Dynamic Behavior Modeling of Solenoid Valves Used for Proportional Fuel Control: PWM-Based Flow Rate Prediction

This study presents a predictive modeling framework for estimating transient flow rates in PWM-driven solenoid valves. Building on a previously validated dynamic model, the proposed framework enables flow prediction under varying process conditions and valve configurations. Flow rates at fully open conditions are obtained using computational fluid dynamics (CFD) and validated experimentally. CFD analyses are further performed at partial valve openings, and the resulting data are incorporated into a numerical algorithm based on piecewise linear interpolation for prediction throughout the opening–closing cycle of the valve. The model is validated under PWM operation, and parametric analyses are conducted to examine the effects of duty ratio, period, and coil voltage. The maximum difference between the experimental and numerical results was 1.3% under fully open conditions and 2.8% under PWM operation, demonstrating good agreement across the investigated conditions. By incorporating flow characteristics at intermediate spool positions that cannot be directly measured experimentally, the proposed approach allows accurate prediction of both transient and time-averaged flow rates. This provides a computationally efficient alternative to fully coupled transient CFD simulations.