Fluid Mechanics (0905241) Flow Over Bodies: Drag and Lift Dr.-Eng. Zayed dal-hamamre 1 Content Overview Drag and Lift Flow Past Objects Boundary Layers Laminar Boundary Layers Transitional and Turbulent Boundary Layers Drag on Immersed Objects Lift on Immersed Objects 2
External Flows: Overview If a body is immersed in a flow, we call it an external flow. External flows involving air are typically termed aerodynamics. Some important external flows include airplanes, motor vehicles, and flow around buildings, under water submarine. In internal flows, the entire flow field is dominated by viscous effects, while In external flow, the viscous effects are confined to a portion of the flow field such as the boundary layers and wakes. When a fluid moves over a solid body, it exerts pressure forces normal to the surface and shear forces parallel to the surface along the outer surface of the body. The component of the resultant pressure and shear forces that acts in the flow direction is called the drag force (or just drag), and the component that acts normal to the flow direction is called the lift force (or just lift). 3 External Flows: Overview Often flow modeling is used to determine the flow fields in a wind tunnel or water tank. Fuel economy, speed, acceleration, maneuverability, stability, and control are directly related to the aerodynamic/hydrodynamic forces and moments. correct design Typical quantities of interest are lift and drag acting on these objects. The flow fields and geometries for most external flow problems are too complicated to be solved analytically, and thus we have to rely on correlations based on experimental data Such testing is done in wind tunnels 4
Example: Automobile Drag Development of the C w value for motor vehicles 5 External Flows: Overview Types of External Flows: Two-Dimensional: infinitely long and of constant cross- sectional size and shape the flow is normal to the body. the end effects are negligible Axisymmetric: formed by rotating their crosssectional shape about the axis of symmetry. Three-Dimensional: may or may not possess a line of symmetry. The bodies can be classified as streamlined or blunt, tends to block the flow, buildings. Streamlined object typically move more easily through a fluid, airfoils, racing cars. A fluid may exert forces and moments on a body in and about various directions The force a flowing fluid exerts on a body in the flow direction is called drag 6
External Flows: Drag and Lift When any body moves through a fluid, an interaction between the body and the fluid occurs; forces at the fluid body bd it interface. Normal stresses due to the pressure, Pressure Distributions around an object lead to lift and drag. Shear Stresses on the surface also lead to lift and drag. Drag: Aligned with the Flow Lift: Normal to the Flow 7 Example: Automobile Drag Scion XB Porsche 911 C D = 1.0, A = 25 ft 2, C D A = 25ft 2 C D = 0.28, A = 10 ft 2, C D A = 2.8ft 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 V=1/2 V D 3 (C D A) for both scales with V 3! 8
Example Air at standard conditions flows past a flat plate as is indicated. In case a the plate is parallel to the upstream flow, and in case b it is perpendicular to the upstream flow. If the pressure and shear stress distributions on the surface are as indicated, obtained either by experiment or theory, determine the lift and drag on the plate. 9 Example Cont. 10
Example Cont. The friction drag is zero for a flat surface normal to flow, and maximum for a flat surface parallel to flow The pressure drag is proportional to the frontal area and to the difference bt between the pressures acting on the front and back of the immersed body. 11 External Flows: Flow Past Objects The fluid velocity ranges from zero at the surface (the no-slip condition) to the freestream value away from the surface The character of the flow field is a function of the shape of the body size, orientation,s peed, and fluid properties. Low Reynolds, Number: Re = 0.1 strong viscous effects, Large Boundary Layer Large Reynolds Number: Re = 10 5 Thin Boundary Layer viscous effects are negligible Medium Reynolds Number: Re = 10 Boundary layer: Chemical a thin Engineering region on Department the surface University of a body of Jordan in which Amman viscous 11942, effects Jordan are very important and outside of Tel. which +962 the 6 535 fluid 5000 behaves 22888 essentially as if it were inviscid 12
Flow Over Flat Plate : 13 External Flows: Flow Past Objects Symmetric The viscous effects are important several diameters in any direction from the cylinder. 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. 14
