Superimposed steady and oscillatory shear in dispersed systems

Rheologica Acta - A viscometer has been designed to measure the behaviour of dispersed systems in oscillatory shear. The apparatus permits determination of the dynamic properties within the linear...     

Dynamic viscosity of various samples of polypropene and polyvinylchloride

Summary Complex dynamic viscosity experiments carried out on a balance rheometer CONTRAVES (Dr. Képès' system) for the polypropene samples and on a RHEOMETRICS viscometer apparatus for the polyvinylchloride formulations have allowed to determine the rheological behaviour of these materials. In the case of polypropene, the Maxwell-Wiechert model seems to be in good agreement with the rheological behaviour of this material. For the polyvinylchloride, a dynamic power-law has been proposed. This law correlates the complex dynamic viscosity modulus | ^*| with the pulsation of the frequency. It shows a certain analogy with that determined in the static mode.With 7 figures and 8 tables     

Spatial direct numerical simulation of boundary-layer transition mechanisms: Validation of PSE theory

A study of instabilities in incompressible boundary-layer flow on a flat plate is conducted by spatial direct numerical simulation (DNS) of the Navier-Stokes equations. Here, the DNS results are used to evaluate critically the results obtained using parabolized stability equations (PSE) theory and to study mechanisms associated with breakdown from laminar to turbulent flow. Three test cases are considered: two-dimensional Tollmien-Schlichting wave propagation, subharmonic instability breakdown, and oblique-wave breakdown. The instability modes predicted by PSE theory are in good quantitative agreement with the DNS results, except a small discrepancy is evident in the mean-flow distortion component of the two-dimensional test problem. This discrepancy is attributed to far-field boundary-condition differences. Both DNS and PSE theory results show several modal discrepancies when compared with the experiments of subharmonic breakdown. Computations that allow for a small adverse pressure gradient in the basic flow and a variation of the disturbance frequency result in better agreement with the experiments.     

Influence of molecular weight on some rheological properties of plasticized polyvinylchloride

Conclusions From an overall analysis of the above results it appears that the rheological properties of plasticized PVC are governed, below about 200 °C, not only by the usual parameters (composition, temperature, molecular weight) but also by the crystallinity of the polymer. Recent estimations of the crystallinity degree in commercial PVC samples vary from 3% (45) to about 10% (46), the actual value depending on the thermal history of the sample.Apparently even small values of the crystallinity degree can affect rather strongly the rheological behaviour of plasticized PVC in the rubbery and flow regions.For the fractions here investigated, the fractional precipitation procedure used to carry out the separation (1) leads probably to a fractionation based not only on molecular weight but also on stereoregularity (47), the result being that the fractions precipitated firstly are more polydisperse and more crystallizable. In dilute solution, they give easily aggregates (1), stable up to relatively high temperatures (2).The dynamic-mechanical data discussed above (fig. 1) as well as the anomalies presented by the rheological results (fig. 7 to 12) can be therefore explained on the basis of a model in which supermolecular structures linked together by crystalline bonds are present in the samples.The marked dependence of PVC mechanical properties on the annealing temperature described recently byAndrews andKazama (48) seems to give considerable support to such a model.Presented at the Jahrestagung der Deutschen Rheologen, Berlin-Dahlem, 20.–22. Mai 1968.The authors are indebted to Mr.Sangiovanni and Mr.Zinelli for most of the experimental results.     

Linear Instability Analysis of a Suspension of Oxytactic Bacteria in Superimposed Fluid and Porous Layers

The purpose of this paper is to perform a pioneering investigation of the stability of bioconvection of oxytactic bacteria in superimposed fluid and porous layers. A dilute suspension of oxytactic bacteria in a shallow system that consists of superimposed fluid and porous layers is considered. A linear instability analysis of this problem is performed and the Galerkin method is utilized to solve the eigenvalue problem. The analysis leads to an equation for the critical Rayleigh number.*Author for correspondence: Tel.: +1-919-515-5292; Fax: +1-919-515-7968; e-mail: avkuznet@eos.ncsu.edu     

Creep transition in torsion

Stresses for a circular cylinder of compressible material subjected to torsion are derived in closed form for steady state creep. It is shown that the asymptotic solution through stress leads from elastic state to plastic and then to creep and through stress difference leads to the creep state. The effect of compressibility is presented graphically. The results indicate that the value of maximum shear stress for a cylinder of compressible material is greater than that for an incompressible material and increases with the increase in a measure index n. For an incompressible material, as a particular case, the results obtained are the same as given by Marin [9].     

