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Blood Flow Mechanics
Published in Michel R. Labrosse, Cardiovascular Mechanics, 2018
The solutions presented earlier in this chapter were for steady flows in rigid tubes, in which the driving pressure gradient was constant in time. While these approximations are useful to study blood flow in veins or through an extracorporeal circuit during hemodialysis or surgery, it is well known that blood flow in the circulatory system is unsteady, that is, not constant in time. More specifically, blood flow is pulsatile, meaning that the pressure and flow velocities vary periodically. Womersley described the dimensionless parameter α, the Womersley number (Equation 3.16), which characterizes the nature of an unsteady flow. He also developed a method to solve the Navier–Stokes equations for any given pressure wave in a rigid pipe (Womersley 1955).
Computational modelling of nasal respiratory flow
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2020
H. Calmet, K. Inthavong, H. Owen, D. Dosimont, O. Lehmkuhl, G. Houzeaux, M. Vázquez
Experiments and computational inhalation studies have primarily addressed steady-state flow scenarios, while only a small number of studies have applied unsteady inhalation flows (Doorly et al. 2008; Se et al. 2009; Horschler et al. 2010; Lee et al. 2010; Spence et al. 2012), primarily due to the intensive computational resources required. The steady flow solutions provide a mean flow field, smearing out any fluctuating or oscillating behaviour found in real cases. The Womersley number f = 15 breaths per second), ν is the kinematic viscosity, D is a characteristic length scale; has been used to justify the steady flow models deeming it as ‘quasi-steady’ (Wen et al. 2008). The Wo describes the significance of the fluctuations from the breathing cycle onto the flow field. When Wo is small (1 or less), the effects of the oscillations are low enough that the inlet conditions have time to develop without being influenced by fluctuations. When Wo is large (10 or more), the effects of the oscillations are large enough that the velocity profile does not develop in time. The Strouhal number St, uave is the average velocity through the nasal passage, is a ratio of the unsteady forces to the inertial forces has also been used and is defined as for St > 1, the oscillations in the flow become important while for St < 1, the contribution of the velocity dominates the oscillations.
Analysis of the time-velocity curve in phase-contrast magnetic resonance imaging: a phantom study
Published in Computer Assisted Surgery, 2019
Jieun Park, Junghun Kim, Yongmin Chang, Sung Won Youn, Hui Joong Lee, Eun-Ju Kang, Ki-Nam Lee, Vojtěch Suchánek, Sinjae Hyun, Jongmin Lee
For the present study, the rotation speed was ranged from 40 RPM to 90 RPM and the duty ratio was from 3:7 to 6:4. Details about the eighteen flow patterns used for flow velocity measurement are summarized in Table 1. The pattern number indicates the type of flow pattern. Pattern 1 corresponds to 40 RPM and 3:7 of the duty ratio. Rotation per minute (RPM) and duty ratio are equivalent to heart rates and systole/diastole ratio in vivo. The internal capacity of the cylinder was set to 90 cc. The internal diameter of the flow-conducting tube was 19 mm, similar to that of an aorta. The Reynolds numbers for the maximum and mean velocities were ranged from 10,450 to 15,200 and from 4750 to 10,450 for the study, respectively. The Womersley number (α = R(ωρ/µ)1/2) that characterizes the pulsatile flow was ranged from 7.8 to 11.6 in RPM used. The pulsatile flow generated from the present flow system was evaluated using PC-MRI, Doppler ultrasonography, and the electromagnetic flowmeter in Table 1. To keep an experimental consistency, all experiments were performed at a pre-determined location in the flow system using a flat-height supporting device. During PC-MRI, an electromechanical part of the flow system was located outside MR gantry room.
Use of computational fluid dynamics deposition modeling in respiratory drug delivery
Published in Expert Opinion on Drug Delivery, 2019
P. Worth Longest, Karl Bass, Rabijit Dutta, Vijaya Rani, Morgan L. Thomas, Ahmad El-Achwah, Michael Hindle
Developing numerical models of the entire respiratory airways, from the nose, mouth, and throat through the terminal bronchioles and to the alveoli, as illustrated in Figure 2, poses multiple challenges. Division of the flow at each bifurcation, combined with decreasing airway diameters, results in a decrease in Reynolds number through the airways. This means the flow may enter the extrathoracic airways under fully turbulent conditions, and then move through transitional and laminar regimes in more distal regions of the lung. The importance of transient forces, characterized by the Womersley number, also decreases as flow progresses from the upper to lower airways. Therefore, a transient formulation of the Navier–Stokes equations may not be necessary in all conducting airways. Furthermore, distal regions of the lung are more compliant, so the movement of wall boundaries and the associated change in domain volume must be considered. This is especially true when modeling the alveoli, as flow is drawn into the lungs through expansion of these structures. Finally, the sheer number of airway generations in the human lung (over 1 million assuming an average of 20 bifurcation levels) makes it impossible to model all possible flow paths with CFD using current computational resources.