Huidan Yu

SCALAR MIXING AND CHEMICAL REACTION SIMULATIONS USING LATTICE BOLTZMANN METHOD

We simulate scalar mixing and chemical reactions using the lattice Boltzmann method. Simulations of initially non-premixed binary mixtures yield scalar probability distribution functions that are in good agreement with direct numerical simulation (of Navier-Stokes equation) data. One-dimensional chemically-reacting flow simulation of a premixed mixture yields a flame speed that is consistent with experimentally determined value. These results serve to establish the feasibility of the lattice Boltzman method as a viable tool for computing turbulent combustion.

Near-field turbulent simulations of rectangular jets using lattice Boltzmann method

We perform large eddy simulation (LES) of the near field of low aspect ratio (AR) rectangular turbulent jets (RTJ) using the lattice Boltzmann method. The computational technique combines a D3Q19 multiple relaxation time (MRT) lattice Boltzmann equation (LBE) with the Smagorinsky model for the subgrid stress. First and foremost, we demonstrate that the MRT-LBE model is more suitable than the widely used single-relaxation-time LBE model for LES of turbulent flows. Then, we proceed to compute four jets with MRT-LBE: AR-1, 1.5, 2, 5; exit velocity u0(m∕s)-60, 39, 60, 23; and Reynolds number Re-184 000, 25 900, 128 000, 14 000. The investigated near-field behavior includes: (1) Decay of mean streamwise velocity (MSV) and inverse MSV; (2) spanwise and lateral profiles of MSV; (3) half-velocity width development and MSV contours; and (4) streamwise turbulence intensity distribution. The simulation results are compared against experimental data. Two unique features of RTJ—the saddle-back MSV spanwise (major axis...

Lagrangian refined Kolmogorov similarity hypothesis for gradient time evolution and correlation in turbulent flows.

We study time evolution of velocity and pressure gradients in isotropic turbulence by quantifying their autocorrelation functions and decorrelation time scales. The Lagrangian analysis uses data in a public database generated by direct numerical simulation at a Reynolds number Re{lambda} approximately 433. It is confirmed that when averaging over the entire domain, correlation functions decay on time scales on the order of the global Kolmogorov turnover time scale. However, when performing the analysis in different subregions of the flow, turbulence intermittency leads to large spatial variability in the decay time scales. Remarkably, excellent collapse of the autocorrelation functions is recovered when using a locally defined Kolmogorov time scale. This provides new evidence for the validity of Kolmogorovs refined similarity hypothesis, but from a Lagrangian viewpoint that provides a natural frame to describe the dynamics of turbulence.

Rayleigh–Taylor instability in cylindrical geometry with compressible fluids

A linear stability analysis of the Rayleigh–Taylor instability (RTI) between two ideal inviscid immiscible compressible fluids in cylindrical geometry is performed. Three-dimensional (3D) cylindrical as well as two-dimensional (2D) axisymmetric and circular unperturbed interfaces are considered and compared to the Cartesian cases with planar interface. Focuses are on the effects of compressibility, geometry, and differences between the convergent (gravity acting inward) and divergent (gravity acting outward) cases on the early instability growth. Compressibility can be characterized by two independent parameters—a static Mach number based on the isothermal sound speed and the ratio of specific heats. For a steady initial unperturbed state, these have opposite influence, stabilization and destabilization, on the instability growth, similar to the Cartesian case [D. Livescu, Phys. Fluids 16, 118 (2004)]. The instability is found to grow faster in the 3D cylindrical than in the Cartesian case in the converge...

Studying Lagrangian dynamics of turbulence using on-demand fluid particle tracking in a public turbulence database

from a pseudo-spectral direct numerical simulation (DNS) of forced isotropic turbulence. The flow’s Taylor-scale Reynolds number is Re� = 443, and the simulation output spans about one large-scale eddy turnover time. Besides the stored velocity and pressure fields, built-in 1st- and 2nd-order space differentiation as well as spatial and temporal interpolations are implemented on the database. The resulting 27 terabytes (TB) of data are public and can be accessed remotely through an interface based on a modern Web-services model. Users may write and execute analysis programs on their host computers, while the programs make subroutine-like calls (getFunctions) requesting desired variables (velocity and pressure and their gradients) over the network. The architecture of the database and the initial builtin functionalities are described in a previous JoT paper [2]. In the present paper, further developments of the database system are described; mainly the newly developed getPosition function. Given an initial position, integration time-step, as well as an initial and end time, the getPosition function tracks arrays of fluid particles and returns particle locations at the end of the trajectory integration time. The getPosition function is tested by comparing with trajectories computed outside of the database. It is then applied to study Lagrangian velocity structure functions as well as tensor-based Lagrangian time correlation functions. The roles of pressure Hessian and viscous terms in the evolution of the symmetric and antisymmetric parts of the velocity gradient tensor are explored by comparing the time correlations with and without these terms. Besides the getPosition function, several other updates to the database are described such as a function to access the forcing term in the DNS, a new more efficient interpolation algorithm based on partial sums, and a new Matlab interface.

