- Computational Fluid Dynamics and Vortex Dynamics- Research - Z. Jane Wang Research Group
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A novel aspect of our method is its ability to efficiently and accurately couple the dynamics of the freely moving objects with the fluid. We report the falling configuration and the wake pattern of the array, and investigate their dependence on the number of particles, n, as well as the initial inter-particle spacing, d0. We find that, in the case of odd-numbered arrays, the middle cylinder is always leading, whereas in the case of even-numbered arrays, the steady-state shape is concave-down.
Computational Fluid Dynamics and Vortex Dynamics- Research - Z. Jane Wang Research Group
In addition, we analyse detailed kinematics, wakes and forces of three settling cylinders. We find that the middle one experiences a higher drag force in the presence of neighbouring cylinders, compared to an isolated settling cylinder, resulting in a decrease in its settling velocity. For a small initial spacing d0, the middle cylinder experiences a strong sideway repulsive force, the magnitude of which increases with decreasing d0. During the fall, the left and right cylinders rotate outwards and shed vortices in anti-phase. In immersed interface methods, solids in a fluid are represented by singular forces in the Navier-Stokes equations, and flow jump conditions induced by the singular forces directly enter into numerical schemes.
This paper focuses on the implementation of an immersed interface method for simulating fluid-solid interaction in 3D. A fluid-solid interface is tracked by Lagrangian markers. Intersections of the interface with MAC grid lines identify finite difference stencils on which jump contributions to finite difference schemes are needed. To find the intersections and to interpolate jump conditions from the Lagrangian markers to the intersections, parametric triangulation of the interface is used.
The velocity of the Lagrangian markers is interpolated directly from surrounding MAC grid nodes with interpolation schemes accounting for jump conditions. Numerical examples demonstrate that 1 the method has near second-order accuracy in the infinity norm for velocity, and the accuracy for pressure is between first and second order; 2 the method conserves the volume enclosed by a no-penetration boundary; and 3 the method can efficiently handle multiple moving solids with ease.
In the immersed interface method, boundaries are represented as singular force in the Navier-Stokes equations, which enters a numerical scheme as jump conditions. Recently, we systematically derived all the necessary spatial and temporal jump conditions for simulating incompressible viscous flows subject to moving boundaries in 3D with second-order spatial and temporal accuracy near the boundaries [Sheng Xu, Z.
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In this paper we implement the immersed interface method to incorporate these jump conditions in a 2D numerical scheme. We study the accuracy, efficiency and robustness of our method by simulating Taylor-Couette flow, flow induced by a relaxing balloon, flow past single and multiple cylinders, and flow around a flapping wing. Our results show that: 1 our code has second-order accuracy in the infinity norm for both the velocity and the pressure; 2 the addition of an object introduces relatively insignificant computational cost; 3 the method is equally effective in computing flow subject to boundaries with prescribed force or boundaries with prescribed motion.
International Journal of Computational Fluid Dynamics — Instant Formatting Template
While some of the most interesting fluid dynamics originates near a moving sharp interface, computational schemes typically encounter great difficulty in resolving moving interfaces, a known difficulty in nearly all fluid-structure simulations. We have improved a number of computational methods and developed new algorithms for solving the Navier-Stokes equation coupled to moving interfaces. The first set of codes are Navier-Stokes solvers for simulating a 2D rigid flapping wing, based on an essentially compact 4th order finite difference scheme in vorticity and stream function formulation.
In these solvers we took advantage of coordinate transformations and conformal mapping to resolve sharp wing tips so as to avoid grid-regeneration. With these methods, we have investigated the unsteady aerodynamics of forward and hovering flight as well as of plates freely falling in a fluid. To simulate multiple bodies, we have further developed a Cartesian method coupled to an overset grid that are attached to the moving geometries.
To go beyond 2D simulations of rigid objects, we have recently developed a more general purpose code for simulating multiple flexible freely objects. The main advance in the new immersed interface method is to obtain a 2nd order accuracy of the sharp moving surface at an intermediate range of Reynolds flows.
