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7/28/2019 Boundary Layer Lecture 1
1/29
Boundary LayerIntroduction
Jasim Imranhttp://www.ce.sc.edu/DeptInfo/Members/faculty/imran.html
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