Development of a Riemann variables-based technique for on-line fuel injected mass evaluation in direct injection systems

On-line evaluation of injected fuel mass based on physical principles offers the potential for accurate and rapid feedback on actual injection quantities. High-accuracy pressure transducers are commonly used as primary sensors to provide inputs for model-based virtual flowmeters. While increasing the number of transducers allows for a more comprehensive analysis of elementary waves within the system, balancing measurement accuracy and economic efficiency is essential for industrial applications. In this study, a physics-based technique requiring only a single pressure sensor on the injector-feeding pipe is proposed, considering two elementary waves. The algorithm employs a predefined signal that exploits quasi-constant Riemann variables propagating from the rail to the injector, enabling accurate estimation of the flow-rate and mass entering the injector. Correlation relationships are then used to convert the entering mass into the injected mass. This approach achieves an estimation accuracy within 2 mg for single injection events. The proposed method is benchmarked against a previously developed flowmeter utilizing two pressure sensors, demonstrating that comparable accuracy can be obtained with a more economical single-sensor setup. The algorithm is applicable across a wide range of injection sizes and working conditions, offering a practical solution for real-time injected mass evaluation and control in high-pressure fuel systems.