This chapter derives the Reynolds Averaged Navier‐Stokes Equations (RANSE) form of the Navier‐Stokes equations (NSE) for incompressible flow. Conversion of the NSE into the RANSE starts with introducing the approach Equation into the basic equations. If one studies the RANSE, he/she will find that the new terms look similar to the stress terms in the conservation of momentum Equations. The averaging process has introduced six, yet unknown, averages of the turbulent velocity products. Similar to Stokes' approach, which connected the unknown stresses in the conservation of momentum equations to rates of change in the velocity field, one needs to find additional equations for the unknown Reynolds stresses. The chapter outlines the classic approach introduced by Joseph Valentin Boussinesq, a French mathematician and physicist. Boussinesq proposed to link the apparent Reynolds stresses to the space derivatives of the mean velocities. This is known as Boussinesq's eddy viscosity hypothesis.
Reynolds Averaged Navier‐Stokes Equations (RANSE)
2019-05-06
12 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
Proper Orthogonal Decomposition Applied to the Reynolds-Averaged Navier-Stokes Equations
British Library Conference Proceedings | 2012
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