scholarly journals The energetics of flow through a rapidly oscillating tube with slowly varying amplitude

2011 ◽  
Vol 369 (1947) ◽  
pp. 2989-3006 ◽  
Author(s):  
Robert J. Whittaker ◽  
Matthias Heil ◽  
Sarah L. Waters
Keyword(s):  
Flow Structure ◽  
Energy Budget ◽  
High Frequency ◽  
Axial Flow ◽  
Multiple Scale ◽  
Amplitude Equations ◽  
Long Wavelength ◽  
First Order ◽  
Collapsible Tubes ◽  
Flow Through

Motivated by the problem of self-excited oscillations in fluid-filled collapsible tubes, we examine the flow structure and energy budget of flow through an elastic-walled tube. Specifically, we consider the case in which a background axial flow is perturbed by prescribed small-amplitude high-frequency long-wavelength oscillations of the tube wall, with a slowly growing or decaying amplitude. We use a multiple-scale analysis to show that, at leading order, we recover the constant-amplitude equations derived by Whittaker et al . (Whittaker et al. 2010 J. Fluid Mech. 648 , 83–121. ( doi:10.1017/S0022112009992904 )) with the effects of growth or decay entering only at first order. We also quantify the effects on the flow structure and energy budget. Finally, we discuss how our results are needed to understand and predict an instability that can lead to self-excited oscillations in collapsible-tube systems.

Flow through axial-flow-turbomachinery blading

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Flow Velocity ◽  
Compressible Flow ◽  
Dimensional Analysis ◽  
Incompressible Flow ◽  
Compressible Fluid ◽  
Axial Flow ◽  
Linear Cascade ◽  
Dimensional Parameters ◽  
Flow Through

This chapter is concerned primarily with the flow of a compressible fluid through stationary and moving blading, for the most part using the analysis introduced in Chapter 11. The principles of dimensional analysis are applied to determine the appropriate non-dimensional parameters to characterise the performance of a turbomachine. The analysis of incompressible flow through a linear cascade of aerofoil-like blades is followed by the analysis of compressible flow. Velocity triangles for flow relative to blades, and Euler’s turbomachinery equation, are introduced to analyse flow through a rotor. The concepts introduced are applied to the analysis of an axial-turbomachine stage comprising a stator and a rotor, which applies to either a compressor or a turbine.

Influence of Leading Edge Fillet and Nonaxisymmetric Contoured Endwall on Turbine NGV Exit Flow Structure and Interactions With the Rim Seal Flow

2013 ◽  
Author(s):  
Özhan H. Turgut ◽  
Cengiz Camcı
Keyword(s):  
Flow Structure ◽  
Total Pressure ◽  
Guide Vane ◽  
Axial Flow ◽  
Leading Edge ◽  
Turbine Rotor ◽  
Rotor Blades ◽  
Constant Thickness ◽  
Computational Evaluation ◽  
Nozzle Guide

Three different ways are employed in the present paper to reduce the secondary flow related total pressure loss. These are nonaxisymmetric endwall contouring, leading edge (LE) fillet, and the combination of these two approaches. Experimental investigation and computational simulations are applied for the performance assessments. The experiments are carried out in the Axial Flow Turbine Research Facility (AFTRF) having a diameter of 91.66cm. The NGV exit flow structure was examined under the influence of a 29 bladed high pressure turbine rotor assembly operating at 1300 rpm. For the experimental measurement comparison, a reference Flat Insert endwall is installed in the nozzle guide vane (NGV) passage. It has a constant thickness with a cylindrical surface and is manufactured by a stereolithography (SLA) method. Four different LE fillets are designed, and they are attached to both cylindrical Flat Insert and the contoured endwall. Total pressure measurements are taken at rotor inlet plane with Kiel probe. The probe traversing is completed with one vane pitch and from 8% to 38% span. For one of the designs, area averaged loss is reduced by 15.06%. The simulation estimated this reduction as 7.11%. Computational evaluation is performed with the rotating domain and the rim seal flow between the NGV and the rotor blades. The most effective design reduced the mass averaged loss by 1.28% over the whole passage at the NGV exit.

