1. Chapter 9: Flow over bodies; Lift and Drag
Ms SITI KAMARIAH BINTI MD SA’AT
B.Eng Hons(Civil-Env.), M.Eng (Civil- Wastewater) Engineering
School of Bioprocess Engineering

2. Objectives
Have an intuitive understanding of the various physical phenomena such as drag, friction and pressure drag, drag reduction, and lift.
Calculate the drag force associated with flow over common geometries.
Understand the effects of flow regime on the drag coefficients associated with flow over cylinders and spheres
Understand the fundamentals of flow over airfoils, and calculate the drag and lift forces acting on airfoils.

3. External Flow
Flow of fluid over bodies that are immersed in a fluid involve External Flows.
Characterized by freely growing boundary layer surrounded by an outer flow region that involves small velocity and temperature gradients.
The viscous effects are confined to a portion of the flow field such as boundary layer.
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.

4. Introduction
Fluid flow over bodies frequent occurs in practice and physical phenomena:
Drag force acting on automobile, power lines, trees and underwater pipeline
The lift development by airplane wings
Upward draft of rain, snow and dust particles in high winds
The transportation of red blood cells by blood flow
The vibration and noise generated by bodies moving in a fluid
Power generated by wing turbines and...etc

5. Drag
The force flowing fluid exerts on a body in the flow direction is called drag.
The drag force can be measured directly by simply attaching the body subjected to fluid flow to a calibrated spring and measuring the displacement in flow direction (like measuring weight with a spring scale). Example: using drag-measuring device called drag balance-using flexible beams fitted with strain gages to measure the drag electronically.

6. Drag
Drag usually an desireble effect, like friction  we need to minimize it
Reduction of drag associated with:
Reduction of fuel consumption in automobile, aircraft and submarines
Improved safety and durability of structures subjected to high winds and
Reduction of noise and vibration

7. Drag
In some cases, drag produce very beneficial effect and we try to maximize it.
Example
Friction is a life saver in brakes of automobiles
Drag makes possible for people to parachute
For pollens to fly to distant locations
For all of us enjoy the waves of the ocean
Relaxing movement of the leaves in trees

8. Drag and lift
Both of pressure force and wall shear force on the surface in the direction of flow is called drag force.
The components of the pressure and wall shear force in the direction normal to the flow tend to move body in that direction and its sum is called lift.

9. Drag and Lift For 2-D flow: For 3-D
Drag: component parallel to flow direction.
Lift: component normal to flow direction.
For 3-D
There are also side force component in the direction normal to page tend to moves the body in that direction

10. The fluid flow also generated moment and cause the body rotate
The moment about the flow direction is called ‘the rolling moment’
The moment about lift direction is called ‘the yawing moment’
The moment about the side force direction is called ‘the pitching moment’

11. For bodies had possed symetry about lift-drag plane such as car, airplane and ships, the side force, the yawing moment and the rolling moment = 0 when the wind and wave force are aligned with the body. The remain for bodies are drag and lift force and the pitching moment.
For axisymetry bodies aligned with the flow, such as bullet, the only force exerted by a fluid on the body is a drag force.

12. Drag and Lift
The pressure, P and shear force,τ acting on a differential area, dA on the surface are PdA and dA respectively.
The diffrential drag force and the lift force acting on dA in 2-D flows are:

13. Drag and Lift
Lift and drag forces can be found by integrating pressure and wall-shear stress.

14. Drag Force Equation
The function of density  and velocity V and the size, shape and orientation of body. Instead it is convenient to work with π group that present drag characteristics.

15. Drag force coefficient, CD
Values of CD usually found by experiment. For example:
drag force, FD can be measured using a force balance in wind tunnel. Then CD can be calculated.

16. Drag force coefficient, CD
From the equation, the drag force is related to 4 variables
Shape of object because the shape is characterized by value of CD
The size of object because the size is characterized by the frontial area, A
Density of fluid,ρ
The speed of fluid squared, v

17. Friction and Pressure Drag
Pressure drag = Portion of the total drag force associated with the pressure distribution
Friction drag = Portion of the total drag force that is associated with the viscous shear-stress distribution

18. Friction and Pressure Drag
Fluid dynamic forces are comprised of pressure and friction effects.
Often useful to decompose,
FD = FD,friction + FD,pressure
CD = CD,friction + CD,pressure
This forms the basis of ship model testing where it is assumed that
CD,pressure = f(Fr)
CD,friction = f(Re)
Friction drag
Pressure drag
Friction & pressure drag

19. Friction and Pressure Drag

20. Friction drag
Reynold number (Re) is inversely proportional to the viscosity of fluid. At higher Re, the contribution of friction is less or can be negligible.
The friction drag also porportional to surface area. So bodies with a larger surface area experient a larger friction drag.
The friction drag coeeficient is independent to surface roughness in laminar flow, but is a strong friction of surface roughness in turbulent floe due to surface roughness elements protruding further into the boundary layer.
The friction drag coefficeinet is analogous to the friction factor in pipe flow and its factor depend on flow regime.

