Peristaltic flow of a Jeffrey‐six constant fluid in a uniform inclined tube

In this work, we studied the peristaltic flow of a Jeffrey‐six constant fluid in a uniform tube. The governing equations of the Jeffrey‐six constant fluid were simplified by using the assumptions of long wave length and low Reynolds number approximation. The simplified form of equations were solved using the perturbation, homotopy analysis and finite difference methods. The comparison of the three solutions are shown graphically. The variation of pressure rise and frictional forces with the different parameters were also examined numerically. Results are presented at the end of the article. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of PIV to velocity measurements in a liquid film flowing down an inclined cylinder

PIV technique is applied for measurements of instant velocity distributions in a liquid film flowing down an inclined tube in the form of a wavy rivulet. An application of special optical calibration is applied to correct distortion effects caused by the curvature of the interface. A vortex flow of liquid is observed inside a wave hump in the reference system moving with wave phase velocity. Conditionally averaged profiles of longitudinal and transverse components of liquid velocity are obtained for different cross-sections of developed non-linear waves. It is shown that the increase in wave amplitude slightly changes the location of the vortex center. The analysis of modification of vortex motion character due to wavy flow conditions, such as tube inclination angle, film Reynolds number, wave excitation frequency, is fulfilled.     

Shape of a shock wave front diffracting on a perforated wall

 The shape of a shock wave front diffracting on a perforated wall is determined by comparing numerical data and experimental findings. Experiments were conducted in a 60 mm×150 mm cross sectional area shock tube equipped with a double-exposure holographic interferometer. The numerical simulation was conducted using a TVD upwind finite difference scheme. First, a discharge coefficient for the mass flow through the perforations was determined by comparing the numerical results with those obtained using a simplified quasi-one-dimensional analysis. This value agreed well with the experimentally obtained value. Finally, the shape of a backward inclined incident shock wave over a perforated wall was successfully determined by employing this discharge coefficient and the numerical result. Received: 17 March 1995/Accepted: 13 August 1997     

Combined effects of heat and chemical reactions on the peristaltic flow of carreau fluid model in a diverging tube

The study of peristaltic flow of a Carreau fluid in a non‐uniform tube under the consideration of long wavelength in the presence of heat and mass transfer is presented. The flow is investigated in a wave frame of reference moving with velocity of the wave c. Two types of analytical solutions have been evaluated (i) perturbation method (ii) homotopy analysis method for velocity, temperature and concentration field. Numerical integration have been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated for five different peristaltic waves. Copyright © 2010 John Wiley & Sons, Ltd.     

Peristaltic flow of a Johnson-Segalman fluid through a deformable tube

To understand theoretically the flow properties of physiological fluids we have considered as a model the peristaltic motion of a Johnson–Segalman fluid in a tube with a sinusoidal wave traveling down its wall. The perturbation solution for the stream function is obtained for large wavelength and small Weissenberg number. The expressions for the axial velocity, pressure gradient, and pressure rise per wavelength are also constructed. The general solution of the governing nonlinear partial differential equation is given using a transformation method. The numerical solution is also obtained and is compared with the perturbation solution. Numerical results are demonstrated for various values of the physical parameters of interest.      

Experimental and numerical investigation of inclined air/SF6 interface instability under shock wave

The shock tube experiments of inclined air/SF6 interface instability under the shock wave with the Mach numbers 1.23 and 1.41 are conducted. The numerical simulation is done with the parallel algorithm and the multi-viscous-fluid and turbulence (MVFT) code of the large-eddy simulation (LES). The developing process of the interface accelerated by the shock wave is reproduced by the simulations. The complex wave structures, e.g., the propagation, refraction, and reflection of the shock wave, are clearly revealed in the flows. The simulated evolving images of the interface are consistent with the experimental ones. The simulated width of the turbulent mixing zone (TMZ) and the displacements of the bubble and the spike also agree well with the experimental data. Also, the reliability and effectiveness of the MVFT in simulating the problem of interface instability are validated. The more energies are injected into the TMZ when the shock wave has a larger Mach number. Therefore, the perturbed interface develops faster.     

