Numerical Simulation of Film Flow over an Inclined Plate: Effects of Solvent Properties and Contact Angle Janine Carney and Rajesh Singh Multiphase Flow Science Workshop August 5-6, 214 Lakeview Golf Resort & Spa, Morgantown, WV
CFD Modeling of Solvent Absorption Motivation: efficiency of CO 2 absorption is closely related to local flow behavior Purified Gas Lean Solvent FLEXIPAC 1 Column 2 : Φ ~1m H ~3m Challenges: Intalox Ultra tm 1 layer height 2 : ~2cm Cannot model entire column focusing in on all physical phenomenon packing 3 : 25-8 mm Flue Gas corrugation height 2 : O(1mm)-O(1cm) Multi-scale approach required Suitable closure models for interphase interactions have not been developed Source 5 Rich Solvent film thickness 2 : ~ O(.1mm) to stripper Source 4 (1) Koch-Glitsch: http://www.koch-glitsch.com/default.aspx; (2) Raynal & Royon-Lebeaud, CES, 27; (3) Mackowiak, Fluid Dynamics of Packed Columns, Springer, 21; (4) Xu et al., Chem. Eng. Tech., 28; (5) Maiti et al., IECR, 26
Liquid Films Features depend upon various flow parameters and liquid properties Method: Volume of Fluid Simulations Current Goal: study the impact of solvent properties, contact angle, flow rates, inclination angle on hydrodynamics film thickness wetted area interfacial area flow regime Xu et al., Chem. Eng. Tech., 28
Volume of Fluid (VOF) 1 Multiphase Model Governing Equations Continuity and momentum equation of average phase u t = ( ρu ) + ( ρuu) = P + τ + ρg + F ρ + = ρgε G ρlε L µ = µ Gε G + µ Lε L Transport equation for volume fraction ε L t ε L + ε G + u ε =1 L = Stress : turbulence neglected τ = µ ( u + ( u) ) T Interfacial forces Force at interface resulting from surface tension Challenges preserving a sharp boundary between immiscible fluids computations of surface tension 1 Hirt & Nichols, J. Comput. Phys, 1981
Computation of Interfacial Force Surface tension force acts only at surface and is required to maintain equilibrium balances inward intermolecular attractive force with outward pressure gradient force minimizes free energy by decreasing area of interface Continuum surface force model Brackbill et al., J. Comput Phys., (1992): Force at surface expressed as volume force using divergence theorem ρκ ε G F = σ.5 ( ρ + ρ ) L G <= For two phase flow Surface curvature is computed from local gradients in the surface normal to the interface figure 1 Other techniques are available 2 Effects of wall adhesion at fluid interfaces in contact with boundaries is also estimated within the CSF model The contact angle that the fluid is assumed to make with the wall is used to adjust the surface normal in cells near the wall 1 Yuan, Y. and Lee, T. R., Contact Angle and Wetting Properties, in Surface Science Techniques, Bracco, G., and Holst B. (eds), 213. 2 Haroun et al., CES, 21
Liquid Film Down Inclined Plate z y Inlet: constant velocity (through plane) Outlet: pressure ( Pa) Plate: smooth wall (no slip) Sides: smooth walls (no slip) Top: pressure outlet ( Pa) x 1.5x1-6 Q in 1.5x1-5 kg/m 3.3 v in.3 m/s.3 We N 1.49 23.5 Re N 235 Base case Physical Properties Air Water Density ρ (kg/m 3 ) 1.185 997 Viscosity µ (Pa.s) 1.831x1-5.8899x1-3 Surface Tension σ (N/m) Static contact angle with air-steel γ ( ).728 7
