Inviscid circulatory-pressure field derived from the incompressible Navier-Stokes equations

Sven Schmitz, James G. Coder

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

The static-pressure field in the steady and incompressible Navier-Stokes momentum equation is decomposed into circulatory (inviscid) and dissipative (viscous) partial-pressure fields. It is shown analytically that the circulatory-pressure integral over the surface of a lifting body of thickness recovers the lift generating Kutta-Joukowski theorem in the far field, and results in Maskell's formula for the vortex-induced drag plus an additional pressure-loss term that tends to zero for an infinitely thin wake. A Poisson equation for the circulatory-pressure field is implemented as a transport equation into the FLUENT 13 solver. Numerical examples include a circular cylinder at Re = 8.5 × 105, the S809 airfoil at Re = 2 × 106, and the ONERA M6 wing at Re = 1 × 106. It is shown that the circulatory-pressure field does indeed behave as an inviscid pressure field of a fully viscous solution, and provides insight into the nature of pressure drag and its contributions to local form and vortex-induced drag.

Original languageEnglish (US)
Pages (from-to)33-41
Number of pages9
JournalAIAA journal
Volume53
Issue number1
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering

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