Mechanism of axis switching in low aspect-ratio rectangular jets

In this work we systematically study one square jet (AR=1) and four rectangular jets with an aspect ratio of width over height AR=1.5,2,2.5, and 3 respectively using the lattice Boltzmann method for direct numerical simulation. Focuses are on various flow properties on transverse planes downstream to investigate the correlation between the downstream velocity and secondary flow. Three distinct regions of jet development are identified in all the five jets. As the length of the PC (potential core) region maintains about the same, that of the CD (characteristic decay) region strongly depends on the jet aspect-ratio (AR) and Reynolds number (Re). The 45^o and 90^o axis-switching occur in the CD region, with the former followed by the latter at the early and late stages of the CD region respectively. The half-width streamwise velocity contour reveals that 45^o axis-switching is mainly contributed by the corner effect, whereas the aspect-ratio (elliptic) feature affects the shape of the jet when 45^o axis-switching occurs. The close examinations of flow pattern and vorticity contour, as well as the correlation between streamwise velocity and vorticity, indicate that 90^o axis-switching results from the boundary effect. Specific flow patterns for 45^o and 90^o axis-switching are identified to reveal the mechanism of the axis-switchings respectively.

GPU accelerated lattice Boltzmann simulation for rotational turbulence

In this work, we numerically study decaying isotropic turbulence in periodic cubes with frame rotation using the lattice Boltzmann method (LBM) and present the results of rotation effects on turbulence. The implementation of LBM is on a GPU (Graphic Processing Unit) platform using CUDA (Compute Unified Device Architecture). Through the accelerated GPU-LBM simulation, we look into various effects of frame rotation on turbulence. It has been observed that rotation slows down the decay of kinetic energy and enstrophy. Rotation also breaks isotropy and induces vortex tubes in the direction of frame rotation. Characteristics related to velocity and its derivatives have been studied with and without rotation. Without rotation, the kinetic energy and enstrophy decay follow -10/7 and -17/7 scaling respectively whereas in the presence of rotation with the relatively small Rossby number (large rotation intensity), the energy decay slows down to -5/21 scaling when the initial isotropic turbulence energy spectrum is scaled to k^4. These scalings with and without rotation are in quantitative agreements with the predictions from Kolmogorov hypotheses respectively. The skewness and kurtosis are seen more fluctuating in rotational turbulence, which agrees with the results from NS-based computation. Using this accelerated and validated GPU-LBM computation tool, we are further studying the inverse energy transfer behavior with and without rotation aiming to quantify the effects of rotation on the inverse energy transfer to reveal underlying physics of a particular stage of the turbulence development. The results will be presented in near future.

Local and nonlocal pressure Hessian effects in real and synthetic fluid turbulence

The Lagrangian dynamics of the velocity gradient tensor A in isotropic and homogeneous turbulence depends on the joint action of the self-stretching term and the pressure Hessian. Existing closures for pressure effects in terms of A are unable to reproduce one important statistical role played by the anisotropic part of the pressure Hessian, namely the redistribution of the probabilities towards enstrophy production dominated regions. As a step towards elucidating the required properties of closures, we study several synthetic velocity fields and how well they reproduce anisotropic pressure effects. It is found that synthetic (1) Gaussian, (2) multifractal, and (3) minimal turnover Lagrangian map incompressible velocity fields reproduce many features of real pressure fields that are obtained from numerical simulations of the Navier Stokes equations, including the redistribution towards enstrophy-production regions. The synthetic fields include both spatially local, and nonlocal, anisotropic pressure effec...

Extension of compressible ideal-gas rapid distortion theory to general mean velocity gradients

The homogeneity condition in compressible flows requires that mean velocity gradient and mean thermodynamic variables must be spatially invariant. This has restricted the use of rapid distortion theory (RDT) for compressible flows to a small set of mean-velocity gradients. By introducing an appropriate body force, we show that the homogeneity condition can be satisfied for a large class of compressible turbulence. We proceed to derive RDT spectral covariance equations of all relevant moments and recover the limiting behavior at vanishing and infinite (pressure-release) Mach numbers for homogeneous shear, plain-strain, axisymmetric expansion, and contraction cases.

Lattice Boltzmann simulation of mass transfer in thermally driven cavity flows

We study mass transfer in 2D thermally driven cavity using lattice Boltzmann method. Simulations are performed to investigate various effects on enhancement of oxygen mass transfer in lead/lead bismuth eutectic. It is shown that oxygen transfer is dominated by convection although diffusion plays a role. Comparative studies demonstrate that side heating and top-cooling configuration is more efficient than side-heating/cooling and oxygen transfers more rapidly in a square than rectangular cavity with same area. This work supplies supportive information for developing active oxygen control technique in experiments to prevent or reduce corrosion in liquid metal cooled nuclear reactors.