Void fraction profile

Fig. 11.6. Velocity, density, pressure and temperature profiles from a 2D simulation with a uniform void fraction profile. Reprinted with permission by Elsevier [7].

To evaluate the importance of the radial variations in the void fraction profiles, simulations with prescibed radial variations in the bed structure were performed for the s3mthesis gas process. The velocity and pressure profiles were significantly altered. Higher void fractions at the wall induces less friction from... 

FIGURE 15.49 Void fraction profiles in boiling of saturated water at atmospheric pressure (from Shoji [100], with permission from ASME). 

Teyssedou, A., A. Tapucu, and M. Lotie, Impedance Probe to Measure Local Void Fraction Profiles, Rev. Sci. Instrum., 59, 4, April 1988. 

At djdp values below 5, a and b drastically change. From velocity measurements by Bey and Eigenberger [1997] and radial void fraction profiles of de Klerk [2003], Castillo-Araiza and Lopez-Isunda derived values of 270 for a and 2.5 for b. 

Void fraction profiles in a packed bed for various ratios of djclp. From Papageorgiou and Froment [1995]. 

Two-dimensional homogeneous model with porosity and void fraction profile (2D-HOM-PVP). Radial conversion (a) and temperature (b) profiles at a given distance in the bed and for Rsp =175.2 = 2 1 = 0.07 [Papageorgiou and Froment, 1995]. 

THE MEASUREMENT OF VOID FRACTION PROFILES IN PACKED BEDS... 

Lerou and Froment [l] demonstrated that the structure of the packed bed can be defined by its radial void fraction profile. In order to have adequate and reliable data on void fraction profiles an experimental measuring system was constructed, which is presented here together with suggestions for subsequent analysis. 

Three different packings were investigated. Details are given in Table I. Figures 1 to 3 show typical examples of the measured void fraction profiles. 

The information concerning the void fraction profiles can be used in different ways. Cohen and Metzner [T] divided the cross section of the tube in three regions a wall, a transition and a bulk region. 

For each region a mean value of the void fraction was calculated and a hydraulic radius was defined which was used in a pressure drop correlation. Martin [20] divided the bed into two regions a wall and a bulk region. He calculated for both different flow rates and a different rate of heat transfer. Carbonell [2] also used a two zone model for his analysis of the dispersion phenomena. In more recent work Vortmeyer et al. [5>6] tried to use the complete radial void fraction profile, and so did Chang [3]. They followed the same itinerary outlined by Lerou and Froment [l] and Marivoet et al. [2l]. Starting from the void fraction profile the radial velocity profile is calculated. With both profiles the effective thermal conductivity is established and the temperature and concentration profiles can be calculated by means of a two dimensional pseudo homogeneous model for the reactor. 

In a first step the void fraction profile has to be correlated in terms of the aspect ratio. Govindarao and Froment [22] approached the problem by expressing the void fraction in a layer in terms of the contributions to the solid volume in a layer by spheres with centers lying in feasible neighbouring layers. Singleton [23] made a similar, more statistical, approach he assessed the location of all solid material in terms of distribution functions. 

Figure 1. Measured radial void fraction profile of a bed packed with small spheres.

Void Fraction Profiles with Multiple-Impeller Agitators. 

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