Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session L13: Multiphase Flow V: Numerical II 
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Chair: Heinz Pitsch, Stanford University Room: 316 
Monday, November 21, 2011 3:35PM  3:48PM 
L13.00001: A second order Lagrangian Eulerian momentum bounded method for multiphase flows Vincent Le Chenadec, Heinz Pitsch A Lagrangian Eulerian framework relying on both Level Set and Volume of Fluid methods is presented in the context of multiphase flow computations. The resulting interface capturing scheme is shown to preserve planarity, and to conserve mass exactly for solenoidal and linear velocity fields. A novel fractional step approach for the incompressible Navier Stokes equation is also presented. The proposed scheme relies on a consistent transport of volume fraction and momentum fields, which also preserves velocity boundedness. A sharp interface projection step is derived accordingly. The algorithm is shown to conserve momentum exactly for solenoidal linear velocity, and to lead to robust computations. [Preview Abstract] 
Monday, November 21, 2011 3:48PM  4:01PM 
L13.00002: A GPUaccelerated flow solver for incompressible twophase fluid flows Stephen Codyer, Mehdi Raessi, Gaurav Khanna We present a numerical solver for incompressible, immiscible, twophase fluid flows that is accelerated by using Graphics Processing Units (GPUs). The NavierStokes equations are solved by the projection method, which involves solving a pressure Poisson problem at each time step. A secondorder discretization of the Poisson problem leads to a sparse matrix with five and seven diagonals for two and threedimensional simulations, respectively. Running a serial linear algebra solver on a single CPU can take 5099.9\% of the total simulation time to solve the above system for pressure. To remove this bottleneck, we utilized the large parallelization capabilities of GPUs; we developed a linear algebra solver based on the conjugate gradient iterative method (CGIM) by using CUDA 4.0 libraries and compared its performance with CUSP, an opensource, GPU library for linear algebra. Compared to running the CGIM solver on a single CPU core, for a 2D case, our GPU solver yields speedups of up to 88x in solver time and 81x overall time on a single GPU card. In 3D cases, the speedups are up to 81x (solver) and 15x (overall). Speedup is faster at higher grid resolutions and our GPU solver outperforms CUSP. Current work examines the acceleration versus a parallel CGIM CPU solver. [Preview Abstract] 
Monday, November 21, 2011 4:01PM  4:14PM 
L13.00003: The Lagrangian filtered mass density function (LFMDF) or LES/PDF method for turbulent twophase flows Sergio Chibbaro, JeanPierre Minier In this talk, a new formalism for the filtered density function (FDF) approach is developed for the treatment of turbulent polydispersed twophase flows in LES simulations. Contrary to the FDF used for turbulent reactive singlephase flows, the present formalism is based on Lagrangian quantities and, in particular, on the Lagrangian filtered mass density function (LFMDF) as the central concept. This framework allows modeling and simulation of particle flows for LES to be set in a rigorous context and various links with other approaches to be made. In particular, the relation between LES for particle simulations of singlephase flows and Smoothed Particle Hydrodynamics (SPH) is put forward. Then, the discussion and derivation of possible subgrid stochastic models used for Lagrangian models in twophase flows can set in a clear probabilistic equivalence with the corresponding LFMDF. Finally, a first stochastic model will be proposed in this framework and numerical simulations will show the comparison of LES simulations against DNS. [Preview Abstract] 
Monday, November 21, 2011 4:14PM  4:27PM 
L13.00004: An extended quadrature method of moments for polydisperse multiphase flows Cansheng Yuan, Rodney Fox Polydisperse multiphase flows arise in many applications, and thus there has been considerable interest in the development of numerical methods to find solutions to the kinetic equation used to model such flows. Quadraturebased moment methods (QBMM) are an important class of methods for which the accuracy of solution can be improved in a controlled manner by increasing the number of nodes. However, when large numbers of nodes are required to achieve the desired accuracy, the momentinversion problem can become illconditioned. In this work, a new generation of quadrature algorithms is introduced that uses an explicit form for the distribution function. This extended quadrature method of moments (EQMOM) approximates the distribution function by a sum of classical weight functions, which allow unclosed source terms to be computed with great accuracy by increasing the number of quadrature nodes independent of the number of transported moments. Here we use EQMOM to solve a kinetic equation with evaporation, aggregation and breakage terms and compare the results with analytical solutions. [Preview Abstract] 
Monday, November 21, 2011 4:27PM  4:40PM 