Interaction of a gasdynamic shock with small disturbances

The stability of shock wave based on the definition of Landau and Lifschitz^[1] is treated in this paper. This is tantamount to solving the problem of interaction of small disturbances with a shock wave. Small disturbances are introduced on both sides of a steady, non-dissipative, plane shock wave. Landau et al.^[1] obtained the stability criterionM ₁>1,M ₂<1 for small disturbances which are travelling in the direction perpendicular to the shock wave. In the present paper, we assume that the small disturbances may be two dimensional, i.e. they may be propagating in the direction inclined to the shock wave. The conclusions obtained are: regardless of whether the incident wave and diverging wave are defined according to the direction of the phase velocity or the group velocity, the shock wave is unstable for some frequencies and longitudinal wave lengths of the disturbances, even if the conditionsM ₁>1,M ₂<1 are fulfilled. Then several experiments are proposed, and the problem of ways to define the incident wave and diverging wave is discussed. The meaning of this problem is illustrated. The same results can be obtained for the steady shock wave in a tube.     

A numerical study of shock wave reflections on low density foam

A continuum mixture theory is used to describe shock wave reflections on low density open-cell polyurethane foam. Numerical simulations are compared to the shock tube experiments of Skews (1991) and detailed wave fields are shown of a shock wave interacting with a layer of foam adjacent to a rigid wall boundary. These comparisons demonstrate that a continuum mixture theory describes well the shock interactions with low density foam.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Propagation characteristics of shock waves driven by gaseous detonation waves

We experimentally investigated propagation characteristics of the shock wave driven by a gaseous detonation wave emerging from the open end of a cylindrical detonation tube. In the present study, we visualized the shock wave and exhaust flowfields using a shadowgraph optical system and we obtained peak overpressure in the tube axial direction and the continuous shape transformation of shock waves around the tube open end. We also obtained overpressure histories of the shock wave using piezo-pressure transducers within 201 m from the open end of the tube. We normalized and classified these results by four regions using non-dimensional pressure and distance which are independent of variety of mixture and tube diameter. In the vicinity of the open end of the tube, the shock wave is nearly planar and does not significantly attenuate, and the peak overpressure maintains approximately C–J pressure. Subsequently, the shock wave attenuates rapidly, transforming from quasi-spherical to spherical. Farther from the tube open end, the shock wave propagates with approximately sound characteristic so that the peak overpressure decreases proportional to 1/r. Eventually, the shock wave begins to attenuate more rapidly than ideal sound attenuation, which may be due to the viscous effect.     

Drift of an inclined plate counter oncoming waves

The dependence of the velocity of the motion of a tow with an inclined plate mounted in a wave water channel on the wave parameters, the submergence depth, and the angle of inclination and dimensions of the plate is experimentally investigated. The effect of tow motion counter to the waves is detected and theoretically justified. The free surface profiles for periodic waves above an inclined plate obtained using the elolutionary system of the Boussinesq approximation equations correspond to the measured ones. The pulse generated as a result of wave breakup is estimated.     

Experimental and numerical studies on interactions of a spherical flame with incident and reflected shocks

Observations are presented from experiments and calculations where a laminar spherical CH4/air flame is perturbed successively by incident and reflected shock waves. The experiments are performed in a standard shock tube arrangement, in which a high-speed shadowgraph imaging system is used to record evolutions of the flame. Numerical simulations are conducted by using second-order wave propagation algorithms, based on two-dimensional axisymmetric Navier-Stokes equations with detailed chemical reactions. Qualitative agreements are obtained between the experimental and numerical results. Under actions of incident shock waves, Richtmyer-Meshkov instability responsible for the flame deformation is induced in the flame, and the distoned flame takes a barrel shape. Then, under subsequent actions of the shock wave reflected from a planar wall, the flame takes an inclined non-symmetrical kidney shape in a symmetric cross section, which means a mushroom-like shape of the flame comes finally into being. The vorticity direction in the ring cap has been altered by the reflected shock＇s action, which makes the head of the mushroom-like flame extend quickly to the side wall.     

