Causal Inference Analysis to Find Relationships Found in Boundary-Layer Transition – Part I: Theoretical

Understanding the transition from laminar to turbulent flow – Boundary-Layer Transition (BLT), we can design better state-of-the-art vehicles for defense and space applications, which can mitigate the limitations in current high-speed temperature conditions. BLT is a subject of fluid flow disturbances created by geometric parameters and flow conditions, such as surface roughness, increased velocity, and high-pressure fluctuations, to name a few. These disturbances lead to the development of turbulent spots and differential heating. Historically, the Reynolds number has been used to predict whether a system will develop turbulent flow. However, it has been known for decades that it is not always reliable and cannot indicate where the BLT will occur: some experiments present scenarios where the flow is laminar at a high Reynolds number and vice versa. We can predict the BLT from performing physical experiments, but they are expensive and physical configurations are limited. Despite many community efforts and successes, no general computational solution to simulate different flows and vehicle types that fully incorporate BLT exists. Many are a considerable number of parameters that affect BLT. Therefore, we use Causal Inference to predict BLT by cause-and-effect analysis on multivariate data obtained from BLT studies. Data generated using high-fidelity Computational Fluid Dynamics (CFD) with resolved Large-Eddy Simulations (LES) scales, will be analyzed for turbulence intensity by decomposing velocity in mean and fluctuations. In this paper, we will be discussing approaches on how we predict BLT scenarios using cause and effect relationships driven by causal inference analysis.