8/6/2019 Fluid Flow in Cylindrical Channel Filled With Porous Medium (Need Corrected Proof)

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D r a f t : r e q u i r e d

c o r r e

c t e d p r

o o f

D r a f t : r e q u i r e d

c o r r e

c t e d p r

o o f

[Fluid flow in cylindrical channel filled with porous medium ] MOTA group (2011)

The incompressible fluid flow in cylindrical channel filled with porous medium is numerically investigated. The porous medium ismade of packed bed of spherical particles (d p=20mm) inserted directly at the center of the model. The inflow velocity is assumed to be fully-developed. The Navier-Stokes equation is employed for conventional pipe flow region (A and C), whereas the porous region (B) is solvednumerically using Brinkman equation (1947) . The out flow section is assumed to be neglecting in normal stress, in which resulting in zero

pressure at the outlet of pipe. It must be noted that employing this boundary condition show no significant different in pressure drop as comparedto the case of ambient pressure at the outlet. The channel wall boundaries are assumed to be smooth pipe with no-slip condition. The advancenumerical technique is applied to solve the corresponding momentum equation to find the influence of Reynolds number and porosity on velocityand pressure. The schematic diagram of the model is illustrated in Fig. 1.

Fig. 1 the schematic diagram of the model

Model validation

The pressure drop in porous medium obtain from the model iscompared with the Ergun equation (1952) as illustrated in Fig. 4,and the discrepancy between those two is less than five percent.This proof that that the numerical model presented in this work isefficient to predict the fluid flow phenomena in the channel filledwith porous medium.

The velocity field

As illustrated in Fig. 3, he presence of porous medium at the center of the channel laminarizes the fully-developed flow, and change itsvelocity profile to become relatively low uniform flow. However,

the flow begins to develop again after pass the porous region.

Effect of Reynolds number

The influence of Reynolds number on pressure distribution isshown in Fig 4. As expect, with increasing in Reynolds number,the pressure drop in porous region is dramatically increased.

Effect of porosity

As illustrated in Fig 5, the uniformed effect of porous medium onvelocity profiles is gradually vanished by the increasing in

porosity.

Fig 2 Velocity contour with (Left) no porous, (Center) porosity =0.4, and (Right) porosity = 0.8

Reynolds number, Re D

0 50 100 150 200 250 300 350 400 450

P r e s s u r e

d r o p ,

P

0.0

.5

1.0

1.5

2.0

2.5

3.0

Ergun, S. (1952)This model

=0.4, d p = 20mm

Tf = 30oC

Ergun Equation:

Fig. 2 Model validation

Distance, x (m)

0 .0 0 .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65

P r e s s u r e

( P a

)

0.0

.5

1.0

1.5

2.0

2.5

3.0

Re D=25

Re D=50

Re D=100

Re D=200

Re D=300

Re D=400

=0.4, d p = 20mm

Tf = 30oC

Porous Medium

Fig. 4 Effect of Re D on pressure distribution in the model

Distance, x (m)

0 .00 .05 . 10 .15 . 20 .25 . 30 .35 . 40 .45 .50 . 55 . 60 . 65

C e n

t e r l i n e

V e l o c i t y ,

V m a x

( m / s )

.02

.03

.04

.05

.06

Re = 100, d p = 20mmTf = 30 oC Porous Medium

Fig. 4 Effect of porosity on velocity distribution in the model