Triple-deck and direct numerical simulation analyses of high-speed subsonic flows past a roughness element

Abstract

This paper is concerned with the boundary-layer separation in subsonic and transonic flows caused by a two-dimensional isolated wall roughness. The process of the separation is analysed by means of two approaches: the direct numerical simulation (DNS) of the flow using the Navier-Stokes equations, and the numerical solution of the triple-deck equations. Since the triple-deck theory relies on the assumption that the Reynolds number (Re) is large, we performed the Navier-Stokes calculations at Re = 4 × 10 5 based on the distance of the roughness element from the leading edge of the flat plate. This Re is also relevant for aeronautical applications. Two sets of calculation were conducted with the free-stream Mach number Ma ∞ = 0.5 and Ma ∞ = 0.87. We used different roughness element heights, some of which were large enough to cause a well-developed separation region behind the roughness. We found that the two approaches generally compare well with one another in terms of wall shear stress, longitudinal pressure gradient and detachment/reattachment points of the separation bubbles (when present). The main differences were found in proximity to the centre of the roughness element, where the wall shear stress and longitudinal pressure gradient predicted by the triple-deck theory are noticeably different from those predicted by DNS. In addition, DNS predicts slightly longer separation regions.

Non-modal analysis of spectral element methods: Towards accurate and robust large-eddy simulations

“…However, with the increase in computing power, LES is becoming a feasible technique to underpin the complexity of challenging industrial flows at high-Reynolds numbers, and spectral element methods (also referred to as spectral/hp methods, briefly SEM) are a competitive candidate to improve the performance of the overall computer-aided workflow [45]. In fact, the adoption of SEM in the context of LES, including the use of continuous Galerkin (CG) methods [28,30], standard discontinuous Galerkin (DG) methods [5,21,22,35,47,57,69,73], hybridized DG methods [16,17], spectral difference (SD) methods [33,54] and flux reconstruction (FR) methods [53,70], is emerging as a promising approach to solve complex turbulent flows. First, they allow for high-order discretizations on complex geometries and unstructured meshes.…”

Receptivity of supersonic boundary layers over smooth and wavy surfaces to impinging slow acoustic waves

“…For example, comparisons with experiments (Wu 2001a, b) indicate that the theory, especially with the extension to second-order accuracy, predicts fairly accurately receptivity in the incompressible regime. Recent DNS studies (Mengaldo et al 2015, De Tullio & Ruban 2015 showed that the same is true for subsonic boundary layers. Nevertheless, further work is still needed in order to validate the present theoretical results for supersonic boundary layers.…”

Direct numerical simulation of a compressible boundary-layer flow past an isolated three-dimensional hump in a high-speed subsonic regime

“…Moreover, it is a good approximation of the skin temperature close to the leading edge of civil aircraft at similar altitudes and speeds. In addition, this choice permitted a direct comparison of the results with those obtained for the equivalent two-dimensional simulations in [31,32]. The Prandtl number Pr, defined as the ratio of kinematic viscosity ν to thermal diffusivity α = k/ρC p , that is, Pr = C p μ/k, where C p is the specific heat at constant pressure, was fixed and corresponds to the value commonly adopted for air.…”

“…The computational domain is a Cartesian box extending for L x ≈ 40δ, L y ≈ 20δ, and L z ≈ 6δ in the streamwise (x), spanwise (y), and normal (z) directions, where δ is the compressible boundarylayer thickness at the roughness location at Ma = 0.87 chosen as the reference length of the domain. The size of the domain in the streamwise direction was based on a sensitivity study performed in [31] for a similar two-dimensional problem. The size of the domain in the spanwise direction was based on considerations of the dimensions of flow structures behind the hump.…”

“…The aim of this paper is to start closing the gap between the DNS results in the high-speed subsonic regime and the data present in the literature for similar analyses in supersonic and hypersonic regimes. The DNS study is the three-dimensional extension of the work done by Mengaldo et al in [31]. Specifically, we perform a DNS study of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussianshaped hump at Ma = 0.87.…”