Acceleration wave speeds in a hypoplastic constitutive model

The paper presents a theoretical investigation of acceleration waves in a plastic material described by an incrementally non-linear hypoplastic constitutive equation. Speeds of plane acceleration waves and their dependence on the stress state are calculated. The spectrum of possible wave speeds is found to be continuous, which is in contrast to discrete wave speed spectra in incrementally linear models. Two types of ill-posedness are revealed, known as flutter ill-posedness and stationary discontinuity. The wave speed analysis is also performed by the characteristic method, leading to different equations compared to the acceleration wave approach. It is proved that for the considered hypoplastic constitutive equation both approaches give identical wave speed spectra.     

Incompressible ionized fluid mixtures

The model-combining Navier-Stokes equation for barycentric velocity together with Nernst-Planck's equation for concentrations of particular mutually reacting constituents, the heat equation, and the Poisson equation for self-induced quasistatic electric field is formulated and its thermodynamics is discussed. Then, existence of a weak solution to an initial-boundary-value problem for this system is proved in two special cases: zero Reynolds' number and constant temperature. Mathematics Subject Classification (2000) 35Q35 · 76T30 · 80A32 Physics and Astronomy Classification Scheme (2001) 47.27Ak ⋅ 47.70Fw     

Shock wave interference on a fenced wing at hypersonic speeds

High-pressure zones on the wing, created by the reflected shocks, are experimentally demonstrated and their influence on the aerodynamic characteristics of the wing is investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 135–140, May–June, 1992.The authors are grateful to V. E. Mosharov, V. N. Tarasov, and V. I. Plyashechnik for assisting with the experiments.     

On hydrodynamic phase field models for binary fluid mixtures

Two classes of thermodynamically consistent hydrodynamic phase field models have been developed for binary fluid mixtures of incompressible viscous fluids of possibly different densities and viscosities. One is quasi-incompressible, while the other is incompressible. For the same binary fluid mixture of two incompressible viscous fluid components, which one is more appropriate? To answer this question, we conduct a comparative study in this paper. First, we visit their derivation, conservation and energy dissipation properties and show that the quasi-incompressible model conserves both mass and linear momentum, while the incompressible one does not. We then show that the quasi-incompressible model is sensitive to the density deviation of the fluid components, while the incompressible model is not in a linear stability analysis. Second, we conduct a numerical investigation on coarsening or coalescent dynamics of protuberances using the two models. We find that they can predict quite different transient dynamics depending on the initial conditions and the density difference although they predict essentially the same quasi-steady results in some cases. This study thus cast a doubt on the applicability of the incompressible model to describe dynamics of binary mixtures of two incompressible viscous fluids especially when the two fluid components have a large density deviation.     

Structure and stability of one-dimensional detonationsin ethylene-air mixtures

The propagation of one-dimensional detonations in ethylene-air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit, first-order-accurate, time marching algorithm. The ethylene-air combustion is modeled with a 20-species, 36-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies over an equivalence ratio range of for different initial pressures and degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel-air equivalence ratio. For equivalence ratios less than approximately 1.2 the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures ( 1.2$" align="middle" border="0"> ) exhibit a low-frequency mode that includes large fluctuations in the detonation wave speed. At high degrees of overdrive, stable detonation wave propagation is obtained. A modified McVey-Toong short-period wave-interaction theory is in excellent agreement with the numerical simulations.Received: 13 September 2004, Revised: 1 November 2004, Published online: 3 March 2005[/PUBLISHED]Correspondence to: S. Yungster     

Taylor-Couette stability analysis for a Doi-Edwards fluid

The stability of Taylor-Couette flow of entangled polymeric solutions to small axisymmetric stationary disturbances is analyzed using the Doi-Edwards constitutive equation in the small gap limit. A previous analysis of Karlsson, Sokolov, and Tanner for the general K-BKZ equation, of which the Doi-Edwards equation is a special case, reduces the problem to one of numerically evaluating seven viscoelastic functions of the shear rate in the gap. Of these seven, only three — two of which are related to the second normal stress difference, and one of them to shear thinning — significantly affect the flow stability. The negative second normal stress difference of the Doi-Edwards fluid stabilizes the flow at low values of the Weissenberg number ₁ , while shear thinning produces strong destabilization at moderate Weissenberg number. Here ₁ is the longest relaxation time. Non-monotonic effects of viscoelasticity on Taylor-Couette stability analogous to those predicted here have been observed in experiments of Giesekus. The extreme shear thinning of the Doi-Edwards fluid is also predicted to produce a large growth in the height of the Taylor cells, a phenomenon that has been seen experimentally by Beavers and Joseph.     

