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.

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

Reference Formula The pressure drop, Δp across the orifice and the mass flow rate,

qm are linked by equation below:

.2

41

2

4pd

Cq dm

For a D and D/2 pressure tapping, concentric orifice plate flowmeter, the standard discharge coefficient is given in equation:

3.11.1224

4710

3.065.3

7.0682

8.0031.01

11.01123.0080.0043.0

Re

100063.00188.0

Re

10000521.0216.00261.05961.0

11

MMAee

AC

LL

DDd

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.

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.

Background of Problem (2)

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

National Engineering Laboratory (NEL)Flow conditioners performance review - 1998

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Back row: Honeycomb, Sprenkle, Etoile, Tube bundleFront row: Laws, Spearman, Mitsubishi

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: a famous example of a fractal

Romanesco broccoli: a naturally occurring fractal

The first four iterations of the Koch snowflake

Pictures from Wikipedia

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.

Fractal Flow Conditioner

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

1st Design – Koch curve snowflake fractal

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.

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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

Space filling circle grids – after modification to fit with the size and shape of pipe.

Fractal space filling square grids

Fractal space filling circle grids

Fractal space filling circle grids

2nd Design – Space filling fractal

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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

3rd order

2nd order

Final design – after modification

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.

MethodologyExperimental

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.

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,

Manometer

Manometer

Flow in

Reference pipe

Test pipe

Air fan

Removable part (on wheel)

Fixed part

Flow out

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.

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 disturbance

1/8 block disturbance

Swirl disturbance

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.

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.

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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.

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

Flow

Disturbance

3D

2DFractal plate

Arrangement and conditions of CFD model:

Fractal flow conditioner used.

CFD model for standard flow

(a) Standard flow (b) Fractal flow

(a)

(a) Block flow (b) Block+Fractal flow

(a) Standard flow (b) Swirl+Fractal flow

(b)

(a) (b)

(a) (b)

Grid Generations

Results

•Air•Water•Experimental •Simulation (CFD)

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.

Effect of disturbances (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.

Effect of location (experiment air)

Fractal placed 1.5D upstream of the orifice plate.

Effect of fractal on disturbed flow (experiment air)

Fractal placed 2D upstream of the orifice plate.

Effect of fractal on disturbed flow (experiment air)

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.

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.

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.

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.

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.

Standard flow Cond. flow

Block flow Block+Cond. flow

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

Swirl flow Swirl+Cond. flow

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.

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.

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.

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

Gantt Chart

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