Three-dimensional temperature field reconstruction for scramjet combustors based on L_p-Norm regularized gradient iteration with a priori smoothness constraints

In-depth investigation of the flow field and combustion characteristics in scramjet combustors is crucial for the intelligent optimization of next-generation engines. This work establishes a physical model of the scramjet combustor and investigates the variation patterns of the combustion field under different Mach numbers and flight altitudes. To address the ill-posed challenge of temperature reconstruction caused by the extreme environment within scramjet engines, characterized by wide temperature ranges, large gradients, and the coexistence of shock waves, this study proposes a novel reconstruction method—L _p -norm regularization based on Gradient Iterative Optimization combined with prior smoothness constraints (L _p -GIO). This method integrates the radiative transfer equation with light field tomography theory. It not only enhances the algorithm's noise immunity and shock wave capturing capability through the L _p -norm regularization strategy, but also addresses the limitations of traditional algorithms when processing extreme combustion flow fields. Performance analysis indicates that L _p -GIO ( p = 2) achieves the optimal performance in overall temperature field reconstruction (RMSE = 32.1 K, NRMSE = 2.8%, SSIM = 0.9973), while L _p -GIO ( p = 1) demonstrates significant advantages in local detail reconstruction (RMSE = 1.25 K, NRMSE = 0.9‰, SSIM = 0.999997). Even under high noise conditions, the method maintains high accuracy (ARE = 0.9% at 10% noise level). Furthermore, three-dimensional temperature fields within the range of different Mach numbers (Mach = 5, 6, 7, 8) and flight altitudes (H = 20 km, 25 km, 30 km) were reconstructed. The results demonstrate that this method effectively achieves high-fidelity reconstruction of large-gradient combustion fields across a wide temperature range of 500–2600 K, and clearly captures shock wave structures, providing a novel technical approach for combustion diagnostics in scramjet engines under extreme environments.