Physics-Informed Deep Learning for Real-Time Thermal Anomaly Detection in Regenerative Cooling Channels of RP-1 Liquid Rocket Engines

Physics-Informed Deep Learning for Real-Time Thermal Anomaly Detection in Regenerative Cooling Channels of RP-1 Liquid Rocket Engines Siripuram Karthikeya Independent Researcher India karthike[email protected] Abstract—Liquid Rocket Engines (LREs) utilizing RP-1 fuel are susceptible to “coking,” a thermal degradation phenomenon where carbon deposits impair heat transfer in regenerative cooling channels. Traditional Computational Fluid Dynamics (CFD) methods are computationally prohibitive for flight-time monitoring. This paper proposes a Physics-Informed Neural Network (PINN) framework functioning as a virtual sensor to predict nominal wall temperatures. By integrating a calibrated Bartz approximation directly into the loss function, the model establishes a physics-consistent baseline. We demonstrate that this approach achieves real-time thermal anomaly detection with a Root Mean Square Error (RMSE) of 5.55 K. The model exhibits an inference latency of <10 ms on a standard CPU, offering a viable pathway for autonomous abort systems in next-generation reusable launch vehicles. Index Terms—Physics-Informed Neural Networks, Liquid Rocket Engines, Regenerative Cooling, Fault Detection, RP-1. I. INTRODUCTION The reusability of launch vehicles, exemplified by the Falcon 9 class, relies heavily on the structural integrity of the liquid rocket engine (LRE) nozzle. In engines using RP1 (kerosene) and Liquid Oxygen (LOX), a critical failure mode is “coking”—the deposition of carbon/soot on the inner walls of regenerative cooling channels [1]. This deposition acts as a thermal insulator, leading to localized wall overheating, “thermal runaway,” and catastrophic structural failure. Current fault detection systems primarily rely on sensor redundancy and threshold-based limits. However, recent advances in Artificial Intelligence (AI) offer predictive capabilities. While deep learning has been applied to system-level diagnostics [2], these “black-box” models often lack the physical consistency required for safety-critical flight hardware. This work bridges the gap by introducing a PhysicsInformed Neural Network (PINN) specifically designed for the nozzle throat region. By constraining the network with the Bartz heat transfer correlation, we ensure reliable extrapolation even in rare failure regimes. II. RELATED WORK A. AI in Rocket Propulsion The application of AI to aerospace propulsion has accelerated significantly. Zhang et al. (2025) recently proposed an interpretable fault diagnosis framework using Granger Causality and Multi-Layer Perceptrons (MLP) [2]. While their method achieved 97% accuracy for system-level faults (e.g., turbopump failures), it operates on macroscopic sensor data and does not model specific thermodynamic degradations like coking within the cooling channels. B. Physics-Informed Neural Networks (PINNs) The concept of embedding partial differential equations (PDEs) into neural networks was formalized by Cai et al. (2021) [3]. This approach has been successfully applied to heat transfer problems where data is sparse. Yasar and Sevinc (2024) extended this to hypersonic flows, using PINNs to predict critical heat flux on vehicle bodies [4]. Similar methodologies have also been explored for two-phase flow applications [5]. However, these works focused on external aerodynamics or general flows rather than internal regenerative cooling channels. C. Research Gap To the best of our knowledge, no prior work has combined real-time PINN architectures specifically for RP-1 coking detection using a simplified Bartz-constraint for flight feasibility. III. METHODOLOGY To validate the architecture, we utilize a scaled laboratoryequivalent thermal model. This ensures the framework’s stability on a safe, low-temperature surrogate dataset before extrapolation to high-temperature flight regimes. A. Physics Constraints To ensure the model adheres to thermodynamic laws, we incorporate two specific governing constraints into the data generation and loss function