Numerical methods in flow metrology Sampo Sillanpää, Centre for metrology and accreditation

2 Contents (Flow) metrology in short Numerical methods in flow metrology Calculation examples Conclusions

3 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?

4 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.

5 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

6 Metrology - the science of measurement An example of a calibration chain: small gas flow measurements in Finland.

7 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

8 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 90 o bend, double-elbow out of plane, diffuser or nozzle. Turbulent pipe flow

9 Velocity and temperature field inside the meter More complex geometry Usually time depended situation Turbulent or laminar flow

10 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.

11 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.

12 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

13 The flow conditioner before a turbine flow meter The computatio- nal grid for gene- rating the veloci- ty field for the flow conditioner Computational grid for flow conditioner

14 The flow conditioner before a turbine flow meter Calculation at volume flow rate 1000 m 3 /h RANS and k -  RNG turbulence model Wall function Fully implicit (time) discretisation

15 The flow conditioner before a turbine flow meter Contours of axial and radial velocity vectors 10D upstream of the flow conditioner Without conditionerWith single perforated plate With compounded conditioner

16 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.

17 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.

18 A Vortex flow meter with an ultrasonic barrier Comparison between measured and simulated pressure fields behind the bluff body

19 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

20 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