CP502 Advanced Fluid Mechanics Flow of Viscous Fluids and Boundary Layer Flow [ 10 Lectures + 3 Tutorials ] Computational Fluid dynamics (CFD) project Midsemester (open book) examination
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Jan 29, 2016
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CP502 Advanced Fluid Mechanics
Flow of Viscous Fluids and Boundary Layer Flow
[ 10 Lectures + 3 Tutorials ]
Computational Fluid dynamics (CFD) projectMidsemester (open book) examination
R. Shanthini 18 Aug 2010
What do we mean by ‘Fluid’? Physically: liquids or gases
Mathematically: A vector field u (represents the fluid velocity)
A scalar field p (represents the fluid pressure)
fluid density (d) and fluid viscosity (v)
R. Shanthini 18 Aug 2010
Recalling vector operations Del Operator:
Laplacian Operator:
Gradient:
Vector Gradient:
Divergence:
Directional Derivative:
R. Shanthini 18 Aug 2010
Continuity equation for incompressible (constant density) flow
where u is the velocity vector
u, v, w are velocities in x, y, and z directions
- derived from conservation of mass
R. Shanthini 18 Aug 2010
ρυ
Navier-Stokes equation for incompressible flow of Newtonian (constant viscosity) fluid
- derived from conservation of momentum
kinematic viscosity
(constant)density
(constant)pressure
external force(such as gravity)
R. Shanthini 18 Aug 2010
Navier-Stokes equation for incompressible flow of Newtonian (constant viscosity) fluid
- derived from conservation of momentum
ρυ
ρυ
R. Shanthini 18 Aug 2010
Navier-Stokes equation for incompressible flow of Newtonian (constant viscosity) fluid
- derived from conservation of momentum
ρυ
Acceleration term: change of velocity
with time
R. Shanthini 18 Aug 2010
Navier-Stokes equation for incompressible flow of Newtonian (constant viscosity) fluid
- derived from conservation of momentum
ρυ
Advection term: force exerted on a
particle of fluid by the other particles of fluid
surrounding it
R. Shanthini 18 Aug 2010
Navier-Stokes equation for incompressible flow of Newtonian (constant viscosity) fluid
- derived from conservation of momentum
ρυ
viscosity (constant) controlled
velocity diffusion term: (this term describes how fluid motion is
damped) Highly viscous fluids stick together (honey)
Low-viscosity fluids flow freely (air)
R. Shanthini 18 Aug 2010
Navier-Stokes equation for incompressible flow of Newtonian (constant viscosity) fluid
- derived from conservation of momentum
ρυ
Pressure term: Fluid flows in the
direction of largest change
in pressure
R. Shanthini 18 Aug 2010
Navier-Stokes equation for incompressible flow of Newtonian (constant viscosity) fluid
- derived from conservation of momentum
ρυ
Body force term: external forces that act
on the fluid (such as gravity,
electromagnetic, etc.)
R. Shanthini 18 Aug 2010
Navier-Stokes equation for incompressible flow of Newtonian (constant viscosity) fluid
- derived from conservation of momentum
ρυ
change in
velocitywith time
advection diffusion pressurebody force= + + +
R. Shanthini 18 Aug 2010
Continuity and Navier-Stokes equations for incompressible flow of Newtonian fluid
ρυ
R. Shanthini 18 Aug 2010
Continuity and Navier-Stokes equations for incompressible flow of Newtonian fluidin Cartesian coordinates
Continuity:
Navier-Stokes:x - component:
y - component:
z - component:
R. Shanthini 18 Aug 2010
Steady, incompressible flow of Newtonian fluid in an infinite channel with stationery plates- fully developed plane Poiseuille flow
Fixed plate
Fixed plate
Fluid flow direction h
x
y
Steady, incompressible flow of Newtonian fluid in an infinite channel with one plate moving at uniform velocity
- fully developed plane Couette flow
Fixed plate
Moving plate
h
x
yFluid flow direction
R. Shanthini 18 Aug 2010
Continuity and Navier-Stokes equations for incompressible flow of Newtonian fluidin cylindrical coordinates
Continuity:
Navier-Stokes:Radial component:
Tangential component:
Axial component:
R. Shanthini 18 Aug 2010
Steady, incompressible flow of Newtonian fluid in a pipe- fully developed pipe Poisuille flow
Fixed pipe
z
r
Fluid flow direction 2a 2a
φ
R. Shanthini 18 Aug 2010
Steady, incompressible flow of Newtonian fluid between a stationary outer cylinder and a rotating inner cylinder- fully developed pipe Couette flow
φ
aΩ
ab
r