Momentum Preserving Research Articles

Remarks on tension instability of Eulerian and Lagrangian corrected smooth particle hydrodynamics (CSPH) methods

AbstractThe paper discusses the problem of tension instability of particle‐based methods such as smooth particle hydrodynamics (SPH) or corrected SPH (CSPH). It is shown that tension instability is a property of a continuum where the stress tensor is isotropic and the value of the pressure is a function of the density or volume ratio. The paper will show that, for this material model, the non‐linear continuum equations fail to satisfy the stability condition in the presence of tension. Consequently, any discretization of this continuum will result in negative eigenvalues in the tangent stiffness matrix that will lead to instabilities in the time integration process. An important exception is the 1‐D case where the continuum becomes stable but SPH or CSPH can still exhibit negative eigenvalues. The paper will show that these negative eigenvalues can be eliminated if a Lagrangian formulation is used whereby all derivatives are referred to a fixed reference configuration. The resulting formulation maintains the momentum preservation properties of its Eulerian equivalent. Finally a simple 1‐D wave propagation example will be used to demonstrate that a stable solution can be obtained using Lagrangian CSPH without the need for any artificial viscosity. Copyright © 2001 John Wiley & Sons, Ltd.

A KINETIC MODEL FOR DROPLET COALESCENCE IN DENSE SPRAYS

This paper is devoted to the matematical analysis of a kinetic equation describing the process of droplet coalescence in a spatially homogeneous spray. In the first part, existence of a positive measure valued solution is proved, under very general assumptions on the collision kernel. In the second part, mass conservation and momentum preservation, as well as uniqueness and continuous dependence is established, under some more restrictive — but physically reasonable — assumptions on the model. Lastly, the time-asymptotic behavior of the solution is studied.

Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems

The purpose of this work is twofold. First, we demonstrate analytically that the classical Newmark family as well as related integration algorithms are variational in the sense of the Veselov formulation of discrete mechanics. Such variational algorithms are well known to be symplectic and momentum preserving and to often have excellent global energy behavior. This analytical result is veried through numerical examples and is believed to be one of the primary reasons that this class of algorithms performs so well. Second, we develop algorithms for mechanical systems with forcing, and in particular, for dissipative systems. In this case, we develop integrators that are based on a discretization of the Lagrange d'Alembert principle as well as on a variational formulation of dissipation. It is demonstrated that these types of structured integrators have good numerical behavior in terms of obtaining the correct amounts by which the energy changes over the integration run.

Conserving Properties in Constrained Dynamics of Flexible Multibody Systems

The context of this work is the non-linear dynamics ofmultibody systems (MBS). The approach followed for parametrisation ofrigid bodies is the use of inertial coordinates, forming a dependent setof parameters. This approach mixes naturally with nodal coordinates in adisplacement-based finite element discretisation of flexible bodies,allowing an efficient simulation for MBS dynamics. An energy-momentumtime integration algorithm is developed within the context of MBSconstraints enforced through penalty methods. The approach follows theconcept of a discrete derivative for Hamiltonian systems proposed byGonzalez, achieving exact preservation of energy and momentum. Thealgorithm displays considerable stability, overcoming the traditionaldrawback of the penalty method, namely numerical ill-conditioning thatleads to stiff equation systems. Additionally, excellent performance isachieved in long-term simulations with rather large time-steps.

Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulations

This paper presents a new variational framework for various existing Smooth Particle Hydrodynamic (SPH) techniques and presents a new corrected SPH formulation. The linear and angular momentum preserving properties of SPH formulations are also discussed. The paper will show that in general in order to preserve angular momentum, the SPH equations must correctly evaluate the gradient of a linear velocity field. A corrected algorithm that combines kernel correction with gradient correction is presented. The paper will illustrate the theory presented with several examples relating to simple free surface flows.

Design and implementation of a jet actuator for active structural control

AbstractIn active control applications to civil engineering structures, large control forces are required, but the generation of such forces may render the active control implementation impractical.To overcome this drawback, the actuator force can be supplied by the flow of compressed air: it applies a force to the jet supporting structure thanks to the principle of Momentum Preservation (Conservation). The air is stored in a tank and it flows towards a semi‐rigid pipe to the final actuator‐jets, simply realized as nozzles. The flow through each nozzle is controlled by an on‐off electro‐valve, and the system response is monitored by accelerometers.The main achievement is that the resulting control system is indipendent of external energy supply, enough energy having been stored, as compressed air, in a tank. In this way the reliability of the control system is not affected by the availability of external electric power, that in case of earthquake can easily be interrupted.While many studies have been made on pulse‐control methods, only a few have investigated the implementation of such nonlinear control schemes. The focus of this work is on the experimental investigation of some of the numerous practical issues one meets in the development of actuators based on mass‐ejection techniques.A single degree of freedom system, i.e. a simple vertical cantiliver with a lumped mass at the top, is tested on a shaking‐table under different excitation time‐histories, and the efficiency of the controller is evaluated.

Temperature Fluctuation under Bubbles of Pool Boiling at decompression.

Experiments on pool boiling of water were performed under decompression. Temperature fluctuation measured with 3 thermocouples which were equipped on copper block surface by plating. Rapid temperature drops in this fluctuation arise at same times. This shows the existence of evaporation of microlayer under bubbles. The evaluation of this evaporation of the microlayer and rapid temperature drops showed the existence of a new evaporation factor in obedience to the liquid surface overheating. Temperature drops have two types at decompression. One is rapid drop due to the cavity existence and the other is slow drop due to the generation in the superheated bulk liquid on the mirror surface. This rapid temperature drop have gradual drop at first stage. For verification of gradual drops, we introduced a equation concerned micro film thickness under the bubble on the basis of the viscosity and the preservation of momentum. This equation has exponential factor about microfilms. Numerical calculations showed a good agreement with the experimental data.