Aspects of steady and pulsatile flow in branched tubes with particular reference to blood flow

• Main Author: Brech, Robert
• Published: University of Oxford 1971
• Subjects: 620.106
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.479914

The nature of the flow in branching blood vessels is of importance to physiologists, mainly on account of the formation of atheromatic deposits which occur frequently at sites of branching. The reasons for the occurrence of these deposits are not yet understood but it is generally agreed that the effects of fluid dynamics may well be important. There is, however, a lack of knowledge as to the detailed nature of the flow at and around branches and this study has been undertaken in order to provide such knowledge. The flow in symmetrical branches, typical of the blood vessels in man, has been studied using rigid-walled models perfused with steady and pulsatile water flows. The streamline patterns have been studied using dye and hydrogen bubble tracers and the effects of pressure differences and obstructions have also been investigated. Detailed measurements of axial velocity distribution and wall shear stress have been made with heated element probes developed for these applications. The design of these probes and the development of a digital output system are described. The following observations and conclusions have been made: 1. Contra-rotating, helical vortices are set up on the outside of each limb, their strength varying with the mean square of the input velocity. These vortices spread across the whole of the tube to give an approximately symmetrical velocity distribution within about six diameters downstream, this distance being independent of input velocity and profile. 2. There is markedly high shear stress on the inside wall of each limb and low shear stress on the outside wall. This differential is only maintained significantly, however, for 4 or 5 diameters downstream. 3. The mass flow distribution between the two limbs of a branch is very sensitive to small pressure differences between the limbs. This is not a flow switching (Coanda) effect, but a consequence of the relatively small pressure drop in each limb, Obstructions near the apex of the branch do not in general affect the mass flow distribution. 4. The stability of the downstream flow development depends on the input velocity, the stability increasing with decrease of velocity. 5. The interior geometry of the branch has only minimal effect on any downstream measurements. 6. The downstream flow patterns and velocity distributions in pulsatile flow show that there is little difference between the downstream effects in pulsatile and steady flow and that most pulsatile flows can be considered quasi-steady. Pulsatile flow tends to stabilise the downstream flow development. 7. Preliminary observations in a confluence show that there is no high shear stress at any position. In steady flow, vortices are shed from the apex causing pulse-shaped velocity and shear stress variations downstream. The frequency of the vortex shedding increases linearly with velocity.