Session QA: CFD: Multiphase and Mixing Applications

A lattice Boltzmann code for direct numerical simulation of skin-friction drag reduction by superhydrophobic surfaces in turbulent channel flow

A lattice Boltzmann code for direct numerical simulation of flow over superhydrophobic surfaces has been developed. The code solves the Boltzmann equation for two different sets of particle distribution functions based on the Shan and Chen model [1], to account for the gas-liquid interactions. The immiscibility and inter-phase interactions are controlled through an interaction body force between the distribution functions. The recently proposed model of Hunag et al. [2] is used to set the contact angle in the simulations, in which by tuning the values of the interaction force, one can control the contact angle at the interfaces, simulating hydrophobicity or superhydrophobicity on the solid walls. Test results in channel flow will be presented and discussed.\\[4pt] [1] X.Shan and H.Chen, Phys. Rev. E, {\bf 47(3):1815} (1993)\\[0pt] [2] H.Huang, D.T.Throne, M.G.Schaap, and M.C.Sukop, Phys. Rev. E, {\bf 76:066701} (2007)   

Evaluation of CFD predictions of mixing properties of hydrogen as a fuel in a model premixer by experimental and statistical tools

Mixing properties of hydrogen, as a new fuel of interest in combustion community research, have been numerically studied utilizing various CFD approaches in both axial and radial fuel injection type premixer configurations to be applied in lean combustion techniques research for design purposes. Numerical predictions of RANS and LES turbulent models have been evaluated by conducting experimental measurements. Comprehensive qualitative and quantitative comparisons have been made between numerical and experimental results to investigate capabilities of different CFD approaches to provide reliable predictions of flow field properties. Moreover, extensive statistical study has been accomplished, and ANOVA results are interpreted beside other comparison approaches to draw fruitful conclusions. In general, sensitivity of numerical predictions to different turbulent models as well as sensitivity to different turbulent Schmidt numbers has been explored. The result of comparison suggests more sensitivity to turbulent models for radial injection configurations. However, more sensitivity to Sc$_{t}$ has been witnessed for the axial configuration. In general, RSM turbulent model with Sc$_{t}$=0.7 provides the most promising predictions for various combinations of different fuels and injection types.   

A Quadrature Free Discontinuous Galerkin Conservative Level Set Scheme

In an effort to improve the scalability and accuracy of the Accurate Conservative Level Set (ACLS) scheme [Desjardins et al., J COMPUT PHYS 227 (2008)], a scheme based on the quadrature free discontinuous Galerkin (DG) methodology has been developed. ACLS relies on a hyperbolic tangent level set function that is transported and reinitialized using conservative schemes in order to alleviate mass conservation issues known to plague level set methods. DG allows for an arbitrarily high order representation of the interface by using a basis of high order polynomials while only using data from the faces of neighboring cells. The small stencil allows DG to have excellent parallel scalability. The diffusion term present in the conservative reinitialization equation is handled using local DG method [Cockburn et al., SIAM J NUMER ANAL 39, (2001)] while the normals are computed from a limited form of the level set function in order to avoid spurious oscillations. The resulting scheme is shown to be both robust, accurate, and highly scalable, making it a method of choice for large-scale simulations of multiphase flows with complex interfacial topology.   

A Diffuse Interface Method with Adaptive Mesh Refinement for Simulation of Incompressible Multi-Phase Flows with Moving Contact Lines

Diffuse Interface (DI) methods are employed widely for the numerical simulation of two-phase flows, even with moving contact lines. In a DI method, the interface thickness should be as thin as possible to simulate spreading phenomena under realistic flow conditions, so a fine grid is required, beyond the reach of current methods that employ a uniform grid. Here we have integrated a DI method based on a uniform mesh, to a block-based adaptive mesh refinement method, so that only the regions near the interface are resolved by a fine mesh. The performance of the present method is tested by simulations including drop deformation in shear flow, Rayleigh-Taylor instability and drop spreading on a flat surface, et al. The results show that the present method can give accurate results with much smaller computational cost, compared to the original DI method based on a uniform mesh. Based on the present method, simulation of drop spreading is carried out with Cahn number of 0.001 and the contact line region is well resolved. The flow field near the contact line, the contact line speed as well as the apparent contact angle are investigated in detail and compared with previous analytical work.   

Droplet deformation in shear flow: a comparison between multicomponent Lattice-Boltzmann method (LBM) and Phase Field method (PFM)

Prediction of droplet breakup, droplet coalescence and phase separation are crucial in many industrial and environmental processes. We present a direct comparison between two numerical approaches on the problem of deformation and breakup of a droplet under shear flow conditions. In order to quantitatively benchmark the Lattice Boltzmann and the Phase Field methods we consider the same flow conditions. Through the comparison of the two approaches we can assess respective advantages and disadvantages. For different values of the dimensionless problem parameters we investigate quantitatively both physical properties as well as numerical issues related to the two different methodology.   

