14.6 Hierarchy of CFD Simulation Methods

numerical simulation (DNS) techniques; at the bottom are panel methods. A rough guide to the members of the hierarchy and their respective abilities is provided in the following subsections.

14.6.1 DNS Simulation Technique

DNS is capable of simulating time-dependent turbulent flows, capturing the dynamics of the entire spectrum of eddy sizes. This requires grids and time steps that are finer than the length and time scales at which turbulent energy is dissipated. Lowdiffusion numerical schemes are necessary. DNS is useful for supplementing experimental data and aiding the development of turbulence models, but it is prohibitively expensive at the flight Re numbers. It is not used in the design process. Currently, DNS is the most sophisticated method.

14.6.2 Large Eddy Simulation (LES) Technique

LES takes advantage of the fact that the smallest dissipative eddies are isotropic and can be efficiently modeled using simple subgrid scale models. Meanwhile, the dynamics of larger eddies, which are anisotropic, is simulated using a grid and time step sufficiently fine to resolve them accurately. The method, therefore, is applicable to flows at relatively high Re numbers but is still expensive for use as an engineering design tool.

14.6.3 Detached Eddy Simulation (DES) Technique

DES is considered halfway between the LES and the Reynolds Averaged Navier– Stokes (RANS) techniques. The method employs a RANS turbulence model for near-wall regions of the flow and a LES-like model away from the wall. The method was first proposed by Spalart et al. in 1997 and is still the subject of research. It may become a standard engineering tool, but it is currently unlikely to be an element of the conceptual and preliminary design toolkits.

14.6.4 RANS Equation Technique

The time-dependence of turbulent fluctuations is averaged to form the RANS equations. This results in the appearance of the so-called Reynolds stresses in the equations, and the modeling of these equations (i.e., turbulence modeling) becomes problematic. There are many turbulence models but each falls prey to the fact that turbulence is flow-dependent; consequently, no turbulence model can be generally applicable, and a CFD practitioner must be cognizant of the strengths and failings of the models employed. Nonetheless, RANS allows relatively inexpensive modeling of complex flows; when allied to a suitable optimization method, it can be a powerful tool for design synthesis.

14.6.5 Euler Method Technique

Euler equations are obtained when the viscous terms are omitted from Navier– Stokes equations, allowing faster predictions of pressure distributions. They can be

usefully employed at the preliminary design stage. Viscous effects can be included by integrating boundary-layer methods and by displacing the surface of the aerofoil, wing, or aircraft by an amount equal to the local boundary-layer displacement thickness.

14.6.6 Full-Potential Flow Equations

The full-potential flow equations assume that the flow is irrotational. Compressible flows can be modeled but the “shocks” that are predicted are isentropic. The method is now quite dated but it can provide rapid information about pressure distributions and – like the Euler method – it can be integrated with a boundary-layer method.

14.6.7 Panel Method

This is simplest of all numerical methods for predicting flow around an aircraft. The surface of an aircraft is covered with panels, each one a source of sink, and some (e.g., those on lifting surfaces) are assigned a bound vortex (with its associated trailing vortex system). The strengths of the sources and bound vortices are initially unknown but can be determined through application of the boundary conditions (e.g., flow tangency at solid surfaces).

Descending through the hierarchy, the methods provide less physical fidelity but also require less computational effort. It is conceivable that the panel method, full-potential flow equations, Euler equations, and RANS method can be used in an undergraduate aircraft-design project (as a separate task), although not at the conceptual design stage. These methods provide a qualitative pressure-distribution pattern to help shape the geometrical details. Whichever method is used, the issue of grid generation must be addressed: More time is spent on the generation of a suitable mesh than on the prediction of flow.

A 3D model created in CAD is useful at this stage. The planning to prepare the 3D model in CAD should be done in such a way that Boolean operations can build it from isolated components, while still retaining the isolated components for a separate analysis. The wing-fuselage analysis provides the tail-less pitching moment data, which are useful in designing the aircraft H-tail and its setting relative to the fuselage to minimize trim drag.

CFD results can be compared with results obtained through use of the semiempirical relationship (e.g., drag) (see Chapter 9). Generally, semi-empirical drag results are considered to provide good accuracy, validated on many aircraft consistent over a long period of use.

Figure 9.8 presents the wave drag, CDw , for the Mach number. CFD provides an opportunity to generate a more accurate viscous-independent wave drag versus the Mach number. When the CFD results are available, the data in Figure 9.9 may be replaced, thereby obtaining a further iteration on the drag polar of the aircraft. CFD is also a good place to generate CDp values to be used for comparison. In general, CFD-generated CDp values should provide good values if the CFD is set up properly.

If the CFD results are within 10% of the results obtained using semi-empirical relations, then they may be considered good. Some adjusting of the CFD runs should