Conclusion

Moving towards the routine use of Navier-Stokes methods in aerodynamic design, the adequate representation of turbulent effects constitutes an absolute necessity. Thus, the improved modelling of turbulence formed an integral part of the MEGAFLOW project throughout its course and is continued in subsequent projects such as the ongoing TAURUS programme. At the start of MEGAFLOW, algebraic models and the standard Wilcox $k$-$\omega$ two-equation model formed the backbone of applied viscous simulations. Owing to their unsatisfactory predictive accuracy, the development and transfer of more advanced approaches from academia to industry became an important issue in the project.

To this end, a variety of enhanced one- and two-equation models have been either taken from the literature or developed, integrated and validated in FLOWer and, more recently, also in the TAU code. Starting from one-equation and enhanced linear two-equation approaches, the focus gradually shifted towards the more general non-linear EASM, with their linear truncations forming an intermediate stepping stone.

The validation exercises performed, ranging from simple profiles to three-dimensional configurations featuring a high degree of physical and geometric complexity, demonstrate the capabilities of the integrated turbulence models. In general, the application of enhanced modelling concepts leads to a predictive accuracy that has improved significantly as compared to the standard approaches available at the start of MEGAFLOW. Table 2 gives a qualitative rating for high-lift and cruise-flight conditions, respectively. Furthermore, as the models presented imply only a tolerable computational overhead, their use in the industrial design process can be advocated, especially when their applicability in parallel algorithms is ensured. This will become of even bigger importance in the future, since flow solver parallelization (whether MPP or PVP) is the only feasible strategy to attack large-size problems.

Table 2: Qualitative rating of the EVM available in FLOWer and TAU (Predictive performance indicator: -: poor, 0: average, +: fair, ++: good)

Additionally, it should be noted that the robustness of the numerical algorithm can be significantly increased by means of physically consistent modelling, e.g. by enforcing the length-scale variable to obey an integral formulation of the Schwarz inequality resulting from realizability constraints. Such a limiter has been integrated in both FLOWer and TAU and proved very helpful.

However, a few further remarks seem to be in order here. While cruise-flight simulations can be computed quite accurately today, albeit not with the exactness needed for drag prediction, it has to be stated that in high-lift flows, quantitative agreements with experimental data are much harder to achieve than in transonic conditions. Nevertheless, even a qualitative improvement of the flow simulation accuracy is useful to the aerodynamic design. Enhanced turbulence modelling can help to propel the evaluation of such systems, especially if the general behaviour of a turbulence model has been determined on known cases. However, contrary to earlier aspirations, as no universal approach is available, it might prove necessary to use several computations with different models and the design engineer's expertise to judge a new configuration.

While turbulence modelling efforts in MEGAFLOW concentrated on steady simulations, future developments will also include unsteady flows. Suggestions of hybrid methods such as Detached-Eddy Simulation (DES) have shown promising results [21], however, whether DES will become a pillar of practical aerodynamic computations soon remains a controversial issue [2]. Additionally, measures dedicated to enhance efficiency and robustness, such as generalized boundary conditions [22] or interation schemes ensuring positivity [23] will be investigated. Finally, as also the results presented here indicate, the pressing need for adequate engineering methods for transition prediction should be mentioned. Thus, the effort towards accurate and reliable viscous flow prediction methods will continue.