Film flow Rivulets Computational Domain Fine mesh required to resolve rivulets 3D view showing mesh of domain higher mesh density near plate higher mesh density near center line Simulations conducted for pseudo-steady state t = 1 1-5 1 1-4 (Co=.5) Fails to correctly predict flow behavior Number of elements: 1.15M* (Literature: 1. 1.5M elements) Typical Run Times Case No of Cells Simulation time Wall Time No of Processor Coarse 5K 2s 24hrs 32 Fine 1 1.12M 2s 48 hrs 128 Fine 2 1.37M 2s 48 hrs 128
Snapshot of Interface (ε L =.5) Comparison with Experiments Impact of inertia on flow transition & wetted area 1 Specific Wetted Area AA nn = WWWWWWWWWWWW AAAAAAAA GGGGGGGGGGGGGGGGGGGGGG AAAAAAAA We=.2 We=.75 We=4.8.6 A n.4 We=.47 We=.76 We=1.1 Increasing We Present Study Exp-Hoffmann CFD-Hoffman (25) (26) CFD-Hoffman Exp-Hoffman (26) (25) WWWW llll = ρρ llvv llll 2 δδ llll σσ Droplet Rivulet Full Film.3.6.9 1.2 1.5 We Excellent Match with Experiments Hoffman et al., Trans IChemE, 26 and Hoffman et al., Comp. Chem. Eng. 25
Effect of Solvent Properties on Hydrodynamics Film thickness Kapitza Number only depends on fluid Wetted area properties ρρ ll Interfacial area Fixed for each solvent KKKK = σσ ll Independent of flow rate ggμμ ll 4 1 3 Low Ka high solvent viscosity Solvent µ l (Pa-s) ρ l (kg/m 3 ) σ l (N/m) Water.89 997..728 8.92578E-7 3969.4 3% MEA.252 113..548 2.48766E-6 749.71 26.7% AMP.27 995.8.431 2.71136E-6 533.65 4% MEA.371 115.3.55 3.64917E-6 45.42.75m MPZ.556 15.3.5442 5.53489E-6 258.27 48.8% MDEA.925 116.6.4756 9.9896E-6 116.6.51m MPZ.1336 946.41.3437 1.41165E-5 49.72.41m MPZ.2348 962.2.3589 2.4422E-5 24.62.31m MPZ.3642 981.31.384 3.71137E-5 14.77 ν l Ka Flow rate computation 3 3We Q = W sin g α µ l ρ σ l ρl Q l = liquid flow rate We = Weber number W = Width of plate ρ l = density of liquid ρ = ρ l ρ g µ l = viscosity of liquid σ l = surface tension of liquid g = gravitational acceleration.6
Film Thickness for Fully Wetted Plate Fixed Q = 1.53 1-5 m 3 /s To yield fully wetted plate Snapshot of liquid and gas distribution in the central xz-plane Longitudinal Plane Flow Solvent Plane P film Air Volume Fraction of Water δδ = Entrained area of Solvent in PP ffffffff Width ofplate
Film Thickness for Fully Wetted Plate δ decreases with increase Ka Impact of solvent properties 1.5 1.5 1 CFD Nusselt (1916) 1 δ (mm) δ (mm).5 Increasing viscosity 1 1 1 2 1 3 1 4 Ka Excellent agreement with Nusselt theory.5.1.3 Ka -1/4.4.5 Flow rate: δδ~ 11 KKKK 11/44 δδ~ QQ 11/33 KKKK 11/44
Film Thickness for Fully Wetted Plate Impact of contact angle γ < 9 γγ = 9 γ > 9 γ σ lv σ sv 1 figure σ sl Characteristics of solid- liquid system in specific environment Dictates the wetting behavior of solvent Film thickness unaffected by contact angle for fully wetted plate What about for partially wetted plate? δ (mm) 2 1.5 1.5 Two Contact Angles (γ= 7 and 4 ) γ= 7 o γ= 4 o Ka -.5.4.6 Ka -1/4 δδ~ 11 KKKK 11/44 1 Yuan, Y. and Lee, T. R., Contact Angle and Wetting Properties, in Surface Science Techniques, Bracco, G., and Holst B. (eds), 213.
