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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: marimuthusundar@gmail.com

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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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