Large Eddy Simulation of Premixed Turbulent Combustion Using Ξ Flame Surface Wrinkling Model

One commonly-used method for deriving the RANS equations for multicomponent flow is the technique of conditional averaging. In this paper the concept is extended to LES, by introducing the operations of conditional filtering and surface filtering. Properties of the filtered indicator function are investigated mathematically and computationally. These techniques are then used to derive conditionally filtered versions of the Navier–Stokes equations which are appropriate for simulating multicomponent flow in LES. Transport equations for the favre-averaged indicator function and the unresolved interface properties (the wrinkling and the surface area per unit volume) are also derived. Since the paper is directed towards modelling premixed combustion in the flamelet regime, closure of the equations is achieved by introducing physical models based on the picture of the flame as a wrinkled surface separating burnt and unburnt components of the fluid. This leads to a set of models for premixed turbulent combustion of varying complexity. The results of applying one of this set of models to propagation of a spherical flame in isotropic homogeneous turbulence are analysed. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Remarkable Nature of Cylindrically Anisotropic Elastic Materials Exemplified by an Anti-Plane Deformation

A material is cylindrically anisotropic when its elastic moduli referred to a cylindrical coordinate system are constants. Examples of cylindrically anisotropic materials are tree trunks, carbon fibers [1], certain steel bars, and manufactured composites [2]. Lekhnitskii [3] was the first one to observe that the stress at the axis of a circular rod of cylindrically monoclinic material can be infinite when the rod is subject to a uniform radial pressure (see also [4]). Ting [5] has shown that the stress at the axis of the circular rod can also be infinite under a torsion or a uniform extension. In this paper we first modify the Lekhnitskii formalism for a cylindrical coordinate system. We then consider a wedge of cylindrically monoclinic elastic material under anti-plane deformations. The stress singularity at the wedge apex depends on one material parameter γ. For a given wedge angle α, one can choose a γ so that the stress at the wedge apex is infinite. The wedge angle 2α can be any angle. It need not be larger than π, as is the case when the material is homogeneously isotropic or anisotropic. In the special case of a crack (2α=2π) there can be more than one stress singularity, some of them are stronger than the square root singularity. On the other hand, if γ < there is no stress singularity at the wedge apex for any wedge angle, including the special case of a crack. The classical paradox of Levy [6] and Carothers [7] for an isotropic elastic wedge also appears for a cylindrically anisotropic elastic wedge. There can be more than one critical wedge angle and, again, the critical wedge angle can be any angle. This revised version was published online in August 2006 with corrections to the Cover Date.     

Transient Free Convection from a Horizontal Surface in a Porous Medium Subjected to a Sudden Change in Surface Heat Flux

This paper presents an analytical and numerical study of transient free convection from a horizontal surface that is embedded in a fluid-saturated porous medium. It is assumed that for time steady state velocity and temperature fields are obtained in the boundary-layer which occurs due to a uniform flux dissipation rate q ₁ on the surface. Then, at the heat flux on the surface is suddenly changed to q ₂ and maintained at this value for . Firstly, solutions which are valid for small and large are obtained. The full boundary-layer equations are then integrated step-by-step for the transient regime from the initial unsteady state ( ) until such times at which this forward marching approach is no longer well posed. Beyond this time no valid solutions could be obtained which matched the final solution from the forward integration to the steady state profiles at large times .     