Fluctuating Lattice Boltzmann

Fluctuations are important for many hydrodynamic phenomena such as colloid diffusion or phase-separation near the critical point. However, the standard LB-schemes do not take fluctuations into account. Based on Ladd's [1] and later Adhikari's [2] work we explain how one can practically implement noise in Lattice Boltzmann algorithms for different dimensionality and base velocity sets. We also present a new velocity moment method for deriving the hydrodynamic equations from the underlying Multi Relaxation Time models [3,4]. This sets the foundation for formulating more general fluctuating lattice Boltzmann methods for energy conserving thermal systems and multi-component systems.\\[4pt] [1] A.J.C.~Ladd, Phys. Rev. Lett {\bf70}, 1339 (1993)\\[0pt] [2] R.~Adhikari, K.~Stratford, M.E.~Cates and A.J.~Wagner, Europhys. Lett. {\bf71}, 473 (2005)\\[0pt] [3] D.~d'Humieres, in {\it Rarefied Gas Dynamics: Theory and Simulations, Prog. Astronaut. Aeronaut} {\bf159} 450 (1992)\\[0pt] [4] R.~Benzi, S.~Succi, and M.~Vergassola, Physics Reports {\bf222}, 145 (1992)   

Lattice Boltzmann modeling for energy conversion systems

The study of advanced small energy conversion systems, such as fuel cells (SOFCs, PEFCs) and microcombustors, requires the use of lattice Boltzmann models that can handle heat transfer and mixing effects. Heat transfer effects can be efficiently studied on the standard lattices (D2Q9, D3Q27) with the thermal model introduced in Ref. [1]. This model can simulate the compressible Navier-Stokes and Fourier equations for large temperature and density variations [2,3]. For multi-component isothermal flows, the model of Ref.[4] is used to simulate the flow through a porous anode of a SOFC. Simulation results show that by decreasing the characteristic length scale of the simulated geometry, micro flow effects that alter the flow field start to emerge. A model that combines the properties and the novelties of both aforementioned thermal and multi-component models will be outlined. References [1] N.I. Prasianakis, I.V. Karlin, Phys. Rev. E 76, 016702 (2006) [2] N.I. Prasianakis, PhD Thesis No 17739, ETH Zurich (2008) [3] N.I. Prasianakis, I.V. Karlin, J. Mantzaras, K. Boulouchos, Phys. Rev. E 79, 066702 (2009) [4] S. Arcidiacono, I.V. Karlin, J. Mantzaras, C.E. Frouzakis, Phys. Rev. E 76, 046703 (2007)   

Performance Limitation by Reactant Crossover in a Membraneless Fuel Cell

In the past decade, the paradigm of using micro fuel cells for portable power applications has inspired novel innovations in fuel cell technology. One such example is the laminar flow fuel cell (LFFC) which utilizes colaminar flow to maintain the separation between the anode and cathode instead of a membrane. Although the membraneless LFFC provides a simple design for prototype development, the lack of a physical separation can permit oxidant as well as fuel to crossover and impact device performance adversely. To understand the effect of reactant crossover and its effect on the performance of LFFC a mathematical model is developed. The model includes a more general treatment of reactant crossover than the common method where it is assumed that the crossover flux is fully utilized as crossover current. This model is used to study the performance of a LFFC operating with different electrode lengths and separations. Numerical results show that the reactant crossover, transport limitations, and Ohmic losses are the primary performance limitation factors. The fuel cells with shorter channel heights suffer from transport limitations at the longer electrode lengths even when reactant crossover is neglected.   

A study on improving numerical stability by applying filter operation to concentration flux for reverse simulation

A reverse simulation based on CFD is considered to be a resolution for identifying pollutant source, which is the solution of a transport equation in negative time advancing. The process is equivalent to positive time advancing with negative diffusion and convection. However, there is a numerical instability problem when solving the negative diffusion. Therefore, in this study, we propose a method to improve numerical stability by applying a low-pass filter to concentration flux in RANS analysis. The following equations are summary of the low-pass filter. By setting an appropriate filter width ($\Delta )$, the reverse simulation can be realized. F(x) is the concentration flux in RANS analysis. $\bar {F}(x)=\int_{-\infty }^\infty {G(r)F(x-r)dr ,G(r)} =\sqrt {\frac{6}{\pi \Delta ^2}} \exp \left( {-\frac{6r^2}{\Delta ^2}} \right) ,F(x)=\Gamma \frac{\partial C}{\partial x}$ The aim of filter operation to concentration flux is to stabilize concentration balance in control volume. As the result, the following conclusion can be drawn. 1. Filter operation is a useful method for improving numerical stability. 2. The concentration center moves and the standard division of concentration shrink adequately in reverse simulation, which makes it easy to identify pollutant source. In the next stage, we will develop a method to identify the pollutant source stochastically.   

Coarse Grid CFD for underresolved simulation

CFD simulation of the complete reactor core of a nuclear power plant requires exceedingly huge computational resources so that this crude power approach has not been pursued yet. The traditional approach is 1D subchannel analysis employing calibrated transport models. {\it Coarse grid CFD} is an attractive alternative technique based on strongly under-resolved CFD and the inviscid Euler equations. Obviously, using inviscid equations and coarse grids does not resolve all the physics requiring additional volumetric source terms modelling viscosity and other sub-grid effects. The source terms are implemented via correlations derived from fully resolved representative simulations which can be tabulated or computed on the fly. The technique is demonstrated for a Carnot diffusor and a wire-wrap fuel assembly [1]. \\[4pt] [1] Himmel, S.R. phd thesis, Stuttgart University, Germany 2009, http://bibliothek.fzk.de/zb/berichte/FZKA7468.pdf