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This work presents a novel framework for the evaluation of far‐field sound radiation, specializing to a low Mach number jet flow. The framework comprises an analytical and a numerical part. In the analytical part, a low Mach number asymptotic analysis is presented to obtain the spectral sources of sound radiation starting from a pressure wave equation that is directly obtained from the Navier–Stokes equations. The derivation procedure is based on the fundamental premise of Lighthill's acoustic analogy. In the numerical part, a reduced‐order model for turbulent flow, the one‐dimensional turbulence model, is used to simulate the velocity field of a low Mach number turbulent round jet, assumed fully developed and statistically steady, hence homogeneous in the azimuthal direction and for a cross‐sectional slab assumed locally homogeneous in axial direction, too. The generated velocity field is used for the calculation of the spectral pressure sources, and consequently, to estimate the far‐field sound pressure level (SPL) of the jet. The results of the analysis are compared against available experimental SPL measurements from a subsonic jet. A reasonable agreement is obtained for the SPL. Furthermore, the analysis sheds light into the different contributions of the subsonic flow to sound radiation. The framework is readily extendable for any kind of low Mach number flow, including variable density flows and jet flames. [ABSTRACT FROM AUTHOR]

One-dimensional turbulence (ODT) is a simulation methodology that represents the essential physics of three-dimensional turbulence through stochastic resolution of the full range of length and time scales on a one-dimensional domain. In the present study, full compressible modifications are incorporated into ODT methodology, based on an Eulerian framework and a conservative form of the governing equations. In the deterministic part of this approach, a shock capturing scheme is introduced for the first time. In the stochastic part, one-dimensional eddy events are modeled and sampled according to standard methods for compressible flow simulation. Time advancement adjustments are made to balance comparable time steps between the deterministic and stochastic parts in compressible flows. Canonical shock–turbulence interaction cases involving Richtmyer–Meshkov instability at Mach numbers 1.24, 1.5, and 1.98 are simulated to validate the extended model. The ODT results are compared with available reference data from large eddy simulations and laboratory experiments. The introduction of a shock capturing scheme significantly improves the performance of the ODT method, and the results for turbulent kinetic energy are qualitatively improved compared with those of a previous compressible Lagrangian ODT method [Jozefik et al., "Simulation of shock–turbulence interaction in non-reactive flow and in turbulent deflagration and detonation regimes using one-dimensional turbulence," Combust. Flame 164, 53 (2016)]. For the time evolution of profiles of the turbulent mixing zone width, ensemble-averaged density, and specific heat ratio, the new model also yields good to reasonable results. Furthermore, it is found that the viscous penalty parameter Z of the ODT model is insensitive to compressibility effects in turbulent flows without wall effects. A small value of Z is appropriate for turbulent flows with weak wall effects, and the parameter Z serves to suppress extremely small eddy events that would be dissipated instantly by viscosity. [ABSTRACT FROM AUTHOR]

Accurate but economical modeling of supersonic turbulent boundary layers is a standing challenge due to the intricate entanglement of temperature, density, and velocity fluctuations on top of the mean-field variation. Application of the van Driest transformation may describe well the mean state but cannot provide detailed flow information. This lack-in modeling coarse and fine-scale variability is addressed by the present study using a stochastic one-dimensional turbulence (ODT) model. ODT is a simulation methodology that represents the evolution of turbulent flow in a low-dimensional stochastic way. In this study, ODT is extended to fully compressible flows. An Eulerian framework and a conservative form of the governing equations serve as the basis of the compressible ODT model. Computational methods for statistical properties based on ODT realizations are also extended to compressible flows, and a comprehensive way of turbulent kinetic energy budget calculation based on compressible ODT is put forward for the first time. Two canonical direct numerical simulation cases of supersonic isothermal-wall channel flow at Mach numbers 1.5 and 3.0 with bulk Reynolds numbers 3000 and 4880, respectively, are used to validate the extended model. A rigorous numerical validation is presented, including the first-order mean statistics, the second-order root mean square statistics, and higher-order turbulent fluctuation statistics. In ODT results, both mean and root mean square profiles are accurately captured in the near-wall region. Near-wall temperature spectra reveal that temperature fluctuations are amplified at all turbulent scales as the effects of compressibility increase. This phenomenon is caused by intensified viscous heating at a higher Mach number, which is indicated by the steeper profiles of viscous turbulent kinetic energy budget terms in the very near-wall region. The low computational cost and predictive capabilities of ODT suggest that it is a promising approach for detailed modeling of highly turbulent compressible boundary layers. Furthermore, it is found that the ODT model requires a Mach-number-dependent increase in a viscous penalty parameter Z in wall-bounded turbulent flows to enable accurate capture of the buffer layer. [ABSTRACT FROM AUTHOR]