External Flows: Flow Past Objects Separation As the Reynolds number is increased, the region ahead of the cylinder in which viscous effects are important becomes smaller, The viscous region extending only a short distance ahead of the cylinder. The flow loses its symmetry and the flow separates from the body at the separation location With the increase in Reynolds number, the fluid inertia becomes more important and at some location 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. The result is a separation bubble behind the cylinder in which some of the fluid is actually flowing upstream, against the direction i of the upstream flow 15 External Flows: Flow Past Objects Wake At larger Reynolds numbers, the area affected by the viscous forces is forced farther downstream until it involves only a thin boundary layer on the front portion of the cylinder Irregular, unsteady perhaps turbulent wake region that extends far downstream of the cylinder. The fluid in the region outside of the boundary layer and wake region flows as if it were inviscid. The velocity gradients within the boundary layer and wake regions are much larger than those in the remainder of the flow field The viscous effects are confined to the boundary layer and wake regions. 16
Streamlining Streamlining reduces drag by reducing F D,pressure, at the cost of increasing wetted surface area and F D,friction. Goal is to eliminate flow separation and minimize total drag F D Also improves structural acoustics since separation and vortex shedding can excite structural modes. 17 Streamlining 18
Streamlining The friction drag is zero for a flat surface normal to flow, and maximum for a flat surface parallel to flow The pressure drag is proportional to the frontal area and to the difference between the pressures acting on the front and back of the immersed body. The pressure drag becomes most significant ifi when the velocity of the fluid is too high h for the fluid to be able to follow the curvature of the body, and thus the fluid separates from the body at some point and creates a very low pressure region in the back. The part of drag that is due directly to wall shear stress τ w is called the skin friction drag (or friction drag F D, friction ) since it is caused by frictional effects, The part that is due directly to pressure P is called the pressure drag (also called the form drag because of its strong dependence on the form or shape of the body) 19 Streamlining The first thought that comes to mind to reduce drag is to streamline a body in order to reduce flow separation and thus to reduce pressure drag Streamlining has opposite effects on pressure and friction drags. It decreases pressure drag by delaying boundary layer separation and thus reducing the pressure difference between the front and back of the body and increases the friction drag by increasing the surface area Optimization study to reduce the drag of a body must consider both effects and must attempt to minimize the sum of the two The minimum total drag 20
C D of Common Geometries At higher Reynolds numbers, the drag coefficients for most geometries remain essentially constant This is due to the flow at high Reynolds numbers becoming fully turbulent. 21 C D of Common Geometries 22
C D of Common Geometries 23 C D of Common Geometries 24
Example As part of the continuing efforts to reduce the drag coefficient and thus to improve the fuel efficiency of cars, the design of side rearview mirrors has changed drastically from a simple circular plate to a streamlined shape. Determine the amount of fuel and money saved per year as a result of replacing a 13-cmdiameter e flat mirror by one with a hemispherical e back. Assume the car is driven 24,000 km a year at an average speed of 95 km/h. The densities of air and gasoline are taken to be 1.20 kg/m 3 and 800 kg/m 3, respectively. The heating value of gasoline is given to be 44,000 kj/kg. Price of gasoline is $0.60/L, and the overall efficiency of the engine to be 30 percent 25 Example Cont. The amount of work done to overcome this drag force and the required energy input for a distance of 26
External Flows: Boundary Layers Turbine blades 27 External Flows: Boundary Layers divides the flow over a plate into two regions: The boundary layer region, in which the viscous effects and the velocity changes are significant, viscous shearing forces and The irrotational flow region, in which the frictional effects are negligible and the velocity remains essentially constant. For parallel flow over a flat plate, the pressure drag is zero, and thus the drag coefficient is equal to the friction drag coefficient 28
External Flows: Boundary Layers When both sides of a thin plate are subjected to flow, A becomes the total area of the top and bottom surfaces. The Reynolds number at a distance x from the leading edge of a flat plate is 29 External Flows: Boundary Layers Friction Coefficient 30
Friction Coefficient the average friction coefficient over the entire plate The local friction coefficients are higher in turbulent flow than they are in laminar flow because of the intense mixing that occurs in the turbulent boundary layer 31 External Flows: Boundary Layers 32
Transitional and Turbulent Boundary Layers Turbulent Spots in Transitional Flow No real theories for transitional boundary layers. The turbulent profiles are flatter, have a larger velocity gradient at the wall, and produce a larger boundary layer thickness than do the laminar profiles 33 Transitional and Turbulent Boundary Layers Flat Plate Drag: Analogous to Moody Chart Surface roughness, in general, increases the drag coefficient in turbulent flow. 34
