Continuous spectrum growth and modal instability in swirling duct flow

We present results on the stability of compressible inviscid swirling flows in an annular duct. Such flows are present in aeroengines, for example in the by-pass duct, and there are also similar flows in many aeroacoustic or aeronautical applications. The linearised Euler equations have a ('critical layer') singularity associated with pure convection of the unsteady disturbance by the mean flow, and we focus our attention on this region of the spectrum. By considering the critical layer singularity, we identify the continuous spectrum of the problem and describe how it contributes to the unsteady field. We find a very generic family of instability modes near to the continuous spectrum, whose eigenvalue wavenumbers form an infinite set and accumulate to a point in the complex plane. We study this accumulation process asymptotically, and find conditions on the flow to support such instabilities. It is also found that the continuous spectrum can cause a new type of instability, leading to algebraic growth with an exponent determined by the mean flow, given in the analysis. The exponent of algebraic growth can be arbitrarily large. Numerical demonstrations of the continuous spectrum instability, and also the modal instabilities are presented.

Simulation of Coal Combustion by AUSM Turbulence-Chemistry Char Combustion Model and a Full Two-Fluid Model

An algebraic unified second-order moment (AUSM) turbulence-chemistry model of char combustion is introduced in this paper, to calculate the effect of particle temperature fluctuation on char combustion. The AUSM model is used to simulate gas-particle flows, in coal combustion in a pulverized coal combustor, together with a full two-fluid model for reacting gas-particle flows and coal combustion, including the sub-models as the k-epsilon-k(p) two-phase turbulence niodel, the EBU-Arrhenius volatile and CO combustion model, and the six-flux radiation model. A new method for calculating particle mass flow rate is also used in this model to correct particle outflow rate and mass flow rate for inside sections, which can obey the principle of mass conservation for the particle phase and can also speed up the iterating convergence of the computation procedure effectively. The simulation results indicate that, the AUSM char combustion model is more preferable to the old char combustion model, since the later totally eliminate the influence of particle temperature fluctuation on char combustion rate.

Weaknesses of Margulis and Ramanujan-Margulis low-density parity-check codes

We report weaknesses in two algebraic constructions of low-density parity-check codes based on expander graphs. The Margulis construction gives a code with near-codewords, which cause problems for the sum-product decoder; The Ramanujan-Margulis construction gives a code with low-weight codewords, which produce an error-floor. © 2004 Elsevier B.V.

Weaknesses of margulis and ramanujan-margulis low-density parity-check codes

We report weaknesses in two algebraic constructions of low-density parity-check codes based on expander graphs. The Margulis construction gives a code with near-codewords, which cause problems for the sum-product decoder; The Ramanujan-Margulis construction gives a code with low-weight codewords, which produce an error-floor. ©2003 Published by Elsevier Science B. V.

Numerical Simulation and Experimental Investigation about Internal and External Flows

In this paper, TASCflow3D is used to solve inner and outer 3D viscous incompressible turbulent flow (R-e = 5.6 X 10(6)) around axisymmetric body with duct. The governing equation is a RANS equation with standard k-epsilon turbulence model. The discrete method used is a finite volume method based on the finite element approach. In this method, the description of geometry is very flexible and at the same time important conservative properties are retained. The multi-block and algebraic multi-grid techniques are used for the convergence acceleration. Agreement between experimental results and calculation is good. It indicates that this novel approach can be used to simulate complex flow such as the interaction between rotor and stator or propulsion systems containing tip clearance and cavitation.

Studies of the Effect of a Coal Concentrator on NO Formation in Swirling Coal Combustion

To develop low-pollution burners, the effect of a coal concentrator on NO formation in swirling coal combustion is studied using both numerical simulation and experiments. The isothermal gas-particle two-phase velocities and particle concentration in a cold model of swirl burners with and without coal concentrators were measured using the phase Doppler particle anemometer (PDPA). A full two-fluid model of reacting gas-particle flows and coal combustion with an algebraic unified second-order moment (AUSM) turbulence-chemistry model for the turbulent reaction rate of NO formation are used to simulate swirling coal combustion and NO formation with different coal concentrators. The results give the turbulent kinetic energy, particle concentration, temperature and NO concentration in cases of with and without coal concentrators. The predicted results for cold two-phase flows are in good agreement with the PDPA measurement results, showing that the coal concentrator increases the turbulence and particle concentration in the recirculation zone. The combustion modeling results indicate that although the coal concentrator increases the turbulence and combustion temperature, but still can remarkably reduce the NO formation due to creating high coal concentration in the recirculation zone.