An accurate prediction of the turbulent jet noise is usually only possible with direct numerical simulation (DNS) or high-resolution large-eddy simulation (LES) of the turbulent sources in the acoustic near field. The required level of fidelity comes at the price of high numerical resolution requirements, a severe restriction of the accessible parameter space, and high computational costs in general. These limitations can be partially mitigated by reduced-order models. In the present work, the stochastic one-dimensional turbulence (ODT) model is utilized as a stand-alone tool in order to study turbulent fluctuations in the far downstream region of turbulent round jets with finite co-flow velocity. ODT is a dimensionally reduced turbulence model that aims to resolve flow-field over a broad range of scales and, thus, the turbulent noise sources at all relevant scales, but only for a single, radially oriented, physical coordinate that is advected downstream with the flow during a simulation run. Here, unheated round jets with nozzle diameter D, nominal Mach number Ma = 0.9 but Reynolds number R e D ∈ { 9 × 10 4 , 2 × 10 5 , 4 × 10 5 } are studied as a canonical problem. An ensemble of ODT realizations is used to obtain flow statistics from a detailed representation of fluctuations that may be used to estimate turbulent noise by small-scale resolved sources in the near future. As the first step in this direction, we analyze the model representation of the flow field and the participating flow scales in detail. This is done even far downstream of the nozzle, which is not possible with high-resolution LES or DNS. The present ODT results agree well with the available reference data. The model accurately reproduces the asymptotic mean and fluctuating velocity behavior, and radial turbulence spectra of the jet that approximately obey large-scale jet similarity but are modified by axially decreasing the turbulence intensity. Based on these results, an outlook on the model application for turbulent jet noise prediction is given. [ABSTRACT FROM AUTHOR]

Cylindrical pipe‐flow is evaluated by means of the One‐Dimensional Turbulence (ODT) model applying both an incompressible and a low Mach number variable density framework. In the variable density formulation, the velocity field is decomposed into density‐related (non‐divergence‐free) and density‐unrelated (divergence‐free) contributions, as detailed in Medina et al. [Combust. Flame 190 (2018) 388‐401]. Both contributions to the velocity field are subject to the effects of diffusion and turbulent transport, as it is normally the case for the incompressible velocity field in traditional ODT formulations. The turbulent transport is implemented by means of stochastic eddy events. These are influenced by the available kinetic energy given by the divergence‐free velocity contribution. An eddy may arise from the different regions of shear caused by varying velocity gradients in the 1‐D domain, but also as a consequence of the temperature‐varying dynamic viscosity. The cylindrical low Mach number variable density formulation is tested in a very low heat transfer regime and compared to the passive scalar results of the incompressible pipe‐flow formulation. ODT model parameters are assumed equal for both formulations. ODT results are compared to DNS results from Satake and Kunugi [Int. J. Numer. Methods Heat Fluid Flow 12 (2002) 958‐1008]. The passive scalar and variable density results show very good agreement with each other as well as with DNS data, respectively, thus suggesting new possible applications for ODT. [ABSTRACT FROM AUTHOR]

• We introduce an extension of the spatial ODT formulation (S-ODT), in order to study a variable density internal air flow. • S-ODT results are compared to the results of a traditional temporal ODT formulation (T-ODT) and to reference DNS data. • For bulk quantities, both the T-ODT and S-ODT formulations have a similar performance in comparison to DNSs. • For the evaluation of radial distributions, the S-ODT formulation clearly outperforms the T-ODT formulation. A novel spatial formulation of the One-Dimensional Turbulence (ODT) model is applied to a vertical pipe-flow with heat transfer, analogous to the Direct Numerical Simulation (DNS) performed by Bae et al. [Phys. Fluids 18, (075102) (2006)]. The framework presented here is an extension for radially confined domains of the cylindrical ODT spatial formulation for low Mach number flows with variable density. The variable density simulations for air (Prandtl number P r = 0.71) are performed at an initial bulk Reynolds number R e b , 0 , D N S = 6000 and Grashof number G r 0 , D N S = 6.78 × 10 6. ODT results are presented for both the spatial formulation introduced in this work and the standard temporal formulation for cylindrical flows introduced by Lignell et al. [Theor. Comput. Fluid Dyn. 32, 4 (2018), pp. 495–20]. Streamwise bulk profiles and radial profiles at specific streamwise positions for the temporal and spatial formulations are in good agreement with the DNS results from Bae et al. For the present application, the spatial formulation yields physically better results in comparison to the temporal formulation. Overall, the findings in the original work of Bae et al. were corroborated with ODT. Although the framework proposed in this work is not a compressible framework and has some clear limitations regarding conservation properties, we suggest its use for future studies in the low Mach number variable density regime. [ABSTRACT FROM AUTHOR]