Two-Phase Simulation

Before discussing the details of the numerical experiments performed in this study, the primary mechanisms governing the two-phase transport in the PEFC catalyst layer and gas diffusion layer are discussed, which essentially build the foundations behind the specific assumptions and justifications pertaining to the subsequent two-phase simulations. 

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The computational approach couples the two-phase LB model for the liquid water transport and the DNS model for the species and charge transport for the CL.25-27,68 The two-phase simulation using the LB model is designed based on the ex-situ, steady-state flow experiment for porous media, detailed earlier in the section 4.3, in order to obtain the liquid water distributions within the CL microstructure for different saturation levels resulting from the dynamic interactions between the two phases and the underlying pore morphology. The details of the simulation setup are provided in our work.27,61 62 Once steady state is achieved, 3-D liquid water distributions can be obtained within the CL, as shown in Fig. 13. From the liquid water distributions within the CL structure, the information about the catalytic site coverage effect can be extracted directly. 

Basara et al [3] simulated single- and two-phase turbulent flows in stirred vessels equipped with six- and four blade Rushton-t3q)e turbines using the sliding mesh impeller method. To describe turbulence in the liquid phase a standard k-e model was used for single phase calculations and an extended k-e model was employed for the two-phase simulations. These simulations were performed in transient mode with 1 (ms) time steps. The whole calculation contains 3900 time steps, which means approximately 4s of real time and 17 complete rotations of the impeller. One such simulation took 13 days of CPU time using an Intel single processor with 2.6 GHz). The flow patter predictions were compared with experimental data and fair agreement was obtained. It was stated that the standard k-e model over-predicted the... 

Batirev IG, Alavi A, Firmis MW, Deutsch T (1999) First principles calculations of the ideal cleavage energy of bulk niobimn(lll)/alpha-alumina(0001) interfaces. Phys Rev Let 82 1510-1513 Belonoshko AB (2001) Molecular dynamics simulation of phase transitions and melting in MgSi03 with the perovskite structine-cormnent. Am Mineral 86 193-194 Belonoshko AB, Dubrovinsky LS (1996) Molecular dynamics of NaCl(Bl and B20 and MgO(Bl) melting two-phase simulation. Am Mineral 81 303-316... 

The pores in the simulated microstructure gradually disperse and become smaller, and the mass center migrates towards the pores because of pore diffusion along the grain boundary and pore annihilation in both single-phase and two-phase simulation results. And most pores exist at the triple jimction point of grain boundary. 

DESCRIPTION OF TWO-DIMENSIONAL, TWO-PHASE SIMULATOR WITH POINT MOVING AND CHANGING OF VISCOSITY... 

With these various input modifications, the correct dependence of mass flow on system mass inventory was obtained the pressure and temperatures were then calculated to be in good agreement with test data. However, even in this case, the two-phase flow was overpredicted by 30%, possibly because of incorrect two-phase interface and/or wall friction code models. As in the single-phase liquid natural circulation calculations, the two-phase simulations experienced a lot of subcycling and repeated advancement attempts, and time step cycling. 

Numerous papers have been pubhshed on particularly the topic of this chapter the role of the fluid—particle interaction force in RANS-based simulations of either the Euler—Lagrange or the Euler—Euler type. The reason for this massive effort is in the common perception that the current understanding about the fluid-particle interaction is insufficient and responsible for the generally modest predictive performance of the current RANS-based two-phase flow simulations. This in itself may already be indicative of a serious flaw in the way the fundamental knowledge on fluid—particle interaction in the fluid mechanics hterature has been condensed in the conventional CFD software. An exhaustive review of all RANS-based two-phase simulations reported in the hterature is virtually impossible and also not needed, as various reviews are available, sometimes restricted to a particular canonical interaction force and/or a particular class of two-phase flows (Balachandar and Eaton, 2010 Hibiki and Ishii, 2007 Kuipers and Van Swaaij, 1998 Li et al, 2015 Ochieng and Onyango, 2010 Pourtousi et al, 2014 Sokohchin et al, 2004 Tabib et al, 2008 Visuri et al, 2011 Shah et al, 2015). 

