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Design and Performance Evaluation of a Supersonic Nozzle used for Laser Cutting of
Thick Carbon Steel
M. Sundar1, A. K. Nath2, D.K. Bandyopadhyay1, S.P. Chaudhuri1, P.K. Dey1, D. Misra1, B.T.Rao2
1School of Laser Science & Engineering, Jadavpur University, Kolkata-700032, India
2Industrial CO2 Laser, RRCAT, Indore, India
ABSTRACT Laser cutting of mild steel has been widely used in the manufacturing industries for
many decades because of its accuracy and efficiency. The present work deals with design of a
supersonic nozzle for laser cutting of thick carbon steel by a sub 1 kW laser system utilizing
the heat generated from the oxidation process. In this case, most of the power required for
cutting operation is contributed by the exothermic reaction and laser is used only for heating
the material to facilitate oxidation. The critical part in the proposed approach is the design of a
suitable supersonic nozzle, which is discussed in this paper. An axi-symmetric, straight small
supersonic nozzle has been designed. The nozzle profile is designed on the basis of Method
of Characteristics (MOC) and its performance has been evaluated and compared with results
obtained from FLUENT. The distribution of pressure, velocity and gas density are predicted
and mapped. The behavior of the supersonic jet from the nozzle exit has been investigated
using Computational Fluid Dynamics (CFD) and validated experimentally using shadowgraph
techniques. The designed supersonic nozzle exhibits good gas dynamic characteristics under
high operating pressure. Cutting trials have been conducted using the nozzle assembly with
satisfactory performance.
KEY WORDS: CFD, Laser Cutting, MOC, Supersonic Nozzle, Shadowgraph. Address correspondence to M. Sundar, School of Laser Science & Engineering, USIC Building, Jadavpur University, Kolkata-700032, India. E-mail: [email protected]
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Nomenclature
A Area [m2] x, r, z Cartesian co-ordinates [m/s]
C1ε, C2ε , C3ε, Cµ Constants Greek symbols
D Diameter [m] ρ Density [Kg/m3]
Gk Generation of turbulent kinetic energy due to the mean velocity gradients [kg/ms3]
σk & σε Turbulent Prandtl numbers for k and ε respectively
Gb Generation of turbulent kinetic energy due to buoyancy [kg/ms3] ε Dissipation rate of turbulent
kinetic energy [m2/s3]
k Turbulent kinetic energy [m2/s2] θ Streamline angle [rad]
Lk Length of initial expansion region [m/s] ν Prandtl–Meyer angle [rad]
M Mach number µmol Molecular viscosity [kg/ms]
Mt Turbulent Mach number µeff Effective viscosity [kg/ms]
P Pressure [bar] µt Turbulent viscosity [kg/ms]
R Gas constant [ J/kg mol-K] µ Dynamic viscosity [kg/ms]
Sk User-defined source terms [kg/ms3] γ Specific heat ratio
Sε User-defined source terms [kg/ms4] α Mach angle [rad]
T Temperature [K] Subscript
ui Velocity component along ith direction [m/s] T Throat
V Velocity [m/s] e Exit
Ym Contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate [kg/ms3]
0 Inlet stagnation condition
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1. INTRODUCTION
The traditional laser cutting process is achieved by a combination of laser power and
the power produced by exothermic reaction of iron with oxygen. This oxidation reaction is
exothermic and acts as a secondary energy source, which helps to accelerate the cutting
process. Most of the laser cutting processes uses subsonic or transonic nozzles, which have
the type of geometry shown in Figure 1. These nozzles are simple to construct and are
generally designed by trial and error methods. In these, bulk amount of energy is contributed
by laser /1/ itself and the energy produced by exothermic reaction from oxy-iron combustion
is used only to assist the cut.
