Lumped parameter approach

A lumped-parameter approach seems adequate for practical purposes if ignition effects are absent. Under steady-state conditions, following the approach of Lie et al. [35], the continuity equation for component i in the gas phase is... 

Today most hollow fiber BOs are designed such that the gas phase flows inside the fibers and the blood flows outside and across the fibers (Figure 23.8). Like flat sheet BOs, several investigators have used a lumped parameter approach to determine mass-transfer and friction factor correlations for BOs. Different investigators have developed slightly different correlations. The differences in the correlations are probably indicative of the level of accuracy of this approach. 

It is likely that the correlations (Equations 23.18 through 23.21) are in fact the same, given the accuracy of the lumped parameter approach. 

Solute transport with biodegradation modelled as a first-order decay process (simple, lumped-parameter approach),... 

The development of the computer code RALOC at the German GRS for the simulation of the distribution of hydrogen, air, and steam in a LWR containment after severe accidents has started in 1974. RALOC is based on a lumped parameter approach with a differential equation system which describes the composition of the containment atmosphere, temperature, and the transport phenomena of convection and diffusion. Validation... 

Even though the cells present in an activated sludge bioreactor represent a mixture of microorganisms, the analysis of such facilities is normally based on a lumped-parameter approach that simplifies the kinetics of BOD removal. In many respects the resulting analysis resembles that developed in Section 13.2.4, the major difference being the inclusion of a term to account for the kinetics of cell death. For example, in the present analysis, we can express the net rate of cell growth per unit mass of microorganism as... 

The transient response of the wall materials when modeled as a zero-dimensional lumped parameter approach is more useful when the fluid in the respective segments is also modeled on a zero-dimensional basis. When modeling an entire system in some detail, conduction in the surrounding solid materials will frequently be assumed to be one dimensional and coupled one to one with fluid control volumes. 

In the MELCOR core model, the btmdle region is divided into concentric radial rings and axial segments that define core cells. Each cell may contain one or more components such as fuel pellets, cladding, etc. and a lumped parameter approach is used for each component within a cell. For the... 

Another fluid-dynamic option in ATHLET consists of a four-equation model, with balance equations for liquid mass, vapour mass, mixture energy and mixture momentum. It is based on a lumped-parameter approach. The solution variables are the pressure, mass quality and enthalpy of the dominant phase within a control volume, and the mass flow rates at the junctions. The entire range of fluid conditions, from sub-cooled liquid to superheated vapour, including thermodynamic non-equilibrium is taken into account, assuming the non-dominant phase to be at saturation. The option has also a mixture level tracking capability. 

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