2. momentum transport- theory part 1
TRANSCRIPT
-
7/28/2019 2. Momentum Transport- Theory Part 1
1/16
ADVANCED TRANSPORT
PROCESSES /
TRANSPORT PHENOMENA
CCB/CBB 3033
Momentum Transport Balance The Theory
Part 1
2
Course outcomeCLO1
Explain the theoretical aspect of momentum,
mass and energy transport
-
7/28/2019 2. Momentum Transport- Theory Part 1
2/16
3
Lesson outcomes
5. State two mechanism for momentum transport
6. Express the molecular transport term
7. Express and the viscous stress term in 3-
dimensional orientation (cartesan coordinates)
ijijij p +=
=vv +=vv +
4
Lesson outcome 5 and 65. State two mechanism for momentum transport
6. Express and explain the molecular transport
term
7. Express and explain the viscous stress term in
3-dimensional orientation (cartesancoordinates)
=vv +=vv +
ijijij p +=
-
7/28/2019 2. Momentum Transport- Theory Part 1
3/16
5
Momentum Transport Balance
There are two mechanisms :
1. Molecular transport.
2. Convective transport
Combined momentum flux
= molecular stress+ convective stress
6
Momentum Transport Balance
There are two mechanisms :
1. Molecular transport.
2. Convective transport
Convective transport
Molecular transport
vv
= p+
Combined momentum flux = vv +
-
7/28/2019 2. Momentum Transport- Theory Part 1
4/16
7
Molecular Transport Expression (1.2)
+= p
MolecularMolecularMolecularMolecular
stressesstressesstressesstresses
StaticStaticStaticStatic
pressurepressurepressurepressure
viscousviscousviscousviscous
stressstressstressstress
8
Molecular Transport Expression (1.2)
ijijij p +=i and j is the designation on x,y,z
Recall!
dy
dv xyx
ij
=
Force in thex-direction on a
unit area perpendicular to
y-direction
-
7/28/2019 2. Momentum Transport- Theory Part 1
5/16
9
Molecular Transport Expression (1.2)
+= p
Kronecker delta
10
Molecular Transport Expression (1.2)
ij
i= j , =1; i not equal to j, =0
xx = 1, yy = 1, zz = 1
xy = 0, xz = 0, yz = 0 etc
Kronecker delta,
-
7/28/2019 2. Momentum Transport- Theory Part 1
6/16
11
Lesson outcome 7
5. State two mechanism for momentum transport
6. Express and explain the molecular transport
term
7. Express and explain the viscous stress term in
3-dimensional orientation (cartesan
coordinates)
12
Molecular Motion
Lets imagine a molecule as a particle
Particle
motion in
tornado
-
7/28/2019 2. Momentum Transport- Theory Part 1
7/16
13
Molecular Motion
Lets imagine a molecule as a particleFloating
ball
14
Molecular Transport
Yes!
