Not-A-Knot cubic spline model to predict accurately the viscosity calibration curve of turbine flow meter with experiment validation

Calibration facilities of fluid flow rate measurement, particularly primary standards, require significant operational costs and time. The more measuring points, the more resources will be consumed. Additionally, turbine flow meters are frequently operated in the industry but have nonlinear traits due to viscosity effect, so the prediction and estimation of their calibration curves are challenging research objects. Moreover, the transition between laminar and turbulent flow causes the turbine meter response to be non-linear. Techniques often used in calibration laboratories, such as ordinary regression and polynomial interpolation, still produce unsatisfactory accuracy. In particular,the Not-A-Knot cubic spline model is proposed because it promises excellent continuity and smoothness. This research aims to be a pioneer in developing an accurate prediction model with experimental evidence of calibration curves for turbine flow meters employing the Not-A-Knot cubic spline model. Validation with experimental results showed that the proposed method has better accuracy than common model, particularly 6th-degree polynomial, although it had more complex function. In addition, the cubic spline model had more minor errors and measurement uncertainties in forecasting unknown values with limited sample data, which could achieve an accuracy improvement of 21% compared to the 6th-degree polynomial model. In most case studies, the proposed method, Not-A-Knot cubic spline model was superior to other compared methods, which could reach the natural trait of calibration curves for turbine flow meters that shifted from laminar to turbulent flow.