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### Transcript of Fluid Mechanics (Fluid Mechanics (0905241) Fl O B Mechanics... Fluid Mechanics (Fluid Mechanics...

• Fluid Mechanics (0905241)Fluid Mechanics (0905241)

Fl O B di D d Lift

D E Z d Al H

Flow Over Bodies: Drag and Lift

Dr.-Eng. Zayed Al-Hamamre

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

1

Content

 Overview

 Drag and Lift

 Flow Past Objects Flow Past Objects

 Boundary Layers

 Laminar Boundary Layers

 Transitional and Turbulent Boundary Layers Transitional and Turbulent Boundary Layers

 Drag on Immersed Objects

 Lift on Immersed Objects

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

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

aerodynamics.

, g , 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 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).

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

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

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

4

• Example: Automobile Drag

Development of the Cw value for motor vehicles

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

5

External Flows: Overview Types of External Flows:

Two-Dimensional: infinitely long and of constant cross-y g sectional size and shape the flow is normal to the body. the end effects are negligible

Axisymmetric: formed by rotating their cross- sectional 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.

 The force a flowing fluid exerts on a body in the flow direction is called drag

 A fluid may exert forces and moments on a body in and about various directions

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

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• External Flows: Drag and Lift  When any body moves through a fluid, an interaction

between the body and the fluid occurs; forces at the fl id b d i t f

Pressure Distributions around an object lead to lift and drag.

fluid–body interface. Normal stresses due to the pressure,

Shear Stresses on the surface also lead to lift and drag.

D Ali d ith th FlDrag: Aligned with the Flow Lift: Normal to the Flow

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

7

Example: Automobile Drag Scion XB Porsche 911

CD = 1.0, A = 25 ft2, CDA = 25ft2 CD = 0.28, A = 10 ft2, CDA = 2.8ft2

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 = F V =1/2V3(C A) for both scales with V3! Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

8Power consumption P = FDV =1/2V3(CDA) for both scales with V3!

• 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 orshear stress distributions on the surface are as indicated, obtained either by experiment or theory, determine the lift and drag on the plate.

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

9

Example Cont.

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

10

• Example Cont.

 The friction drag is zero for a flat surface normal to flow and maximum for a flat surface The friction drag is zero for a flat surface normal to flow, and maximum for a flat surface parallel to flow

 Th d i ti l t th f t l d t th diff b t th 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.

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

11

External Flows: Flow Past Objects  The fluid velocity ranges from zero at the surface (the no-slip condition) to the free-

stream value away from the surface  The character of the flow field is a function of the shape of the body size orientation s peed 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 Medium Reynolds Number: Re = 10

Large Reynolds N b R 105

strong viscous effects, Large Boundary Layer

Number: Re = 105

Thin Boundary Layer viscous effects are negligible

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

12 Boundary layer: a thin region on the surface of a body in which viscous effects are very important and outside of which the fluid behaves essentially as if it were inviscid

• Flow Over Flat Plate :

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

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 i i b hi d h li dit is behind the cylinder.

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

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• External Flows: Flow Past Objects

Separationp

 As the Reynolds number is increased, the region ahead of the cylinder in which viscous effects are important becomes smaller,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 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 fl i i h di i f h fl

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

15flowing upstream, against the direction of the upstream flow

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.

 Th l i di i hi h b d l d k i h l h h 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

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan Tel. +962 6 535 5000 | 22888

16 The viscous effects are confined to the boundary layer and wake regions.