Fluid flow in a tube with an elastic membrane insertion

1998 ◽  
Vol 375 ◽  
pp. 39-64 ◽  
Author(s):  
GIANNI PEDRIZZETTI
Keyword(s):  
Circular Tube ◽  
Viscous Incompressible Fluid ◽  
Travelling Waves ◽  
Finite Elasticity ◽  
Elastic Membrane ◽  
Membrane Insertion ◽  
Stationary Waves ◽  
Membrane Elasticity ◽  
Wall Interaction ◽  
Reference Pressure

The unsteady flow of a viscous incompressible fluid in a circular tube with an elastic insertion is studied numerically. The deformation of the elastic membrane is obtained by the theory of finite elasticity whose equations are solved simultaneously with the fluid equations in the axisymmetric approximation. The elastic wall expands outwards due to the positive transmural pressure and represents an idealized model for the response of pathologies in large arteries.It is found that if either the fluid discharge or the reference pressure are imposed downstream of the insertion, the fluid–wall interaction develops travelling waves along the membrane whose period depends on membrane elasticity; these are unstable in a perfectly elastic membrane and are stabilized by viscoelasticity. In the reversed system, when the fluid discharge is imposed on the opposite side, the stable propagation phenomenon remains the same because of symmetry arguments. Such arguments do not apply to the originally unstable behaviour. In this case, even when the membrane is perfectly elastic, propagation is damped and two natural fluctuations appear in the form of stationary waves. In all cases the resonance of the fluid–wall interaction has been analysed. Comparisons with previously observed phenomena and with results of analogous studies are discussed.

A discussion on advanced methods of energy conversion- Magnetohydrodynamic power generation - Wave growth in m .h.d. generators

1967 ◽  
Vol 261 (1123) ◽  
pp. 461-470 ◽  
Keyword(s):  
Thermodynamic Properties ◽  
Acoustic Waves ◽  
Subsonic Flow ◽  
Flow Direction ◽  
Noble Gas ◽  
Travelling Waves ◽  
Combustion Products ◽  
Stationary Waves ◽  
Ohmic Dissipation ◽  
Steady Current

It has been shown that in an m.h.d. generator, acoustic waves can grow due to the coupling of fluctuations in electrical conductivity, Hall parameter and thermodynamic properties of the gas, with the ohmic dissipation and electromagnetic body forces. A new analysis of this phenomenon is presented in which waves travelling at an arbitrary angle to the flow direction in a plane perpendicular to the magnetic field are considered. In contrast to McCune’s (1964) treatment the thermodynamic properties are not restricted to perfect gas laws; and the condition for spatially and temporally growing waves is examined using a general dispersion relation which includes both these types of wave. We consider in detail (i) stationary waves in supersonic flow, and (ii) travelling waves in the subsonic flow found in the G.E.G.B. 200 MW thermal input generator being built at Marchwood, and a possible power station m.h.d. generator. It is found that the waves in the 200 MW rig which burns kerosene in oxygen will be damped. But in an oil-air combustion products generator for Hall parameters of order 3 or greater, it is found that stationary waves which grow rapidly may occur at Mach numbers greater than about 1-7; and in subsonic flow waves propagating antiparallel to the steady current vector may be amplified, though the growth rate is not excessive. In noble gas m.h.d. generators these waves are more unstable than in the oil, air combustion products generator.

scholarly journals Numerical simulation of bubble dynamics in response to acoustic disturbances

2007 ◽  
Author(s):  
Κωνσταντίνος Τσιγκλιφής
Keyword(s):  
Constitutive Law ◽  
Membrane Properties ◽  
Elastic Membrane ◽  
Shear Stresses ◽  
Additional Parameter ◽  
Viscous Effects ◽  
Membrane Elasticity ◽  
Backscatter Signal ◽  
Acoustic Disturbances ◽  
Bending Modulus

