Reynolds-stress balance equations in orthogonal helical coordinates and application

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 84; no. 6; pp. 403 - 416
• Main Authors: Hüttl, T.J., Chaudhuri, M., Wagner, C., Friedrich, R.
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01.06.2004; WILEY‐VCH Verlag; Wiley-VCH
• Subjects: Combinatorics; Combinatorics. Ordered structures; curvature; Designs and configurations; Exact sciences and technology; Germano coordinate system; helical coordinates; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Reynolds-stress balance equations; Sciences and techniques of general use; torsion; turbulent pipe flow; Turbulence; Turbulent flow; Applied mechanics; Pipe flow; Applied mathematics; Reynolds number; Numerical simulation; Curvature
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.200310110

Recently, direct numerical simulations of turbulent flow in helically coiled pipes have been performed and published. Here, computational results are shown for low Reynolds number flow (Reτ = 230) through one helical pipe configuration (curvature κ R = 0.1, torsion τ R = 0.165). The results are shortly discussed and further information of other toroidal or helical pipe flow simulations are given. Besides, the Reynolds‐stress balance equations derived in orthogonal helical coordinates are presented to allow further insight into helical pipe flow. The Reynolds‐stress balance equations are of great importance for turbulence modelling. Compared to their formulation in cylindrical coordinates, further terms occur, describing centrifugal and other inertia force effects which result from pipe curvature and torsion. Except for toroidal flow, where torsion is zero and a symmetry plane exists, no possibility to simplify the equations has been found.