Title: A numerical study of Rayleigh-Taylor instability for various Atwood numbers using ISPH method
Authors: Amin Rahmat; Nima Tofighi; Mehmet Yildiz
Addresses: Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, 34956, Istanbul, Turkey; Integrated Manufacturing Technologies Research and Application Center, Sabanci University, Tuzla, 34956, Istanbul, Turkey ' Department of Mechanical Engineering, University of Victoria, Victoria, BC V8W, 2Y2, Canada ' Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, 34956, Istanbul, Turkey; Integrated Manufacturing Technologies Research and Application Center, Sabanci University, Tuzla, 34956, Istanbul, Turkey; Composite Technologies Center of Excellence, Istanbul Technology Development Zone, Sabanci University-Kordsa, Sanayi Mah. Teknopark Blvd. No: 1/1B, Pendik, 34906 Istanbul, Turkey.
Abstract: In this paper, the wall bounded single-mode Rayleigh-Taylor instability (RTI) for a two-phase immiscible fluid system in a confined domain is investigated numerically for various Atwood numbers ranging from At = 0.2 to At = 0.8. Governing equations are discretised using the smoothed particle hydrodynamics (SPH) method. A robust numerical scheme is used to simulate the RTI phenomenon and in order to model the fluid-flow in the vicinity of the interface, transport parameters such as density and viscosity are smoothed using colour function. The surface tension force is coupled to the momentum equation using continuum surface force (CSF) model. It is shown that in general the RTI evolves in three distinct stages, namely linear stability, mushroom-head formation and long-term evolution. The growth rate in the first stage, i.e. the linear instability, shows good agreement with the analytical solution in the literature. The qualitative and quantitative results of second and third stages are introduced and relevant discussions are made.
Keywords: smoothed particle hydrodynamics; SPH; multi-phase flow; interfacial flow; Rayleigh-Taylor instability; RTI; Atwood number.
Progress in Computational Fluid Dynamics, An International Journal, 2018 Vol.18 No.5, pp.267 - 276
Received: 16 May 2016
Accepted: 15 Feb 2017
Published online: 06 Sep 2018 *