Split into 3D
components
x
z
y
-
7/28/2019 2. Momentum Transport- Theory Part 1
8/16
15
Molecular Transport Expression (1.2)
,Viscous Stress (Force) on a unit area perpendicular to x/y/z-direction
16
Molecular Transport Expression (1.2)
There could be 3 components of the movement; vx, vy and vz
-
7/28/2019 2. Momentum Transport- Theory Part 1
9/16
17
Viscous Stress
ijijij p +=MolecularMolecularMolecularMolecular
stressesstressesstressesstresses StaticStaticStaticStatic
pressurepressurepressurepressure
i and j is the designation on x,y,z
xy xx xz
yy yx yz
zy zx zzx
z
y
18
Viscous stress in cartesan coordinates
Viscous force per unit area in the x-direction on a plane
perpendicular to x-direction
xx
xy
Viscous force per unit area in the y-direction on a plane
perpendicular to x-direction
xz
Viscous force per unit area in the z-direction on a plane
perpendicular to x-direction
Area
perpendicular
to x
-
7/28/2019 2. Momentum Transport- Theory Part 1
10/16
19
Viscous stress in cartesan coordinates
Viscous force per unit area in the x-direction on a plane
perpendicular to y-direction
yy
yx
Viscous force per unit area in the y-direction on a plane
perpendicular to y-direction
yz
Viscous force per unit area in the z-direction on a planeperpendicular to y-direction
Areaperpendicular
to y
20
Viscous stress in cartesan coordinates
Viscous force per unit area in the x-direction on a plane
perpendicular to z-direction
zz
zx
Viscous force per unit area in the y-direction on a plane
perpendicular to z-direction
zy
Viscous force per unit area in the z-direction on a plane
perpendicular to z-direction
Area
perpendicular
to z
-
7/28/2019 2. Momentum Transport- Theory Part 1
11/16
21
Viscous stress in cartesan coordinates
Velocity in thej-direction on a unit area perpendicular to i-direction
+
=
j
i
i
j
ijd
v
d
v
22
Viscous stress in cartesan coordinates
Viscous force per unit area in the x-direction on a plane
perpendicular to x-direction
x
v
x
v
x
v xxxxx
=
+
= 2
+
=
y
v
x
vxy
xy
Viscous force per unit area in the y-direction on a plane
perpendicular to x-direction
+
=
z
v
x
v xzxz
Viscous force per unit area in the z-direction on a plane
perpendicular to x-direction
Area
perpendicular
to x
-
7/28/2019 2. Momentum Transport- Theory Part 1
12/16
23
Viscous stress in cartesan coordinates
Viscous force per unit area in the x-direction on a plane
perpendicular to y-direction
y
v
y
v
y
v yyyyy
=
+
= 2
+
=
x
v
y
v yxyx
Viscous force per unit area in the y-direction on a plane
perpendicular to y-direction
+
=
z
v
y
v yzyz
Viscous force per unit area in the z-direction on a planeperpendicular to y-direction
Areaperpendicular
to y
24
Viscous stress in cartesan coordinates
Viscous force per unit area in the x-direction on a plane
perpendicular to z-direction
z
v
z
v
z
v zzzzz
=
+
= 2
+
=
x
v
z
v zxzx
Viscous force per unit area in the y-direction on a plane
perpendicular to z-direction
+
=
y
v
z
vzy
zy
Viscous force per unit area in the z-direction on a plane
perpendicular to z-direction
Area
perpendicular
to z
-
7/28/2019 2. Momentum Transport- Theory Part 1
13/16
25
Viscous stress in cartesan coordinates
Viscous Stress
Shear Stress Normal Stress
Direction!
xy
xx
xz
yy yx yz
zy zx zz
26
Viscous stress in cartesan coordinates
Viscous Stress
Work out the
direction!
xy xx xz
yy yx yz
zy zx zz
-
7/28/2019 2. Momentum Transport- Theory Part 1
14/16
27
Viscous stress in cartesan coordinates
Viscous Stress
Shear Stress Normal Stress
xx
yy
zz
xy xz
yx yz
zy zx
28
Viscous stress in cartesan coordinates
Shear Stress
xy =yx
zy =yz
xz =zx
Note that:
Look at thedirection!
-
7/28/2019 2. Momentum Transport- Theory Part 1
15/16
29
Lesson outcomes
5. State two mechanism for momentum transport
6. Express and explain the molecular transport
term
7. Express and explain the viscous stress term in
3-dimensional orientation (cartesan
coordinates)
ijijij p +=
=vv +=vv +
30
Summary
There are two mechanisms :
1. Molecular transport.
2. Convective transport
Convective transport
Molecular transport
vv
= p+
Combined momentum flux = vv +
+
=
j
i
i
j
ijd
v
d
v
-
7/28/2019 2. Momentum Transport- Theory Part 1
16/16
Further understanding
Read and understand the textbook;Chapter 1,
page 16 to 17
page35 to 36
31