifying that the ring is close to being homogeneous, the fragmentation process was very different. Monte Carlo simulations highlighted that a larger number of large fragments are generated due to crack branching. Copyright © 2003 John Wiley & Sons, Ltd.     

Methodologies for the optimal design of parallel manipulators

In this paper the problem of determining a manipulator design so that its workspace corresponds to a prescribed workspace is considered. Two different strategies, resulting in two different types of optimization problem are considered. The first strategy attempts to obtain a good overall approximation to the prescribed workspace and results in an unconstrained optimization problem. The second strategy entails designing a manipulator so that its workspace fully encloses the prescribed workspace and results in a constrained optimization problem. Two specific formulations of the constrained problem are proposed. The first constrained problem simply aims to fit the manipulator workspace as exactly as possible to the prescribed workspace, while still ensuring that the prescribed workspace is fully enclosed. The second constrained optimization formulation is used to design a manipulator, the workspace of which fully encloses the prescribed workspace, but which is also well‐conditioned throughout the workspace with respect to some performance measure. The particular manipulator used to illustrate and evaluate these formulations is a simple 2‐dof planar parallel manipulator, and the final formulation is also applied to a 3‐dof planar parallel manipulator. Although the manipulators studied here are simple, the objective of this study is to obtain a robust numerical methodology which can be extended to more practical and complex manipulators. Copyright © 2003 John Wiley & Sons, Ltd.     

Solution of a multidimensional inverse radiation problem by means of mode reduction

The Karhunen–Loève Galerkin procedure is employed to solve an inverse radiation problem of determining the time‐varying strength of a heat source, which mimics flames in a furnace, from temperature measurements in three‐dimensional participating media where radiation and conduction occur simultaneously. The inverse radiation problem is solved through the minimization of a performance function, which is expressed by the sum of square residuals between calculated and observed temperature, using a conjugate gradient method. Through the Karhunen–Loève Galerkin procedure, one can represent the system dynamics with a minimum degree of freedom, and consequently the amount of computation required in the solution of the inverse problem is reduced drastically when the present technique is adopted. Copyright © 2004 John Wiley & Sons, Ltd.     

Electrical conductivity and gas sensitivity of Zn-Sb-O thick films

The thick film of Zn-Sb-O was prepared by coating the paste of nanoparticles mixture (Sb₂O₃:ZnO=1:3) on the alumina substrate, followed by sintering at 500-900 °C for 2 h in air. The electrical resistance and gas-sensing properties to benzene, alcohol and acetone of Zn-Sb-O films were found to be dependent on the change of phase structure caused by sintering temperature.     

Study of liquid injection impact on the performance of new refrigerant mixtures

In this paper, the test results of liquid injection impact on the performance of new alternative refrigerant mixtures such as: R-410A, R-507, R-407C and R-404A are discussed, analysed and presented. The test results were obtained using an air-source heat pump set-up with enhanced surface tubing under various liquid injection ratios. Performance tests were conducted according to the ARI/ASHRAE standards. The performance data demonstrated that as liquid injection ratio increases, compressor head pressure and discharge temperature decrease. This has a positive effect in protecting the compressor. The effect of liquid injection on mixture behaviour varies from one mixture to another depending upon the mixture's composition. Furthermore, liquid injection appears to have a significant influence on R-410A behaviour compared to the other mixtures in question. Copyright © 2002 John Wiley & Sons, Ltd.