Passive-scalar transfer-kernel modelling for thermal transit-time flow measurement in pipe flow

Abstract

Abstract Thermal transit-time flowmeters are attractive for high-temperature, corrosive and irradiating environments, but the usual single-delay relation U = L/τ does not represent the effects of velocity-profile shear, radial scalar mixing, finite thermocouple response and channel mismatch. This study develops and tests a passive-scalar transfer-kernel method intended to replace part of the empirical calibration burden by a physics-informed measurement model. Its measurement significance is that transport-induced bias is separated from instrumentation-induced uncertainty, while heater bandwidth and radial sensor placement become quantitative design variables. Normalised kernels are derived for plug, Poiseuille and power-law profiles, and a diffusion-corrected frequency-domain operator is formulated for turbulent or liquid-metal regimes. The framework is assessed at four levels: analytical and stochastic consistency checks; an independent second-order axisymmetric finite-volume scalar calculation with an out-of-basis Reichardt profile, axial diffusion and radially varying effective diffusivity; a 100-trial Monte Carlo propagation of sensor gain, time-constant mismatch, radial placement, timing, drift, transfer-estimation noise and effective-diffusivity uncertainty; and re-analysis of aggregate calibration results from a published water-loop experiment. On the medium finite-volume grid, the complex transfer response differs from a refined-grid solution by 0.13%. For that independent benchmark, a centreline single-delay estimate overestimates mean speed by 20.2%, a nondiffusive kernel underestimates it by 9.2%, and joint diffusion-corrected inversion gives 2.7% error while estimating an effective-diffusivity ratio of 31.2 for a true area mean of 30. Under the specified Monte Carlo uncertainty model, three-radius kernel inversion reduces mean-flow RMSE from 20.1% for the single-delay method to 0.95%, with a median inversion time of 0.078 s. The results establish a physics-informed design and uncertainty framework for harsh-environment thermal flow measurement; prospective hardware validation remains the next metrological test.