A nonlinear PSE method for two-fluid shear flows with complex interfacial topology

Cheung, Lawrence; Zaki, Tamer A.

doi:10.1016/j.jcp.2011.05.007

Cited by 10 publications

(5 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our numerical method has been extensively validated for studies of transition and turbulence in Newtonian and viscoelastic flows (Lee & Zaki 2017; Esteghamatian & Zaki 2019, 2020, 2021); the latter feature the upper convective derivative seen in the evolution equation for . Validation of the interface tracking algorithm was reported by Jung & Zaki (2015) who computed the evolution of the Zalesak disc (Zalesak 1979) and the evolution of linear and nonlinear instability waves in two-fluid flows (Cheung & Zaki 2010, 2011). In Appendix A, we present an additional validation case to show the accuracy of our two-phase solver in predicting the deformation of a neo-Hookean elastic particle in shear.…”

Section: Methodsmentioning

confidence: 98%

Spatiotemporal characterization of turbulent channel flow with a hyperelastic compliant wall

2022

Self Cite

View full text Add to dashboard Cite

Direct numerical simulations of turbulent flow in a channel with one rigid and one viscoelastic wall are performed. An Eulerian–Eulerian model is adopted with a level-set approach to identify the fluid–compliant material interface. Focus is placed on the propagation of Rayleigh waves in the compliant material, whose speed depends on the shear modulus of elasticity and whose dominant wavelength depends on the thickness of the viscoelastic layer. These parameters are selected to ensure coupling between the compliant surface and turbulence. When the phase speed of Rayleigh waves is commensurate with the advection velocity of near-wall pressure fluctuations, sheets of vorticity are lifted up and detached near the critical layer and lead to a local pressure minimum. These events are caused by the inflectional velocity profile near the troughs, and are controlled by the net vorticity flux at the elastic surface. This phenomenon is central to understanding the statistical characteristics of the flow, including the surface deformation–pressure correlation and enhanced stochastic Reynolds shear stresses. Finally, we discuss the influence of three-dimensionality of the surface topography on the generation of streamwise vorticity, secondary motions and lateral turbulent transport.

show abstract

Section: Methodsmentioning

confidence: 98%

Spatiotemporal characterization of turbulent channel flow with a hyperelastic compliant wall

2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…The EDNN methodlogy is flexible, and can be easily adapted to other types of PDE problems. For example, in boundary-layer flows, the governing equations are often marched in the parabolic streamwise direction [5,6,23] . In this case, the inputs to EDNN would be the spatial coordinates in the cross-flow plane, and the network weights would be marched in the streamwise direction instead of time.…”

Section: Discussionmentioning

confidence: 99%

Evolutional Deep Neural Network

Du,

Zaki

2021

Preprint

Self Cite

View full text Add to dashboard Cite

The notion of an Evolutional Deep Neural Network (EDNN) is introduced for the solution of partial differential equations (PDE). The parameters of the network are trained to represent the initial state of the system only, and are subsequently updated dynamically, without any further training, to provide an accurate prediction of the evolution of the PDE system. In this framework, the network parameters are treated as functions with respect to the appropriate coordinate and are numerically updated using the governing equations. By marching the neural network weights in the parameter space, EDNN can predict state-space trajectories that are indefinitely long, which is difficult for other neural network approaches. Boundary conditions of the PDEs are treated as hard constraints, are embedded into the neural network, and are therefore exactly satisfied throughout the entire solution trajectory. Several applications including the heat equation, the advection equation, the Burgers equation, the Kuramoto Sivashinsky equation and the Navier-Stokes equations are solved to demonstrate the versatility and accuracy of EDNN. The application of EDNN to the incompressible Navier-Stokes equation embeds the divergence-free constraint into the network design so that the projection of the momentum equation to solenoidal space is implicitly achieved. The numerical results verify the accuracy of EDNN solutions relative to analytical and benchmark numerical solutions, both for the transient dynamics and statistics of the system.

show abstract

“…The present level-set algorithm has been validated extensively by comparison to linear and non-linear stability results (see Cheung & Zaki 2011). In addition, two canonical interface tracking problems were also examined: the transport of Zalesak's disk (Zalesak 1979) and the rise of an air bubble in quiescent water (Gueyffier et al 1999;Yang & Stern 2009).…”

Section: Level Set Methodsmentioning

confidence: 99%

The effect of a low-viscosity near-wall film on bypass transition in boundary layers

Jung

Zaki

2015

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

Bypass transition in a two-fluid boundary layer is examined using direct numerical simulations. A less viscous wall film is considered and the impact on transition location is evaluated at two different viscosity ratios and free-stream turbulence intensities. The less viscous wall film absorbs the mean shear from the outer stream, weakens the lift-up mechanism, and alters the disturbance field inside the boundary layer. These effects all favour a delay in the onset of bypass transition. However, the viscosity and mean-shear discontinuities across the two-fluid interface introduce a new mechanism for the generation of wall-normal vorticity in the boundary layer, and can therefore promote transition to turbulence. Conditionally-averaged statistics and streak tracking techniques are adopted in order to examine the impact of the wall film on the bypass transition process. It is shown that the weaker amplification of the streaks in the outer fluid can delay breakdown to turbulence, despite the additional disturbance generation at the two-fluid interface. The efficacy of the wall film in delaying transition is demonstrated at moderate level of free-stream turbulence intensity, but is reduced as the turbulence intensity is increased.

show abstract

A nonlinear PSE method for two-fluid shear flows with complex interfacial topology

Cited by 10 publications

References 53 publications

Spatiotemporal characterization of turbulent channel flow with a hyperelastic compliant wall

Spatiotemporal characterization of turbulent channel flow with a hyperelastic compliant wall

Evolutional Deep Neural Network

The effect of a low-viscosity near-wall film on bypass transition in boundary layers

Contact Info

Product

Resources

About