Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method

Peng, Cheng; Geneva, Nicholas; Guo, Zhaoli; Wang, Lian‐Ping

doi:10.1016/j.jcp.2017.11.040

Cited by 52 publications

(24 citation statements)

References 47 publications

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“…One is that LB method is easy to be implemented and parallelized, benefiting from its local nonlinearity, while the other is that LB method has lower numerical dissipation compared to conventional second-order computational fluid dynamics methods [24][25][26] . During the past several decades, the LB method has been successfully applied to DNS of turbulent flows, including decaying homogeneous isotropic turbulence 27,28 , turbulent channel and pipe flows 29,30 , and turbulent thermal convective flows 31 .…”

Section: Introductionmentioning

confidence: 99%

Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection

Shi

2019

Physics of Fluids

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We report the statistical properties of temperature and thermal energy dissipation rate in low-Prandtl number turbulent Rayleigh-Bénard convection. High resolution twodimensional direct numerical simulations were carried out for the Rayleigh number (Ra) of 10 6 ≤ Ra ≤ 10 7 and the Prandtl number (Pr) of 0.025. Our results show that the global heat transport and momentum scaling in terms of Nusselt number (Nu) and Reynolds number (Re) are Nu = 0.21Ra 0.25 and Re = 6.11Ra 0.50 , respectively, indicating that the scaling exponents are smaller than those for moderate-Prandtl number fluids (such as water or air) in the same convection cell. In the central region of the cell, probability density functions (PDFs) of temperature profiles show stretched exponential peak and the Gaussian tail; in the sidewall region, PDFs of temperature profiles show a multimodal distribution at relative lower Ra, while they approach the Gaussian profile at relative higher Ra. We split the energy dissipation rate into contributions from bulk and boundary layers and found the locally averaged thermal energy dissipation rate from the boundary layer region is an order of magnitude larger than that from the bulk region. Even if the much smaller volume occupied by the boundary layer region is considered, the globally averaged thermal energy dissipation rate from the boundary layer region is still larger than that from the bulk region. We further numerically determined the scaling exponents of globally averaged thermal energy dissipation rates as functions of Ra and Re. a a) This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Xu et al., Phys. Fluids 31, 125101 (2019) and may be found at

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Section: Introductionmentioning

confidence: 99%

Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection

Shi

2019

Physics of Fluids

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“…We applied a perturbation force field (see Ref. [22] for details) in the initial 3 eddy turnover times (the eddy turnover time t * is defined as t * = R/u τ ), so the transition from the laminar to turbulent flow could happen relatively fast. After about 25 eddy turnover times from the initial time, both the IBB and the IBM-B simulations reached a statistically stationary state.…”

Section: Results and Discussion 221 Mean Flow Statisticsmentioning

confidence: 99%

“…The pipe-flow simulation results with Yu et al's linear IBB scheme have been reported in our recent publication [22]. We did not repeat the simulation but directly used the published results for comparison for the sake of saving computational resources.…”

Section: Problem Description and Simulation Setupmentioning

confidence: 99%

“…For more details of the simulations, such as how to set up initial condition, how to accelerate the transition from laminar flow to turbulent flow, and how to compute the turbulence statistics in cylindrical coordinates, readers can refer to Ref. [22]. Here we only recapitulate the key parameters of the two simulations in Table 1.…”

Section: Problem Description and Simulation Setupmentioning

confidence: 99%

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A comparative study of immersed boundary method and interpolated bounce-back scheme for no-slip boundary treatment in the lattice Boltzmann method: Part II, turbulent flows

Peng¹,

Ayala²,

Motta³

et al. 2019

Computers & Fluids

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In the first part of this study [1], we compared the performances of two categories of no-slip boundary treatments, i.e., the interpolated bounce-back schemes and the immersed boundary methods in a series of laminar flow simulations within the lattice Boltzmann method. In this second part, these boundary treatments are further compared in the simulations of turbulent flows with complex geometry to provide a next-level assessment of these schemes. Two non-trivial turbulent flow problems, a fully developed turbulent pipe flow at a low Reynolds number, and a decaying homogeneous isotropic turbulent flow laden with a large number of resolved spherical particles are considered. The major problem of the immersed boundary method revealed by the present study is its incapability in computing the local velocity gradients inside the diffused interface, which can result in significantly

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“…However, many existing works have shown that the BGK model is adequate in simulating many flows accurately for both the continuum and rarefied regimes [14,15,23,16,24,25].…”

Section: Introductionmentioning

confidence: 99%

A general framework for the inverse design of mesoscopic models based on the Boltzmann equation

Chen¹,

Wang²,

Lai³

et al. 2020

Preprint

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In this paper, we present a general framework for the inverse-design of mesoscopic models based on the Boltzmann equation. Starting from the single-relaxation-time Boltzmann equation with an additional source term, two model Boltzmann equations for two reduced distribution functions are obtained, each then also having an additional undetermined source term. Under this general framework and using Navier-Stokes-Fourier (NSF) equations as constraints, the structures of the distribution functions are obtained by the leading-order Chapman-Enskog analysis. Next, five basic constraints for the design of the two source terms are obtained in order to recover the Navier-Stokes-Fourier system in the continuum limit. These constraints allow for adjustable bulk-to-shear viscosity ratio, Prandtl number as well as a thermal energy source. The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements. By employing the truncated Hermite expansion, one design for the two source terms is proposed. Moreover, three well-known mesoscopic models in the literature are shown to be compatible with these five constraints. In addition, the consistent implementation of boundary conditions is also explored by using the Chapman-Enskog expansion at the NSF order. Finally, based on the higher-order Chapman-Enskog expansion of the distribution functions, we derive the complete analytical expressions for the viscous stress tensor and the heat flux. Some underlying physics can be further explored under this framework.

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Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method

Cited by 52 publications

References 47 publications

Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection

Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection

A comparative study of immersed boundary method and interpolated bounce-back scheme for no-slip boundary treatment in the lattice Boltzmann method: Part II, turbulent flows

A general framework for the inverse design of mesoscopic models based on the Boltzmann equation

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