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.     

Rheological aspects of dense lignite-water suspensions; time dependence, preshear and solids loading effects

An investigation of the rheological properties of dense lignite-water suspensions is reported here in order to evaluate the parameters that affect the rheology of these suspensions. Different types of particle size distributions were achieved via wet grinding with particle sizes down to 1 μm. Polyelectrolytes and surfactants were used to improve the stability and rheology of suspensions. The achieved solid volume fraction, φ, with acceptable rheological behavior was 0.45, while the ratio of φ/φ _m was close to 0.85; φ _m is the maximum solid volume fraction. Various types of flow tests were performed on lignite-water suspensions with various preshear times and stress levels. Typical shear rates varied in the range between 10^–2 to 10² s^–1. The low shear behavior was found to be quite different from the high shear behavior for the most concentrated suspensions, with a plateau value at low shear rates indicating the appearance of a yield stress. These plateau values, however, depend on shear history, which is responsible for the development of different structures in the sample. The viscosity curves corresponding to the ascending and descending parts of the flow curve were found to be different; these flow curve parts can be described either by well established models or by modified ones. The non-Newtonian time dependent behavior of the lignite-water suspensions is attributed to the high value of the ratio φ/φ _m , the polydispersity of the particle size distribution, and the non-spherical shape of the lignite particles.     

An analysis of the effects of the prostatic hypertropy on he urinary flow in lower-urinary-tract

In this paper an analytic model corresponding to the collapsible tube for analysing the urinary flow in lower-urinary-tract is set up from physiologic background.By analysing the model it is found that the self-excited oscillations can both occur in the region of negative and positive slope of P_n-Q_n characteristic. So this paper extends the results of Conrad1’1, Griffiths121, Conrad, Cohen and McQueenI3! and others that the self-excited oscillations can only occur in the region of negative slope of P_n-Q_n characteristic. The effects of prostatic hypertropy on the flow parameters in lower-urinary-tract is discussed in detail by numerical calculations. The results show that it is possible to know the conditions of prostatic hypertropy according to the changes of bladder pressure, outlet urinary velocity and other parameters. From these results a theoretical method to detect and diagnose prostatic hypertropy is provided.     

Experiments on the effect of acceleration on the drag of tapwater bubbles

Three-dimensional (3D) trajectories of spherical air bubbles passing through a converging part of a rectangular channel have been measured. Bubble diameters, d _b, were less than 1 mm and the Reynolds numbers, Re _b, for stagnant tapwater and for mean liquid velocity vˉ _L=0.25 m/s were in about same range. Received: 15 January 2001 / Accepted: 12 June 2001     

A study on characteristics of shock train inside a shock tube

Shock tubes are devices which are used in the investigation of high speed and high temperature flow of compressible gas. Inside a shock tube, the interaction between the reflected shock wave and boundary layer leads to a complex flow phenomenon. Initially a normal shock wave is formed in the shock tube which migrates toward the closed end of the tube and that in turn leads to the reflection of shock. Due to the boundary layer interaction with the reflected shock, the bifurcation of shock wave takes place. The bifurcated shock wave then approaches the contact surface and shock train is generated. Till date only a few studies have been conducted to investigate this shock train phenomenon inside the shock tube. For the present study a computational fluid dynamics(CFD) analysis has been performed on a two dimensional axi-symmetric model of a shock tube using unsteady, compressible Navier–Stokes equations. In order to investigate the detailed characteristics of shock train, parametric studies have been performed by varying different parameters such as the shock tube length, diameter, pressure ratio used inside the shock tube.     

Applying the generalized step-function to solve the bending problems of nonuniform beams with variable cross section

The bending problems of nonuniform beams with variable cross-section can be approximated by that of a step beam under sectionally uniform load (including both concentrated forces and couples). In this paper, the concept of Heaviside function {x-a}⁰ will be generalized, and a new function {x-a}⁰, n=0,1,2…,will be defined, which may be named as a generalized step function. The rules of operation will also be given to {x-a}ⁿ{x-b}⁰. The reciprocal of the flexural of rigidity 1/EJ and the bending moment M(x) can all be expressed in terms of {x-a}ⁿ,and substituted into the differential equation of the elastic curve of the beam respectively. Thus we may establish a set of unified method to solve various types of bending problems of straight beams. The general solution of the deflection equation will be given.     

