A theoretical study of viscous effects in peristaltic pumping

1994 ◽  
Vol 279 ◽  
pp. 177-195 ◽  
Author(s):  
Alden M. Provost ◽  
W. H. Schwarz
Keyword(s):  
Wave Propagation ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Mean Flow ◽  
Viscous Effects ◽  
Transverse Waves ◽  
Peristaltic Pumping ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Intuition and previous results suggest that a peristaltic wave tends to drive the mean flow in the direction of wave propagation. New theoretical results indicate that, when the viscosity of the transported fluid is shear-dependent, the direction of mean flow can oppose the direction of wave propagation even in the presence of a zero or favourable mean pressure gradient. The theory is based on an analysis of lubrication-type flow through an infinitely long, axisymmetric tube subjected to a periodic train of transverse waves. Sample calculations for a shear-thinning fluid illustrate that, for a given waveform, the sense of the mean flow can depend on the rheology of the fluid, and that the mean flow rate need not increase monotonically with wave speed and occlusion. We also show that, in the absence of a mean pressure gradient, positive mean flow is assured only for Newtonian fluids; any deviation from Newtonian behaviour allows one to find at least one non-trivial waveform for which the mean flow rate is zero or negative. Introduction of a class of waves dominated by long, straight sections facilitates the proof of this result and provides a simple tool for understanding viscous effects in peristaltic pumping.

Oscillatory forcing of flow through porous media. Part 2. Unsteady flow

2002 ◽  
Vol 465 ◽  
pp. 237-260 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Flow Through Porous Media ◽  
Mean Flow ◽  
Two Fluids ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Numerical computations are employed to study the phenomenon of oscillatory forcing of flow through porous media. The Galerkin finite element method is used to solve the time-dependent Navier–Stokes equations to determine the unsteady velocity field and the mean flow rate subject to the combined action of a mean pressure gradient and an oscillatory body force. With strong forcing in the form of sinusoidal oscillations, the mean flow rate may be reduced to 40% of its unforced steady-state value. The effectiveness of the oscillatory forcing is a strong function of the dimensionless forcing level, which is inversely proportional to the square of the fluid viscosity. For a porous medium occupied by two fluids with disparate viscosities, oscillatory forcing may be used to reduce the flow rate of the less viscous fluid, with negligible effect on the more viscous fluid. The temporal waveform of the oscillatory forcing function has a significant impact on the effectiveness of this technique. A spike/plateau waveform is found to be much more efficient than a simple sinusoidal profile. With strong forcing, the spike waveform can induce a mean axial flow in the absence of a mean pressure gradient. In the presence of a mean pressure gradient, the spike waveform may be employed to reverse the direction of flow and drive a fluid against the direction of the mean pressure gradient. Owing to the viscosity dependence of the dimensionless forcing level, this mechanism may be employed as an oscillatory filter to separate two fluids of different viscosities, driving them in opposite directions in the porous medium. Possible applications of these mechanisms in enhanced oil recovery processes are discussed.

Effects of Fluid Inertia and Compressibility on the Performance of Valves and Flow Meters Operating under Unsteady Conditions

1966 ◽  
Vol 8 (1) ◽  
pp. 52-61 ◽  
Author(s):  
D. McCloy
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Flow Measurement ◽  
Fluid Inertia ◽  
Mean Flow ◽  
Flow Meters ◽  
Orifice Area ◽  
Flow Through ◽  
The Mean ◽  
Compressibility Effects

Incompressible flow theory is used in the investigation of the effects of fluid inertia on unsteady flow through valves and flow meters. Two types of oscillatory disturbance are considered, one being due to valve oscillation at constant pressure drop and the other to pressure pulsation at constant orifice area. With the former type of disturbance it is shown that the mean flow rate decreases with frequency of oscillation. When the pressure drop pulsates the mean flow rate increases with frequency. These phenomena are shown to be of importance in hydraulic servomechanisms and in dynamic flow measurement. Compressibility effects are considered and it is shown that cavitation can occur at the valve during oscillation.

Peristaltic Waves in Circular Cylindrical Tubes

1969 ◽  
Vol 36 (3) ◽  
pp. 579-587 ◽  
Author(s):  
F. Yin ◽  
Y. C. Fung
Keyword(s):  
Pressure Gradient ◽  
Wall Motion ◽  
Amplitude Ratio ◽  
Cylindrical Tube ◽  
Critical Value ◽  
Mean Flow ◽  
Navier Stokes Equation ◽  
Mean Pressure ◽  
The Mean ◽  
Set Up

Peristaltic pumping in a circular cylindrical tube is analyzed. The problem is a viscous fluid flow induced by an axisymmetric traveling sinusoidal wave of moderate amplitude imposed on the wall of a flexible tube. A perturbation method of solution is sought. The amplitude ratio (wave amplitude/tube radius) is chosen as a parameter. The nonlinear convective acceleration terms in the Navier-Stokes equation is retained. The governing equations are developed up to the second order in the amplitude ratio. The zeroth-order terms yield the classical Poiseuille flow, the first-order terms yield the Sommerfeld-Orr equation. If there is no pressure gradient in the absence of wall motion, the mean flow and mean pressure gradient (averaged over time) are both shown to be proportional to the square of the amplitude ratio. Numerical results are obtained for this simple case by approximating a complicated group of products of Bessel functions by a polynomial. The results show that the mean axial velocity is dominated by two terms. One term corresponds to a parabolic profile which is due to the mean pressure gradient set up by the wall motion. The other term arises from satisfying the no-slip boundary condition at the wavy wall rather than at the mean position of the wall. In addition, there are perturbations arising from the convective acceleration. If the mean pressure gradient set up by the wall motion itself reaches a certain positive critical value, the velocity becomes zero on the axis. Values of the mean pressure gradient larger than the critical value will induce backward flow in the fluid. Values of the critical pressure gradient for several cases are presented.

Peristaltic Transport

1968 ◽  
Vol 35 (4) ◽  
pp. 669-675 ◽  
Author(s):  
Y. C. Fung ◽  
C. S. Yih
Keyword(s):  
Velocity Profile ◽  
Pressure Gradient ◽  
Amplitude Ratio ◽  
Critical Value ◽  
Positive Pressure ◽  
Peristaltic Motion ◽  
Mean Flow ◽  
Peristaltic Pumping ◽  
Order Of Magnitude ◽  
The Mean

Peristaltic pumping (viscous fluid flow induced by a sinusoidal traveling wave motion of the walls of a tube) at moderate amplitudes of motion is analyzed in the two-dimensional case. The nonlinear convective acceleration is considered and the nonslip condition is applied on the wavy wall (rather than on the mean position) in order to account for the mean flow induced by the wall motion. In the case in which there is no other cause of flow, the mean flow induced by the peristaltic motion of the wall is proportional to the square of the amplitude ratio (wave amplitude/half width of channel). The velocity profile depends on the mean pressure gradient. In this paper only those cases in which the pressure gradient will produce a flow of the same order of magnitude as that induced by the peristaltic motion are considered. If the pressure gradient is positive and equal to a certain critical value, then the velocity is zero on the center line. Pumping against a positive pressure gradient greater than the critical value would induce a backward flow (reflux) in the core region of the stream. There will be no reflux if the pressure gradient is smaller than the critical value. The velocity profile and the value of the critical pressure gradient are presented in this paper.

Long-wavelength peristaltic pumping at low Reynolds number

1975 ◽  
Vol 68 (3) ◽  
pp. 467-476 ◽  
Author(s):  
M. J. Manton
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Low Reynolds Number ◽  
Separated Flow ◽  
Axial Direction ◽  
Reynolds Number Flow ◽  
Peristaltic Pumping ◽  
Mean Pressure ◽  
The Mean ◽  
Low Reynolds

An asymptotic expansion is found for the low Reynolds number flow induced in an axisymmetric tube by long peristaltic waves of arbitrary shape. Expressions are determined for the relationship between the mean pressure gradient and the volume flux, for the mean rate of working by the wall of the tube and for the shear stress a t the wall. A necessary and sufficient condition for the occurrence of trapping (that is, regions of separated flow near the axis of the tube in a reference frame moving at the wave speed) is obtained. It is shown that reflux (that is, a mean flux in the negative axial direction in a layer of fluid adjacent to the wall when the net mean flux is positive) occurs whenever there is an adverse mean pressure gradient, independently of the shape of the wave. A n estimate of the amount of reflux is derived.

Modelling the effect of mean pressure gradient on the mean flow within forests

1994 ◽  
Vol 68 (3-4) ◽  
pp. 201-212 ◽  
Author(s):  
Xuhui Lee ◽  
Roger H. Shaw ◽  
T.Andrew Black
Keyword(s):  
Pressure Gradient ◽  
Mean Flow ◽  
Mean Pressure ◽  
The Mean

scholarly journals Use and success evaluation of percutaneous aortic balloon valvuloplasty in different hemodynamic entities of severe aortic stenosis in the TAVR era

2020 ◽  
Vol 41 (Supplement_2) ◽  
Author(s):  
K Piayda ◽  
A Wimmer ◽  
H Sievert ◽  
K Hellhammer ◽  
S Afzal ◽  
...  
Keyword(s):  
Heart Failure ◽  
Aortic Valve ◽  
Aortic Stenosis ◽  
Aortic Valve Replacement ◽  
Pressure Gradient ◽  
Severe Aortic Stenosis ◽  
Primary Treatment ◽  
Low Flow ◽  
Mean Pressure ◽  
The Mean

