ON THE 3-D INVERSE POTENTIAL TARGET PRESSURE PROBLEM .1. THEORETICAL ASPECTS AND METHOD FORMULATION

CHAVIAROPOULOS, P; DEDOUSSIS, V; PAPAILIOU, KD

dc.contributor.author	CHAVIAROPOULOS, P	en
dc.contributor.author	DEDOUSSIS, V	en
dc.contributor.author	PAPAILIOU, KD	en
dc.date.accessioned	2014-03-01T01:44:02Z
dc.date.available	2014-03-01T01:44:02Z
dc.date.issued	1995	en
dc.identifier.issn	0022-1120	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/24259
dc.subject.classification	Mechanics	en
dc.subject.classification	Physics, Fluids & Plasmas	en
dc.subject.other	DESIGN	en
dc.subject.other	FLOW	en
dc.title	ON THE 3-D INVERSE POTENTIAL TARGET PRESSURE PROBLEM .1. THEORETICAL ASPECTS AND METHOD FORMULATION	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1995	en
heal.abstract	An inverse potential methodology is introduced for the solution of the fully 3-D target pressure problem. The method is based on a potential function/stream function formulation, where the physical space is mapped onto a computational one via a body-fitted coordinate transformation. A potential function and two stream vectors are used as the independent natural coordinates, whilst the velocity magnitude, the aspect ratio and the skew angle of the elementary streamtube cross-section are assumed to be the dependent ones. A novel procedure based on differential geometry and generalized tenser analysis arguments is employed to formulate the method. The governing differential equations are derived by requiring the curvature tenser of the flat 3-D physical Eucledian space, expressed in terms of the curvilinear natural coordinates, to be zero. The resulting equations are discussed and investigated with particular emphasis on the existence and uniqueness of their solution. The general 3-D inverse potential problem, with 'target pressure' boundary conditions only, seems to be ill-posed accepting multiple solutions. This multiplicity is alleviated by considering elementary streamtubes with orthogonal cross-sections. The assumption of orthogonal stream surfaces reduces the number of dependent variables by one, simplifying the governing equations to an elliptic p.d.e. for the velocity magnitude and to a second-order o.d.e. for the streamtube aspect ratio. The solution of these two equations provides the flow field. Geometry is determined independently by integrating Frenet equations along the natural coordinate lines, after the flow field has been calculated. The numerical implementation as well as validation test cases for the proposed inverse methodology are presented in the companion paper (Paper 2).	en
heal.publisher	CAMBRIDGE UNIV PRESS	en
heal.journalName	JOURNAL OF FLUID MECHANICS	en
dc.identifier.isi	ISI:A1995QD78900006	en
dc.identifier.volume	282	en
dc.identifier.spage	131	en
dc.identifier.epage	146	en