The Onset of Convection in a Suspension of Gyrotactic Microorganisms in Superimposed Fluid and Porous Layers: Effect of Vertical Throughflow

The purpose of this paper is to investigate the effect of vertical throughflow on the onset of bioconvection in a suspension of gyrotactic microorganisms. A dilute suspension of gyrotactic microorganisms in a shallow system that consists of superimposed fluid and porous layers is considered. A linear instability analysis of this problem is performed and the Galerkin method is utilized to solve the eigenvalue problem. The analysis leads to an equation for the critical Rayleigh number. It is shown that the vertical throughflow stabilizes the system.     

Localized transition waves in bistable-bond lattices

Discrete two-dimensional square- and triangular-cell lattices consisting of point particles connected by bistable bonds are considered. The bonds follow a trimeric piecewise linear force-elongation diagram. Initially, Hooke's law is valid as the first branch of the diagram; then, when the elongation reaches the critical value, the tensile force drops to the other. The latter branch can be parallel with the former (mathematically this case is simpler) or have a different inclination. For a prestressed lattice the dynamic transition is found analytically as a wave localized between two neighboring lines of the lattice particles. The transition wave itself and dissipation waves carrying energy away from the transition front are described. The conditions are determined which allow the transition wave to exist. The transition wave speed as a function of the prestress is found. It is also found that, for the case of the transition leading to an increased tangent modulus of the bond, there exists nondivergent tail waves exponentially localized in a vicinity of the transition line behind the transition front. The previously obtained solutions for crack dynamics in lattices appear now as a partial case corresponding to the second branch having zero resistance. At the same time, the lattice-with-a-moving-crack fundamental solutions are essentially used here in obtaining those for the localized transition waves in the bistable-bond lattices. Steady-state dynamic regimes in infinite elastic and viscoelastic lattices are studied analytically, while numerical simulations are used for the related transient regimes in the square-cell lattice. The numerical simulations confirm the existence of the single-line transition waves and reveal multiple-line waves. The analytical results are compared to the ones obtained for a continuous elastic model and for a related version of one-dimensional Frenkel-Kontorova model.     

Swirling flows in circular-to-rectangular transition ducts

Miniature axisymmetric supersonic nozzles were produced with exit Mach numbers ranging from 1.0 to 2.8 by forming Pyrex^® capillary tubing of 0.6 and 1.2 mm inside diameter into converging-diverging channels. The nozzle contours were measured and were found to compare favorably to ideal solutions given by the axisymmetric method of characteristics. In addition, the surfaces of these nozzles were quite smooth, providing featureless flows at perfect expansion. Schlieren visualization and pitot pressure measurements of the resulting microjets were compared to the literature available for jets produced by larger-scale nozzles. A postponed transition to turbulence is noted in these microjets due to their low Reynolds number. The pitot pressure on centerline is nearly uniform at perfect expansion over core lengths up to 12 nozzle exit diameters. Supersonic microjet nozzles thus provide a more effective small-scale high-pressure gas delivery device than do sonic nozzles of comparable scale at equivalent mass flow rates. Supersonic microjets may therefore have several industrial applications.List of symbols ^* boundary layer displacement thickness, mm - d diameter of nozzle exit, mm - L length of nozzle diverging section, mm - L _c inviscid core length, mm - L _s supersonic region length, mm - M _c convective Mach number - M _e exit Mach number - P _b backpressure at nozzle exit, (equal to ambient pressure in this experiment) - P _e exit pressure of the supersonic jet - P _be exit pressure ratio (P _b /P _e ) - P _p impingement pressure (pitot pressure) - P ₀ stagnation pressure supplied to nozzle - P _n overall pressure ratio (P ₀/P _b ,) - r radial dimension (cylindrical coordinate system), mm - r ₀ radius of throat, mm - Re _d Reynolds number, based on nozzle exit diameter - V _e exit velocity, m/s - x axial dimension (cylindrical coordinate system), mm This research was sponsored by National Science Foundation Grant DMI 9400119, as part of a study of the assist-gas dynamics of laser cutting.     