21. Pressure drag
The pressure drag is proportional to the frontal area and to the difference between the pressure acting on the front and back of the immerse body.  the pressure drag is usually dominant for blunt bodies, small for streamlined bodies such as airfoil and zero for thin plated parallel to the flow
Becomes most significant when velocity is too high.

22. Example:
The drag coefficient of a car at design condition of 1 atm, 20oC and 96 km/h is to be determined experimentallt in a large wind tunnel in a full scale test. The frontial area of the car is 2 m2. If the force acting on the car in flow direction is mesured to 300N, determine the drag coefficient.

23. Drag and Lift
For applications such as tapered wings, CL and CD may be a function of span location. For these applications, a local CL,x and CD,x are introduced and the total lift and drag is determined by integration over the span L

24. Drag Coefficients of common geometries
Depend on Re number especially for Re<104. At higher Re number, the drag coefficient for most geometry remain constant  the flow become fully turbulent. However for rounded bodies (circular cylinder and spheres), the drag coefficient are usually application to flows at high Re number.
The drag coefficient exhibit different behavior in low (creeping), moderate (laminar) and high (turbulent) region of Re number.

25. Drag Coefficients of common geometries
For, Re < 1 is called creeping flow and fluid wrap around the bodies smoothly. The drag coefficient in this case is inversly proportional to the Re number.
For sphere
CD= 24/Re
then FD = CD A ρv2/2 =
 known as Stokes Law

26. The drag coefficients for low Reynolds number flows past some other geometries are given in figure.
Note that at low Reynolds numbers, the shape of the body does not have a major influence on the drag coefficient.

27. CD of Common Geometries

28. CD of Common Geometries

29. CD of Common Geometries

30. CD of Common Geometries
The variation of drag coefficient of long elliptical cylinder with aspect ratio.

31. CD of Cylinder and Sphere

32. Example: Drag force on a cylinder
A verticle cylinder that is 30m high and 30cm diameter is being used to support a tv transmitting antenna. Find the drag force acting on the cylinder and the bending moment at its base. The wind speed is 35 m/s, the air pressure is 1 atm and the temperature is 20oC (ρ= 1.2 kg/m3, μ = 1.81 x 10-5 N s/m2)
Ans:
Calculate Re
CD from Figure 11-12
Calculate FD
Calculate moment at base, M = FD.L/2

33. Re = ρVD/μ = 7.0 x 105
From Figure 11-12, CD = 0.2
Drag force = 1323 N
Moment at the base = 19,800 N.m

34. Drag Coefficient of vehicles
The term drag coefficient is commonly used in various area of daily life.
For example:
Car manufacturer try to attract consumers by pointing out the low drag coefficient of their cars.
The drag coefficient of vehicles range from 1.0 for large semitrailer, 0.4 for minivan and 0.3 for passanger car.
In general, the more blunt the vehicle, the higher the drag coefficient.

35. Automobile Drag Scion XB Porsche 911 CD = 1.0, A = 25 ft2, CDA = 25ft2
Drag force FD=1/2V2(CDA) will be ~ 10 times larger for Scion XB
Source is large CD and large projected area
Power consumption P = FDV =1/2V3(CDA) for both scales with V3!

36. Drag Coefficient of vehicles
As rule of thumb, the percentage of fuel saving due to the reduced drag is about half the percentage of drag reduction.
When the effect of the road on air-motion is disregarded, the ideal shape of a vehicle is the basic teardrop with the coefficient of about 0.1 for the turbulent flow case.
The CD for well-built racing cars nowadays is about 0.2 but this achived after making comfort of drivers become secondary consideration.
The CD for passager car current value is 0.3.

37. Drag Coefficient of vehicles
When travelling in group, a sneaky way to reduce drag is drafting approaching moving body from behind and being drafted into the low pressure region in the rear of the body. The drag coeff. Can be reduced from 0.9 to 0.5 by drafting.
We also can reduce drag of vehicles and fuel consumption by more conscientious driver.
Driving over speed limit on highways not only increase the chances of getting into accident or speeding ticket but also increase amount of fuel consumption. Drive at moderate speed is safe and economical.

38. Drag Coefficient of vehicles
Driving with the open window also increase drag and fuel consumption.
At highway speeds, a driver can save fuel in hot-weathered by running on aircond. Usually the turbulence and additional drag generated by open windows consume more fuel than does the aircond.
Also, anything extents from the car even an arm, increase drag coeff.

