Computational single phase

Kandilikar SG, Upadhye H (2005) Extending the heat flux limit with enhanced microchannels in direct single-phase cooling of computer chips. In Proceedings of 21st SemiTherm Symposium, San Jose, 15-17 March 2005, pp 8-15... 

The number of equations to be solved is, among other things, related to the turbulence model chosen (in comparison with the k-e model, the RSM involves five more differential equations). The number of equations further depends on the character of the simulation whether it is 3-D, 21/2-D, or just 2-D (see below, under The domain and the grid ). In the case of two-phase flow simulations, the use of two-fluid models implies doubling the number of NS equations required for single-phase flow. All this may urge the development of more efficient solution algorithms. Recent developments in computer hardware (faster processors, parallel platforms) make this possible indeed. 

Leaving aside the difficult question of whether this model holds for multiphase flows, we still have the problem of determining in terms of the computed properties of the flow. The reader should appreciate that choosing an effective viscosity for a multiphase flow is much more complicated than just adding a turbulence model as done in single-phase turbulent flows. Indeed, even for a case involving two fluids (e.g., two immiscible liquids) for which the molecular viscosities are constant, the choice of the effective viscosities is not obvious. For example, even if the mass-average velocity defined by... 

Computational fluid dynamics (CFD) is rapidly becoming a standard tool for the analysis of chemically reacting flows. For single-phase reactors, such as stirred tanks and empty tubes, it is already well-established. For multiphase reactors such as fixed beds, bubble columns, trickle beds and fluidized beds, its use is relatively new, and methods are still under development. The aim of this chapter is to present the application of CFD to the simulation of three-dimensional interstitial flow in packed tubes, with and without catalytic reaction. Although the use of... 

Frequency domain resampling is attractive in the present context because the timescaling and the resampling operations can be performed in a single phase-vocoder analysis, thus reducing the computational cost. The interested reader may consult [Moulines and Laroche, 1995] for a complete description of the algorithm. 

Computational fluid dynamics enables us to investigate the time-dependent behavior of what happens inside a reactor with spatial resolution from the micro to the reactor scale. That is to say, CFD in itself allows a multi-scale description of chemical reactors. To this end, for single-phase flow, the space resolution of the CFD model should go down to the scales of the smallest dissipative eddies (Kolmogorov scales) (Pope, 2000), which is inversely proportional to Re-3/4 and of the orders of magnitude of microns to millimeters for typical reactors. On such scales, the Navier-Stokes (NS) equations can be expected to apply directly to predict the hydrodynamics of well-defined system, resolving all the meso-scale structures. That is the merit of the so-called DNS. 

Since a multiphase flow usually takes place in a confined volume, the desire to have a mathematical description based on a fixed domain renders the Eulerian method an ideal one to describe the flow field. The Eulerian approach requires that the transport quantities of all phases be continuous throughout the computational domain. As mentioned before, in reality, each phase is time-dependent and may be discretely distributed. Hence, averaging theorems need to be applied to construct a continuum for each phase so that the existing Eulerian description of a single-phase flow may be extended to a multiphase flow. 

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