Locating order-chaos-order transition in elastic pendulum

An undamped elastic pendulum being a nonintegrable Hamiltonian system always has some chaotic trajectories observable on choosing appropriate initial conditions. This is true even if the pendulum is in libration with small amplitude; in this situation, the pendulum may be seen as a nearly integrable system. Since the measure of the set of the local chaotic trajectories in the phase space may be very small, the trajectories are hard to locate. However, the emergence of widespread chaos when the elastic pendulum is at autoparametric resonance is well-documented. The transition from the local and the widespread chaos is typically established through the Chirikov overlap criterion that approximates the phase portrait around a resonance using a one degree-of-freedom pendulum Hamiltonian. We argue in this paper that the aforementioned transition in the elastic pendulum is due to interaction between two resonances of same kind and their coexistence can be analytically located using perturbation methods, like the method of averaging, whereas the technique of the pendulum Hamiltonian is inapplicable. Furthermore, in the course of validating the result numerically, we also showcase the order-chaos-order transition in the elastic pendulum using the fast Lyapunov indicator.

     

Flow transition in dual bell nozzles

The dual bell nozzle is a concept of altitude adaptive nozzles. The flow adapts to the altitude by separation at the wall inflection at low altitude, and full flowing at high altitude. To understand the phenomenology of the flow by the transition from sea-level mode to high altitude mode, a series of tests have been made at the cold flow test bench P6.2 at DLR Lampoldshausen. A dual bell nozzle have been successively shorten and driven in the same conditions for each length. Hence it was possible to observe the flow in the vicinity of the wall inflection using Schlieren optics. Furthermore this study yields the influence of the length ratio between basis and extension on the transition conditions.

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Bubbles in liquids with phase transition

In the forthcoming second part of this paper a system of balance laws for a multi-phase mixture with many dispersed bubbles in liquid is derived where phase transition is taken into account. The exchange terms for mass, momentum and energy explicitly depend on evolution laws for total mass, radius and temperature of single bubbles. Therefore in the current paper we consider a single bubble of vapor and inert gas surrounded by the corresponding liquid phase. The creation of bubbles, e.g. by nucleation is not taken into account. We study the behavior of this bubble due to condensation and evaporation at the interface. The aim is to find evolution laws for total mass, radius and temperature of the bubble, which should be as simple as possible but consider all relevant physical effects. Special attention is given to the effects of surface tension and heat production on the bubble dynamics as well as the propagation of acoustic elastic waves by including slight compressibility of the liquid phase. Separately we study the influence of the three phenomena heat conduction, elastic waves and phase transition on the evolution of the bubble. We find ordinary differential equations that describe the bubble dynamics. It turns out that the elastic waves in the liquid are of greatest importance to the dynamics of the bubble radius. The phase transition has a strong influence on the evolution of the temperature, in particular at the interface. Furthermore the phase transition leads to a drastic change of the water content in the bubble. It is shown that a rebounding bubble is only possible, if it contains in addition an inert gas. In Part 2 of the current paper the equations derived are sought in order to close the system of equations for multi-phase mixture balance laws for dispersed bubbles in liquids involving phase change.     

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.     

Predicting crossflow induced transition with laminar kinetic energy transition model

The hypersonic laminar kinetic energy transition model is developed to be appropriate for crossflow induced boundary layer transition prediction. A crossflow timescale is constructed and incorporated in the k_T-k_L-ω transition model to reflect crossflow effect during three-dimensional boundary layer transition. The stream-wise vorticity is selected as the indicator of crossflow strength. Regarding the inviscid unstable characteristic of crossflow instability, the crossflow timescale is constructed by reference to the second mode timescale. To eliminate inappropriate development of the crossflow timescale where the effective length scale is large enough while the crossflow strength remains at a quite low level, a crossflow velocity limit function is proposed. The revised k_T-k_L-ω transition model has been applied to HIFiRE-5 and blunt cone with 1°angle of attack test cases. Results show good correspondence with the experimental data and DNS data, which demonstrates that the constructed crossflow timescale makes the revised transition model capable of reproducing crossflow induced transition behavior with a reasonable degree of accuracy.     

