Introduction• The differential pressure flowmeter is the most common form offlowmeter used in industry.• According to recent market studies this kind of flowmeter accounts forabout half of all industrial flow meters used in industry. (D.Johnson – 2005)• Many types of differential flow meters are used in industry, and ofthese the orifice plate flowmeter is the most common form.• The reasons for this is that the orifice plate is simple to construct, hasa low maintenance cost and a wide applicability to different fluidsincluding both liquids and gases.
Orifice Flowmeter The orifice meter consists of an accurately machined and drilled plateconcentrically mounted between two flanges. The position of thepressure taps is somewhat arbitrary. The orifice meter has several practical advantages when compared toother differential pressure meters. - Lower cost - Smaller physical size - Flexibility to change throat to pipe diameter ratio to measure alarger 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: Cd π 2 qm = ε d 2∆p.ρ 4 4 1− β• For a D and D/2 pressure tapping, concentric orifice plateflowmeter, 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
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.
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.
Flow Conditioner Flow Conditioner – A device that used to remove swirl and producesa repeatable downstream velocity irrespective of the upstream flowdisturbances. It is desirable for a good flow conditioner to fulfill its dutywithin 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
Fractal Fractal – A geometrical or physical structure having an irregular orfragmented shape at all scales of measurement between a greatest andsmallest scale. The geometrical figure can be for example a square, a hexagon, arectangular, 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
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 Conditioner1st Design – Koch curve snowflake fractal One of the objectives of this study is to investigate a fractal basedflow conditioner and measure the level of conditioning provided andits limitations. The idea of this is to evaluate the concept of fractal based patternsregards to eddy and velocity profile formation. The fractal pattern is based on a forth order Koch curve . The Kochcurve starts life as a linear length and is split in the fraction of ln(4) /ln(3) = 1.2619
Continue…• An equilateral triangle is the added tothe middle section of the line segment setby the given ratio, and the middle linesection is removed.• The infinite length comes fromcontinued iterations on each of theproduced line segments, which ofcontinued 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.
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 gridsFractal space filling circle grids • Space filling circle grids – after modification to fit with the size and shape of pipe. Fractal space filling circle grids
Continue… The fractal pattern is based on a third order space filling circle grids. Another modification to make the fractal more effective as a flowconditioner had been done as shown in figure. This pattern of fractal fulfilled the requirement of the flow conditionerdesign: - easy installation - cheap manufacturing & maintenance - adequately robust 1st order 2nd order 3rd 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 platecombined with a fractal flow conditioner.* This type of flow conditioner and flow meter must have theattributes to offer a homogenous and fully developed flowbefore 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 whilewater 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 ofthe effect of the flow conditioner on a disturbed flow Fluent software is a robust tool that can demonstrate most aspects ofexperimental behavior.
Air test rig• In order to assess the effect of disturbed flow and fractal flow conditioneron 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 numberand β ratio of 0.5.•The air rig contained two orifice plates will be positioned in series insmooth, 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
Analysis of the air test rig• The percentage change in flow rate (error) taken from the test pipe to thereference pipe. The magnitude error around 6% - either the test rig is not perform as requiredor some undetected sealing problem through the pipe network.
Disturbances for air test rig Velocity profiles different from those in fully developed flow can beproduced using disturbances upstream of the orifice plate. Thesedisturbances 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
Water test rig 50mm internal pipe diameter with 25D and 20D upstream and downstreamof the orifice plate respectively.. The dynamic weighing method was used to measure the mass flow rate. For a accuracy, both U-tube manometer and pressuretransducer were used to measure the pressure drop acrossthe 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% erroron each reading. At the higher Reynolds numbers, there is better correlation due a possible increase inthe uniformity of the velocity profile.
Continue…• ΔCd of the standard discharge coefficient is the main quantity that had beenused in the most of the results to express the effect of disturbed flow onmetering 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 Arrangement and conditions of CFD model: Fractal plate 2D Flow Disturbance 3D Fractal flow conditioner used.
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)
Effect of disturbances (experiment air)• Swirl disturbance give the highest changing in Cd compare to the blockdisturbances.• The change in Cd decrease due to the increase of Reynolds number.
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% inCd while the fractal located 2D contributed 0.20% to 0.25% errors in Cd.
Effect of fractal on disturbed flow (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.
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 ondisturbed 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 ofthe orifice plate for block disturbance. Axial velocity profile is almost identical for the fractal flow conditioner with andwithout the block disturbance. However, velocity profile for disturbances is far from the fully developed profile.
Upstream velocity profile (swirl disturbance), CFDwater Variations of the axial velocity profile on a vertical line located oneD 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/2downstream of the orifice plate for block disturbance.
Downstream velocity profile (swirl disturbance) Variations of the axial velocity profile on a vertical line located D/2downstream of the orifice plate for swirl disturbance.
Contours of velocity magnitude (block disturbance) Four conditions of velocity magnitude for a surface one D upstream of the orificeplate for block disturbance. Velocity magnitude with disturbance is disturbed and non-uniform. After passingthrough the fractal flow conditioner, the contours tends to be as Cond. Flow. Standard flow Cond. flow Block flow Block+Cond. flow
Contours of velocity magnitude (swirl disturbance) Four conditions of velocity magnitude for a surface one D upstream ofthe orifice plate for swirl disturbance. Same conditions as block disturbance. Standard flow Cond. flow Swirl flow Swirl+Cond. flow
Conclusions (1) The disturbances produced a significant error in the standard orificeplate. However, this error was damped by using the fractal conditionerin front of the orifice plate to become a acceptable error as defined bystandards. The confirmation that a fractal pattern can dampen out flowdisturbances has a potential benefit for flow measurement If properly calibrated, a form of fractal flow conditioner similar to theones used in this study could be fitted upstream of existing differentialpressure flow meters in order to increase the accuracy of the flow ratemeasurements.
Conclusions (2) From the simulation results, the fractal flow conditioner wouldrequire fewer than the 2 pipe diameters of straight pipe upstream ofthe orifice plate - far less than 20 straight pipe lengths needed for anorifice plate alone. The downstream spacing of the fractal flow conditioner is around2D - this is less than other flow conditioners proposed in thestandards.
Future Work After completing the current stages, several achievable planshave been made in order to achieve results that are morecomprehensive. 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