Drag on Immersed Objects The critical Reynolds number for flow across a circular cylinder or sphere is about the fluid completely wraps around the cylinder and the two arms of the fluid meet on the rear side of the cylinder in an orderly manner. At higher velocities, The fluid still hugs the cylinder on the frontal side, but it is too fast to remain attached to the surface as it approaches the top (or bottom) of the cylinder. As a result, the boundary layer detaches from the surface, forming a separation region behind the cylinder Flow in the wake region is characterized by periodic vortex formation and pressures much lower than the stagnation point pressure. 35 The high pressure in the vicinity of the stagnation point and the low pressure on the opposite side in the wake produce a net force on the body in the direction of flow. The drag force is primarily due to friction drag at low Reynolds numbers (Re < 10) and to pressure drag at high Reynolds numbers (Re > 5000). 36
Drag on Immersed Objects Drag on a Smooth Sphere and Cylinder: 37 Drag on a Smooth Sphere and Cylinder 38
Drag on a Smooth Sphere and Cylinder 39 Drag on Immersed Objects If there were not viscous effects acting on an object there would be no friction drag nor any pressure drag. Viscosity causes friction and separation which causes pressure drag. Friction Drag: the part of drag due directly to the shear stress Pressure Drag/Form Drag: the part of drag due directly to the pressure The Drag Coefficient is highly dependent on shape and the Reynolds Number: At the same Reynolds number, the above shapes have the same amount of drag. 40
Drag on Immersed Objects For small Reynolds Number flows, the coefficient of drag varies inversely with the Reynolds Number, Re < 1. 41 Effect of Surface Roughness This is done by tripping the boundary layer into turbulence at a lower Reynolds number, Chemical and thus Engineering causing Department the fluid University to close of in Jordan behind Amman the body, 11942, narrowing Jordan the wake Tel. and +962 reducing 6 535 5000 pressure 22888 drag onsiderably. 42
Effect of Surface Roughness For blunt bodies such as a circular cylinder or sphere, an increase in the surface roughness may actually decrease the drag coefficient This is done by tripping i the boundary layer into turbulence at a lower Reynolds number, and thus causing the fluid to close in behind the body, narrowing the wake and reducing pressure drag considerably This results in a much smaller drag coefficient and thus drag force for a rough-surfaced cylinder or sphere in a certain range of Reynolds number compared to a smooth one of identical size at the same velocity 43 Drag on Immersed Objects 44
Drag on Immersed Objects Shock waves, which cannot exist in subsonic flows, provide a mechanism for the generation of drag that is not present in the relatively low-speed subsonic flows If the velocity of the object is sufficiently large, compressibility effects become important The Mach number and Reynolds number effects are often closely connected because both are directly proportional to the upstream velocity. Independent for Ma < 0.5 Strongly dependent 45 Drag on Immersed Objects blunt and sharp bodies This behavior is due to the nature of the shock wave structure and the accompanying flow separation. The leading edges of wings for subsonic aircraft are usually quite rounded and blunt, while those of supersonic aircraft tend to be quite pointed and sharp 46
Drag on Immersed Objects Froude number is a ratio of the free-stream speed to a typical wave speed on the interface of two fluids, such as the surface of the ocean 47 Example Engine oil at 40 C flows over a 5-m-long flat plate with a free-stream velocity of 2 m/s. Determine the drag force acting on the plate per unit width. laminar flow over the entire plate, and the average friction coefficient 48
Example A 2.2-cm-outer-diameter pipe is to span across a river at a 30-m-wide section while being completely immersed in water. The average flow velocity of water is 4 m/s and the water temperature is 15 C C. Determine the drag force exerted on the pipe by the river. C D = 1.0. 49 Example 50
Example Cont. 51 Example 52
Lift on Immersed Objects The component of the resultant pressure and shear forces that acts normal to the flow direction is called the lift force (or just lift). A typical device designed to produce lift does so by generating a pressure distribution that is different on the top and bottom surfaces V is the upstream velocity of the fluid (or, equivalently, the velocity of a flying body in a quiescent fluid). Lift is generated because the flow velocity at the top surface is higher, and thus the pressure on that surface is lower Because of the asymmetry of the nonsymmetric airfoil,the il pressure distributions on the upper and lower surfaces are different,and a lift is produced even with the angle between the upstream flow and the axis of the object 53 Lift on Immersed Objects Flow starts out with no lift, but the lower fluid stream separates at the trailing edge when the velocity reaches a certain value. This forces the separated upper fluid stream to close in at the trailing edge, initiating clockwise circulation around the airfoil. This clockwise circulation increases the velocity of the upper stream while decreasing that of the lower stream, causing lift A starting vortex of opposite sign (counterclockwise circulation) is then shed downstream and smooth streamlined flow is established over the airfoil 54
