Modeling the Process of Drying Stationary Objects inside a Tumble Dryer Using COMSOL Multiphysics

Transcription

1 Presented at the COMSOL Conference 2008 Hannover Modeling the Process of Drying Stationary Objects inside a Tumble Dryer Using COMSOL Multiphysics Tarek H.M. Zeineldin

2 Outline Introduction - Drying processes Modeling Approach Transport Phenomena Governing Equations Boundary Conditions Results and Validation Summary and Conclusion T. H.M. Zeineldin,

3 Introduction Textile is stationary Air enters dry; warm and leaves moist; cool Modeled Domains: - Air Domain Air and Vapor - Textile Domain Textile and Water Continuous exchange of heat and moisture Dry Zone Wet Zone Symmetry Axis Heat Flux Moisture Air Domain Air Flow Textile Domain Air Flow Drum/Duct Moisture Transport: - Wet Zone: Free Water & Vapor - Dry Zone: Bound Water & Vapor - Textile Surface: Vapor Vapor front migrates to the symmetry axis T. H.M. Zeineldin,

4 Modeling Approach Transport phenomena Textile (Energy) Energy Transport Boundary Equation kt T =α (Ta T) +ρw Dw X Δh v Convective Energy Textile Domain 2. Energy lost due to phase change Energy Transport Subdomain Equation T. ρ t c p,t = (kt T) mev Δhv t Conductive Energy 2. Energy lost due to phase change k t : Textile heat conductivity T, T a : Temperature of textile and air α: Coefficient of heat transfer ρ w, ρ t : Density of water and textile D w : Capillary conductivity X: Textile moisture content Δh v : Enthalpy of evaporation c p,t : Textile specific heat capacity m ev : Evaporative mass flow rate T. H.M. Zeineldin,

5 Modeling Approach Transport phenomena Textile (Mass) Mass Transport Subdomain Equation X ρw =ρw (Dw X) m t Capillary conduction 1. { ev 2 Textile Domain 2. Vapor conduction Mass Transport Boundary Equation D M β M v w w v,a v,t pv,t +ρw Dw X = ( ) R T R Ta T Vapor conduction 2. Vapor convection p p D v : Vapor diffusion coefficient M w : Water molecular weight R: Universal gas constant p v : Vapor pressure β : Coefficient of mass transfer T. H.M. Zeineldin,

6 Modeling Approach Transport phenomena Air (Energy/Mass) E. Transport Boundary Equation (1,2,3 & 4) ka T =α (T T t) +ρa cp,a v T M. Transport Boundary Equation (1,2,3 & 4) β M p w v,a pv,t Dv Mw ρ D X u{ X = ( ) p R T T R T v v v,t t t Energy Transport Subdomain Equation T ρa c p,a = (ka T) ρa cp,a u T t Mass Transport Subdomain Equation X t = (Dv X) u123 X Additional convective terms due to air velocity Textile Domain a: Air u, v: Air velocity in the x and y direction α: Coefficient of heat transfer T. H.M. Zeineldin,

7 Modeling Approach Q=0 Transport phenomena Air (Energy/Mass) m=0 7 Boundary Equations (5) T = T 0 X = X 0 Boundary Equations (6) Textile Domain k a T = 0 D v X = 0 Convective flux Boundary Equations (7 & 8) ka T ρa cp, a u T = 0 D v X u X = 0 Insulation T 0,X 0 8 Q=0 m=0 T. H.M. Zeineldin,

8 Modeling Approach Transport phenomena Air (Momentum) 7 Boundary Equations (1,2,3,4,7 & 8) u = 0 No slip Boundary Equation (5) u = u 0 Fully developed flow Boundary Equation (6) p = p 0 Outflow 5 u Textile Domain T. H.M. Zeineldin,

9 Results and Validation Test bench Drum Temperature Sensor Heater Temperature Sensor Relative Humidity Sensor Cooling air Cond. Schematic of the test bench and sensor position T. H.M. Zeineldin,

10 Results and Validation Modeled phenomena: Energy transport - Textile Mass transport - Textile Temperatures measured at different positions Thermocouple Simulation conditions: 10x7mm thick layers of cotton textile 0.6 initial moisture content 2.9KW commercial condenser dryer as test bench 120 m 3 /hr volume flow rate Textile temperature measured for validation Temperature and vapor pressure measured at drum inlet as boundary conditions 1/3 Real-time Textile Measured textile temperature: 3 measurement series T. H.M. Zeineldin,

11 Results and Validation Simulation results 5 c max. temperature error Misplacement of the thermocouple (human error) Thermocouple temperature averaging affect Nonuniform textile geometry/surface Sensitivity of relative humidity sensors to water drops Temperature along the boundaries was held constant (Air flow was not simulated) Simulation results vs. measurements T. H.M. Zeineldin,

12 Results and Validation Model extension Modeled phenomena: Energy transport - Textile 17 times smaller than the original volume 1 2 Textile 3 Mass transport - Textile Energy transport - Air Mass transport - Air Momentum transport - Air Simulation conditions: 4x1mm thick layers of cotton textile 0.6 initial moisture content 120 m3/hr volume flow rate Temperature & vapor pressure given at drum inlet Reduced dimensions due to limited computer power Difference in temperature between inlet and boundaries. T. H.M. Zeineldin,

13 Results and Validation Model extension Simulation conditions: 0.1 sec integration step 1 2 Textile X,m vap X c X ms Ι ΙΙ ΙΙΙ Moisture content Ideal profile t T. H.M. Zeineldin,

14 Results and Validation Model B Sharp curves due to large integration steps Strong tendency to enhancement by decreasing the integration step Agreement with the ideal drying curves inlet inlet A A Model B Momentum transport Reduced size of the drum in order to meet the required mesh resolution Assumed laminar flow at the inlet Increase in velocity at lower cross sectional areas Velocity profile along the drum T. H.M. Zeineldin,

15 Summary and Conclusion Two successful models of stationary drying processes were built with COMSOL Multiphysics Successful application of governing equations in COMSOL Multiphysics despite nonlinearity Successful coupling of the five main drying transport phenomena Simulation results agreement with measurements Agreement with ideal drying curves Promising tendency for result enhancement with decreasing integration steps Using smaller thermocouples for future model validation Future opportunity of modeling the original geometry on increasing computer power T. H.M. Zeineldin,

16 Thank You for Your Attention Heinz Nixdorf Institut Universität Paderborn Regelungstechnik und Mechatronik Pohlweg Paderborn Tel.: / Fax.: / tarek.zeineldin@rtm.upb.de