To avoid introducing ad-hoc boundary conditions at the moving interface, we derived systematically from the 3D Navier-Stokes equation the jump conditions on the fluid variables caused by the singular force. Our analysis showed that a 2nd order accuracy along the sharp interface requires jump conditions on derivatives of velocity that are of higher order than those appearing in the principal jump conditions. In addition, the temporal jump conditions must be included in order to have a correct scheme. To handle the spatial and temporal jump conditions in the finite difference scheme, we derived a generalized Taylor expansions for functions with discontinuity of an arbitrary order.
This code has been adapted to studies of passive wing pitching in insect flight.
Most recently, the code has been further developed to simulate hydrodynamic interactions of multiple objects at intermediate Reynolds numbers. As a solid body approaches a wall in a viscous fluid, the flow in the gap between them is dominated by the viscous effect and can be approximated by the lubrication theory. Here we show that without gravity, a cylinder comes to rest asymptotically at a finite separation from the wall, whereas with gravity, the cylinder approaches the wall asymptotically and contact does not happen in finite time.
A cylinder approaches the wall much slower compared to a sphere under matching conditions, implying that the lubrication approximates hold longer before the molecular scale sets in. Our results further serve as a building block for analyzing particle interactions in close proximity, and provide analytic results for integrating the lubrication theory into the computations of Navier-Stokes equations. Motivated by our interest in understanding collective behaviour and self-organization resulting from hydrodynamic interactions, we investigate the two-dimensional dynamics of horizontal arrays of settling cylinders at intermediate Reynolds numbers.
Algebraic disturbances and their consequences in rotating channel flow. Physical Review Fluids, 2, , Two initially spherical bubbles rising in quiescent liquid. Nonmodal stability of Jeffery-Hamel flow. Effects of viscosity and conductivity stratification on the linear stability and transient growth within compressible Couette flow.
Clustering of heavy particles in vortical flows: a selective review. Universal evolution of a viscous-capillary spreading drop.
Effect of Prandtl number on the linear stability of compressible Couette flow. Relaxation of a highly deformed elastic filament at a fluid interface. Dynamics of circular arrangements of vorticity in two dimensions. Rohith V. Swaminathan, S. Linear stability analysis and direct numerical simulation of two-layer channel flow.
9th International Conference on Computational Fluid Dynamics
Flow around a rotating, semi-infinite cylinder in an axial stream, S. Derebail Muralidhar, B. Pier, J.
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Global linear instability of flow through a converging-diverging channel. Inviscid instability of two-fluid free surface flow down an incline. Ghosh, R. Caustics and clustering in the vicinity of a vortex. Ravichandran and Rama Govindarajan. Physics of Fluids, 27, , Dynamics of an initially spherical gas bubble rising in quiescent liquid. Nature Communications, 6, , Morphological evolution of domains in spinodal decomposition. Charu Datt, Sumesh P. Physical Review E Rapid Comm. The effect of initial momentum flux on the circular hydraulic jump. Rolling motion in moving droplets.
Numerical study of laminar, standing hydraulic jumps in a planar geometry. Anuual Review of Fluids Mechanics, Rama Govindarajan and Kirti Sahu.
The International Journal of Computational Fluid Dynamics
Attracting fixed points for heavy particles in the vicinity of a vortex pair. Physics of Fluids, 26, , A minimal model for flow control on an airfoil using a poro-elastic coating.
Journal of Fluids and Structures, 47, —, Scientific Reports, 4, No. On vortex filament methods for linear instability analysis of aircraft wakes, Juan A. Nonlinear dynamical systems, their stability and chaos. Effect of density stratification on vortex merger. Do liquid drops roll or slide on inclined surfaces? Sumesh P Thampi, R. Spatio-temporal linear stability of double-diffusive two-fluid channel flow. Oscillatory settling in wormlike-micelle solutions: bursts and a long time scale. ISSN X.