Passive shock wave/boundary layer control of wing at transonic speeds

At supercritical conditions a porous strip(or slot strip) placed beneath a shock wave can reduce the drag by a weaker lambda shock system, and increase the buffet boundary, even may increase the lift. Passive shock wave/boundary layer control(PSBC) for drag reduction was conducted by SC(2)-0714 supercritical wing, with emphases on parameter of porous/slot and bump, such as porous distribution, hole diameter,cavity depth, porous direction and so on. A sequential quadratic programming(SQP) optimization method coupled with adjoint method was adopted to achieve the optimized shape and position of the bumps.Computational fluid dynamics(CFD), force test and oil test with half model all indicate that PSBC with porous, slot and bump generally reduce the drag by weaker lambda shock at supercritical conditions.According to wind tunnel test results for angle of attack of 2? at Mach number M = 0.8, the porous configuration with 6.21% porosity results in a drag reduction of 0.0002 and lift–drag ratio increase of 0.2, the small bump configuration results in a drag reduction of 0.0007 and lift–drag ratio increase of 0.3.Bump normally reduce drag at design point with shock wave position being accurately computed. If bump diverges from the position of shock wave, drag will not be easily reduced.     

Free wave propagation in binary gas mixtures

The problem concerning the propagation of free waves in binary mixtures of monatomic ideal gases is analyzed by using a kinetic model of the Boltzmann equation which is compatible with the two-fluid hydrodynamic theory. Comparison of the theoretical results with available experimental data shows that the two-fluid model equation can be used to describe the wave-vector dependence of the free sound waves in both continuum and kinetic regimes.     

Shear stability studies on polymer-polymer and polymer-fibre mixtures

The shear stability of drag reducing polymer-polymer and polymer-fibre mixtures has been studied at a Reynolds number of 14,000 using a turbulent flow rheometer. The ratio of the drag reduction at a particular pass number to the initial drag reduction has been determined for the mixtures at various pass numbers and compositions in order to determine the effect of composition on the shear stability of the mixtures.It has been found in both cases that when there is a drastic difference in the shear stabilities of the constituents of the mixtures, the incorporation of a small amount of the less shear stable drag reducing agent reduces the shear stability drastically. On the other hand, when the shear stability of the constituents are of the same order, there is only a proportional change in the shear stability of the mixtures on addition of one component to the other. A correlation between the decay coefficient of the mixture (R _M ), the decay coefficients of the constituents (R ₁ andR ₂ ) and the weight fractions of the mixture components (W ₁ andW ₂) is suggested. An efficacious method for preparing asbestos fibre stock suspensions is also described.     

Exponential stability in thermoviscoelastic mixtures of solids

In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a one-dimensional mixture of thermoviscoelastic solids. Our main result is to establish the exponential stability of the corresponding semigroup and the lack of exponential stability of the corresponding semigroup.     

Quasi-steady regimes of wave propagation in active mixtures

Regimes of multifront, spinning, marginal, and galloping detonation, quasi-detonation, and supersonic and subsonic (turbulent and laminar) flames are discussed. Criteria for identification of different wave regimes include not only the wave velocity or its deficit, but also the relation between the cell size (or the size of the induction zone) and the characteristic size of equipment. New applications of detonation and combustion are also discussed. This paper is based on an invited presentation at the 21st International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

On the phase transitions in fluid mixtures

Summary The integral equations of balance for a binary fluid mixture are stated when the mixture presents two phases which are separated by an interface. The equilibrium conditions are derived together with the Gibbs phase rule for plane interfaces. The theory is extended to the mixture with three phases.

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Sommario Si scrivono le equazioni integrali del bilancio per una miscela fluida binaria che una interfaccia separa dalla miscela del suo vapore. Si derivano le condizioni di equilibrio e, nel caso di interfaccia piana, la regola delle fasi di Gibbs. La teoria proposta è poi estesa a sistemi di miscela binaria con tre fasi.

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This paper is made under the auspices of G.N.F.M. of the Italian C.N.R.