Numerical simulation of heat and mass transfer in direct membrane distillation in a hollow fiber module with laminar flow

Numerical simulation of heat and mass transfer in direct membrane distillation in a hollow fiber module with laminar flow

This is the Accepted version of the following publication

Yu, Hui, Yang, Xing, Wang, Rong and Fane, Anthony G (2011) Numerical simulation of heat and mass transfer in direct membrane distillation in a hollow fiber module with laminar flow. Journal of Membrane Science, 384 (1-2). pp.

107-116. ISSN 0376-7388

The publisher’s official version can be found at

http://www.sciencedirect.com/science/article/pii/S037673881100682X

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Downloaded from VU Research Repository https://vuir.vu.edu.au/25291/

Material Density kg/m³

Specific heat J/(kg·K)

Thermal conductivity W/(m·K)

PVDF[23] 1775 1325 0.2622

Vapor^* 0.554 2014 0.0261

Membrane 302.2 1896.9 0.0662

Table 1. Properties of the PVDF membrane

Material Density kg/m³

Specific heat J/(kg·K)

Thermal conductivity w/(m·K)

Viscosity

×10^-4 Pa·s 3.5% synthetic

seawater(~323K) [24]

1013.2 4064.8 0.642 5.86

Pure water(~303K)

[25] 995.2 4182.1 0.613 8.38

Table 2. Properties of the fluids

Table 3. PVDF membrane characterization and module specifications

Membrane properties Material Dimension Contact angle

(°)

Porosity ε (%)

LEPw (Bar)

Tensile modulus E_t ,MPa

Strain at break δ_b, % PVDF R_mo: 1.45 mm

δ_m: 275 μm 105±1 85 1.38 44.60 98.60

Module specifications

Housing diameter, d_s, mm No. of fibers, n Effective fiber length L, m

9.5 1 0.25~1.02

L (m) T_fi (K) T_fo (K) Error (%) T_pi (K) T_po (K) Error (%)

0.25 Exp. 327.2 325.7 - 294.0 301.4 -

Sim. - 325.9 0.0614 300.9 -0.166

0.34 Exp. 327.2 325.2 - 293.5 302.8 -

Sim. - 325.4 0.0615 302.5 -0.0991

0.54 Exp. 327.2 324.8 - 294.0 306.0 -

Sim. 324.6 -0.0616 306.6 0.196

0.64 Exp. 327.2 324.2 - 294.0 306.3 -

Sim. - 324.1 -0.0308 308.6 0.848

0.74 Exp. 327.2 323.7 - 294.7 307.8 -

Sim. - 323.7 0.00 310.6 0.910

0.84 Exp. 327.2 322.7 - 293.7 310.0 -

Sim. 323.3 0.185 311.4 0.452

1.02 Exp. 327.2 322.0 - 294.0 312.1 -

Sim. - 322.6 0.186 313.9 0.577

Table. 4. The temperature comparison of experimental data and simulation results (Re_f=836, Re_p= 460)

x

r 0

T

_fm

T

_f

T

_pm

T

_p

Feed Membrane

Permeate

N

_m

q

_MD

Shell wall

R

_mi

R

_mo

Fig. 1. Schematic diagram of heat & mass transfers

Fig. 2 CFD domain & meshes of the single-fiber module in a 2D model

Fig. 3. Temperature distribution inside the module (Re_f=836, T_fi = 327.2 K, Re_p= 460, T_pi = 294.0 K)

Fig. 4. q_f & ΔT_f distributions along the dimensionless module length x/L (Re_f=836, T_fi = 327.2 K, Re_p= 460, T_pi = 294.0 K )

0.0 0.2 0.4 0.6 0.8 1.0

3500 4000 4500 5000 5500 6000 6500 7000 7500

q f (W·m-2 )

x / L

qf

L = 0.25m L = 0.34m L = 0.84m L = 1.02m

2 4 6 8 10

T f =T f -T fm (K)

T

f

Fig. 5. q_p & ΔT_p distributions on the membrane surface along the dimensionless module length x/L (Re_f=836, T_fi = 327.2 K, Re_p= 460, T_pi = 294.0 K)

