Elemental mechanisms of hydrodynamic instabilities

The elemental mechanisms for many hydrodynamic instabilities can be identified as negative damping, negative diffusion or ellipticity. Identifications of some well-known hydrodynamic instabilities are made. Model equations in connection with the instability associated with ellipticity should be studied more extensively.     

On tensile instabilities and ellipticity loss in fiber-reinforced incompressible non-linearly elastic solids

Loss of ellipticity and associated failure in fiber-reinforced non-linearly elastic solids is examined for uniaxial plane deformations. We consider separately fiber reinforcement that either endows the material with additional stiffness only in the fiber direction or introduces additional stiffness under shear deformations. In the first case it is shown that loss of ellipticity under tensile loading in the fiber direction corresponds to a turning point of the nominal stress and requires concavity of the Cauchy stress–stretch curve. For the second example loss of ellipticity occurs after the nominal stress maximum and prior to a turning point of the Cauchy stress.     

Three-dimensional numerical simulation of thermocapillary instabilities in floating zones

Instability of thermocapillary convection in liquid bridges of low Prandtl number fluids is investigated by direct three-dimensional and time-dependent simulation of the problem. The field equations are numerically solved explicit in time and with finite difference methods in a staggered cylindrical grid. The numerical results are analyzed and interpreted in the general context of the bifurcation's theory. According to recent stability analyses the computations show that for semiconductor melts the first bifurcation is characterized by the loss of spatial symmetry rather than by the onset of oscillatory flow. When the basic axisymmetric flow field becomes unstable, after a short transient, a three-dimensional supercritical steady state is obtained. It is shown that the flow field organization, depending on the critical wave number, is related to the geometrical aspect ratio of the liquid bridge and that lower is the aspect ratio, higher is the critical wave number and more complex the thermofluid-dynamic field structure.     

Moving inelastic discontinuities and applications to martensitic phase transition

Summary In this work, equations of the kinetics and kinematics are developed for heterogeneous materials containing inelastic discontinuities with moving boundaries. From the derived free energy and the power of external forces one obtains the driving force acting on the moving boundary. Introducing the interface operators and some hypothesis on inelastic fields, one gets the driving force for the formation of an ellipsoidal domain. The theoretical model is illustrated by the derivation of nucleation and growth conditions of a martensitic plate inside an inhomogeneous plastic strain field. The obtained results are combined with a study of the kinetics and kinematics to derive the constitutive equation of an austenitic single crystal, from which the overall behavior of polycrystalline TRIP steels is deduced using the self-consistent scale-transition method. Comparison with experimental data shows a good agreement. Received 7 May 1999; accepted for publication 14 June 1999     

Spatial chaos in boundary layer transition

Experiments have been performed on a laminar flat plate boundary layer undergoing transition to turbulence. Reproducible disturbances were introduced via a loudspeaker embedded at some upstream location and their evolution over the plate measured using hot-wire anemometry. A new technique has been used to estimate the number of nonlinearly independent modes in the reconstructed phase portraits. Nonlinear maps were then fitted that explicitly model the spatial evolution of disturbances. These maps are consistent with classical linear stability theory for small disturbances, and give rise to Smale horse-shoe like behaviour for larger amplitude distrubances. Thus a mechanism for generating chaos has been uncovered.     

The transition of flow-induced cylinder vibrations to chaos

Flow-induced oscillations of rigid cylinders exposed to fully developed turbulent flow can be described by a fourth order autonomous system. Among the pertinent constants, the mass ratio is the control parameter governing the transition from limit cycle oscillations to chaotic vibrations. Particular attention is paid to the stability of the limit cycles: it has been found that they lose their stability at the point of appearance of quasi-periodic motion. The documentation of this transition is performed in terms of Lyapunov exponents, phase plots, Fourier spectra, bifurcation diagrams, and Poincaré maps. As opposed to the calculation of the Lyapunov exponents where remarkable numerical difficulties were encountered, the investigation of the remaining quantities shows clearly the passage of cylinder motions from limit cycle oscillations to more and more irregular vibrations, leading finally to chaos.     

