DOC PREVIEW
Vorticity dynamics

This preview shows page 1-2-3-20-21-22-41-42-43 out of 43 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 43 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 43 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 43 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 43 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 43 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 43 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 43 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 43 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 43 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 43 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

J. Fluid Mech. (2000), vol. 421, pp. 185–227. Printed in the United Kingdomc 2000 Cambridge University Press185Vorticity dynamics of dilute two-way-coupledparticle-laden mixing layersBy E. MEIBURG1,2†, E. WALLNER1,3, A. PAGELLA1,4,A. RIAZ1,C.H¨ARTEL2ANDF. NECKER21Department of Aerospace and Mechanical Engineering, University of Southern California,Los Angeles, CA 90089-1191, USA2Institute of Fluid Dynamics, Swiss Federal Institute of Technology, ETH Zentrum,CH-8092 Z¨urich, Switzerland3Present address: Institute of Flight Mechanics and Flight Control, University of Stuttgart,Pfaffenwaldring 7a, D-70550 Stuttgart, Germany4Present address: Institute of Aero- and Gasdynamics, University of Stuttgart,Pfaffenwaldring 21, D-70550 Stuttgart, Germany(Received 20 August 1999 and in revised form 22 May 2000)The two-way coupling mechanisms in particle-laden mixing layers are investigated,with and without particle settling, and with an emphasis on the resulting modificationsto the fluid vorticity field. The governing equations are interpreted with respect tothe production and cancellation of vorticity. These mechanisms are shown to berelated to the misalignment of the concentration gradient and the slip velocity, aswell as to the difference in fluid and particle vorticities. Preliminary insight into thephysics is obtained from an analysis of the unidirectional base flow. For this modelproblem, the conditions are established under which the particle velocity remainsa single-valued function of space for all times. The resulting simplified set of two-way-coupled equations governing the vorticity of the fluid and particulate phases,respectively, is solved numerically. The formation of a decaying travelling wavesolution is demonstrated over a wide range of parameters. Interestingly, the downwardpropagation of the fluid vorticity field is not accomplished through convection, butrather by the production and loss of vorticity on opposite sides of the mixing layer.For moderate settling velocities, the simulation results reveal an optimal couplingmechanism between the fluid and particle vorticities at intermediate values of themass loading parameter. For large settling velocities and intermediate mass loadings,more than one local maximum is seen to evolve in the vorticity field. A scaling lawfor the downward propagation rates of the vorticity fronts is derived.Two-dimensional particle-laden mixing layers are investigated by means of a mixedLagrangian–Eulerian approach which is based on the vorticity variable. For uniformlyseeded mixing layers, the simulations confirm some of the features observed byDruzhinin (1995b) for the model problem of a two-way-coupled particle-laden Stuartvortex, as well as by Dimas & Kiger (1998) in a linear stability analysis. For smallvalues of the Stokes number, a mild destabilization of the mixing layer is observed.At moderate and large Stokes numbers, on the other hand, the transport of vorticityfrom the braids into the core of the evolving Kelvin–Helmholtz vortices is seen tobe slowed by the two-way coupling effects. As a result, the particle ejection from thevortex cores is weakened. For constant mass loadings, the two-way coupling effects† Author to whom correspondence should be addressed. Present address: Department ofMechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106,USA, e-mail: [email protected] E. Meiburg, E. Wallner, A. Pagella, A. Riaz, C. H¨artel and F. Neckerare strongest at intermediate Stokes number values. For moderately large Stokesnumbers, the formation of two bands of high particle concentration is observed inthe braids, which reflects the multi-valued nature of the particle velocity field. Formixing layers in which only one stream is seeded, the particle concentration gradientacross the mixing layer leads to strong vorticity production and loss, which resultsin an effective net motion of the vortex in the flow direction of the seeded stream.Under particle settling, the vortex propagates downward as well. For the parameterrange explored here, its settling velocity agrees well with the scaling law derived fromthe unidirectional flow analysis.1. IntroductionOver the last decade, much insight into the evolution of particle-laden flows hasbeen gained on the basis of one-way-coupled numerical simulations, which are basedon formulations of the governing equations in which the fluid flow is not affectedby the particle motion. As an example, numerous investigations of this kind fortransitional free shear flows have shed light on the mechanisms that result in thepreferential dispersion of particles whose aerodynamic response time is comparableto the characteristic time scale of the flow (Crowe, Gore & Troutt 1985; Chein &Chung 1988; Chung & Troutt 1988; Aggarwal & Xiao 1994; Uthuppan et al. 1994;Martin & Meiburg 1994; Raju & Meiburg 1995; Marcu & Meiburg 1996a; Ling etal. 1998; Soteriou & Yang 1999). Additional detailed studies have addressed suchissues as particle accumulation due to inertial effects and during settling, as well as theformation of concentration waves in simplified models of particle-laden flows (Maxey1987, 1990; Ganan-Calvo & Lasheras 1991; Tio et al. 1993b; Tio, Ganan-Calvo &Lasheras 1993a; Druzhinin 1994, 1995a, 1997; Marcu, Meiburg & Newton 1995;Marcu, Meiburg & Raju 1996; Marcu & Meiburg 1996b; Raju & Meiburg 1997).Statistical aspects of particle dispersion by fully turbulent flows have been the focusof several numerical investigations as well (Wang & Maxey 1993; Reeks 1991, 1992;Hyland, McKee & Reeks 1999; Elghobashi & Truesdell 1992).As the mass loading of the particle phase increases, it can substantially alter theevolution of the fluid flow, so that an approach based on one-way coupling only isno longer appropriate. The effects of two-way coupling on the statistical propertiesof both isotropic and homogenous turbulence have been addressed in the numericalsimulations of several authors (Squires & Eaton 1990; Elghobashi & Truesdell 1993;Truesdell & Elghobashi 1994; Maxey et al. 1997; Sundaram & Collins 1999), whileother investigators have focused on the modification of wall turbulence (Pan &Banerjee 1996) and fully developed channel flows (Kulick, Fessler & Eaton 1994)by heavy particles. However, very little numerical work has been done regarding theeffects of particle loading on the nonlinear stages of transitional free shear flows.Hence, a detailed understanding of


Vorticity dynamics

Download Vorticity dynamics
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Vorticity dynamics and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Vorticity dynamics 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?