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Approximate Analytical Methods
Published in Daniel Zwillinger, Vladimir Dobrushkin, Handbook of Differential Equations, 2021
Daniel Zwillinger, Vladimir Dobrushkin
Homogenization seems to be related to renormalization group theory. Renormalization group methods study the asymptotic behavior of a system (i.e., the macroscopic behavior) when the scale of observation is much larger than the scale of microscopic description. See Goldenfeld et al.[501].
Assessment of RANS turbulence models and Zwart cavitation model empirical coefficients for the simulation of unsteady cloud cavitation
Published in Engineering Applications of Computational Fluid Mechanics, 2020
A brief mathematical description of the RANS two-equation models used in our simulations is given as follows, but more detailed formulation can be found in the CFX help manual (ANSYS, 2015). The k-ϵ model calculates μt from the turbulent kinetic energy, k, and its dissipation rate, ϵ, with Eq. 14: where cμ = 0.09. The RNG model is based on renormalization group analysis of the Navier-Stokes equations. The transport equations for turbulence generation and dissipation are the same as those for the k-ϵ model (Eq. 10), but the model constant cμ = 0.085. Finally, the SST model, which improves the accuracy of prediction of the onset and the amount of flow separation under adverse pressure gradients, assumes that μt is linked to k and to the turbulent frequency, ω, via Eq. 15: where F2 is a function that equals 1 for boundary layer flows and 0 for free shear layers, S is an invariant measure of the strain rate and a1 = 0.31.
CFD modeling and testing of an extended-duct air delivery system in high bay buildings
Published in Science and Technology for the Built Environment, 2019
Ryan Kennett, Tao Cao, Yunho Hwang
Indoor environment flows can be classified as low-velocity, low-Reynolds-number (Re) flows with flow regimes that can span laminar to turbulent flow (Zhai et al. 2007). Numerous papers have been published that judge the relative strengths and applicability of turbulence models to indoor environment flows, such as Chen (1995), Zhai et al. (2007), and Rohdin and Moshfegh (2011). Reynolds-averaged Navier–Stokes (RANS) models remain the most commonly used turbulence models due to their robustness, speed, and large set of validation studies in the literature. Of the RANS models, the k-ε model is most common. Of k-ε models, there exist the standard, renormalization group (RNG), and realizable models. The RNG model is the most common turbulence model for indoor environment flows and is generally the most accurate (Zhai et al. 2007). The realizable k-ε model usually produces improved results for swirling flows and separation flows. Shih et al. (1995) showed that the realizable model outperforms the RNG model for predicting buoyancy in plumes. The realizable and RNG models were both tested using the validated baseline CFD model in this study. The two models produced nearly identical results, but the RNG model predicted turbulent viscosity ratios far exceeding the software’s default maximum value. Therefore, the realizable model was chosen with the Fluent 15.0 default coefficients as the turbulence model used in this work.
Examination and optimization of classroom indoor environments in China’s hot summer and cold winter regions
Published in Science and Technology for the Built Environment, 2022
Mengyu Ren, Kang Zhao, Ziwei Huang, Jian Ge
The flow inside the classroom was assumed to be incompressible and turbulent. This simulation adopted the Renormalization Group k-ε model. The basis to verify the calculation’s convergence was the time at which the continuity equation and velocity component deviation equation were less than 10−3 and the residual curve of the energy equation was less than 10−6. To ensure the calculation results’ accuracy, the grid of the CO2 release surface and doors and windows was densified. The maximum grid size in each direction was 0.1 m.