2. Introduction
• The differential pressure flowmeter is the most common form of
flowmeter used in industry.
• According to recent market studies this kind of flowmeter accounts for
about half of all industrial flow meters used in industry. (D.Johnson – 2005)
• Many types of differential flow meters are used in industry, and of
these the orifice plate flowmeter is the most common form.
• The reasons for this is that the orifice plate is simple to construct, has
a low maintenance cost and a wide applicability to different fluids
including both liquids and gases.

3. Orifice Flowmeter
The orifice meter consists of an accurately machined and drilled plate
concentrically mounted between two flanges. The position of the
pressure taps is somewhat arbitrary.
The orifice meter has several practical advantages when compared to
other differential pressure meters.
- Lower cost
- Smaller physical size
- Flexibility to change throat to pipe diameter ratio to measure a
larger range of flow rates
Fluid Meters: Their Theory and Applications, 6th ed.,
American Society of Mechanical Engineers, New
York

4. Reference Formula
• The pressure drop, Δp across the orifice and the mass flow rate,
qm are linked by equation below:
Cd π 2
qm = ε d 2∆p.ρ
4 4
1− β
• For a D and D/2 pressure tapping, concentric orifice plate
flowmeter, the standard discharge coefficient is given in equation:
0.7 0.3
 10 6 β  3.5  10 
6
Cd = 0.5961 + 0.0261β − 0.216β + 0.000521  Re  + ( 0.0188 + 0.0063 A) β  Re 
2 8
  
 D   D
(
+ 0.043 + 0.080e −10 L1
− 0.123e )
− 7 L1
(1 − 0.11A) β4
1− β 4
( ′ )
′1.1
− 0.031 M 2 − 0.8M 2 β 1.3

5. Background of Problem (1)
The most important assumption in flow measurement is that the flow
approaching the orifice plate must be fully developed and turbulent,
without any asymmetry or swirl.
In practical applications, however valves, bends, heat exchangers,
compressors and also other piping devices can generate swirl and
distort the flow.
In order to produce a uniform fully developed flow, which is free from
disturbance, a long straight pipe must be installed before the orifice
plate.

6. Background of Problem (2)
• There is a minimum upstream length for this pipe that depends on
the Reynolds number, pipe diameter, orifice diameter, the ratio of pipe
diameter to hole diameter (β) and the pipe fittings.
• In general, this requirement means that at least 10 pipe diameters of
smooth straight pipe is required for plates with small holes increasing
to 36 pipe diameters for plates with large holes.

7. Flow Conditioner
Flow Conditioner – A device that used to remove swirl and produces
a repeatable downstream velocity irrespective of the upstream flow
disturbances. It is desirable for a good flow conditioner to fulfill its duty
within the following requirements:
- Low pressure loss across the device
- Short upstream length from the disturbances
- Short downstream length to the orifice plate
- Easy installation
- Cheap to manufacture and maintenance
- Adequately robust

8. Continue…
Back row: Honeycomb, Sprenkle, Etoile, Tube bundle
Front row: Laws, Spearman, Mitsubishi
National Engineering Laboratory (NEL)
Flow conditioners performance review - 1998

9. Fractal
Fractal – A geometrical or physical structure having an irregular or
fragmented shape at all scales of measurement between a greatest and
smallest scale.
The geometrical figure can be for example a square, a hexagon, a
rectangular, a triangle shape or even circular shape.
The Mandelbrot set: Romanesco broccoli: The first four iterations of the Koch
a famous example of a fractal a naturally occurring fractal snowflake
Pictures from Wikipedia

10. Why Fractal?
Research on fluid transporting fractals was suggested three
hypotheses which suggest a broad range of applications.
The fluid flow through engineered fractal cascades can exhibit a
functional equivalent to turbulence.
The fluid flow through engineered fractal cascades can provide
control led formation of macroscopic fluid structure.
The fluid flow through engineered fractal cascades can provide
dynamics alteration of a fluid structure’s gross measure of
dimension.
The fractal shaped orifice flowmeters also can give a significant
effect on recovery the velocity profile after the disturbances.

