Large-eddy and unsteady RANS simulations of a shock-accelerated heavy gas cylinder

• Published in: Shock waves Vol. 26; no. 4; pp. 355 - 383
• Main Authors: Morgan, B. E., Greenough, J. A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2016; Springer Nature B.V
• Subjects: Acoustics; Closures; Condensed Matter Physics; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Fluid- and Aerodynamics; Gas cylinders; Heat and Mass Transfer; Large eddy simulation; Original Article; Reynolds averaged Navier-Stokes method; Thermodynamics; Richtmyer–Meshkov instability; Turbulent mixing; Large-eddy simulation
• ISSN: 0938-1287; 1432-2153
• DOI: 10.1007/s00193-015-0566-3

Two-dimensional numerical simulations of the Richtmyer–Meshkov unstable “shock-jet” problem are conducted using both large-eddy simulation (LES) and unsteady Reynolds-averaged Navier–Stokes (URANS) approaches in an arbitrary Lagrangian–Eulerian hydrodynamics code. Turbulence statistics are extracted from LES by running an ensemble of simulations with multimode perturbations to the initial conditions. Detailed grid convergence studies are conducted, and LES results are found to agree well with both experiment and high-order simulations conducted by Shankar et al. (Phys Fluids 23, 024102, 2011 ). URANS results using a k – L approach are found to be highly sensitive to initialization of the turbulence lengthscale L and to the time at which L becomes resolved on the computational mesh. It is observed that a gradient diffusion closure for turbulent species flux is a poor approximation at early times, and a new closure based on the mass-flux velocity is proposed for low-Reynolds-number mixing.