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