THEORY OF VISCOUS BUCKLING AND GRAVITY INSTABILITY OF MULTILAYERS WITH LARGE DEFORMATION
An exact treatment of the stability of multilayered viscous fluids in slow motion with large deformations leads to an analog model which includes the effect of gravity. A distinction can be made between true mechanical instability and an apparent instability of purely kinematic nature. A mechanism for concentric folding is derived, leading to predictions in good agreement with experimental results (De Sitter, 1939). Exact equations are obtained for the time history of viscous buckling of multilayered fluids for small deflections superimposed upon a large variable compressible strain. A numerical application to the single embedded layer checks the practical validity of the simplified thin-layer theory with interfacial slip. For gravity instability, the analog model provides a method of analysis applicable to very large deformations in salt structures.
A computer program for the simulation of folds of different sizes under the influence of gravity
Folding&g is a computer program, based on the finite element method, developed to simulate the process of natural folding from small to large scales in two dimensions. Written in Pascal code and compiled with Borland Delphi 3.0, the program has a friendly interactive user interface and can be used for research as well as educational purposes. Four main menu options allow the user to import or to build and to save a model data file, select the type of graphic output, introduce and modify several physical parameters and enter the calculation routines. The program employs isoparametric, initially rectangular elements with eight nodes, which can sustain large deformations. The mathematical procedure is based on the elasticity equations, but has been modified to simulate a viscous rheology, either linear or of power-law type. The parameters to be introduced include either the linear viscosity, or, when the viscosity is non-linear, the material constant, activation energy, temperature and power of the differential stress. All the parameters can be set by rows, which simulate layers. A toggle permits gravity to be introduced into the calculations. In this case, the density of the different rows must be specified, and the sizes of the finite elements and of the whole model become meaningful. Viscosity values can also be assigned to blocks of several rows and columns, which permits the modelling of heterogeneities such as rectangular areas of high strength, which can be used to simulate shearing components interfering with the buckling process. The program is applied to several cases of folding, including a single competent bed and multilayers, and its results compared with analytical and experimental results. The influence of gravity is illustrated by the modelling of diapiric structures and of a large recumbent fold.
HYPERGOLIC REACTION MECHANISMS OF CATALYTICALLY PROMOTED FUELS WITH ROCKET GRADE HYDROGEN PEROXIDE
Abstract The coupling of the physical and chemical processes controlling the ignition delays (τ ign ) of hypergolic propellants complicates the direct analysis of the transient ignition processes. The transport properties of both the propellants and the ambient gas, and the heat of vaporization and reaction affect τ ign and must be considered experimentally. Furthermore, since hypergolic ignition occurs, by definition, on contact, the mechanics of initial contact and subsequent mixing can affect τ ign and must also be considered. Experimental results from a study of the hypergolic ignition of a catalytically promoted fuel with rocket grade hydrogen peroxide (RGHP) are presented. Statistical analysis of the experimental data was conducted to evaluate the relative effects of RGHP concentration, initial ambient pressure, and the ambient gas on τ ign . At RGHP concentrations of less than 92% in water, stable ignition was difficult to achieve. At sufficiently high Lewis number, an oscillatory ignition process is observed. A phenomenological model comprising mixing, RGHP decomposition, fuel heating and vaporization, and auto-ignition is presented and compared to the experimental results.