ME 408 Fluid Mechanics II Chapter 9 Flow Over Immersed Bodies

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ME 408 Fluid Mechanics II Chapter 9 Flow Over Immersed Bodies. Content. Classification of External Viscous Flow Fluid Dynamic Forces: Lift and Drag Reynolds Number Effect Boundary Layer: Laminar and Turbulent Flow Separation Experimental Drag Data Airfoil and Wing Characteristics.

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## ME 408 Fluid Mechanics II Chapter 9 Flow Over Immersed Bodies

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ME 408

Fluid Mechanics II

Chapter 9

Flow Over Immersed Bodies

Content
• Classification of External Viscous Flow
• Fluid Dynamic Forces: Lift and Drag
• Reynolds Number Effect
• Boundary Layer: Laminar and Turbulent
• Flow Separation
• Experimental Drag Data
• Airfoil and Wing Characteristics
09_01

Flow Classification

2-Dimensional:

Axi-symmetric:

3-Dimenstional:

09_01

09_04

Reynolds Number Effect

The Reynolds number,Re= U l/n , is the ratio between the inertial force and the viscous force.

Low Re: Mostly viscous flow

Moderate Re: Partial viscous flow around body

High Re: Viscous Boundary Layer near surface

09_04

09_05

Flow Past Cylinder

Low Re: Mostly viscous flow

Moderate Re: Partial viscous flow around body with separation and re-circulation flow in wake

High Re: Viscous Boundary Layer near surface till separation and wake

09_05

Surface Forces

Pressure: Normal to surface

Shear Stress: Tangent to surface

09_03

09_03

09_02

Lift and Drag

The sum of forces due to pressure distribution and skin friction (shear stress) is the resultant force on a 2-D object.

This net force can be represented by its two components:

Lift: Component normal to the flow

Drag: Component in the flow direction

09_02

E_09_01

Example 9.1 (p. 329)

Flow parallel to flat plate

Skin Friction Drag only:

D = 0.0992 lbf, L = 0

Flow normal to flat plate:

Pressure Drag only

D = 55.6 lbf, L = 0

Flow at an angle with plate:

Both Lift and Drag are present.

Drag consists of both pressure drag and skin friction drag.

E_09_01

Boundary Layer Flow Along a Smooth Flat Plate

Experimental observation:

At local Reynolds number (Rex = U x/n) around 5x105, transition from Laminar to Turbulent Boundary Layer Flow occurs. This Rex of 5x105 is known as the critical or transitional Reynolds number.

09_06
09_09

Velocity Profiles

The gradient (du/dy) of the turbulent velocity profile at the wall (y=0) is higher than that of the laminar velocity profile.

Hence skin friction drag of turbulent boundary layer is higher than that of laminar one.

09_08

Boundary layer thickness d (x): The location normal to surface at which the velocity reaches 0.99 of the velocity U in the inviscid free-stream. It increases in the x-direction along the plate.

Displacement thickness d*(x): The distance normal to the surface that the streamline passing d(x) is displaced from its original distance (h) at the leading edge of the plate. Hence,

d*(x) = d(x) – h

09_08

Laminar Boundary Layer on Flat Plate
• Blasius Solution
• Momentum Integral Method

Experimental Skin Friction Drag Data

Curve fit formula for turbulent boundary layer (Re > 500,000):

09_10

Drag Coefficient

of Flat Plate with Roughness

Curve fitting of

Experimental Data

09_10

09_01tbl

Drag Coefficient of Flat Plate

Empirical Formulas

Boundary Layer Flow Separation

When flow separation occurs,

there is also pressure drag.

Pressure (Form) Drag due to Flow Separation

100% Pressure Drag

Total Profile Drag

= Skin Friction Drag

+ Form Drag

Development of velocity profile in the boundary layer on curved surface:

Flow separation occurs when the gradient of the velocity profile at the wall is zero, forming a re-circulating wake downstream.

09_12

09_12

Wind Tunnel Tests

Force transducer behind model senses lift, drag and pitching moment directly.

Motor-controlled mechanism adjusts the model’s angle of attack.

Typical Experimental Data

Notice the sudden drop at the transition Re of 5x105 (Point E)

09_15
09_15

For Re > 5x105, the boundary is turbulent, which has a fuller velocity profile.

Flow separation is delayed, resulting in a smaller wake, and hence the pressure drag.

09_18

Adding surface roughness on circular and spherical shapes triggers turbulence at lower Re, and hence helps to reduce the drag coefficient

Benefit of Streamlining

Pressure drag is greatly reduced by preventing flow separation using a gradually tapering tail. Though skin friction increases with larger area, the total drag is much less. Hence streamlined bodies are made of smooth surfaces to reduce skin friction.

These objects have approximately the same drag:

09_14

Test Data of

Axi-Symmetric Objects

09_20

Test Data of 3D Objects

09_21

Recommended films:

http://web.mit.edu/hml/ncfmf.html

Fluid Dynamics of Drag Part I-IV

09_22

Airfoil Characteristics

09_25

09_25