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New constitutive equation for the volume viscosity in fluids

The traditional volume viscosity, Stokes' hypothesis, and acoustical relaxation are reviewed. The lossy Navier-Stokes 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.

Zuckerwar, Allan J.↗

Unsteady Analysis of Inlet-Compressor Acoustic Interactions Using Coupled 3-D and 1-D CFD Codes

It is well known that the dynamic response of a mixed compression supersonic inlet is very sensitive to the boundary condition imposed at the subsonic exit (engine face) of the inlet. In previous work, a 3-D computational fluid dynamics (CFD) inlet code (NPARC) was coupled at the engine face to a 3-D turbomachinery code (ADPAC) simulating an isolated rotor and the coupled simulation used to study the unsteady response of the inlet. The main problem with this approach is that the high fidelity turbomachinery simulation becomes prohibitively expensive as more stages are included in the simulation. In this paper, an alternative approach is explored, wherein the inlet code is coupled to a lesser fidelity 1-D transient compressor code (DYNTECC) which simulates the whole compressor. The specific application chosen for this evaluation is the collapsing bump experiment performed at the University of Cincinnati, wherein reflections of a large-amplitude acoustic pulse from a compressor were measured. The metrics for comparison are the pulse strength (time integral of the pulse amplitude) and wave form (shape). When the compressor is modeled by stage characteristics the computed strength is about ten percent greater than that for the experiment, but the wave shapes are in poor agreement. An alternate approach that uses a fixed rise in duct total pressure and temperature (so-called 'lossy' duct) to simulate a compressor gives good pulse shapes but the strength is about 30 percent low.

Suresh, A.↗