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Development of Boundary Singularity Method for Partial-Slip and Transition Molecular-Continuum Flow Regimes with Application to Filtration

Zhao, Shunliu

Abstract Details

2009, Doctor of Philosophy, University of Akron, Mechanical Engineering.

Efficient modeling of pressure drop, flowfield, particle capturing and sensing is needed for low Reynolds number micro- and nano-scale filtration flows with unstructured nets of multi-diameter fibers. For computational modeling of two- and three-dimensional partial-slip flows, a Stokeslet-based boundary singularity method (BSM) was developed in this study. For transition flows, the coupling of the BSM with the Direct Simulation Monte Carlo (DSMC) was proposed and developed.

First, regular Stokeslets, regularized Stokeslets located at the boundary of the flow domain and submerged Stokeslets located outside of the flow domain were employed and compared with respect to the accuracy of the numerical results for three-dimensional flows. It was shown in the current study that the use of submerged Stokeslets removed the inaccuracy of pressure and velocity at the particle surface, typical for the prior approaches. Computations were then conducted using the proposed BSM for representative sets of spheres in translational and rotational motions in the partial-slip regime. The cases considered are typical for particles’ capturing and sensing in filtration. The partial slip at the particles’ surface appeared to affect significantly the velocity field and pressure distribution. In a more broad sense, the applications of the proposed methodology include assembly of particles under action of electromagnetic forces, synthesis of nano-particles and nanotubes, and micro-pumping, to name a few applications.

Second, the BSM for two-dimensional partial-slip flows was developed and applied to partial-slip filtration flows. The numerical accuracy was investigated in terms of the location and the number of the Stokeslets for the benchmark study of the flow past an infinite long cylinder. It was shown that the numerical accuracy did not deteriorate with the dramatic decrease in the number of Stokeslets as long as the Stokeslets were sufficiently submerged. A relatively small number of Stokeslets with a substantial submergence depth was thus chosen for modeling fibrous filtration flows. For the no-slip filtration flow, the obtained flowfield and pressure drop agreed well with the experimental data available. The developed BSM was then applied to partial-slip flows about fibers to investigate the slip effect at fiber-fluid interface on the pressure drop. The numerical results compared favorably with the analytical solution available for the limit case of infinite number of structured fibers.

Finally the BSM was coupled with the DSMC near rigid boundary to investigate flows in transition flow regime in which partial-slip closures are no longer accurate. A flow about a single fiber was first chosen to optimize the parameters used in the hybrid method. The number of simulated particles, the thickness of the DSMC region, the cell size for the DSMC procedure and the number of coupling determined successively by parametric study. The developed hybrid method was then applied to multi-fiber filtration flows. The velocity distribution from the hybrid method around a fiber deviated much from that from the BSM with partial-slip heuristic boundary conditions. An increase in pressure drop across fiber was also observed when the hybrid method was applied compared to that for the BSM.

It was concluded that the BSM based on submerged Stokeslets and the coupling of the BSM and DSMC-related methods were useful tools for modeling creep flows in the partial-slip and transition flow regimes. The BSM with the first-order partial-slip boundary conditions was sufficient for simulating partial-slip fibrous filtration flows. For higher Knudsen numbers, the hybrid BSM-DSMC method was preferred.

Alex Povitsky, Ph. D (Advisor)
154 p.

Recommended Citations

Citations

  • Zhao, S. (2009). Development of Boundary Singularity Method for Partial-Slip and Transition Molecular-Continuum Flow Regimes with Application to Filtration [Doctoral dissertation, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1247718304

    APA Style (7th edition)

  • Zhao, Shunliu. Development of Boundary Singularity Method for Partial-Slip and Transition Molecular-Continuum Flow Regimes with Application to Filtration. 2009. University of Akron, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1247718304.

    MLA Style (8th edition)

  • Zhao, Shunliu. "Development of Boundary Singularity Method for Partial-Slip and Transition Molecular-Continuum Flow Regimes with Application to Filtration." Doctoral dissertation, University of Akron, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=akron1247718304

    Chicago Manual of Style (17th edition)