Pressure-flow relations in coronary circulation

1990 ◽  
Vol 70 (2) ◽  
pp. 331-390 ◽  
Author(s):  
J. I. Hoffman ◽  
J. A. Spaan
Keyword(s):  
Coronary Vessels ◽  
Good Evidence ◽  
The Body ◽  
Vascular Compression ◽  
Exact Nature ◽  
Coronary Veins ◽  
Collapsible Tubes ◽  
External Pressures ◽  
Flow Through

The blood vessels that run on the surface of the heart and through its muscle are compliant tubes that can be affected by the pressures external to them in at least two ways. If the pressure outside these vessels is higher than the pressure at their downstream ends, the vessels may collapse and become Starling resistors or vascular waterfalls. If this happens, the flow through these vessels depends on their resistance and the pressure drop from their inflow to the pressure around them and is independent of the actual downstream pressure. In the first part of this review, the physics of collapsible tubes is described, and the possible occurrences of vascular waterfalls in the body is evaluated. There is good evidence that waterfall behavior is seen in collateral coronary arteries and in extramural coronary veins, but the evidence that intramural coronary vessels act like vascular waterfalls is inconclusive. There is no doubt that in systole there are high tissue pressures around the intramyocardial vessels, particularly in the subendocardial muscle of the left ventricle. The exact nature and values of the forces that act at the surface of the small intramural vessels, however, are still not known. We are not certain whether radial (compressive) or circumferential and longitudinal (tensile) stresses are the major causes of vascular compression; the role of collagen struts in modifying the reaction of vessel walls to external pressures is unknown but possibly important; direct examination of small subepicardial vessels has failed to show vascular collapse. One of the arguments in favor of intramyocardial vascular waterfalls has been that during a long diastole the flow in the left coronary artery decreases and reaches zero when coronary arterial pressure is still high: it can be as much as 50 mmHg in the autoregulating left coronary arterial bed and approximately 15-20 mmHg even when the vessels have been maximally dilated. These high zero flow pressures, especially during maximal vasodilatation, have been regarded as indicating a high back pressure to flow that is due to waterfall behavior of vessels that are exposed to tissue pressures.(ABSTRACT TRUNCATED AT 400 WORDS)

Chaotic Amplitude Dynamics for Parametrically Excited Systems With Quadratic Nonlinearities

1995 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj
Keyword(s):  
Harmonic Balance ◽  
Chaotic Dynamics ◽  
Degrees Of Freedom ◽  
Order Approximation ◽  
Amplitude Equations ◽  
Analytical Technique ◽  
First Order ◽  
Numerical Studies ◽  
Quadratic Nonlinearities ◽  
First Order Approximation

Abstract Dynamical systems with two degrees-of-freedom, with quadratic nonlinearities and parametric excitations are studied in this analysis. The 1:2 superharmonic internal resonance case is analyzed. The method of harmonic balance is used to obtain a set of four first-order amplitude equations that govern the dynamics of the first-order approximation of the response. An analytical technique, based on Melnikov’s method is used to predict the parameter range for which chaotic dynamics exist in the undamped averaged system. Numerical studies show that chaotic responses are quite common in these quadratic systems and chaotic responses occur even in presence of damping.

scholarly journals Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 2. Stability of cnoidal waves

2007 ◽  
Vol 73 (6) ◽  
pp. 933-946
Author(s):  
S. PHIBANCHON ◽  
M. A. ALLEN ◽  
G. ROWLANDS
Keyword(s):  
Growth Rate ◽  
Nonlinear Waves ◽  
Electron Distribution ◽  
Magnetized Plasma ◽  
Weakly Nonlinear ◽  
Long Wavelength ◽  
First Order ◽  
Wave Solutions ◽  
Linear Waves ◽  
Weakly Nonlinear Waves

