External flow, Drag and Lift Chapter 11 External flow, Drag and Lift 11.1 - Introduction 11.2 – Drag and Lift 11.3 – Friction and pressure drag

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.

Introduction In this chapter, we consider the flow of fluids over bodies that are immersed in a fluid, called external flow, with emphasis on the resulting lift and drag forces. External flow is characterized by a freely growing boundary layer surrounded by an outer flow region that involves small velocity and temperature gradients. 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.

External flow… how & what??? 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 resultant of the pressure and shear forces acting on the body is important rather than the details of the distributions of these forces along the entire 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).

Learning time…! discussion of drag and lift, and explore the concepts of pressure drag, friction drag, and flow separation. Find the drag coefficients of various two- and three-dimensional geometries encountered in practice and determine the drag force using experimentally determined drag coefficients. examine the development of the velocity boundary layer during parallel flow over a flat surface, and develop relations for the skin friction and drag coefficients for flow over flat plates, cylinders, and spheres. discuss the lift developed by airfoils and the factors that affect the lift characteristics of bodies.

Question to ponder… Which bicyclist is more likely to go faster: one who keeps his head and his body in the most upright position or one who leans down and brings his body closer to his knees? Why? Answer: The bicyclist who leans down and brings his body closer to his knees goes faster since the frontal area and thus the drag force is less in that position. The drag coefficient also goes down somewhat, but this is a secondary effect.

Another question… What is the difference between the upstream velocity and the free-stream velocity? For what types of flow are these two velocities equal to each other? Answer: The velocity of the fluid relative to the immersed solid body sufficiently far away from a body is called the free-stream velocity, V. The upstream (or approach) velocity V is the velocity of the approaching fluid far ahead of the body. These two velocities are equal if the flow is uniform and the body is small relative to the scale of the free-stream flow.

Yet another question … Explain when an external flow is two-dimensional , three-dimensional and axisymmetric. What type of flow is the flow of air over a car? Answer: The flow over a body is said to be two-dimensional when the body is very long and of constant cross-section, and the flow is normal to the body (such as the wind blowing over a long pipe perpendicular to its axis). There is no significant flow along the axis of the body. The flow along a body that possesses symmetry along an axis in the flow direction is said to be axisymmetric (such as a bullet piercing through air). Flow over a body that cannot be modeled as two-dimensional or axisymmetric is three-dimensional. The flow over a car is three-dimensional.

Streamlined and bluff body What is the difference between streamlined and bluff bodies? Is a tennis ball a streamlined or bluff body? Answer: A body is said to be streamlined if a conscious effort is made to align its shape with the anticipated streamlines in the flow. Otherwise, a body tends to block the flow, and is said to be blunt. A tennis ball is a blunt body (unless the velocity is very low and we have “creeping flow”). In creeping flow, the streamlines align themselves with the shape of any body – this is a much different regime than our normal experiences with flows in air and water. A low-drag body shape in creeping flow looks much different than a low-drag shape in high Reynolds number flow.

Drag What is drag? What causes it? Why do we usually try to minimize it?

A case study… Andy, the manager of EZ Trucking, would like to convince his boss to invest in installing air deflectors on their 18-wheelers. Research has shown that the drag coefficient, CD, is lower for an 18-wheeler with an air deflector (from 0.95 to 0.75). How can he show that the air deflector will save the company a small fortune?

Question: What is the drag exerted on the 18-wheeler with and without the air deflector? Approach: The drag force is directly proportional to the fuel consumption. Base the analysis on a frontal area, A, of 100 ft2. Assume the 18-wheeler runs at an average speed of 65 mph on the highway.

When fluid flows over an immersed body, forces are exerted on that body. The resultant force parallel to the fluid motion is referred to as the drag. Determining drag is important in many engineering applications, such as the design of automobiles, airplanes, submarines and buildings. Drag (FD) consists of both friction and pressure drag, and it is often expressed in terms of a drag coefficient (CD) as in; Eq. 11.5

where ρ is the fluid density; A is the characteristic area and V is the upstream velocity. The characteristic area can be chosen as: the projected frontal area (often used for flow over automobiles and submarines), the planform area (often used for flow over wings and hydrofoils), the wetted area (often used for flow over ships and barges).

Question … What is drag? What causes it? Why do we usually try to minimize it? Answer: The force a flowing fluid exerts on a body in the flow direction is called drag. Drag is caused by friction between the fluid and the solid surface, and the pressure difference between the front and back of the body. We try to minimize drag in order to reduce fuel consumption in vehicles, improve safety and durability of structures subjected to high winds, and to reduce noise and vibration. In some applications, such as parachuting, high drag rather than low drag is desired. When sailing efficiently, however, the lift force on the sail is more important than the drag force in propelling the boat.

