Numerical simulations on vortex dominated delta wings wıth anisotropic adaptive mesh generation

Abstract

In the world of aerospace engineering, Computational Fluid Dynamics (CFD) has firmly established itself as an indispensable resource, primarily due to its ability to simulate and analyze highly complex fluid phenomena. Within this topic, the aerodynamics of delta wings present a particularly challenging yet highly efficient application for CFD methods. Delta wings, characterized by their slender and sharply swept geometry, are fundamental components in the design of high-performance aircraft, largely because of their distinctive aerodynamic properties, especially when operating at high angles of attack. CFD provides detailed insights into these intricate flow behaviours, and is developed in conjunction with experimental investigations. A key characteristic for which delta wings are known and specifically designed is their capability to generate strong, stable leading-edge vortices (LEVs) at moderate to high angles of attack. These vortices, which due to the sharp leading-edge, operate on the principle of leading-edge suction, creating a significant region of low pressure above the upper wing surface. The phenomenon contributes substantially to the enhancement of the lift mechanism, allowing the aircraft to maintain lift well beyond the stall angle typically observed in conventional airfoils. However, the stability of these beneficial LEVs is not infinite; as the angle of attack increases further, they become unstable and undergo a critical phenomenon known as vortex breakdown. This breakdown is characterized by a sudden disorganization of the vortex structure, an abrupt increase in turbulence, and can lead to detrimental consequences such as a reduction in lift, an increase in drag, and potentially unstable or unpredictable flight characteristics. The precise details of these vortical structures and their breakdown mechanism are crucial areas of study. Through these sophisticated studies and simulations, CFD enables aerodynamic solutions to visualize three-dimensional flow structures, quantify aerodynamic forces and moments acting on the wing, optimize wing designs for enhanced performance, and investigate various flow control strategies aimed at mitigating adverse effects like vortex breakdown. Despite significant advancements in CFD methodologies and computational power, simulating delta wing aerodynamics accurately remains a demanding task. The fidelity of CFD simulations relies heavily on the appropriate selection of modeling parameters, turbulence models. and numerical schemes. Consequently, experimental validation, such as data provided by well-established test cases like the Second Vortex Flow Experiments (VFE-2) and the Sydney Standard Aerodynamic Models (SSAM) 5th Generation Fighter Delta Wing (Gen5) are examined in this study. As mentioned, the present study uses the experimental benchmarks VFE-2 and SSAM-Gen5 delta wing models for the validation of the in-house solver and to examine delta wing flow physics. The studies will be executed by using the in-house RANS solver the HEMLAB algorithm, a vertex-based finite volume method with an efficient edge-based data structure on hybrid meshes to solve the non-dimensional RANS equations. The solver uses the Negative Spalart-Allmaras (SA-neg). For this study SA-neg, SA-neg with Kato-Launder correction, and the Negative Spalart-Allmaras with rotation correction (SA-neg-R) with different rotation constant values are compared. The HEMLAB algorithm uses the HLLC, Roe, and AUSM+up flux discretization methods for the inviscid fluxes. The HEMLAB solver uses the non-linear exact Newton method and the PETSc library, which uses several Krylov subspace algorithms to solve equations. The PETSc-matrix free non-linear solver (SNES) is used by the algorithm. Grid generation has an important role in the process. The quality of the computational mesh is essential for accurately resolving the sharp leading edges of the delta wing and capturing the steep gradients in the pressure and velocity that occur around and in the vortex regions. Unstructured grids provide flexibility for handling complex geometries, whereas structured grids can offer accuracy in regions where the flow is smoother. In this study, despite using fixed meshes, an anisotropic adaptive mesh generation tool the pyAMG library by INRIA, is used in combination of the HEMLAB solver. This tool generates and refines meshes according to the selected functions and necessary regions by using the solution to iteratively refine the mesh resolution.