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
Introduction: External Flows 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. 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, water towers, wind turbines), and Ocean Engineering (buoys, breakwaters, pilings, cables, moored instruments).
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 Classifications A body immersed in a moving fluid experiences a resultant force due to the interaction between the body and the fluid surrounding it. For a given -shaped object, the characteristics of the flow depend very strongly on various 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 align its shape with the anticipated streamlines in the flow. Streamlined bodies such as race cars and airplanes appear to be contoured and sleek. Otherwise, a body (such as a building) tends to block the flow and is said to be bluff or blunt. Usually it is much easier to force a streamlined body through a fluid, and thus streamlining has been of great 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 Low Pressure High velocity Low Pressure High velocity High Pressure Low 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. C D = f (shape, Re, Surface roughness) Total drag on an object can be viewed as a combination of Friction drag (C Df ) and Pressure Drag (C Dp ).
Example: Automobile Drag C D = 1.0, A = 2.5 m 2, C D A = 2.5m 2 C D = 0.28, A = 1 m 2, C D A = 0.28m 2 Drag force F D =1/2 V 2 (C D A) will be ~ 10 times larger for Scion XB Source is large C D and large projected area Power consumption P = F D V =1/2 V 3 (C D A) for both scales with V 3!
Friction has two effects: Skin friction due to shear stress at wall Pressure drag due to flow separation Friction drag D D D friction pressure Drag due to skin friction Drag due to separation Pressure drag Less for laminar More for turbulent More for laminar Less for turbulent Total drag due to viscous effects Called Profile Drag Friction & pressure drag
C D Shape Dependence
Streamlining reduces drag by reducing F D,pressure, Eliminate flow separation and minimize total drag F D
Streamlining
C D of Common Geometries For many shapes, total drag C D is constant for Re > 10 4
C D of Common Geometries
C D 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 10~10 9. 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 = 10 7, 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=10 5 ), 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 turbulent flow since turbulent boundary layer is more resistant to separation. sep, lam 80º sep,tur 140º