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

Abstract

Periodically-oscillated pipe flows in which the bulk velocity is varied about a non-zero mean level (Ub = Ub0[1 + γ cos ωt]) are computed using a low-Reynolds-number k–ε 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, ωt) = k 0 + k 1 cos(ωt + ψ); k 0, k 1,ψ = 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/γ k0 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