(a)original module. Fig. 1. Schematic of axially-symmetry single fiber modules in CFD simulating domains

Transcription

1 (a) (b) Module with spacers (c) Amplified local domains for dimension specification (d) Module with baffles (e) Module with alternate spacers and baffles Fig. 1. Schematic of axially-symmetry single fiber modules in CFD simulating domains

2 Fig. 2. Local heat-transfer coefficients distributions along the module length under various operating conditions (T fi = & K, T pi = & K, u fi =0.06 m s -1, u pi =0.417m s -1, C = 2.0& kg m -2 s -1 Pa -1 ) local resistance 10-4 /m 2 K W -1 local resistance 10-4 /m 2 K W C= kg m-2 s-1 Pa-1 T fi =327.15K, T pi =293.85K Fiber length/ m (a) Small C, low temperature T C= kg m-2 s-1 Pa-1 T fi =360.15K, T pi =326.85K (c) Small C, high temperature T 1/hf 1/hp 1/hm Fiber length/ m 1/hf 1/hp 1/hm local resistance 10-4 /m 2 K W local resistance 10-4 /m 2 K W C= kg m-2 s-1 Pa-1 T fi =327.15K, T pi =293.85K 1/hf 1/hp 1/hm Fiber length/ m (b) Large C, low temperature T C= kg m-2 s-1 Pa-1 T fi =360.15K, T pi =326.85K Fiber length/ m (d) Large C, high temperature T 1/hf 1/hp 1/hm

3 h f /(W.m -2.K -1 ) h p /(W.m -2.K -1 ) (a) h f distributions vs. module length L (b) h p distributions vs. module length L Fig. 3. h f &h p distributions along the fiber length for various turbulence promoters (C= kg m -2 s -1 Pa -1, L=0.25m, u fi =0.06 m s -1, u pi =0.417m s -1, T fi = K, T pi = K)

4 TPC no spacer quadspacer quadspacer quadspacer quadspacer quadspacer quadspacer floating quadspacer roundspacer0.5 floating roundspacer baffle baffle+spacer Fig. 4. TPC distribution along the fiber length for modules with turbulence aids of various specification (C = kg m -2 s -1 Pa -1, L=0.25m, u fi =0.06 m s -1, u pi =0.417m s -1, T fi = K, T pi = K)

5 (a) Round spacers annular spacers with circular cross-section r=0.5mm, Lx=10mm r=0.75mm, Ly=0.5mm (b) Quad spacers annular spacers with square cross-section x y Lx Ly= mm x y Lx Ly= mm x y Lx Ly= mm (c) Floating quad spacers and/or baffles (c) Floating quad spacers and/or baffles x y Lx Ly= mm x y Lx= mm, baffles x y Lx= mm, baffles+spacers Fig. 5. Local flow field visualization for modules with various turbulence promoters ( C = kg m -2 s -1 Pa -1, L=0.25m, u fi =0.06 m s -1, u pi =0.417m s -1, T fi = K, T pi = K)

6 0.009 no spacer floating roundspacer0.75 quadspacer quadspacer quadspacer baffle roundspacer0.5 quadspacer quadspacer quadspacer floating quadspacer baffle+spacer Fig. 6. Mass flux N m distribution along the fiber length for modules with turbulence aids of various specification (C = kg m -2 s -1 Pa -1, L=0.25m, u fi =0.06 m s -1, u pi =0.417m s -1, T fi = K, T pi = K)

7 0.90 no spacer floating roundspacer0.75 spacers+baffles round spacer0.5 quad spacer baffle η h Fig. 7. η h distribution along the module length for modules with various turbulence promoters (C = kg m -2 s -1 Pa -1, L=0.25m, u fi =0.06 m s -1, u pi =0.417m s -1, T fi = K, T pi = K)

8 h f /(W.m -2.K -1 ) h f /(W.m -2.K -1 ) (a) C= kg m -2 s-1 Pa-1 (b) C= kg m-2 s-1 Pa-1 Fig. 8. Effects of turbulence promoters on h f distributions along the fiber length at high temperatures for membranes with different C values (L=0.25m, T fi = K, T pi = K, u fi =0.06 m s -1, u pi =0.417m s -1 )

9 TPC TPC (a) C= kg m-2 s-1 Pa-1 (b) C= kg m-2 s-1 Pa-1 Fig. 9. Effect of turbulence promoters on TPC distributions along the fiber length at high temperatures for membranes with different C values (L=0.25m, T fi = K, T pi = K, u fi =0.06 m s -1, u pi =0.417m s -1 )

10 N m /kg.m -2.s no spacer quadspacers quadspacers floating roundspacers0.75 baffles N m /kg.m -2.s no spacer quadspacers quadspacers floating roundspacers0.75 baffles (a) C= kg m -2 s-1 Pa-1 (b) C= kg m-2 s-1 Pa-1 Fig. 10. Effect of turbulence promoters on N m distributions along the fiber length at high temperatures for membranes with different C values (L=0.25m, T fi = K, T pi = K, u fi =0.06 m s -1, u pi =0.417m s -1 )

11 TPC Thermal efficiency η h Operating temperature T f,in Potential selected-system C / X10-7 kg m -2 Pa Operating temperature T f,in C / X10-7 kg m -2 Pa -1 (a) C&T vs. TPC (b) C&T vs. η h Fig. 11. Effects of C values and operating temperatures on the TPC and thermal efficiency for the original module (C = kg m -2 s -1 Pa -1, L=0.25m, u fi =0.06 m s -1, u pi =0.417m s -1, T fi = K, T pi = K)

