Section sudden contraction. It is also to determine

Section
B:

A
diffuser is used in this CFD problem. Its purpose is to reduce the velocity of
the working fluid. Hence the increase in the pressure present in the pipe. An
efficiently designed diffuser would be able to minimize the total pressure loss
while providing nearly uniform flow from the inlet to the outlet of a pipe. CFD
was used in conducting this experimental study with intention to investigate
the effects of sudden contraction of pipe. The objective is to study the
pressure from the inlet to the axial of the sudden contraction. It is also to
determine the suitable mesh size that produces stable grid independent results.

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Simulation
Setup:

1)     Geometry

a)     X-Y
plane is selected. Click Z axis.

 

a)     Draw
the dimension of the geometry.

 

Lextend / D2 =
0.2mm*(default)

Lextend / 2 =
0.2mm

Lextend =
0.4mm

H3 = 0.4mm

 

The geometry dimensions:

V1
(inlet)

4
mm

H2
(axis 1)

10
mm

H3
(axis 2)

0.4
mm

V4
(outlet)

1
mm

Table
1: Model Dimension

 

1)     Mesh

 

a)     Define
boundary with proper name as shown below.

 

b)     Select
mesh control and click inflation. Select wall as a boundary.

 

 

c)     The
following Table is the mesh size that was used in this assignment:

Min Size

0.007mm – 0.1 mm

Max Face Size

0.02mm – 0.5 mm

Max Size

0.02mm – 0.5 mm

 

 Example picture of mesh where its (min size=
0.06mm, max face size & max size = 0.1mm, mesh size = 6520)

 

d)     Since
there are multiple mesh sizes to be studied and investigated upon, therefore a
single size was chosen to be the best average for this experiment. Each mesh
size is recorded after the completion of generating mesh process into data and
then updated.

 

2)     Setup

Some settings at
setup mode were not altered and left in default mode. The only settings that
were changed is stated in Table below:

 

General

Type

Pressure-Based

Velocity
Formation

Absolute

Time

Steady

2D space

Axisymmetric

Models

Viscous

Standard k-e, Standard Wall Fn

 

 

Materials

Fluid

Water-liquid

solid

aluminium

 

Boundary
Condition

Inlet Velocity

3 m/s

Outlet Pressure

0 Pa

 

Calculation

Number of iterations

1000

 

3)     Solution

–       
Run calculation to gain
result.

PART
1

Table of average pressure at different number
of elements.

Point

Min
size
(mm)

Max face
(mm)

Max
Size
(mm)

No.
of elements
 

Average
Pressure (Mpa)

A

0.1

0.5

0.5

672

1.50

B

0.09

0.4

0.4

890

1.26

C

0.08

0.3

0.3

1270

1.06

D

0.07

0.2

0.2

2259

2.00

E

0.06

0.1

0.1

6520

1.40

F

0.05

0.09

0.09

7735

1.83

G

0.04

0.08

0.08

9528

1.94

H

0.03

0.07

0.07

11869

2.08

I

0.02

0.06

0.06

15434

1.97

J

0.01

0.05

0.05

21154

1.96

K

0.009

0.04

0.04

31428

1.90

L

0.008

0.03

0.03

53128

1.92

M

0.0075

0.025

0.025

74726

1.90

N

0.007

0.02

0.02

113436

1.84

Table
2

Plotted graph for X-Y-plot of average
pressure against number of elements.

Based
on the tabulation result that was calculated, a graph of pressure against number
of elements is plotted. From the graph drawn, it is to be observed that the
line fluctuated and is not stable until when it reached to a point where the number
of elements (Mesh size) is 31 428. Then, the pressure only finally be stable
with minimum fluctuation where one can consider it be negligible as the
percentage difference among them are so small, proving that the percentage
different among each different point from the number of elements of 31 428
until 113 436 is lower than 3% when calculated.

To
further understand this fluid flow simulation, further research had to done for
result’s greater accuracy to real-life application. The following diagram was
obtained from the research material submitted by (Shabbir, 2015)

Diagram 1 – Sudden contraction of flow

Reference
to the diagram above, it can be seen sudden contraction of flow is affected by
the sudden decrease in pipe diameter. This sudden contraction would cause a
section where flow was narrower than usual. This narrow flow is called a ‘Vena
Contracta’ and it has the maximum velocity and minimum pressure at this part as
it obeys the law of Conservation of Energy. It is after this ‘Vena Contracta’
region where flow velocity would slow down and stabilize. The turbulence zones
were due to backflow occurring at those regions, in which the smaller diameter
pipe had a virtual diffuser acting at the flow that causes ‘Vena Contracta’.
Following formula was given as to calculate the loss of head (Sellens, 2014):

Where,

           Ac = cross-section area
of Vena Contracta

           Cc = coefficient of
contraction

And Cc can be
expressed in,

But the usual expression
of hL is as follows:

Where K is
represented by,

From
the graph, it can be observed that point K is the ideal choice to be the best
grid resolution for the pressure to be grid independent. This is because, at
this point, the pressure different between this point and the point after this
is already considered relatively small and is labelled as stable. Although the
point after this has smaller pressure difference than the next point, but
obviously need a much longer time to generate the mesh. Hence, time is wasted
as there is no need for it since point ‘K’ was good enough. Following is the
mesh of the chosen point: