Numerical analysis of the influence of turbulence on the exchange processes between porous-medium and free flow

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1 Numerical analysis of the influence of turbulence on the exchange processes between porous-medium and free flow T. Fetzer Institut für Wasser- und Umweltsystemmodellierung Universität Stuttgart January 9, 213

2 Outline Motivation Why Turbulence? Model Concepts Results Summary and outlook

3 Motivation Mosthaf et al. - A coupling concept for two-phase compositional porous-medium and single-phase compositional flow

4 Motivation - Other applications Baber - Modeling the transfer of therapeutic agents from the vascular space to the tissue compartment You and Liu - A two-phase flow and transport model for PEM fuel cells

5 Motivation - Coupled Model Experimental setup (Navier-)Stokes wind channel Interface y =.75 m p = Pa MUSIS ū = 3.5 m /s Darcy soil Multi-Scale Interfaces in Unsaturated Soil x =.5 m

6 Motivation - Evaporation rate Stokes flow ] evaporation rate of water [ mm d time [d] experimental data Stokes

7 Why turbulence? - Free flow transport processes isothermal Stokes flow Stokes profile advection diffusion phase transition

8 Why turbulence? - Free flow transport processes isothermal Stokes flow non-isothermal turbulent flow turbulent mixing Stokes profile advection diffusion phase transition turbulent mean profile latent heat

9 Why turbulence? - Boundary layer theory outer layer laminar laminar boundary layer turbulent boundary layer turbulent log layer viscous sublayer

10 Model concepts - Reynolds decomposition Reynolds decomposition u = ū + u v ū v u u = ū + u v = v + v t t

11 Model concepts - Reynolds decomposition Reynolds decomposition u = ū + u Time averaging u = ū u v = }{{} ū v + }{{} u v advection turbulent diffusion closure problem v ū v ū u t u = ū + u v = v + v accelerated flow steady state flow t t min t max t

12 Model concepts - Reynolds decomposition Reynolds decomposition u = ū + u Time averaging u = ū u v = }{{} ū v + }{{} u v advection turbulent diffusion closure problem 1. Reynolds stress tensor 2. Eddy viscosity ϱv v = τ t ϱv v = µ t v v ū v ū u t u = ū + u v = v + v accelerated flow steady state flow t min t max t t

13 Models concepts - Algebraic eddy viscosity models µ g y/d [ ] µ t [ kg /m s] Prandtl s mixing length µ t = ϱκ 2 y 2 u y Prandtl

14 Models concepts - Algebraic eddy viscosity models µ g y/d [ ] µ t [ kg /m s] Prandtl s mixing length µ t = ϱκ 2 y 2 u y Prandtl Hanna et al.

15 Models concepts - Algebraic eddy viscosity models µ g y/d [ ] µ t [ kg /m s] Prandtl s mixing length µ t = ϱκ 2 y 2 u y Prandtl Hanna et al. Michel et al.

16 Models concepts - Algebraic eddy viscosity models µ g y/d [ ] µ t [ kg /m s] Prandtl s mixing length µ t = ϱκ 2 y 2 u y Prandtl Hanna et al. Michel et al.

17 Models concepts - Algebraic eddy viscosity models µ g y/d [ ] µ t [ kg /m s] Prandtl s mixing length µ t = ϱκ 2 y 2 u y Prandtl Hanna et al. Michel et al. Baldwin and Lomax

18 Models concepts - Algebraic eddy viscosity models µ g y/d [ ] µ t [ kg /m s] Prandtl s mixing length µ t = ϱκ 2 y 2 u y Prandtl Hanna et al. Michel et al. Baldwin and Lomax Deissler

19 Results - Evaporation rate eddy viscosity ] evaporation rate of water [ mm d time [d] experimental data Stokes Baldwin

20 Results - Evaporation rate eddy diffusivity ] evaporation rate of water [ mm d time [d] experimental data Stokes Baldwin Baldwin + Deissler

21 Results - Evaporation rate non-isothermal ] evaporation rate of water [ mm d time [d] experimental data Stokes Baldwin Baldwin + Deissler Baldwin + Deissler + ni

22 Results - Interpretation δ vs δ vs

23 Summary and outlook - Summary Transport behavior vertical transport in viscous sublayer is diffusion-limited advection near interface influences evaporation rate Comparison with experiment good agreement in beginning and end decreasing rate not captured Other results small effects of the surface roughness no grid convergence oscillating pressure

24 Summary and outlook - Outlook Presented model numerical problems more complex turbulence model REV description for the surface moisture pattern Field scale surface roughness heterogeneities gravity and buoyancy effects Beyond the evaporation application to other problems (fuel cells, etc.) PhD k-ω, staggered grid, DNS

25 Thank you for your attention.

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