Quasihomogeneous critical swirling flows in expanding pipes, part I
Groesen, E. van and Fliert, B.W. van de and Fledderus, E.R. (1995) Quasihomogeneous critical swirling flows in expanding pipes, part I. Journal of Mathematical Analysis and Applications, 192 (3). pp. 764788. ISSN 0022247X

PDF
804kB 
Abstract:  Timeindependent swirling flows in rotationally symmetric pipes of constant and varying diameter are constructed using variational techniques. Critical flows in pipes of uniform cross section are found by extremizing the crosssectional energy at constrained value of the crosssectional helicity and the axial how rate. Discrete classes of hows are found explicitly, parameterized by the radius and the value of the crosssectional helicity. These flows are steady Beltramitype hows and are independent of the axial coordinate. Solution branches can show the phenomenon of flowreversal at the central axis of the pipe: the axial velocity becomes negative with increasing radius. An approximation for swirling flows in a pipe with varying circular cross section is constructed in a quasihomogeneous way as a succession in the axial direction of critical flows in uniform pipes. With the changing value of the radius, the value of the crosssectional helicity is determined by the requirement that the approximation satisfies the correct energy and flux conservation. It will be shown that these requirements are equivalent to satisfying the necessary solvability conditions that arise from a perturbation analysis around the quasihomogeneous approximation. The approximate flows have the property that in lowest order approximation the local crosssectional energy density increases linearly with R, while the local crosssectional helicity density is constant. 
Item Type:  Article 
Copyright:  © 1995 Academic Press, Inc. 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
Research Group:  
Link to this item:  http://purl.utwente.nl/publications/30291 
Official URL:  http://dx.doi.org/10.1006/jmaa.1995.1202 
Export this item as:  BibTeX EndNote HTML Citation Reference Manager 
Repository Staff Only: item control page
Metis ID: 140931