Fig.1 Subsonic Nozzle Fig.2 Supersonic Nozzle
The exothermic reaction between oxygen and iron produces vast amount of energy,
which is not used effectively in the traditional laser cutting process due to the restriction in
operation of subsonic nozzle. In the traditional laser cutting process the power produced by
exothermic reaction is only about 10 % of the total cutting power /2/. With considerable
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increase of exothermic power, the total energy supplied for cutting can be increased for
effective utilization in cutting thicker materials.
Using subsonic nozzle it is not possible to supply high volume of oxygen at high
velocity. In subsonic and transonic nozzle the inlet stagnation pressure is restricted till it
reaches sonic velocity /3/. A further increase in pressure results in transversal expansion of the
jet in an explosive fashion. Besides, periodic intermittent shock waves /4/ are formed which
makes the jet thinner in some sections and thicker in others.
When a supersonic nozzle (Figure 2) is used, the exit jet condition can be greatly
improved because of its good gas dynamic characteristics /5-7/. Especially under the
conditions of a correct design, the potential energy of inlet pressure is converted totally into
the effective kinetic energy, so that the velocity of the jet used in laser cutting will surpass the
sonic speed and increase further with the increase of inlet pressure P0. Consequently, a higher
momentum with high mass flow of the jet can be obtained which will improve the exothermic
reaction and will increase the capability of removing the molten debris /8/.
It is not possible and viable to increase the laser power to a great extent for cutting
material of higher thickness. Hence an attempt has been made to increase the energy produced
through exothermic reaction in a manner that can be effectively utilized in cutting materials of
higher thickness. The main criterion in this model is to supply high volume of oxygen for the
exothermic reaction and to make sure all the oxygen reacts with iron to facilitate exothermic
reaction. This is achieved by making the diameter /9/ of laser beam footprint over the work
piece higher than the diameter of gas jet, so that all the oxygen react with iron to produce the
required power. A short focal length lens is used to achieve greater beam diameter than gas jet
diameter. The schematic diagram of the nozzle assembly is shown in Figure 3.
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Fig. 3 Schematic diagram of nozzle assembly
In this process the power delivered by laser beam is used only to heat the temperature
of the work piece to kindling temperature /10/ whereas the power produced by the exothermic
reaction between oxygen and iron is used for cutting. The traditional subsonic nozzle /11/ is
not fit for this application as it has restriction in the mass flow rate and exit velocity. Hence, a
convergent-divergent supersonic nozzle is designed which is capable of operating at high
stagnation pressure and deliver the exit jet with high velocity
Keeping this in consideration, an attempt has been made to design a supersonic nozzle
capable of operating at high inlet stagnation pressure, high mass flow rate, high velocity at
output and which can operate using short focal length lens. Theoretical analyses have been
made to access the relationship between the shape and dimensions of a nozzle tip, the
dynamic characteristics of the gas jet and the inlet stagnation pressure. Computational Fluid
Dynamics (CFD) has been used to predict flow patterns inside the nozzle, geometry of which
is obtained by applying MOC. The CFD equations have been solved using commercial finite
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volume based code FLUENT 6.2.9. Based on the analysis from FLUENT, necessary
modification in the nozzle geometry is introduced so as to accommodate the required mass
flow rate.
2. SUPERSONIC NOZZLE DESIGN BASED ON GAS DYNAMIC THEORY
Supersonic nozzles (Figure 4) consist of four regions /11/. These are: stable,
convergent, throat and divergent region. In order to produce an exit jet with high momentum
and low turbulence and energy loss, the dimensions of each section in supersonic nozzle need
to be designed correctly on the basis of gas dynamic theories.
Fig. 4 Conceptual diagram of supersonic nozzle
The function of the stable section is to make the incoming flow from a tank more
uniform, non-turbulent. In theory greater the diameter and length L0 of stable section the
performance of nozzle is better. However, in reality, diameter and length are restricted by the
nozzle structure, focal length of lens and diameter of the laser beam.
