ASA 127th Meeting M.I.T. 1994 June 6-10

4pPA6. New constitutive equation for the volume viscosity of fluids.

Allan J. Zuckerwar

NASA Langley Res. Ctr., MS 238, Hampton, VA 23681

Robert L. Ash

Old Dominion Univ., Norfolk, VA 23508

The traditional constitutive equation for the volume viscosity of fluids, written for one-dimensional flow as (sigma)[sub x][sup ']=((lambda)+2(mu))(cursive beta)u/(cursive beta)x, has no theoretical foundation and no established relationship to known relaxation processes in fluids. [for notation see H. Schlichting, Boundary Layer Theory (McGraw-Hill Classic Textbook Reissue Series, New York, 1987)]. When applied to periodic flow, i.e., sound propagation, this equation yields expressions for the dispersion and absorption of sound, which indeed have the expected forms for a single relaxation process; but it inherently leads to the absurd conclusion that the relaxation strength must equal unity (among other deficiencies). It is shown here that a constitutive equation of the form (sigma)[sub x][sup ']=(eta)[sub v]((cursive beta)u/(cursive beta)x)+(eta)[sub p](Dp/Dt) yields expressions which conform to the acoustical single relaxation process, whereby (eta)[sub v]=-(rho)[sub 0]c[sub 0][sup 2](tau)[sub ps], (eta)[sub p]=-(tau)[sub vs], and (tau)[sub ps] and (tau)[sub vs] are the isentropic relaxation times at constant pressure and constant volume, respectively. An application to a simple problem in steady compressible flow is presented.