Dynamic measurement of gas flow using acoustic resonance tracking

The National Institute of Standards and Technology measured gas flows exiting large, unthermostated, gas-filled, pressure vessels by tracking the time-dependent pressure P(t) and resonance frequency f_N(t) of an acoustic mode N of the gas remaining in each vessel. This is a proof-of-principle demonstration of a gas flow standard that uses P(t), f_N(t), and known values of the gas's speed of sound w(p,T) to determine a mode-weighted average temperature ⟨T⟩_φ of the gas remaining in a pressure vessel while the vessel acts as a calibrated source of gas flow. To track f_N(t) while flow work rapidly changed the gas's temperature, we sustained the gas's oscillations using positive feedback. Feedback oscillations tracked ⟨T⟩_φ with a response time of order 1/f_N. In contrast, driving the gas's oscillations with an external frequency generator yielded much slower response times of order Q/f_N. (For our pressure vessels, Q ∼ 10³-10⁴, where Q is the ratio of the energy stored to the energy lost in one cycle of oscillation.) We tracked f_N(t) of radial modes in a spherical vessel (1.85 m³) and of longitudinal modes of a cylindrical vessel (0.3 m³) during gas flows ranging from 0.24 to 12.4 g/s to determine the mass flows with an uncertainty of 0.51 % (95 % confidence level). We discuss the challenges in tracking f_N(t) and ways to reduce the uncertainties.