New constitutive equation for the volume viscosity in fluids
Abstract
The traditional volume viscosity, Stokes' hypothesis, and acoustical relaxation are reviewed. The lossy NavierStokes Equation is applied to periodic (acoustic) flow, and it is shown that the traditional volume viscosity leads to a result which contradicts that describing acoustical relaxation. It is demonstrated that the addition of a second volume viscosity term to the constitutive equation, to account for pressure relaxation, resolves the conflict, and leads to a direct correspondence between the volume viscosity parameters and the acoustical relaxation parameters. The representation of volume viscosity is formulated for the case of multiple relaxations, as occur in air. Finally, an application of the new constitutive equation to a simple convective compressible flow, namely a linearly accelerating flow, demonstrates the impact of volume viscosity upon the flow and the physical conditions for which it is important.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 March 1994
 Bibcode:
 1994STIN...9427867Z
 Keywords:

 Compressible Flow;
 Constitutive Equations;
 Convective Flow;
 NavierStokes Equation;
 Viscosity;
 Hypotheses;
 Sound Waves;
 Fluid Mechanics and Heat Transfer