AbstractWe determine the growth rate of linear instabilities resulting from long-wavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation which governs weakly nonlinear waves in a strongly magnetized cold-ion plasma whose electron distribution is given by two Maxwellians at slightly different temperatures. To obtain the growth rate it is necessary to evaluate non-trivial integrals whose number is kept to a minimum by using recursion relations. It is shown that a key instance of one such relation cannot be used for classes of solution whose minimum value is zero, and an additional integral must be evaluated explicitly instead. The SKdVZK equation contains two nonlinear terms whose ratio b increases as the electron distribution becomes increasingly flat-topped. As b and hence the deviation from electron isothermality increases, it is found that for cnoidal wave solutions that travel faster than long-wavelength linear waves, there is a more pronounced variation of the growth rate with the angle θ at which the perturbation is applied. Solutions whose minimum values are zero and which travel slower than long-wavelength linear waves are found, at first order, to be stable to perpendicular perturbations and have a relatively narrow range of θ for which the first-order growth rate is not zero.

Dynamic Pumping Performance of the Hemopump®-A Small Intraventricular Blood Pump

1992 ◽  
Vol 15 (8) ◽  
pp. 493-498 ◽  
Author(s):  
E.E. Kunst ◽  
J.A. Van Alsté
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Axial Flow ◽  
Pressure Head ◽  
Blood Pump ◽  
First Order ◽  
Mock Circulation ◽  
Temporary Support ◽  
Axial Flow Pump ◽  
Flow Pump

We studied the pumping characteristics of the Hemopump®, a commercially availabe miniature intraventricular blood pump for temporary support of failing hearts. The Hemopump® is an axial flow pump of which the characteristics can be described by turbomachine theory. Experiments with water and a mock circulation verified that the pumping characteristics of the Hemopump®, in terms of both pressure head and flow as a function of rotational speed, very well can be described by a first order differential equation. The influence of blood with its non-Newtonian character is being investigated

Perfusion through vessels open in zone 1 contributes to gas exchange in rabbit lungs in situ

1995 ◽  
Vol 79 (6) ◽  
pp. 1895-1899 ◽  
Author(s):  
W. J. Lamm ◽  
T. Obermiller ◽  
M. P. Hlastala ◽  
R. K. Albert
Keyword(s):  
High Frequency ◽  
Pulmonary Arterial Pressure ◽  
Venous Pressure ◽  
High Frequency Oscillation ◽  
Bias Flow ◽  
Flow Through ◽  
Pulmonary Arterial ◽  
Zero Reference ◽  
The Mean

We previously found that up to 15% of the normal cardiac output can flow through lungs that are entirely in zone 1 and that the zone 1 pathway utilizes alveolar corner vessels. Because of the proximity of these vessels to alveoli, we hypothesized that lungs perfused under zone 1 conditions would exchange gas. We used the multiple inert gas elimination technique to assess the ventilation-perfusion (VA/Q) distribution under zones 1 and 2 in six rabbit lungs perfused with tris(hydroxymethyl)aminomethane-buffered Tyrode solution containing 1% albumin, 4% dextran, and papaverine (25 mg/l). High-frequency oscillation (tidal volume = 2.8 ml at 20 Hz, bias flow = 1 l/min) kept alveolar pressure (PA) nearly constant at 10 or 20 cmH2O. Pulmonary arterial pressure was set 2.5 cmH2O below or 5 cmH2O above PA (zones 1 and 2, respectively). Pulmonary venous pressure was kept at 0 cmH2O, with zero reference being the bottom of the lung. At PA of 10 cmH2O, flow was 64 +/- 40 and 5 +/- 3 ml/min (P < 0.05) and the mean VA/Q for perfusion was 1.1 +/- 0.4 and > 5 (P < 0.05) in zones 2 and 1, respectively. At PA of 20 cmH2O, flow was 89 +/- 36 and 22 +/- 13 ml/min (P < 0.05) and the mean VA/Q for perfusion was 0.8 +/- 0.3 and 3.7 +/- 2.4 (P < 0.05) in zones 2 and 1, respectively. Shunt averaged < 5% of total flow in all conditions. Blood flowing through vessels remaining open under zone 1 conditions 1) exchanges gas, 2) does not occur through anatomic or physiological shunts, and 3) may explain the high VA/Q seen with positive end-expiratory pressure.

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