Linear and nonlinear dynamics of a fast response air-to-fuel ratio sensor

In another work, Guibert and Dicocco have designed and tested a sensor for measuring the equivalence ratio of a mixture of hydrocarbon fuel and air. This sensor utilized the operating principles of constant temperature anemometry (CTA) with hot-wires. Thus, it should have a dynamic response that is comparable to CTA, even though Guibert and Dicocco verified the sensor's functioning at frequencies well below typical CTA cut-off frequencies. This paper therefore proposes quasi-analytic transfer functions that govern the sensor's linear dynamics. These linearized models are validated against numerical simulations of the fully nonlinear device dynamics, suggesting that the sensor has CTA-like bandwidth and can be considered linear for fluctuation amplitudes common in most combustion systems.