The effect of internal surface modification on flow instabilities in forced convection boiling in a horizontal tube

This paper presents the experimental result of a study on the effects of heat transfer enhancement on two-phase flow instabilities in a horizontal in-tube flow boiling system. Five different heat transfer surface configurations and five different inlet temperatures are used to observe the effect of heat transfer enhancement and inlet subcooling. All experiments are carried out at constant heat input, system pressure and exit restriction. Dynamic instabilities, namely pressure-drop type, density-wave type and thermal oscillations are found to occur for all the investigated temperatures and enhancement configurations, and the boundaries for the appearance of these oscillations are found. The effect of the enhancement configurations on the characteristics of the boiling flow dynamic instabilities is studied in detail. The comparison between the bare tube and the enhanced tube configurations are made on the basis of boiling flow instabilities. Differences among the enhanced configurations are also determined to observe which of them is the most stable and unstable one. The amplitudes and periods of pressure-drop type oscillations and density-wave type oscillations for tubes with enhanced surfaces are found to be higher than those of the bare tube. The bare tube is found to be the most stable configuration, while tube with internal springs having bigger pitch is found to be the most unstable one among the tested tubes. It is found that system stability increases with decreasing equivalent diameter for the same type heater tube configurations; however, on the basis of effective diameter there is no single result such as stability increase/decrease with increasing/decreasing effective diameter.     

A simple phase transition relaxation solver for liquid–vapor flows

Determining liquid–vapor phase equilibrium is often required in multiphase flow computations. Existing equilibrium solvers are either accurate but computationally expensive or cheap but inaccurate. The present paper aims at building a fast and accurate specific phase equilibrium solver, specifically devoted to unsteady multiphase flow computations. Moreover, the solver is efficient at phase diagram bounds, where non‐equilibrium pure liquid and pure gas are present. It is systematically validated against solutions based on an accurate (but expensive) solver. Its capability to deal with cavitating, evaporating, and condensing two‐phase flows is highlighted on severe test problems both 1D and 2D. Copyright © 2016 John Wiley & Sons, Ltd.     

Combined stress waves with phase transition in thin-walled tubes简

The incremental constitutive relation and governing equations with combined stresses for phase transition wave propagation in a thin-walled tube are established based on the phase transition criterion considering both the hydrostatic pressure and the deviatoric stress. It is found that the centers of the initial and subsequent phase transition ellipses are shifted along the σ-axis in the στ-plane due to the tension-compression asymmetry induced by the hydrostatic pressure. The wave solution offers the "fast" and "slow" phase transition waves under combined longitudinal and torsional stresses in the phase transition region. The results show some new stress paths and wave structures in a thin-walled tube with phase transition, differing from those of conventional elastic-plastic materials.     

Flow-induced mixing,demixing, and phase transitions in polymeric fluids

In polymer solutions or blends, flow can strongly influence the degree of mixing of the components. In a shearing flow, droplets in a dispersion can be broken down to sizes comparable to the dimensions of the polymer molecules themselves, thereby inducing molecular-scale mixing. Demixing can also occur when the two components of the mixture differ greatly in viscoelastic properties. Shear or extensional flow can induce polymer migration in nonhomogeneous flows or in flows with curved streamlines, and can render turbid solutions or blends that are otherwise transparent. Flow can also induce polymer gelation, and can induce ordering transitions in liquid crystals or block copolymers. Here, we review these phenomena, discuss proposed mechanisms, and assess the degree to which recent theories can account for the observations. Because the phenomena are complex, multiple experimental probes and theoretical methods are required to study them. Successful theories must incorporate polymer/polymer or polymer/solvent thermodynamics, critical phenomena, and phase transitions, as well as polymer theology and the kinetics of diffusion or crystallization. The experimental techniques used to study these phenomena are equally wide ranging, and include turbidity measurements, light, x-ray, and neutron scattering, fluorescence quenching, microscopy, and theology.     

Combustion with phase transition

The paper deals with a mathematical problem describing an exothermic chemical reaction in a diffusing substance possibly undergoing a change of phase. Global well-posedness in the classical sense is proved for the corresponding system of PDEs. Moreover, cases in which the phases are separated by sharp interphases or by transition regions are discussed. The limit case of negligible diffusion is also considered.

