Establishing Vehicle Design Criteria to Postpone Transition Onset along Trajectories of Generic Flight Vehicles
Frederik Jacobs 1*, Johan Steelant 2
* Corresponding author
1 Young Graduate Trainee, ESA/ESTEC, Keplerlaan 1, 2201AZ Noordwijk, The Netherlands, Frederik.Jacobs@esa.int
2 Senior Flight Vehicles & Aerothermodynamics Engineer, ESA/ESTEC, Keplerlaan 1, 2201AZ Noordwijk, The Netherlands, Johan.Steelant@esa.int
Keywords: Transition visualization, High-speed transition modelling, Boundary layer, Post-processing
To assure an improved aerodynamic and thermo-structural design for high-speed flight vehicles, engineering tools are required to map instantaneously the most plausible transition locations while incorporating features to postpone this onset to minimize the integral heat load and impulse loss. As highlighted in , pending on the exact location of the transition onset, the vehicle weight could differ with a factor of two. Additionally, for reusable spacecraft, the location of transition onset is equally important to estimate accurately the heat load at each position to size the thermal protection system accordingly and to reduce the overall impulse loss during the propelled ascent phase.
From an aerodynamic point of view, the internal or external flowfield of a vehicle can be adapted or shaped to postpone the transition onset and its extent. Despite an optimal mold line being realized, it still intrinsically assumes an aerodynamically smooth surface and precludes any practical structural considerations such as interfaces, junctions, materials, protuberances…. For the thermo-structural design however, it is important to have an envelope of allowable tolerances at hand to assure the outer shape still remains aerodynamically smooth while introducing steps, gaps and joints intrinsically linked to the manufacturability of the vehicle. Contrary to the above, for particular geometries such as air intakes and flaps facing adverse pressure gradients inherently needed for their functionality, the onset needs to be guaranteed and to take place at predefined locations requiring the right tripping geometries in terms of location, shape and size.
In a first iteration, the use of correlations should provide a fast and adequate assessment of the transition location. Various correlations exist, but they usually depend on parameters such as displacement thickness, momentum thickness, canonical protuberance geometries … which are not readily available for aero-propulsive databases generated by standard CFD-tools. Furthermore, as the flight conditions evolve throughout a trajectory, the actual onset locations are not fixed but evolve over time. Therefore, an engineering tool  was developed to post-process the aerodynamic database generated by CFD-simulations and to extract and generate the required parameters for transition predictions. To properly assess the transition parameters an accurate interpolation is required. A new methodology is implemented which interpolates the boundary layer linearly within the point cloud given by the CFD simulation. Using linear interpolation allows to use more advanced boundary layer edge detection algorithms based on the first and second derivative of the velocity profile, which could not be used in the previously existing nearest neighbour interpolation. Even though they can still result in local erroneous results due to discontinuities in the derivatives, the overall accuracy of the boundary layer edge detection will be increased. Additionally, this methodology is parallelized which allows the linear interpolation of large simulations, needed to assess the transition of complex vehicles. Further elaboration of the design tool allows to visualize and to assess the temporal evolution of the transition onset and length throughout the flight trajectory of a vehicle.
A first test case of transition onset evolution along the launch trajectory of Ariane 5’s fairing can be seen in Figure 1 for Mach numbers ranging from subsonic to hypersonic regime using the Bowcutt transition criterion . The results for two geometries can be seen: the original contour of Ariane 5 as well as an elliptic profile which eliminates the discontinuity in the second derivative of the profile at the nose cap. The simulations are performed using TAU (CFD tool by DLR) in the laminar regime and are post-processed with the presented tool using linear interpolation. For lower Mach numbers the transition location for the actual contour is located just behind the nose cap. Only as from Mach 2.5, the transition onset starts moving backwards towards the start of the cylindrical profile with a rapid shift as from Mach 3.5 onwards. For the elliptic profile the transition onset location is initially slightly behind the original one. However, it moves backwards earlier starting around Mach 2 up till the location of the connection between the elliptic profile and the cylindrical profile near the end. The transition location, for both profiles, stays at the intersection to the cylindrical profile up to Mach 4, at which time is starts moving backwards quickly. Optimizing the geometry by eliminating discontinuities in the second derivative of the profile results in an overall gradual delay of transition reducing the integral heat load and total impulse loss. Additionally, it would also be possible to optimize the trajectory of a vehicle based on a certain geometry to keep the vehicle in laminar state as long as possible.
The previously described result was based on natural transition. However, also roughness induced transition can occur. To assess this, the allowed roughness along the body over time to prevent roughness induced transition can be calculated as well. The allowed discrete roughness for the original Ariane 5 contour can be seen Figure 1.a . Since the most forward point has the lowest allowed roughness, it would be recommended to focus roughness reduction on the nose cap. Comparing left and right of Figure 1 shows that reducing the discrete roughness below 0.1mm would not further delay the transition, since in this case natural transition (left) would dominate over roughness induced transition (Figure 1.b). The critical roughness for the elliptical profile is almost identical to the one of the original Ariane 5 contour. Therefore, changing to an elliptical profile is beneficial if natural transition is happening, but does not have any influence when roughness induced transition is present.
A similar analysis on the trajectory of the reusable HXI vehicle will be performed. To ascertain during manufacture and integration an aerodynamically smooth surface, Figure 2 provides the maximum affordable step size at each point along the geometry using the methodology elaborated in . As one can e.g. notice at the nose-fuselage interface, a backward facing step has a 10 times larger tolerance than a forward facing step, allowing the designer to anticipate the needed step at (cold) integration, while anticipating the differential thermal expansion of the copper nose with respect to the titanium fuselage at their common interface. Having this information in an early stage of development is useful to properly decide about the allowed roughness to optimize the aerodynamic properties of the vehicle.
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