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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.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...

A few linear theories [Swift, J. Acoust. Soc. Am. 84(4), 1145-1180 (1988); Swift, J. Acoust. Soc. Am. 92(3), 1551-1563 (1992); Olson and Swift, J. Acoust. Soc. Am. 95(3), 1405-1412 (1994)] and numerical models, based on low-Mach number analysis [Worlikar and Knio, J. Comput. Phys. 127(2), 424-451 (1996); Worlikar et al., J. Comput. Phys. 144(2), 199-324 (1996); Hireche et al., Canadian Acoust. 36(3), 164-165 (2008)], describe the flow dynamics of standing-wave thermoacoustic engines, but almost no simulation results are available that enable the prediction of the behavior of practical engines experiencing significant temperature gradient between the stack ends and thus producing large-amplitude oscillations. Here, a one-dimensional non-linear numerical simulation based on the method of characteristics to solve the unsteady compressible Euler equations is reported. Formulation of the governing equations, implementation of the numerical method, and application of the appropriate boundary conditions are presented. The calculation uses explicit time integration along with deduced relationships, expressing the friction coefficient and the Stanton number for oscillating flow inside circular ducts. Helium, a mixture of Helium and Argon, and Neon are used for system operation at mean pressures of 13.8, 9.9, and 7.0 bars, respectively. The self-induced pressure oscillations are accurately captured in the time domain, and then transferred into the frequency domain, distinguishing the pressure signals into fundamental and harmonic responses. The results obtained are compared with reported experimental works [Swift, J. Acoust. Soc. Am. 92(3), 1551-1563 (1992); Olson and Swift, J. Acoust. Soc. Am. 95(3), 1405-1412 (1994)] and the linear theory, showing better agreement with the measured values, particularly in the non-linear regime of the dynamic pressure response.

Few numerical works simulate the laminar-flow behavior within the diverging passages of typical thermoacoustic jet pumps. The associated boundary-layer separation is mostly delayed by maintaining a slowly increasing flow passage and thereby the corresponding pressure drop and consumed acoustic energy are noticeably reduced. Of equal importance is the effect of the transition to turbulence on the boundary-layer separation and the resulting flow-pattern. To our knowledge, no simulation has been developed that numerically predict and capture the conditionally turbulent flow regime within typical jet pumps. Here, a new finite-volume model is reported that employs the non-linear CFD solver of ANSYS FLUENT. The k-kl-ω transition model is considered and its parameters are particularly adjusted for present application. A sinusoidal pressure oscillation is enforced at one end, while the far-field approximation is considered at the other end to model the non-reflecting boundary condition. An axisymmetric model alon...