Simulations in the Gibbs ensemble attempt to combine features of Widom s test particle method with the direct simulation of two-phase coexistence in a box. The method of Panagiotopoulos et al [162. 163] uses two fiilly-periodic boxes, I and II. 

The alternative to direct simulation of two-phase coexistence is the calculation of free energies or chemical potentials together with solution of the themiodynamic coexistence conditions. Thus, we must solve (say) pj (P) = PjjCT ) at constant T. A reasonable approach [173. 174. 175 and 176] is to conduct constant-AT J simulations, measure p by test-particle insertion, and also to note that the simulations give the derivative 3p/3 7 =(F)/A directly. Thus, conducting... 

Equilibration of the interface, and the establislnnent of equilibrium between the two phases, may be very slow. Holcomb et al [183] found that the density profile p(z) equilibrated much more quickly than tire profiles of nonnal and transverse pressure, f yy(z) and f jfz), respectively. The surface tension is proportional to the z-integral of Pj z)-Pj z). The bulk liquid in the slab may continue to contribute to this integral, indicatmg lack of equilibrium, for very long times if the initial liquid density is chosen a little too high or too low. A recent example of this kind of study, is the MD simulation of the liquid-vapour surface of water at temperatures between 316 and 573 K by Alejandre et al [184]. 

The radial distribution function can also be used to monitor the progress of the equilibration. This function is particularly useful for detecting the presence of two phases. Such a situation is characterised by a larger than expected first peak and by the fact that g r) does not decay towards a value of 1 at long distances. If two-phase behaviour is inappropriate then the simulation should probably be terminated and examined. If, however, a two-phase system is desired, then a long equilibration phase is usually required. 

If an opportunistic preconcentration of the feed is used instead, an entirely different flow sheet results. In this case the MSA composition is a two-phase mixture of methylene chloride and water. Detailed simulations ate requited to determine which of these (or other) 2-ptopanol dehydration flow sheet alternatives is the economically advantaged process. 

The reader is encouraged to use a two-phase, one spatial dimension, and time-dependent mathematical model to study this phenomenon. The UCKRON test problem can be used for general introduction before the particular model for the system of interest is investigated. The success of the simulation will depend strongly on the quality of physical parameters and estimated transfer coefficients for the system. 

Computer simulations of bulk liquids are usually performed by employing periodic boundary conditions in all three directions of space, in order to eliminate artificial surface effects due to the small number of molecules. Most simulations of interfaces employ parallel planar interfaces. In such simulations, periodic boundary conditions in three dimensions can still be used. The two phases of interest occupy different parts of the simulation cell and two equivalent interfaces are formed. The simulation cell consists of an infinite stack of alternating phases. Care needs to be taken that the two phases are thick enough to allow the neglect of interaction between an interface and its images. An alternative is to use periodic boundary conditions in two dimensions only. The first approach allows the use of readily available programs for three-dimensional lattice sums if, for typical systems, the distance between equivalent interfaces is at least equal to three to five times the width of the cell parallel to the interfaces. The second approach prevents possible interactions between interfaces and their periodic images. 

Spalding, D. B. 1981. A general purpose computer program for multi-dimensional one- and two-phase flow. Mathematics and Computers in Simulation, IMACS, XXll. 267-276. 

Two-phase flow in parallel pipes, fed from a common manifold, displays interesting phenomena, as two phases may split unevenly when entering the parallel piping. Ozawa et al. (1979, 1989) performed experimental smdies on two-phase flow systems in parallel pipes of 3.1 mm diameter. They simulated the flow in boiling channels by injection of air and water into the pipes. 

Riber, E., et al.. Towards large eddy simulation of non-homogeneous particle laden turbulent gas flows using Euler-Euler approach, in Eleventh Workshop on Two-Phase Flow Predictions. 2005, Merseburg, Germany. 

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