Effect of an inhibitor on high-speed turbulent flames and the transition to detonation

The influence of an inhibitor (CF₃Br or Halon 1301) on the propagation of high-speed turbulent flames, quasi-detonations and the transition to detonation has been investigated for methane-air, propane-air and acetylene-air mixtures. The experiments are carried out in a 13 m tube (15 cm diameter) filled with regularly spaced orifice plates (blockage ratio of 0.39) to ensure rapid flame acceleration. In all cases, the addition of the inhibitor reduces the turbulent flame velocity and extinguishes the flame with sufficient inhibitor concentration (2.7% and 7.5% for methane-air and propane-air, respectively). For acetylene-air mixtures, the quasi-detonation speed is progressively reduced with increasing inhibitor concentration and eventually causes the failure of the quasi-detonation and transition back to a fast turbulent flame. The inhibitor also narrows the propagation limits in all cases. To elucidate the inhibition mechanism, detailed modelling of both the turbulent flame structure as well as the chemical kinetics are required.     

Determination of the complex shear modulus of structural adhesives using a doubly clamped sandwich beam

A method is described for calculating the complex shear modulus of structural adhesives from dynamic test data on a doubly clamped sandwich beam in which the adhesive is contained as a thin layer. The accuracy of the technique is validated by finite-element analysis. Values of modulus obtained using the doubly clamped beam technique are found to be in excellent agreement with values obtained from dynamic tests on bulk specimens of an epoxy adhesive.     

Non-linear creep damage under one-dimensional variable tensile stress

A non-linear damage relation, containing the axial strain history and a time integral over the stress history, is proposed for the case of one-dimensional time dependent tensile stress. Non-linear steady and transient creep terms are included in the axial strain relation, and elastic and creep Poisson's ratios are introduced into the lateral strain relation. Using these relations, complete damage solutions are obtained for the constant stress rate, step stress, relaxation and constant load tests. Observations are made concerning the associated rupture times.     

Corona-induced electrohydrodynamic instabilities in low conducting liquids

The rose-window electrohydrodynamic (EHD) instability has been observed when a perpendicular field with an additional unipolar ion injection is applied onto a low conducting liquid surface. This instability has a characteristic pattern with cells five to 10 times greater than those observed in volume instabilities caused by unipolar injection. We have used corona discharge from a metallic point to perform some measurements of the rose-window instability in low conducting liquids. The results are compared to the linear theoretical criterion for an ohmic liquid. They confirmed that the minimum voltage for this instability is much lower than that for the interfacial instability in high conducting liquids. This was predicted theoretically in the dependence of the critical voltage as a function of the non-dimensional conductivity. It is shown that in a non-ohmic liquid the rose window appears as a secondary instability after the volume instability.     

A finite element analysis of strain localization for soft rock using a constitutive equation with strain softening

Summary It is well known that deformation and/or strain of geological materials localize when they come close to the failure state. In the present: study, we try to analyze the deformation problem using a constitutive relation with strain hardening and strain softening. The constitutive model of a soft rock and overconsolidated clay using an elasto-plastic constitutive theory with memory was originally developed by Adachi and Oka. This type of formulation is shown to be easily applied to analyze the material behavior of strain softening because there is a similarity to that in viscoplasticity. Using the proposed model, the loss of uniqueness of the solution to the initial value problem can be avoided and a special or complicated numerical technique, e.g., an arc length method, does not need to be used. When we use constitutive equations with strain softening in a finite element analysis, there is a problem of strong mesh size dependency of numerical results. To remedy the mesh size dependency, we generalize the Adachi-Oka model based on the concept of non-localization by Bazant. We apply the proposed constitutive model to the behavior of a sedimentary soft rock in the drained triaxial compression test. It is found that mesh size dependency becomes smaller using the non-localization of the constitutive model.

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Eine Finite-Element-Analyse der lokalisierten Verformung von weichem Gestein bei einem Stoffgesetz mit Entfestigung

Übersicht Bekanntlich findet bei geologischen Stoffen in der Nähe des Versagenszustandes eine Lokalisierung der Verformung statt. Die Analyse dieses Problems wird in diesem Beitrag auf der Grundlage eines Stoffansatzes mit Ver- und Entfestigung unternommen. Entwickelt wurde das zugrunde gelegte elastischplastische Stoffmodell mit Gedächtnis von Adachi und Oka für weiches Gestein und übermäßig verdichteten Ton. Wegen der Ähnlichkeit zur Viskoplastizität läßt sich diese Formulierung des Stoffgesetzes leicht auf die Analyse des Verhaltens von entfestigendem Material anwenden, da der Eindeutigkeitsverlust der Lösung des Anfangswertproblems vermieden wird und besondere Rechenverfahren wie etwa die Bogenlängenmethode nicht benötigt werden. Bei der Benutzung von Stoffgesetzen in einer Finite-Element-Rechnung hängen die Ergebnisse stark von der Netzeinteilung ab. Um dies abzustellen, wird das Modell von Adachi und Oka auf der Grundlage von Bazant's Konzept der Nichtlokalisierung verallgemeinert. Anwendungsbeispiel ist das Verhalten von weichem Gestein im drainierten Triaxial-Test. Es zeigt sich, daß mit dem Konzept der Nichtlokalisierung im Stoffmodell der Einfluß der Netzeinteilung geringer wird.

