The Prediction of Pressure Drop and Flow Distribution in Packed Bed Filters

A CFD technique for predicting the performance of axisymmetric packed bed filters has been developed. The effect on the pressure drop of a non-uniform voidage distribution within the filter bed has been modelled. A radial voidage distribution was derived from a predictive model based on a modified Mueller equation. The pressure loss through the bed was calculated from the Ergun equation, using the local voidage. The technique has been validated against experimental measurements of pressure drop and velocity distribution in a model of a filter system for a range of filter parameters and inlet velocities. Generally good agreement has been obtained between experiment and predictions. In addition a simple adsorption model has been developed. NOMENCLATURE C vapour concentration, kg/m3 Ci interfacial vapour concentration, kg/m3 dp bead diameter, m db bed diameter, m D diffusivity of water vapour in air, m2/s k mass transfer coefficient, m/s K turbulence kinetic energy, m2/s2 m uptake of vapour, g/g r radial position in bed, m So bead specific surface, /m (=6/dp for sphere) u local, or interstitial, velocity, m/s U superficial velocity, m/s (= u.ε) uτ friction velocity, m/s ( = (τw/ρ)*) y distance from wall, m y+ non-dimensional distance from wall ( = y.uτ/ν) ν kinematic viscosity, m2/s τw wall shear stress, Pa ρz zeolite density, kg/m3 ε local void fraction Ε dissipation of turbulence kinetic energy, m2/s3 ∂C/∂t adsorption rate per unit fluid volume, kg/m3/s ∂m/∂t uptake rate per unit zeolite mass, g/g/s δt timestep size, s INTRODUCTION Packed bed filters have been used for some time to remove toxic gases and vapours from contaminated airstreams. DERA Porton Down, in conjunction with S&C Thermofluids Ltd, are currently developing a CFD technique for predicting the flow through filters of this type. The work so far has included experimental measurements of velocities and pressure drops through packed beds and accompanying CFD predictions of the flowfield using the PHOENICS code. Earlier work carried out by DERA involved the development of a CFD model including a pressure drop formulation based on the Ergun equation [1], but using a uniform voidage for the filter bed. The predicted pressure drops appeared to show some level of agreement with measured values but indicated that further experimental data was required. Further experimental work was then carried out by DERA in two areas. Firstly, further measurements of the velocity distributions and pressure drops were made, and secondly measurements were made of the voidage distribution within the packed beds. As a result, DERA have determined a formula for predicting the radial voidage distribution within a packed bed for a given filter diameter and bead size. A brief summary of this work is included below. S&C Thermofluids were then asked by DERA to include the predicted voidage distribution in a CFD model of the filter bed, and to validate the CFD model in the first instance against pressure drop data for one bead size and filter geometry at various air velocities. Further validation was subsequently carried out for a range of filter configurations. The following paragraphs describe this work and present some of the results of the validation. The initial CFD results showed reasonable agreement with the test data, but there remained some discrepancies between the measured and predicted velocity profiles [2]. It was felt that these discrepancies were possibly due to the turbulence model, or to axial variations in the measured voidage distributions which were not included in the model. Furthermore, no systematic study of the effects of grid dependence had been carried out. These areas have now also been examined [3], and the amendments to the model and new results are described below.