Free Convection from a Vertical Plate in a Porous Medium Subjected to a Porous Medium Subjected to a Sudden Change in Surface Heat Flux

An analysis is made of the transient free convection from a vertical flat plate which is embedded in a fluid-saturated porous medium. It is assumed that for time a steady state temperature or velocity has been obtained in the boundary-layer which occurs due to a uniform flux dissipation rate . Then at time the heat flux on the plate is suddenly changed to and maintained at this value for 0$$ " align="middle" border="0"> . An analytical solution has been obtained for the temperature/velocity field for small times in which the transport effects are confined within an inner layer adjacent to the plate. These effects cause a new steady boundary layer. A numerical solution of the full boundary-layer equations is then obtained for the whole transient from to the steady state, firstly by means of a step-by-step method and then by a matching technique. The transition between the two distinct solution methods is always observed to occur very near to the turning point of the plate surface temperature, a time at which the fluid temperature is close to its steady state profile. The solution obtained using the step-by-step method shows excellent agreement with the small time analytical solution. Results are presented to illustrate the occurrence of transients from both small and large increases and decreases in the levels of existing energy inputs.     

Effect of a Short Roughness Strip on a Turbulent Boundary Layer

The response of a turbulent boundary layer to a short roughness strip is investigated using laser Doppler velocimetry (LDV) and laser induced fluorescence (LIF). Skin friction coefficients are inferred from accurate near-wall measurements. There is an undershoot in , where is the undisturbed smooth wall skin friction coefficient, immediately after the strip. Downstream of the strip, overshoots before relaxing back to unity in an oscillatory manner. The roughness strip has a major effect on the turbulent stresses ; these quantities increase, relative to the undisturbed smooth wall, in the region between the two internal layers originating at the upstream and downstream edges of the strip. The increase in the ratio suggests a decrease in near-wall anisotropy. From the flow visualizations, it is inferred that streamwise vortical structures are weakened immediately downstream of the strip. Consistently, streamwise length scales are also reduced; direct support for this is provided by measured two-point velocity correlations.     

Global Attractors: Topology and Finite-Dimensional Dynamics

Many dissipative evolution equations possess a global attractor with finite Hausdorff dimension d. In this paper it is shown that there is an embedding X of into , with N=[2d+2], such that X is the global attractor of some finite-dimensional system on with trivial dynamics on X. This allows the construction of a discrete dynamical system on which reproduces the dynamics of the time T map on and has an attractor within an arbitrarily small neighborhood of X. If the Hausdorff dimension is replaced by the fractal dimension, a similar construction can be shown to hold good even if one restricts to orthogonal projections rather than arbitrary embeddings.     

Numerical validation of the shear compression specimen. Part II: Dynamic large strain testing

Part I of this work addressed quasi-static loading of the shear compression specimen (SCS), which has been especially developed to investigate the shear dominant response of materials at various strain rates. The stress and strain states were characterized numerically. Approximations were presented to reduce the measured load,P, and displacement,d, into equivalent stress and strain . This paper addresses dynamic loading of the SCS. Several simulations were made for representative materials, whose stress-strain behavior is assumed to be rate-independent. The results show that stress wave loading induces strong oscillations in theP-d curve. However, the curve remains smooth in the gage section. The oscillations are about the quasistatic load values, so that with suitable filtering of the dynamicP-d curves, the quasi-static ones are readily recovered. Consequently, the approach that was developed for quasi-static loading of the SCS is now extended to dynamic loading situations. The average strain rate is rather constant and scales linearly with the prescribed velocity. As the plastic modulus becomes smaller, the strain rate reaches higher values. Friction at the end pieces of the specimen is also investigated, and shown to have a small overall influence on the determined mechanical characteristics. This paper thereby confirms the potential of the SCS for large strain testing of materials, using a unified approach, over a large range of strain rates in a seamless fashion.     

A Helmholtz/Weyl Decomposition in Energy Space

For a bounded region in a Helmholtz/Weyl decomposition of the Sobolev space is given,with orthogonality with respect to the strain-energy inner product of elasticity (anisotropic or isotropic).     

Transient response of a finite crack in an orthotropic strip under the in-plane shear impact

The transient response of a central crack in an orthotropic strip under the in-plane shear impact loading is studied by using the dual integral equation method proposed by Copson and Sih. The general formula for the shear stress intensity factor near the crack tip is derived. Numerical results of with in various cases are obtained by solving the second kind Fredholm integral equation and by performing the inverse Laplace transform.     

