dc.contributor.author	Youssef, Khaled Saad II	en
dc.contributor.committeechair	Ragab, Saad A.	en
dc.contributor.committeemember	Mook, Dean T.	en
dc.contributor.committeemember	Hajj, Muhammad R.	en
dc.contributor.committeemember	Devenport, William J.	en
dc.contributor.committeemember	Thangjitham, Surot	en
dc.contributor.department	Engineering Science and Mechanics	en
dc.date.accessioned	2014-03-14T20:21:29Z	en
dc.date.adate	1998-03-26	en
dc.date.available	2014-03-14T20:21:29Z	en
dc.date.issued	1998-03-03	en
dc.date.rdate	1999-03-26	en
dc.date.sdate	1998-03-03	en
dc.description.abstract	Wakes of lifting bodies contain vortex sheets that roll up into strong streamwise vortices. The long time behavior of such vortices depends on the turbulence in the wake and the stability characteristics of the vortices themselves. In the near wake of a rectangular wing the flow field consists of a spiraling wake that winds around a pair of vortex cores. The study of the turbulence structure and life of wing tip vortices is of great importance to air traffic control in congested airports. In this dissertation a computer code is developed for the temporal as well as spatial simulations of trailing vortices. A sixth-order compact finite-difference method is used in the cross plane. The streamwise derivatives are represented either by a Fourier series for temporal simulations (periodic flow) or by a sixth-order compact scheme for spatial simulations. The time marching scheme is a third-order Runge-Kutta method. The code is used to study the nonlinear development of temporal helical instability waves in a trailing vortex. Contours of a passive scalar are used to study the entrainment process that redistributes angular and axial momenta between the core and its surroundings. Such a process leads to quenching of the instability waves in the vortex core. The code is also used to predict the spatial development of mean flow in the wake of a rectangular wing. New treatment of the outflow boundary condition on the pressure is formulated so that a strong streamwise vortex can exit the computational domain without distortion. Temporal large-eddy simulation (LES) is performed to study the development of large scale structures in the wake and their interaction with the tip vortex. A modified MacCormack scheme developed by Gottlieb and Turkel(1976) has been used to solve the LES equations. A model of the initial conditions in the near wake of a rectangular wing is devised to investigate mechanisms of turbulence production in the spiral wake around the core of a tip vortex. The model consists of a streamwise vortex sheet whose strength is found from Prandtl lifting line theory. A Gaussian streamwise velocity profile is superimposed on the field of the vortex sheet. This profile represents the spanwise vorticity. The integrated spanwise vorticity of this profile is zero. A novel feature of this study is that the mean flow contains both streamwise and spanwise vorticity. The model is then used to initialize the flow field for temporal LES of the instabilities of the spanwise vorticity during roll up. The results show that the sinuous mode prevails in the spiral wake around the core. The strength and streamwise length scale of the instability vary along the span because of the continuous variation of the wake thickness due to stretching by the tip vortex. The large scale structures produced by the instability of the spiral wake cause the formation of undulations on the core - consistent with the hypothesis of Devenport et al. (1996).	en
dc.description.degree	Ph. D.	en
dc.identifier.other	etd-22098-182744	en
dc.identifier.sourceurl	http://scholar.lib.vt.edu/theses/available/etd-22098-182744/	en
dc.identifier.uri	http://hdl.handle.net/10919/30347	en
dc.publisher	Virginia Tech	en
dc.relation.haspart	wake1.pdf	en
dc.relation.haspart	diss.pdf	en
dc.relation.haspart	w3d25.pdf	en
dc.relation.haspart	w3d50.pdf	en
dc.relation.haspart	wake2.pdf	en
dc.rights	In Copyright	en
dc.rights.uri	http://rightsstatements.org/vocab/InC/1.0/	en
dc.subject	Wake of a rectangular wing	en
dc.subject	Trailing vortex	en
dc.subject	q-vortex	en
dc.subject	Large eddy simulation	en
dc.subject	Temporal simulation	en
dc.subject	spatial simulation	en
dc.title	Numerical Investigation of the Wake of a Rectangular Wing	en
dc.type	Dissertation	en
thesis.degree.discipline	Engineering Science and Mechanics	en
thesis.degree.grantor	Virginia Polytechnic Institute and State University	en
thesis.degree.level	doctoral	en
thesis.degree.name	Ph. D.	en

Numerical Investigation of the Wake of a Rectangular Wing

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