Effect of Turbulence and Roughness on Coupled Porous-Medium/Free-Flow Exchange Processes

Transport in Porous Media

Volumn 114, Issue 2, 2016, Pages 395-424

  Fetzer, Thomas ^a   Smits, Kathleen M ^b   Helmig, Rainer ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

^b Department of Metallurgical and Materials Engineering   (United States)

Author keywords

Evaporation; Porous medium free flow interface; Roughness; Turbulence

Indexed keywords

ATMOSPHERIC THERMODYNAMICS; BOUNDARY LAYERS; EVAPORATION; POROUS MATERIALS; SENSITIVITY ANALYSIS; SURFACE ROUGHNESS; TURBULENCE; TURBULENCE MODELS; VISCOSITY;

BOUNDARY LAYER MODELS; EXCHANGE PROCESS; INTERFACE CONDITIONS; MODELING CONCEPTS; NON-ISOTHERMAL CONDITION; POROUS MEDIUM; POROUS MEDIUM FLOW; REYNOLDS AVERAGED;

FLOW OF FLUIDS;

EVAPORATION; POROUS MEDIUM; ROUGHNESS; SENSITIVITY ANALYSIS; TURBULENCE; TURBULENT FLOW;

EID: 84960085490     PISSN: 01693913     EISSN: 15731634     Source Type: Journal    
DOI: 10.1007/s11242-016-0654-6     Document Type: Article

References (74)

1. Arbogast, T., Pencheva, G., Wheeler, M.F., Yotov, I.: A multiscale mortar mixed finite element method. Multiscale Model. Simul. 6(1), 319–346 (2007). doi:10.1137/060662587
2. Assouline, S.: Modeling the relationship between soil bulk density and the water retention curve. Vadose Zone J. 5(2), 554–563 (2006). doi:10.2136/vzj2005.0083
3. Assouline, S., Narkis, K., Or, D.: Evaporation from partially covered water surfaces. Water Resour. Res. 46(W10), 539 (2010). doi:10.1029/2010WR009121
4. Baber, K., Mosthaf, K., Flemisch, B., Helmig, R., Müthing, S., Wohlmuth, B.: Numerical scheme for coupling two-phase compositional porous-media flow and one-phase compositional free flow. IMA J. Appl. Math. 77(6), 887–909 (2012). doi:10.1093/imamat/hxs048
5. Baldwin, B.S., Lomax, H.: Thin layer approximation and algebraic model for separated turbulent flows. AIAA J. 78–257, 1–9 (1978). doi:10.2514/6.1978-257
6. Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Kornhuber, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE. Computing 82(2–3), 121–138 (2008a). doi:10.1007/s00607-008-0004-9
7. Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework. Computing 82(2–3), 103–119 (2008b). doi:10.1007/s00607-008-0003-x
8. Beavers, G.S., Joseph, D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30(1), 197–207 (1967). doi:10.1017/S0022112067001375
9. Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena, 2nd edn. Wiley, New York (2007)
10. Breugem, W.P., Boersma, B.J.: Direct numerical simulations of turbulent flow over a permeable wall using a direct and a continuum approach. Phys. Fluids 17(2), 15 (2005). doi:10.1063/1.1835771
11. Cebeci, T.: Calculation of incompressible rough-wall boundary layer flows. AIAA J. 16(7), 730–735 (1978). doi:10.2514/3.7571
12. Chauhan, V.P., Stylianopoulos, T., Boucher, Y., Jain, R.K.: Delivery of molecular and nanoscale medicine to tumors: transport barriers and strategies. Ann. Rev. Chem. Biomol. Eng. 2, 281–298 (2011). doi:10.1146/annurev-chembioeng-061010-114300
13. Ciocca, F., Lunati, I., Parlange, M.B.: Effects of the water retention curve on evaporation from arid soils. Geophys. Res. Lett. 41, 3110–3116 (2014). doi:10.1002/2014GL059827
14. Colebrook, C.F.: Turbulent flow in pipes, with particular reference to the transition region between smooth and rough pipe laws. J. Inst. Civ. Eng. 11, 133–156 (1939). doi:10.1680/ijoti.1939.13150
15. Dahmen, W., Gotzen, T., Müller, S., Rom, M.: Numerical simulation of transpiration cooling through porous material. Int. J. Numer. Meth. Fluids 76(6), 331–365 (2014). doi:10.1002/fld.3935
16. Davarzani, H., Smits, K., Tolene, R.M., Illangasekare, T.: Study of the effect of wind speed on evaporation from soil through integrated modeling of the atmospheric boundary layer and shallow subsurface. Water Resour. Res. 50, 1–20 (2014). doi:10.1002/2013WR013952
17. de Lemos, M.J.S.: Turbulent flow around fluid–porous interfaces computed with a diffusion-jump model for k and ε transport equations. Transp. Porous Media 78, 331–346 (2009). doi:10.1007/s11242-009-9379-0
18. Defraeye T (2011) Convective heat and mass transfer at exterior building surfaces. PhD thesis, Katholieke Universiteit Leuven
19. Defraeye, T., Blocken, B., Carmeliet, J.: CFD analysis of convective heat transfer at the surfaces of a cube immersed in a turbulent boundary layer. Int. J. Heat Mass Transf. 53(1–3), 297–308 (2010). doi:10.1016/j.ijheatmasstransfer.2009.09.029
20. Deissler, R.G.: Analysis of turbulent heat transfer, mass transfer, and friction in smooth tubes at high Prandtl and Schmidt numbers. NACA Rep. 1210, 69–82 (1954)
21. Demmel, J.W., Eisenstat, S.C., Gilbert, J.R., Li, X.S., Liu, J.W.H.: A supernodal approach to sparse partial pivoting. SIAM J. Matrix Anal. Appl. 20(3), 720–755 (1999). doi:10.1137/S0895479895291765
22. Discacciati, M., Quarteroni, A.: Navier–Stokes/Darcy coupling: modeling, analysis, and numerical approximation. Revista Matemática Complutense 22(2), 315–426 (2009)
23. Fetzer, T.: Numerical analysis of the influence of turbulence on exchange processes between porous-medium and free flow. Diploma thesis, University of Stuttgart (2012)
24. Flemisch, B., Darcis, M., Erbertseder, K., Faigle, B., Lauser, A., Mosthaf, K., Müthing, S., Nuske, P., Tatomir, A., Wolff, M., Helmig, R.: DuMuX: DUNE for Multi- { Phase, Component, Scale, Physics, … } Flow and Transport in Porous Media. Adv. Water Resour. 34(9), 1102–1112 (2011). doi:10.1016/j.advwatres.2011.03.007
25. Fujimaki, H., Shimano, T., Inoue, M., Nakane, K.: Effect of a salt crust on evaporation from a bare saline soil. Vadose Zone J. 5(4), 1246–1256 (2006). doi:10.2136/vzj2005.0144