Abstract Background In the era of transcatheter aortic valve replacement (TAVR), there is renewed interest in percutaneous balloon aortic valvuloplasty (BAV), which may qualify as the primary treatment option of choice in special clinical situations. Success of BAV is commonly defined as a significant mean pressure gradient reduction after the procedure. Purpose To evaluate the correlation of the mean pressure gradient reduction and increase in the aortic valve area (AVA) in different flow and gradient patterns of severe aortic stenosis (AS). Methods Consecutive patients from 01/2010 to 03/2018 undergoing BAV were divided into normal-flow high-gradient (NFHG), low-flow low-gradient (LFLG) and paradoxical low-flow low-gradient (pLFLG) AS. Baseline characteristics, hemodynamic and clinical information were collected and compared. Additionally, the clinical pathway of patients (BAV as a stand-alone procedure or BAV as a bridge to aortic valve replacement) was followed-up. Results One-hundred-fifty-six patients were grouped into NFHG (n=68, 43.5%), LFLG (n=68, 43.5%) and pLFLG (n=20, 12.8%) AS. Underlying reasons for BAV and not TAVR/SAVR as the primary treatment option are displayed in Figure 1. Spearman correlation revealed that the mean pressure gradient reduction had a moderate correlation with the increase in the AVA in patients with NFHG AS (r: 0.529, p<0.001) but showed no association in patients with LFLG (r: 0.145, p=0.239) and pLFLG (r: 0.030, p=0.889) AS. Underlying reasons for patients to undergo BAV and not TAVR/SAVR varied between groups, however cardiogenic shock or refractory heart failure (overall 46.8%) were the most common ones. After the procedure, independent of the hemodynamic AS entity, patients showed a functional improvement, represented by substantially lower NYHA class levels (p<0.001), lower NT-pro BNP levels (p=0.003) and a numerical but non-significant improvement in other echocardiographic parameters like the left ventricular ejection fraction (p=0.163) and tricuspid annular plane systolic excursion (TAPSE, p=0.066). An unplanned cardiac re-admission due to heart failure was necessary in 23.7% patients. Less than half of the patients (44.2%) received BAV as a bridge to TAVR/SAVR (median time to bridge 64 days). Survival was significantly increased in patients having BAV as a staged procedure (log-rank p<0.001). Conclusion In daily clinical practice, the mean pressure gradient reduction might be an adequate surrogate of BAV success in patients with NFHG AS but is not suitable for patients with other hemodynamic entities of AS. In those patients, TTE should be directly performed in the catheter laboratory to correctly assess the increase of the AVA. BAV as a staged procedure in selected clinical scenarios increases survival and is a considerable option in all flow states of severe AS. (NCT04053192) Figure 1 Funding Acknowledgement Type of funding source: None

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

scholarly journals Turbulence structure of non-uniform rough open channel flow

2018 ◽  
Vol 40 ◽  
pp. 05039
Author(s):  
Priscilla Williams ◽  
Vesselina Roussinova ◽  
Ram Balachandar
Keyword(s):  
Pressure Gradient ◽  
Channel Flow ◽  
Friction Velocity ◽  
Open Channel ◽  
Open Channel Flow ◽  
Shear Stresses ◽  
Turbulence Structure ◽  
Mean Flow ◽  
Rough Bed ◽  
The Mean

This paper focuses on the turbulence structure in a non-uniform, gradually varied, sub-critical open channel flow (OCF) on a rough bed. The flow field is analysed under accelerating, near-uniform and decelerating conditions. Information for the flow and turbulence parameters was obtained at multiple sections and planes using two different techniques: two-component laser Doppler velocimetry (LDV) and particle image velocimetry (PIV). Different outer region velocity scaling methods were explored for evaluation of the local friction velocity. Analysis of the mean velocity profiles showed that the overlap layer exists for all flow cases. The outer layer of the decelerated velocity profile was strongly affected by the pressure gradient, where a large wake was noted. Due to the prevailing nature of the experimental setup it was found that the time-averaged flow quantities do not attained equilibrium conditions and the flow is spatially heterogeneous. The roughness generally increases the friction velocity and its effect was stronger than the effect of the pressure gradient. It was found that for the decelerated flow section over a rough bed, the mean flow and turbulence intensities were affected throughout the flow depth. The flow features presented in this study can be used to develop a model for simulating flow over a block ramp. The effect of the non-uniformity and roughness on turbulence intensities and Reynolds shear stresses was further investigated.

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