11. Fractal Flow Conditioner
1st Design – Koch curve snowflake fractal
One of the objectives of this study is to investigate a fractal based
flow conditioner and measure the level of conditioning provided and
its limitations.
The idea of this is to evaluate the concept of fractal based patterns
regards to eddy and velocity profile formation.
The fractal pattern is based on a forth order Koch curve . The Koch
curve starts life as a linear length and is split in the fraction of ln(4) /
ln(3) = 1.2619

12. Continue…
• An equilateral triangle is the added to
the middle section of the line segment set
by the given ratio, and the middle line
section is removed.
• The infinite length comes from
continued iterations on each of the
produced line segments, which of
continued would continue to infinity.
The use this fractal on a fluid is to provide a means for the formation of
turbulent eddies on many different scales creating an artificial, total mixing of
the fluid.
By forcing the complete change using the fractal it is hoped the standard
fully developed profile can be attained with all the relevant scales of eddies.

13. 2nd Design – Space filling fractal
• Static pressure drop for the space filling fractals is
independent of the thickness factor. (Hurst & Vassilicos – 2007)
• The decay of turbulence downstream of this fractal is
statistically homogenous and isotropic. (Seoud & Vassilicos – 2007)
• Space filling circle grids Fractal space filling square grids
Fractal space filling circle grids
• Space filling circle grids –
after modification to fit with the
size and shape of pipe.
Fractal space filling circle grids

14. Continue…
The fractal pattern is based on a third order space filling circle grids.
Another modification to make the fractal more effective as a flow
conditioner had been done as shown in figure.
This pattern of fractal fulfilled the requirement of the flow conditioner
design:
- easy installation
- cheap manufacturing & maintenance
- adequately robust
1st order 2nd order
3rd order Final design – after modification

15. Objectives of Study
To develop the orifice plate with a fractal flow conditioner.
To conduct experimental study and calibrate the orifice plate
combined with a fractal flow conditioner.
* This type of flow conditioner and flow meter must have the
attributes to offer a homogenous and fully developed flow
before and after the orifice plate.

16. Methodology
Experimental
Two experimental test rigs have been established:
- Air test rig (air as a working fluid).
- Water test rig (water as a working fluid).
• The air test rig can achieve a maximum Reynolds number up to 25000 while
water test rig can reach the Reynolds number up to 75000 for β = 0.5.
Simulation
Simulations were carried out in order to perform an analytical investigation of
the effect of the flow conditioner on a disturbed flow
Fluent software is a robust tool that can demonstrate most aspects of
experimental behavior.

17. Air test rig
• In order to assess the effect of disturbed flow and fractal flow conditioner
on the orifice plate, an experimental using air rig was used.
• The mass flow rate of the orifice plate with both standard and non-
standard velocity profiles has been measured for different Reynolds number
and β ratio of 0.5.
•The air rig contained two orifice plates will be positioned in series in
smooth, circular pipes. The experimental set up is shown below,
Air fan
Test pipe Manometer
Flow out
Flow in
Reference Manometer
pipe
Removable part (on wheel)
Fixed part

18. Analysis of the air test rig
• The percentage change in flow rate (error) taken from the test pipe to the
reference pipe.
The magnitude error around 6% - either the test rig is not perform as required
or some undetected sealing problem through the pipe network.

19. Disturbances for air test rig
Velocity profiles different from those in fully developed flow can be
produced using disturbances upstream of the orifice plate. These
disturbances provide either an asymmetric velocity profile or a swirling flow.
• Block disturbances – used to achieve an asymmetric velocity profile.
• 1800 twist swirler disturbance – used to produce swirling flow in pipe.
1/4 block 1/8 block Swirl
disturbance disturbance disturbance

20. Water test rig
50mm internal pipe diameter with 25D and 20D upstream and downstream
of the orifice plate respectively..
The dynamic weighing method was used to measure the mass flow rate.
For a accuracy, both U-tube manometer and pressure
transducer were used to measure the pressure drop across
the orifice.

21. Analysis of the water test rig
• Error in Cd compared to the standard value.
The results give a small amount of scatter but a good trend given a 2.0% to 2.5% error
on each reading.
At the higher Reynolds numbers, there is better correlation due a possible increase in
the uniformity of the velocity profile.

22. Continue…
• ΔCd of the standard discharge coefficient is the main quantity that had been
used in the most of the results to express the effect of disturbed flow on
metering accuracy.
The trend of error between standard and experimental discharge coefficient.

23. CFD Modelling
CFD simulation:
- phenomena of the flow can be clearly visualized and detailed.
- computational costs are lower than instrument costs in laboratory.
- determine a suitable location of the device with various locations and
types of disturbances (design optimization).
A standard flow modeled in 2D, other models were modeled in 3D.
The CFD model parameter and settings
-The standard k-ε turbulence model was used.
- Water as a working fluid
- Based on a Reynolds number of 80,000.
- β = 0.73
Arrangement and conditions of CFD model:
Fractal plate 2D
Flow
Disturbance
3D Fractal flow conditioner used.