26. Haaland, S.E.: Simple and explicit formulas for the friction factor in turbulent pipe flow. J. Fluids Eng. 105(1), 89–90 (1983). doi:10.1115/1.3240948
27. Haghighi, E., Or, D.: Evaporation from porous surfaces into turbulent airflows: coupling eddy characteristics with pore scale vapor diffusion. Water Resour. Res. 49(12), 8432–8442 (2013). doi:10.1002/2012WR013324
28. Haghighi, E., Or, D.: Interactions of bluff-body obstacles with turbulent airflows affecting evaporative fluxes from porous surfaces. J. Hydrol. 530, 103–116 (2015). doi:10.1016/j.jhydrol.2015.09.048
29. Haghighi, E., Shahraeeni, E., Lehmann, P., Or, D.: Evaporation rates across a convective air boundary layer are dominated by diffusion. Water Resour. Res. 49(3), 1602–1610 (2013). doi:10.1002/wrcr.20166
30. Hahn, S., Je, J., Choi, H.: Direct numerical simulation of turbulent channel flow with permeable walls. J. Fluid Mech. 450, 259–285 (2002). doi:10.1017/S0022112001006437
31. Hanna, O.T., Sandell, O.C., Mazet, P.R.: Heat and mass transfer in turbulent flow under conditions of drag reduction. AIChE J. 27(4), 693–697 (1981). doi:10.1002/aic.690270424
32. Helmig, R.: Multiphase Flow and Transport Processes in the Subsurface: A Contribution to the Modeling of Hydrosystems. Springer, Berlin (1997)
33. Huber, R., Helmig, R.: Node-centered finite volume discretizations for the numerical simulation of multiphase flow in heterogeneous porous media. Comput. Geosci. 4, 141–164 (2000). doi:10.1023/A:1011559916309
34. Jambhekar, V.A., Helmig, R., Schröder, N., Shokri, N.: Free-Flow–Porous-Media Coupling for Evaporation-Driven Transport and Precipitation of Salt in Soil. Transp. Porous Media. 110, 251–280 (2015). doi:10.1007/s11242-015-0516-7
35. Johansen, O.: Thermal conductivity of soils. Ph.D. Thesis, (CRREL draft transl. 637, 1977), Norwegian University of Science and Technology, Trondheim, Norway (1975)
36. Krafczyk, M., Kucher, K., Wang, Y., Geier, M.: DNS/LES studies of turbulent flows based on the cumulant lattice boltzmann approach. In: Nagel, W.E., Kröner, D.H., Resch, M.M. (eds) High Performance Computing in Science and Engineering’14, Springer International Publishing, pp 519–531. doi:10.1007/978-3-319-10810-0_34 (2015)
37. Kuznetsov, A.V.: Numerical modeling of turbulent flow in a composite porous/fluid duct utilizing a two-layer k- ε model to account for interface roughness. Int. J. Therm. Sci. 43(11), 1047–1056 (2004). doi:10.1016/j.ijthermalsci.2004.02.011
38. Kuznetsov, A.V., Becker, S.M.: Effect of the interface roughness on turbulent convective heat transfer in a composite porous/fluid duct. Int. Commun. Heat Mass Transf. 31(1), 11–20 (2004). doi:10.1016/S0735-1933(03)00197-0
39. Laurindo, J.B., Prat, M.: Numerical and experimental network study of evaporation in capillary porous media. Drying rates. Chem. Eng. Sci. 53(12), 2257–2269 (1998). doi:10.1016/S0009-2509(97)00348-5
40. Lehmann, P., Assouline, S., Or, D.: Characteristic lengths affecting evaporative drying of porous media. Phys. Rev. E 77(5), 056,309 (2008). doi:10.1103/PhysRevE.77.056309
41. Millington, R., Quirk, J.: Permeability of porous solids. Trans. Faraday Soc. 57, 1200–1207 (1961). doi:10.1039/TF9615701200
42. Mosthaf, K., Baber, K., Flemisch, B., Helmig, R., Leijnse, A., Rybak, I., Wohlmuth, B.: A coupling concept for two-phase compositional porous-medium and single-phase compositional free flow. Water Resour. Res. 47(10), W10522 (2011). doi:10.1029/2011WR010685
43. Mosthaf, K., Helmig, R., Or, D.: Modeling and analysis of evaporation processes from porous media on the REV scale. Water Resour. Res. 50, 1059–1079 (2014). doi:10.1002/2013WR014442
44. Nield, D.: The Beavers–Joseph boundary condition and related matters: a historical and critical note. Transp Porous Med 78, 537–540 (2009). doi:10.1007/s11242-009-9344-y
45. Nuske, P., Joekar-Niasar, V., Helmig, R.: Non-equilibrium in multiphase multicomponent flow in porous media: an evaporation example. Int. J. Heat Mass Transf. 74, 128–142 (2014). doi:10.1016/j.ijheatmasstransfer.2014.03.011
46. Pedras, M.H., de Lemos, M.J.: Macroscopic turbulence modeling for incompressible flow through undeformable porous media. Int. J. Heat Mass Transf. 44(6), 1081–1093 (2001). doi:10.1016/S0017-9310(00)00202-7
47. Penman, H.L.: Natural evaporation from open water, bare soil and grass. Proc. R Soc. Lond. A Math. Phys. Eng. Sci. 193(1032), 120–145 (1948). doi:10.1098/rspa.1948.0037
48. Pope, S.B.: Turbulent Flows, 4th edn. Cambridge University Press, Cambridge (2006)
49. Rotta, J.C.: Turbulent boundary layers in incompressible flow. Progr. Aerosp. Sci. 2, 1–219 (1962). doi:10.1016/0376-0421(62)90014-3
