Numerical Simulation of Rayleigh-Taylor Instability with Large Density Ratios Based on RKDG Method

2013 ◽  
Vol 423-426 ◽  
pp. 1751-1756 ◽  
Author(s):  
Jun Wu Tian ◽  
Xiang Jiang Yuan
Keyword(s):  
Body Force ◽  
Contact Discontinuity ◽  
Density Ratio ◽  
Taylor Instability ◽  
Interface Capturing ◽  
Instability Problem ◽  
Large Density ◽  
Large Density Ratio ◽  
Rayleigh Taylor Instability ◽  
Density Ratios

Rayleigh-Taylor instability problem with large density ratios is simulated by RKDG method which is developed for Euler equations with an additional body force corresponding to the gravity. The interface capturing ability of RKDG method is testified, while the density ratio (heavy to light) ranges from 3 to 20. Numerical results show that RKDG method has capability to pursue contact discontinuity in Rayleigh-Taylor instability with large density ratio. In the late stage of Rayleigh-Taylor instability problem, the contact line begins to crash, but the numerical solution is still smooth near the interface and has high resolution.

Effects of Coolant Density Ratio on Film Cooling Performance on a Vane

2003 ◽  
Author(s):  
J. Michael Cutbirth ◽  
David G. Bogard
Keyword(s):  
Film Cooling ◽  
Density Ratio ◽  
Operating Conditions ◽  
Cooling Performance ◽  
Large Density ◽  
Performance Trends ◽  
Large Density Ratio ◽  
Small Density ◽  
Adiabatic Effectiveness ◽  
Density Ratios

Film cooling performance was studied on a simulated turbine vane model with an objective of determining how much the coolant density ratio affects this performance. Experiments were conducted using coolant density ratios of 1.8 and 1.2. The purpose of the study was to determine if tests done at small density ratios (which is often more viable in a laboratory) can give reasonable predictions of performance at more realistic large density ratios. Furthermore, appropriate scaling parameters were determined. The mainstream flow was operated with low and high turbulence levels. Adiabatic effectiveness was measured in the showerhead region of the vane, and following the first row of coolant holes on the pressure side. Adiabatic effectiveness performance using small density ratio coolant gave performance trends similar to the large density ratio coolant, but quantitative values differed by varying amount depending on operating conditions.

Rayleigh–Taylor instability in a finite cylinder: linear stability analysis and long-time fingering solutions

2013 ◽  
Vol 734 ◽  
pp. 338-362 ◽  
Author(s):  
H. Sweeney ◽  
R. R. Kerswell ◽  
T. Mullin
Keyword(s):  
Density Ratio ◽  
Linear Instability ◽  
Taylor Instability ◽  
Viscous Fluids ◽  
Finite Cylinder ◽  
Dimensional Parameter ◽  
Instability Problem ◽  
Time Flow ◽  
Long Time ◽  
Rayleigh Taylor Instability

AbstractWe consider the Rayleigh–Taylor instability problem of two initially stationary immiscible viscous fluids positioned with the denser above the less dense in a finite circular cylinder, such that their starting fluid–fluid interface is the horizontal midplane of the cylinder. The ensuing linear instability problem has a five-dimensional parameter space – defined by the density ratio, the viscosity ratio, the cylinder aspect ratio, the surface tension between the fluids and the ratio of viscous to gravitational time scales – of which we explore only part, motivated by recent experiments where viscous fluids exchange in vertical tubes (Beckett et al., J. Fluid Mech., 2011, vol. 682, pp. 652–670). We find that for these experiments, the instability is invariably ‘side-by-side’ (of azimuthal wavenumber 1 type) but we also uncover parameter regions where the preferred instability is axisymmetric. The fact that both ‘core-annular’ (axisymmetric) and ‘side-by-side’ (asymmetric) long-time flows are seen experimentally highlights the fact that the initial Rayleigh–Taylor instability of the interface does not determine the long-time flow configuration in these situations. Finally, long-time flow solutions are presented on the basis that they will be slowly varying fingering solutions.

Modified Outlet Boundary Condition Schemes for Large Density Ratio Lattice Boltzmann Models

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Long Li ◽  
Xiaodong Jia ◽  
Yongwen Liu
Keyword(s):  
Boundary Condition ◽  
Distribution Function ◽  
Lattice Boltzmann ◽  
Density Ratio ◽  
Neumann Boundary ◽  
Momentum Balance ◽  
Two Phase ◽  
Large Density ◽  
Large Density Ratio ◽  
Density Ratios

Outlet boundary conditions (OBCs) and their numerical descriptions are critical to computational fluid dynamics (CFD) since they have significant influence on the numerical accuracy and stability. They present significant challenges to the two-phase lattice Boltzmann (LB) method, especially in the limit of large density ratio. In this study, three commonly used OBCs: convection boundary condition (CBC), Neumann boundary condition (NBC), and extrapolation boundary condition (EBC), are investigated and improved on basis of two LB models for large density ratios (single and double distribution function models). The existing numerical schemes for the OBCs are not directly applicable to the LB models because of the deviation of the momentum balance at the outlet boundary. The deviation becomes substantial at a large density ratio. Thus, in this work, modified OBC schemes are proposed to make the OBCs suitable for the two-phase LB models by adding an independent equation to obtain the outlet velocity. Numerical tests on droplet flowing in a channel are performed to evaluate the performance of the modified OBC schemes. Results indicate that the modified OBC schemes may be extended to tackle large density ratio situations. The modified NBC and EBC schemes are only suitable for the LB model with single distribution function. Three modified CBC schemes exhibit optimum performance for both single and double distribution function LB models which can be implemented for large density ratios.

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