The function of the convergent section is to accelerate gas flow, but at the same time,
to keep the flow uniform and parallel. The characteristics of the convergent section are mainly
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determined by two factors, one being the converging ratio, i.e. A0 / At, which accelerates the
gas flow and ensures the speed of flow to reach sonic speed, whilst the second is the
convergent curve which maintains uniform velocity of flow. From theory of one-dimensional
steady state gas dynamics flow, the equation of A0 / At can be written as
2 ( 1) /( 1)20
2
1 2 111 2t
A MA M
γ γγ
γ
+ −⎛ ⎞ ⎡ ⎤−⎛ ⎞= +⎜ ⎟ ⎜ ⎟⎢ ⎥+ ⎝ ⎠⎣ ⎦⎝ ⎠
(1)
and the mass flow rate equation is given by
VAρ = constant and M = VRTγ
(2)
The design of the throat section is relatively important because it is a transitional
cross-sectional area, which transfers the subsonic speed into the supersonic speed. The cross-
sectional area closer to the throat section cannot be varied drastically, so that a circular arc
with quite a large radius is provided over the region of transition using Eq. (3).
Radius of curvature /12/ of throat:
y = Dt + ρt (1 - cosα) + (x - ρt sinα ) tanα (3)
The value of the throat diameter is determined by the requirement of the cutting flow
according to the range of cutting thickness. The function of the divergent section is to further
accelerate the flow, which has achieved sonic speed at the throat section, by means of
expansion until the exit jet reaches the expected Mach number. This section is the most
important section in the supersonic nozzle. The dimensions of the exit area can be calculated
by means of Eq. (1) according to the given inlet stagnation pressure P0 which can be
calculated using Eq. (4) and the exit velocity of flow.
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/( 1)
20 112
P Mp
γ γγ −−⎛ ⎞= +⎜ ⎟⎝ ⎠
(4)
The flow properties at throat and outlet are calculated using Eq. (5) and Eq. (6) as
follows:
20 112
T MT
γ −= + (5)
1/( 1)20 11
2M
γρ γρ
−−⎛ ⎞= +⎜ ⎟⎝ ⎠
(6)
Using the above gas dynamic equations, the minimum length nozzle is designed for
shock free supersonic gas jet. Oxygen is considered as the working fluid. For designing, the
ambient pressure is taken at the exit to avoid any under expansion or overexpansion of the gas
jet. A design stagnation pressure of 7.58 bar and stagnation temperature of 328 K is
considered at the inlet. The designed exit Mach number is found to be 1.98 with exit velocity
of 538 m/s and the mass flow rate of 5.6 × 10-3 kg/s. The exit diameter and throat diameter
have been computed as 2.5 mm and 1.98 mm, respectively. This velocity and mass flow rate
are considered to be sufficient to cut steel of higher thickness.
3. DESIGN PARAMETERS FOR SUPERSONIC NOZZLE
3.1. Requirement for cutting thick carbon steel
The successful design of the process parameters depends on the computation of the
oxygen flow rate as oxidation of iron acts as the major supplier of energy in this process.
Theoretically, 0.277 parts by weight of pure oxygen is required to remove /13/ one part of
iron from the kerf.
1 part of Fe + 0.277 part of O2 ⇒ 1.277 parts of FeO, Fe3O4 and Fe (7)
So the volume of oxygen required to burn one cubic centimeter of Fe is given by
Voxygen = (7.86 × 0.277)/1.33 = 1.64 lit/cm3 of Fe. (8)
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where 7.86 and 1.33 are the specific gravity of iron and oxygen respectively.
To cut 5.0 cm thick carbon steel with 0.25 cm kerf width and with a cutting speed of
0.6 cm/s, the material removal rate is 1.05 cm3/s and the volume of oxygen required = 1.64 ×
1.05 lit/s = 1.73 lit/s. The mass flow rate of oxygen should be equal to 1.73 × 1.33 × 10-3 =
2.30 × 10-3 kg/s (where specific gravity of oxygen = 1.33 × 10-3 kg/lit).
