Derivation of Realistic Forcing Schemes to Reproduce Turbulent Characteristics of Round Jets on Centerline

Citation

Rah, Kyupaeck Jeff (2020) Derivation of Realistic Forcing Schemes to Reproduce Turbulent Characteristics of Round Jets on Centerline. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7SXH-V275. https://resolver.caltech.edu/CaltechTHESIS:08262019-191842947

Abstract

Turbulence forcing techniques are often required in the numerical simulation of statistically stationary turbulent flows. However, the existing forcing techniques are not based on physics, but rather arbitrary numerical methods that sustain the turbulent kinetic energy. In this work, a realistic forcing technique is devised to reproduce the centerline turbulent characteristics of round jets in a triply periodic box.

A velocity forcing term is derived from the Navier-Stokes equations by applying a Reynolds decomposition with the mean velocity of the axisymmetric jet. The result is an anisotropic linear forcing term. A series of direct numerical simulations (DNS) are performed over a range of Reynolds numbers by applying the derived velocity forcing term in a 3D cubic box. The budget of the terms in the kinetic energy equation is found to be very close to the experimental measurement on the centerline. The anisotropy ratio, kinetic energy, and dissipation rate of the simulations are also comparable to experimental values. Finally, the kinetic energy spectrum in the axial direction is presented. With appropriate normalizations, the spectrum agrees well with the round jet spectrum on its centerline.

A similar procedure is applied to passive scalars to derive a scalar forcing term to simulate the centerline mixing properties of round jets. The term is derived from the scalar transport equation using a Reynolds-like decomposition of the scalar field. The equation is closed by applying the known mean velocity and scalar profiles of axisymmetric jets. The result is a combination of a mean gradient term and a linear scalar term. DNS at different Reynolds numbers have been performed with these source terms for unity Schmidt number. Scalar flux values and scaling exponents of scalar energy spectra from simulations are comparable to experimental values. In addition, a dimensional analysis shows that the normalized scalar statistics, such as variance, flux, and dissipation rate, should only be a function of Reynolds number; indeed, such quantities computed from our simulations approach constant values as the Reynolds number increases. The effects of velocity forcing on scalar fields are also investigated; changing velocity forcing terms may result in unstable scalar fields even under the same scalar forcing.

More computations on higher Schmidt number scalars are performed with the same velocity and scalar forcing terms. It is found that the scalar flux values decrease with increasing Schmidt number for low Reynolds number flows, and reach plateaus as the Schmidt number increases. The flux values also increase with the Reynolds number for all non-unity Schmidt numbers. The scaling exponents of scalar energy spectra are found to decrease with increasing Schmidt number for all Reynolds numbers.

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