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Fine Grid Numerical Solutions of Triangular Cavity Flow
Numerical solutions of 2-D steady incompressible flow inside a triangular
cavity are presented. For the purpose of comparing our results with several
different triangular cavity studies with different triangle geometries, a
general triangle mapped onto a computational domain is considered. The
Navier-Stokes equations in general curvilinear coordinates in streamfunction
and vorticity formulation are numerically solved. Using a very fine grid mesh,
the triangular cavity flow is solved for high Reynolds numbers. The results are
compared with the numerical solutions found in the literature and also with
analytical solutions as well. Detailed results are presented
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The hybrid grid implemented DSMC method used in 2D triangular micro cavity flows
This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.In this study a new hybrid grid is implemented in a 2D DSMC solver to be used in 2D triangular micro cavity flows. Currently DSMC is the prominent method to analyze micro scale gas flows which are rarefied. Because of the computational cost, DSMC solvers are generally used in rarefied gas conditions in which continuum based solvers are useless. If the efficiency of DSMC solvers is improved, the application range of these solvers can be increased further where the continuum based solvers dominate. Indexing the particles according to their cells is one of the main steps in the DSMC method. Either the particles are traced cell-by-cell along their trajectories or coordinate transformation techniques are used in this step. The first option requires complex trigonometric operations and search algorithms which are computationally expensive. But it can be used in both structured and unstructured grids. Although the second option is computationally more efficient, it demands specially tailored structured grids which are more geometry dependent compared to the unstructured grids. Here it is shown that a novel hybrid grid structure can be used successfully in 2D DSMC solver to analyze triangular shaped lid-driven micro cavity flows. Hybrid grids used in this study are much less dependent of the geometry like unstructured grids. Additionally, hybrid grids like structured grids facilitate coordinate transformation techniques in order to increase the efficiency of the particle indexing step in the DSMC method
Three-dimensional flow instability in a lid-driven isosceles triangular cavity
Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed
h-multigrid agglomeration based solution strategies for discontinuous Galerkin discretizations of incompressible flow problems
In this work we exploit agglomeration based -multigrid preconditioners to
speed-up the iterative solution of discontinuous Galerkin discretizations of
the Stokes and Navier-Stokes equations. As a distinctive feature -coarsened
mesh sequences are generated by recursive agglomeration of a fine grid,
admitting arbitrarily unstructured grids of complex domains, and agglomeration
based discontinuous Galerkin discretizations are employed to deal with
agglomerated elements of coarse levels. Both the expense of building coarse
grid operators and the performance of the resulting multigrid iteration are
investigated. For the sake of efficiency coarse grid operators are inherited
through element-by-element projections, avoiding the cost of numerical
integration over agglomerated elements. Specific care is devoted to the
projection of viscous terms discretized by means of the BR2 dG method. We
demonstrate that enforcing the correct amount of stabilization on coarse grids
levels is mandatory for achieving uniform convergence with respect to the
number of levels. The numerical solution of steady and unsteady, linear and
non-linear problems is considered tackling challenging 2D test cases and 3D
real life computations on parallel architectures. Significant execution time
gains are documented.Comment: 78 pages, 7 figure
Numerical Simulations of the Flow Field of a Submerged Hydraulic Jump over Triangular Macroroughnesses
The submerged hydraulic jump is a sudden change from the supercritical to subcritical flow, specified by strong turbulence, air entrainment and energy loss. Despite recent studies, hydraulic jump characteristics in smooth and rough beds, the turbulence, the mean velocity and the flow patterns in the cavity region of a submerged hydraulic jump in the rough beds, especially in the case of triangular macroroughnesses, are not completely understood. The objective of this paper was to numerically investigate via the FLOW-3D model the effects of triangular macroroughnesses on the characteristics of submerged jump, including the longitudinal profile of streamlines, flow patterns in the cavity region, horizontal velocity profiles, streamwise velocity distribution, thickness of the inner layer, bed shear stress coefficient, Turbulent Kinetic Energy (TKE) and energy loss, in different macroroughness arrangements and various inlet Froude numbers (1.7 < Fr1 < 9.3). To verify the accuracy and reliability of the present numerical simulations, literature experimental data were considered
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