Navier-Stokes simulation

M. Richer, A. Frohn. Navier-Stokes simulation of droplet collision dynamics. In Proceedings of the 7th ISCFD in Beijing, China, 1997 (to be published). 

Results of Reynolds Averaged Navier- Stokes Simulations... 

Several investigators have studied the potentially complex flow in actual stagnation-flow reactors, using two-and three-dimensional Navier-Stokes simulations [116,117,133,183, 203,228,348,419] and flow visualization [45], Generally speaking, the departure from... 

There are commercial offerings that include Chemkin capabilities in Navier-Stokes simulations (e.g., CFD-ACE written by CFD Research Corporation, Huntsville, AL, in conjunction with Reaction Design, Inc., San Diego, CA). The applications that are part of the Chemkin package, however, focus on low-dimensional simulation. 

Persillon, H. and Braza, M., Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier-Stokes simulation, J. Fluid Mech., Vol. 365, pp. 23-88, 1998. 

Rai, M.M. (1985). Navier-Stokes Simulations of Rotor-Stator Interaction Using Patched and Overlaid Grids, AlAA-85-1519, American Institute of Aeronautics and Astronautics. 

Keywords Binary drop colUsions Bouncing Coalescence Collision model Crossing separation Gaseous environment Immiscible liquids Lattice-Boltzmann simulation Miscible liquids Navier-Stokes simulation Reflexive separation Satellite droplets Spray flow simulation SPH simulation Stretching separation... 

M. Rieber, A. Frohn Three-dimensional Navier-Stokes simulation of binary collisions between droplets of equal size, J. Aerosol Sci. 26(Suppl. 1), S929-S930 (1995). 

Comprehensive Nernst-Planck-Poisson-Navier-Stokes Simulation of Flows over Heterogeneous Surfaces... 

Sharatchandra MC, Sen M, Gad-El-Hak M (1997) Navier-Stokes Simulations of a Novel Viscous Pump. J Fluid Eng 119 372-382... 

However, the length and time scales that molecular-based simulations can probe are still very limited (tens of nanosecond and a few nanometers), due to computer memory and CPU power limitations. On the other hand, nanoscale flows are often a part of larger scale devices that could contain both nanochannels and microfluidic domains. The dynamics of these systems depends on the intimate connection of different scales from nanoscale to microscale and beyond. MD simulation cannot simulate the whole systems due to its prohibitive computational cost, whereas continuum Navier-Stokes simulation cannot elucidate the details in the small scales. These limitations and the practical needs arising from the study of multiscale problems have motivated research on multiscale (or hybrid) simulation techniques that bridge a wider range of time and length scales with the minimum loss of information. A hybrid molecular-continuum scheme can make such multiscale computation feasible. A molecular-based method, such as MD for liquid or DSMC for gas, is used to describe the molecular details within the desired, localized subdomain of the large system. A continuum method, such as finite element or finite volume based Navier-Stokes/Stokes simulation, is used to describe the continuum flow in the remainder of the system Such hybrid method can be applied to solve the multiscale phenomena in gas, liquid, or solid. 

Dissipative particle dynamics (DPD) is a technique for simulating the motion of mesoscale beads. The technique is superficially similar to a Brownian dynamics simulation in that it incorporates equations of motion, a dissipative (random) force, and a viscous drag between moving beads. However, the simulation uses a modified velocity Verlet algorithm to ensure that total momentum and force symmetries are conserved. This results in a simulation that obeys the Navier-Stokes equations and can thus predict flow. In order to set up these equations, there must be parameters to describe the interaction between beads, dissipative force, and drag. 

Turbulent inlet conditions for LES are difficult to obtain since a time-resolved flow description is required. The best solution is to use periodic boundary conditions when it is possible. For the remaining cases, there are algorithms for simulation of turbulent eddies that fit the theoretical turbulent energy distribution. These simulated eddies are not a solution of the Navier-Stokes equations, and the inlet boundary must be located outside the region of interest to allow the flow to adjust to the correct physical properties. 

We use computational solution of the steady Navier-Stokes equations in cylindrical coordinates to determine the optimal operating conditions.Fortunately in most CVD processes the active gases that lead to deposition are present in only trace amounts in a carrier gas. Since the active gases are present in such small amounts, their presence has a negligible effect on the flow of the carrier. Thus, for the purposes of determining the effects of buoyancy and confinement, the simulations can model the carrier gas alone (or with simplified chemical reaction models) - an enormous reduction in the problem size. This approach to CVD modeling has been used extensively by Jensen and his coworkers (cf. Houtman, et al.) ... 

An Eulerian-Eulerian (EE) approach was adopted to simulate the dispersed gas-liquid flow. The EE approach treats both the primary liquid phase and the dispersed gas phase as interpenetrating continua, and solves a set of Navier-Stokes equations for each phase. Velocity inlet and outlet boundary conditions were employed in the liquid phase, whilst the gas phase conditions consisted of a velocity inlet and pressure outlet. Turbulence within the system was account for with the Standard k-e model, implemented on a per-phase basis, similar to the recent work of Bertola et. al.[4]. A more detailed description of the computational setup of the EE method can be found in Pareek et. al.[5]. 

Since MPC dynamics yields the hydrodynamic equations on long distance and time scales, it provides a mesoscopic simulation algorithm for investigation of fluid flow that complements other mesoscopic methods. Since it is a particle-based scheme it incorporates fluctuations, which are essential in many applications. For macroscopic fluid flow averaging is required to obtain the deterministic flow fields. In spite of the additional averaging that is required the method has the advantage that it is numerically stable, does not suffer from lattice artifacts in the structure of the Navier-Stokes equations, and boundary conditions are easily implemented. 

In the macroscopic limit, this model running on a square lattice tends to the Navier-Stokes equation, but a hexagonal lattice rather than a square lattice gives a simulation that is more scientifically justifiable and permits the determination of a range of parameters, such as transport coefficients. 

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