3.2 Mass flow from the designed supersonic nozzle
Design of a supersonic nozzle capable of delivering the huge volume flow rate of
oxygen is the most critical part of the present system. In practice, excess oxygen needs to be
provided, to ensure complete oxidation. The following computation checks the adequacy of
the nozzle in supplying oxygen for complete oxidation.
Mass flow rate = density × area × velocity
Density at exit = 2.19 kg/m3; Ae = 4.9 mm2; Ve = 538 m/s.
Mass flow rate through the nozzle = 5.6 × 10-3 kg/s. Hence, the designed nozzle, based
on 1-D steady state gas dynamic equation, is capable of supplying enough oxygen for
complete oxidation to harness maximum heat of exothermic reaction.
3.3 Heat Produced by Exothermic Reaction
The ability of oxygen to react violently with steel above kindling temperature is
governed by the reaction
2
1Fe + O FeO + ∆H
2 ⇒ (9)
where ∆H = −257.58 kJ/mol
If one assumes that complete combustion of the iron takes place the heat of reaction is
Er = −4600 kJ/kg /14/. For a cutting depth of 50 mm, kerf width of 2.5 mm and cutting speed
of 6 mm/s the total power produced is about 26.4 kW. By consulting the above quantities, it is
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found that the mass flow rate and velocity of the proposed supersonic nozzle is sufficient for
cutting steel up to thickness of 5.0 cm.
4. SUPERSONIC MINIMUM LENGTH NOZZLE BASED ON METHOD OF
CHARACTERISTICS
The majority of design criteria used in the proposed laser cutting process can be meet
using a minimum length nozzle - MLN (Figure 5). These nozzles have very small length to
diameter ratio, which is essential for a nozzle assembly with a lens of short focal length.
Another advantage associated with minimum length nozzles is that boundary layer growth can
be kept to an absolute minimum in contrast to De Laval nozzles. MLN also eliminates the use
of exotic gas mixtures at the laser-material interaction zone.
The design of nozzles described here /15/ is based on an inviscid flow field. MOC
provides a technique for accurately designing the contour of a supersonic nozzle for shock
free, isentropic flow taking into account multidimensional flow inside the duct and assuming
that the flow is inviscid and does not form a boundary layer.
Along the Mach lines, flow properties remain constant and they are therefore called
‘characteristic lines’. There are two distinct types of characteristic lines, right running and left
running, which are denoted as C+ and C− (Figure 6). The angle that the lines make with a
streamline at an arbitrary angle θ to the X-axis is given by Eq. (10) and Eq. (11).
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Fig. 5 Minimum length Nozzle
Fig. 6 Part of characteristic net showing left and right running characteristic lines
tan( )drdx
θ α= − for C_ characteristics (10)
tan( )drdx
θ α= + for C+ characteristics (11)
1 1sinM
α − ⎛ ⎞= ⎜ ⎟⎝ ⎠
(12)
Eq. (10) and Eq. (11) are called the characteristic equations /16, 17/. When two
characteristic lines meet, their directions change. For axi-symmetric flow, Eq. (13) and Eq.
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(14) describe the change in flow properties at the characteristic lines after the intersection
point.
For C_ characteristics ( )( )2
1 01 cot
drddxM
θ νθ
+ − =− −
(13)
For C+ characteristics ( )( )2
1 01 cot
drddxM
θ νθ
− − =− +
(14)
The quantity (θ + α) is not constant along a C− characteristic line, its value depends on
the spatial location in the flow field as indicated by the dr/dx term in Eq. (13). The same
qualification is made for (θ + α) along the C+ characteristic. The process of computing an axi-
symmetric flow field can be achieved by replacing Eq. (13) and Eq. (14) with a finite
difference solution. Flow properties and their locations are found by a step-by-step solution of
these equations, which when coupled with the characteristic equations (10) and (11), are used
to construct the characteristic net.
