Interactions between compressibility and heat release in turbulent mixing layers

Reduced turbulence activity and growth rate of a compressible mixing layer when the convective Mach number increases, are well-known phenomena. Heat release due to combustion has similar effects and important implications for applications such as scramjet engines the efficiency of which depends on a proper mixing of oxidizer and fuel. To understand the underlying mechanisms, highly resolved DNS of inert and reacting, temporally evolving mixing layers at different convective Mach numbers and Reynolds numbers ensuring a self-similar state are performed and analyzed with a particular focus on the pressure-strain correlations in the Reynolds-stress transport equations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Introduction of non-uniformity through linearization of the system governing turbulent, mixing of a scalar quantity in a 2-d mixing layer

The introduction of mathematical non-uniformity in the formulation of the turbulent mixing of a scalar quantity (mass, temperature, etc.) for a 2-d, free shear flow using Goertler's [ZAMM 22 (1942) 244] perturbation argument is discussed. Approximate, i.e. thin shear layer self-similar forms for mass, momentum and the scalar quantity are derived, and then linearized using Goertler's method. Though successful for the mean velocity field, the regular expansion yields inconsistent solutions for the transport of a scalar. Sources of the non-uniformity are identified using appropriate numerical methods for both non-linear and linear formulations. A consistent result is obtained by rescaling the independent variable and equation system and identifying dominant behavior. The results of this corrected formulation are shown to be consistent with the relationships obtained by the author using an approximate matched asymptotic expansion procedure.     

An assessment of streamline curvature effects on the mixing region of a turbulent plane jet in crossflow

The flow field of a turbulent plane jet in a weak or moderate crossflow, which is characterised by mild streamline curvature, has been investigated computationally. The values of the jet-to-crossflow velocity ratios chosen are 6, 9 and 10. The time-averaged Navier–Stokes equations are solved on a staggered Cartesian grid using the standard k–ϵ model and the k–ϵ model with streamline curvature modification. The predictions using both the models are compared with available experimental data. It has been shown that by accounting for the effect of streamline curvature in the k–ϵ model results in good prediction of this flow configuration.     

两层流体界面上的孤立波

本文讨论两水平固壁间两层不可压无粘流体界面上的孤立波,计及界面上的表面张力效应.首先建立了适用于这种模型的基本方程组,并在弱色散近似下应用约化摄动法,导得了一阶界面升高所满足的Korteweg-de Vries方程,指出了按该方程系数α和μ的符号的异同,KdV孤立波可能凸向上或凸向下.然后详细讨论了原有近似下非线性效应与色散效应不能平衡的两种临界情形.在采用了适当的近似之后,对第一种临界情形(α=0)得到了修正的KdV方程,并指出,在所考虑的情形中,当μ>0时孤立波不存在,当μ<0时,孤立波仍可能存在,其形式与KdV孤立波不同;对第二种临界情形(μ=0),导得了推广的KdV方程,这时存在振荡型孤立波.文中还对近临界情形作了讨论.本文结果与一些经典结果完全一致,并把它们作了拓广.     

On the curvature/buoyancy analogy for turbulent shear flows

Similarity in the near wall region of turbulent curved shear flows is examined. It is found that the normalized mean velocity is a function only of the dimensionless distance _c =z/L _c whereL _c is a corresponding Monin-Oboukhov length for curved shear flows. Again, the universal function is found to obey the log-linear law. Therefore, this result and the earlier derivation of So affirm that there is a very close analogy between the effects of streamline curvature and buoyancy for turbulent shear flows.

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Zusammenfassung Die Ähnlichkeitsverhältnisse in turbulenten, gekrümmten Strömungen mit Schubkräften wird für das Gebiet in der Nähe einer Wand untersucht. Es ergibt sich, daß die normalisierte mittlere Geschwindigkeit nur von der dimensionslosen Entfernung _c =z/L _c abhängt.L _c ist hierbei eine zugeordnete Monin-Oboukhov-Länge für gekrümmte Strömungen mit Schubkräften. Auch in diesem Falle geohorcht die allgemeine Gleichung dem logarithmisch-linearen Gesetz. Dieses Ergebnis und die frühere Ableitung von So bestätigen, daß eine ausgeprägte Analogie zwischen den Auswirkungen der Strömungslinienkrümmung und dem Auftrieb bei turbulenten Strömungen mit Schubkräften besteht.

     

Instability at the interface of bodies subjected to high-elastic deformations

The problem of instability at the interface of two elastic half-planes in compression is investigated within the framework of the plane problem of the stability of deformation of compressible and incompressible elastic bodies at finite subcritical strains [1, 2]. The results are obtained for the plane deformation of bodies with an arbitrary form of the elastic potential. Numerical examples are presented for high-elastic bodies with potentials of the Mooney and Treloar types.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 999–1002, November–December, 1971.     

Integral equations in the wave scattering problem at an irregular interface of domains

Modeling the scattering of electromagnetic waves at an interface of media with different characteristics, one encounters the conjugation problem. Using the method of boundary integral equations and the theory of generalized potentials, we prove the classical resolvability of this problem. The boundary is assumed to be irregular. This means that the plane is divided into two domains by a curve which coincides with a straight line, except for a finite part, producing the irregularity. We propose algorithms for the approximate solution of the conjugation problem based on the spline methods for the solution of integral equations. We theoretically substantiate the computational scheme, namely, we prove the convergence and estimate the convergence rate.     

The reflection and interference of electrons at the interface of superlattice

A new algorithm for the calculation of the electron state of superlattice was proposed. From the electron wave point of view, the reflection and interference of electron wave at the interface of superlattice were accounted for and the electron states of the superlattice were discussed. The electron energy levels calculated using this algorithm are in good agreement with experimental results.     