24. Grid Generations
CFD model for standard flow
(a) Standard flow
(b) Fractal flow
(a) (b)
(a) Block flow
(b) Block+Fractal flow
(a) (b)
(a) Standard flow
(b) Swirl+Fractal flow
(a) (b)

25. Results
•Air
•Water
•Experimental
•Simulation (CFD)

26. Effect of disturbances (experiment air)
• Swirl disturbance give the highest changing in Cd compare to the block
disturbances.
• The change in Cd decrease due to the increase of Reynolds number.

27. Effect of location (experiment air)
• The individual fractal itself contributed an error on Cd.
• The fractal located 1.5D upstream give an errors around 0.25% to 0.30% in
Cd while the fractal located 2D contributed 0.20% to 0.25% errors in Cd.

28. Effect of fractal on disturbed flow (experiment air)
Fractal placed 1.5D upstream of the orifice plate.

29. Effect of fractal on disturbed flow (experiment air)
Fractal placed 2D upstream of the orifice plate.

30. Simulation Results
Simulation was carried out by using space filling circle grids.
The simulations were run using six conditions which are:
1. Standard flow.
2. Block
3. Swirl flow
4. Fractal/Cond. flow.
5. Block+fractal flow
6. Swirl+fractal flow
Variations of the axial velocity for all the conditions examined.
To demonstrate the visual effect of the fractal flow conditioner on
disturbed flow, the contours of velocity magnitude were produced.

31. Upstream velocity profile (block disturbance)
Variations of the axial velocity profile on a vertical line located one D upstream of
the orifice plate for block disturbance.
Axial velocity profile is almost identical for the fractal flow conditioner with and
without the block disturbance.
However, velocity profile for disturbances is far from the fully developed profile.

32. Upstream velocity profile (swirl disturbance), CFD
water
Variations of the axial velocity profile on a vertical line located one
D upstream of the orifice plate for swirl disturbance.
Same conditions as block disturbance.

33. Downstream velocity profile (block disturbance) CFD water
Variations of the axial velocity profile on a vertical line located D/2
downstream of the orifice plate for block disturbance.

34. Downstream velocity profile (swirl disturbance)
Variations of the axial velocity profile on a vertical line located D/2
downstream of the orifice plate for swirl disturbance.

35. Contours of velocity magnitude (block disturbance)
Four conditions of velocity magnitude for a surface one D upstream of the orifice
plate for block disturbance.
Velocity magnitude with disturbance is disturbed and non-uniform. After passing
through the fractal flow conditioner, the contours tends to be as Cond. Flow.
Standard flow Cond. flow
Block flow Block+Cond. flow

36. Contours of velocity magnitude (swirl disturbance)
Four conditions of velocity magnitude for a surface one D upstream of
the orifice plate for swirl disturbance.
Same conditions as block disturbance.
Standard flow Cond. flow
Swirl flow Swirl+Cond. flow

37. Conclusions (1)
The disturbances produced a significant error in the standard orifice
plate. However, this error was damped by using the fractal conditioner
in front of the orifice plate to become a acceptable error as defined by
standards.
The confirmation that a fractal pattern can dampen out flow
disturbances has a potential benefit for flow measurement
If properly calibrated, a form of fractal flow conditioner similar to the
ones used in this study could be fitted upstream of existing differential
pressure flow meters in order to increase the accuracy of the flow rate
measurements.

38. Conclusions (2)
From the simulation results, the fractal flow conditioner would
require fewer than the 2 pipe diameters of straight pipe upstream of
the orifice plate - far less than 20 straight pipe lengths needed for an
orifice plate alone.
The downstream spacing of the fractal flow conditioner is around
2D - this is less than other flow conditioners proposed in the
standards.

39. Future Work
After completing the current stages, several achievable plans
have been made in order to achieve results that are more
comprehensive. The plans are as follows:
- Run the experiment for flow through fractal flow conditioner,
flow through disturbances and combination of fractal and
disturbances using water test rig.
- Propose 3rd design of the fractal flow conditioner.
- Determine the mathematical relation for the new fractal pattern
design.
- Suggestion of new discharge coefficient for the new fractal-
orifice flowmeter

40. Gantt Chart

41. Thank you