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Steady and pulsatile flow in curved vessels


Mahmoudi Zarandi, Mehrdad (2000) Steady and pulsatile flow in curved vessels. Dissertation (Ph.D.), California Institute of Technology.


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An experimental investigation is carried out on the nature of secondary flow patterns in a curved vessel. This study concentrates on the role of the upstream spatial boundary conditions and the time-periodicity of the formation of the secondary flow patterns in curved vessels. Four sets of studies are made. In the first set, steady flow is compared to a pulsatile flow simulating the physiological conditions in the human aorta. To study the effect of spatial upstream boundary conditions, we investigated the effect of an upstream constriction, which represents the actual physiological conditions in the human aorta. All in vitro studies are carried out in models with dimensions close to those of the human aorta and with the Reynolds number (1400 < Re < 7000), Dean number (1470 < De < 7300) and Womersley number (8.6 < [...] < 12.6) all in a range close to the physiological values. The technique of Digital Particle Image Velocimetry is used to measure instantaneous and average flow fields.

In the first stage of this research, an orifice with a stenosis ratio of ~3 = 80% is used to simulate the upstream constriction and study its effect on the secondary flow patterns. It is found that the existence of the upstream constriction profoundly changes the nature of the secondary flow pattern. In the presence of the upstream constriction, the double circulation pattern of Dean flow is substituted with a single circulation pattern.

Next, to investigate where the transition from one pattern to the other occurs, similar sets of experiments are carried out with constrictions of different sizes corresponding to stenosis ratios of, [...] = 65% and [...] = 88%. In addition, to investigate the sense of rotation for the single circulation pattern, an orifice with an asymmetric opening mounted at different angular positions is used.

The comparison of the secondary flow patterns for steady versus pulsatile flow revealed that the flow pattern does not change its main structure due to the time-periodicity of the flow. However, the pulsatile flow in general shows secondary flow rates greater than the steady flow.

On the other hand, the spatial boundary conditions are found to be central in determining the secondary flow patterns. First, the presence of an upstream constriction or stenosis ratio of [...] = 65% will result in a single circulation pattern. Therefore, the transition between the double circulation pattern of the non-constrained flow and the single circulation pattern occur at constrictions less than [...] = 65%. Secondary flow velocities and shear rate along the vessel wall are much higher for the flow with an upstream constriction than those for the flow without an upstream constriction. In the presence of an upstream constriction, the axial velocity and secondary flow maximum velocity are of the same order of magnitude.

The results of the experiments with the asymmetric orifice show that the sense of rotation depends on the position of the upstream opening with respect to the central axis of the vessel. The clinical data show that the aortic valve opening, even at the full open stage, is less than the maximum diameter of the sinus of valsalva at the base of the human aorta by at least 30% which is equivalent to a stenosis ratio of [...] = 51%. Therefore, our results are important in the understanding of the nature of shear stress development along the vessel walls and in the study of the radial distribution of blood cells in a secondary flow field. Similarly, for industrial application these results are important for the assessment of the transport properties in coiled heat exchangers or fluid-fluid absorption systems. In order to investigate the spatial condition which determines the sense of rotation in single-circulation patterns, a series of experiments were carried out changing the position of orifice opening in [...] increments with respect to anterior-posterior wall axis. These results strongly support the conjecture that the incoming jet impingement on the vessel wall is redirected by the local curvature of the vessel wall into a helical pattern which overcomes the Dean's flow and causes the single-circulation patterns.

To summarize, three distinct secondary flow patterns are observed in our experimental study. The first one is the known Dean flow, which is a double-circulation pattern. The second and third patterns, which are discovered for the first time, are the clockwise and counterclockwise single-circulation patterns. The transition from one pattern to another is dependent on the spatial boundary conditions and is independent of the temporal boundary conditions. The secondary flow velocity gradient and hence its shear stress is comparable to the axial flow velocity gradient and shear stress in the single-circulation pattern. For the Dean flow or double-circulation secondary flow pattern, shear stress values are much less than those for the axial flow. This finding can greatly contribute to our understanding of blood flow-related pathology. In addition, the position of the upstream orifice opening with respect to the anterior-posterior vessel wall is an important factor in the design of artificial aortic valves. The dependence of the sense of the rotation of single-circulation patterns on the relative position of orifice opening with respect to the anterior-posterior vessel wall axis suggests that the out of plane curvature of aorta may play an important role in the re-direction of the incoming jet in the arch.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Chemistry and Chemical Engineering
Major Option:Chemical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Gharib, Morteza
Thesis Committee:
  • Gharib, Morteza (chair)
  • Tirrell, David A.
  • Brady, John F.
  • Kornfield, Julia A.
Defense Date:3 January 2000
Record Number:CaltechETD:etd-09232005-081558
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3724
Deposited By: Imported from ETD-db
Deposited On:23 Sep 2005
Last Modified:26 Dec 2012 03:02

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