Interaction of two-dimensional spots with a heat releasing/absorbing shock wave: linear interaction approximation results

Abstract

The canonical interaction between a two-dimensional weak Gaussian disturbance (entropy spot, density spot, weak vortex) with an exothermic/endothermic planar shock wave is studied via the Linear Interaction Approximation. To this end, a unified framework based on an extended Kovasznay decomposition that simultaneously accounts for non-acoustic density disturbances along with a poloidal-toroidal splitting of the vorticity mode and for heat-release is proposed. An extended version of Chu's definition for the energy of disturbances in compressible flows encompassing multi-component mixtures of gases is also proposed. This new definition precludes spurious non-normal phenomena when computing the total energy of extended Kovasznay modes. Detailed results are provided for three cases, along with fully general expressions for mixed solutions that combine incoming vortical, entropy and density disturbances.where M t and M 1 are the upstream turbulent and mean Mach numbers, respectively. This criterion was later refined using DNS with higher resolution by Ryu & Livescu (2014), yieldingwith M t2 and M 2 the downstream (LIA-predicted) turbulent Mach number and the † Email address for correspondence: pierre.boivin@univ-amu.fr

Compositional and entropy indirect noise generated in subsonic non-isentropic nozzles

“…In the supersonic case, the entropic indirect noise generation was analysed in detail by Moase, Brear & Manzie (2007) and Leyko et al. (2011), while the interaction of entropy spots with two-dimensional shock waves was studied in detail by Mahesh, Lele & Moin (1997) and Farag, Boivin & Sagaut (2019).…”

Effect of equivalence ratio fluctuations on planar detonation discontinuities

“…The motivation was to improve descriptions of the influences of compressible turbulence on detonation propagation and, in particular, to determine how passage of a planar detonation modifies the turbulence. This work complements these fundamental studies, particularly the work of Huete et al (2013) on the interaction of detonation with density perturbations, by placing the focus on the mixture imperfections that add another type of convective perturbation (Griffond 2005;Farag, Boivin & Sagaut 2019), i.e. the local heat of combustion of the mixture.…”

On the performance of WENO/TENO schemes to resolve turbulence in DNS/LES of high‐speed compressible flows

“…8 Nevertheless, the sensor type would not have a noticeable effect on the results of the present study due to the absence of shocks and flow discontinuities. C T is dynamically adjusted by the shock sensor Φ as C T = 10 −⌊ 1 − 2 (1−g(Φ))⌋ , where g(Φ) = (1−Φ) 4 (1 + 4Φ) and ⌊⌋ is the Gauss bracket. 8,35 The adjustable parameters 1 and 2 are taken as 1 = 10.5 and 2 = 4.5 in the present study.…”

“…DNS and LES of subsonic and supersonic plane channel flows with a domain size of 4 H × 2H × 4 3 H are conducted. H denotes the channel half height and is set to H = 1 in the present study.…”

“…High-speed compressible turbulent flows play a significant role in a variety of advanced fluid mechanics related applications and disciplines such as supersonic or hypersonic aerodynamics and combustion, aerospace propulsion, inertial confinement fusion, and astrophysics. [1][2][3][4][5] Those flows typically contain shockwaves and flow discontinuities and have been widely modeled using Weighted Essentially Non-Oscillatory (WENO) schemes 6,7 due to their high-order accuracy and sharp shock/discontinuity capturing capability. However, those schemes, which aim to stabilize the solution by adding numerical dissipation, may damp some scales of turbulence and as a consequence result in inaccurate solutions in the context of turbulence-resolving simulations, unless excessively fine spatial resolutions are used, which is not practical for direct numerical simulation (DNS) of complex flows.…”