생물필터내의 균일한 층 흐름 분포를 위한 수치해석

노창현, 장영미, 최호석

충남대학교 공과대학 화학공학과

Numerical simulation for uniform porous flow in biofilter

Chang-Hyun Rho, Young-Mi Jang, Ho-Suk Choi

Department of Chemical Engineering, Chungnam National University

Taejon, 305-764, Korea

Introduction

Biofiltration is an air pollution control technology in which microorganisms immobilized on organic/inorganic packing materials at an off-gas containing biodegradable volatile organic or inorganic compounds.1 Volatile organic compounds, emitted from a variety of industrial sources, are raising concerns about the consequential damage inflicted on ecological systems. It is also a potentially cost-effective alternative for the treatment of air streams with low concentrations of pollutants. It utilizes a microbial population immobilized in the biofilm grown on a solid support to degrade organic pollutants in waste gas streams. Under proper conditions biofilters can offer a high removal efficiency through a process that is environmentally friendly.

On the other hand, the advances in computational fluid dynamics(CFD) over the recent years and the rise of computing power allow one to solve the governing equations of fluid dynamics for the complex geometry. They are particularly suitable for design and scale up studies.

In the present work, we used the Fluent software(CFD code) to solve the flow distribution at the porous zones in a biofilter. And, we tried to find out the optimum design of air distributor for the uniform air flow in a biofilter bed.

Mathematical Model and Simulation Methods

The porous media model can be used for a wide variety of problems including flows through packed beds, filter paper, perforated plates, and tube banks.

The conservation equations2 can be written as follows:

Continuity :

[eqn: { □C} over {□t } + { □} over {□x_i } (`rho u_i`)`=`S_m]                      (1)

Momentum :

[eqn: { □} over {□t }`+` { □} over {□x_i }( rho u_i`u_j`)`=`- { □p} over {□x_i` }`+` { □ tau_ij` } over {□x_j }`+` rho g_i`+`S_i]         (2)

where, [eqn: p] : static pressure

[eqn: tau_ij] : stress tensor

[eqn: rho g_i] : gravitational body force

The stress tensor [eqn: tau_ij] is given by [eqn: tau _ij`=`[ mu ( { □u_i} over {□x_j } + { □u_j} over {□x_i })]`-` { 2} over {3 } mu { □u_l} over {□x_l } delta _ij].

where [eqn: mu] is the molecular viscosity and the second term on the right hand side is the effect of volume dilation.

For porous media, Eq.(2) is modified by the addition of a momentum source term to the standard fluid flow equations. The source term is composed of two parts, a viscous loss term(Darcy), and a inertial loss term.

[eqn: S_i`=` SUM from { {j }=1} to 3 D_ij` mu v_j`+` SUM from { { j}=1} to 3 C_ij { 1} over {2 }|`v_j`|v_j]                  (3)

where [eqn: S_i] is the source term for the [eqn: i]th(x, y, or z) momentum equation, and D and C are prescribed metrics. This momentum sink contributes to the pressure gradient in the porous cell, creating a pressure drop that is proportional to the fluid velocity(or velocity squared) in the cell.

To recover the case of simple homogeneous porous media,

[eqn: S_i`=` { mu } over { alpha } v_i`+C_2` { 1} over {2 } rho |v_i`|v_i]                      (4)

where [eqn: alpha] is the permeability and [eqn: C_2] is the inertial resistance factor, simply specify D and C as diagonal matrices with [eqn: 1/ alpha] and [eqn: C_2], respectively, on the diagonals (and zero for the other elements).

Energy :

[eqn: {{ □} over {□t }( phi rho _f`h_f`+(1- phi ) rho_s`h_s`)}`+` {{ □} over {□x_i}( rho _f`u_i`h_f `)}}= {{ □} over {□x_i }(k_eff` { □T} over {□x_i })`-`}]

[eqn: {phi { □} over {□x_i } SUM from { { j'}}h_{j^'}J_{j^'}}`+` phi { Dp} over {Dt}`+` phi tau _{ik} {□u-_i} over {□x-_k }`+` phi {S^h`_f}`+`(1- phi )S^h`_s`}]    (5)

where

[eqn: h_f] : fluid enthalpy ([eqn: INT c_{p,f}`dT])

[eqn: h_s] : solid medium enthalpy ([eqn: INT c_{p,s}`dT])

[eqn: phi] : porosity of the medium

[eqn: k_eff] : effective thermal conductivity of the medium

[eqn: S^h`_f] : fluid enthalpy source term

[eqn: S^h`_s] : solid enthalpy source term.

In the porous medium, the conduction flux uses an effective conductivity and the transient term includes the thermal inertial of the solid region on the medium.

The effective thermal conductivity([eqn: k_eff]) in the porous medium can be written as follows :

[eqn: k_eff`=` phi k_f`+`(1- phi )k_s]                     (6)

where

[eqn: phi] : porosity of the medium

[eqn: k_f] : fluid phase thermal conductivity

[eqn: k_s] : solid medium thermal conductivity.

The commercial software package Fluent V5.2 is used in order to calculate the flow pattern in biofilter. The two-dimensional laminar flow field is numerically simulated by a finite volume method on a body-fitted coordinate grid. The continuity, momentum, and energy conservation equations are solved for an incompressible fluid. In this work, the laminar model is used to calculate the flow pattern. This model is the most widely tested and the results are generally considered reliable with a low calculation time.

Results

The simulations were performed for a 3m×2m in biofilter. The diameter of inlet and outlet is 10cm. The biofilter has 1m height with the porous section which is located at the middle part of biofilter. The inlet gas superficial velocity was 15m/s. Boundary condition of the outlet was 0 pascal. Distribution effects have been shown to effect the overall flow pattern in the biofilter. However, in the present simulations, distribution effects have been ignored and the distribution plate has been modeled as a uniform surface source. The numerical simulation was performed on a quadrilateral grid. Eqs.(1),(2),(6) were solved in a transient fashion with a time step of 0.01s. Fig. 1 and Fig. 3 represent a velocity plot of the simulated flow profile. From the simulation results, we can see that the flow in the porous zone is uniform at the distributor with about 5°angle.

Conclusion

Using Fluent software, we knew the angle of distributor section for the uniform flow distribution in the biofilter bed. With this result, we can design an optimum structure of distributor.

References

1. Md. Amanullah, S. Farooq, and Shekar Viswanathan., 1999, Modeling and

Simulation of a Biofilter. Ind. Eng. Chem. Res. 38, 2765-2774

2. Fluent Incorporated, Fluent User's Guide, Volume 1, 6-103

Fig.1 The velocity profile in biofilter   Fig.2 The velocity of distribution plate

Fig.3 The velocity profile in biofilter   Fig.4 The velocity of distribution plate        with angle