flow past immersed bodies stress and pressure integrated over body surface • drag: force component...

Download Flow Past Immersed Bodies stress and pressure integrated over body surface • Drag: Force component in the direction of upstream velocity ... Pressure drag due to flow separation

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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)


    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

    High Pressure

    Low velocity

    High Pressure

    Low velocity

    Low Pressure

    High velocity

    Low Pressure

    High velocity

    Bernoullis 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


    Lift: component

    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

    (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 = 2.5m

    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 drag

    Pressure drag

    Friction & pressure drag

    pressurefriction DDD

    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

  • Streamlining

  • 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

    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.


  • 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


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