Showing papers by "Sanjoy Banerjee published in 2009"

Generalized lattice Boltzmann equation with forcing term for computation of wall-bounded turbulent flows.

Abstract: In this paper, we present a framework based on the generalized lattice Boltzmann equation (GLBE) using multiple relaxation times with forcing term for eddy capturing simulation of wall-bounded turbulent flows. Due to its flexibility in using disparate relaxation times, the GLBE is well suited to maintaining numerical stability on coarser grids and in obtaining improved solution fidelity of near-wall turbulent fluctuations. The subgrid scale (SGS) turbulence effects are represented by the standard Smagorinsky eddy viscosity model, which is modified by using the van Driest wall-damping function to account for reduction of turbulent length scales near walls. In order to be able to simulate a wider class of problems, we introduce forcing terms, which can represent the effects of general nonuniform forms of forces, in the natural moment space of the GLBE. Expressions for the strain rate tensor used in the SGS model are derived in terms of the nonequilibrium moments of the GLBE to include such forcing terms, which comprise a generalization of those presented in a recent work [Yu et al., Comput. Fluids 35, 957 (2006)]. Variable resolutions are introduced into this extended GLBE framework through a conservative multiblock approach. The approach, whose optimized implementation is also discussed, is assessed for two canonical flow problems bounded by walls, viz., fully developed turbulent channel flow at a shear or friction Reynolds number (Re) of 183.6 based on the channel half-width and three-dimensional (3D) shear-driven flows in a cubical cavity at a Re of 12 000 based on the side length of the cavity. Comparisons of detailed computed near-wall turbulent flow structure, given in terms of various turbulence statistics, with available data, including those from direct numerical simulations (DNS) and experiments showed good agreement. The GLBE approach also exhibited markedly better stability characteristics and avoided spurious near-wall turbulent fluctuations on coarser grids when compared with the single-relaxation-time (SRT)-based approach. Moreover, its implementation showed excellent parallel scalability on a large parallel cluster with over a thousand processors.

Incorporating forcing terms in cascaded lattice Boltzmann approach by method of central moments.

Abstract: Cascaded lattice Boltzmann method (cascaded-LBM) employs a class of collision operators aiming to stabilize computations and remove certain modeling artifacts for simulation of fluid flow on lattice grids with sizes arbitrarily larger than the smallest physical dissipation length scale [Geier et al., Phys. Rev. E 63, 066705 (2006)]. It achieves this and distinguishes from other collision operators, such as in the standard single or multiple relaxation-time approaches, by performing relaxation process due to collisions in terms of moments shifted by the local hydrodynamic fluid velocity, i.e., central moments, in an ascending order by order at different relaxation rates. In this paper, we propose and derive source terms in the cascaded-LBM to represent the effect of external or internal forces on the dynamics of fluid motion. This is essentially achieved by matching the continuous form of the central moments of the source or forcing terms with its discrete version. Different forms of continuous central moments of sources, including one that is obtained from a local Maxwellian, are considered in this regard. As a result, the forcing terms obtained in this formulation are Galilean invariant by construction. To alleviate lattice artifacts due to forcing terms in the emergent macroscopic fluid equations, they are proposed as temporally semi-implicit and second order, and the implicitness is subsequently effectively removed by means of a transformation to facilitate computation. It is shown that the impressed force field influences the cascaded collision process in the evolution of the transformed distribution function. The method of central moments along with the associated orthogonal properties of the moment basis completely determines the analytical expressions for the source terms as a function of the force and macroscopic velocity fields. In contrast to the existing forcing schemes, it is found that they involve higher-order terms in velocity space. It is shown that the proposed approach implies ``generalization'' of both local equilibrium and source terms in the usual lattice frame of reference, which depend on the ratio of the relaxation times of moments of different orders. An analysis by means of the Chapman-Enskog multiscale expansion shows that the cascaded-LBM with forcing terms is consistent with the Navier-Stokes equations. Computational experiments with canonical problems involving different types of forces demonstrate its accuracy.

Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzmann method

Abstract: In this paper, we discuss the incorporation of dynamic subgrid scale (SGS) models in the lattice-Boltzmann method (LBM) for large-eddy simulation (LES) of turbulent flows. The use of a dynamic procedure, which involves sampling or test-filtering of super-grid turbulence dynamics and subsequent use of scale-invariance for two levels, circumvents the need for empiricism in determining the magnitude of the model coefficient of the SGS models. We employ the multiple relaxation times (MRT) formulation of LBM with a forcing term, which has improved physical fidelity and numerical stability achieved by proper separation of relaxation time scales of hydrodynamic and non-hydrodynamic modes, for simulation of the grid-filtered dynamics of large-eddies. The dynamic procedure is illustrated for use with the common Smagorinsky eddy-viscosity SGS model, and incorporated in the LBM kinetic approach through effective relaxation time scales. The strain rate tensor in the SGS model is locally computed by means of non-equilibrium moments of the MRT-LBM. We also discuss proper sampling techniques or test-filters that facilitate implementation of dynamic models in the LBM. For accommodating variable resolutions, we employ conservative, locally refined grids in this framework. As examples, we consider the canonical anisotropic and inhomogeneous turbulent flow problem, i.e. fully-developed turbulent channel flow at two different shear Reynolds numbers R e ∗ of 180 and 395. The approach is able to automatically and self-consistently compute the values of the Smagorinsky coefficient, C S . In particular, the computed value in the outer or bulk flow region, where turbulence is generally more isotropic, is about 0.155 (or the model coefficient C = C S 2 = 0.024 ) which is in good agreement with prior data. It is also shown that the model coefficient becomes smaller and approaches towards zero near walls, reflecting the dampening of turbulent length scales near walls. The computed turbulence statistics at these Reynolds numbers are also in good agreement with prior data. The paper also discusses a procedure for incorporation of more general scale-similarity based SGS stress models.

A method for three-dimensional interfacial particle image velocimetry (3D-IPIV) of an air–water interface

Abstract: A new stereoscopic method for collecting particle image velocimetry (PIV) measurements within ~1 mm of a wavy air–water interface with simultaneous measurements of the morphology of the interface is described. The method, termed three-dimensional interfacial particle image velocimetry (3D-IPIV), is tested in a wind wave channel with a wind speed of 5.8 m s−1, water depth of 10 cm and a fetch of ~9 m. Microscale breaking waves populate the interface and their flow patterns are clearly visible in the velocimetry results. The associated capillary waves and surface divergence patterns are observed. Several statistical measurements of the flow are compared with independent measurements and good agreement is found. The method shows great promise for investigating the transfer of momentum, heat and gases across an air–water interface, both in the laboratory and in field settings. Additional methods are described for manufacturing the flow tracers needed for the 3D-IPIV method. These tracers are likely to be useful for other researchers, and have the characteristics of being fluorescent, neutrally buoyant, non-toxic, monodisperse, inexpensive and easy to manufacture.

Computation of turbulent flow and secondary motions in a square duct using a forced generalized lattice Boltzmann equation.

Abstract: Turbulent flow in a straight square duct driven by a pressure gradient exhibits remarkable flow structures such as the presence of mean streamwise vorticity or secondary flows. These secondary circulations take the form of two counter-rotating vortices near each corner of the duct. Even though their magnitudes are small compared with primary streamwise motions, they have a significant influence on flow and scalar transport and are challenging to accurately predict using computational approaches. In this paper, we employ a recently developed formulation of the generalized lattice Boltzmann equation (GLBE) with forcing term to perform large eddy simulation of fully developed turbulent flow in a square duct at a shear Reynolds number based on duct width equal to 300. Subgrid scale effects are represented by the Smagorinsky eddy viscosity model, which is modified by the van Driest damping function in the near-wall regions, in this GLBE approach, which is based on multiple relaxation times. It was found that the GLBE is able to correctly reproduce the existence of mean secondary motions and the computed detailed structure of first- and second-order statistics of main and secondary motions are in good agreement with prior direct numerical simulations based on the solution of the Navier-Stokes equations and experimental data.