6 - Computational Fluid Dynamics for Steady and Unsteady Flows

Summary

The knowledge gained in the previous two chapters leads to procedures for computing solutions to the Navier–Stokes equations in 2D and 3D. Chapter 6 explains the major components and functions of a typical Reynolds-averaged Navier–Stokes (RANS) code, including the modeling of turbulence in steady or unsteady flows. Convergence acceleration devices, including multigrid techniques, are explained. Finite-volume formulation and standard physical modeling for turbulence yields the RANS equations used in most computational fluid dynamics (CFD) codes directed toward compressible-flow aeronautical applications. By taking the reader through a RANS application step by step, this chapter illustrates the process that an informed CFD user needs to know for applying a typical code of this genus to aerodynamic design. Two practical cases of transonic flow over an airfoil – one in steady flow and the other in unsteady buffeting flow – demonstrate execution of the workflow. Computing a Mach sweep across the entire transonic regime, the steady-flow example exhibits the nonlinear phenomenon of shock stall. Mastering this chapter makes the student a reasonably well-informed CFD user who understands how to carry out a sensitivity analysis to demonstrate CFD due diligence.