Energy Principle And Nonlinear Electric-Mechanical Behavior Of Ferroelectric Ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u(i), electric displacement D-i and volume fraction rho(I) of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [ 1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction rho(I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction rho(I) of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction rho(I) of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

Hydrodynamic interaction between two vertical cylinders in water waves

The hydrodynamic interaction between two vertical cylinders in water waves is investigated based on the linearized potential flow theory. One of the two cylinders is fixed at the bottom while the other is articulated at the bottom and oscillates with small amplitudes in the direction of the incident wave. Both the diffracted wave and the radiation wave are studied in the present paper. A simple analytical expression for the velocity potential on the surface of each cylinder is obtained by means of Graf's addition theorem. The wave-excited forces and moments on the cylinders, the added masses and the radiation damping coefficients of the oscillating cylinder are all expressed explicitly in series form. The coefficients of the series are determined by solving algebraic equations. Several numerical examples are given to illustrate the effects of various parameters, such as the separation distance, the relative size of the cylinders, and the incident angle, on the first-order and steady second-order forces, the added masses and radiation-damping coefficients as well as the response of the oscillating cylinder.

Energy principle of ferroelectric ceramics and single domain mechanical model

Many physical experiments have shown that the domain switching in a ferroelectric material is a complicated evolution process of the domain wall with the variation of stress and electric field. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of ferroelectric ceramic and used to study the nonlinear constitutive behavior of ferroelectric body in this paper. The principle of stationary total energy is put forward in which the basic unknown quantities are the displacement u (i) , electric displacement D (i) and volume fraction rho (I) of the domain switching for the variant I. Mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion. On the basis of the domain switching criterion, a set of linear algebraic equations for the volume fraction rho (I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. Then a single domain mechanical model is proposed in this paper. The poled ferroelectric specimen is considered as a transversely isotropic single domain. By using the partial experimental results, the hardening relation between the driving force of domain switching and the volume fraction of domain switching can be calibrated. Then the electromechanical response can be calculated on the basis of the calibrated hardening relation. The results involve the electric butterfly shaped curves of axial strain versus axial electric field, the hysteresis loops of electric displacement versus electric filed and the evolution process of the domain switching in the ferroelectric specimens under uniaxial coupled stress and electric field loading. The present theoretic prediction agrees reasonably with the experimental results given by Lynch.

Computation of stress intensity factors by the sub-region mixed finite element method of lines

Based on the sub-region generalized variational principle, a sub-region mixed version of the newly-developed semi-analytical 'finite element method of lines' (FEMOL) is proposed in this paper for accurate and efficient computation of stress intensity factors (SIFs) of two-dimensional notches/cracks. The circular regions surrounding notch/crack tips are taken as the complementary energy region in which a number of leading terms of singular solutions for stresses are used, with the sought SIFs being among the unknown coefficients. The rest of the arbitrary domain is taken as the potential energy region in which FEMOL is applied to obtain approximate displacements. A mixed system of ordinary differential equations (ODEs) and algebraic equations is derived via the sub-region generalized variational principle. A singularity removal technique that eliminates the stress parameters from the mixed equation system eventually yields a standard FEMOL ODE system, the solution of which is no longer singular and is simply and efficiently obtained using a standard general-purpose ODE solver. A number of numerical examples, including bi-material notches/cracks in anti-plane and plane elasticity, are given to show the generally excellent performance of the proposed method.

A unified model for dislocation nucleation, dislocation emission and dislocation free zone

In this paper, a unified model for dislocation nucleation, emission and dislocation free zone is proposed based on the Peierls framework. Three regions are identified ahead of the crack tip. The emitted dislocations, located away from the crack tip in the form of an inverse pileup, define the plastic zone. Between that zone and the cohesive zone immediately ahead of the crack tip, there is a dislocation free zone. With the stress field and the dislocation density field in the cohesive zone and plastic zone being, respectively, expressed in the first and second Chebyshev polynomial series, and the opening and slip displacements in trigonometric series, a set of nonlinear algebraic equations can be obtained and solved with the Newton-Raphson Method. The results of calculations for pure shearing and combined tension and shear loading after dislocation emission are given in detail. An approximate treatment of the dynamic effects of the dislocation emission is also developed in this paper, and the calculation results are in good agreement with those of molecular dynamics simulations.

