Open-source Framework for Transonic Boundary Layer Natural Transition Analysis over Complex Geometries in Nektar++

We introduce an open-source and unified framework for transition analysis for laminar boundary layer natural transition at transonic conditions and over complex geometries, where surface irregularities may be present. Different computational tools are integrated in the framework, and therefore overcomes the difficulties of two separate and usually quite disparate processes when using $e^N$ method for transition analysis. To generate a baseflow with desired pressure distribution, appropriate pressure compatible inflow boundary condition needs to be developed and enforced. We first derive the system for 1D numerical stability analysis for boundary conditions, and construct three types of pressure compatible inflow. We demonstrate that the entropy-pressure compatible inflow is stable unlike other choices. Compared with the steady baseflow computation, the unsteady simulation for the disturbance field is more challenging for compressible flows because of complex wave reflections, which can easily contaminate the results. We therefore introduce the two main sources of wave decontamination and corresponding methods to obtain clean signal. The workflow within the framework is then verified by computing the disturbance development in 2D flat plate boundary layer flows at Mach $0.8$. The $N$-factors over a clean flat plate and a flat plate with a forward-facing step are generated, and agree well with the results from the reference. Following the verified workflow, We then analyze the disturbance growth on a wing section of the CRM-NLF model. The N-factor on a 2D simulation is generated and studied.