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Sommario Si studia il problema matematico che descrive una reazione chimica esotermica in una sostanza che diffonde e puo' subire cambiamenti di fase. Si dimostra esistenza globale in senso classico del relativo sistema di equazioni alle derivate parziali e si discute la possibilita' che le fasi siano separate da una regione di transizione e non da una netta superficie di interfase. Il caso limite di assenza di diffusione e' anche brevemente esaminato.

     

Convective and absolute instabilities in counter-rotating spiral Poiseuille flow

We present results of an experimental study on the stability of Taylor–Couette flow in case of counter-rotating cylinders and an imposed axial through flow. We are able to confirm results form recent numerical investigations done by Pinter et al. [24] by measuring the absolute and convective stability boundaries of both propagating Taylor vortices (PTV) and spiral vortices (SPI). Thus our work shows that these theoretical concepts from hydrodynamic stability in open flows apply to experimental counter-rotating Taylor–Couette systems with an imposed axial through flow. PACS 47.20.-k, 05.45.-a, 47.15.fe     

Simulation of bacterial flagellar phase transition by non-convex and non-local continuum modeling

Bacterial flagellar filament can undergo a stress-induced polymorphic phase transition in both vitro and vivo environments. The filament has 12 different helical forms (phases) characterized by different pitch lengths and helix radii. When subjected to the frictional force of flowing fluid, the filament changes between a left-handed normal phase and a right-handed semi-coiled phase via phase nucleation and growth. This paper develops non-local finite element method (FEM) to simulate the phase transition under a displacement-controlled loading condition (controlled helix-twist). The FEM formulation is based on the Ginzburg-Landau theory using a one-dimensional non-convex and non-local continuum model. To describe the processes of the phase nucleation and growth, viscosity-type kinetics is also used. The non-local FEM simulation captures the main features of the phase transition: two-phase coexistence with an interface of finite thickness, phase nucleation and phase growth with interface propagation. The non-local FEM model provides a tool to study the effects of the interfacial energy/thickness and loading conditions on the phase transition.     

Shock-induced phase transformation and vortex instabilities in shock loaded titanium alloys

Spall-tests of four kinds of high-strength titanium alloys (VT-6, VT-14, VT-20 and VT-23) have been performed by using a two-channel velocity interferometer for recording free surface velocity profiles and a SEM-technique for microstructure investigations of post-shocked specimens. Screw rotational structures in the spall zone are thought to be responsible for the more effective shock-wave energy scattering during spallation. Free surface velocity profiles display forward and reverse phase transitions in the all alloys under investigation. The threshold stress for the forward and reverse phase transitions turns out to be practically independent of the chemical and phase compositions of specimens, and monotonously increases with strain rate. Received 7 February 1999 / Accepted 3 November 1999     

On problems in the weakly nonlinear theory of hydrodynamic stability and its improvement

There are three main problems in the weakly nonlinear theory of hydrodynamic stability: (1)The radius of convergence with respect to the perturbation parameter is too small and there is no concrete estimation for it. (2)The solution has a special structure, thus in general, it can not satisfy the initial condition posed by many practical problems. (3)When the linear part of its solution does not correspond to a neutral case, there are more than one way in determining the Landau constants, and practically no one knows which is the best way. In this paper, problems(1) and (2)are solved theoretically, and ways for its improvement have been proposed. By comparing the theoretical results with those obtained by numerical simulations, problem(3)has also been clarified. Project supported by the National Natural Science Foundation of China     

Thermomechanics of shells undergoing phase transition

The resultant, two-dimensional thermomechanics of shells undergoing diffusionless, displacive phase transitions of martensitic type of the shell material is developed. In particular, we extend the resultant surface entropy inequality by introducing two temperature fields on the shell base surface: the referential mean temperature and its deviation, with corresponding dual fields: the referential entropy and its deviation. Additionally, several extra surface fields related to the deviation fields are introduced to assure that the resultant surface entropy inequality be direct implication of the entropy inequality of continuum thermomechanics. The corresponding constitutive equations for thermoelastic and thermoviscoelastic shells of differential type are worked out. Within this formulation of shell thermomechanics, we also derive the thermodynamic continuity condition along the curvilinear phase interface and propose the kinetic equation allowing one to determine position and quasistatic motion of the interface relative to the base surface. The theoretical model is illustrated by two axisymmetric numerical examples of stretching and bending of the circular plate undergoing phase transition within the range of small deformations.     