Reflection and transmission of plasma waves at the interface of crystallites

A linearized problem of the reflection and transmission of a plasma wave at the boundary of a half-space (namely, the plane separating two crystallites) is formulated and analytically solved. The electron distribution function and the electric field inside the half-space of a degenerate plasma are found. The reflection and transmission coefficients are determined as functions of the input parameters of the problem. The longwave limit (i.e., the resonance case when the oscillation frequency of the self-consistent electric field is close to the natural (Langmuir) oscillation frequency) is analyzed.     

Heat and mass transfer in annular liquid jets: II. g-jitter

The effects of g-jitter on heat and mass transfer in underpressurized, annular liquid jets are analyzed numerically as a function of the amplitude and frequency of the gravitational modulation by means of a mapping technique that transforms the time-dependent geometry of these jets into a unit square and a conservative finite difference method. It is shown that the pressure coefficient, gas concentration at the jet's inner interface, heat fluxes at the jet's inner and outer interfaces and interfacial temperature are periodic functions of time whose amplitudes increase as the amplitude of the g-jitter is increased, but decrease as the jitter frequency is increased. The pressure coefficient is almost in phase with the heat flux at the jet's outer interface, and out of phase with the mass transfer rate at the jet's inner interface. It is also shown that the temperature field adapts itself rapidly to the imposed gravity modulation, and thermal equilibrium is reached quickly. However, mass transfer phenomena are very slow and require a very long time to become periodic.     

Adhesion bond and temperature stresses at the polymer - filler interface in polyethylene composites

The temperature stresses in polyethylene composites with fibrous fillers have been estimated. It is shown that they do not represent a threat to the adhesion bond or the cohesion strength of the components of the systems investigated. Model experiments have revealed the presence of an adhesion interaction between the filler and the matrix in the composite itself and have made it possible to estimate the actual threat posed by the temperature stresses. The mechanism of action of the filler particles on the thermal expansion of the composite is explained.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1049–1056, November–December, 1970.     

Singularities at the tip of a crack on the interface of piezoelectric bodies

Singularities of elastic and electric fields are investigated at the tip of a crack on the interface of two anisotropic piezoelectric media under various boundary conditions on the crack surfaces. The singularity exponents form the spectrum of a certain polynomial pencil, and although explicit formulas are not available, this spectrum is described completely though. The mathematical results apply to problems in fracture mechanics. In this way the Griffith formulas are obtained for increments of energy functionals due to the growth of the crack, and the notion of energy release matrix is introduced. Normalization conditions for bases of singular solutions are proposed to adapt them to energy, stress, and deformation fracture criteria. Connections between these bases are determined, and additional properties of the deformation basis related to the notion of electric surface enthalpy are established. Bibliography: 44 titles. Dedicated to Vsevolod Alekseevich Solonnikov Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 362, 2008, pp. 241–271.     

Nonlinear responses from the interaction of two progressing waves at an interface

For scalar semilinear wave equations, we analyze the interaction of two (distorted) plane waves at an interface between media of different nonlinear properties. We show that new waves are generated from the nonlinear interactions, which might be responsible for the observed nonlinear effects in applications. Also, we show that the incident waves and the nonlinear responses determine the location of the interface and some information of the nonlinear properties of the media. In particular, for the case of a jump discontinuity at the interface, we can determine the magnitude of the jump.     

The concentration of a wave field at the interface of elastic media

The steady symmetrical oscillations of a transversely non-uniform elastic rectangular region, consisting of three bonded uniformisotropic rectangles, are considered, where the elastic characteristics of the inner rectangle are assumed to be different from those of the external rectangles. Using methods developed previously [1,2], the dependence of the order of the singularity of the stress field at the interface on the combinations of the constants of elasticity of the joined media and on their wave impedances is investigated.     

Effect of reaction at the polymer-solid interface on the mechanical properties of alkyd coatings

IR spectroscopy is used to investigate the intermolecular reaction between alkyd resin and the surface of aerosil. It is shown that the nature of the reaction has a considerable influence on the mechanical and adhesion properties of the coatings. Modification of the aerosil surface with octadecylamine leads to the formation of a hydrogen bond between the NH groups of the modifier and the OH groups of the aerosil surface. In the presence of alkyd resin the NH groups are almost completely displaced from the surface of the filler.Mekhanika Polimerov, Vol. 3, No. 1, pp. 19–23, 1967     

Derivation of a rod theory for biphase materials with dislocations at the interface

Starting from three-dimensional elasticity we derive a rod theory for biphase materials with a prescribed dislocation at the interface. The stored energy density is assumed to be non-negative and to vanish on a set consisting of two copies of SO(3). First, we rigorously justify the assumption of dislocations at the interface. Then, we consider the typical scaling of multiphase materials and we perform an asymptotic study of the rescaled energy, as the diameter of the rod goes to zero, in the framework of Γ-convergence.     

Exploring the dynamics of African swine fever transmission cycles at a wildlife-livestock interface

African swine fever (ASF), a contagious disease of pigs, can be economically devastating. At a wildlife–livestock interface, depending on the presence and interactions of domestic pigs, wild pigs, and soft ticks, three transmission cycles have been proposed for the persistence of ASF: a wild pig-domestic pig-tick cycle, a domestic pig-tick cycle, and a domestic pig cycle, but to date, their relative importance on the outbreak and persistence of the disease is not clear. A stochastic model that considers these cycles is formulated and analysed to assess their impacts on the outbreak and persistence of the disease. Using a multitype branching process approximation, it is shown that all cycles can result in very large probabilities of disease outbreaks. Numerical results show that the disease can be endemic if the ticks are not controlled. If ticks are controlled, disease extinction is certain, regardless of the cycle, but the time to extinction can be long. These findings have important implications for the prevention and control of ASF outbreaks at a wildlife–livestock interface.