Aero Therm

1
Aero Therm

• Lecture 18
• Solutions to Homework 3

2
Agenda

• Solutions to homework 3

3
Boundary Layer
4
Boundary Layer
5
Boundary Layer Separation
U
?
X
6
Blasius Solution
7
Blausius Solution
8
Boundary layer Limitations
Blasius Breaks down near separation
9
Boundary Layers
?
u/U
turbulent
laminar
y
Higher skin friction
10
Boundary Layer Reynolds Number
11
Turbulent Boundary Layers
12
Laminar Boundary Layer
?
x
13
Turbulent Boundary Layer
?
x
14
Boundary Layer Separation
15
Boundary Layer Separation
16
Turbulent Boundary Layers
17
Example Boundary layer
18
Example separation
19
Flow in a Inlet
Expanding flow
x
shock
Flow slows
20
Homework 3

• 1(30 points) Flow in a jet engine inlet of
  length 10 m varies as Uo(1-x/15m) A. what is
  the point in x of boundary layer separation if
  the boundary layer is laminar? B. what is the
  point in x of boundary layer separation if the
  boundary layer is Turbulent?

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Laminar separation
22
Turbulent Separation
23
Viscosity
24
Flow in a Inlet II
Straight flow
x
Growing Boundary layers
shock
Constricted flow
25
Homework 3

• 2 (30 points) A straight inlet of radius .5
  meters develops boundary layers that constrict a
  flow as the displacement thickness ? . Assuming
  no flow separation , at what point will the flow
  go supersonic if the initial flow conditions are
  M0.8 and T 373K and the boundary layer is (A.)
  Laminar (B.) Turbulent. Neglect the increase of
  viscosity with temperature and decrease of
  velocity in main stream.

26
Boundary Layers
27
Boundary layer constriction
28
Boundary Layers
29
Boundary layer constriction
30
Boundary layer constriction
31
Boundary Layers
32
Homework 3

• 2 (30 points) A straight inlet of radius .5
  meters develops boundary layers that constrict a
  flow as the displacement thickness ? . Assuming
  no flow separation , at what point will the flow
  go supersonic if the initial flow conditions are
  M0.8 and T 373K and the boundary layer is (A.)
  Laminar (B.) Turbulent. Neglect the increase of
  viscosity with temperature and decrease of
  velocity in main stream.

33
Homework 3

• 3 (15 points extra credit ) Estimate the point of
  appearance of flow separation for a turbulent
  boundary layer in the previous problem.

34
Assume Incompressional flow
35
Shocks in constricted flows
36
Shock Induced Separation