Flow Exergy as a Lagrangian for the Navier-Stokes Equations for Incompressible Flow

Authors : Enrico Sciubba

Pages : 115-122

View : 13 | Download : 7

Publication Date : 2004-09-01

Article Type : Research Paper

Abstract :A novel variational derivation of the Navier-Stokes equations for incompressible flows is presented and discussed. The Lagrangian density is obtained from the exergy balance equation written for both the insert ignore into journalissuearticles values(Lagrangian); steady and quasi-stationary isothermal flows of an incompressible fluid. The exergy of a fluid mass insert ignore into journalissuearticles values(composed of a kinetic, a pressure-work, a diffusive, and a dissipative portion, the latter being the result of viscous irreversibility); is derived first, and it is then shown that a formal minimisation of the exergy variation insert ignore into journalissuearticles values(i.e. destruction); generates, without recurring to “local potentials”, the Navier-Stokes equations of motion under the given assumptions. The acceleration being held constant, the proposed variational method can be classified as a “restricted” principle. The problem is also briefly discussed both in its historical perspective and in its possible formal and practical implications.
Keywords : Navier Stokes variational, Navier Stokes Lagrangian, Exergy based Lagrangian