Section 1: Fluid flow, boundary layers, velocity profiles, drag (Reynolds number) Flashcards
SI base units of density
ρ= kg m-3
SI base unit of velocity
u= m s-1
SI base unit of acceleration
a= m s-1
Newton’s first law of motion
Unless a force acts on a body, its velocity will not change. If F = 0 then Du = 0 provides an intuitive meaning of force: a force is that agent which changes the velocity of a body
Newton’s second law of motion
The rate of change of momentum (mu) of a body, is proportional to the force that acts on it
F = m*a Force = mass x acceleration
Newton’s third law of motion
For any force exerted, there is an equal force in the opposite direction
SI base unit of viscosity
μ= kg m-1 s-1
Common method for observation of fluid dynamics
Smoke generation in air
Dye injection into water and other fluids
Define streamlines
A line that is tangential to the instantaneous velocity direction
At anyone point its tangential to the path
Fluid does not cross this line and streamlines cannot cross
Define pathlines
The trajectory or path of a given fluid particle
A record of the path a fluid particle has take (its history)
Pathlines may intersect since different particles may follow different paths at different times
Define streaklines
A streakline is the instantaneous locus or trace of all the fluid particles that pass through a given fixed point in space.
If we injected dye continuously from a fixed point – the dye would form a streakline as it passed down stream
Streaklines cannot intersect because two particles cannot occupy the same space at the same instant
What occurs to the lines of movement in steady flow
When velocity is not changing with time (steady flow) then streamlines, pathlines and streaklines are identical
Define timelines
A time line is the instantaneous location of a line of fluid particles in the flow usually the initial formed line is perpendicular to the flow boundary
Deformed timelines
If one end of the line is ahead of the other, fluid is moving faster
Changes in shape of the line tells use about relative changes in velocity
Define streamtube
A streamtube is an imaginary tube whose walls are streamlines. It may be envisaged as a bundle of streamlines
The boundary of the stream tube can’t be crossed
Just as streamlines cannot cross so the boundary of the streamtube cannot be crossed
Outside streamlines form duct boundary
Key features to form turbulence
Disorder (irreproducible in detail)
Efficient mixing
Vorticity (irregularly distributed in 3 dimensions) - eddies on varies scales included
What is turbulence ‘energy cascade’
Largest eddies have biggest kinetic energy
Continuous but irregular
Progressively decay into smaller eddies until ‘smeared out’ by viscosity
Energy reflects size of the system
Forces dominant in a high Reynolds number world
Inertial forces are dominant
Forces dominant in a low Reynolds number world
Viscous forces dominant
When velocity doesn’t change, what distribution will the flow be
Uniform flow will have a parabolic velocity distribution
Stress in Laminar flow
Viscous shear stress is transmitted through the fluid
Stress in Turbulent flow
Turbulent shear stress dominates
Define boundary layer
region of fluid next to the boundary across which the velocity of the fluid grades from that of the boundary to that of the unaffected part of the flow
Define free stream
Unaffected part of the flow
Define ‘no slip’ condition
Assumes that the speed of the fluid layer in direct contact with the boundary is identical to the velocity of this boundary
Define birefringence
Rod-like particles align when sheared and create birefringence when illuminated with polarized light
Free stream: no sheer, rods aren’t aligned so no birefringence
Boundary layer: shearing due to fluid resistance along the skin
Boundary layers always expand downstream until:
Flow passes an obstruction and viscous forces degrade shearing in boundary
Boundary layer meets another one growing from another surface
Are boundary layers laminar or turbulent
Usually start as laminar flow but as the grow become abruptly turbulent
Once the boundary layer becomes turbulent it expands more rapidly due to mixing of turbulent boundary fluid with free stream
Are boundary layers laminar or turbulent
Usually start as laminar flow but as the grow become abruptly turbulent
Once the boundary layer becomes turbulent it expands more rapidly due to mixing of turbulent boundary fluid with free stream
Define flow separation
Overall pattern of flow at fairly high Re past blunt bodies or through sharply expanding channels
Near the point where the surface of the solid boundary diverges from the direction of the mean flow the boundary layer separates or breaks away from the boundary
Zone of highly turbulent fluid in a detached boundary layer (i.e. downstream of an immersed object) is called a wake
What is pressure drag
Drag caused by separation bubbles that result net imbalance of pressure forces across surface
Main source of drag over a sphere
Skin friction
Flow past a sphere at increasing Reynolds numbers
0.14
1.5
24
100
10^2-^3
10^3-2x10^5
Re 0.14: creeping flow
Re 1.5: fore and aft symmetry lost
Re 24: small internal eddied after of sphere
Re 100: irregular eddies shed pressure drags accounts for 90% of drag, Karman Vortex street
Re 10^2-^3: Laminar wake
Re 10^3-2x10^5: Wake fully turbulent, instantaneous flow
What is ‘drag crisis’
Before: subcritical
After: supercritical
The boundary layer becomes turbulent, size of wake reduces
Drag reduces by 1/3 of previous value
Main difference before and after is the delay in separation causes reduction in size of wake
Imbalance of pressure forces on the sphere surface is much smaller and pressure drag is reduced
This reduction swamps a small increase in skin-friction drag produced by the greater length of the boundary layer and its transition
How and why reduce drag
Delay the separation of the boundary layer and hence reduce the size of the wake or ‘recirculation bubble’
Streamlined shapes are best for this
Larger wake increases drag
What is the Reynolds number at which supercritical flow occurs
> 200,000
High Re inertial world
Objects slowed by frictional resistance of water or the effects of pressure drag
A continuous application of force will lead to an increase in velocity
An episodic exertion of force can result in continuous motion
Low Re viscous world
Persistent motion require the continuous action of a force
If the force ceases, then motion stops almost instantaneously
How do bacteria get around (prokaryotes)
Rotation a rigidly helical flagellum by a wheel and axle