Existence of Weak Solutions to the Equations of Non-Stationary Motion of Non-Newtonian Fluids with Shear Rate Dependent Viscosity

In the present paper we prove the existence of weak solutions to the equations of non-stationary motion of an incompressible fluid with shear rate dependent viscosity in a cylinder Q = Ω × (0,T), where denotes an open set. For the power-low model with we are able to construct a weak solution with ∇ · u = 0.     

On the Denseness of the Set of Unsolvable Cauchy Problems in the Set of All Cauchy Problems in the Case of an Infinite-Dimensional Banach Space

We prove the following statement: Theorem 1. Let E and be an arbitrary infinite-dimensional Banach space and a continuous mapping, respectively. Then, for every and > 0, there exists a continuous mapping such that

Analysis of thermally activated formation and breakdown of Kear-Wilsdorf barriers in Ni<Subscript>3</Subscript>Ge single crystals of various orientations

The orientation dependence of the yield stress in Ni₃Ge single crystals has been examined both theoretically and experimentally. The positive temperature dependence of the yield stress in the low temperature region is attributed to formation of Kear-Wilsdorf barriers. The forces driving the formation and breakdown of barriers are calculated within the framework of the Hirsch scheme. A distinctive feature of the model proposed is that the barrier is considered on the screw component of the a/2[ 01](111) superdislocation in the primary octahedral plane. The major role in barrier formation belongs to anisotropy of elastic moduli, energy of antiphase boundaries in the octahedral plane, shear stresses in the cubic and octahedral planes, and friction-induced stress in the cubic plane. A comparison of predicted values of the driving force of barrier formation and breakdown with experimental values reveals their good agreement. An analysis of the orientation dependence of the driving force of barrier formation in the temperature range T = 77–293 K shows that the dependence (T) has an extremum for crystals deformed along the [ 39] crystallographic direction, which is confirmed experimentally.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 116–125, January–February, 2005.     

Pseudo-molecular dynamics study of grain boundary segregation

The segregation of bismuth atoms on the [101] tilt copper grain boundaries Σ3 ( ) 70.53°, Σ33 ( ) 58.99°, Σ11 ( ) 50.48° and Σ9 ( ) 38.94° has been studied by pseudo-molecular dynamics using the empiricalN-body potentials. The relationship between bismuth segregation and grain boundary structure has been discussed in detail. The subject supported by the Chinese Academy of Sciences and National Natural Science Foundation of China     

About a condition for blow up of solutions of cauchy problem for a wave equation

ＣｏｎｓｉｄｅｒｔｈｅＣａｕｃｈｙｐｒｏｂｌｅｍｆｏｒｔｈｅｗａｖｅｅｑｕａｔｉｏｎｉｎＲＮ×Ｒ＋（Ｎ≥２）：２ｕ（ｘ,ｔ）ｔ２－ｘｉａｉｊ（ｘ）ｘｊｕ＝｜ｕ｜ｐ－１·ｕ　　（（ｘ,ｔ）∈ＲＮ×（０,Ｔ））,ｕ（ｘ,０）＝ｇ（ｘ）　（ｘ∈ＲＮ）,ｕｔ（ｘ,０）＝ｈ（ｘ）　（ｘ∈ＲＮ）,（１）ｗｈｅｒｅｕ（ｘ,ｔ）ｉｓｎｏｎｔｒｉｖｉａｌｓｏｌｕｔｉｏｎｗｉｔｈｆｉｎｉｔｅｓｐｅｅｄｏｆｐｒｏｐａｇａｔｉｏｎａｎｄｉｓｓｕｐｐｏｒｔｅｄｏｎａｆｏｒｗａｒｄｃｏｎｅ（ｘ,ｔ）·ｔ≥０,｜…     

Solution for plane strain forward and backward extrusions with a fractional reductionR=0.5 by the integartion depending on a parameter

A parameter t is introduced to boundary slip line of rigid regions for plane strain and indirect extrusions with a fractional reduction R=0.5. Integration by substitution has been used along the boundary slip line in order to obtain the extrusion pressure. By the integration depending on a parameter, the following results are obtained, and die pressure is 5.14k for backward extrusion; and pad average pressure is 2.57k for forward extrusion. All the results from this method are the same as those of the conventional solution.     

