6. Appendix 2 — Axisymmetric gyratory viscous unsteady flow equations

In a uniformly rotating reference frame, for an axisymmetric flow (¶ / ¶ θ = 0), the Navier-Stokes equations are as follows [J.P. Veuillot and F. Desbois, ONERA].

6.1 Continuity equation

$\frac{\partial ρ}{\partial t} + \frac{\partial ({ρrW}_{r})}{r \partial r} + \frac{\partial ({ρW}_{z})}{\partial z} = 0$

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Appendix 2 — Axisymmetric gyratory viscous unsteady flow equations

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Appendix 3 — Reminder of the Navier-Stokes equations

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References

(1) - LORENZ (H.) - Theorie und Berechung der Volturbinen und Kriseslpumpen. - Zeitschrift des Vereines deutscher Ingenieure, Vol. 49, p. 1650-1675, (1905).
(2) - WU (C.H.) - A general through flow theory of fluid flow with subsonic or supersonic velocity in...

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