Modified Setup for Rivulet Flow Inlet (4 2 mm 2 ) Fixed Q = 2 1-6 m 3 /sec Normalized Areas A n.15.1.5 Base Base Interface Interface Snapshot of Interface (ε L =.5) 1 1 1 2 1 3 1 4 Ka Water Ka=3969 3MEA Ka=749 48MDEA Ka=116 31MPZ Ka=15
Interfacial Area for Rivulet Flow Impact of inlet size and solvent property Interface at ε L =.5 for.31m MPZ (Ka=15) 4mm 1mm 2mm 25mm 4mm 4mm 4mm Developed width of rivulet remains constant at a fixed Q Developed width only depends on Q Slight increase in interfacial area is due to entrance effects A In decreases with increased Ka A Int 5.15.1.5 25 mm 2 mm 1 mm 4 mm 1 1 1 2 1 3 1 4 Ka
Interfacial Area for Rivulet Flow Impact of inlet size and solvent property 5 5.15 25 mm 2 mm 1 mm 4 mm.15 A Int.1.5 A Int.1.5 25 mm 2 mm 1 mm 4 mm 1 1 1 2 1 3 1 4 Ka AA IIII ~ 11 KKKK 11/22.1 Ka -.5.3 Flow rate: AA IIII ~ QQ 11/33 KKKK 11/22
Normalized Areas A n.5.4.3.1 Wetted/Interfacial Areas for Rivulet Flow Impact of contact angle For.31m MPZ (Ka=15) Base Interface Base Interface Normalized Interfacial Area x A In.5.4.3.1 For all solvents Ka= 15 Ka= 26 Ka= 52 Ka= 271 Ka= 783 Ka= 4164 3 4 5 6 7 8 θ Contact Angle Wettability decreases with increased γ Impact is greater on wetted area Leads to increase in δ with increased γ 3 4 5 6 7 8 Contact θ Angle
A In /A 7 Re-normalized Interfacial Areas for Rivulet Flow 2.5 2 1.5 1.5 AA = AA IIII AA 7777 A 7 = Interfacial area at γ = 7 Low σ Medium, High σ 3 4 5 6 7 8 γ Contact Angle Impact of contact angle ka= 15 Ka= 26 Ka= 52 Ka= 271 Ka= 783 Ka= 4164 Two regimes are evident for Low σ ( < 5 mn/m) Medium & High σ (>5 mn/m; 7 mn/m) Pioneering work of Zisman and coworkers 1 found 2 : For given solid, contact angle (γ) does not vary randomly with liquid The change of cos γ vs surface tension (σ) falls in a linear trend Lower values of σ corresponds to smaller γ 1 Yuan, Y. and Lee, T. R., Contact Angle and Wetting Properties, in Surface Science Techniques, Bracco, G., and Holst B. (eds), 213. 2W.A. Zisman, in Contact Angle, Wettability and Adhesion: Advances in Chemistry Series, vol. 43, ed. by R.F. Gould (ACS, Washington, 1964), p. 1
Interfacial Area for Rivulet Flow Impact of contact angle.5 Areas scale as.4 A ~ 1 ( 1 cosγ ) m A In.3 Low σ Medium, High σ Interfacial Area (A In ) m =.5 σ < 5mN/m =.33 5mN/m.1 Ka = 15 Ka = 783 Wetted Area (A n ) m =.6 σ < 5mN/m =.45 5mN/m 1 2 3 4 (1 - cosγ) -m
Interfacial Area for Rivulet Flow.5 Impact of Ka at various γ γ=3 o 5 Impact of Ka and γ.4 A In.3.1 γ=5 o γ=7 o γ=8 o A In (1-cosγ) -m.15.1.5 γ=3 o γ=5 o γ=7 o γ=8 o.1 Ka -1/2.3.1 Ka -1/2.3 AA IIII ~ 11 KKKK 11/22 Valid for all γ A In = C Ka 1 2 Q 1 3 ( 1 cosγ ) m
Summary & Conclusions Multiphase flow VOF simulations can be used to explore film flow down a plate Results presented in terms of the Kapitza number KKKK = σσ ll ρρ ll ggμμ ll 4 1 3 Scaling relations were obtained to describe impact of solvent properties and contact angle on interfacial area Full Film Flow: Film thickness decreases with increase Ka Rivulet Flow: Wetted/Interfacial areas decrease with increased Ka Wetted/Interfacial areas decrease with increased γ δδ~ QQ 1/3 KKKK 1/4 A = C Ka 1 2 Q 1 3 ( 1 cosγ ) m Work in progress Identifying critical We for flow regime transition Impact of varying inclination angle
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