DAMAGE PREDICTION OF BALL JOINTS IN ANTI-ROLL BARS

72
STATIC MIXER
Mixing is a common unit operation in a large number of processes, and it is used
in many different applications where a defined degree of homogeneity of a fluid is
desired. Common mixing devices are dynamic mixers for agitated tanks in batch
operations and static mixers for inline mixing in continuous operations.
Static mixers have been utilized over a wide range of applications such as
continuous mixing, blending, heat transfer processes, chemical reactions, etc. A static
mixer consists of a contacting device with a series of internal stationary mixing
elements of specific and patented geometry, inserted in a pipe. Some of the advantages
of static mixers over dynamic mixers are that they have no moving parts, low
maintenance, low space requirements, no moving parts and a short residence time.
D.1 Theory
D.1.1 Governing Equations.
For steady incompressible flow, the mass conservation equation can be written
as
∂ui
= 0
Eq.D-1
∂xi
and the momentum conservation equation can be written as
∂( uiu
j
) ∂p
∂τ
ij
ρ + = + ρg
i
+ Fi
Eq.D-2
∂x
∂x
∂x
j
i
In the absence of a gravitational body force and any external body force, the two last
terms on the right side of Eq.D-2 are zero. The stress tensor, τ ij , in Eq.D-2 is given by
⎛ u u
j
⎞
i
uk
τ
ij
µ ⎜
∂ ∂
⎟
2 ∂
= + − µ δ
ij
Eq.D-3
x
j
x
⎝ ∂ ∂
i ⎠ 3 ∂xk
Considering the conservation of mass for incompressible flow, ∂u k /∂x k =0, gives
⎛ ⎞
⎜
∂u
∂u
i j
τ + ⎟
ij=
µ
Eq.D-4
⎝ ∂x
j
∂xi
⎠
D.1.2 Pressure drop and Z factor
The pressure drop over the static mixer was computed for the repeating unit of
two mixer elements, and converted to a pressure per meter. The pressure drop for
empty tube, ∆P et , under laminar flow conditions is calculated as
∆l
vx
µ
∆ Pet
= 32
Eq.D-5
2
D
When considering the pressure drop for the static mixer, ∆P sm , a common
approach is to define a dimensionless number comparing the pressure drop over a
static mixer with that over an empty pipe of the same length as the static mixer. The
dimensionless number, referred to as the Z factor, is essentially the increase in energy
input required when the static mixer is installed in the pipe. The Z factor is
Psm
Z & ∆
= Z(Re)
=
∆P
Eq.D-6
At Re ≤ 10, the correlation of Wilkinson and Cliff given by
j
et