formulation: •Calibrated Bartz Approximation: We utilize a simplified form of the Bartz equation to estimate the gas-side heat transfer coefficient (hg). To ensure unit consistency in the loss function, we introduce a calibration coefficient Ccal: hg=Ccal P0.8 c D0.1 t (1) Where Pcis chamber pressure and Dtis the throat diameter. The coefficient Ccal accounts for the specific transport properties of the coolant and is determined via a least-squares fit to the nominal steady-state baseline. •1D Energy Balance: We enforce a steady-state equilibrium where the heat flux from the combustion gas (Qin) equals the heat removed by the coolant (Qout). B. Virtual Sensor Strategy The PINN is trained strictly on nominal (clean) engine data to act as a Virtual Sensor. •Input Layer: 3 Neurons (Pc,O/F,˙m). •Hidden Layers: 4 layers with 64 neurons each (tanh activation). •Output: 1 Neuron (Nominal Wall Temperature Tw,pred). Fault detection is achieved by monitoring the residual between the observed sensor temperature (Tsensor) and the PINN prediction (Tw,pred). A divergence (Tsensor > Tw,pred) indicates the presence of an unmodeled thermal resistance, i.e., coking. IV. RESULTS A. Model Accuracy The PINN model was trained for 2,000 epochs on a synthetic dataset of 5,000 samples generated via the Bartzconstrained physics engine. The dataset was split into 80% training and 20% validation. On the unseen validation set, the model achieved a Root Mean Square Error (RMSE) of 5.55 Kelvin (Fig. 1). The simulation utilized the scaled surrogate domain (coolant-side wall boundary), where temperatures ranged from 285 K to 320 K. While flight-ready RP-1 coking typically initiates at wall temperatures exceeding 600 K, this low-temperature validation confirms the PINN’s ability to learn the governing heat transfer dynamics. Fig. 1. PINN Model Predictions vs. Physics Simulation (Ground Truth). The tight linear correlation confirms high accuracy (RMSE = 5.55 K). B. Fault Detection Capability The Virtual Sensor approach successfully distinguished between “Nominal” and “Coked” conditions. In scenarios with injected coking faults (increased thermal resistance), the physics simulation showed a rise in wall temperature while the PINN correctly predicted the lower nominal baseline. This generated a clear residual signal, allowing for anomaly detection even in the presence of 10% added sensor noise. C. Inference Speed A key advantage of this architecture is speed. The average inference time for a single batch prediction was measured at <10 ms on a standard CPU. This represents a speedup of roughly 1000x compared to transient 2D/3D CFD simulations, making it viable for real-time flight controllers. V. CONCLUSION This study demonstrated the feasibility of using PhysicsInformed Neural Networks for real-time thermal monitoring of RP-1 liquid rocket engines. By embedding a calibrated Bartz approximation into the learning process, we achieved a model that is both physically consistent and computationally efficient (1.8% error, <10 ms latency). Future work will involve integrating this model into a hardware-in-the-loop (HIL) simulation to validate its performance on embedded flight computers. REFERENCES [1] J. Meinert, “Experimental Investigation of Coking Characteristics of Kerosene Jet A-1 with Respect to Practical Applications in Rocket Engines,” in 1st CEAS European Air and Space Conference, Berlin, 2007. [2] L. Zhang, Z. Zhai, C. Wang, et al., “Interpretable Fault Diagnosis for Liquid Rocket Engines via Component-Wise MLP-Based Granger Causality Feature Extraction,” Journal of Dynamics, Monitoring and Diagnostics, vol. 4, no. 3, pp. 203-212, 2025. [3] S. Cai, Z. Mao, Z. Wang, et al., “Physics-Informed Neural Networks for Heat Transfer Problems,” Journal of Heat Transfer, vol. 143, no. 6, 2021. [4] H. A. Yasar and O. K. Sevinc, “Physics Informed Neural Networks for Enhanced Critical Heat Flux Prediction in Hypersonic Flows,” in AIAA Aviation Forum, 2024. [5] D. Jalili et al., “Physics-Informed Neural Networks for Two-Phase Flow and Heat Transfer Applications,” International Journal of Heat and Mass Transfer, vol. 235, 2024.