Assessment of the transition k-k-ω model application to transitional oscillatory pipe flows.

Abstract

The flow transition from laminar to turbulent inside of typical thermoacoustic devices influences the heat-exchange capacities of these devices and dramatically impacts overall performances as well. A few measurements [Eckmann and Grotberg (1991), J. Fluid Mech. 222, 329-350; Hino, Sawamoto, and Takasu (1976). J. Fluid Mech. 75, 193-207] and direct simulations [Feldmann and Wagner (2012). J. Turbul. 13(32), 1-28; Feldmann and Wagner (2016a). New Results in Numerical and Experimental Fluid Mechanics X, pp. 113-122] were reported that describe the transitional oscillatory flows; however, almost no turbulence model has been developed that enables accurate detection and characterization of the reported intermittent turbulent fluctuations. The present work aims to assess the applicability of the k-kL-ω transition model to transitional oscillatory pipe flows. A sinusoidal pressure gradient is introduced into ANSYS finite-volume solver for flow field simulation at different acoustic frequencies, while a friction Reynolds number of 1440 is retained. The stationary turbulent and the laminar oscillatory pipe flows are first considered for validation and model calibration against published LDA measurements [Durst, Kikura, Lekakis, Jovanovic, and Ye (1996). Exp. Fluids 20, 417-428] and DNS results [Feldmann and Wagner (2012). J. Turbul. 13(32), 1-28] in addition to the Sexl's laminar-flow theory [Sexl (1930). Zeitschrift Phys. 61(5), 349-362]. Investigation of the total fluctuation kinetic energy of transitional oscillations reveals the appearance of intermittent fluctuations within the near-wall region at Wo = 13 during deceleration, while fully turbulent oscillations are predicted in the entire pipe domain at Wo = 5. Although the present results are qualitatively in good agreement with reported experimental [Eckmann and Grotberg (1991). J. Fluid Mech. 222, 329-350] and DNS findings [Feldmann and Wagner (2012). J. Turbul. 13(32), 1-28], the velocity profiles show poor agreement with corresponding DNS data during flow acceleration at Wo = 5.