Future sustainable growth of the aviation and aerospace industry relies on continued improvements in efficiency giving reductions in fuel consumption and increases in payload. Research efforts therefore focus on aerodynamic performance and structural weight savings. This inherently requires more highly performing wings, control surfaces and nozzles, in which transonic flow and supersonic is common place, and the formation of shock waves the key aerodynamic challenge. In particular, the interaction of shock waves with boundary-layers is one of, if not the main performance-limiting or safety critical flow phenomena across all of these flow fields. Thus, solid understanding of the interaction of shock waves with boundary layers (SBLI) is essential for the development of future, more efficient, air vehicles and engines. Increased aerodynamic forces can lead to flow separation and reductions in engine and airframe efficiency. In such cases, flow control is needed to maintain system performance. However, novel designs are also likely to increase the extent of laminar flow and this implies that flow control devices need to operate in a laminar or transitional regime. This requires a better understanding of their function and their interaction with flow transition. In the present research project we aim at improving the understanding and predictive capabilities of SBLI through (1) improvement of fundamental understanding of SBLI physics including three-dimensionality and unsteadiness; and (2) development of novel high-fidelity numerical methods for the prediction of SBLI effects.
The proposed research project is intended to go substantially beyond the state-of-the-art in numerical simulations of SBLI in at least two ways:
i) the project will lead to further improvement of the current CFD predictive capabilities both with reference of shock-capturing and shock-fitting numerical methods;
ii) the project will yield improved physical understanding of the complex phenomena involved in SBLI, with special reference to flow three-dimensionality and unsteadiness.
The innovative aspects and scientific challenges inherent to the present project are discussed in detail below.
Computational challenges
One of the long-standing issues in the CFD community is whether shock-capturing (SC) or shock-fitting (SF) algorithms should be used in the study of compressible turbulence. The two approaches have relative strengths and weaknesses. The main strength of the SC approach is simplicity, as the same algorithm is used at all grid points, with no need to explicitly trace shock waves. On the other hand, this implies that shock are necessarily spread over a certain (hopefully limited) number of grid points, with incurred uncertainty on the actual shock position. As it turns out, this limitation causes the effective order of accuracy in the presence of moving shock wave to drop to unity, irrespective of the formal order of accuracy of the SC discretization. This problem is cured by SF methods which instead explicitly track shock waves and enforce precisely the Rankine-Hugoniot jump relations across. Hence, uniformly high order of accuracy is recovered, however at the price of greater code complexity, as shock fitting requires a considerable amount of book-keeping, and changes of flow topology are harder to handle. Research carried out in the present project with state-of-the-art codes in the respective fields is eventually aimed at answering the question of which of the two methodologies is most accurate and computationally efficient in shock-turbulence interaction problems.
Physical and technological challenges
Based on the description of the state-of-the-art, we believe that further study of CSBLI is appropriate. In particular, limited information about the detailed three-dimensional structure of the interaction can be gained based on the available experimental data. Furthermore, no high-fidelity computation (i.e. LES and/or DNS) has been reported so far. Hence, we believe that a reliable DNS database of CSBLI can help the research community in achieving improved physical understanding of the phenomenon. To make our analysis sufficiently general, we will consider a relatively simple geometrical set-up, whereby a turbulent boundary layer develops over a flat surface, and a conical shock wave is made to interact with it. LES and DNS have obvious limitations in terms of maximum achievable Reynolds number, mainly due to to the need to resolve the viscous sublayer. Achieving Reynolds numbers typical of realistic aerospace applications inevitably requires the use wall models (Kawai & Larsson, 2012; Larsson et al., 2016). Part of the research work will thus be devoted to applying wall models for the prediction of CSBLI at high Reynolds number. This is quite challenging, as all existing models to date have been developed and tuned for the case of two-dimensional mean flow, and correct prediction in the presence of cross-stream pressure gradients is far from granted.
Regarding the study of SBLIs in nozzles, the technology is still somewhat obsolete, mainly relying on classical steady RANS simulations. However, those are known to suffer from poor prediction of shock location and separation extent in over-expanded nozzles (Stark & Hagemann 2007). Furthermore, owing to intrinsic limitations, they cannot provide information about unsteady mechanisms of shock oscillation, which may negatively affect the nozzle performance and cause significant structural vibrations. Unsteady, three-dimensional simulations based on the DES methodology have only started to emerge in recent years, with substantial contribution from the applicant group (Martelli et al. 2017, 2019). However, those high-fidelity simulations were carried out for planar geometries, which limits somewhat their relevance for practical cases. Within the present research we aim at applying this technology to the case of a realistic, axi-symmetric nozzle, by considering both shock-capturing and shock-fitting numerical discretizations.