The computation process starts at the throat radius, expansion point (Figure 5), with a
known value for θmax which is the maximum expansion angle that can be obtained using the
Prandtl–Meyer function, ν(M), for a required Mach number and is given by the following
equation,
1/ 2 1/ 21 2 1 2 1/ 21 1( ) tan ( 1) tan ( 1)
1 1M M Mν
γ γγ γ
− −⎡ ⎤ ⎡ ⎤+ −= − − −⎢ ⎥ ⎢ ⎥− +⎣ ⎦ ⎣ ⎦
(15)
( )2MaxMνθ = (16)
The characteristic equations are solved by iterations /18-20/ using new values of
properties at intersections, and locations obtained from compatibility equations, in the form of
finite difference. By calculating the gradients of new C− and C+ characteristic lines, the
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solution of the conditions at the nozzle contour can be obtained by propagating downstream
from the initial data line. By analyzing the intersection of each Mach line in the flow regime,
the nozzle shape for shock-free, isentropic flow is obtained.
Fig. 7 Characteristic lines and contours
It should be noted that the prediction of a nozzle contour does not take into account
viscosity of the fluid and hence it ignores the formation of both subsonic and supersonic
boundary layers, which may adversely affect the performance of a supersonic nozzle. The
presence of a boundary layer on the nozzle wall lowers the exit Mach number, compared to
inviscid flow predictions that are based on an area ratio. A computer program was developed
using MATLAB 7.3 software for designing an axi-symmetric, straight MLN, with a sharp
throat corner. Figure 7 show the characteristic line for exit Mach number of 1.98 and throat
diameter of 1.98 mm. Results obtained from the computer program gave an exit area of 5.109
mm2 as that of 5.11mm2 that is obtained from one-dimensional equation (Eq. 1). The
percentage of error between MOC and one-dimensional equation is less than one percent.
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5. ANALYSIS OF NOZZLE PROFILE BY COMPUTATIONAL FLUID DYNAMICS
The CFD analysis has been done by using the finite volume based FLUENT 6.2.9
code. The two dimensional axi-symmetric mesh is generated using GAMBIT 2.3.16 software
and then imported to FLUENT for analysis. Axi-symmetric steady state compressible flow is
assumed for the analysis. Based on the Reynolds-averaged Navier-Stokes equations with the
standard k–ε turbulence model, the governing equations for solving the problem are as
follows:
( )jj
ux
ρ∂∂
= 0 (17)
( )i j jieff
i i j i i
u u uu px x x x x
ρµ⎡ ⎤⎛ ⎞∂ ∂∂∂ ∂
= + −⎢ ⎥⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂⎢ ⎥⎝ ⎠⎣ ⎦ (18)
The effective viscosity µeff = µt + µmol, µeff can be obtain as
eff molmol
C1 kµµ µµ ε
⎡ ⎤= +⎢ ⎥
⎢ ⎥⎣ ⎦ (19)
The values of k and ε can be obtained from Eq. (20) and (21) as shown below.
( ) ti k b M k
i j k j
kku G G Y Sx x x
µρ µ ρεσ
⎡ ⎤⎛ ⎞∂ ∂ ∂= + + + − − +⎢ ⎥⎜ ⎟∂ ∂ ∂⎢ ⎥⎝ ⎠⎣ ⎦
(20)
2
1 3 2( ) ( )ti k b
i j j
u C G C G C Sx x x k kε ε ε ε
ε
µ ε ε ερε µ ρσ
⎡ ⎤⎛ ⎞∂ ∂ ∂= + + + − +⎢ ⎥⎜ ⎟∂ ∂ ∂⎢ ⎥⎝ ⎠⎣ ⎦
(21)
One significant characteristic of turbulent flow is the transfer of momentum, heat and
mass by means of molecular transport processes, namely, viscosity and diffusion. The
conservation equations used for turbulent flows are obtained from those of laminar flows
using the time averaging procedure commonly known as Reynolds averaging.
