Fluid-dynamic stability tools in OpenFOAM

Turbulent flow separation is a critical phenomenon that occurs in a wide range of industrial applications, such as airfoils at high angles of attack, bluff body wakes, and engine inlets and nozzles. Separated flows are characterized by unsteady behavior with broad ranges of frequency and length scales; however, the most dramatic effects are often associated with low-frequency large-scale motions that significantly impact flow dynamics by introducing strong frequency peaks into the entire fluid domain. The prediction and characterization of these unsteady flow features has been the object of several research initiatives aimed at modelling low-frequency oscillations or aiding the design of flow control systems. Standard stability analyses of laminar and turbulent flows often rely on highly accurate numerical approaches such as spectral methods, high-order finite-element methods, and high-order finite-difference schemes. However, it can be argued that these high-order methodologies are often ill-suited for typical industrial configurations, which generally feature unstructured and strongly non-orthogonal grids with near-wall prismatic layers. In this work, we present a numerical toolbox for the stability analysis of incompressible flows on complex grids. The proposed framework utilizes a transient solver developed as an in-house modification of the standard incompressible solvers embedded in the open-source code OpenFOAM, relying on a second-order spatio-temporal discretization based on the finite volume method. The numerical workflow involves generating snapshots representing the perturbation evolution, obtained by advancing the linearized perturbation equations in time from a random initial condition. Physically meaningful stability modes are subsequently extracted from the snapshot data using Dynamic Mode Decomposition, coupled with specific tools to eliminate numerically spurious eigenmodes. Several linearized solvers are implemented within the toolbox, covering the "standard" stability analysis for laminar base flows, as well as the quasi-laminar and frozen eddy-viscosity approaches for turbulent mean flows. The proposed framework is validated against test cases for both laminar and turbulent flows. Laminar benchmarks include the cubical lid-driven cavity flow and the vortex shedding past a circular cylinder at low Reynolds numbers. Regarding turbulent flows, the solver capabilities are assessed through the analysis of the confined turbulent wake past a D-shaped cylinder and through the analysis of a turbulent separation bubble developing over a flat plate under a combination of adverse and favourable pressure gradients.