Dilute-phase flow

Obviously, the closer the particles are to each other, the more likely it is that they will stick together and form larger clumps, which usually means that the flow is not uniform. This view combined with Eq. (14.18) is a greatly simplified explanation of why the mass flow ratio q, for dry wood chips can rise to five or even higher and still the flow of the mixture of air and large chip particles can be handled as a uniform suspension, a uniform dilute-phase flow, although it is not actually dilute. The mass flow ratio for fine coal powder, however, has to be much less than five in order for the flow to be handled as a uniform dilute flow. 

The way in which the force /j j is modeled clearly determines the type of the pneumatic flow this has been discussed earlier in Section 14.2.2, where we considered the classification of different types of flow. In the following we will give a detailed description for the force in a way that suits a particular type of flow. This approach will be adequate for so-called dilute-phase flow or, more generally speaking, for homogeneous flow where the particles move separately. 

The new pressure loss equation presented here is based on determining two parameters the velocity difference between gas and conveyed material and the falling velocity of the material. The advantage of this method is that no additional pressure loss coefficient is needed. The two parameters are physically clear and they are quite easily modeled for different cases by theoretical considerations, which makes the method reliable and applicable to various ap>-plications. The new calculation method presented here can be applied to cases where solids are conveyed in an apparently uniform suspension in a so-called lean or dilute-phase flow. 

Considerably more work has been carried out on horizontal as opposed to vertical pneumatic conveying. A useful review of relevant work and of correlations for the calculation of pressure drops has been given by Klinzing et a/.(68). Some consideration will now be given to horizontal conveying, with particular reference to dilute phase flow, and this is followed by a brief analysis of vertical flow. 

Pressure drops and solid velocities for dilute phase flow... 

Three types of theoretical approaches can be used for modeling the gas-particles flows in the pneumatic dryers, namely Two-Fluid Theory [1], Eulerian-Granular [2] and the Discrete Element Method [3]. Traditionally the Two-Fluid Theory was used to model dilute phase flow. In this theory, the solid phase is being considering as a pseudo-fluid. It is assumed that both phases are occupying every point of the computational domain with its own volume fraction. Thus, macroscopic balance equations of mass, momentum and energy for both the gas and the solid... 

In the present study, two-dimensional Two-Fluid Eulerian model was used to describe the steady state, dilute phase flow of a wet dispersed phase (wet solid particles) in a continuous gas phase through a pneumatic dryer. The predictions of the numerical solutions were compared successfully with the results of other one-dimensional numerical solutions and experimental data of Baeyens et al. [5] and Rocha [13], Axial and the radial distributions of the characteristic properties were examined. 

The boundary between dilute phase flow and dense phase flow, however, is not clear cut and there are as yet no universally accepted definitions of dense phase and dilute phase transport. 

Konrad (1986) lists four alternative means of distinguishing dense phase flow from dilute phase flow ... 

In the region E and F some solids may move in dense phase flow along the bottom of the pipe whilst others travel in dilute phase flow in the gas in the upper part of the pipe. The saltation velocity marks the boundary between dilute phase flow and dense phase flow in horizontal pneumatic transport. 

It is often assumed that in vertical dilute phase flow the slip velocity is equal to the single particle terminal velocity Ut. 

Fast fluidization is characterized by a dense region at the bottom of a circulating fluidized bed, leading smoothly (without a sharp interface) into a lean region above (Li and Kwauk, 1980). In contrast, in the dilute-phase flow regime, the pressure gradient, except for an acceleration zone at the bottom, is nearly uniform. Hence the transition from fast fluidization to dilute flow can be characterized by the disappearance of the S-shaped inflection point (Li and Kwauk, 1980), or by the disappearance of nonuniform axial density profiles (Takeuchi et al., 1986). 

Standpipes generally operate in three basic flow regimes packed bed flow, fluidized bed flow, and a dilute-phase flow called streaming flow. 

In order to measure the in-situ particle size of flowing streams, this firm has developed a rather reliable imit for dilute phase flows. The device has been tested by Bell, et al. [18, 19] with promising results. 

Using the basic measurement of pressure drop, we have also found that for dilute phase flow a linear relationship can be given for the relative pressure drop increase with solids flow and solids loading. Recently this concept has been shown to apply in some rather large industrial situations. Davies and Tallon [20] have used the pressure drop fluctuations to also explore solids flow measurement with some success. 

However, in dilute phase pneumatic conveying, the overall volumetric concentration is likely to be less than 2%. Fully suspended material is therefore not currently resolvable and this has meant that studies of dilute phase flow has been limited to situations where the local volumetric concentration is greater than the concentration resolution. Such studies have included the evolution of suspension flow as material is collected [30]. 

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