Torsional buckling of an elastic thick-walled tube made of rubber-like material

The elastic stability of a rubber-like, thick-walled tube which is subjected to finite torsional deformation is investigated both theoretically and experimentally. The analysis is based on the theory of finite elastic deformations, in cojunction with the method of small displacements superposed on large elastic deformations. The governing field equations are solved by a numerical scheme which determines the critical buckling torque and the associated buckling mode of the tube. The predicted results compare closely with the experimental measurements of the buckling of thick-walled silicone rubber tubes tested under finite twist.     

Lyapunov stable penalty methods for imposing holonomic constraints in multibody system dynamics

This paper presents stability and convergence results on a novel approach for imposing holonomic constraints for a class of multibody system dynamics. As opposed to some recent techniques that employ a penalty functional to approximate the Lagrange multipliers, the method herein defines a penalized dynamical system using penalty-augmented kinetic and potential energies, as well as a penalty dependent constraint violation dissipation function. In as much as the governing equations are not typically cocreive, the usual convergence criteria for linear variational boundary value problems are not directly applicable. Still numerical simulations by various researchers suggest that the method is convergent and stable. Despite the fact that the governing equations are nonlinear, the theoretical convergence of the formulation is guaranteed if the multibody system is natural and conservative. Likewise, stability and asymptotic stability results for the penalty formulation are derived from well-known stability results available from classical mechanics. Unfortunately, the convergence theorem is not directly applicable to dissipative multibody systems, such as those encountered in control applications. However, it is shown that the approximate solutions of a typical dissipative system converge to a nearby collection of trajectories that can be characterized precisely using a Lyapunov/Invariance Principle analysis. In short, the approach has many advantages as an alternative to other computational techniques:

The cantilever strip plate under torision, bending or flexure at infinity

A homogeneous, isotropic plate occupies the region 0x ₁, |x ₂|a, |x ₃|h, where the ratio h/a is sufficiently small so that the classical theory of thin plate bending applies. The short end of the plate at x ₁=0 is clamped while the long sides are free. This cantilever plate is now loaded at x ₁=+ by an applied twisting moment, by a bending moment or by flexure. Despite the fundamental nature of these problems, and the long history of thin plate theory, no solutions are to be found in the existing literature that will determine (for instance) the important unknown resultants V ₁, M ₁₁ at the clamped end x ₁=0. The main reason for this is that this combination of boundary conditions leads to severe oscillating singularities of the field in the corners (0, ±a). The fact that such singularities must exist is widely known, but we present here for the first time a method of solution that takes these singularities fully into account.Our numerical results show that the values of M ₁₁, V ₁ on x ₁=0 bear little resemblance to those of the corresponding Saint-Venant solutions, which do not fully satisfy the boundary conditions at the clamped end. Indeed, significantly large values of these resultants were found at points far enough from the corners so as to be relevant in actual engineering applications. Also of interest are certain weighted integrals of M ₁₁, V ₁ which we calculate. These constants determine the effect of the clamping at large distances (greater than 4a, say) from the cla,ped end. At such distances, the effect of the clamping is merely to impose an additional rigid body deflection on the plate.Finally, we consider the plate of finite length. Provided that the aspect ratio is 2 or more, we give accurate approximate solutions for the torsion, bending or flexure of a finite plate clamped at both ends.     

A Second-Order Solution of Saint-Venant's Problem for a Piezoelectric Circular Bar Using Signorini's Perturbation Method

We study electromechanical deformations of a homogeneous transversely isotropic piezoelectric prismatic circular bar loaded only at the end faces. The constitutive relations for the material of the bar are taken to be quadratic in the displacement gradients and the electric field. It is found that the two end faces of the bar when twisted with no electric charge applied to them will exhibit a difference in the electric potential. Thus the piezoelectric cylinder could be used to measure the torque or the angular twist. This revised version was published online in August 2006 with corrections to the Cover Date.     

Improved general correlation for critical heat flux during upflow in uniformly heated vertical tubes

An improved version of the author's earlier correlation for CHF in vertical tubes is presented. It is compared with data that include 23 fluids (water, refrigerants, cryogens, chemicals, and liquid metals), tube diameters 0.315 to 37.5 mm, tube length 1.3 to 940 times diameter, mass flux 4 to 29051 kg/m²s, reduced pressures 0.0014 to 0.96, inlet quality −4 to +0.85, and critical quality −2.6 to +1. These data, from 62 independent sources, are also compared with Katto's general correlation and those of Bowring for water and Subbotin for helium. The present correlation shows much better agreement with data.     

Real-Space Renormalization Estimates for Two-Phase Flow in Porous Media

We present a spatial renormalization group algorithm to handle immiscibletwo-phase flow in heterogeneous porous media. We call this algorithmFRACTAM-R, where FRACTAM is an acronym for Fast Renormalization Algorithmfor Correlated Transport in Anisotropic Media, and the R stands for relativepermeability. Originally, FRACTAM was an approximate iterative process thatreplaces the L × L lattice of grid blocks, representing the reservoir,by a (L/2) × (L/2) one. In fact, FRACTAM replaces the original L× L lattice by a hierarchical (fractal) lattice, in such a way thatfinding the solution of the two-phase flow equations becomes trivial. Thistriviality translates in practice into computer efficiency. For N=L ×L grid blocks we find that the computer time necessary to calculatefractional flow F(t) and pressure P(t) as a function of time scales as N^1.7 for FRACTAM-R. This should be contrasted with thecomputational time of a conventional grid simulator N^2.3. The solution we find in this way is an accurateapproximation to the direct solution of the original problem.     

Friction factor and holdup studies for lubricated pipelining—I. Experiments and correlations

Results from new experiments on the lubricated pipelining of emulsified waxy crude oil and No. 6 fuel oil are presented and compared with other sources of literature. A correlation formula which estimates the holdup fraction is introduced and evaluated for all available experimental data. A simple theory is given which is based on the concentric core-annular flow model and leads to a Reynolds number and friction factor which reduce a large body of experimental data onto one curve; with the best results in the high Reynolds number flow regime.     

On the relation between low-dimensional models and the dynamics of coherent structures in the turbulent wall layer

In this paper we establish some rigorous connections between the dynamics of coherent structures in the wall region of the turbulent boundary layer and the low-dimensional models of the type studied by Aubry et al. (1988). An important first step is to determine what sort of connection is feasible. We choose to study the energy budget of the models in comparison with the energy budget of the real flow. This is done by comparing the respective kinetic energy equations. In the process we reexamine some of the assumptions and approximations of Aubry et al. (1988) and perform order of magnitude analyses to determine when they hold. We find that, for the models developed in that paper, involving modes which do not vary in the streamwise direction, the energy production lies within positive, experimentally determined, bounds. Moreover, the dissipation due to neglected modes may be reproduced correctly with an order 1 value of the Heisenberg parameter , as assumed by Aubry et al. This work was supported by AFOSR F49620-92-J-0287.     

Parametric identification of transient electromagnetic systems

Data into and out of a transient eletromagnetic system are considered in the framework of modern system identification. System solutions that take the form of a complex exponential series are discussed. Since the identification of the parameters in the series is non-linear, emphasis shifts to the identification of the parameters in the difference equation whose solution is the exponential series. The subject is cast in the formalism of system identification with generalizations to more complex systems. Two examples are given, one involving an actual electromagnetic experiment.