The model constants C1ε, C2ε , Cµ, σk and σε are assigned the following values /21/:
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C1ε = 1.44, C2ε = 1.92, Cµ = 0.09, σk = 1.0, σε = 1.3 and YM = 2ρεMt2 (22)
2 , tkM a RTa
γ= = (23)
The supersonic jet is a pressure driven system, which creates shear stresses on a
molten film. The magnitude of the shear stress applied depends on the jet velocity and the
surface tension of the gas-liquid-solid interface. For simplicity, boundaries in CFD models are
treated as a solid surface with no external heat source. In this analysis the flow is treated as
isentropic obeying the ideal gas law. The gas dynamic equations are same as that discussed in
the one-dimensional design (Eq. 1 to Eq. 6).
The governing equations are solved using segregated solution method. Simplex
algorithm is used. As the governing equations are non-linear and coupled, several iterations of
the solution loop is performed before a converged solution is obtained. The convergence
criterion for all the simulations was set to 10-6. Convergent solutions were obtained
approximately in 900 iterations. An additional grid independence test was made to confirm
the convergence of the simulation.
CFD results for MLN with a throat diameter of 1.98 mm and exit diameter of 2.5 mm
are shown in Figures 8 through 16. The inlet stagnation pressure is set at 7.58 bar and the
outlet is set at atmospheric condition. The nozzle geometry using MOC and the actual contour
obtained following FLUENT are shown in Figure 8. Due to the formation of boundary layer,
the actual mass flow rate is lesser than that obtained from MOC. To compensate the loss of
mass flow rate, the actual contour is reconstructed in such a way so that it can accommodate
the theoretical mass flow rate.
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Fig. 8 Minimum Length Nozzle Contour in Non Dimensional parameter
Fig. 9 Variation of velocity along the nozzle axis
Velocity, Mach number, density and pressure variation along the axis of the
supersonic minimum length nozzle obtained from FLUENT and MOC are shown through
Figure 9-12. In these figures, the first 15 mm corresponds to the variations in the convergent
part and the rest 7 mm is for the divergent part. The effect of boundary layer on the overall
Mach number distribution in the convergent-divergent part of the nozzle has been analyzed by
considering axi-symmetric flow equations. It is observed that the presence of a boundary layer
on the nozzle wall lowers the exit velocity and Mach number compared to inviscid flow
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predictions. For the same reason, the prediction of pressure and density from Fluent is higher
than that from MOC.
Fig. 10 Variation of Mach number along the nozzle axis
Fig. 11 Variation of Density along the nozzle axis
Fig. 12 Variation of Pressure along the nozzle axis
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Figures 13 through 16 shows the two-dimensional contour plots for static pressure,
density, Mach number and velocity. Flow parameters are seen to vary smoothly inside the
nozzle and no abruptness of flow structures are noticed in the analysis. Analyses show that
velocity and Mach number at the nozzle exit are around 518 m/s and 1.85 respectively in
comparison to 538 m/s and 1.98 respectively as obtained from one-dimensional gas dynamics
equations. This is due to the strong boundary layer formation in the wall of the nozzle, as
evident in Figures 15 and 16.
Fig. 13 Contour of Static Pressure in bar
Fig. 14 Contour of Density in kg/m3
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Fig. 15 Contour of Mach number
Fig. 16 Contour of velocity in m/s
6. PERFORMANCE EVALUATION OF THE SUPERSONIC NOZZLE EXIT JET
The behavior of the supersonic jet from the nozzle exit has been investigated to study
the exit jet characteristic for velocity, pressure Mach number and shear force. Effects of the
supersonic impinging jet on the cutting front from a straight supersonic nozzle have been
recently studied by Chen et al. /22, 23/. They have shown that in specific conditions of the
supersonic laser jet, shock waves can be generated which thus significantly change the cutting
results /22/. The model used for this simulation is standard k–ε turbulence model derived from
instantaneous Navier - Stroke equation, which is the same as that discussed in the CFD
simulation of supersonic nozzle. The computation domain (all the dimensions shown in the
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figure are in mm) used for the analysis is shown in Figure 17. In the Figure 17 the solid line
shows the wall boundary condition and the dashed line shows the pressure boundary
condition. The gas inlet stagnation pressure P0 is 7.58 bar and the outlet Pe is assumed to be
atmospheric. As mentioned earlier, the variation of pressure and hence the density, takes place
only at the convergent and divergent part of the supersonic nozzle. Hence, for evaluating the
performance of the exit gas jet, only the convergent & divergent parts of the nozzle, including
the domain of exit gas, are taken for computation. A stand off distance of 2.5 mm is given
between the nozzle exit and the laser cutting kerf. The jet passes through the kerf and reaches
the atmosphere. The nozzle exit diameter is 2.5 mm and the kerf diameter is 2.5mm. To find
the effect of aspect ratio (ratio of hole length to hole diameter) on shear force, three different
kerf lengths (5 mm, 10 mm and 20 mm) have been considered for the present study. The kerf
walls are assumed to be straight, smooth and without external heat generation.