Nonstationary pandom vibpation analysis of linear elastic structures with finite element method

At present, the finite element method is an efficient method for analyzing structural dynamic problems. When the physical quantities such as displacements and stresses are resolved in the spectra and the dynamic matrices are obtained in spectral resolving form, the relative equations cannot be solved by the vibration mode resolving method as usual. For solving such problems, a general method is put forward in this paper. The excitations considered with respect to nonstationary processes are as follows: P(t)={P_i(t)},P_i(t)=a_i(t)P_i(t), a_i(t) is a time function already known. We make Fourier transformation for the discretized equations obtained by finite element method, and by utilizing the behaviour of orthogonal increment of spectral quantities in random process^[1], some formulas of relations about the spectra of excitation and response are derived. The cross power spectral denisty matrices of responses can be found by these formulas, then the structrual safety analysis can be made. When a_i(t)=l (i= 1,2,…n), the. method stated in this paper will be reduced to that which is used in the special case of stationary process.     

On near-wall hot-wire measurements

A specially constructed hot-wire probe was used to obtain very near-wall velocity measurements in both a fully developed turbulent channel flow and flat plate boundary layer flow. The near-wall hot-wire probe, having been calibrated in a specially constructed laminar flow calibration rig, was used to measure the mean streamwise velocity profile, distributions of streamwise and spanwise intensities of turbulence and turbulence kinetic energy k in the viscous sublayer and beyond; these distributions compare very favorably with available DNS results obtained for channel flow. While low Reynolds number effects were clearly evident for the channel flow, these effects are much less distinct for the boundary layer flow. By assuming the dissipating range of eddy sizes to be statistically isotropic and the validity of Taylor's hypothesis, the dissipation rate ɛ _iso in the very near-wall viscous sublayer region and beyond was determined for both the channel and boundary layer flows. It was found that if the convective velocity U _c in Taylor's hypothesis was assumed to be equal to the mean velocity Uˉ at the point of measurement, the value of (ɛ⁺ _iso)₁ thus obtained agrees well with that of (ɛ ⁺)_DNS for y ⁺ ≥ 80 for channel flow; this suggests the validity of assuming U _c=Uˉ and local isotropy for large values of y ⁺. However, if U _c was assumed to be 10.6u _τ , the value of (ɛ⁺ _iso)₂ thus obtained was found to compare reasonably well with the distribution of (ɛ⁺ _iso)_DNS for y ⁺≤ 15. Received: 31 May 1999/Accepted: 20 December 1999     

MARTEN SOLUTION FOR ONE-DIMENSIONAL UNSTEADY EQUATION

In order to use the second-order5-point difference scheme mentioned to computethe solution of one dimension unsteady equations of the direct reflection of the strongplane detonation wave meeting a solid wall barrier,in this paper,we technicallyconstruct the difference schemes of the boundary and sub-boundary of the problem,and deduce the auto-analogue analytic solutions of the initial value problem,and at thesame time,we present a method for the singular property of the initial value problem,from which we can get a satisfactory computation result of this difficult problem.The difference scheme used in this paper to deal with the discontinuity problemsof the shock wave are valuable and worth generalization.     

Studying the stability of equilibrium solutions in a planar circular restricted four-body problem

The Newtonian circular restricted four-body problem is considered. We obtain nonlinear algebraic equations determining equilibrium solutions in the rotating frame and find six possible equilibrium configurations of the system. Studying the stability of equilibrium solutions, we prove that the radial equilibrium solutions are unstable, while the bisector equilibrium solutions are stable in Lyapunov’s sense if the mass parameter satisfies the conditions μ ∈ (0, μ₀, where μ₀ is a sufficiently small number, and μ ≠ μ_j, j = 1, 2, 3. We also prove that, for μ = μ₁ and μ = μ₃, the resonance conditions of the third order and the fourth order, respectively, are satisfied and, for these values of μ, the bisector equilibrium solutions are unstable and stable in Lyapunov’s sense, respectively. All symbolic and numerical calculations are done with the Mathematica computer algebra system. Published in Neliniini Kolyvannya, Vol. 10, No. 1, pp. 66–82, January–March, 2007.     

Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I

This paper analyzes a coupled thermo-hydro-mechanical behavior of unsaturated soils based on the theory of mixtures. Unsaturated soil is considered as a mixture composed of soil skeleton, liquid water, vapor, dry air, and dissolved air. In addition to the mass and momentum conservation equations of each component and the energy conservation equation of the mixture, the system is closed using other 37 constitutive （or restriction） equations. As the change in water chemical potential is identical to the change in vapor chemical potential, a thermodynamic restriction relationship for the phase transition between pore water and pore vapor is formulated, in which the impact of the change in gas pressure on the phase transition is taken into account. Six final govern- ing equations are given in incremental form in terms of six primary variables, i.e., three displacement components of soil skeleton, water pressure, gas pressure, and temperature. The processes involved in the coupled model include thermal expansions of soil skeleton and soil particle, Soret effect, phase transition between water and vapor, air dissolution in pore water, and deformation of soil skeleton.     