39. Reducing Drag by Streamlining
An engineer can design a body shape to minimize the drag force. The process is called a ‘streamlining’ and is often focused on reducing from drag.
has opposite effect on friction and pressure force. It is decrease pressure force and increase friction drag by the surface.
Produce minimum drag at high Re number and will probably not produce minuimum drag at very low Re number.

40. Streamlining

41. Streamlining
Streamlining reduces drag by reducing FD,pressure, at the cost of increasing wetted surface area and FD,friction.
Goal is to eliminate flow separation and minimize total drag FD
Also improves structural acoustics since separation and vortex shedding can excite structural modes.

42. Streamlining via Active Flow Control
Pneumatic controls for blowing air from slots: reduces drag, improves fuel economy for heavy trucks (Dr. Robert Englar, Georgia Tech Research Institute).

43. Biological System and Drag
The concept of drag has also important consequences for biological systems.
For example:
The body of fist that swim fast for long distance such as dolphin taht are highly stramlined to minimize drag. Dolphine has CD = So its not surprise that we build submarines that mimic large fish
Tropical fist with fascinating beauty and elegance like arowana, flower horns swim gracefully short distance, not in high speed.

44. Biological System and Drag
2. Bird – reducing drag by extenting their beak forward and folding their feet backward during flight.
Airplane (look like a bird birds) retract their wheel after take off to reduce drag and thus reduce fuel consumption.
3. The flexible structure of plants enables them to reduce drag at high winds by changing their shape.
For example leaves curl into a conical shape at high wind speed; branch cluster to reduce drag; flexible truks bend under the influence of the wind to reduce drag and the bending moment is lowered by reducing frontal area.

45. Boundary layer
Region adjacent to a surface over which the velocity changes from the free-stream value to the zero at the surface. This region occur because of the viscosity of the fluid. The velocity gradient at the surface is responsible for viscous shear stress and surface resistance.
The figure in next slide show the boundary layer for flow over a flat plate.

46. Flat Plate Drag
Drag on flat plate is solely due to friction created by laminar, transitional, and turbulent boundary layers.

47. Flat Plate Drag
Local friction coefficient
Laminar:
Turbulent:
Average friction coefficient
For some cases, plate is long enough for turbulent flow, but not long enough to neglect laminar portion

48. Effect of Roughness Similar to Moody Chart for pipe flow
Laminar flow unaffected by roughness
Turbulent flow significantly affected: Cf can increase by 7x for a given Re

49. Effect of Surface Roughness

50. Example: Drag force acting on a pipe in the river
A 2.2cm outer diameter pipe is to span across a river at 30-m wide section while being completely immmersed in water. The average flow velocity of water is 4 m/s and the water temperature is 15oC. Determine the drag force exerted on the pipe by the river.

52. Lift
Lift is the net force (due to pressure and viscous forces) perpendicular to flow direction.
Lift coefficient
A=bc is the platform area

53. Computing Lift
Potential-flow approximation gives accurate CL for angles of attack below stall: boundary layer can be neglected.
Thin-foil theory: superposition of uniform stream and vortices on mean camber line.
Java-applet panel codes available online:
Kutta condition required at trailing edge: fixes stagnation pt at TE.

54. Effect of Angle of Attack
Thin-foil theory shows that CL≈2 for  < stall
Therefore, lift increases linearly with 
Objective for most applications is to achieve maximum CL/CD ratio.
CD determined from wind-tunnel or CFD (BLE or NSE).
CL/CD increases (up to order 100) until stall.

55. Effect of Foil Shape
Thickness and camber influences pressure distribution (and load distribution) and location of flow separation.
Foil database compiled by Selig (UIUC)

56. Effect of Foil Shape Figures from NPS airfoil java applet.
Color contours of pressure field
Streamlines through velocity field
Plot of surface pressure
Camber and thickness shown to have large impact on flow field.

57. End Effects of Wing Tips
Tip vortex created by leakage of flow from high-pressure side to low-pressure side of wing.
Tip vortices from heavy aircraft persist far downstream and pose danger to light aircraft. Also sets takeoff and landing separation at busy airports.

58. End Effects of Wing Tips
Tip effects can be reduced by attaching endplates or winglets.
Trade-off between reducing induced drag and increasing friction drag.
Wing-tip feathers on some birds serve the same function.

59. Lift Generated by Spinning
Superposition of Uniform stream + Doublet + Vortex

60. Lift Generated by Spinning
CL strongly depends on rate of rotation.
The effect of rate of rotation on CD is small.
Baseball, golf, soccer, tennis players utilize spin.
Lift generated by rotation is called The Magnus Effect.