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Nearfield and Farfield Acoustic Models for Rectangular Jets

Chakrabarti, Suryapratim
http://orcid.org/0000-0001-8077-8127
http://rave.ohiolink.edu/etdc/view?acc_num=osu1654532427822202

Abstract Details

2022, Doctor of Philosophy, Ohio State University, Aerospace Engineering.
Rectangular propulsion nozzles offer thrust-vectoring and air-frame-integration advantages over their more commonly studied circular counterparts. However, they display many distinguishing features which violate assumptions, such as azimuthal homogeneity, typically used in acoustic prediction tools for circular jets. In the present work, we examine the turbulent dynamics of rectangular jets from a range of nozzle geometries and operating conditions with the aim of highlighting their distinct nearfield dynamics and developing simplified models for their acoustics. First, the nearfield dynamics of a heated overexpanded rectangular jet of aspect ratio~(AR) two are examined with an implicit Large-Eddy Simulation using experimental data for validation purposes. The conical nozzle, representative of practical configurations, results in multiple shock trains from the throat region as well as the overexpanded operating condition. Each train introduces unsteadiness that influences the external shock cell and plume structure. A detailed analysis of the terms contributing to the turbulent kinetic energy (TKE) is performed to examine the evolution of the plume. The major axis shear layer experiences significant amplification of the TKE compared to the minor axis, particularly near the core-collapse region, and thus, pressure fluctuations in the near acoustic field are correspondingly larger in that direction. The most prominent source of TKE in this region is associated with strong mean flow gradients across the major axis shear layer and larger corresponding cross-correlations of velocity fluctuations. These effects are shown to be consistent with protrusions of vortical perturbations arising in the minor axis shear layer into the potential core. The evolution of pressure perturbations from asymmetric to axisymmetric occurs relatively quickly, to achieve agreement with far-field experimental data. Given the overall similarity of the acoustics from both low AR rectangular and circular jets, we seek to adapt the more advanced acoustic models developed for the latter to rectangular jets. To that end, we examine the utility of an azimuthal Fourier decomposition for rectangular Mach~1.3 jets of aspect ratios 1, 4 and 8 using Large-Eddy Simulations, with a circular jet of same equivalent diameter for reference. The simulations manifest key features of rectangular jets, including higher spreading rates, shorter potential core, axis switching, and azimuthal variation in peak acoustic intensity. We show that, after projection on a cylindrical frame, a sine-cosine ansatz for the azimuthal Fourier series affords a more convenient representation of non-axisymmetric flow features than the commonly used complex exponential ansatz. Fluctuation magnitudes of the higher azimuthal modes show a rapid reduction in amplitude, similar to those observed in circular jets, especially if an acoustic fluctuation field based on momentum potential theory is chosen instead of pressure fluctuations. The leading modes differ, however, from those of a circular jet in two important aspects, namely, the mechanisms represented by the sine and cosine coefficients of the first azimuthal mode and the rate of streamwise decay of all modes with increasing AR. These differences are traced to the near and farfield rectangular jet asymmetry by examining azimuthal inhomogeneity, whose implications are assessed with a generalized expression for acoustic intensity based on energies of leading modes. The significant simplicity of circular plumes is recovered as a special case of the analysis. Invocation of the two-fold mirror symmetry property of rectangular jets eases the prediction procedure so that only two extra terms, representing mechanisms unique to rectangular jets, specifically preferential flapping in the minor axis direction and coupling of axisymmetric and second azimuthal modes, are sufficient to recover the advantages of azimuthal decomposition. The model order reduction afforded by the azimuthal Fourier decomposition is then leveraged to develop wavepacket models for rectangular jets by educing their coherent structures using Spectral Proper Orthogonal Decomposition~(SPOD) of the individual azimuthal modes as is common in the circular jet literature. Despite the azimuthal inhomogeneity of rectangular jets, the method is shown to capture the full 3D fluctuation fields with relatively small errors related to the coupling between the axisymmetric and second azimuthal modes. Although the axisymmetric fluctuations in both circular and rectangular jets exhibit a qualitatively similar spatially modulated wavepacket form, the latter exhibits important distinctions such as more rapid growth of coherent structures close to the nozzle exit, a shorter streamwise length, and more abrupt truncation close to the end of the potential core. Additionally, the preferential flapping in the minor axis direction is shown to be caused by more coherent flapping motions along the minor axis direction with distinct phase velocities and spatial distributions. Finally, the coupling of the axisymmetric and second azimuthal modes is studied using a new Cross POD technique and is shown to be related to two distinct mechanisms namely, the disparity in the lengths of the major and minor axes for high AR jets as well as the non-isotropic acoustic refraction from the asymmetric rectangular jet mean flowfield.
Datta Gaitonde (Advisor)
Jen-Ping Chen (Committee Member)
Mo Samimy (Committee Member)
207 p.
Aerospace Engineering
Jet Noise, Wavepackets, Computational Fluid Dynamics, Large-Eddy Simulations,Fourier Analysis, Aeroacoustics

Recommended Citations

Citations

  • Chakrabarti, S. (2022). Nearfield and Farfield Acoustic Models for Rectangular Jets [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1654532427822202

    APA Style (7th edition)

  • Chakrabarti, Suryapratim. Nearfield and Farfield Acoustic Models for Rectangular Jets. 2022. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1654532427822202.

    MLA Style (8th edition)

  • Chakrabarti, Suryapratim. "Nearfield and Farfield Acoustic Models for Rectangular Jets." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1654532427822202

    Chicago Manual of Style (17th edition)

osu1654532427822202
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