The dynamic behavior and the fashion of collapse of a free bubble play a significant role in the phenomenon of single cavitation bubble luminescence (SCBL) and single bubble sono-luminescence (SBSL), in which light is emitted during its breakdown. In SCBL, the bubble is produced by the application of a laser pulse, in the host liquid, with a duration of 10⁻¹⁵ sec (femtosecond bubbles) and 10⁻⁹ sec (nanosecond bubbles). The resulting bubbles have size of the order of 5 and 500 μm, respectively. The femtosecond bubbles display severe elongation with regards to the axis of symmetry, while light is not emitted during their collapse. In contrast, the nanosecond bubbles exhibit almost spherosymmetric shape initially and collapse producing light. A parametric study is conducted on the fashion of collapse of bubbles, of various sizes, for weak or strong elongation and vanishing small or large internal overpressure, considering axisymmetric oscillations with weak viscous effects. Further, an effort is made to reproduce, as close as possible, respective SCBL and SBSL experiments, aiming to investigate the effect of the initial asymmetry on the fashion of collapse and the velocity of the resulting jet during collapse. Recently, a significant number of applications in diagnostic and therapeutic medicine use the ability of microbubbles, encapsulated by an elastic membrane (contrast agents), to reflect the ultrasound waves. Initially, a model that predicts the backscatter signal of the microbubble as a function of the membrane properties, of the host liquid and the width and the frequency of the acoustic disturbances, is presented. This model predicts with accuracy the effect of the non linear membrane constitutive law on the microbubble response for large acoustic disturbances in comparison to experimental measurements. The control of cohesion of microbubbles is desirable in several applications, such as in quantitative evaluation of heart blood flow (contrast perfusion imaging). In order to gain understanding regarding its cohesion range, the large-amplitude axisymmetric oscillation and collapse of an encapsulated microbubble is examined. The shear stresses that develop on the membrane due to the bending moments are accounted for, based on the shell stability theory, and are determined by the scalar bending modulus. This is a measure of the shell resistance to bending and is introduced as an additional parameter, due to the anisotropy of the membrane elasticity along the interface and perpendicular to it. With the help of stability analysis, it is feasible to estimate the range of the parameters for shape oscillations of the microbubble, as well as for the buckling of the shell. In combination with the model of the spherosymmetric oscillations, a theoretical tool is developed for the characterisation of a microbubble with regards to its membrane elasticity, bending resistance and viscosity. Phase diagrams are constructed where the regions of stable or unstable oscillation of a microbubble are defined. Finally, axisymmetric simulations of the interaction of the external flow field and the encapsulated microbubble are performed, implementing a hybrid boundary-finite element method, in order to determine the conditions under which a jet is created during the oscillation of the microbubble; a phenomenon which is observed when a microbubble oscillates near the walls of neighbouring tissues.

scholarly journals Planetary wave activity in the Arctic and Antarctic lower stratospheres during 2007 and 2008

2009 ◽  
Vol 9 (4) ◽  
pp. 14601-14643
Author(s):  
S. P. Alexander ◽  
M. G. Shepherd
Keyword(s):  
Northern Hemisphere ◽  
Planetary Wave ◽  
Travelling Waves ◽  
Maximum Amplitude ◽  
Wave Activity ◽  
Planetary Waves ◽  
The Arctic ◽  
Stationary Waves ◽  
Wave Amplification ◽  
Zonal Wavenumber

Abstract. Temperature data from the COSMIC GPS-RO satellite constellation are used to study planetary wave activity in both polar stratospheres from September 2006 until November 2008. One major and several minor sudden stratospheric warmings (SSWs) were recorded during the boreal winters of 2006/2007 and 2007/2008. Planetary wave morphology is studied using space-time spectral analysis while individual waves are extracted using a linear least squares fitting technique. Results show the planetary wave frequency and zonal wavenumber distribution varying between hemisphere and altitude. Most of the large Northern Hemisphere wave activity is associated with the winter SSWs, while the largest amplitude waves in the Southern Hemisphere occur during spring. Planetary wave activity during the 2006/2007 and 2007/2008 Arctic SSWs is due largely to travelling waves with zonal wavenumbers |s|=1 and |s|=2 having periods of 12, 16 and 23 days and stationary waves with |s|=1 and |s|=2. The latitudinal variation of wave amplification during the two Northern Hemisphere winters is studied. Most planetary waves show different structure and behaviour during each winter. Abrupt changes in the latitude of maximum amplitude of some planetary waves is observed co-incident in time with some of the SSWs.

