Three-dimensional flow in cavity with elevated helicity driven by parallel walls

The proposed flow in a 3-D cubic cavity is driven by its parallel walls moving in perpendicular directions to create a genuinely three-dimensional highly separated vortical flow yet having simple single-block cubical geometry of computational domain. The elevated level of helicity is caused by motion of a wall in the direction of axis of primary vortex created by a parallel wall. The velocity vector field is obtained numerically by using second-order upwind scheme and 200^3 grid. Helicity, magnitude of normalized helicity and kinematic vorticity number are evaluated for Reynolds numbers ranging from 100 to 1000. Formation of two primary vortices with their axis oriented perpendicularly and patterns of secondary vortices are discussed. Computational results are compared to the well-known 3-D recirculating cavity flow case where the lid moves in the direction parallel to the cavity side walls. Also results are compared to the diagonally top-driven cavity and to cavity flow driven by moving top and side walls. The streamlines for the proposed flow show that the particles emerging from top and bottom of cavity do mix well. Quantitative evaluation of mixing of two fluids in the proposed cavity flow confirms that the mixing occurs faster than in the benchmark case.Comment: 38 pages, 13 figures The revised includes quantification of mixing rate; numerical modeling of the transient version.The revised version has four substantially improved figures and three new figures; number of literature references increased from 26 to 4

Mixing in 3-D Cavity by Moving Cavity Walls

The mixing in three-dimensional enclosures is investigated numerically using flow in cubical cavity as a geometrically simple model of various natural and engineering flows. The mixing rate is evaluated for up to the value of Reynolds number Re=2000 for several representative scenarios of moving cavity walls: perpendicular motion of the parallel cavity walls (Case A), motion of a wall in its plane along its diagonal (Case B1), motion of two perpendicular walls outward the common edge (Case B2), and the parallel cavity walls in motion either in parallel directions (Case B3) or in opposite directions (Case B4). The mixing rates are compared to the well-known benchmark case in which one cavity wall moves along its edge (Case C). The intensity of mixing for the considered cases was evaluated for (i) mixing in developing cavity flow initially at rest, which is started by the impulsive motion of cavity wall(s), and (ii) mixing in the developed cavity flow. For both cases, the initial interface of the two mixing fluids is a horizontal plane located at the middle of the cavity. The mixing rates are ranked from fastest to slowest for twenty time units of flow mixing. The pure convection mixing is modeled as a limit case to reveal convective mechanism of mixing. Mixing of fluids with different densities is modeled to show the advantage in terms of mixing rate of genuinely 3-D cases A and B1. Grid convergence study and comparison with published numerical solutions for 3-D and 2-D cavity flows are presented. The effects of three-dimensionality of cavity flow on the mixing rate are discussed.Comment: 52 pages, 17 figures, 4 Tables, 36 Ref

Vorticity Confinement and TVD Applied to Wing Tip Vortices for Accurate Drag Prediction

The vorticity confinement (VC) method was used with total variation diminishing (TVD) schemes to reduce possible over-confinement and applied to tip vortices shed by edges of wings in order to predict induced drag using far-field integration. The optimal VC parameter was determined first by application to 2-D vortices and then to tip vortices shed by a 3-D wing. The 3-D inviscid simulations were post-processed using the wake-integral technique to determine lift-induced drag force. Dependence of the VC parameter on the flight Mach number and the angle of attack was evaluated. Grid convergence studies were conducted for 2-D vortices and for induced drag generated by 3-D wing. VC was used with TVD minmod and differentiable flux limiters to evaluate their effect on the VC method. Finally, the VC approach was combined with the Reynolds stress equation turbulence model, and the results were compared to experimental data of tip vortex evolution.Comment: 40 pages, 12 Figure

Coupled Continuum and Molecular Model of Flow through Fibrous Filter

A coupled approach combining the continuum boundary singularity method (BSM) and the molecular direct simulation Monte Carlo (DSMC) is developed and validated using Taylor-Couette flow and the flow about a single fiber confined between two parallel walls. In the proposed approach, the DSMC is applied to an annular region enclosing the fiber and the BSM is employed in the entire flow domain. The parameters used in the DSMC and the coupling procedure, such as the number of simulated particles, the cell size, and the size of the coupling zone are determined by inspecting the accuracy of pressure drop obtained for the range of Knudsen numbers between zero and unity. The developed approach is used to study flowfield of fibrous filtration flows. It is observed that in the partial-slip flow regime, Kn ⩽ 0.25, the results obtained by the proposed coupled BSM-DSMC method match the solution by BSM combined with the heuristic partial-slip boundary conditions. For transition molecular-to-continuum Knudsen numbers, 0.25 \u3c Kn ⩽ 1, the difference in pressure drop and velocity between these two approaches is significant. This difference increases with the Knudsen number that confirms the usefulness of coupled continuum and molecular methods in numerical modeling of transition low Reynolds number flows in fibrous filters

Modeling of Sedimentation of Particles near Corrugated Surface by Boundary Singularity Method

The velocity and trajectory of particle moving along the corrugated surface under action of gravity is obtained by meshless Boundary Singularity Method (BSM). This physical situation is found often in biological systems and microfluidic devices. The Stokes equations with no-slip boundary conditions are solved using the Green function for Stokeslets. In the present study, the velocity of a moving particle is not known and becomes a part of the BSM solution. This requires an adjustment of the matrix of BSM linear system to include the unknown particle velocity and incorporate in the BSM the balance of hydrodynamic and gravity forces acting on the particle. Comparison has been made to prior published analytical and experimental results to verify the effectiveness of this methodology to predict the trajectory of particle including its deviation from vertical trajectory and select the optimal set of computational parameters. The developed BSM methodology is applied to sedimentation of two spherical particles in proximity for which the analytical solution is not feasible.Comment: 14 pages, 6 figure

National Aeronautics and

We consider propagation of disturbances in a non-uniform mean #owby high-order numerical simulation. Monopole and dipole acoustic, vortical and entropy pulses are embedded in an incompressible stagnation #ow, which is taken as a prototype of a non-uniform low Machnumber mean #ow near a rigid wall at high angle of attack