Fig. 17 Computational Domain for the free jet
The grid selection is an important technique to improve the accuracy of the solutions
in most of the numerical simulation methods. Since the flow field is axi-symmetric, a square
grid mesh of the length 0.1 mm has been used in the GAMBIT 2.3.16. The total number of
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cells in the domain is 10,200. The flow field were meshed by the software GAMBIT and
computed by the FLUENT 6.2.9. This allowed the non-standard geometry of the nozzle to be
mapped into cylindrical geometry /21/. The acceptability of the grid generation and iteration
times has been checked automatically by the FLUENT and from the residual list of the
convergence in the computation with the default settings /21/. As the governing equations are
non-linear and coupled, several iterations of the solution loop is performed before a
converged solution is obtained. The convergence criterion for all the simulations was 10-6.
Converged results were obtained after 3000 iterations, approximately.
Fig. 18 Velocity Profile for the free jet in m/s
Fig. 19 Contour of Mach Number for the free jet
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Figure 18 and Figure 19 show the velocity and Mach number profile of the free jet
inside the kerf for the kerf length of 5 mm. As expected the jet shows a high momentum, good
uniformity and tidy boundary. There is a high boundary layer formation along the walls of
kerf and nozzle. The velocity inside the kerf varies between 350 m/s to 450 m/s and Mach
number varies from 1.3 to 1.6. These high values are suitable for the high pressure laser
cutting process.
Figure 20 shows the pressure contour of the supersonic exit jet for a kerf length of 5
mm. As the laser cutting process is a pressure driving system the force produced by the jet
should be high enough to remove the molten metals instantaneously. The primary means for
removing molten and oxidized materials in laser cutting is increased by the pressure gradient
between the interaction zone and the surrounding atmosphere. Since the pressure gradient
induces a shear force at the boundary the variation of the pressure gradient will significantly
affect the material removal rate and the appearance of the cut front in laser cutting.
Fig. 20 Pressure Profile for the free jet in bar
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Fig. 21 Shear Force distribution in the cut kerf
Figure 21 show the shear force on the wall of the cutting kerf for various kerf depths
of 5mm, 10mm and 20mm. The magnitude of the shear force depends on the supersonic jet
velocity and gas-liquid-solid interface. It is well evidenced from the Figure 21 that at some
distance along the kerf length the amount of shear force increases in magnitude and start
decreasing. This is because the pressure gradient is favorable to the exit of the kerf. The shear
force mainly depends on the aspect ratio. As the length of the cut kerf increases the shear
force reduces, i.e., as the aspect ratio increases the shear force decreases.
7. EXPERIMENTAL FLOW VISUALIZATION
For high-speed liquid jets, effective flow visualization is necessary to investigate the
characteristics of the flow. It is widely recognized that optical flow visualization is the most
suitable method to observe the shock waves in a compressible flow. The shadowgraph is the
simplest visualizing procedure and it is especially convenient for clearly indicating shock
wave location. The shadowgraph technique has been applied to many related areas; high-
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speed liquid jets, interaction of a turbulent round jet with a free surface /24/, unsteady jet
characteristics in a stratified fluid /25/ and aerodynamic characteristics of annular impinging
jets /26/. The shadowgraph can effectively capture supersonic flow jets and their shock wave
characteristics.
