Prediction of heat and mass transfer in canister filters Tony Smith S & C Thermofluids Limited PHOENICS User Conference Melbourne 2004 Co-authors - Martin Smith, Dstl, Porton Down Kate Taylor, S & C Thermofluids

Overview Introduction to S & C Thermofluids Canister filters Porous media modelling Voidage distribution Geometry Pressure drop calculation Adsorption Results Conclusion and recommendations

S & C Thermofluids Formed in 1987 Research into fluid (gas/liquid) flow and heat transfer Based in BATH, U.K.

S & C Thermofluids Use combination of analysis (mainly CFD) and experimental validation and demonstration RR Gnome engine test rig CFD prediction of Gnome exhaust

Experimental facilities RR Gnome turbojet and turboshaft engines Universal jet flow rig Water tunnel JPX turbojet Ejector performance test rig Catalyst research engines

CFD modelling External aerodynamics Propulsion system (nozzle flows) Exhaust plume mixing Exhaust reactions Interactions Catalytic converters Filters

From vacuum cleaners to supersonic aircraft

From green houses to nuclear reactors

From leaf blowers to rockets

Canister filters for respirators

Drivers for porous media modelling Pressure drop Flow distribution Performance –Adsorption –Break-through –Conversion (reactions) –Minimise use of materials

Modelling approach Typical filter monolith Porous media such as catalytic converters and packed bed filters often contain very high surface areas which are difficult to represent in detail whilst modelling the bulk flowfield

Modelling philosophy Continuum approach –macroscopic model of complete system Single channel –detailed model of one flow path

Continuum methodology Solving gas and solid (adsorbed) species separately but within the same computational space with mass transfer Gas and solid energy can also solved separately with heat transfer This methodology has been described in earlier papers relating to filter performance prediction

Canister geometry Air Flow Impregnated granular activated carbon Glass Fibre Filter

VOIDAGE DISTRIBUTION IN CYLINDRICAL FILTER BEDS Radial voidage distribution in ‘snowstorm’ packed filter beds is a function of the ratio: particle size/bed diameter Affects the velocity distribution within the filter bed Measurements made of voidage distribution for range of particle sizes Fitted to modified ‘Mueller’ model

Voidage distribution  =  b + (1-  b )e -br J o (ar*)

Geometry Canister key dimensions converted to FEMGEN geometry input Mesh generated in FEMGEN Output as PHOENICS 2D, axisymmetric BFC mesh using Phirefly PHOENICS Q1 file written out

Voidage distribution - canister Grid fixed by geometry Voidage calculated locally according to modified Mueller equation Voidage set in ground coding

Pressure drop Local voidage distribution coupled to Ergun-Orning equation for pressure loss through bed:  p/L = 5 S o 2 (1-  ) 2  U/  S o (1-  )  U 2 /  3 || viscous loss turbulent loss This pressure drop is applied to both axial and radial velocities Earlier work using this equation have given rise to good agreement with experimental data for pressure drop.

Pressure drop Predicted pressure drop 275Pa Measured pressure drop 110Pa Filter paper section pressure drop 40Pa Flowrate 30l/min

Adsorption model Transient model to predict ‘breakthrough’ Steady state flowfield used as initial conditions Adsorption rate source term: -  C/  t = 1/  S o k (C - C i ) Sh = 1.15 (Re p /  ) 0.5 Sc 0.33 for Re p >1 Sh = k d p /D

Adsorption model Rate of uptake in adsorbent:  m/  t =  /(1-  ) (-  C/  t)/  z Maximum uptake from isotherm equation Cumulative uptake is calculated :  m/  t. /  t Uptake value stored Interface concentration C i set to be in local equilibrium with uptake value

Velocity distribution

Predicted uptake of contaminant after 10 minutes

Conclusions A CFD model of a canister filter has been produced The model provides predictions of pressure drop, flow distribution and adsorption in transient conditions The model uses PHOENICS as the main solver with additional ground coding for voidage distribution, pressure drop and adsorption

Conclusions (2) FEMGEN is used to create the BFC grid for use in PHOENICS Pressure drop predictions show some discrepancy with measurement – unlike earlier packed bed filter work Early predictions of contaminant adsorption look realistic but require validation

Recommendations Investigate pressure drop prediction discrepancies Improve adsorption model Include heat of adsorption Provide axial variations of voidage Modify aspects of canister model (eg gap at rear wall) Provide full transient input of contaminant concentration as well as flowrate Provide validation

Acknowledgements Martin Smith, Dstl, Porton Down Kate Taylor, S & C Thermofluids