scholarly journals The existence of steady flow in a collapsed tube

1989 ◽  
Vol 206 ◽  
pp. 339-374 ◽  
Author(s):  
O. E. Jensen ◽  
T. J. Pedley
Keyword(s):  
Pressure Drop ◽  
Energy Loss ◽  
Steady Flow ◽  
Flow Rate ◽  
Transmural Pressure ◽  
Tube Model ◽  
Collapsible Tube ◽  
One Dimensional ◽  
Flow Through ◽  
Range Of Values

Self-excited oscillations arise during flow through a pressurized segment of collapsible tube, for a range of values of the time-independent controlling pressures. They come about either because there is an (unstable) steady flow corresponding to these pressures, or because no steady flow exists. We investigate the existence of steady flow in a one-dimensional collapsible-tube model, which takes account of both longitudinal tension and jet energy loss E downstream of the narrowest point. For a given tube, the governing parameters are flow-rate Q, and transmural pressure P at the downstream end of the collapsible segment. If E = 0, there exists a range of (Q, P)-values for which no solutions exist; when E ≠ 0 a solution is always found. For the case E ≠ 0, predictions are made of pressure drop along the collapsible tube; these solutions are compared with experiment.

Chaotic Oscillations in a Simple Collapsible-Tube Model

1992 ◽  
Vol 114 (1) ◽  
pp. 55-59 ◽  
Author(s):  
O. E. Jensen
Keyword(s):  
Internal Flow ◽  
Tube Model ◽  
Steady Flows ◽  
Collapsible Tube ◽  
Laboratory Apparatus ◽  
Chaotic Oscillations ◽  
Dimensional Model ◽  
One Dimensional ◽  
Flow Through ◽  
Relaxation Structure

A steady flow through a segment of externally pressurized, collapsible tube can become unstable to a wide variety of self-excited oscillations of the internal flow and tube walls. A simple, one-dimensional model of the conventional laboratory apparatus, which has been shown previously to predict steady flows and multiple modes of oscillation, is investigated numerically here. Large amplitude oscillations are shown to have a relaxation structure, and the nonlinear interaction between different modes is shown to give rise to quasiperiodic and apparently aperiodic behavior. These predictions are shown to compare favorably with experimental observations.

Multiple solutions and flow limitation for steady flow through a collapsible tube held open at the ends

1987 ◽  
Vol 174 ◽  
pp. 467-493 ◽  
Author(s):  
J. W. Reyn
Keyword(s):  
Steady Flow ◽  
Cross Section ◽  
Flow Rate ◽  
Higher Order ◽  
Tube Length ◽  
Flow Limitation ◽  
Collapsible Tube ◽  
Gradual Loss ◽  
All Solutions ◽  
Flow Through

Equations for the steady flow of an incompressible, inviscid fluid through a collapsible tube under longitudinal tension are derived by treating the tube longitudinally as a membrane, and taking the collapsibility of the tube into account in an approximate way by replacing in the equation for an axisymmetric membrane a term representing the resistance of the tube to area change by the tube law for collapsible tubes. The flow is assumed to be uniform in a cross-section. A nonlinear differential equation is obtained for the shape of the tube for given values of total pressure p0, flow rate q, longitudinal tension τ and tube law P = P(ρ); where ρ = (A/πR2)½ is the equivalent radius of the tube (A = area of a cross-section, R = radius of the unloaded, then circular tube). The equation can be integrated and analysed in the phase plane. Equilibrium points correspond to uniform flow through cylindrical tubes; saddle points correspond to subcritical flow (S < 1), centrepoints to supercritical (S > 1) and a higher-order point to critical flow (S = 1). Here S is the speed index, the ratio of the flow speed to the speed of long waves. Near centrepoints there are solutions, that represent area-periodic tubes. For a finite tube, held open at the ends, the steady flow is formulated as a two-point boundary-value problem. On the basis of numerical calculations, and a bifurcation analysis using the method of Lyapunov–Schmidt, the existence and multiplicity of the solutions of this problem are discussed and the process of flow limitation studied. For negative total pressures two collapsed solutions are found that disappear at the flow-limitation value of the flow rate. For positive total pressures a distinction is made between subcritical, critical and supercritical total pressures. In all these cases there is a multiplicity, proportional to the ratio of the tube length to [Lscr ]1(0), the wavelength of the collapsed periodic solution for vanishing flow rate, and having maximum radius ρ = 1. For subcritical total pressures increase of the flow rate leads to a gradual loss of all solutions in higher-order flow limitations until final flow limitation occurs by the mergence of two collapsed solutions. For supercritical total pressures increase of the flow rate also leads to a gradual loss of all solutions in higher-order flow limitations in a process which now also depends upon the ratio of the tube length to the wavelength L of periodic solutions with vanishing amplitude and ρ ≡ 1.

Steady Flow Hemodynamic and Energy Loss Measurements in Normal and Simulated Calcified Tricuspid and Bicuspid Aortic Valves

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Clara Seaman ◽  
A. George Akingba ◽  
Philippe Sucosky
Keyword(s):  
Pressure Drop ◽  
Aortic Valve ◽  
Energy Loss ◽  
Steady Flow ◽  
Flow Rate ◽  
Maximum Flow ◽  
Maximum Flow Rate ◽  
Type I ◽  
Orifice Area ◽  
The Impact

The bicuspid aortic valve (BAV), which forms with two leaflets instead of three as in the normal tricuspid aortic valve (TAV), is associated with a spectrum of secondary valvulopathies and aortopathies potentially triggered by hemodynamic abnormalities. While studies have demonstrated an intrinsic degree of stenosis and the existence of a skewed orifice jet in the BAV, the impact of those abnormalities on BAV hemodynamic performance and energy loss has not been examined. This steady-flow study presents the comparative in vitro assessment of the flow field and energy loss in a TAV and type-I BAV under normal and simulated calcified states. Particle-image velocimetry (PIV) measurements were performed to quantify velocity, vorticity, viscous, and Reynolds shear stress fields in normal and simulated calcified porcine TAV and BAV models at six flow rates spanning the systolic phase. The BAV model was created by suturing the two coronary leaflets of a porcine TAV. Calcification was simulated via deposition of glue beads in the base of the leaflets. Valvular performance was characterized in terms of geometric orifice area (GOA), pressure drop, effective orifice area (EOA), energy loss (EL), and energy loss index (ELI). The BAV generated an elliptical orifice and a jet skewed toward the noncoronary leaflet. In contrast, the TAV featured a circular orifice and a jet aligned along the valve long axis. While the BAV exhibited an intrinsic degree of stenosis (18% increase in maximum jet velocity and 7% decrease in EOA relative to the TAV at the maximum flow rate), it generated only a 3% increase in EL and its average ELI (2.10 cm2/m2) remained above the clinical threshold characterizing severe aortic stenosis. The presence of simulated calcific lesions normalized the alignment of the BAV jet and resulted in the loss of jet axisymmetry in the TAV. It also amplified the degree of stenosis in the TAV and BAV, as indicated by the 342% and 404% increase in EL, 70% and 51% reduction in ELI and 48% and 51% decrease in EOA, respectively, relative to the nontreated valve models at the maximum flow rate. This study indicates the ability of the BAV to function as a TAV despite its intrinsic degree of stenosis and suggests the weak dependence of pressure drop on orifice area in calcified valves.

Study of fluid flow through a channel deformed by piezoelement

2018 ◽  
Vol 13 (3) ◽  
pp. 1-10 ◽  
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh Nasibullaeva ◽  
O.V. Darintsev
Keyword(s):  
Fluid Flow ◽  
Pressure Drop ◽  
Boundary Conditions ◽  
Flow Rate ◽  
Contact Surface ◽  
Piezoelectric Element ◽  
Neumann Boundary ◽  
Differential Pressure ◽  
Physical Parameters ◽  
Flow Through

The flow of a liquid through a tube deformed by a piezoelectric cell under a harmonic law is studied in this paper. Linear deformations are compared for the Dirichlet and Neumann boundary conditions on the contact surface of the tube and piezoelectric element. The flow of fluid through a deformed channel for two flow regimes is investigated: in a tube with one closed end due to deformation of the tube; for a tube with two open ends due to deformation of the tube and the differential pressure applied to the channel. The flow rate of the liquid is calculated as a function of the frequency of the deformations, the pressure drop and the physical parameters of the liquid.

Lateral-Flow Effect on Endwall Heat Transfer and Pressure Drop in a Pin-Fin Trapezoidal Duct of Various Pin Shapes

2000 ◽  
Vol 123 (1) ◽  
pp. 133-139 ◽  
Author(s):  
Jenn-Jiang Hwang ◽  
Chau-Ching Lu
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Flow Rate ◽  
Lateral Flow ◽  
Transfer Enhancement ◽  
Pin Fin ◽  
Flow Reynolds Number ◽  
Outlet Flow ◽  
Flow Through

The effects of lateral-flow ejection 0<ε<1.0, pin shapes (square, diamond, and circular), and flow Reynolds number (6000<Re<40,000) on the endwall heat transfer and pressure drop for turbulent flow through a pin-fin trapezoidal duct are studied experimentally. A staggered pin array of five rows and five columns is inserted in the trapezoidal duct, with the same spacings between the pins in the streamwise and spanwise directions: Sx/d=Sy/d=2.5. Three different-shaped pins of length from 2.5<l/d<4.6 span the distance between two endwalls of the trapezoidal duct. Results reveal that the pin-fin trapezoidal duct with lateral-flow rate of ε=0.3-0.4 has a local minimum endwall-averaged Nusselt number and Euler number for all pin shapes investigated. The trapezoidal duct of lateral outlet flow only (ε=1.0) has the highest endwall heat transfer and pressure drop. Moreover, the square pin results in a better heat transfer enhancement than the diamond pin, and subsequently than the circular pin. Finally, taking account of the lateral-flow rate and the flow Reynolds number, the work develops correlations of the endwall-averaged heat transfer with three different pin shapes.

Lateral-Flow Effect on Endwall Heat Transfer and Pressure Drop in a Pin-Fin Trapezoidal Duct of Various Pin Shapes

2000 ◽  
Author(s):  
Jenn-Jiang Hwang ◽  
Chau-Ching Lu
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Flow Rate ◽  
Lateral Flow ◽  
Transfer Enhancement ◽  
Pin Fin ◽  
Flow Reynolds Number ◽  
Outlet Flow ◽  
Flow Through

Effects of the lateral-flow ejection (0 ≦ ε ≦ 1.0), pin shapes (square, diamond and circular) and flow Reynolds number (6,000 ≦ Re ≦ 40,000) on the endwall heat transfer and pressure drop for turbulent flow through a pin-fin trapezoidal duct are studied experimentally. The trapezoidal duct are inserted with a staggered pin array of five rows and five columns, with the same spacings between the pins in streamwise and spanwise directions of Sx/d = Sy/d = 2.5. Three different-shaped pins of length from 2.5 < l/d < 4.6 span the distance between two endwalls of the trapezoidal duct. Results reveal that the pin-fin trapezoidal duct with a lateral-flow rate of ε = 0.3–0.4 has a local minimum endwall-averaged Nusselt number and Euler number for all pin shapes investigated. The trapezoidal duct of lateral outlet flow only (ε = 1.0) has the highest endwall heat transfer and pressure drop. Moreover, the square pin performs a better heat transfer enhancement than the diamond pin, and subsequently than the circular pin. Finally, taking account of the lateral-flow rate and the flow Reynolds number develops correlations of the endwall-averaged heat transfer for three different pin shapes.

scholarly journals Variation of Pressure Drop along the Straight and Bifurcated Channel: Experiment and Simulation

2019 ◽  
Vol 8 (12) ◽  
pp. 2728-2731
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Aspect Ratio ◽  
Computational Model ◽  
Flow Rate ◽  
Normal Water ◽  
Flow Through ◽  
Experiment And Simulation

This paper derives an experimental and simulated investigation carried to analyze the performance of channel for calculating the pressure drop in laminar flow through rectangular shaped (straight and branched) microchannels. The microchannels taken ranged in variable aspect ratio from 0.75 to 1. Every check piece was made from copper and contained only one channel along a direction. The experiments were conducted with normal water, with Reynolds range starting from some 720 to 3500. Predictions obtained supported that with the variation in the aspect ratio the properties of the fluid also change. It is observed that the pressure drop changes with the change in the aspect ratio and flow rate and found that there is a correlation between the experimental and computational model results.

Pressure drop due to viscous flow through cylinders

1959 ◽  
Vol 6 (4) ◽  
pp. 542-546 ◽  
Author(s):  
Howard Brenner
Keyword(s):  
Pressure Drop ◽  
Circular Cylinder ◽  
Viscous Fluid ◽  
Viscous Flow ◽  
Steady Flow ◽  
Equations Of Motion ◽  
Point Force ◽  
Flow Through ◽  
Bounding Surfaces ◽  
Simple Fashion

A general formula is developed which permits a calculation of the pressure drop arising from the slow steady flow of a viscous fluid through a circular cylinder for arbitrarily assigned conditions of velocity on the bounding surfaces of the cylinder. In particular, the diminution in pressure can be calculated directly from the prescribed boundary velocities without requiring a detailed solution of the equations of motion. Hence it is possible to compute, in comparatively simple fashion, the magnitude of this macroscopic parameter for a large variety of complex motions which would normally present great analytical difficulties.By way of illustration the additional pressure drop arising from the presence of a point force situated along the axis of a cylinder is calculated. The additional force required to maintain the motion in the presence of the obstacle is exactly twice the magnitude of the point force itself.

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