Dislocation nucleation and emission from crack-tip

The problems of dislocation nucleation and emission from a crack tip are analysed based on Peierls model. The concept adopted here is essentially the same as that proposed by Rice. A slight modification is introduced here to identify the pure linear elastic response of material. A set of new governing equations is developed, which is different from that used by Beltz and Rice. The stress field and the dislocation density field can be expressed as the first and second Chebyshev polynomial series respectively. Then the opening and slip displacements can be expanded as the trigonometric series. The Newton-Raphson Method is used to solve a set of nonlinear algebraic equations. The new governing equations allow us to extend the analyses to the case of dislocation emission. The calculation results for pure shearing, pure tension and combined tension and shear loading are given in detail.

Mechanical modeling of grain boundary sliding of polycrystals

Using a variational method, a general three-dimensional solution to the problem of a sliding spherical inclusion embedded in an infinite anisotropic medium is presented in this paper. The inclusion itself is also a general anisotropic elastic medium. The interface is treated as a thin interface layer with interphase anisotropic properties. The displacements in the matrix and the inclusion are expressed as polynomial series of the cartesian coordinate components. Using the virtual work principle, a set of linear algebraic equations about unknown coefficients are obtained. Then the general sliding spherical inclusion problem is accurately solved. Based on this solution, a self-consistent method for sliding polycrystals is proposed. Combining this with a two-dimensional model of an aggregate polycrystal, a systematic analysis of the mechanical behaviour of sliding polycrystals is given in detail. Numerical results are given to show the significant effect of grain boundary sliding on the overall mechanical properties of aggregate polycrystals.

Character of simplified Navier-Stokes (SNS) equations near separation point for two-dimensional laminar flow over a flat plate

It is proved that the simplified Navier-Stokes (SNS) equations presented by Gao Zhi[1], Davis and Golowachof-Kuzbmin-Popof (GKP)[3] are respectively regular and singular near a separation point for a two-dimensional laminar flow over a flat plate. The order of the algebraic singularity of Davis and GKP equation[2,3] near the separation point is indicated. A comparison among the classical boundary layer (CBL) equations, Davis and GKP equations, Gao Zhi equations and the complete Navier-Stokes (NS) equations near the separation point is given.

Basic equations for suspension flows with interphase mass-transfer

In the case of suspension flows, the rate of interphase momentum transfer M(k) and that of interphase energy transfer E(k), which were expressed as a sum of infinite discontinuities by Ishii, have been reduced to the sum of several terms which have concise physical significance. M(k) is composed of the following terms: (i) the momentum carried by the interphase mass transfer; (ii) the interphase drag force due to the relative motion between phases; (iii) the interphase force produced by the concentration gradient of the dispersed phase in a pressure field. And E(k) is composed of the following four terms, that is, the energy carried by the interphase mass transfer, the work produced by the interphase forces of the second and third parts above, and the heat transfer between phases. It is concluded from the results that (i) the term, (-alpha-k-nabla-p), which is related to the pressure gradient in the momentum equation, can be derived from the basic conservation laws without introducing the "shared-pressure presumption"; (ii) the mean velocity of the action point of the interphase drag is the mean velocity of the interface displacement, upsilonBAR-i. It is approximately equal to the mean velocity of the dispersed phase, upsilonBAR-d. Hence the work terms produced by the drag forces are f(dc) . upsilonBAR-d, and f(cd) . upsilonBAR-d, respectively, with upsilonBAR-i not being replaced by the mean velocity of the continuous phase, upsilonBAR-c; (iii) by analogy, the terms of the momentum transfer due to phase change are upsilonBAR-d-GAMMA-c, and upsilonBAR-d-GAMMA-d, respectively; (iv) since the transformation between explicit heat and latent heat occurs in the process of phase change, the algebraic sum of the heat transfer between phases is not equal to zero. Q(ic) and Q(id) are composed of the explicit heat and latent heat, so that the sum Q(ic) + Q(id)) is equal to zero.