Reduced-order modelling of jet noise using a map-based stochastic turbulence approach
Final Report Abstract
Accurately predicting turbulent jet noise typically necessitates the application of either direct numerical simulation (DNS) or high-resolution large-eddy simulation (LES) techniques to capture turbulent sources in the acoustic near field. These approaches demand high numerical resolution, limit the accessible parameter space, and incur substantial computational costs. Reduced-order models offer a means to alleviate these limitations. In this study, we employ the stochastic one-dimensional turbulence (ODT) model as an independent tool to investigate turbulent fluctuations in the far downstream region of turbulent round jets with finite co-flow velocity. ODT is a dimensionally reduced turbulence model designed to resolve flow fields over a wide range of scales, encompassing turbulent noise sources at all relevant scales, but for a single, radially oriented, physical coordinate advected downstream with the flow during simulation. The focus was on unheated round jets with a nozzle diameter (D), nominal Mach number (Ma) of 0.9, and Reynolds number (Re_D) of 9×10^4, 2×10^5, and 4×10^5, serving as a canonical problem. An ensemble of ODT realizations yields flow statistics, allowing for the estimation of turbulent noise generated by small-scale resolved sources. Our analysis delves into the model representation of the flow field and the participating flow scales, extending even far downstream of the nozzle—unattainable with high-resolution LES or DNS. Our ODT results closely match existing reference data, accurately reproducing asymptotic mean and fluctuating velocity behavior, as well as radial turbulence spectra conforming to large-scale jet similarity, albeit influenced by the axial reduction in turbulence intensity. These results offer an outlook on the model's potential for turbulent jet noise prediction. The reduced-dimensional ODT formulation enables the resolution of small-scale turbulent fluctuations up to axial locations of x=100r_0 downstream of the nozzle with radius r_0. Such extensive axial spans present challenges for high-resolution LES and DNS, constrained by resolution and computational costs for gathering flow statistics. ODT results suggest that statistical jet similarity is approximately achieved at x/r_0≥60. However, there persists a need for advanced numerical methods capable of providing a detailed representation of turbulent fluctuation phenomenology down to the smallest flow scales, particularly for engineering applications such as jet noise prediction. Consequently, this study represents a step toward quantitative estimations of turbulent and high-frequency mixing noise sources. We intended to utilize the model representation of local eddy turnover-time and length scales for turbulent noise source estimation, as it offers a more cost-effective and robust alternative. The model results for the velocity field demonstrate ODT's capacity as a stand-alone tool to capture pertinent flow features of round jets. It accurately represents the spatial development of turbulent jets, especially at far downstream distances, encompassing turbulent fluctuations and spectra, providing a foundation for turbulent noise estimation. Furthermore, the mean flow and turbulence properties in the far-field of the nozzle align satisfactorily with available reference data. In sum, this study demonstrates ODT's overall suitability for small-scale-resolving numerical simulations of turbulent phenomena.
Publications
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Modelling turbulent jets at high-Reynolds number using one-dimensional turbulence. AIAA AVIATION 2021 FORUM. American Institute of Aeronautics and Astronautics.
Sharma, Sparsh; Klein, Marten & Schmidt, Heiko
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Features of far-downstream asymptotic velocity fluctuations in a round jet: A one-dimensional turbulence study. Physics of Fluids, 34(8).
Sharma, Sparsh; Klein, Marten & Schmidt, Heiko
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Toward the use of a reduced‐order and stochastic turbulence model for assessment of far‐field sound radiation: Low Mach number jet flows. PAMM, 23(3).
Medina, Méndez Juan A.; Sharma, Sparsh; Schmidt, Heiko & Klein, Marten
