Papers by Martin J. Pattison
A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering
A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering
Proceeding of Fifth International Symposium on Turbulence and Shear Flow Phenomena
ABSTRACT The lattice Boltzmann method (LBM) is a relatively recent approach for solving fluid mec... more ABSTRACT The lattice Boltzmann method (LBM) is a relatively recent approach for solving fluid mechanics problems (Chen and Doolen, 1998; Succi, 2001). It is based on the solution of a kinetic equation, the lattice Boltzmann equation (LBE), which describes the evolution of distributions of particles on a lattice whose collective behav-ior reproduces fluid flow. The lattice, possessing sufficient symmetry, restricts the collisions and movements of particle populations along discrete directions in such a way that in the continuum, fluid flow represented by weakly compressible Navier-Stokes equations is reproduced. The attractiveness of the LBM comes from the simplicity of the numerical procedure, avoiding the use of time consuming Poisson-type equation for pres-sure field, and ease in handling boundary conditions for representation of complex geometries. Moreover, LBM involves algorithms that are local and explicit, resulting in excellent performance on a variety of parallel computers with near-linear scaling and thus suitable for large problems. However, the standard LBM employs a single relaxation time (SRT) to represent the effect of particle collisions, in which particle distributions relax to their local equilibrium at a rate determined by just one param-eter. This approach has limitations in representing some essential aspects of the phenomena involved properly, and can lead to numerical instability, particularly at higher Reynolds numbers. A recent approach that over-comes such limitations is the multiple-relaxation times (MRT) models (d'Humires et al., 2002; Premnath and Abraham, 2006). In this MRT-LBM, the relaxation rates of different hydrodynamic and kinetic modes during collision processes can be adjusted independently. Not only does it reproduce the physics better, but the stabil-ity is substantially improved as compared with the SRT-LBE. For larger eddy simulations (LES) of turbulent flows, subgrid scale (SGS) models can naturally be incorporated in MRT-LBM through appropriate relaxation times that determine hydrodynamics. This MRT-LBM approach has not, however, been assessed yet for wall-bounded turbulent flow applications. A canonical problem in this regard is the turbulence-induced secondary flows in a square duct. Turbulent fluid flow through a square duct is characterized by the existence of net flows in directions perpendicular to the bulk flow. These circulations, frequently termed secondary flows of the second kind, also arise in turbulent flow through channels of other non-circular cross-sections, but are not found in laminar flows. Although long recognized to be associated with turbulence, the exact cause of these circulations has been a subject of debate, though it is generally recognized to be associated with the inhomogeneity and anisotropy in the Reynolds stress in the cross-sectional plane. In a square duct, on an average, these secondary flows manifest themselves as a set of eight vortices, each one enclosed by a wall, a corner bisector and a wall bisector. The general features are not sensitive to the Reynolds number, except that it should be high enough that the flow be fully turbulent. The velocities associated with these flows is relatively small, of the order of 1% of the mean streamwise velocity, and thus significantly smaller than the turbulent velocity fluctuations. The mechanisms responsible for the secondary flows result from a fine balance involving the gradients in the Reynolds stress and pressure strain terms, making the square duct a particularly challenging problem for turbulence models. For example, computations based on commonly used Reynolds-averaged models, such as the k– model, do not perform well, while more complex anisotropic Reynolds stress models have been successful to a degree though not without a priori information on the stress terms. In this regard, eddy capturing schemes based on subgrid scale (SGS) models appears to be more promising.
Proceeding of First Symposium on Turbulence and Shear Flow Phenomena
The purpose of this study was to explore the central core region of a plane turbulent Cou- ette f... more The purpose of this study was to explore the central core region of a plane turbulent Cou- ette flow by means of large-eddy simulations. First it was demonstrated how accurately a low Reynolds number flow could be simulated. After having verified the reliability of the LES approach. simulations were performed at a substantially higher Re. It was observed that the mean velocity exhibited a practically linear variation in the core region. The extent of the core increased with Re, whereas the slope of the mean velocity profile was significantly reduced.