Surface folding of viscoelastic fluids: finite elasticity membrane model

2004 ◽  
Vol 15 (4) ◽  
pp. 385-408 ◽  
Author(s):  
T. PODGORSKI ◽  
A. BELMONTE
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Pressure Field ◽  
Numerical Study ◽  
Finite Elasticity ◽  
Viscoelastic Fluids ◽  
Deborah Number ◽  
Elastic Membrane ◽  
Surface Wetting ◽  
Qualitative Behaviour

When a dry sphere sinks into a fluid, a funnel-shaped free surface develops behind the sphere if the sinking occurs faster than the surface wetting. If the fluid is viscoelastic, the interface can become unstable to a loss of axisymmetry. The stress near this surface concentrates into boundary layers, as also seen in other free surface extensional flows of viscoelastic fluids. At high Deborah number and low Reynolds number, the qualitative behaviour can be recovered by considering the static equilibrium of a stretched elastic membrane in an hydrostatic pressure field. We treat this problem in the framework of finite elasticity using a neo-Hookean constitutive model, and show how the conditions of instability can be recovered. A numerical study of this model is presented.

Part II. finite periodic stationary gravity waves in a perfect liquid

1952 ◽  
Vol 244 (882) ◽  
pp. 254-284 ◽  
Keyword(s):  
Gravity Waves ◽  
Travelling Waves ◽  
Wave Length ◽  
Finite Depth ◽  
Travelling Wave ◽  
Maximum Height ◽  
Stationary Waves ◽  
Fifth Order ◽  
Individual Particles ◽  
Crest Height

The possible existence, form and maximum height of strictly periodic finite stationary waves on the surface of a perfect liquid are discussed. A method of successive approximation to the solution of the hydrodynamical equations is formulated, and the solution is carried to the fifth order for the case of two-dimensional waves on a deep liquid. The convergence of the method has not been established, so that the existence of truly periodic stationary waves is not beyond doubt, but the calculations provide strong presumptive evidence for their existence, and for the existence of a finite stable wave of greatest height. The crest of this wave has a right-angled nodal form, in contrast with that of the greatest stable travelling wave for which the nodal angle is 120°. The maximum crest height is 0.141A, where A is the wave-length, and the maximum trough depth is 0.078 A. This means that the greatest stationary waves are greater than the maximum travelling waves, the ratio being 1.53. The motions of individual particles are studied and it is shown that particles in the surface, particularly those near the anti-nodes have large horizontal motions. For a given wave-length, the period increases with wave height. The wave pressure on a breakwater is examined, and the modification of the calculations to allow for the finite depth of water is considered. Doubly modulated oscillations in a deep rectangular tank are also briefly discussed.

Instability of two annular layers or a liquid thread bounded by an elastic membrane

2000 ◽  
Vol 405 ◽  
pp. 211-241 ◽  
Author(s):  
C. POZRIKIDIS
Keyword(s):  
Surface Tension ◽  
Circular Tube ◽  
Thin Sheet ◽  
Normal Modes ◽  
Boundary Integral ◽  
Constitutive Law ◽  
Elastic Membrane ◽  
Cylindrical Shape ◽  
Stable Mode ◽  
Annular Layer