50. Rybak, I., Magiera, J., Helmig, R., Rohde, C.: Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems. Comput. Geosci. 19(2), 299–309 (2015). doi:10.1007/s10596-015-9469-8
51. Saffman, P.: On the boundary condition at the surface of a porous medium. Stud. Appl. Math. L, 93–101 (1971). doi:10.1002/sapm197150293
52. Sahraoui, M., Kaviany, M.: Slip and no-slip velocity boundary conditions at interface of porous, plain media. Int. J. Heat Mass Transf. 35(4), 927–943 (1992). doi:10.1016/0017-9310(92)90258-T
53. Schlichting, H., Gersten, K.: Grenzschicht-Theorie, 9th edn. Springer, Berlin (1997)
54. Schneider-Zapp, K., Ippisch, O., Roth, K.: Numerical study of the evaporation process and parameter estimation analysis of an evaporation experiment. Hydrol. Earth Syst. Sci. 14(5), 765–781 (2010). doi:10.5194/hess-14-765-2010
55. Schwenck, N., Beck, M., Becker, B., Class, H., Fetzer, T., Flemisch, B., Grüninger, C., Hommel, J., Jambhekar, V., Kissinger, A., Koch, T., Schneider, M., Schröder, N., Seitz, G., Weishaupt, K.: DuMuX 2.8.0. doi:10.5281/zenodo.31611 (2015)
56. Shahraeeni, E., Or, D.: Thermo-evaporative fluxes from heterogeneous porous surfaces resolved by infrared thermography. Water Resour. Res. 46(9), W09,511 (2010). doi:10.1029/2009WR008455
57. Shahraeeni, E., Lehmann, P., Or, D.: Coupling of evaporative fluxes from drying porous surfaces with air boundary layer: characteristics of evaporation from discrete pores. Water Resour. Res. 48(9), W09525 (2012). doi:10.1029/2012WR011857
58. Shokri, N., Or, D.: What determines drying rates at the onset of diffusion controlled stage-2 evaporation from porous media? Water Resour. Res. (2011). doi:10.1029/2010WR010284
59. Shukla, J., Mintz, Y.: Influence of land-surface evapotranspiration on the earth’s climate. Science 215, 1498–1501 (1982). doi:10.1126/science.215.4539.1498
60. Smits, K.M., Sakaki, T., Limsuwat, A., Illangasekare, T.H.: Thermal conductivity of sands under varying moisture and porosity in drainage–wetting cycles. Vadose Zone J. 9(1), 172–180 (2010). doi:10.2136/vzj2009.0095
61. Smits, K.M., Cihan, A.C., Sakaki, T., Illangasekare, T.H.: Evaporation from soils under thermal boundary conditions: experimental and modeling investigation to compare equilibrium- and nonequilibrium-based approaches. Water Resour. Res. 47(5), W05540 (2011). doi:10.1029/2010WR009533
62. Sugita, F., Kishii, T.: Effect of roughness distribution on evaporation processes over non-homogeneous sand surfaces: a wind tunnel investigation. Hydrol. Process. 16(11), 2141–2153 (2002). doi:10.1002/hyp.1147
63. Suzuki, S., Maeda, S.: On the mechanism of drying of granular bed. J. Chem. Eng. Jpn. 1, 26–31 (1968). doi:10.1252/jcej.1.26
64. Trautz, A.C., Smits, K.M., Cihan, A.: Continuum-scale investigation of evaporation from bare soil under different boundary and initial conditions: An evaluation of nonequilibrium phase change. Water. Resour. Res. 51, 7630–7648 (2015). doi:10.1002/2014WR016504
65. Truckenbrodt, E.: Elementare Strömungsvorgänge dichteveränderlicher Fluide. In: Fluidmechanik, 4th edn, Klassiker der Technik, Springer, Berlin, pp. 1–111. doi:10.1007/978-3-540-79024-2_1 (2008)
66. van Brakel, J.: Advances in drying, vol 1, Hemisphere, Chap Mass transfer in convective drying, pp. 217–267 (1980)
67. van Driest, E.R.: On turbulent flow near a wall. AIAA J. 23(11), 1007–1011 (1956). doi:10.2514/8.3713
68. van Genuchten, M.T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44(5), 892–898 (1980). doi:10.2136/sssaj1980.03615995004400050002x
69. Vanderborght, J., Graf, A., Steenpass, C., Scharnagl, B., Prolingheuer, N., Herbst, M., Franssen, H.J.H., Vereecken, H.: Within-field variability of bare soil evaporation derived from eddy covariance measurements special section: patterns. Vadose Zone J. 9(4), 943–954 (2010). doi:10.2136/vzj2009.0159
70. Verboven, P., Flick, D., Nicolaï, B., Alvarez, G.: Modelling transport phenomena in refrigerated food bulks, packages and stacks: basics and advances. Int. J. Refrig 29(6), 985–997 (2006). doi:10.1016/j.ijrefrig.2005.12.010
71. White, F.M.: Fluid Mechanics, 7th edn. McGraw-Hill, Singapore (2011)
72. Wilcox, D.C.: Turbulence Modeling for CFD, 3rd edn. DCW Industries, La Cañada (2006)
73. Yiotis, A.G., Tsimpanogiannis, I.N., Stubos, A.K., Yortsos, Y.C.: Coupling between external and internal mass transfer during drying of a porous medium. Water Resour. Res. 43(W06403), 1–12 (2007). doi:10.1029/2006WR005558
74. Zhang, C., Li, L., Lockington, D.: A physically based surface resistance model for evaporation from bare soils. Water Resour. Res. 51, 1084–1111 (2015). doi:10.1002/2014WR015490