flow past immersed bodies stress and pressure integrated over body surface • drag: force component...
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Flow Past Immersed Bodies
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)
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:
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
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
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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
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
Bernoullis equation says where pressure is high, velocity will be low and vice versa.
forces are due to
parallel to flow
normal to flow
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
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 = 2.5m
2 CD = 0.28, A = 1 m2, CDA = 0.28m
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 V
Friction has two effects:
Skin friction due to shear stress at wall
Pressure drag due to flow separation
Friction & pressure drag
Total drag due to viscous effects Called Profile
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
CD of Common Geometries For many shapes, total drag CD is constant for Re > 10
CD of Common Geometries
CD of Common Geometries
Automobile Design change over
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.
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