The instability of an annular layer coated on the interior side of an outer circular tube and surrounding another annular layer coated on the exterior side of an inner circular tube, is studied in the absence of an imposed flow due to a pressure gradient or boundary motion. As the radius of the inner cylinder tends to vanish and the radius of the outer cylinder tends to infinity, the inner layer reduces to a liquid thread suspended in a quiescent infinite ambient fluid. The fluids are separated by a membrane that exhibits constant surface tension and develops elastic tensions due to deformation from the unstressed cylindrical shape. The surface tension is responsible for the Rayleigh capillary instability, but the elastic tensions resist the deformation and slow down or even prevent the growth of small perturbations. In the first part of this paper, we formulate the linear stability problem for axisymmetric perturbations, and derive a nonlinear eigenvalue system whose solution produces the complex phase velocity of the normal modes. When inertial effects are negligible, there are two normal modes; one is stable under any conditions, and the second may be unstable when the interfacial elasticity is sufficiently small compared to surface tension, and the wavelength of the perturbation is sufficiently long. Stability graphs are presented to illustrate the properties of the normal modes and their dependence on the ratio of the viscosity of the outer to inner fluid, the interfacial elasticity, and the ratios of the cylinders' radii to the interface radius. The results show that as the interfacial elasticity tends to vanish, the unconditionally stable mode becomes physically irrelevant by requiring extremely large ratios of axial to lateral displacement of material points along the trace of the membrane in an azimuthal plane. In the second part of this paper, we investigate the nonlinear instability of an infinite thread in the limit of vanishing Reynolds numbers by dynamical simulation based on a boundary-integral method. In the problem formulation, the elastic tensions derive from a constitutive equation for a thin sheet of an incompressible isotropic elastic solid described by Mooney's constitutive law. The numerical results suggest that the interfacial elasticity ultimately restrains the growth of disturbances and leads to slowly evolving periodic shapes, in agreement with laboratory observations.

Transient flow of a viscous incompressible fluid in a circular tube after a sudden point impulse

2009 ◽  
Vol 637 ◽  
pp. 285-303 ◽  
Author(s):  
B. U. FELDERHOF
Keyword(s):  
Incompressible Fluid ◽  
Transient Flow ◽  
Stokes Equations ◽  
Circular Tube ◽  
Viscous Incompressible Fluid ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Long Time

The flow of a viscous incompressible fluid in a circular tube generated by a sudden impulse on the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. At short time the flow is irrotational and may be described by a potential which varies with the square root of time. At later times there is a sequence of moving and decaying vortex rings. At long times the flow velocity decays with an algebraic long-time tail. The impulse generates a time-dependent pressure difference between the ends of the tube.

scholarly journals Planetary wave activity in the polar lower stratosphere

2010 ◽  
Vol 10 (2) ◽  
pp. 707-718 ◽  
Author(s):  
S. P. Alexander ◽  
M. G. Shepherd
Keyword(s):  
Planetary Wave ◽  
Travelling Waves ◽  
Stationary Wave ◽  
Wave Activity ◽  
The Arctic ◽  
Small Scale ◽  
Stationary Waves ◽  
Significant Activity ◽  
Zonal Wavenumber ◽  
The Times

Abstract. Temperature data from the COSMIC GPS-RO satellite constellation are used to study the distribution and variability of planetary wave activity in the low to mid- stratosphere (15–40 km) of the Arctic and Antarctic from September 2006 until March 2009. Stationary waves are separated from travelling waves and their amplitudes, periods and small-scale vertical distribution then examined. COSMIC observed short lived (less than two weeks and less than 5 km vertically) but large enhancements in planetary wave amplitudes occurring regularly throughout all winters in both hemispheres. In contrast to recent Arctic winters, eastward wave activity during 2008–2009 was significantly reduced during the early part of the winter and immediately prior to the major SSW. The eastward waves which did exist had similar periods to the two preceding winters (~16–20 days). A westward wave with zonal wavenumber two, with distinct peaks at 22 km and 35 km and period around 16–24 days, as well as a stationary wave two were associated with the 2009 major SSW. In the Southern Hemisphere, the height structure of planetary wave amplitudes also exhibited fluctuations on short time and vertical scales superimposed upon the broader seasonal cycle. Significant inter-annual variability in planetary wave amplitude and period are noticed, with the times of cessation of significant activity also varying.

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