Experimental and numerical investigations on flashing-induced instabilities in a single channel

During the start-up phase, natural circulation BWRs (NC-BWRs) need to be operated at low pressure conditions. Such conditions favor flashing-induced instabilities due to the large hydrostatic pressure drop induced by the tall chimney. Moreover, in novel NC-BWR designs the steam separation is performed in the steam separators which create large pressure drops at the chimney outlet, which effect on stability has not been investigated yet.In this work, flashing-induced oscillations occurring in a tall, bottom heated channel are numerically investigated by using a simple linear model with three regions and an accurate implementation for estimating the water properties. The model is used to investigate flashing-induced instabilities in a channel for different values of the core inlet friction value. The results are compared with experiments obtained by using the CIRCUS facility at the same conditions, showing a good agreement. In addition, the experiments on flashing-induced instabilities are presented in a novel manner allowing visualizing new details of the phenomenon numerical stability investigations on the effect of the friction distribution are also done. It is found that by increasing the total restriction in the channel the system is destabilized. In addition, the chimney outlet restriction has a stronger destabilizing effect than the core inlet restriction. A stable two-phase region is observed prior to the instabilities in the experiments and the numerical simulations which may help to pressurize the vessel of NC-BWRs and thus reducing the effects of flashing instabilities during start-up.     

Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels

This paper uses the thermodynamic data of aqueous solutions of uncrosslinked poly(N-isopropylacrylamide) (PNIPAM) to study the phase transition of PNIPAM hydrogels. At a low temperature, uncrosslinked PNIPAM can be dissolved in water and form a homogenous liquid solution. When the temperature is increased, the solution separates into two liquid phases with different concentrations of the polymer. Covalently crosslinked PNIPAM, however, does not dissolve in water, but can imbibe water and form a hydrogel. When the temperature is changed, the hydrogel undergoes a phase transition: the amount of water in the hydrogel in equilibrium changes with temperature discontinuously. While the aqueous solution is a liquid and cannot sustain any nonhydrostatic stress in equilibrium, the hydrogel is a solid and can sustain nonhydrostatic stress in equilibrium. The nonhydrostatic stress can markedly affect various aspects of the phase transition in the hydrogel. We adopt the Flory-Rehner model, and show that the interaction parameter as a function of temperature and concentration obtained from the PNIPAM-water solution can be used to analyze diverse phenomena associated with the phase transition of the PNIPAM hydrogel. We analyze free swelling, uniaxially and biaxially constrained swelling of a hydrogel, swelling of a core-shell structure, and coexistent phases in a rod. The analysis is related to available experimental observations. Also outlined is a general theory of coexistent phases undergoing inhomogeneous deformation.     

On the energy equation for a spatially developing instability wave in the theory of hydrodynamic stability

In this article, it is shown that the energy equation for a spatially developing disturbance used in all the literatures dealing with the problem of hydrodynamic stability suffers from a small, but crucial error.     

On the theory of stability of a cylindrical hydrodynamic suspension

The stability of a cylindrical hydrodynamic suspension is investigated with complete account for the dependence of the fluid velocity distribution profile on the radial coordinate in the supporting layer without an a priori representation of the inertial terms in the fluid layer in terms of the velocity averaged over the clearance cross-section. It is shown that the central position of a light inner body in the cylindrical hydrodynamic suspension is asymptotically stable. The suspension remains asymptotically stable for a fairly long time as the light inner body is displaced from the central position along the dynamic equilibrium curve. The central position of a heavy inner body is unstable; however, as it is displaced from the central position under the action of a constant external decentering force a stability domain develops.