Several applications exist in which lattice Boltzmann methods (LBM) are used to compute stationar... more Several applications exist in which lattice Boltzmann methods (LBM) are used to compute stationary states of fluid motions, particularly those driven or modulated by external forces. Standard LBM, being explicit time-marching in nature, requires a long time to attain steady state convergence, particularly at low Mach numbers due to the disparity in characteristic speeds of propagation of different quantities. In this paper, we present a preconditioned generalized lattice Boltzmann equation (GLBE) with forcing term to accelerate steady state convergence to flows driven by external forces. The use of multiple relaxation times in the GLBE allows enhancement of the numerical stability. Particular focus is given in preconditioning external forces, which can be spatially and temporally dependent. In particular, correct forms of moment-projections of source/forcing terms are derived such that they recover preconditioned Navier-Stokes equations with non-uniform external forces. As an illust...
Fusion Science and Technology, 2007
Abstract Fusion reactors designs frequently involve the use of liquid metal flows in the presence... more Abstract Fusion reactors designs frequently involve the use of liquid metal flows in the presence of strong magnetic fields. Simulation of the flows involves the solution of continuum equations for fluid flow and magnetic induction, usually done with finite difference methods. In this paper, an alternative method, based on the generalized lattice Boltzmann equation (GLBE), and implemented in the MetaFlow code is discussed. It has a number of desirable features, including fast execution, excellent parallel scalability, and can easily handle complex geometries. The use of the recent GLBE variant greatly enhances stability and accuracy. To simulate magnetohydrodynamic (MHD) flows relevant to fusion applications using GLBE, several new models have been developed, including new boundary condition formulations, preconditioners for faster steady-state convergence, variable electrical conductivity materials, and to resolve thin Hartmann layers. These models are discussed, and validations against MHD benchmarks, including 3-D driven cavity, high Hartmann number and turbulent cases are presented.
Fusion Science and Technology, 2011
In a Dual-Coolant Lead-Lithium (DCLL) blanket, tritium losses from the PbLi into cooling helium s... more In a Dual-Coolant Lead-Lithium (DCLL) blanket, tritium losses from the PbLi into cooling helium streams may occur when the liquid-metal breeder is moving in the poloidal ducts. Quantitative analysis of the mass transfer processes associated with the tritium transport in the breeder as well as tritium diffusion through the structural and functional materials is important for two main reasons. The first is that there can be a substantial cost in extracting tritium from helium. The second is that tritium can make its way from the helium stream into the environment. In the present study, we analyze tritium transport in the front section of the DCLL DEMO-type Outboard blanket, where PbLi moves poloidally in a rectangular duct with an insulating flow channel insert (FCI) in the presence of a strong plasma-confining magnetic field. This involves two steps, the computation of the flow field with an MHD code, followed by the solution of the mass transfer equation with a newly-developed transport code CATRYS. The analyses included a sensitivity study to investigate how uncertainties in the properties of the materials (diffusion coefficient, solubility constant) affect the results and to assess the effect of an impervious crystalline sealing layer on the FCI.
A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering
Physica A: Statistical Mechanics and its Applications, 2009
In this paper, we discuss the incorporation of dynamic subgrid scale (SGS) models in the lattice-... more 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 Re * 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 2 S = 0.024) which is in good agreement with prior data. It is also shown that the model coefficient becomes smaller and Preprint submitted to Elsevier 31 October 2018 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.
Physical Review E, 2009
Turbulent flow in a straight square duct driven by a pressure gradient exhibits remarkable flow s... more 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 ͑GLBE͒ 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.
