Vipin Michael - Academia.edu (original) (raw)

Papers by Vipin Michael

Passive porous coatings have been proposed in literature as a means of delaying transition to tur... more Passive porous coatings have been proposed in literature as a means of delaying transition to turbulence in hypersonic boundary layers. The nonlinear stability of hypersonic viscous flow over a sharp slender cone with passive porous walls is investigated in this study. Hypersonic flows are unstable to viscous and inviscid disturbances, and following Mack (1984) these have been called the first and second Mack modes. A weakly nonlinear analysis of the instability of the flow to axisymmetric and non-axisymmetric viscous (first Mack mode) disturbances is performed here. The attached shock and effect of curvature are taken into account. Asymptotic methods are used at large Reynolds number and large Mach number to examine the viscous modes of instability, which may be described by a triple-deck structure. Various porous wall models have been incorporated into the stability analysis. The eigenrelations governing the linear stability of the problem are derived.

Effects of regular and random microstructures on hypersonic boundary layers

6th AIAA Theoretical Fluid Mechanics Conference, 2011

Effects of Passive Porous Walls on the First Mode of Hypersonic Boundary Layers Over a Sharp Cone

Nonlinear stability of hypersonic flow over a cone with passive porous walls

Journal of Fluid Mechanics, 2012

ABSTRACT This study investigates the nonlinear stability of hypersonic viscous flow over a sharp ... more ABSTRACT This study investigates the nonlinear stability of hypersonic viscous flow over a sharp slender cone with passive porous walls. The attached shock and effect of curvature are taken into account. Asymptotic methods are used for large Reynolds number and large Mach number to examine the viscous modes of instability (first Mack mode), which may be described by a triple-deck structure. A weakly nonlinear stability analysis is carried out allowing an equation for the amplitude of disturbances to be derived. The coefficients of the terms in the amplitude equation are evaluated for axisymmetric and non-axisymmetric disturbances. The stabilizing or destabilizing effect of nonlinearity is found to depend on the cone radius. The presence of porous walls significantly influences the effect of nonlinearity, and results for three types of porous wall (regular, random and mesh microstructure) are compared.

Journal of Theoretical Biology, 2009

We develop a simple mathematical model for forced flow of culture medium through a porous scaffol... more We develop a simple mathematical model for forced flow of culture medium through a porous scaffold in a tissue-engineering bioreactor. Porous-walled hollow fibres penetrate the scaffold and act as additional sources of culture medium. The model, based on Darcy's law, is used to examine the nutrient and shear-stress distributions throughout the scaffold. We consider several configurations of fibres and inlet and outlet pipes. Compared with a numerical solution of the full Navier-Stokes equations within the complex scaffold geometry, the modelling approach is cheap, and does not require knowledge of the detailed microstructure of the particular scaffold being used. The potential of this approach is demonstrated through quantification of the effect the additional flow from the fibres has on the nutrient and shear-stress distribution.

Effects of Passive Porous Walls on Hypersonic Boundary Layers

A theoretical linear stability analysis is used to consider the effect of a porous wall on the fi... more A theoretical linear stability analysis is used to consider the effect of a porous wall on the first mode of a hypersonic boundary layer on a sharp slender cone. The effect of curvature and of the attached shock are included. The flow in the hypersonic boundary layer is coupled to the flow in the porous layer. The theoretical model of a porous wall developed by Fedorov and his co-workers is used for regular microstructures. The resulting transcendental equations are solved numerically. Neutral solutions are presented, indicating a destabilizing effect of the porous wall. The spatial growth rates determined demonstrate that the porous wall leads to a significant increase in growth rates.

Passive porous coatings have been proposed in literature as a means of delaying transition to tur... more Passive porous coatings have been proposed in literature as a means of delaying transition to turbulence in hypersonic boundary layers. The nonlinear stability of hypersonic viscous flow over a sharp slender cone with passive porous walls is investigated in this study. Hypersonic flows are unstable to viscous and inviscid disturbances, and following Mack (1984) these have been called the first and second Mack modes. A weakly nonlinear analysis of the instability of the flow to axisymmetric and non-axisymmetric viscous (first Mack mode) disturbances is performed here. The attached shock and effect of curvature are taken into account. Asymptotic methods are used at large Reynolds number and large Mach number to examine the viscous modes of instability, which may be described by a triple-deck structure. Various porous wall models have been incorporated into the stability analysis. The eigenrelations governing the linear stability of the problem are derived.

Effects of regular and random microstructures on hypersonic boundary layers

6th AIAA Theoretical Fluid Mechanics Conference, 2011

Effects of Passive Porous Walls on the First Mode of Hypersonic Boundary Layers Over a Sharp Cone

Nonlinear stability of hypersonic flow over a cone with passive porous walls

Journal of Fluid Mechanics, 2012

ABSTRACT This study investigates the nonlinear stability of hypersonic viscous flow over a sharp ... more ABSTRACT This study investigates the nonlinear stability of hypersonic viscous flow over a sharp slender cone with passive porous walls. The attached shock and effect of curvature are taken into account. Asymptotic methods are used for large Reynolds number and large Mach number to examine the viscous modes of instability (first Mack mode), which may be described by a triple-deck structure. A weakly nonlinear stability analysis is carried out allowing an equation for the amplitude of disturbances to be derived. The coefficients of the terms in the amplitude equation are evaluated for axisymmetric and non-axisymmetric disturbances. The stabilizing or destabilizing effect of nonlinearity is found to depend on the cone radius. The presence of porous walls significantly influences the effect of nonlinearity, and results for three types of porous wall (regular, random and mesh microstructure) are compared.

Journal of Theoretical Biology, 2009

We develop a simple mathematical model for forced flow of culture medium through a porous scaffol... more We develop a simple mathematical model for forced flow of culture medium through a porous scaffold in a tissue-engineering bioreactor. Porous-walled hollow fibres penetrate the scaffold and act as additional sources of culture medium. The model, based on Darcy's law, is used to examine the nutrient and shear-stress distributions throughout the scaffold. We consider several configurations of fibres and inlet and outlet pipes. Compared with a numerical solution of the full Navier-Stokes equations within the complex scaffold geometry, the modelling approach is cheap, and does not require knowledge of the detailed microstructure of the particular scaffold being used. The potential of this approach is demonstrated through quantification of the effect the additional flow from the fibres has on the nutrient and shear-stress distribution.

Effects of Passive Porous Walls on Hypersonic Boundary Layers

A theoretical linear stability analysis is used to consider the effect of a porous wall on the fi... more A theoretical linear stability analysis is used to consider the effect of a porous wall on the first mode of a hypersonic boundary layer on a sharp slender cone. The effect of curvature and of the attached shock are included. The flow in the hypersonic boundary layer is coupled to the flow in the porous layer. The theoretical model of a porous wall developed by Fedorov and his co-workers is used for regular microstructures. The resulting transcendental equations are solved numerically. Neutral solutions are presented, indicating a destabilizing effect of the porous wall. The spatial growth rates determined demonstrate that the porous wall leads to a significant increase in growth rates.