Resonant responses in periodic turbulent flows:: computations using a k-ε eddy viscosity model

Periodically-oscillated pipe flows in which the bulk velocity is varied about a non-zero mean level (U-b = U-bo [1 + y cos omega t]) are computed using a low-Reynolds-number k-epsilon turbulence model. Comparison is made with data for periodic pipe flow and it is shown that model is capable of resolving the principal features of the highly non-universal turbulence profiles that occur under conditions of harmonic forcing. There follows an examination of the frequency response of the phase-averaged turbulent kinetic energy, k, which is analysed in terms of its first harmonic variation (k(r, omega t) = k(0) + k(1) cos(omega t + psi); k(0), k(1), psi = f(r)). In confirmation of the stress-transport model results of Cotton and Guy [J. Hydraul. Res. 42 (2004) 293], it is found that the modulation of the turbulent kinetic energy, k(1)/gamma k(0) first responds in a quasi-steady manner and then, with increasing frequency, exhibits resonant behaviour, which is itself succeeded by a frozen response at higher frequencies. The resonant condition occurs when the time scale of large-scale turbulence is an order of magnitude less than the period of the imposed oscillation. The paper concludes with a discussion of the parallels that may be drawn between the present results and the experimental study of Mizushina et al. [J Chem. Engng. Jpn. 6 (1973) 487] in which the effect of external pulsation on the turbulence "bursting" process was investigated.