Designs of proposed fusion reactors, such as the ITER project, typically involve the use of liqui... more Designs of proposed fusion reactors, such as the ITER project, typically involve the use of liquid metals as coolants in components such as heat exchangers, which are generally subjected to strong magnetic fields. These fields induce electric currents in the fluids, resulting in magnetohydrodynamic (MHD) forces which have important effects on the flow. The objective of this SBIR project was to develop computational techniques based on recently developed lattice Boltzmann techniques for the simulation of these MHD flows and implement them in a computational fluid dynamics (CFD) code for the study of fluid flow systems encountered in fusion engineering. The code developed during this project, solves the lattice Boltzmann equation, which is a kinetic equation whose behaviour represents fluid motion. This is in contrast to most CFD codes which are based on finite difference/finite volume based solvers. The lattice Boltzmann method (LBM) is a relatively new approach which has a number of advantages compared with more conventional methods such as the SIMPLE or projection method algorithms that involve direct solution of the Navier-Stokes equations. These are that the LBM is very well suited to parallel processing, with almost linear scaling even for very large numbers of processors. Unlike other methods, the LBM does not require solution of a Poisson pressure equation leading to a relatively fast execution time. A particularly attractive property of the LBM is that it can handle flows in complex geometries very easily. It can use simple rectangular grids throughout the computational domain-generation of a body-fitted grid is not required. A recent advance in the LBM is the introduction of the multiple relaxation time (MRT) model; the implementation of this model greatly enhanced the numerical stability when used in lieu of the single relaxation time model, with only a small increase in computer time. Parallel processing was implemented using MPI and demonstrated the ability of the LBM to scale almost linearly. The equation for magnetic induction was also solved using a lattice Boltzmann method. This approach has the advantage that it fits in well to the framework used for the hydrodynamic equations, but more importantly that it preserves the ability of the code to run efficiently on parallel architectures. Since the LBM is a relatively recent model, a number of new developments were needed to solve the magnetic induction equation for practical problems. Existing methods were only suitable for cases where the fluid viscosity and the magnetic resistivity are of the same order, and a preconditioning method was used to allow the simulation of liquid metals, where these properties differ by several orders of magnitude. An extension of this method to the hydrodynamic equations allowed faster convergence to steady state. A new method of imposing boundary conditions using an extrapolation technique was derived, enabling the magnetic field at a boundary to be specified. Also, a technique by which the grid can be stretched was formulated to resolve thin layers at high imposed magnetic fields, allowing flows with Hartmann numbers of several thousand to be quickly and efficiently simulated. In addition, a module has been developed to calculate the temperature field and heat transfer. This uses a total variation diminishing scheme to solve the equations and is again very amenable to parallelisation. Although, the module was developed with thermal modelling in mind, it can also be applied to passive scalar transport. The code is fully three dimensional and has been applied to a wide variety of cases, including both laminar and turbulent flows. Validations against a series of canonical problems involving both MHD effects and turbulence have clearly demonstrated the ability of the LBM to properly model these types of flow. As well as applications to fusion engineering, the resulting code is flexible enough to be applied to a wide range of other flows, in particular those requiring parallel computations with many processors. For example, at present it is being used for studies in aerodynamics and acoustics involving flows at high Reynolds numbers. It is anticipated that it will be used for multiphase flow applications in the near future.
Process Safety and Environmental Protection, 1998
T his paper presents a methodology for the prediction of the dispersion of a two-phase release fr... more T his paper presents a methodology for the prediction of the dispersion of a two-phase release from a chemical or process plant. A set of one-dimensional conservation equations for modelling such a release is derived, by taking an approach analogous to the boundary-layer integral method, in which the instantaneous conservation equations are averaged over a volume slice transverse to the direction of predominant plume/cloud motion. Averaging, which makes the problem computationally tractable, removes information regarding local gradients that govern transport of momentum, heat and massÐ this information must then be supplied in the form of`closure relationships'. An appropriate set of closure relationships is then discussed, covering models for interfacial heat and mass transfer, entrainment of air, and interactions with the wind ® eld. Particular features of the approach are that it is¯exible enough to deal with condensation of water vapour, thermal non-equilibrium between the phases, sloping terrain, and can handle both elevated and ground-bounded releases. Suitable formulations for the initial and source boundary conditions, for both instantaneous and continuous releases, are also presented.
Physical Review E, 2009
In this paper, we present a framework based on the generalized lattice-Boltzmann equation (GLBE) ... more 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 non-uniform 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 non-equilibrium 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.
Journal of Hazardous Materials, 1996
The CLOUD (concentration levels of unconfined dispersion) code has been developed, the nucleus of... more The CLOUD (concentration levels of unconfined dispersion) code has been developed, the nucleus of which is an innovative two-phase fluid dispersion model characterized by conservation equations for mass, momentum, energy and species, averaged over a volume slice transverse to the direction of plume motion. The initial and boundary conditions for the above equations are determined either by using auxiliary models or by direct input of the space distribution, and respectively of the time evolution, of the relevant variables. The initial conditions model for an instantaneous, puff release has been based on an experimental programme carried out at the Swiss Federal Institute of Technology. The boundary conditions for semi-continuous, jet releases have been based on literature models for critical two-phase flow at the rupture. The code has been validated with data from three large scale release test series: the Desert Tortoise series (ammonia), the Goldfish series (HF), and the Thorney Island series (heavy gas).
Journal of Geophysical Research: Oceans, 2001
The recent paper by Pattison and Belcher [1999] contains some mathematical errors that led to the... more The recent paper by Pattison and Belcher [1999] contains some mathematical errors that led to their misinterpreting how well their spray generation function agrees with one reported by Andreas [1992]. We here correct that mathematical error and show that now, Pattison and ...