Energy dissipation mechanisms in ductile fracture

The objective is to investigate energy dissipation mechanisms that operate at different length scales during fracture in ductile materials. A dimensional analysis is performed to identify the sets of dimensionless parameters which contribute to energy dissipation via dislocation-mediated plastic deformation at a crack tip. However, rather than using phenomenological variables such as yield stress and hardening modulus in the analysis, physical variables such as dislocation density, Burgers vector and Peierls stress are used. It is then shown via elementary arguments that the resulting dimensionless parameters can be interpreted in terms of competitions between various energy dissipation mechanisms at different length scales from the crack tip; the energy dissipations mechanisms are cleavage, crack tip dislocation nucleation and also dislocation nucleation from a Frank-Read source. Therefore, the material behavior is classified into three groups. The first two groups are the well-known intrinsic brittle and intrinsic ductile behavior. The third group is designated to be extrinsic ductile behavior for which Frank-Read dislocation nucleation is the initial energy dissipation mechanism. It is shown that a material is predicted to exhibit extrinsic ductility if the dimensionless parameter bρ_disl^1/2 (b is Burgers vector, ρ_disl is dislocation density) is within a certain range defined by other dimensionless parameters, irrespective of the competition between cleavage and crack tip dislocation nucleation. The predictions compare favorably to the documented behavior of a number of different classes of materials.     

Forerunning mode transition in a continuous waveguide

We have discovered a forerunning mode transition as the periodic wave changing the state of a uniform continuous waveguide. The latter is represented by an elastic beam initially rested on an elastic foundation. Under the action of an incident sinusoidal wave, the separation from the foundation occurs propagating in the form of a transition wave. The critical displacement is the separation criterion. Under these conditions, the steady-state mode exists with the transition wave speed independent of the incident wave amplitude. We show that such a regime exists only in a bounded domain of the incident wave parameters. Outside this domain, for higher amplitudes, the steady-state mode is replaced by a set of local separation segments periodically emerging at a distance ahead of the main transition point. The crucial feature of this waveguide is that the incident wave group speed is greater than the phase speed. This allows the incident wave to deliver the energy required for the separation. The analytical solution allows us to show in detail how the steady-state mode transforms into the forerunning one. The latter studied numerically turns out to be periodic. As the incident wave amplitude grows the period decreases, while the transition wave speed averaged over the period increases to the group velocity of the wave. As an important part of the analysis, the complete set of solutions is presented for the waves excited by the oscillating or/and moving force acting on the free beam. In particular, an asymptotic solution is evaluated for the resonant wave corresponding to a certain relation between the load's speed and frequency.     

超燃冲压发动机燃烧模态转换试验研究

在模拟飞行高度为25 km、来流马赫数为6的情况下,采用试验研究的方法对超燃冲压发动机燃烧模态转换进行了直连式试验。根据燃烧室壁面压力分布和一维模型分析表明,燃料喷射位置和当量比的动态改变,实现了燃烧室内燃烧模态的动态转换。不同燃料喷射位置切换顺序比较表明,燃烧室内燃烧状态的改变受燃料分布所决定,但是燃烧室自身具有一定的抗波动能力。     

Creep transition in bending of rectangular plates

Transitional stresses of a rectangular plate bent into the form of a circular cylinder have been derived in closed form. The effect of compressibility is presented graphically. The result indicate that for n (measure index)>1, the circumferential stress is maximum at the inner surface for an incompressible material and not for the compressible material, while for $\text{n=}\text{1}\text{N}$,(N ? 1), it is found to be maximum at some inner point and not at the inner surface. The neutral surface alters with compressibility of the material and n.