0.0 0.2 0.4 0.6 0.8 1.0

6000 7000 8000 9000 10000 11000 12000

q p / W·m-2

x / L qp

L = 0.25m L = 0.34m L = 0.84m L = 1.02m

2 4 6 8 10

T

p

T p = T pm-T p / K

0.0 0.2 0.4 0.6 0.8 1.0 4

6 8 10 12 14 16 18 20 22 24 26 28 30

Nu

x / L

Nuf Nu

p

L = 0.25m L = 0.34m L = 0.84m L = 1.02m

Fig. 6. Distribution of Nu along the dimensionless x distance (Re_f=836, T_fi = 327.2 K, Re_p= 460, T_pi = 294.0 K)

Fig. 7. Nu_f & Nu_p distributions along the module length at different Re_p (L=0.25m, Re_f=836, T_fi = 327.2 K, Re_p= 200~2000, T_pi = 294.0 K)

0.0 0.2 0.4 0.6 0.8 1.0

4 6 8 10 12 14 16 18 20 22 24 26 28 30

Nu

x / L Nuf , Nu

p , Re

f=836, Re

p=200

Nuf , Nu

p , Re

f=836, Re

p=460

Nuf , Nu

p , Re

f=836, Re

p=1000 Nuf , Nu

p , Re

f=836, Re

p=2000

Fig. 8. Nu_f & Nu_p distributions along the module length at different Re_f (L=0.25m, Re_f=500~2000, T_fi = 327.2 K, Re_p= 460, T_pi = 294.0 K)

0.0 0.2 0.4 0.6 0.8 1.0

0 10 20 30 40

Nu_f , Nu_p , Re_f=500, Re_p=460 Nu_f , Nu_p , Re_f=836, Re_p=460 Nu_f , Nu_p , Re_f=1000, Re_p=460 Nuf , Nu

p , Re_f=2000, Re_p=460

Nu

x / L

0.0 0.2 0.4 0.6 0.8 1.0 1000

2000 3000 4000 5000 6000

h (W·m-2 ·K-1 )

x / L hf

hp

Fig. 9. h_f & h_p distributions along the module length at constant flow conditions (L=0.25m, Re_f= 836, T_fi = 327.2 K, Re_p=460, T_pi = 294.0 K)

0.0 0.2 0.4 0.6 0.8 1.0 0.60

0.65 0.70 0.75 0.80

TPC

x / L TPC

L = 0.25m L = 0.34m L = 0.84m L = 1.02m

Fig. 10. TPC distributions along the dimensionless module length x/L (Re_f= 836, T_fi = 327.2 K, Re_p=460, T_pi = 294.0 K)

0.0 0.2 0.4 0.6 0.8 1.0 0.0011

0.0012 0.0013 0.0014 0.0015 0.0016 0.0017 0.0018 0.0019

N m / kg·m-2 ·s-1

x / L

L = 0.25m L = 0.34m L = 0.84m L = 1.02m

Fig. 11. Distributions of local mass fluxes along the dimensionless x/L distance (Re_f= 836, T_fi = 327.2 K, Re_p=460, T_pi = 294.0 K)

0.0 0.2 0.4 0.6 0.8 1.0 0.0015

0.0016 0.0017 0.0018 0.0019 0.0020 0.0021 0.0022 0.0023

Re_f=836, Re_p=200 Re_f=836, Re_p=460 Re_f=836, Re_p=1000 Re_f=836, Re_p=2000 Re_f=500, Re_p=460 Re_f=1000, Re_p=460 Ref=2000, Re

p=460

Ref=2000, Re

p=200

Re_f=2000, Re_p=2000

N m (kg.m-2 .s-1 )

x / L

Fig. 12. Distributions of local N_m along the dimensionless module length x/L (L=0.25m, Re_f=500~2000, T_fi = 327.2 K, Re_p= 200~2000, T_pi = 294.0 K)

0.0 0.2 0.4 0.6 0.8 1.0 0.40

0.42 0.44 0.46 0.48 0.50 0.52

0.54 Re

f=836, Re

p=200

Ref=836, Re

p=460

Re_f=836, Re_p=1000 Re_f=836, Re_p=2000 Re_f=500, Re_p=460 Re_f=1000, Re_p=460 Re_f=2000, Re_p=460 Re_f=2000, Re_p=200 Re_f=2000, Re_p=2000

 h

x / L

Fig. 13. Distributions of η_h along the dimensionless x/L distance (L=0.25m, Re_f=500~2000, T_fi = 327.2 K, Re_p= 200~2000, T_pi = 294.0 K)