Internal combustion engines generally operate as open loop feedback systems. Present engine control strategy involves sensors that simply provide data for comparison with an “engine map” of tables in engine control computers. Closing the feedback loop in real time and for individual cylinders would allow improved engine control, resulting in reduced pollution and increased efficiency. This treatise presents a simulation of the output of a solid state sensor located in each cylinder of a lean direct injection engine. The amperometric sensor provides continuous, analog feedback of oxygen partial pressure to monitor performance and to improve control of each cylinder. The geometry of the sensor is different from oxygen sensors presently used in automobiles, especially the electrode and electrolyte layout.
The model simulates both mass and charge transfer, and assumes that either of these transport phenomena are rate limiting. To simulate mass transfer, the properties of air inside a cylinder undergoing a diesel cycle were calculated. The diffusivity, which changes throughout the cycle, was used to calculate the diffusion current due to the arrival rate of oxygen at the sensor’s cathode. To simulate the transfer of charge, conductivity values for partially stabilized zirconia were adjusted for porosity and temperature. Conductivity values were used to calculate the drift current of the sensor. The lower of the diffusion and drift current was taken as the sensor output.
The model provided increased understanding of the physicochemical processes of sensor operation by allowing variation of design parameters. The simulation work yielded the following: The sensor temperature must exceed 900ºC if the electrolyte is porous in order to obtain acceptable electrolytic conductivity. Otherwise the sensor output is not diffusion limited, and the sensor cannot discern between various partial pressures of oxygen. For the same reason, the electrolyte thickness must be on the micron scale. Otherwise the electric field will be too small to obtain acceptable conductivity and the device will operate in the conduction-limited regime, which does not provide useful information for control purposes. The shape and size of electrodes must be carefully controlled in order to ensure that diffusion is the rate limiting step. The temperature of the sensor temperature must be determined in order to assess the sensor signal. Knowing the temperature of the device allows extraction of useful information from the signal depending on the stroke. During intake, the signal is proportional to oxygen partial pressure, which is useful to control exhaust gas circulation. During compression prior to pilot fuel injection, the output of the sensor is proportional to the total pressure. Because combustion has not yet occurred, no oxygen has been yet consumed, but the diffusivity changes inversely with pressure, thus altering the signal. During the power stroke, a low signal provides confirmation of combustion. Finally during the exhaust stroke, the signal is proportional to oxygen partial pressure, providing information that can be used for exhaust gas recirculation. Thermal cycling may prove detrimental to device performance, so the sensor may be better suited for gas turbines where it could operate as a pressure detector. A thorough experimental investigation should include thermal cycling and ageing studies.
October 31, 2008
Rheaume, J. M. (2008). Simulation of in Situ Solid State Electrochemical Sensor for Improved Diagnostics and Control of Lean Engines. United States: University of California, Berkeley.