Fully developed mixed convection in horizontal and inclined tubes with uniform heat flux using nanofluid

Fully developed laminar mixed convection of a nanofluid consists of water and Al₂O₃ in horizontal and inclined tubes has been studied numerically. Three-dimensional elliptic governing equations have been solved to investigate the flow behaviors over a wide range of the Grashof and Reynolds numbers. Comparisons with previously published experimental and numerical works on mixed convection in a horizontal and inclined tube are performed and good agreements between the results are observed. Effects of nanoparticles concentration and tube inclinations on the hydrodynamics and thermal parameters are presented and discussed. It is shown that the nanoparticles concentration does not have significant effects on the hydrodynamics parameters. Heat transfer coefficient increases by 15% at 4 Vol.% Al₂O₃. Skin friction coefficient continually increases with the tube inclination, but the heat transfer coefficient reaches a maximum at the inclination angle of 45°.     

Stability of converging cylindrical shock waves

An experimental and numerical study was made of converging cylindrical shock waves. The goal of the present study was to clarify the movement and instability of the converging cylindrical shock waves. Experiments were conducted in an annular shock tube of 230 mm o.d. and 210 mm i.d. connected to a cylindrical test section of 210 mm diameter. Double exposure holographic interferometry was used to visualize the converging cylindrical shock waves. Incident shock Mach numbers ranged between 1.1 and 2.0 in air. A numerical simulation was conducted using the TVD finite difference scheme. It was found in the experiments that although the initial shock wave configuration looked cylindrical, it was gradually deformed with propagation towards the center and finally showed mode-four instability. This is attributable to the existence of initial disturbances which were introduced by the struts which supported the inner tube of the annular shock tube. This trend was significant for stronger shock waves indicating that at the last stage of shock wave convergence the initial perturbations of the converging cylindrical shock wave were amplified to form the triple point of Mach reflection. The numerical results correctly predicted the experimental trend.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Multi-shock structure of roll wavesStructure multi-chocs d'ondes à rouleaux

The special class of periodic travelling waves which is known as roll waves is investigated for nonhomogeneous hyperbolic equations of gas dynamics type. In this Note these equations are applied to shallow water flows in inclined open channels, but the results obtained are more general and far-reaching. The necessary conditions for the existence of a roll wave are derived. It is shown that for a nonconvex pressure term, multi-shock configurations of roll waves of finite amplitude exist. A new type of periodic travelling wave, which corresponds to the slug flow regime in two-layer flows, is found. To cite this article: A. Boudlal, V.Yu. Liapidevskii, C. R. Mecanique 332 (2004).     

Stability of roll waves in open channel flowsStabilité de trains d'ondes dans un canal découvert

The stability of finite amplitude roll waves that may develop at a liquid free surface in inclined open channels of arbitrary cross-section is studied. In the framework of shallow water theory with turbulent friction the modulation equations for wave series are derived and a nonlinear stability criterion is obtained. To cite this article: A. Boudlal, V.Yu. Liapidevskii, C. R. Mecanique 330 (2002) 291–295.     

Evolution of blast wave profiles in simulated air blasts: experiment and computational modeling

Shock tubes have been extensively used in the study of blast traumatic brain injury due to increased incidence of blast-induced neurotrauma in Iraq and Afghanistan conflicts. One of the important aspects in these studies is how to best replicate the field conditions in the laboratory which relies on reproducing blast wave profiles. Evolution of the blast wave profiles along the length of the compression-driven air shock tube is studied using experiments and numerical simulations with emphasis on the shape and magnitude of pressure time profiles. In order to measure dynamic pressures of the blast, a series of sensors are mounted on a cylindrical specimen normal to the flow direction. Our results indicate that the blast wave loading is significantly different for locations inside and outside of the shock tube. Pressure profiles inside the shock tube follow the Friedlander waveform fairly well. Upon approaching exit of the shock tube, an expansion wave released from the shock tube edges significantly degrades the pressure profiles. For tests outside the shock tube, peak pressure and total impulse reduce drastically as we move away from the exit and majority of loading is in the form of subsonic jet wind. In addition, the planarity of the blast wave degrades as blast wave evolves three dimensionally. Numerical results visually and quantitatively confirm the presence of vortices, jet wind and three-dimensional expansion of the planar blast wave near the exit. Pressure profiles at 90° orientation show flow separation. When cylinder is placed inside, this flow separation is not sustained, but when placed outside the shock tube this flow separation is sustained which causes tensile loading on the sides of the cylinder. Friedlander waves formed due to field explosives in the intermediate-to far-field ranges are replicated in a narrow test region located deep inside the shock tube.     