L13.00005: Realizable HighOrder FiniteVolume Schemes for Diffusion in QuadratureBased Moment Methods Rodney O. Fox, Varun Vikas, Z.J. Wang Population balance equations (PBEs) can be reformulated in terms of the moments of the distribution function and a quadraturebased moment method (QBMM) can be used to solve them. The success of the QBMM is based on a momentinversion algorithm that does not work if the moments are nonrealizable. For convection terms, the authors have shown that when using a finitevolume approach, a momentbased cellwise reconstruction may lead to nonrealizable schemes and hence a reconstruction based on weights and abscissas should be used instead. However, researchers working with diffusive PBEs have not reported realizability problems when using cellwise momentbased reconstruction. This work shows that when momentbased reconstruction with a $2^{nd}$order finitevolume scheme is used, realizability is automatically guaranteed by the satisfaction of CourantFriedrichsLewy (CFL) condition. However, for any highorder finitevolume schemes, a momentbased reconstruction may fail to guarantee realizability. We present highorder realizable schemes based on reconstruction of weights and abscissas. These new schemes give a better performance for a certain class of diffusive PBE problems. Realizability conditions are also presented for a general unstructured mesh. [Preview Abstract] 
Monday, November 21, 2011 4:40PM  4:53PM 
L13.00006: DNS of dropletladen incompressible turbulence: surface tension in a VoF method Alberto Baraldi, Antonino Ferrante We investigated the continuous surface force (CSF) model to include the surface tension within a splitadvection and massconserving volume of fluid (VoF) method for DNS of dropletladen incompressible turbulence. The liquidgas interface curvature is computed accurately using a variablestencil heightfunction technique. Different implementations of the surface tension and pressure gradient terms within a projection method were tested, and their stability evaluated in terms of the magnitude of spurious currents for a droplet at rest in both two and three dimensions. The inherent asymmetry of the splitadvection algorithm is reflected in the results of this test case. Our results show that a machineaccurate balance between pressure and surface tension forces can be achieved by enforcing symmetry of the VoF function. We have modified the sequence of the advection sweeps, and our results show that, in the case of nonzero Weber number, e.g.~when a mean droplet velocity is present, the algorithm is accurate and stable. We present DNS results of fullyresolved dropletladen incompressible isotropic turbulence. [Preview Abstract] 
Monday, November 21, 2011 4:53PM  5:06PM 
L13.00007: A Multiscale Approach to Compute Mass Transfer in Bubbly Flows Bahman Aboulhasanzadeh, Gretar Tryggvason Mass transfer in the liquid phase of gasliquid multiphase flows usually takes place at a considerably slower rate than the transfer of momentum, so mass flux boundary layers are much thinner than momentum boundary layers. In Direct Numerical Simulations (DNS) the resolution requirement for flows where the Schmidt number (kinematic viscosity divided by mass diffusivity) is high are therefore significantly higher than for flow without mass transfer. While it is, in principle, possible to capture the mass transfer using adaptive grid refinement, the structure of the boundary layer is relatively simple and well understood. Here we develop a multi scale approach to compute the mass transfer from buoyant bubbles, using a boundarylayer approximation next to the bubble and a relatively coarse grid for the rest of the flow. We show that the approach works well by comparing the results both with fully resolved simulations for modest Schmidt number and with empirical correlations for high Schmidt numbers. [Preview Abstract] 

L13.00008: ABSTRACT WITHDRAWN 

L13.00009: ABSTRACT WITHDRAWN 
Monday, November 21, 2011 5:32PM  5:45PM 
L13.00010: An improved connectivityfree point set method to simulate multiphase flow Chu Wang, Lucy Zhang An improved connectivityfree point set method is presented to simulate the multiphase flow. Similar to the front tracking method, the pointset method tracks the interface explicitly. However, it does not require any logical connectivity among interface markers, which provides the flexibility in modeling large morphological changes such as bubble merging and breaking up. The topology changes are handled automatically by proper interface reconstruction scheme and also conveniently ease the small interface undulation due to advection. A meshfree RKPM interpolation method is employed to improved the algorithm which can handle nonuniform meshes and provide boundary corrections for free surface flows in situations when interface markers end at walls. Great accuracy is achieved for both the unit normal and curvature calculation. The incompressible twophase flow is simulated using stabilized finite element method. Several test cases are performed to validate the improved method and show its capability in simulating multiphase type of flows successfully. [Preview Abstract] 
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