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

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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Flow Classification

2-Dimensional:

Axi-symmetric:

3-Dimenstional:

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Reynolds Number Effect

The Reynolds number, Re = U l/, 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

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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

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Surface Forces

Pressure: Normal to surface

Shear Stress: Tangent to surface

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

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 onlyD = 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.

Boundary Layer Flow Along a Smooth Flat Plate

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

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.

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

*(x) = (x) – h

Laminar Boundary Layer on Flat Plate

• Blasius Solution

• Momentum Integral Method

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

Experimental Skin Friction Drag Data

09_10

Drag Coefficientof Flat Plate

with Roughness

Curve fitting ofExperimental Data

Drag Coefficient of Flat Plate

Empirical Formulas

Boundary Layer Flow Separation

When flow separation occurs, there is also pressure drag.

100% Pressure Drag

Pressure (Form) Drag due to Flow Separation

Total Profile Drag= Skin Friction Drag

+ Form Drag

09_12

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.

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)

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.

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:

Test Data of 2D Objects

Test Data ofAxi-Symmetric Objects

Test Data of 3D Objects

Recommended films:

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

Fluid Dynamics of Drag Part I-IV

Airfoil Characteristics

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