Flow stability of a conducting liquid flowing down an inclined plane in the presence of a magnetic field

The stability of a steady flow of incompressible, conducting liquid down an inclined plane in the presence of longitudinal and transverse magnetic fields is studied. Solutions of the linearized magnetohydrodynamic equations with corresponding boundary conditions are found on the assumption that the Reynolds number R_g and the wave number are small. It is shown that the longitudinal magnetic field plays a stabilizing role. It is known [1] that the flow of a viscous liquid over a vertical wall is always unstable. In this article it is shown that the instability effect at small wave numbers may be eliminated if the longitudinal magnetic field satisfies the conditions found. The case when the Alfvén number and the wave number are small and the Reynolds number is finite is also examined.     

Shock waves from an open-ended shock tube with different shapes

A new method for decreasing the attenuation of a shock wave emerging from an open-ended shock tube exit into a large free space has been developed to improve the shock wave technique for cleaning deposits on the surfaces in industrial equipments by changing the tube exit geometry. Three tube exits (the simple tube exit, a tube exit with ring and a coaxial tube exit) were used to study the propagation processes of the shock waves. The detailed flow features were experimentally investigated by use of a two-dimensional color schlieren method and by pressure measurements. By comparing the results for different tube exits, it is shown that the expansion of the shock waves near the mouth can be restricted by using the tube exit with ring or the coaxial tube exit. Thus, the attenuation of the shock waves is reduced. The time histories of overpressure have illustrated that the best results are obtained for the coaxial tube exit. But the pressure signals for the tube exit with ring showed comparable results with the advantage of a relatively simple geometry. The flow structures of diffracting shock waves have also been simulated by using an upwind finite volume scheme based on a high order extension of Godunov's method as well as an adaptive unstructured triangular mesh refinement/unrefinement algorithm. The numberical results agree remarkably with the experimental ones.     

横向冲击载荷下不同约束泡沫铝夹芯圆管的动态响应

以泡沫铝夹芯圆管为研究对象,采用数值模拟研究了横向冲击载荷作用下4种不同约束夹芯圆管的动态响应。研究了夹芯圆管的几何参数、冲击速度和芯层泡沫铝相对密度对夹芯圆管力学行为的影响,对比分析了不同约束条件对泡沫铝夹芯圆管变形模式和吸能性能的影响。结果表明:随着内管直径的减小、冲击速度的增大和芯层泡沫铝相对密度的增大,泡沫铝夹芯圆管的比吸能增大;内管壁厚的增加使无约束和倾斜约束下夹芯圆管的比吸能增大,对侧壁约束和组合约束下夹芯圆管的吸能影响不明显;采用一定的外部约束条件是提高泡沫铝夹芯圆管吸能性能的一种可行的方法。     

Non-linear waves in a viscous fluid contained in an elastic tube with variable cross-section

In the present work, treating the large arteries as a thin-walled, long and circularly cylindrical, prestressed elastic tube with variable cross-section and using the reductive perturbation method, we have studied the amplitude modulation of non-linear waves in such a fluid-filled elastic tube. By considering the blood as an incompressible viscous fluid, the evolution equation is obtained as the dissipative non-linear Schrödinger equation with variable coefficients. It is shown that this type of equations admit a solitary wave solution with a variable wave speed. It is observed that, the wave speed increases with distance for narrowing tubes while it decreases for expanding tubes.