Aerospace Engineering
PINN Aided Scramjet Inlet Design and Analysis
The governing equations of almost all flow fields are characterized by a coupled partial differential equation named the Navier Stokes equations. A branch of fluid mechanics called Computational Fluid Dynamics (CFD) is the most used way to numerically solving the NS equations to simulate the features of the desired flow field.
Equation Set 1, Navier-Stokes Equations Excluding Energy Term
Physics-Informed Neural Networks (PINNs) are a powerful tool for solving problems in CFD by incorporating the governing equations (e.g. NS equations) directly into the neural network training process. Major advantages including a mesh-free simulation (no need of using conventional Finite-Volume Method) and small computation time. For sonic (compressible) flow field applications, current research has showed a potential of using PINNs in shock wave predictions [1] (Guo et. al 2024), [2] (Villanueva D. et. al 2022), in which the correct prediction and re-construction of shock structure is crucial for the design and performance evaluations of super/hypersonic vehicle.
Figure 4, Cone-Derived Waverider [4]
Various popular design methods exist, namely cone-derived, osculating cone and osculating flowfield method. The core design thoughts of all these methods are solving the sonic 3-dimensional flow field numerically for either cones, or a class of power law bodies. Consider the example of a cone-derived waverider, where the sonic flow passes a cone is solved to obtain a working design, in which the governing equations are the Taylor-Maccoll (TM) equations and the streamline equation.
In such case for our project, we would like to focus on applying ML methods for more engineering feasible waverider design methodologies, such as the osculating cone method. The aerodynamic performance of the ML derived waverider will be studied, validated and compared with conventional derived waverider using CFD. Finally, we would like to bring this insight into more complex but feasible methodologies such as the osculating flow field method, in which ML techniques will be implemented into hypersonic small disturbance theory, and the Method of Characteristics (MoC).
Figure 5, Deep Neural Network Implementation with Missile Flight Control [8]
Under this background, for our research project, we would like to focus on bring ML techniques into some basic flight control scenarios such as pitching (longitudinal) movement of the waverider at its on-design condition, or low subsonic speed. For scenarios at on-design condition, the work will be centered on using implicit unsteady CFD methods to obtain large amounts of experimental flight data, then carry out the training of ML models for either designing a control law set, or selection of gain for existing controllers. For low-subsonic flight scenarios, the flight data gathering step could be done by building a technical demonstrator and doing test flights instead of using implicit unsteady CFD methods.
Figure 6, 3V73 Conical Shock and Waverider Solver Developed by the Author
The solver numerically solves non-dimensional TM equation from Equation Set 1 using 5th order Runge-Kutta method and solves the streamline equation using Euler Integration method. With the input of the flow field’s basic properties, and user defined trailing edge curve, the program automatically outputs a correct waverider geometry and its key curves’ coordinate sets for CAD/CAE software modeling interface. The generated geometry is validated by comparing the result with the works of Ding et. al 2015 [4].
The success of this solver allowed our team to be capable of efficiently generating matured waverider designs for any conical flow conditions, therefore it is a remarkable progress that would offer great engineering and mathematical convenience for all our potential research criterions.
Figure 7, Future Solver Development Layout and Research Workflow
Future plans including solver development for more engineering feasible waverider design methodologies such as the osculating cone and flowfield method. These solvers will also be taking major part in the research topic of ANN, DNN Aided Waverider Design.