Determination and Verification of the Forchheimer Coefficients for Ceramic Foam Filters Using COMSOL CFD Modelling

Transcription

1 Norges teknisk-naturvitenskapelige universitet 1 Determination and Verification of the Forchheimer Coefficients for Ceramic Foam Filters Using COMSOL CFD Modelling Presented by M.W. Kennedy Co-Authors: K. Zhang, J.A. Bakken, R.E. Aune Excerpt from the Proceedings of the 2012 COMSOL Conference in Milan

2 Forchheimer Equation 2 P µ ρ = V + V L k s k 1 where ΔP is the pressure drop across the CFF [Pa], L the filter thickness [m], μ the fluid viscosity (which for water at 280 K is 1.382x10-3 [Pa s]), V s the fluid superficial velocity [m/s], k 1 the first order Darcy coefficient [m 2 ], ρ the fluid density (which for water at 280 K is ~1000 [kg/m 3 ]), and k 2 the non-darcy coefficient [m]. 2 s 2

3 Permeability Apparatus 3 Tested with Long and Short Inlet Lengths Issues: 1. Inlet boundary conditions 2. Sealing 3. Flow field diameter Drawn to scale Smooth Plexiglas Pipe 49.8 mm ID 60 mm OD Expanding flow field Differential Pressure Transducer 102 mm dia. 2 mm thick O-ring 20 cm long, copper impulse lines, 4 mm ID Pressure taps 4 mm dia. hole Drawn to scale Smooth Plexiglas pipe 49.8 mm ID 60 mm OD Straight Through Differential Pressure Transducer 102 mm dia. 2 mm thick O-ring 20 cm long, copper impulse lines, 4 mm ID Pressure taps 4 mm dia. hole 30, 40, 50 or 80 PPI commercial ceramic foam filter ~101 mm dia. and 50 mm thick Plexiglas housing 2 mm thick rubber gasket top and bottom of filter ~0.5 mm grease with 49 mm dia. hole impregnated cellulose 30, 50 or 80 PPI commercial ceramic foam filter ~49 mm dia., and 50 mm thick Plexiglas housing Rubber O-ring seal ~0.5 mm thick silicone grease impregnated cellulose 50 mm dia. inlet and 48 mm dia. outlet to hold filter in place

4 Measured Pressure Gradients 4 Measured Differential Pressure, Pa Long and Short Inlet Give Same Results Water Mass Flow, kg/s 30 PPI 40 PPI 50 PPI - S 50 PPI - L 80 PPI

5 Sealing of the filters into the housing 5 High Viscosity Silicone Grease Cellulose fibre, i.e. paper!

6 How to obtain a true pressure gradient? 6 1.8E E+06 Measured Pressure Gradient, Pa/m 1.4E E E E E E+05 Correct Wrong Highly obvious loss of seal. 2.0E E+00 Silicone Only Silicon+Cellulose After Loss of Sealant Dietrich Superficial Velocity, m/s B. Dietrich, G. I. Garrido, P. Habisreuther, N. Zarzalis, H. Martin, M. Kind, and B. Kraushaar-Czarnetzki, Industrial & Engineering Chemistry Research, 48, (2009),

7 7 How to determine the effective Flow Field Diameter? Measure: ΔP, Diameter, L, Mass Flow, Temperature (i.e. μ and ρ) Guess an effective diameter What diameter, which if occupied by a homogeneous fluid velocity in only the z- direction for the same total fluid flow would give the actual measured pressure gradient? Drawn to scale Differential Pressure Transducer 20 cm long, copper impulse lines, 4 mm ID Calculate k 1 and k 2 CFD flow field, ΔP/L vs. V Guess a new effective diameter No Same as measured? Smooth Plexiglas Pipe 49.8 mm ID 60 mm OD 102 mm dia. 2 mm thick O-ring Pressure taps 4 mm dia. hole Yes Effective diameter is correct 30, 40, 50 or 80 PPI commercial ceramic foam filter ~101 mm dia. and 50 mm thick Plexiglas housing 2 mm thick rubber gasket top and bottom of filter ~0.5 mm grease with 49 mm dia. hole impregnated cellulose

8 501 kpa/m 1612 kpa/m Comparison of Expanding Flow Field with Straight Through 8 Expansion of the flow field has resulted in a greatly reduced pressure gradient for the same inlet velocity. 0.5 m/s velocity

9 Comparison of 50 PPI, 49 mm and 101 mm L and S 9 Measured Pressure Gradient, Pa/m 1.4E E E E E E E+05 FEM Actual Effective Eq. 1 Eq. 1 Filter Filter Flow Field Forchheimer Forchheimer Inlet Type Diameter Diameter k 1 k 2 Length (PPI) (m) (m) (m 2 ) (m) (m) N/A 5.08E E E E E E N/A 1.57E E E E E E N/A 6.52E E E E S 101-L 49-S 0.0E Superficial Velocity, m/s

10 Comparison of COMSOL with Experimental E+06 FEM Calculated Pressure Gradient, Pa/m 1.4E E E E E E E L S E+00 0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 1.E+06 1.E+06 1.E+06 2.E+06 Measured Pressure Gradient, Pa/m

11 Correlation of Forchheimer Terms 11 with Measured Window Dimensions 6.0E E E E-04 Darcy Term, k 1 4.0E E E E E E-04 Non-Darcy Term, k 2 1.0E-08 k1-49 k1-101 k2-49 k E E E Window Area, μm 2

12 Conclusions Correct sealing of the entire side of the ceramic foam filter was required to obtain the true pressure gradients for the straight through 49 mm filter design. Sealing verified by agreement with COMSOL. 12 COMSOL was required to calculated the equivalent flow field diameter and obtain the true Forchheimer coefficients for the 101 mm design. 49 and 101 mm results agree with each other and with COMSOL with deviations of < ±7%.

13 Acknowledgement 13 Funding from the Norwegian Research Council (NRC) for the RIRA (Remelting and Inclusion Refining of Aluminium). The Project partners include: Hydro Aluminium, SAPA Heat Transfer, Alcoa Norway, NTNU and Sintef Materials and Chemistry. Special thanks to: Egil Torsetnes and Kurt Sandaunet for experimental support. Thank you for your attention! Mark William Kennedy Department of Materials Science and Engineering Phone: Mobile: