Modification of Poiseuille Flow to a Pulsating Flow Using a Periodically Expanding-Contracting Balloon
Abstract
:1. Introduction
2. Materials and Methods
2.1. Governing Equations
2.2. Vessel Model
2.3. Numerical Method
2.4. Boundary Conditions
2.5. Space and Time Domain Discretization
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
IABP | Intra-Aortic Balloon Pump |
PCI | Percutaneous Coronary Intervention |
CPB | Cardiopulmonary Bypass |
ECMO | Extracorporeal Membrane Oxygenation |
Nomenclature | |
oscillation amplitude of the equatorial radius of the prolate balloon | |
metric tensor element, , | |
contravariant base vector, | |
J | Jacobian determinant |
length of the aorta | |
p | flow field pressure |
inlet pressure | |
outlet pressure | |
inlet flow volume rate | |
outlet flow volume rate | |
r | radial coordinate |
radius of the aorta | |
central value in time of the equatorial radius of the prolate balloon | |
t | time |
T | period of balloon oscillation |
u | longitudinal Cartesian velocity component |
Cartesian velocity component, | |
contravariant velocity component, | |
radial velocity component | |
angular velocity component | |
flow field velocity vector | |
balloon volume | |
x | streamwise coordinate |
Cartesian coordinate, | |
longitudinal position of prolate balloon center of symmetry | |
y | Cartesian cross-stream coordinate |
z | Cartesian cross-stream coordinate |
Womersley number | |
length of ellipsoid major semi-axis | |
length of ellipsoid median semi-axis | |
length of ellipsoid minor semi-axis | |
numerical time step | |
numerical longitudinal step | |
phase shift between outlet pressure and outlet volume rate | |
angular coordinate | |
dynamic viscosity of the fluid | |
kinematic viscosity of the fluid | |
curvilinear coordinate, | |
partial derivative of with respect to | |
density of the fluid | |
angular frequency of balloon oscillation |
Appendix A. The Flow Field around the Balloon for Qin = 0.01 L/s, rb0 = 0.32 cm and Ab = 0.02 cm
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Quantity | Value (cm) |
---|---|
0.925 | |
18 (for L/s), 40 (for L/s) | |
3 | |
0.32, 0.36, 0.44 | |
0.02, 0.06, 0.14 | |
7 |
Quantity | Value |
---|---|
dynamic viscosity | 0.04 g/(cm·s) |
density | 1.06 g/cm3 |
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Moulinos, I.; Manopoulos, C.; Tsangaris, S. Modification of Poiseuille Flow to a Pulsating Flow Using a Periodically Expanding-Contracting Balloon. Fluids 2023, 8, 129. https://doi.org/10.3390/fluids8040129
Moulinos I, Manopoulos C, Tsangaris S. Modification of Poiseuille Flow to a Pulsating Flow Using a Periodically Expanding-Contracting Balloon. Fluids. 2023; 8(4):129. https://doi.org/10.3390/fluids8040129
Chicago/Turabian StyleMoulinos, Iosif, Christos Manopoulos, and Sokrates Tsangaris. 2023. "Modification of Poiseuille Flow to a Pulsating Flow Using a Periodically Expanding-Contracting Balloon" Fluids 8, no. 4: 129. https://doi.org/10.3390/fluids8040129
APA StyleMoulinos, I., Manopoulos, C., & Tsangaris, S. (2023). Modification of Poiseuille Flow to a Pulsating Flow Using a Periodically Expanding-Contracting Balloon. Fluids, 8(4), 129. https://doi.org/10.3390/fluids8040129