Fig. 22 Schematic diagram of shadowgraph arrangement
As illustrated in Figure 22, a defocused He-Ne laser (wavelength of 632.8 nm) was
used as a light source to illuminate the flow structure in the jet streams. Oxygen gas is used as
the working fluid. Due to the sharp change of gas pressure and density near the shock wave
fronts of the gas flow, a clear shadowgraph can be projected onto the screen and captured by a
CCD image system.
5 bar
6.5 bar
7.5 bar
8.5 bar
9 bar
10 bar
Fig. 23 Gas flow pattern for supersonic nozzle obtained using Shadowgraph for various
pressures
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Figure 23 shows the shadowgraph results of the supersonic nozzle with various nozzle
pressures ranges from 5 to 10 bar. Under the process conditions as indicated in Figure 23, the
shock waves were visualized and the shadowgraphs of shock wave were intensified with the
increase of air pressure. It can be found that the location of the shock waves moves
downstream from the nozzle exit with the increase of air pressure. It can be seen that the
Mach disc occurred at an entrance pressure larger than 7.5 bar in the present experiment.
These shock discs will cause loss of energy, which results in turbulence and loss of
momentum. As the stagnation pressure is greater than the design pressure there is an under
expansion of the gas jet at the nozzle tip. An over expansion of the gas jet takes place when
the stagnation pressure is less than the design pressure.
8. CUTTING TRIALS
Cutting trials have been carried out at School of Laser Science and Engineering,
Jadavpur University, India, to determine the performance of the proposed cutting process. An
indigenously developed 2.5 kW CO2 laser, with TEM 01* (doughnut) /27/ laser beam, has
been used for the cutting process. Oxygen gas with an exit pressure of 7.5 bar and mild steel
plate of 50 mm thickness has been used. The nozzle assembly has been aligned so that the
beam and nozzle were concentric. The laser beam diameter was then set to 3 mm at the
surface of the steel to ensure that the gas jet diameter (2.5 mm) is less than the laser beam
diameter.
Page 26 of 30
Fig. 24 Photograph of 50 mm cut sample obtained using this process
Fig. 25 Photograph of cutting process in action (Thickness = 50 mm)
Figure 24 shows the cut sample and Figure 25 shows a photograph of the cutting
process operating under stable conditions cutting 50 mm thick mild steel, with oxygen
pressure of 7.5 bar, laser power 1kW and speed of 320 mm/min. The kerf widths of the cuts
produced with the cutting process are controlled by the width of the gas jet.
9. CONCLUSION
The designed supersonic nozzle has good gas dynamic characteristics under high
operating pressure, which can be effectively used for cutting higher thickness carbon steel.
Page 27 of 30
Gas dynamic theories and CFD techniques have been used for design of supersonic MLN.
The designed supersonic nozzle shows very good flow characteristics inside and outside the
nozzle under the operating pressure of 7.58 bar. The supersonic flow exhibits satisfactory
characteristics as evident from the velocity and Mach number contours inside the kerf width.
CFD studies of supersonic jet interaction with walls of varying aspect ratio have highlighted
that the shear force distribution in the kerf is good enough to remove molten materials and
debris. As the aspect ratio of the kerf increases shear force decreases. The flow information
obtained, such as the pressure contours, velocity contours and the wall shear force are found
to be effective in determining the structure of impinging jets in laser cutting. The
shadowgraph flow visualization shows the exit jet of the nozzle with good flow properties.
The nozzle design is capable of cutting up to 50 mm thickness. The supersonic nozzle regions
should be designed strictly on the basis of gas dynamic theories and any deviation will result
in strong Mach shock in the gas jet.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge the financial support (Sanction No. 2004/34/3-
BRNS/275) provided by the Board of Research in Nuclear Sciences, DAE, India, for carrying
out the present research work.
Page 28 of 30
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