A solving new method for the urea-selective catalytic reduction (SCR) system in a diesel engine using coupled hyperbolic-parabolic partial differential equations (PDEs)

To control the diesel engine urea SCR system with high accuracy, firstly, the partial differential equations of the SCR system are simplified through variable substitution and the method of characteristic lines to eliminate the partial derivative terms of the hyperbolic partial differential equations in the flow direction. The backward difference method is used to solve the problem, and the adaptive time step is adjusted to improve computational efficiency. Secondly, the Levenberg-Marquardt algorithm is applied to identify the model parameters per second based on the 1800-s test bench data. By combining the experimental data with the parameter identification results, this paper calculated the downstream NOx concentration with 99.5 % accuracy. Finally, the 1800s transient test data was applied to a commonly used single-state SCR control model, and cell numbers 1–4 of the cases were numerically simulated. It was found that the reduced-order model had a computation time of 1 s but was less accurate. When the test data was applied to the model presented in this study, the calculation time was 27s, and the model's calculation results show that the average error of the downstream NOx concentration is 16.95 ppm, which is 14.3 ppm lower than that of the two-cell one-state model.