Large conversion of energy in dielectric elastomers by electromechanical phase transition

When air is pumped in, a tubular balloon initially inflates slightly and homogeneously. A short section of the balloon then forms a bulge, which coexists with the unbulged section of the balloon. As more air is pumped in, the bulged section elongates at the expense of the unbulged section, until the entire balloon is bulged. The phenomenon is analogous to the liquid-to-vapor phase transition. Here we study the bulging transition in a dielectric elastomer tube as air is pumped into the balloon and a voltage is applied through the thickness of the membrane. We formulate the condition for coexistent budged and unbulged sections, and identify allowable states set by electrical breakdown and mechanical rupture. We find that the bulging transition dramatically amplifies electromechanical energy conversion. Energy converted in an electromechanical cycle consisting of unbulged and bulged states is thousands of times that in an electrome-chanical cycle consisting of only unbulged states.     

Air flow exploration of abrasive feed tube

An abrasive water-jet cutting process is one in which water pressure is raised to a very high pressure and forced through a very small orifice to form a very thin high speed jet beam. This thin jet beam is then directed through a chamber and then fed into a secondary nozzle, or mixing tube. During this process, a vacuum is generated in the cham- ber, and garnet abrasives and air are pulled into the chamber, through an abrasive feed tube, and mixes with this high speed stream of water. Because of the restrictions introduced by the abrasive feed tube geometry, a vacuum gradient is generated along the tube. Although this phenomenon has been recog- nized and utilized as a way to monitor nozzle condition and abrasive flowing conditions, yet, until now, conditions inside the abrasive feed line have not been completely understood. A possible reason is that conditions inside the abrasive feed line are complicated. Not only compressible flow but also multi- phase, multi-component flow has been involved in inside of abrasive feed tube. This paper explored various aspects of the vacuum creation process in both the mixing chamber and the abrasive feed tube. Based on an experimental exploration, an analytical framework is presented to allow theoretical calculations of vacuum conditions in the abrasive feed tube.     

The criterion of the existence or inexistence of transverse shock wave at wedge supported oblique detonation wave

A simplified theoretic method and numerical simulations were carried out to investigate the characterization of propagation of transverse shock wave at wedge supported oblique detonation wave.After solution validation,a criterion which is associated with the ratio Φ (u 2 /u CJ) of existence or inexistence of the transverse shock wave at the region of the primary triple was deduced systematically by 38 cases.It is observed that for abrupt oblique shock wave (OSW)/oblique detonation wave (ODW) transition,a transverse shock wave is generated at the region of the primary triple when Φ < 1,however,such a transverse shock wave does not take place for the smooth OSW/ODW transition when Φ > 1.The parameter Φ can be expressed as the Mach number behind the ODW front for stable CJ detonation.When 0.9 < Φ < 1.0,the reflected shock wave can pass across the contact discontinuity and interact with transverse waves which are originating from the ODW front.When 0.8 < Φ < 0.9,the reflected shock wave can not pass across the contact discontinuity and only reflects at the contact discontinuity.The condition (0.8 < Φ < 0.9) agrees well with the ratio (D ave /D CJ) in the critical detonation.     

Experimental study on detonation parameters and cellular structures of fuel cloud

In this paper,detonation parameters of fuel cloud,such as propylene oxide(PO),isopropyl nitrate(IPN),hexane,90 # oil and decane were measured in a self-designed and constructed vertical shock tube.Results show that the detonation pressure and velocity of PO increase to a peak value and then decrease smoothly with increasing equivalence ratio.Several nitrate sensitizers were added into PO to make fuel mixtures,and test results indicated that the additives can efficiently enhance detonation velocity and pressure of fuel cloud and one type of additive n-propyl nitrate(NPN) played the best in the improvement.The critical initiation energy that directly initiated detonation of all the test liquid fuel clouds showed a U-shape curve relationship with equivalence ratios.The optimum concentration lies on the rich-fuel side(φ > 1).The critical initiation energy is closely related to molecular structure and volatility of fuels.IPN and PO have similar critical values while that of alkanes are larger.Detonation cell sizes of PO were respectively investigated at 25 C,35 C and 50 C with smoked foil technique.The cell width shows a U-shape curve relationship with equivalence ratios at all temperatures.The minimal cell width also lies on the rich-fuel side(φ > 1).The cell width of PO vapor is slightly larger than that of PO cloud.Therefore,the detonation reaction of PO at normal temperature is controlled by gas phase reaction.     

Oscillatory flow of second grade fluid in cylindrical tube

The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.     

