TY - JOUR
T1 - Effects of surface tension on the Richtmyer-Meshkov instability in fully compressible and inviscid fluids
AU - Tang, Kaitao
AU - Mostert, Wouter
AU - Fuster, Daniel
AU - Deike, Luc
N1 - Publisher Copyright:
© 2021 American Physical Society.
PY - 2021/11
Y1 - 2021/11
N2 - Novel numerical simulations investigating the Richtmyer-Meshkov instability (RMI) with surface tension are presented. We solve the two-phase compressible Euler equation with surface tension and interface reconstruction by a volume-of-fluid method. We validate and bridge existing theoretical models of effects of surface tension on the RMI in the linear, transitional, and nonlinear postshock growth regimes. After deriving a consistent nondimensional formulation from an existing linear incompressible theory predicting perturbation development under large surface tension, we find good agreement with theoretical prediction in the small-amplitude (linear) oscillatory regime for positive Atwood numbers, and we show that negative Atwood numbers can be accommodated by an appropriate modification to the theory. Next, we show good agreement with nonlinear theory for asymptotic interface growth in the limit of small surface tension. Finally, we use the nondimensional formulation to define a heuristic criterion which identifies the transition from the linear regime to the nonlinear regime at intermediate surface tension. These results highlight the utility of this numerical method for compressible problems featuring surface tension, and they pave the way for a broader investigation into mixed compressible/incompressible problems.
AB - Novel numerical simulations investigating the Richtmyer-Meshkov instability (RMI) with surface tension are presented. We solve the two-phase compressible Euler equation with surface tension and interface reconstruction by a volume-of-fluid method. We validate and bridge existing theoretical models of effects of surface tension on the RMI in the linear, transitional, and nonlinear postshock growth regimes. After deriving a consistent nondimensional formulation from an existing linear incompressible theory predicting perturbation development under large surface tension, we find good agreement with theoretical prediction in the small-amplitude (linear) oscillatory regime for positive Atwood numbers, and we show that negative Atwood numbers can be accommodated by an appropriate modification to the theory. Next, we show good agreement with nonlinear theory for asymptotic interface growth in the limit of small surface tension. Finally, we use the nondimensional formulation to define a heuristic criterion which identifies the transition from the linear regime to the nonlinear regime at intermediate surface tension. These results highlight the utility of this numerical method for compressible problems featuring surface tension, and they pave the way for a broader investigation into mixed compressible/incompressible problems.
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U2 - 10.1103/PhysRevFluids.6.113901
DO - 10.1103/PhysRevFluids.6.113901
M3 - Article
AN - SCOPUS:85120005738
SN - 2469-990X
VL - 6
JO - Physical Review Fluids
JF - Physical Review Fluids
IS - 11
M1 - 113901
ER -