12 TPC Turbulence Laminar Turbulence Laminar C= kg m-2 s-1 Pa-1 C= kg m-2 s-1 Pa-1 N m /kg.m -2.s Turbulence Laminar Turbulence Laminar C= kg m-2 s-1 Pa-1 C= kg m-2 s-1 Pa-1 C= kg m-2 s-1 Pa-1 (a) TPC distributions vs. module length L (b) N m distributions vs. module length L Fig. 12. Effects of flow velocity on TPC and N m distributions along the fiber length for unaltered modules with different C values (C=2 & kg m -2 s -1 Pa -1, L=0.25m, Re f =836, 2500 & 4000, T fi = K, Re p = 460, T pi = K)

13 HEC/ J kg Hydraulic loss Unaltered module Re f =2500, u fi =0.178 m s -1 vapor flux B FQ Q+B N m /Kg.m -2.h Q Q Q FR Re f =836, u fi =0.06 m s -1 Unaltered module Q Q Turbulence promoters Fig. 13. Hydraulic loss and vapor flux comparisons for various turbulence promoters [C = kg m -2 s -1 Pa -1, L=0.25m, u fi =0.06 m s -1 for all modified modules and u fi =0.06 & m s -1 for the original module, u pi =0.417m s -1 (Re p = 460), T fi = K, T pi = K, Q=quad spacer, FR=floating round spacer, B=baffle, FQ=floating quad spacer, Q+B=quad spacer + baffle]

14 Table. 1. specification of various turbulence promoters Insertion type Spacer Baffle Δx / Δy / Lx / Ly / Δx / Δy / Lx / mm mm mm mm mm mm mm 1 No spacer Original Round Attached round spacer 0.5 r= spacer Floating round spacer 0.75 r= Quad spacer Quad spacer Quad spacer Quad spacer 7 Quad spacer Quad spacer Floating quad spacer Baffle Baffle 11 Alternate spacer + baffle Note: 1. quad spacer indicates an annular spacers with quad cross section; while a round spacer means an annular spacer with circular cross section; For instance, a modified module named quad spacer indicates a total number of 24 regularly distanced quad spacers, Δx is 0.2 mm, Δy is 1.0 mm, the interval Lx is 10 mm and Ly 0 mm (attached spacer) 2. Δx and Δy are the dimensions of the annular baffle in x and r directions, respectively; Lx is the interval between two spacers or baffles, Ly is the vertical gap between the spacers and the membrane outer surface.

15 Table. 2. Summary of CFD mathematical models, boundary conditions and algorithms Governing transport equations Continuity equation =0 (1) p h = p g Momentum transport equation* (2) Energy conservation equation c T = kt S (3) Boundary conditions Entrance of fluids (feed/ permeate)** Exits of fluids (feed/permeate) Membrane wall Pressure-velocity coupling Conservation equation discretization u fi = m s -1, u pi =0.417m s -1, T fi = K, T pi = K outlet pressure is 0.0 Pa (gauge pressure) no-slip condition, conjugate heat conduction: qf q rr m r R mo Tf T rr m r R mo mo mo Solution algorithms SIMPLE (Semi-Implicit Method for Pressure Linked Equations) QUICK (Quadratic Upstream Interpolation for Convective Kinetics) q m rr mi mi q p rr Tp T rr m r R mi mi *The momentum equation here only involves the motion in fluids, not the penetration through the membrane matrix. no-slip condition and no molecular transport across the membrane is applied in this model; ** typical experimental values

16 Table. 3. Summary of heat-transfer equations and definitions in MD [32] * Heat transfer rate Q ** Q Qf Qp QMD QHL (4) Latent heat flux q MD qmd Nm HT hmd Tfm Tpm = C P (5) Rmo K h h h R Overall heat-transfer coefficient, K [43] (6) f m p mi q f Local heat-transfer coefficient of the feed h f hf (7) Tf Tfm qp Local heat-transfer coefficient of the permeate h hp p (8) T T Equivalent heat-transfer coefficient of the membrane km R lm 1 h h [34] m CP HT (9) fm m b Rmo Tfm Tpm QMD hmd MD thermal efficiency η [33] h h QMD Q R HL lm (10) hmd hhl R Temperature-polarization coefficient (TPC) [45] (11) Hydraulic energy consumption (HEC) (12) pm T TPC T HEC fm f P N p T T fluid m pm p fm V A mo *The MD related mass- and heat-transfer equations here only involves in the CFD data postprocessing; **The heat-transfer rate Q=q A

17 Table. 4. Heat-transfer model verification--comparison of experimental data and simulation results (C = kg m -2 s -1 Pa -1, L=0.25 m, T fi =327 K, T pi =294 K) Temperature verification Conditions T fi (K) T pi (K) Exp. Mass flux (kg m -2 s -1 ) Sim. Error (%) (u pi =0.417 m s -1 ) Modified modules (u fi =0.06m s -1, u pi =0.417m s -1 ) u fi =0.107m s u fi =0.178m s Q Q Conditions (u fi =0.06m s -1, u pi =0.417m s -1 ) Modified modules (u fi =0.06m s -1, u pi =0.417m s -1 ) Pressure-drop verification (shell side) Exp. P f (Pa) Sim. Error (%) Q Q