Research interests of V. Kumaran
Flow in flexible tubes:
Introduction
The flow of a fluid in flexible tubes and channels is
encountered in many biological systems, such as the flow of
blood in arteries and veins. Many reaction and separation
processes in biotechnological industries also involve this type
of flow. A salient feature of parallel flows is the transition
from laminar to
turbulent flow at a critical Reynolds number, because the
characteristics of the laminar and turbulent states are very
different. For example, the mass and heat transfer coefficient of the
turbulent flow is three orders of magnitude greater than that of
the laminar flow. An accurate knowledge of the transition point
is of importance for the design of these systems. In a rigid
tube, the transition takes place at a Reynolds number of about
2300, but in flexible tubes the wall flexibility could
influence the transition.
Objectives
The objective of this project is to determine the effect of the
wall flexibility on the transition in rigid tubes and channels,
and to study the flow structure in the turbulent regime.
Results
The stability of the flow is a function of the Reynolds number,
which is the ratio of inertial and viscous forces, and an
additional parameter which gives the ratio of the
viscous forces in the fluid and the elastic forces in the wall.
- The stability of the flow in the low Reynolds number limit
has been studied using asymptotic analysis. In this limit the
viscous forces are neglected and it is found that the flow
becomes unstable when the velocity is increased beyond a
critical value.
- Asymptotic analysis was used to study the stability
of axisymmetric modes in the high Reynolds limit. In this, there are two
types of modes -- {\em inviscid modes} and {\em wall modes}. The
asymptotic analysis revealed that both these types of modes are
stable.
- Numerical calculations of the variation in
the critical velocity over five orders of magnitude was
undertaken. These computations reveal that there is indeed an
instability at high Reynolds number, and the most unstable mode
is the wall mode modified by the inertia of the flexible wall of
the tube.
- The possibility of unstable non - axisymmetric modes has been
analysed. For plane surfaces, the Squire's theorem states
that two dimensional perturbations are always unstable than
three dimensional perturbations. No such theorem exists for
flows in cylindrical tubes. The equivalents of the Rayleigh
theorem have been derived for the flow in a flexible tube, and it is
found that the axisymmetric modes are always stable for a
parabolic mean flow, but non - axisymmetric modes could become
unstable.
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