Lift on Immersed Objects since roughness affects the wall shear, not the pressure, Most common lift-generating devices i.e., airfoils, fans, spoilers on cars, etc. operate in the large Reynolds number range. Viscous effects to lift is usually negligible since the bodies are streamlined, and wall shear is parallel to the surfaces of such devices and thus nearly normal to the direction of lift The most important parameter that affects the lift coefficient is the shape of the object 55 Lift on Immersed Objects Airfoils are specifically designed to generate lift while keeping the drag at a minimum The spoilers s and inverted ed airfoils on racing cars are designed ed for the opposite purpose pose of avoiding lift or even generating negative lift to improve traction and control Most lift generating devices are not symmetrical. Lift can be generated by adjusting the angel of attack of the object. Lift and drag coefficients i of wings are dependent d on angle of attack. At large angles of attack, the boundary layer separates and the wing stalls. The average lift per unit planform area F L /A is called the wing loading, which is simply the ratio of the weight of the aircraft to the planform area of the wings (since lift equals the weight during flying at constant altitude) 56
Lift on Immersed Objects The lift acting on an airfoil can be determined by simply integrating the pressure distribution around the airfoil ignoring the very thin boundary layer on the airfoil (zero vorticity, irrotational flow) Net viscous forces are zero for flow past an airfoil il since the pressure changes in the flow direction along the surface, but it remains essentially constant through the boundary layer in a direction normal to the surface In many lift-generating i devices the important quantity is the ratio of the lift to drag developed, To change the lift and drag characteristics of an airfoil is to change the angle of attack. This represents a change in the shape of the object. 57 Lift on Immersed Objects In general, the lift coefficient increases and the drag coefficient decreases with an increase in aspect ratio 58
Lift on Immersed Objects Other shape changes can be used to alter the lift and drag when desirable. In modern airplanes it is common to utilize leading edge and trailing edge flaps i.e. change the shape of the airfoil il by the use of movable leading edge and trailing edge flaps 59 Lift on Immersed Objects High-performance airfoils generate lift that is perhaps 100 or more times greater than their drag The minimum flight velocity can be determined from the requirement that the total weight Wof the aircraft be equal to lift and 60
Lift Generated by Spinning When the ball is not spinning, the lift is zero because of top bottom symmetry. But when the cylinder is rotated about its axis, the cylinder drags some fluid around because of the no-slip condition and the flow field reflects the superposition of the spinning and nonspinning flows. The stagnation points shift down, and the flow is no longer symmetric about the horizontal plane that passes through the center of the cylinder. The average pressure on the upper half is less than the average pressure at the lower half 61 Lift Generated by Spinning C L strongly depends on rate of rotation. The effect of rate of rotation on C D is small. Baseball, golf, soccer, tennis players utilize spin. Lift generated by rotation is called The Magnus Effect. 62
Example 63 Example Cont. 64
Example Cont. 65 Example A commercial airplane has a total mass of 70,000 kg and a wing planform area of 150 m 2. The plane has a cruising speed of 558 km/h and a cruising altitude of 12,000 m, where the air density is 0.312 kg/m3. The plane has double-slotted flaps for use during takeoff and landing, but it cruises with all flaps retracted. Assuming the lift and the drag characteristics of the wings can be approximated by NACA 23012, determine (a) the minimum safe speed for takeoff and landing with and without extending the flaps, (b) the angle of attack to cruise steadily at the cruising altitude, and (c) the power that needs to be supplied to provide enough thrus to overcome wing drag. 66
Example tennis ball with a mass of 0.125 lbm and a diameter of 2.52 in is hit at 45 mi/h with a backspin of 4800 rpm. Determine if the ball will fall or rise under the combined effect of gravity and lift due to spinning shortly after being hit in air at 1 atm and 80 F F. The translational and angular velocities of the ball are 67 Example Cont. The ball will drop under the combined effect of gravity and lift due to spinning 68