flow past immersed bodies stress and pressure integrated over body surface • drag: force component...
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Lecture-4
Flow Past Immersed Bodies
Learning objectives
After completing this lecture, you should be able to:
Identify and discuss the features of external flow
Explain the fundamental characteristics of a boundary layer, including laminar,
transitional, and turbulent regimes.
Calculate the lift and drag forces for various objects
Bodies in motion, experience fluid forces and moments.
Examples include: aircraft, automobiles, buildings, ships,
submarines, turbo machines.
Fuel economy, speed, acceleration, stability, and control are
related to the forces and moments.
Introduction: External Flows
Airplane in level steady flight:
drag = thrust & lift = weight.
Internal vs. external flows (Flow past objects is termed external flow)
Applications
air flow over aircraft and surface vehicles (aerodynamics)
wind flow around buildings
water flow about marine vehicles
water flow around marine structures
Immersed-body flows are commonly encountered in engineering studies: Aerodynamics(airplanes, rockets, projectiles), Hydrodynamics (ships, submarines, torpedos),transportation (automobiles, trucks, cycles), Wind Engineering (buildings, bridges, watertowers, wind turbines), and Ocean Engineering (buoys, breakwaters, pilings, cables, mooredinstruments).
General External Flow Characteristics
A body immersed in a moving fluid experiences a resultant force due
to the interaction between the body and the fluid surrounding it. In
many cases, the fluid far from the body is stationary and the body
moves through the fluid with velocity U (the upstream velocity).
In such a case, we can fix the coordinate system in the body and treat
the situation as fluid flowing past a stationary body with velocity U. In
most practical cases, U may be considered as uniform and constant
over time. Even with a steady, uniform upstream flow, the flow in the
vicinity of an object may be unsteady.
Flow ClassificationsA body immersed in a moving fluid experiences a resultant force due to the interactionbetween the body and the fluid surrounding it.
For a given -shaped object, the characteristics of the flow depend very strongly onvarious parameters such as size, orientation, speed, and fluid properties.
Flow classification according to the nature of the immersed body:
Two-dimensional (infinitely long and of constant cross-sectional size and shape)
Axisymmetric (formed by rotating their cross sectional shape about the axis of symmetry)
Three-dimensional (may or may not possess a line of symmetry)
Another classification based on the shape of body:
Streamlined
Blunt
A body is said to be streamlined if a conscious effort is made to alignits shape with the anticipated streamlines in the flow. Streamlinedbodies such as race cars and airplanes appear to be contoured andsleek.
Otherwise, a body (such as a building) tends to block the flow and issaid to be bluff or blunt. Usually it is much easier to force astreamlined body through a fluid, and thus streamlining has been ofgreat importance in the design of vehicles and airplanes.
Drag and Lift
When any body moves through a fluid, an interaction between the body
and the fluid occurs. This can be described in terms of the stresses-wall
shear stresses due to viscous effect and normal stresses due to the pressure
P.
Before going into the detail, its better to discuss the important terminology
Upper surface (upper side of wing): low pressure
Lower surface (underside of wing): high pressure
AIRFOIL NOMENCLATURE
Mean Chamber Line: Points halfway between upper and lower surfaces
Leading Edge: Forward point of mean chamber line
Trailing Edge: Most reward point of mean chamber line
Chord Line: Straight line connecting the leading and trailing edges
Chord, c: Distance along the chord line from leading to trailing edge
Chamber: Maximum distance between mean chamber line and chord line
Frontal area: The area you would see if you looked at the body from the direction of approach flow
Planform area: The area that you would see if you looked at the body from above
shear stress and pressure integrated over body surface
• Drag: Force component in the direction of upstream velocity
• Lift: Force normal to upstream velocity
AERODYNAMIC FORCE
Relative Wind: Direction of V∞ We used subscript ∞ to indicate far upstream conditions
Angle of Attack, a: Angle between relative wind (V∞) and chord line
Total aerodynamic force, R, can be resolved into two force components Lift, L: Component of aerodynamic force perpendicular to relative wind Drag, D: Component of aerodynamic force parallel to relative wind
Pressure Forces acting on the Airfoil
High Pressure
Low velocity
High Pressure
Low velocity
Low Pressure
High velocity
Low Pressure
High velocity
Bernoulli’s equation says where pressure is high, velocity will be low and vice versa.
Fluid dynamic
forces are due to
pressure and
viscous forces.
Drag: component
parallel to flow
direction.
Lift: component
normal to flow
direction.
Drag D is the component of force on a body acting parallel to
the direction of relative motion.
Lift L is the component of force on a body acting perpendicular
to the direction of relative motion.
Dimensional analysis: lift and drag coefficients.
• Area A can be frontal area (drag applications), plan form area
(wing aerodynamics).
• The drag coefficient is a function of object shape, Reynolds
number, Re, and relative roughness of the surface.
