Development of a Model for Temperature Estimation in a Prototype Fuel Heating System

Fuel thermal management in ethanol-fueled Direct Injection (DI) engines is a key factor during cold starts, as the fuel's low volatility and high vaporization enthalpy hinder mixture formation and increase emissions. While heating systems help improve vaporization, operating at high pressures between 150 to 250 bar requires careful thermal control. Approaching the supercritical region can alter the fluid's thermophysical properties and degrade sealing materials. As a potential approach for thermal monitoring, this study proposes a one-dimensional 1D thermal model to estimate the internal temperature of electric-coil-heated fuel rails. The physical domain is discretized into five elements, combining radial and axial heat transfer mechanisms using empirical Nusselt correlations and iterative natural convection calculations. Validation was performed in two stages: a baseline atmospheric calibration using surrogate fluids (water/air) to evaluate convective parameters, followed by an operational high-pressure validation (150 bar) with pure ethanol under randomized PWM excitation. The experimental results demonstrated outstanding agreement between monitored and estimated fuel temperatures, achieving a coefficient of determination (R2) exceeding 0.98 and root mean square error (RMSE) values below 2.14 °C across all dynamic test cases. These findings indicate that the proposed model presents a viable alternative as a non-invasive virtual temperature sensor for Flex Fuel DI engines.