Core-annular flow model

In the core-annular flow model, the mass balance of the solid phase can be expressed as... 

Models Based on the Core-Annular Flow Structure... 

Bannwart, A. C. (2001). Modeling aspects of oil—wattn core—annular flows. Journal of Petroleum... 

HYDRODYNAMIC MODELING, 278 Radial Gas Velocity Profiles, 278 Gas Mixing, 280 Radial and Axial Dispersion, 281 Core-Annular Flow, 284 Contact Efficiency, 285... 

Various core-annular models have been developed to describe the gas-solid flow (Horio et al., 1988 Bai et al., 1995 Bolton and Davidson, 1998). The main difference among these models lie in the degree of complexity and in the assumptions associated with simplifications. Core-annular flow structures become dominant in the upper dilute region. Thus, when the dilute flow is predominantly present in the riser, models based on core-annular structures can be applied to reactor models. Kunii and Levenspiel (1990) extended the conventional fluidized bed model (a dense lower region coupled with a freeboard upper region) to cir-... 

Pressure oscillations with RMS value up to 10 kPa in two models of lean-burn gas turbine combustors, with heat release around 100 kW, have been actively controlled by the oscillation of fuel flow. The flames were stabilized behind an annular ring and a step in one arrangement, and downstream of an expansion and aided by swirl in the other. Control was sensitive to the location of addition of oscillated fuel. Oscillations in the annular flow were attenuated by 12 dB for an overall equivalence ratio of 0.7 by the oscillation of fuel in the core flow and comprising 10% of the total fuel flow, but negligibly for equivalence ratios greater than 0.75. Oscillation of less than 4% of the total fuel in the annulus flow led to attenuation by 6 dB for all values of equivalence ratio considered. In the swirling flow, control was more effective with oscillations imposed on the flow of fuel in a central axial jet than in the main flow, and oscillations were ameliorated by 10 dB for equivalence ratio up to 0.75, above which the flame moved downstream so that the effectiveness of the actuator declined. The amelioration of pressure oscillations resulted in an increase in NOj, emissions by between 5% and 15%. 

Example 10.3 A riser is of 0.15 m in diameter and 8 m in height. Particles with a mean diameter of 200 pm and a density of 384 kg/m3 are used in the riser, which operates at U — 2.21m/sand/p = 3.45kg/m2 -s. The gas used is air. For this operating condition, Davidson (1991) reported a particle downward velocity, npw, of 0.5 m/s and a particle downward flow rate, Ww, of 0.2 kg/s in the annular region. Assume that the solids volume fraction in the central core region, apc, is 0.015. Calculate the cross-sectionally averaged solids holdup and the decay constant, Kd, defined in Eq. (10.33) in terms of the core-annular model. 

A schematic of the flow pattern used to represent annular flow is shown in Figure 10. A preliminary model for pressure drops in the annular flow regime for the circular tubes under consideration here was reported in Garimella et al. [27], followed by the more detailed model [28] described below. For the development of this model the following assumptions were made steady flow, equal pressure gradients in the liquid and gas core at any cross section, uniform thickness of the liquid film and no entrainment of the liquid in the gas core. The measured pressure drops were used to compute the Darcy form of the interfacial friction factor to represent the interfacial shear stress as follows ... 

Prediction of Critical Heat Flux in Annular Flow. In annular flow, the situation to be modeled is illustrated in Fig. 15.106. There is a thin liquid film on the channel wall that has a flow rate T per unit periphery. Droplets are being entrained from this film into the vapor core at a rate mE (mass rate of entrainment per unit peripheral area, kg/m2s) and are being redeposited from the core at a rate mD (kg/m2s). In addition, the liquid film is being evaporated at a rate q"/i,g per unit peripheral area. Thus, the rate of change of T with distance is given by... 

In summary, a single model has not been developed that can fully characterize riser gas phase hydrodynamics. The studies indicate that under dense phase conditions, typical of commercial FCC riser operation, a simple axial dispersion model may be adequate to characterize gas mixing. Under dilute conditions, a two-phase core-annular model is a good first approximation to the flow structure. However, both radial dispersion and radial gas velocity profiles must be accounted for to provide a realistic and reliable interpretation. The model suggested by Martin et al. should be further developed and applied to risers of different geometry operating with different powders [83]. However, contact efficiency may provide the simplest means from which scale-up criteria can be developed. 

The hydrodynamic model development for a circulating fluidized bed follows the same approach as bubbling and turbulent beds. In the macroscale, the gas-solid flow is characterized by a coexistence of a bottom dense region and an upper dilute region. The flow in the radial direction can be described by a core-annular structure with a dense particle region close to... 

Bai DR, Zhu JX, Jin Y, Yu ZQ. Internal recirculation flow structure in vertical upward flowing gas-solid suspensions I, a core/annular model. Powder Technol 85 171-178, 1995. 

We begin our derivation of the core flow model with a flow balance relating the average axial flow velocity, in the annular region located between radii Rc and R, to the average velocity normally computed or measured out... 

Finally, the TRACE reactor design Is based on the reference reactor case defined in Enclosure 1 to Attachment D of the Reference 12-1 concept selection report. This annular flow block core uses UN fuel. The most recent NRPCT core concepts had switched to UO2 fuel. The TRACE UN core model... 

Shown in Figure 12-4. By having six paths in the core block region the model can represent radial primary flow maldistribution as well as a radial power profile. TRACE heat structures (7) are used to model the core block between each ring of annular flow passages, This heat structure detail allows the model to determine core structural temperature profiles in both the axial and radial directions. 

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