Homologies of Intersections of Pseudomanifolds with Local Homotopic Conditions on Links of Strata

In terms of local homotopic properties of the links of strata of an n-dimensional PL-pseudomanifold X, we obtain a sufficient condition for the natural homomorphisms of the jth intersection homology groups with perversity multiindices and to be isomorphisms for all j i, where i < n – 3.     

High Reynolds Number Flow past a Plate Mounted at a Small Angle of Attack

A plane incompressible fluid flow past a plate mounted in a homogeneous stream at a small angle of attack ^* is investigated on the basis of an asymptotic analysis of the Navier-Stokes equations at high Reynolds numbers (Re). In the neighborhood of the leading edge the flow structure is studied in detail. It is found that separation is initiated in a small vicinity of the leading edge at and the length of the slow reverse stream zone is of the order O(1) at . The nonuniqueness of the solution is detected at and the hysteresis phenomenon is explained. It is shown that under certain conditions the solutions obtained also hold for flows past bodies of small thickness.     

Molecular dynamics study of deformation and fracture of Bi-segregated copper bicrystals

The microprocesses of deformation and fracture of Bi-segregated copper bicrystals Σ33 ( ) 58.99°, Σ11 ( ) 50.48° and Σ9 ( ) 38.94° have been simulated by molecular dynamics in order to study the relationship between the grain boundary embrittlement (GBE) and grain boundary (GB) structure. It is shown that GBE is related to the segregated concentration and distribution of Bi atoms, while Bi segregation is related to the GB structure. Due to their different structures, the bicrystals Σ33, Σ11 and Σ9 show an increasing propensity for Bi segregated concentration. So under the action of external force, Σ33, Σ11 and Σ9 show transgranular ductile, intergranular tearing and intergranular brittle fracture modes, respectively. The subject supported by the Chinese Academy of Sciences and National Natural Science Foundation of China     

Energetic formulation of multiplicative elasto-plasticity using dissipation distances

We introduce a new energetic formulation for the inelastic rate-independent behavior of standard generalized materials. This formulation is solely based on the classical elastic energy-storage potential and a dissipation potential , and it replaces the classical variational inequalities which describe the flow rules for the inelastic variables like the plastic deformation and the hardening parameters. The energetic formulation has the major advantage that it is defined for a larger class of processes since it does not involve any derivatives of the strains or the internal variables, thus allowing for an analysis of processes involving sharp interfaces, localization or microstructure. Two new quantities are derived from and . First, this is the global dissipation distance on the manifold of internal states. Second, the reduced stored-energy density contains the comprised information of the elastic and plastic material properties via minimization of over the new internal variable. Several stability concept are derived and used to analyze failure mechanism. Finally, a natural incremental method is proposed which reduces to a minimization problem and can be solved efficiently using .Received: 5 December 2002, Accepted: 10 February 2003, Published online: 27 June 2003PACS: 66.20.F2, 62.40.+i, 80.40.cmA. Mielke: Research partially supported by DFG within the SFB 404 Multifield Problems     

Flow in Random Porous Media

Flow in a porous medium with a random hydraulic conductivity tensor K(x) is analyzed when the mean conductivity tensor (x) is a non-constant function of position x. The results are a non-local expression for the mean flux vector (x) in terms of the gradient of the mean hydraulic head (x), an integrodifferential equation for (x), and expressions for the two point covariance functions of q(x) and (x). When K(x) is a Gaussian random function, the joint probability distribution of the functions q(x) and (x) is determined.