The development of a two-dimensional viscous incompressible flow generated from an infinitesimally thin flat plate, impulsively started or uniformly accelerated normal to the free stream is studied computationally. An adaptive numerical scheme, based on vortex methods, is used to integrate the vorticity–velocity formulation of the Navier–Stokes equations. The results of the computations complement relevant experimental works while providing us with quantities such as the vorticity field and the unsteady forces experienced by the body. For the uniformly accelerated plate the present simulations capture the development of a number of centers of vorticity along the primary separating shear layer. This phenomenon has been observed in experimental works but has not been predicted by inviscid models. The present simulations suggest that this Kelvin–Helmholtz-type instability is driven by the interaction of primary and secondary vorticity near the tips of the plate and depends on the acceleration of the plate.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112096008695

Simulations of the viscous flow normal to an impulsively started and uniformly accelerated flat plate

The experiments were conducted in water to study the initial wake formations behind various polygonal plates placed normal to the starting flow. The models included triangular, square, hexagonal, and octagonal plates. Because of nonuniform self-induced velocity, the initial vortex structure behind each polygonal plate was arched in the axial direction, and pairs of counter-rotating longitudinal vortices induced inward motion of the vortex structure at each corner. The evolution of free polygonal vortex loops was numerically simulated using a simplified three-dimensional vortex segment method to demonstrate the mechanism for the observed vortex deformation. Nomenclature Ap . = acceleration parameter, Deqa/ UQ a = acceleration, dU/dt D = side length of square plate Z)eq = equivalent disk diameter Re = steady-state Reynolds number, Rec = acceleration Reynolds number, T = nondimensional time, U0t/Deq t = time tc = time scale, J(Deq/d) U = freestream velocity UQ = steady freestream velocity X = axial distance v = kinematic viscosity

Three-dimensional wake formations behind a family of regular polygonal plates

Recent contributions to the 3-D vortex method for bluff-body flows are presented. The numerical method - a vortex method combined with a boundary element method - is briefy reviewed. It is applied to direct numerical simulation (DNS) of the flow past a sphere (Re = 300, 500 and 1000). The on-going work to extend the method towards vortex-based large-eddy simulation (LES) for high Reynolds number flows is also presented. Preliminary results for the flow past a hemisphere are discussed.

Simulation of three-dimensional bluff-body flows using the vortex particle and boundary element methods

Fast Laqrangian analysis of three dimensional unsteady reacting flow with heat release

An experimental investigation of the twodimensional(2-D) flow normal to a flat plate at low to medium Reynolds numbers (ranging from 25 to 393 based on the breadth of the plate) is described. Both horizontal and vertical soap film tunnels are used to set up a truly 2-D experiment. The flow in the soap film is very thin and is a close approximation to 2-D flow. Momentum defect measurements are used to obtain the time averaged mean drag coefficient, cl, experienced by a normal flat plate via laser Doppler velocimetry. It is found that cl = 2.1 for the current Re range. The present data agree well with available nominally 2-D experimental results from previously published papers which were obtained in traditional towing tank, wind tunnel and water tunnel experiments with high plate aspect ratios. This measurement implies that the intrinsic 3-D motions in the previously nominally 2-D experiments are not significant on cl and the computational fluid dynamics results from previously published papers which are reviewed have overestimated cl. Introduction Bluff body flows are by nature very complex. Inevitably they involve boundary layer, free shear layer and wake flows, all accompanied by associated instabilities and non-linear interactions with each other and with the bluff body itself. Bluff body wake flows have direct engineering significance. The alternate shedding of vorticies in the near wake, in the classical vortex street configuration, leads to large fluctuating pressure forces in a direction some cases can trigger failure. A normal flat plate is in many ways the simp* Associate Professor, Department of Mechanical Engineering , Member AIAA ** Graduate Research Assistant, Department of Mechanical Engineering Copyright O 1998 by the American Institute of Aeronautics and Astronautics Inc . All right reserved. lest possible bluff body, since it has geometrically fixed separation points, and since the interaction between the body and the near wake formation region is minimized. However, in comparison to the bulk of contemporary literature dealing with circular cylinder flows, very few results have been published for normal flat plates. Of the normal flat plate results which are available, typically Strouhal shedding frequency, force and/or pressure coefficients are presented only as time averaged mean quantities. Lisoski' has reviewed published experimental and computational results for time averaged mean drag coefficient, cT, and Strouhal number, St, of nomianlly 2-D noraml flat plates extensively. The main thing to note about the reviewed results is the large difference in cT between the experimental results( typically c7 = 2.0 ) and the 2-D numerical models( typically c7 = 3.2 ),which in some cases have a drag of almost twice the experimental values. There has been a tendency to think of these truly 2-D computer models as being wrong, and to modify them by various means so that their results conform with "2-D" experiments which are indeed threedimensional. As has been noted by Lisoski, "this is the wrong approach." He then went on investigating the intrinsic( small scale ) and extrinsic( large scale ) 3-D motions in the towing tank and water channel experiments. A 2-D vortex element numerical model developed by Chua was also used for comparison with his experimental results. It is shown that agreement between normally 2-D experimental and 2-D numerical-model results is good at early times, indicating the experiments are 2-D until the breakdown of the closed wake bubble following the initial accerlation. The approach of this paper is different. A truly 2-D experiment is conducted to have a direct comparison with the previously 2-D numerical results on cl. Freely suspended flowing soap films are used to set up the truly 2-D flows. These films, which have a thickness of the order of a micron, offer an excellent opportunity for studying hydrodynamics American Institute of Aeronautics and Astronautics Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc.

On the drag of two-dimensional flow about a normal flat plate

This thesis is concerned with the applications of vortex methods to the problem of unsteady, separated flows in two and three dimensions, and can be divided into three parts In the first part, an improved method for satisfying the boundary conditions on a flat plate is developed and applied to the two-dimensional separated flow problem In this method, boundary layers on both side of the plate are represented by stacks of multiple vortex panels, the strength of which are determined by enforcing both the no-through flow and no-slip boundary conditions at the plate Vortex shedding at the sharp edge of the plate is represented as the separation of the boundary vortex elements Both forced and unforced flows are studied and comparisons to experiments are carried out For the case without forcing, large discrepancy between calculations and experiments, which is also reported by other workers using a different vortex method or Navier-Stokes calculations, is observed In the case with forcing, the discrepancy is reduced with lateral forcing at low amplitude; and eliminated, regardless of amplitude, with streamwise forcing (acceleration) In the second part, an improved three-dimensional vortex particle method is developed In this method, vortex elements of vorticity that move with the local velocity and are stretched and rotated according to the local strain field, are used To mimic the effects of vorticity cancellations, close pairs of opposite sign vortex elements are replaced by high order dipoles The method is designed to handle complex high Reynolds number vortical flows and a non-linear viscosity model is included to treat small-scale effects in such flows Applications to two problems involving strong interactions of vortex tubes are carried out and core deformation with complex internal strucures and induced axial flow within vortex tubes are observed Qualitative comparison to experiments are encouraging In the third part, the two-dimensional method developed in the first part is modified and extended to three dimensions Here, solenoidal condition for vorticity is considered and closed vortex loops are used to represent the boundary layer vorticity and the vorticity at shedding For the evolution of the vortex wake, the vortex particle method developed in the second part is used Applications to the flow past a normal square plate is carried out and the early stages of the flow are studied

Kiat Chua

Papers

Vortex simulation of separated flows in two and three dimensions