Influence of the pressure drop and the air lock on the solid flux in a cross-flow moving bed

The gas-solid flow pattern in a rectangular cross-flow moving bed is simulated by the multiphase particle-in-cell(MP-PIC)model with the Barracuda software.The computed results are verified by the experimental data.In the bed,the actual solid flux generally equals the solid flow rates in the solid feed and discharge tubes.However,these two flow rates are greatly influenced by the air lock and the pressure drop in the solid feed and discharge tubes,namely,the negative and positive pressure gradients,respectively,rather than the traditional opinion that they are merely controlled by the valve openings.The pressure drops in these tubes are calculated by the proposed“common pressure pool with multiple outlets”(CPPMO)and the“common pressure pool”(CPP)methods.It is found that the local gas resistance dominates the pressure drop in the solid discharge tubes,while the gas frictional resistance determines the pressure drop in the solid feed tube.In addition,when the solid flow rate nearly tends to zero in the solid feed tube,the air lock forms.A solid flux equation is then given by considering both the air lock and the pressure drop factors in the cross-flow moving bed.     

A Physical Model of the Structure and Attenuation of Shock Waves in Metals

In this paper,a physical model of the structure and attenuation of shockwaves in metals is presented.In order to establish the constitutive equa-tions of materials under high velocity deformation and to study the struc-ture of transition zone of shock wave.two independent approaches are in-volved.Firstly,the specific internal energy is decomposed into the elasticcompression energy and elastic deformation energy,and the later is represent-ed by an expansion to third-order terms in elastic strain and entropy.includ-ing the coupling effect of heat and mechanical energy.Secondly,a plasticrelaxation function describing the behaviour of plastic flow under high tem-perature and high pressure is suggested from the viewpoint of dislocationdynamics.In addition.a group of ordinary differential equations has beenbuilt to determine the thermo-mechanical state variables in the transitionzone of a steady shock wave and the thickness of the high pressure shockwave.and an analytical solution of the equations can be foun     

ACOUSTOELASTIC THEORY FOR FLUID-SATURATED POROUS MEDIA

Based on the finite deformation theory of the continuum and poroelastic theory, the aeoustoelastic theory for fluid-saturated porous media （FSPM） in natural and initial coordi- nates is developed to investigate the influence of effective stresses and fluid pore pressure on wave velocities. Firstly, the assumption of a small dynamic motion superimposed on a largely static pre- deformation of the FSPM yields natural, initial, and final configurations, whose displacements, strains, and stresses of the solid-skeleton and the fluid in an FSPM particle could be described in natural and initial coordinates, respectively. Secondly, the subtraction of initial-state equations of equilibrium from the final-state equations of motion and the introduction of non-linear constitu- rive relations of the FSPM lead to equations of motion for the small dynamic motion. Thirdly, the consideration of homogeneous pre-deformation and the plane harmonic form of the small dynamic motion gives an acoustoelastic equation, which provides analytical formulations for the relation of the fast longitudinal wave, the fast shear wave, the slow shear wave, and the slow longitudinal wave with solid-skeleton stresses and fluid pore-pressure. Lastly, an isotropic FSPM under the close-pore jacketed condition, open-pore jacketed condition, traditional unjacketed condition, and triaxial condition is taken as an example to discuss the velocities of the fast and slow shear waves propagating along the direction of one of the initial principal solid-skeleton strains. The detailed discussion shows that the wave velocities of the FSPM are usually influenced by the effective stresses and the fluid pore pressure. The fluid pore-pressure has little effect on the wave velocities of the FSPM only when the components of the applied initial principal solid-skeleton stresses or strains are equal, which is consistent with the previous experimental results.     

Peristaltic transport of rheological fluid: model for movement of food bolus through esophagus

Fluid mechanical peristaltic transport through esophagus is studied in the paper.A mathematical model has been developed to study the peristaltic transport of a rheological fluid for arbitrary wave shapes and tube lengths.The Ostwald-de Waele power law of a viscous fluid is considered here to depict the non-Newtonian behaviour of the fluid.The model is formulated and analyzed specifically to explore some important information concerning the movement of food bolus through esophagus.The analysis is carried out by using the lubrication theory.The study is particularly suitable for the cases where the Reynolds number is small.The esophagus is treated as a circular tube through which the transport of food bolus takes place by periodic contraction of the esophageal wall.Variation of different variables concerned with the transport phenomena such as pressure,flow velocities,particle trajectory,and reflux is investigated for a single wave as well as a train of periodic peristaltic waves.The locally variable pressure is seen to be highly sensitive to the flow index "n".The study clearly shows that continuous fluid transport for Newtonian/rheological fluids by wave train propagation is more effective than widely spaced single wave propagation in the case of peristaltic movement of food bolus in the esophagus.