• CD = f (shape, Re, Surface roughness)
• Total drag on an object can be viewed as a combination of
Friction drag (CDf) and Pressure Drag (CDp).
Example: Automobile Drag
CD = 1.0, A = 2.5 m2, CDA = 2.5m2 CD = 0.28, A = 1 m2, CDA = 0.28m2
Drag force FD=1/2V2(CDA) will be ~ 10 times larger for Scion XB
Source is large CD and large projected area
Power consumption P = FDV =1/2V3(CDA) for both scales with V3!
Friction has two effects:
Skin friction due to shear stress at wall
Pressure drag due to flow separation
Friction drag
Pressure drag
Friction & pressure drag
pressurefriction DDD
Total drag due to viscous effects Called Profile
Drag
Drag due toskin friction
Drag due toseparation
Less for laminarMore for turbulent
More for laminarLess for turbulent
CD – Shape Dependence
Streamlining reduces drag by reducing FD,pressure,
Eliminate flow separation and minimize total drag FD
Streamlining
CD of Common Geometries For many shapes, total drag CD is constant for Re > 104
CD of Common Geometries
CD of Common Geometries
Automobile Design change over
the years
Reason of Using Spoiler
Cars have spoilers to increase their grip on the road. Normally the weight of a car is the
only thing that forces the tires down onto the pavement. Without spoilers, the only way
to increase the grip would be to increase the weight, or to change the compound the tire
was made out of. The only problem with increasing the weight is that it doesn't help in
turns, where you really want to grip. All that extra weight has inertia, which you have to
overcome to turn, so increasing the weight doesn't help at all. The way the spoiler
works is like an airplane wing, but upside down. The spoiler actually generates what's
called 'down force' on the body of the car.
DRAG: As Function of Reynolds Number
• For the present, we consider how the external flow and its
associated lift and drag vary as a function of Reynolds number.
• For most external flows, the characteristic length of objects are
on the order of 0.10m~10m. Typical upstream velocities are on
the order of 0.01m/s~100m/s. The resulting Reynolds number
range is approximately 10~109.
Re>100. The flows are dominated by inertial effects.
Re<1. The flows are dominated by viscous effects.
Flow Past a Flat Plate
With Re = 0.1, the viscous effects are relatively strong and the plate
affects the uniform upstream flow far ahead, above, below, and
behind the plate. In low Reynolds number flows the viscous effects
are felt far from the object in all directions.
With Re = 10, the region in which viscous effects are important
become smaller in all directions except downstream. One does not
need to travel very far ahead, above, or below the plate to reach
areas in which the viscous effects of the plate are not felt.
The streamlines are displaced from their original uniform
upstream conditions, but the displacement is not as great as for the
Re = 0.1 situation.
With Re = 107, the flow is dominated by inertial effects and the
viscous effects are negligible everywhere except in a region very
close to the plate and in the relatively thin wake region behind the
plate.
Since the fluid must stick to the solid surface, there is a thin
boundary layer region of thickness δ << l next to the plate in which
the fluid velocity changes from U to zero on the plate.
Flow Past an Circular Cylinder When Re≒0.1, the viscous effects are important several diameters in any
direction from the cylinder. A somewhat surprising characteristic of this flow is
that the streamlines are essentially symmetric about the center of the cylinder-the
streamline pattern is the same in front of the cylinder as it is behind the cylinder.
As Reynolds number is increased (Re =50), the region ahead of the cylinder in
which viscous effect are important becomes smaller, with the viscous region
extending only a short distance ahead of the cylinder.
As Reynolds number is increased (Re =50), the region ahead of the cylinder in
which viscous effect are important becomes smaller, with the viscous region
extending only a short distance ahead of the cylinder.
The flow separates from the body at the separation point.
With the increase in Reynolds number, the fluid inertia becomes more important
and at the some on the body, denoted the separation location, the fluid’s inertia is
such that it cannot follow the curved path around to the rear of the body.
Some of the fluid is actually flowing upstream,
against the direction of the upstream flow.
With larger Reynolds numbers (Re=105), the area affected by the viscous
forces is forced farther downstream until it involve only a then (δ<<D)
boundary layer on the front portion of the cylinder and an irregular, unsteady
wake region that extends far downstream of the cylinder.
The velocity gradients within the boundary layer and wake regions are much
larger than those in the remainder of the flow field.
Separation and Wake formation
Character of the drag coefficient as a function of Reynolds
number for a smooth circular cylinder and a smooth sphere.
The turbulent boundary layer travels further along the
surface into the adverse pressure gradient on the rear
portion of the cylinder before separation occurs. This
results a thinner wake ,small pressure drag ,and
sudden decrease in CD.
The drag coefficient decreases when the
boundary layer becomes turbulent.
• Wake narrows for turbulentflow since turbulentboundary layer is moreresistant to separation.
sep, lam ≈ 80º
sep,Tur ≈ 140º
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