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Presented at the workshop on Numerical Methods for Localization and Bifurcation of Granular bodies, held at the Technical University of Gdask (Poland), September 25–30, 1989.     

Testing theoretical bases of caustic methods in fracture mechanics and stress analysis

Determination of stress intensity factors using shadow optical method of caustics attracts increasing attention. However, the reliability and ranges of applicability of this method are seldom discussed. This paper presents such an analysis regarding the reliability and predictive power of caustic method in fracture mechanics. This analysis is performed according to the accepted methodology of testing any analytical, numerical, or experimental procedure, namely by testing its theoretical bases. The following four basic assumptions of the shadow optical method of caustics in fracture mechanics, and their consequences, are analyzed: assumption of a generalized plane stress state near crack tip; assumption that the radiant energy used to produce shadow images propagates rectilinearly inside a stressed body; assumption that the light velocity inside a stressed body depends only on stress components in planes normal to wave normals; assumption that there is no alteration in state of polarization of radiation impinging upon a stressed plate at oblique incidence.The first two basic assumptions are tested using results obtained by means of three analytical-experimental procedures, namely isodynes, gradient index method, and classical strain gages. It is known that the inaccuracies of the fourth assumption are within the noise level only when the angles of incidence are small.It is shown that the magnitudes of the effects caused by the geometric lens effect and the gradient index lens effect are comparable, and that the stress states near crack tips and bottoms of notches, which produce the geometric lens effect, are clearly three-dimensional.It is also indicated that the gradient index lens effect is caused jointly by the stress/strain-induced alteration of the optical path and by the bending of the light path caused by strain gradient.Obtained empirical evidence shows the existence of a particular relationship between the observed gradient index lens effect and the order of singularity in a particular singular solution of linear fracture mechanics, with the exception of the vicinity of the crack tip where singularities are inadmissible.     

A symmetry analysis of some classes of evolutionary nonlinear (2+1)-diffusion equations with variable diffusivity

In this paper the (2+1)-nonlinear diffusion equation u _t ?div(f(u)grad u)=0 with variable diffusivity is considered. Using the Lie method, a complete symmetry classification of the equation is presented. Reductions, via two-dimensional Lie subalgebras of the equation, to first- or second-order ordinary differential equations are given. In a few interesting cases exact solutions are presented.     

Reduced‐order modelling of an adaptive mesh ocean model

A novel proper orthogonal decomposition (POD) model has been developed for use with an advanced unstructured mesh finite‐element ocean model, the Imperial College Ocean Model (ICOM, described in detail below), which includes many recent developments in ocean modelling and numerical analysis. The advantages of the POD model developed here over existing POD approaches are the ability:

• 1. To increase accuracy when representing geostrophic balance (the balance between the Coriolis terms and the pressure gradient). This is achieved through the use of two sets of geostrophic basis functions where each one is calculated by basis functions for velocities u and v.
• 2. To speed up the POD simulation. To achieve this a new numerical technique is introduced, whereby a time‐dependent matrix in the discretized equation is rapidly constructed from a series of time‐independent matrices. This development imparts considerable efficiency gains over the often‐used alternative of calculating each finite element over the computational domain at each time level.
• 3. To use dynamically adaptive meshes in the above POD model.

Copyright © 2008 John Wiley & Sons, Ltd.     

Thermoacoustically driven flame motion and heat release variation in a swirl-stabilized gas turbine burner investigated by LIF and chemiluminescence

Laser-induced fluorescence and chemiluminescence, both phase-locked to the dominant acoustic oscillation, are used to investigate phenomena related to thermoacoustic instability in a swirl-stabilized industrial scale gas turbine burner. The observed sinusoidal phase-averaged flame motion in axial (main flow) direction is analyzed using different schemes for defining the flame position. Qualitative agreement between experimental data and theoretical analysis of the observed flame motion is obtained, interpreted as originating primarily from variation of the burning velocity. The heat release variation during an acoustic cycle is determined from the sinusoidally varying total OH* chemiluminescence intensity.

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On the applicability of some approximate similitude laws in hypersonic aerodynamics

The range of applicability of some similitude laws for heat transfer, friction and drag coefficients is discussed on the basis of numerical solutions of the complete viscous shock layer equations describing hypersonic flow past blunt bodies. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 121–130, March–April, 1994.