Journal of Geophysical Research: Oceans, 1999
The question of whether sea-spray droplets make a significant contribution to the transfer of hea... more The question of whether sea-spray droplets make a significant contribution to the transfer of heat and water vapor between the air and sea has been addressed by many researchers over the last few decades. Quantification of the effect is difficult owing to a number of factors; in particular, the available data on droplet concentrations over the sea are limited and the airflow over rough seas is not well known. In the work described in this paper, a model for simulating droplet trajectories over the sea was developed, taking into account the droplet evaporation and the effects of turbulence on the motion. This model was used to simulate the behavior of droplets under conditions for which field data on droplet concentrations were available, and the rates at which droplets are generated were calculated. Estimates of the spray contribution to the heat and mass transfer made using these results suggest that droplets are likely to make only a small contribution to the overall fluxes, except under storm conditions, when they could be a major source of water vapor. 1. Introduction The ability of coupled ocean-atmosphere models to accurately predict long-term climate change depends on, among other things, the formulations for heat and mass transfer at the air-sea interface. Recent work using global climate models has shown that predictions are sensitive to perturbations in the surface heat flux, and it is therefore important to quantify this process as accurately as possible. Another application of models for interfacial transfer is in the investigation of storm development over the ocean, where fluxes of heat, momentum, and moisture fuel cyclogenesis [Fairall et al., 1993]. One contribution to the transfer of heat and mass between the sea and the atmosphere arises from the evaporation of sea spray. This effect is considered to be most pronounced at higher wind speeds, where breaking waves produce large numbers of water droplets, increasing the interfacial area available for heat and mass exchange. Much attention has been focused on this problem in recent years and has included investigations of droplet production mechanisms, measurements of spray concentrations, and simulations of droplet transportation. However, despite the considerable amount of research in this area, the importance of the role played
Journal of Fluids Engineering, 2013
Lattice Boltzmann method (LBM) is a relatively recent computational technique for fluid dynamics ... more Lattice Boltzmann method (LBM) is a relatively recent computational technique for fluid dynamics that derives its basis from a mesoscopic physics involving particle motion. While the approach has been studied for different types of fluid flow problems, its application to eddy-capturing simulations of building block complex turbulent flows of engineering interest has not yet received sufficient attention. In particular, there is a need to investigate its ability to compute turbulent flow involving separation and reattachment. Thus, in this work, large eddy simulation (LES) of turbulent flow over a backward facing step, a canonical benchmark problem which is characterized by complex flow features, is performed using the LBM. Multiple relaxation time formulation of the LBM is considered to maintain enhanced numerical stability in a locally refined, conservative multiblock gridding strategy, which allows efficient implementation. Dynamic procedure is used to adapt the proportionality co...
Journal of Computational Physics, 2009
Fusion Engineering and Design, 2008
In this paper, an approach to simulating magnetohydrodynamic (MHD) flows based on the lattice Bol... more In this paper, an approach to simulating magnetohydrodynamic (MHD) flows based on the lattice Boltzmann method (LBM) is presented. The dynamics of the flow are simulated using a so-called multiple relaxation time (MRT) lattice Boltzmann equation (LBE), in which a source term is included for the Lorentz force. The evolution of the magnetic induction is represented by introducing a vector distribution function and then solving an appropriate lattice kinetic equation for this function. The solution of both distribution functions are obtained through a simple, explicit, and computationally efficient stream-and-collide procedure. The use of the MRT collision term enhances the numerical stability over that of a single relaxation time approach. To apply the methodology to solving practical problems, a new extrapolation-based method for imposing magnetic boundary conditions is introduced and a technique for simulating steady-state flows with low magnetic Prandtl number is developed. In order to resolve thin layers near the walls arising in the presence of high magnetic fields, a non-uniform gridding strategy is introduced through an interpolated-streaming step applied to both distribution functions. These advances are particularly important for applications in fusion engineering where liquid metal flows with low magnetic Prandtl numbers and high Hartmann numbers are introduced. A number of MHD benchmark problems, under various physical and geometrical conditions are presented, including 3-D MHD lid driven cavity flow, high Hartmann number flows and turbulent MHD flows, with good agreement with prior data. Due to the local nature of the method, the LBM also demonstrated excellent performance on parallel machines, with almost linear scaling up to 128 processors for a MHD flow problem.
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Papers by Martin J. Pattison