Standard bubble model

Aerosols were drawn to the filters by Model G, MSA sampling pumps at flow rates of 1.0-2.0 L/min. Pumps were pre- and post calibrated using standard bubble burette methods with an identical sampling train in line. 

Hereafter three examples are presented for the application of CID to analyse advanced combustion systems. Each of the examples covers a specific technical problem and shows how standard CFD models need to be adjusted to address individual questions. The first example deals with the increase of boiler availability due to reduced ash deposition on furnace walls and superheater surfaces. The second one addresses the question of reduced nitrogen oxide emissions from a bubbling fluidised bed combustor and the last example presents a novel model for black liquor droplet combustion. 

In most cases the only appropriate approach to model multi-phase flows in micro reactors is to compute explicitly the time evolution of the gas/liquid or liquid/ liquid interface. For the motion of, e.g., a gas bubble in a surrounding liquid, this means that the position of the interface has to be determined as a function of time, including such effects as oscillations of the bubble. The corresponding transport phenomena are known as free surface flow and various numerical techniques for the computation of such flows have been developed in the past decades. Free surface flow simulations are computationally challenging and require special solution techniques which go beyond the standard CFD approaches discussed in Section 2.3. For this reason, the most common of these techniques will be briefly introduced in... 

Sokolichin, A. and Eigenberger, G. (1999), Applicability of standard k-e turbulence model to the dynamic simulation of bubble columns, Chem. Eng. Sci., 54, 2273-2284. 

Lopez de Bertodano et al [93] proposed a similar extension of the standard single-phase k — e model considering two time scales of turbulence to enable simulations of bubbly two-phase flows. 

Borchers O, Busch C, Sokolichin A, Eigenberger G (1999) Applicability of the standard k-epsilon turbulence model to the dynamic simulation of bubble colmnns. Part II Comparison of detailed experiments and flow simulations. Chem Eng Sci 54(24) 5927-5935... 

The Cb parameter takes values between 0 and 1, and generally depends on bubble size and shape, and on the turbulent length scale. The empirical coefficients in the turbulence model were kept equal to the standard values for the original single phase model. 

To model the measured transient foam displacements, equations 2 through 12 are rewritten in standard implicit-pressure, explicit-saturation (IMPES) finite difference form, with upstream weighting of the phase mobilities following standard reservoir simulation practice (10). Iteration of the nonlinear algebraic equations is by Newton s method. The three primitive unknowns are pressure, gas-phase saturation, and bubble density. Four boundary conditions are necessary because the differential mass balances are second order in pressure and first order in saturation and bubble concentration. The outlet pressure and the inlet superficial velocities of gas and liquid are fixed. No foam is injected, so Qh is set to zero in equation... 

To predict foam behavior mechanistically and quantitatively, it is necessary to account for bubble-size evolution. A foam bubble population-balance provides the necessary framework by including foam as a simple component in a standard reservoir simulator. Reduced gas mobility is modeled by a lowered gas relative permeability and a raised effective viscosity. A Stone-type model for relative permeability provides the requisite rules for modeling the relative permeability of both wetting liquid... 

---