Direct numerical simulation of supersonic flow and acoustics over a compression ramp

Abstract

We present Direct Numerical Simulations (DNS) of shock turbulent boundary layers interaction (SBLI) at Mach 2.9 over a 24 • ramp. We study both the numerical accuracy and flow physics. Two classes of spatial reconstruction schemes are employed: the Monotonic Upstream centred Scheme for Conservation Laws (MUSCL) and the Weighted Essentially Non-Oscillatory (WENO), of accuracy ranging from 2 nd to 11 th-order. Using the canonical Taylor-Green vortex (TGV) test-case, a simple and computationally inexpensive rescaling of the candidate stencil values-within the context of the high-order WENO scheme-is proposed for reducing the numerical dissipation, particularly in underresolved simulations. For the compression ramp case, higher-order schemes are shown to capture the size of the SBLI separation zone more accurately, a consequence of resolving much finer turbulence structures. For second and fifthorder schemes, the energy of the unresolved small scale turbulence shifts the cascade of the turbulence kinetic energy spectrum, thus resulting in more energetic large scale turbulent structures. Consequently, the λ-shock foot shifts further downstream leading to a smaller separation bubble size. Nonetheless, other statistical quantities, such as the turbulence anisotropy invariant map and the turbulence kinetic energy budget terms, show little dependence on the type and order of the spatial reconstruction scheme. Finally, using the more accurate 9 th-order WENO results, it is reasoned that the interaction of the λ-shock with the post-shock relaxation region drives the low-frequency oscillation of the λ-shock.

Unsteadiness boundaries in supersonic flow over double cones

“…The magnitude of these differences would be totally unacceptable in investigations into turbulence structure or acoustics, such as have been studied by Ritos, Kokkinakis & Drikakis (2018) or Kokkinakis et al. (2020) or for studies of instability modes such as that of Tumuklu et al. (2018), where accuracy to several orders of magnitude is essential.…”

“…The magnitude of these differences would be totally unacceptable in investigations into turbulence structure or acoustics, such as have been studied by Ritos, Kokkinakis & Drikakis (2018) or Kokkinakis et al (2020) or for studies of instability modes such as that of Tumuklu et al (2018), where accuracy to several orders of magnitude is essential. However, in our case, the typical unsteadiness that occurs inside the loop of figure 3 involves unsteady motion of the cone 1 and cone 2 shocks of between 10 % and 100 % of the body scale, so that the resolution achieved with the coarse grid is adequate.…”

Large- and small-amplitude shock-wave oscillations over axisymmetric bodies in high-speed flow

“…A commonly encountered example of this is the unsteadiness generated from interactions between a shock wave and boundary-layer flow, where an adverse pressure gradient imposed by the flow geometry or the shock wave leads to boundary-layer separation. The separation bubble, described by a separation length scale L sep , generates a separation shock that exhibits unsteady oscillatory motion along a region of length L i upstream of the bubble (Clemens & Narayanaswamy 2014;Kokkinakis et al 2020). Such interactions typically occur in high-speed flow deflection over a ramp/fin/protuberance or with impingement of an oblique shock onto a surface (see figure 1); here, the ratio L i /L sep is observed to be approximately 0.3 (Dussauge, DuPont & Debieve 2006).…”

“…The separation bubble, described by a separation length scale , generates a separation shock that exhibits unsteady oscillatory motion along a region of length upstream of the bubble (Clemens & Narayanaswamy 2014; Kokkinakis et al. 2020). Such interactions typically occur in high-speed flow deflection over a ramp/fin/protuberance or with impingement of an oblique shock onto a surface (see figure 1); here, the ratio is observed to be approximately 0.3 (Dussauge, DuPont & Debieve 2006).…”

Flow transition to turbulence and induced acoustics at Mach 6

“…We have employed DNS and iLES in the framework of the CFD code CNS3D [29][30][31][32] . In classical Large Eddy Simulations (LES), the smallest length scales, which are the most computationally expensive to resolve, are removed via low-pass filtering of the Navier-Stokes equations.…”