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EGA324
Fluid Mechanics and
Aerodynamics Refresher
403 Engineering North
2021-22
Contents of this lecture
1 Fluid mechanics refresher
– Navier-Stokes equations
– The Reynolds number
– Laminar or turbulent flow
– Other non-dimensional numbers
– Analytical solution for flow in a pipe
– Lift/Drag over bodies in relation to Reynolds number
– Wind tunnels - flow over bodies (e.g. aerofoil)
– Characteristics of flow
– Derivation of lift/drag from
2 The Aerofoil Experiment
– The subsonic AF100 wind tunnel
– Measuring pressure
– NACA foils
– Experimental measurement of pressure over the NACA0012 aerofoil
– Measurement of Lift & Drag using force transducers
• Kahoot quiz (10 mins)
Components of Fluid Mechanics
3
Fluid
Mechanics
Inviscid
Compressible
(air, acoustic)
Incompressible
(Water)
Viscous
Laminar Turbulent
Internal
(pipe/valve)
External
(aerofoil, ship)
Governing Equations (Navier-Stokes)
4
Continuity
Momentum
(F=ma)
= 0
The NS equations completely describes the flow of all fluids (steady or unsteady,
compressible or incompressible, turbulent or laminar) – however numerically the
size of the grid and the time step required are too small to resolve some of the
physics.
= −∇ + ∇2 +
Lets look at the N-S equations again with = (, , ) the velocity vector and ignoring
gravitational terms
For steady flow, the LHS (inertial terms) can be estimated as
Inertial terms of LHS =
While for the RHS, the viscous terms can be estimated as
Viscous terms of RHS = 2 ~
Therefore the ratio of LHS/RHS can be estimated as
Ratio =
∙
The ratio of the inertial to the viscous terms is called the Reynolds number and is dimensionless
The significance of the Reynolds number
Osborne Reynolds (1883) determined
by experiments in pipes that the flow
could remain Laminar if Re<2100, but
was inevitably turbulent if Re>4000.
These numbers are not absolute, and
there will always be some variation
from experiment to experiment.
Laminar or turbulent flow
Reynolds number
Ratio of inertial to viscous forces
Characteristic length taken as
• Sphere (diameter)
• Oblong (axis of length)
Similarity of flows need same geometry
and equal Reynolds number
But could change L, density and dynamic
What is the characteristic length for the Reynolds number of a foil?
Similarity and non-dimensional numbers
Reynolds number
Mach number
Prandtl number
Rayleigh number
Darcy number
Lift coefficient
Drag coefficient
Laminar flow in a pipe (analytical solution)
There is only one known analytical solution of the Navier-Stokes equations
and that is for laminar flow in a pipe.
Starting with N-S equations in cylindrical coordinates (r,θ,z), so velocity
has (, , ) terms.
