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Boundary LayerIntroduction

Jasim Imranhttp://www.ce.sc.edu/DeptInfo/Members/faculty/imran.html

imran@engr.sc.edu

Department of Civil and Environmental Engineering, University of South Carolina

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Introduction to Boundary Layer

What is a Boundary Layer?

A boundary layer is defined as a relatively thinlayer of fluid that is affected by viscosity.

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Introduction to Boundary Layer

What is a Boundary Layer?

A boundary layer is defined as a relatively thinlayer of fluid that is affected by viscosity.

Typically occurs in the immediate vicinity of a

bounding surface.

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Introduction to Boundary Layer

What is a Boundary Layer?

A boundary layer is defined as a relatively thinlayer of fluid that is affected by viscosity.

Typically occurs in the immediate vicinity of a

bounding surface.

A bounding surface distorts the surrounding

flow and creates the boundary layer.

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Introduction to Boundary Layer

What is a Boundary Layer?

A boundary layer is defined as a relatively thinlayer of fluid that is affected by viscosity.

Typically occurs in the immediate vicinity of a

bounding surface.

A bounding surface distorts the surrounding

flow and creates the boundary layer.It is a phenomenon of viscous forces. Theboundary layer characteristics depends

strongly on the Reynolds Number.

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Distortion of Fluid Particles

Distortion of a fluid particle as it flows within the boundary layer. FromMunson, Okishi & Young 2005.

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Examples

In the Earths atmosphere, the planetary

boundary layer is the air layer near theground affected by diurnal heat, moisture ormomentum transfer to or from the surface.

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Examples

In the Earths atmosphere, the planetary

boundary layer is the air layer near theground affected by diurnal heat, moisture ormomentum transfer to or from the surface.

In a river flow, the entire flow depth can beconsidered to be the boundary layer.

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Flow Past a Flatplate

Character of the steady, viscous flow

past a flat plate parallel to theupstream velocity: (a) low Reynolds

number flow, (b) moderate Reynolds

number flow, (c) large Reynolds

number flow. From Munson, Young, Okishi 2005.

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Flow Past a Cylinder

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Potential flow Solution

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Real Fluid Characteristics

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Flow visualization: van Dyke 1988

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Flow visualization: van Dyke 1988

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Flow visualization: van Dyke 1988

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Importance of Boundary Layer

Why care about such a thin layer of fluid?

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Importance of Boundary Layer

Why care about such a thin layer of fluid?

Without the consideration of the boundarylayer, Fluid Mechanics is of not much practical

use!!!

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Importance of Boundary Layer

Why care about such a thin layer of fluid?

Without the consideration of the boundarylayer, Fluid Mechanics is of not much practical

use!!!Using the Shallow Concept, the equationsgoverning the boundary layer flow can be

significantly simplified and solved.

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Importance of Boundary Layer

Why care about such a thin layer of fluid?

Without the consideration of the boundarylayer, Fluid Mechanics is of not much practical

use!!!Using the Shallow Concept, the equationsgoverning the boundary layer flow can be

significantly simplified and solved.The boundary layer flow solution THEN canbe patched to the outside potential flowsolution!

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Governing Equations

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Governing Equations

Conservation of Mass

t+.V = 0

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Governing Equations

Conservation of Mass

t+.V = 0

Conservation of Momentum

dV

dt

= g p +.ij

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Governing Equations (Incompr. Fluid)

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Governing Equations (Incompr. Fluid)

Continuity

.V = 0

or

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Governing Equations (Incompr. Fluid)

Continuity

.V = 0

oru

x +

v

y +

w

z = 0

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Governing Equations (Incompr. Fluid)

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Governing Equations (Incompr. Fluid)

Momentum

dV

dt= g

p

+

2V

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Governing Equations (Incompr. Fluid)

Momentum

dV

dt= g

p

+

2V

or

du

dt

= gx 1

p

x

+

2u

x2

+2u

y2

+2u

z2

dv

dt= gy

1

p

y+

2v

x2+

2v

y2+

2v

z2

dw

dt= gz

1 p

+

2w

2+

2w

2+

2w

2