July 10, 2008 / Vol. 6, No. 7 / CHINESE OPTICS LETTERS 513
Kinetic modeling of a high power fast-axial-flow CO
2
laser
with computational fluid dynamics method
Qing Li (
ooo
) and Youqing Wang (
qqq
)
National Engineering Research Center for Laser Processing, Institute of Optoelectronics Sciences and Engineering,
Huazhong University of Science and Technology, Wuhan 430074
Received November 7, 2007
A new computational fluid dynamics (CFD) method for the simulation of fast-axial-flow CO
2
laser is
developed. The model which is solved by CFD software uses a set of dynamic differential equations to
describe the dynamic process in one discharge tube. The velocity, temperature, pressure and turbulence
energy distributions in discharge passage are presented. There is a good agreement between the theoret-
ical prediction and the experimental results. This result indicates that the parameters of the laser have
significant effect on the flow distribution in the discharge passage. It is helpful to optimize the output of
high power CO
2
laser by mastering its kinetic characteristics.
OCIS codes: 000.4430, 140.3470.
doi: 10.3788/COL20080607.0513.
High power fast-axial-flow CO
2
lasers with convective
cooling have been extensively investigated experimen-
tally and theoretically
[1−9]
. It is continuing to be a
subject of research in purpose to modulate their oper-
ation. Particularly the characteristics of turbulent flow
of laser mixture in high-power industrial CO
2
laser have
an influence on energy parameters of laser beam. Grasps
of the overall kinetics of the discharge process can be re-
liably used to at least predict upper limits of the laser’s
performance
[2]
.
In order to describe and predict the laser mix-
ture’s dynamic characteristics, some numerical models
for the analysis of the fast-axial-flow CO
2
laser were
developed
[1−9]
. The much used approach to solve the
models of the fast flow gas discharge is based on simul-
taneous solution of the rate equations and gas dynamics
equations for the gas flow and light field in an optical
cavity. Many researchers made a lot of contributions in
this field. However, numerical solution of mathematical
model is not precise enough because the precision of those
calculating methods is limited. Computational fluid dy-
namics (CFD) method has become a powerful approach
to analyze the three-dimensional (3D) turbulent flow in
complicated domain
[10]
. CFD code used to solve the 3D
Reynolds-averaged Navier-Stokes equations in a rotating
cylindrical coordinate system for axial-flow pump can be
used for the numerical modeling of the gas flow in fast
flow CO
2
lasers.
The aim of this letter is to get a more accurate re-
sult to a 3D model of a 4-kW fast-axial-flow CO
2
laser
by the CFD method. The model is constructed by a self-
contained set of differential equations describing the flow
and heat transfer and diffusion. The FLUENT software
is chosen to solve the differential equations.
The following assumptions are used in the model:
1) Stimulated emission occurs only on transitions in
the band 001 → 100.
2) The gas flow velocity is homogeneously distributed
in the transverse to the flow direction, and the gas den-
sities are dependent only on the distance along the axis
of the discharge tube.
3) The gas properties such as temperature and pressure
in the discharge tube are constant in time, but a linear
function of the distance from the anode along the direc-
tion of flow.
4) The case is considered as a compressible flow and
3D geometry.
The computation grid is shown in Fig. 1. This laser is
a fast axial flow laser equipped with 12 discharge tubes.
The geometric model is a cylindrical discharge tube. The
grid represents one of the discharge tubes of the laser cav-
ity, whose size is about 320000 cells. The gas inlet and
outlet are modeled as round openings which are located
at each ends of the cylinder. We assume the laser cavity
is axisymmetric. This is not valid in the vicinity of inlets
and outlets but seems to be reasonable in the main part
of the laser cavity. Other boundary conditions include
the inlet static pressure, the total temperature, and the
outlet static pressure
[7]
.
The physical properties of the flow field are all the
function of spatio-temporal coordinates
[4]
. In the present
study, it is assumed that the active medium can be
treated as a compressible ideal gas. The flowing process
in discharge tube is described by the governing equations
as follows.
Continuity equation:
∂(ρu)
∂x
+
∂(ρv)
∂y
+
∂(ρw)
∂z
= 0. (1)
Fig. 1. A general view of the grid used in our computations
from the side of inlet.
1671-7694/2008/070513-04
c
2008 Chinese Optics Letters