The 3d viscous problem

The major flaw of potential theory is the explicit assumption of an inviscid fluid. In the words of Richard Feymann, this is equivalent to the study of “dry water” and has “nothing to do with the real stuff”.

As explained in the short series on xflr5’s theoretical background, the whole 3d model is based on potential flow theory, and the viscous drag is merely extrapolated from 2d data and added in at the end of the 3d analysis. This is a very crude method that cannot be expected to give more than an order of magnitude of the viscous properties. And it is worth bearing in mind that the greater the viscous effect, the less precise the evaluation of lift and drag will be. This observation limits the scope of potential analysis to high Reynolds numbers, low angles of attack and low flap deflections.

In some cases, this may be sufficient, for instance if the goal is only to optimise induced drag or to evaluate flight dynamic stability. In most cases however it is a severe limitation to the use of potential methods.

The improvement of this situation requires the implementation of an Interactive Boundary Layer (IBL) loop.

As a first step, the 2d IBL method described by Professors Cebeci and Cousteix has been implemented as an experimental feature in flow5.

In 3d, the simplest form of the loop is described in the NACA TN-1269 report “Method for calculating wing characteristics by lifting-line theory using nonlinear section lift data”. It is implemented in xflr5 as the “Non-linear LLT”. In fact, there is no BL calculation at all during the loop, since the data is available from experimentation or previous 2d calculations at the start of the 3d analysis.

An analogous loop for the panel methods has been described in (link) and implemented in flow5, with benefits comparable to those of the non-linear LLT.

At the next level of complexity, a 2d boundary layer calculation needs to be performed at each span section, with the displacement thickness being fed back into the 3d analysis, either in the form of a modification of the geometry or as a surface blowing velocity. The calculation is repeated until convergence is achieved, i.e. a solution is reached where the surface velocity at the edge of the BL is a simultaneous solution for the 3d analysis and the 2d analysis at each span station. Such a method could be worth attempting in an application such as flow5. It is however a huge effort to implement and there is no /a priori/ guarantee that convergence will be achieved easily or with consistent accuracy for general configurations.

Lastly, at the next level, a full 3D Integral Viscous Method for General Configurations has been proposed by Pr. Drela, but the complexity of its implementation presently puts it beyond the scope of flow5.

All in all, implementing a 3d viscous model would be hugely valuable and is one of the main challenges facing flow5. It may be an opportunity to work in partnership with research centers or aerospace companies interested in the subject.