Numerical methods in flow metrology

Sampo Sillanpää, Centre for metrology and accreditation

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Contents

• (Flow) metrology in short

• Numerical methods in flow metrology

• Calculation examples

• Conclusions

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Short introduction to metrology

• What about if…

• …one litre would not be equal?

• …the mass of one kilogram would vary?

• …nobody knows the exact time?

• ...the mixture of anesthesia gases would be unknown?

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Metrology - the science of measurement

• The definition of internationally accepted units of a measurement.

• The realisation of units of measurement by scientific methods.

• The establishment of traceability chains in documenting the accuracy of a measurement.

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Metrology - the science of measurement

• A traceability (or calibration) chain

• the documented relationship between the measurement result and a measurement standard of a national standard laboratory.

• Measurement result for mass flow

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Metrology - the science of measurement

An example of a calibration chain: small gas flow measurements in Finland.

M IK E S F lowC a lib ra tio n s fo r cu sto m e rs

M IK E S F lowL F E ca lib ra tio n sys tem

M IK E S F lowC a lib ra tio n s fo r cu sto m e rs

M IK E S F lowD W S ca lib ra tion sys tem

M IK E S M a ssN a tion a l s ta nd a rd fo r m a ss

M IK E S T im e a n d F re qu e n cyN a tion a l s ta nd a rd fo r t im e

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Numerical methods in flow metrology

• Velocity and temperature field before the meter

• Velocity and temperature field inside the meter

• Numerical simulations in evaluation of the measurement uncertainty

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Velocity and temperature field before the flow meter

• The indication of a flow meter might be depended on the velocity profile at upstream of the flow meter.

• Investigation of different flow profiles generated by

• 90o bend,

• double-elbow out of plane,

• diffuser or nozzle.

• Turbulent pipe flow

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Velocity and temperature field inside the meter

• More complex geometry

• Usually time depended situation

• Turbulent or laminar flow

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Monte Carlo simulation in evaluation of the measurement uncertainty

• Usually applied for non-linear measurement models

• Calculation

• Measurement model

• probability density functions

• model evaluation

• approximate distribution function

• estimate of the output quantity value and associated standard uncertainty.

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Simulation examples

• The flow conditioner before a turbine flow meter

• Study the efficiency of a new type compounded flow conditioner,

• evaluation and validation.

• A Vortex flow meter with an ultrasonic barrier

• Optimise the bluff body shape,

• minimise the pressure loss.

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The flow conditioner before a turbine flow meter

Straight length, double-elbow, diffuser and straight length

Flow conditioner at right and at the left the computational domain of it

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The flow conditioner before a turbine flow meter

The computatio-nal grid for gene-rating the veloci-ty field for the flow conditionerComputational grid for flow conditioner

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The flow conditioner before a turbine flow meter

• Calculation at volume flow rate 1000 m3/h

• RANS and k - RNG turbulence model

• Wall function

• Fully implicit (time) discretisation

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The flow conditioner before a turbine flow meter

Contours of axial and radial velocity vectors 10D upstream of the flow conditioner

Without conditioner

With single perforated plate

With compounded conditioner

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A Vortex flow meter with an ultrasonic barrier

• Traditionally pressure sen-sors are used to detect vor-tices generated by a bluff body pressure losses.

• New construction, where an ultrasonic barrier is used instead of pressure sensors smaller bluff body smaller pressure losses.

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A Vortex flow meter with an ultrasonic barrier

• Time depended simulation and structured grid

• Spatial discretisation

• convective terms: upwind biased discretisation,

• viscous terms: central difference.

• Time discretisation

• Runge-Kutta method or

• approximate factorisation.

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A Vortex flow meter with an ultrasonic barrier

Comparison between measured and simulated pressure fields behind the bluff body

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A Vortex flow meter with an ultrasonic barrier

Pressure field of the simulated vortex street of a triangular bluff body with a width of 24 mm facing the edge of the inflow

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Conclusions• Lower costs and better

data analysis

• Installation effects and measurement process

• Uncertainty calculation

• Evaluation of the magnitude of uncertainty components

• Mainly in universities, not yet in NMIs