Generally, the drag coefficient is determined through experiments, and it depends on parameters, such as the body shape, Reynolds number and surface roughness. The value of the drag coefficient for different body shapes subject to different flow conditions are available in the literature. Some of the drag coefficients for flow over two-dimensional and three-dimensional bodies are summarized in Tables 11-1.

Case solution… Andy, the manager of EZ Trucking, would like to convince his boss to invest in installing air deflectors on their 18-wheelers. Research has shown that the drag coefficient, CD, is lower for an 18-wheeler with an air deflector (from 0.95 to 0.75). How can he show that the air deflector will save the company a small fortune?

Question: What is the drag exerted on the 18-wheeler with and without the air deflector? Approach: The drag force is directly proportional to the fuel consumption. Base the analysis on a frontal area, A, of 100 ft2. Assume the 18-wheeler runs at an average speed of 65 mph on the highway.

Flow over a sphere At low Reynolds numbers (i.e., Re << 1), the viscous effects are important in a large area (shaded area). There is no flow separation, and the fluid is stuck to the sphere. The drag coefficient as a function of the Reynolds number is shown in the figure. At very small Reynolds numbers, Stokes has shown that the drag coefficient is a linear function of the Reynolds number, as given by (Eq. 11)

Flow over a sphere At moderate Reynolds number (103 < Re < 2×105), a boundary layer is developed near the sphere. Viscous effects are important inside the region of this boundary layer. Due to the increase of the pressure drag, the fluid can no longer stick to the sphere, and it is separated at an angle (β) of about 80o. A broad wake region is formed downstreams. The drag coefficient decreases with the Reynolds number.

Flow over a sphere As the Reynolds number is increased further (Re > 2×105), the boundary layer becomes thinner in the front of the sphere and begins its transition to turbulent. The flow separation is delayed until an angle of about 120o, and the fluid forms a relatively narrow wake region in which the flow is highly unsteady and turbulent. For turbulent boundary layer flow, the drag coefficient is decreased further (e.g., CD = 0.06 for Re = 4×105). Hence, a turbulent boundary layer develops as fluid flows past an object will reduce the drag force. 

Example: The dimples of a golf ball (i.e., the surface roughness of the object) are used to create turbulent boundary layer flow, and hence reduce the drag force.

Lift What is lift? What causes it?

A case study…

When fluid flows over an immersed body, forces will be exerted on the body. The resultant force parallel to the fluid motion is referred to as the drag while the resultant force perpendicular to the fluid motion is known as the lift.  Determining lift is obviously important in the design of airplanes, and the lift (FL) is often expressed in terms of the lift coefficient (CL) as in Coanda effect? Eq. 11.6

How the lift is produced? Take flow over an airfoil for example. The airfoil is one of the designed shapes known best for generating lift. The angle between the free stream velocity and airfoil chord line is referred to as the angle of attack (α).  How the lift is produced? Lift is produced by generating a pressure difference between the top and bottom surfaces. When flow is past a symmetric airfoil with no angle of attack (i.e., the free stream velocity is parallel to the airfoil chord line), no lift will be produced due to the symmetric flow field. In order to generate lift, either the airfoil should be non-symmetric or the angle of attack nonzero.

Question… What is lift? What causes it? Does wall shear stress contribute to the lift? Answer: The force a flowing fluid exerts on a body in the normal direction to flow that tends to move the body in that direction is called lift. It is caused by the components of the pressure and wall shear forces in the direction normal to the flow. The wall shear contributes to lift (unless the body is very slim), but its contribution is usually small. Typically the nonsymmetrical shape of the body is what causes the lift force to be produced.

Case solution…

To remember… A is ordinarily the frontal area (the area projected on a plane normal to the direction of flow) of the body. Drag Lift A is ordinarily the planform area, which is the area that would be seen by a person looking at the body from above in a direction normal to the body.

Question… What is terminal velocity? How is it determined? Answer: The force a flowing fluid exerts on a body in the normal direction to flow that tends to move the body in that direction is called lift. It is caused by the components of the pressure and wall shear forces in the direction normal to the flow. The wall shear contributes to lift (unless the body is very slim), but its contribution is usually small. Typically the nonsymmetrical shape of the body is what causes the lift force to be produced.

Friction and pressure drag The picture on the right margin of this page shows examples of air flowing past a variety of objects. The pressure drag is caused by the separation of air that is flowing over the aircraft or airfoil.

The need of streamlining… The term "separation" refers to the smooth flow of air as it closely hugs the surface of the wing then suddenly breaking free of the surface and creating a chaotic flow. The bottom shows well behaved, laminar flow (flow in layers) where the flow stays attached (close to the surface) of the object. The object just above has a laminar flow for the first half of the object and then the flow begins to separate from the surface and form many chaotic tiny vortex flows called vortices. The two objects just above them have a large region of separated flow. The greater the region of separated flow, the greater the drag. This is why airplane designers go to such effort to streamline wings and tails and fuselages — to minimize drag.

Friction drag

Friction and pressure drag