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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method

A lattice Boltzmann model is presented which gives the complete Navier-Stokes equation and may provide an efficient parallel numerical method for solving various fluid problems. The model uses the single-time relaxation approximation and a particular Maxwell-type distribution. The model eliminates exactly (1) the non-Galilean invariance caused by a density-dependent coefficient in the convection term and (2) a velocity-dependent equation of state.

Chen, Hudong↗
NASA NTRS2000

Theory of the lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability

The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Lallemand, Pierre↗
NASA NTRS2015

Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments relies upon the global momentum conservation of the fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. Numerical examples illustrate the method's application to predicting bulk fluid motion including lateral propellant slosh in low-g conditions.

Orr, Jeb S.↗
NASA NTRS2015

Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments is based upon a novel approach that relies on the global momentum conservation of the closed fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. A numerical example illustrates the method's application to prediction of bulk fluid behavior during a spacecraft ullage settling maneuver.

Orr, Jeb S.↗
NASA NTRS2002

Lattice Boltzmann Method for 3-D Flows with Curved Boundary

In this work, we investigate two issues that are important to computational efficiency and reliability in fluid dynamics applications of the lattice, Boltzmann equation (LBE): (1) Computational stability and accuracy of different lattice Boltzmann models and (2) the treatment of the boundary conditions on curved solid boundaries and their 3-D implementations. Three athermal 3-D LBE models (D3QI5, D3Ql9, and D3Q27) are studied and compared in terms of efficiency, accuracy, and robustness. The boundary treatment recently developed by Filippova and Hanel and Met et al. in 2-D is extended to and implemented for 3-D. The convergence, stability, and computational efficiency of the 3-D LBE models with the boundary treatment for curved boundaries were tested in simulations of four 3-D flows: (1) Fully developed flows in a square duct, (2) flow in a 3-D lid-driven cavity, (3) fully developed flows in a circular pipe, and (4) a uniform flow over a sphere. We found that while the fifteen-velocity 3-D (D3Ql5) model is more prone to numerical instability and the D3Q27 is more computationally intensive, the 63Q19 model provides a balance between computational reliability and efficiency. Through numerical simulations, we demonstrated that the boundary treatment for 3-D arbitrary curved geometry has second-order accuracy and possesses satisfactory stability characteristics.

Mei, Renwei↗
DOE OSTI2020

Discretization limits of lattice‐Boltzmann methods for studying immiscible two‐phase flow in porous media

Summary Digital images of porous media often include features approaching the image resolution length scale. The behavior of numerical methods at low resolution is therefore important even for well‐resolved systems. We study the behavior of the Shan‐Chen (SC) and Rothman‐Keller (RK) multicomponent lattice‐Boltzmann models in situations where the fluid‐fluid interfacial radius of curvature and/or the feature size of the medium approaches the discrete unit size of the computational grid. Various simple, small‐scale test geometries are considered, and a drainage test is also performed in a Bentheimer sandstone sample. We find that both RK and SC models show very high ultimate limits: in ideal conditions the models can simulate static fluid configuration with acceptable accuracy in tubes as small as three lattice units across for RK model (six lattice units for SC model) and with an interfacial radius of curvature of two lattice units for RK and SC models. However, the stability of the models is affected when operating in these extreme discrete limits: in certain circumstances the models exhibit behaviors ranging from loss of accuracy to numerical instability. We discuss the circumstances where these behaviors occur and the ramifications for larger‐scale fluid displacement simulations in porous media, along with strategies to mitigate the most severe effects. Overall we find that the RK model, with modern enhancements, exhibits fewer instabilities and is more suitable for systems of low fluid‐fluid miscibility. The shortcomings of the SC model seem to arise predominantly from the high, strongly pressure‐dependent miscibility of the two fluid components.

Li, Zhe↗
NASA NTRS2019

Predicting Quadcopter Drone Noise Using the Lattice Boltzmann Method

The market for new vertical takeoff and landing vehicles, including autonomous urban air taxis and drones for applications such as package delivery, imaging, and surveillance, is growing rapidly. However, aerodynamic noise continues to be the biggest roadblock to community acceptance and adoption. To predict the aerodynamic noise generated by an isolated quadcopter drone, derived from from first principles, we used the Lattice Boltzmann flow solver within NASA’s Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework. The solver’s computational efficiency, and the complete absence of labor-intensive manual volume mesh generation in the workflow, are key to making routine aeroacoustic analysis of urban air taxis and drones from first principles possible.

Cadieux, Francois↗
NASA NTRS2016

Unsteady Flow Simulation of a Sweeping Jet Actuator Using a Lattice-Boltzmann Method

Active flow control technology is increasingly used in aerospace applications to control flow separation and to improve aerodynamic performance. In this paper, PowerFLOW is used to simulate the flow through a sweeping jet actuator at two different pressure ratios. The lower pressure ratio leads to a high subsonic flow, whereas the high pressure ratio produces a choked flow condition. Comparison of numerical results with experimental data is shown, which includes qualitatively good agreement of pressure histories and spectra. PIV measurements are also available but the simulation overestimates mean and fluctuation quantities outside the actuator. If supply pressure is matched at one point inside the mixing chamber a good qualitative agreement is achieved at all other monitor points.

Duda, B.↗