Governing Equations and Numerical Solutions of Tension Leg Platform with Finite Amplitude Motion

It is demonstrated that when tension leg platform (TLP) moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP. The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theoretical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.

A further discussion on basic equations for two-phase flow: On collision stress of solid phase

The following points are argued: (i) there are two independent kinds of interaction on interfaces, i.e. the interaction between phases and the collision interaction, and the jump relations on interfaces can accordingly be resolved; (ii) the stress in a particle can also be divided into background stress and collision stress corresponding to the two kinds of interaction on interfaces respectively; (iii) the collision stress, in fact, has no jump on interface, so the averaged value of its derivative is equal to the derivative of its averaged value; (iv) the stress of solid phase in the basic equations for two\|phase flow should include the collision stress, while the stress in the expression of the inter\|phase force contains the background one only. Based on the arguments, the strict method for deriving the equations for two\|phase flow developed by Drew, Ishii et al. is generalized to the dense two\|phase flow, which involves the effect of collision stress.

Semi-analytic slope delay model for CMOS switch-level timing verification

A novel slope delay model for CMOS switch-level timing verification is presented. It differs from conventional methods in being semianalytic in character. The model assumes that all input waveforms are trapezoidal in overall shape, but that they vary in their slope. This simplification is quite reasonable and does not seriously affect precision, but it facilitates rapid solution. The model divides the stages in a switch-level circuit into two types. One corresponds to the logic gates, and the other corresponds to logic gates with pass transistors connected to their outputs. Semianalytic modeling for both cases is discussed.

A Lagrangian for von Karman Equations of Large Deflection Problem of Thin Circular Plate

By the semi-inverse method proposed by He, a Lagrangian is established for the large deflection problem of thin circular plate. Ritz method is used to obtain an approximate analytical solution of the problem. First order approximate solution is obtained, which is similar to those in open literature. By Mathematica a more accurate solution can be deduced.

Thermovibrational Instability Of Rayleigh-Marangoni-Benard Convection In Two-Layer Fluid Systems

The thermovibrational instability of Rayleigh-Marangoni-Benard convection in a two-layer system under the high-frequency vibration has been investigated by linear instability analysis in the present paper. General equations for the description of the convective flow and within this framework, the generalized Boussinesq approximation are formulated. These equations are dealt with using the averaging method. The theoretical analysis results show that the high-frequency thermovibrations can change the Marangoni-Benard convection instabilities as well as the oscillatory gaps of the Rayleigh-Marangoni-Benard convection in two-layer liquid systems. It is found that vertical high-frequency vibrations can delay convective instability of this system, and damp the convective flow down. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

A Cip/Multi-Moment Finite Volume Method For Shallow Water Equations With Source Terms

A novel finite volume method has been presented to solve the shallow water equations. In addition to the volume-integrated average (VIA) for each mesh cell, the surface-integrated average (SIA) is also treated as the model variable and is independently predicted. The numerical reconstruction is conducted based on both the VIA and the SIA. Different approaches are used to update VIA and SIA separately. The SIA is updated by a semi-Lagrangian scheme in terms of the Riemann invariants of the shallow water equations, while the VIA is computed by a flux-based finite volume formulation and is thus exactly conserved. Numerical oscillation can be effectively avoided through the use of a non-oscillatory interpolation function. The numerical formulations for both SIA and VIA moments maintain exactly the balance between the fluxes and the source terms. 1D and 2D numerical formulations are validated with numerical experiments. Copyright (c) 2007 John Wiley & Sons, Ltd.

Analysis and application of ellipticity of stability equations on fluid mechanics

By using characteristic analysis of the linear and nonlinear parabolic stability equations (PSE), PSE of primitive disturbance variables are proved to be parabolic intotal. By using sub-characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic for velocity U, in subsonic and supersonic, respectively; the nonlinear PSE are proved to be elliptical and hyperbolic-parabolic for relocity U + u in subsonic and supersonic, respectively. The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories, the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time, the methods of removing the remained ellipticity are further obtained from the nonlinear PSE.

Dynamic equations for curved submerged floating tunnel

In virtue of reference Cartesian coordinates, geometrical relations of spatial curved structure are presented in orthogonal curvilinear coordinates. Dynamic equations for helical girder are derived by Hamilton principle. These equations indicate that four generalized displacements are coupled with each other. When spatial structure degenerates into planar curvilinear structure, two generalized displacements in two perpendicular planes are coupled with each other. Dynamic equations for arbitrary curvilinear structure may be obtained by the method used in this paper.

Shock tube study of JP-10 ignition delay time

JP-10 (exo-tetrahydrodicyclopentadiene, C10H16) ignition delay times were measured in a preheated shock tube. The vapor pressures of the JP-10 were measured directly by using a high-precision vacuum gauge, to remedy the difficulty in determining the gaseous concentrations of heavy hydrocarbon fuel arising from the adsorption on the wall in shock tube experiments. The whole variation of pressure and emission of the OH or CH radicals were observed in the ignition process by a pressure transducer and a photomultiplier with a monochromator. The emission of the OH or CH radicals was used to identify the time to ignition. Experiments were performed over the pressure range of 151-556 kPa, temperature range of 1000-2100 K, fuel concentrations of 0.1%-0.55% mole fraction, and stoichiometric ratios of 0.25, 0.5, 1.0 and 2.0. The experimental results show that for the lower and higher temperature ranges, there are different dependency relationships of the ignition time on the temperature and the concentrations of JP-10 and oxygen.