A comparative study of pitot tube measurements and CFD results for supersonic nozzles employed for gas atomization of liquid metals.
Gas atomization is one of techniques in the powder production methods. In this method, kinetic energy of a high velocity (greater than Mach 1) impinging inert gas jet disintegrates continuous metal flow into droplets. Nozzles are used to achieve the atomization through break-up of molten metal stream into droplets by fast flowing gas. The heart of the gas atomization process is the nozzle. The schematic diagram of gas atomization process is shown in figure 1.
[FIGURE 1 OMITTED]
The droplets formed during atomization process can be quenched to form the powders or deposited to form the billets as in Spray Casting process. The type and configuration/parameters of the nozzle determines the gas-metal interaction and hence plays a key role in the gas atomization process. Investigators have used different types of nozzles for production of high velocity atomizing gas jets. [1, 2, 3, 4, 5, 6]
A CD nozzle consists of a short converging portion followed by a longer diverging part separated by a throat. In this nozzle, the area increases continuously giving a divergent passage after the throat and exit Mach number will be always greater than 1 which gives the supersonic flow of the gas during the atomization process . In the confined design configuration (also known as close coupled) atomization occurs at the orifice of the metal delivery tube which is also known as flow tube. The melt flow is influenced by the gas flow through the nozzle. In this configuration the energy transfer from the gas to metal is highly efficient and more uniform .
In the supersonic gas atomization process a highly energetic gas jet or jets with supersonic velocity impinge on a stream of molten metal leading to break up of the stream into small, irregular ligaments. The gas velocity will be maximum at exit from the atomizer nozzle and subsequently decreases with distance as its momentum is transferred to the metal phase and to the adjacent gas volume in the surroundings [9, 10].
One of the critical parameter in the gas atomization process is the Mach number. The exit velocity of the gas jet in the atomization process controls the extent of the metal breakup. This breakup is termed as the primary breakup or primary atomization process .
In a C-D nozzle if the exit pressure is less than the backpressure, shock waves occur. If the exit pressure is slightly less than the back pressure, then oblique shock waves occur at the nozzle exit as shown in figure 2. If the difference between back pressure and exit pressure is larger than the accommodated by oblique shock waves, a normal shock wave will occur in the nozzle is shown in the figure 2. The flow becomes subsonic and decelerates in the remaining portion of the divergent section in such a way that the exit pressure is equal to the backpressure. As the backpressure is further increased, the shock wave moves towards the throat region and finally there will be no region of supersonic flow. On the contrary, as the pressure is reduced. The normal shock wave will move downstream closer to the nozzle exit. A nozzle with supersonic flow in which the exit pressure is equal to the backpressure is ideally expanded .
[FIGURE 2 OMITTED]
Mach number is the speed of an object moving through air, or any fluid substance, divided by the speed of sound through that substance. As it is defined as a ratio of two speeds, it is a dimensionless number. The formula to compute Mach number in a supersonic compressible flow is derived from the Rayleigh Supersonic Pitot equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Where M is the Mach number, "qc" is the impact pressure and "p" is static pressure. 
CFD is one of the techniques to obtain the numerical solution to fluid flow problems using computers. Fundamental basis of any CFD problem is the NavierStokes equations, which define any single-phase fluid flow. These equations can be simplified by removing terms describing viscosity to yield the Euler equations. .
Fluent is one among commercially available CFD packages employed for numerical analysis of fluid flow. Fluent can be used for modeling fluid flow and heat transfer in complex geometries. Gambit is Fluent's geometry and mesh generation module. Gambit has a single interface for geometry creation and meshing that brings together most of Fluent's preprocessing technologies in one environment [15, 16]
Fundamental design methodology used for CD nozzle to obtain supersonic velocity of gas
A close-coupled CD nozzle in which the co-axially fitted MDT was considered for the present analysis. The nozzle accelerates the gas from subsonic to supersonic velocities. The fundamental relationships of isentropic compression and subsequent expansion through a flow passage resulting in a supersonic jet have been employed to obtain the areas at the three critical sections i.e. inlet, throat and exit. Since the metal delivery tube was to be coaxially inserted into the nozzle, the effective area of flow had to be considered in all the design steps. The Area-Mach relation was used to obtain both the inlet and the exit area ratios by suitably substituting the stagnation and exit Mach numbers. Experimentation involved measurement of velocity and Mach number at the nozzle exit in both in horizontal/axial and radial directions. This was carried out in a high-speed wind tunnel using the Pitot tube measurement technique. [3, 4, 7, 17, 28]. Figure 3 shows the CD nozzle geometry designed and fabricated to obtain the Mach number of around 2.4 
[FIGURE 3 OMITTED]
This CD nozzle was modeled and meshed using the Gambit software applying the required boundary conditions for CFD analysis. CFD trails were conducted and results obtained were used for comparison with wind tunnel results.
Set up for velocity measurements in Wind tunnel
Figure 4 shows the setup to measure the velocity of gas and Mach number for CD nozzle experimentally using Wind tunnel and Pitot tube. 
[FIGURE 4 OMITTED]
Pitot tube technique is an extensively used experimental method for velocity measurements. Mach number in both horizontal and radial directions was to be recorded at the exit of the nozzle. A traverse was designed and fabricated to move the Pitot tube in the required directions. A mechanism similar to lead screw of a lathe was incorporated for achieving horizontal and vertical movements up to 300 mm. A probe was introduced at the inlet of the nozzle to measure the inlet gas pressure. The pressure readings from all the three channels were noted down. Further, the readings were taken by moving the Pitot probe axially from the exit of the nozzle in steps of 25 mm by keeping the inlet pressure constant at the designed pressure of 0.3 MPa (3 Bar). The Pitot probe was also moved radially at the exit of the nozzle in steps of 1 mm and the readings were recorded. The experiments were repeated by inserting a MDT (8 mm outer diameter, 6 mm inner diameter) coaxially with the nozzle, which represents the metal delivery tube in the actual gas atomization nozzles. 
Parameters considered for numerical analysis of Mach number for CD nozzle
In the present study, CFD trials have been carried on CD nozzle for plotting Mach number. Geometric modeling and meshing of the nozzle were carried out and the results were plotted using Gambit and Fluent software. The table 1 shows the Nozzle parameters and the boundary conditions considered in order to get the Mach number of 2.4 for CFD trials.
The boundary conditions applied were Pressure inlet, Pressure outlet, Wall and the Symmetry. Viscous model was defined as Spalart-Allmaras for the fluid flow, solver as Fluent 5/6 and mesh type as QUAD . Inlet pressure of 3 Bar and inlet temperature values of 300K were given as input. The iteration values were set was about 1000 initially and iterated until the solution converges . Then the results were plotted for velocity, pressure, temperature and Mach number.
The Courant number controls the time step used by Fluent during the inner iterations performed during each time step. The default Courant Number (CFL) for the coupled implicit solver is 5.0. If the solution is diverging, i.e., if residuals are rising very rapidly, and the problem is properly set up and initialized, this is usually a good sign that the Courant number needs to be lowered. Depending on the severity of the startup conditions, the CFL is decreased to a value as low as 0.1 . The Courant number of 5 was used for obtaining Mach number along the radial direction at the nozzle exit and CFL of 0.1 was used for axial measurement of Mach number.
Test Cases considered for the present analysis
The different cases that were considered for conducting the experiments on CD nozzle to measure and compare the Mach number at the exit of the nozzle using CFD and Wind tunnel experiments are: Mach number variation along radial direction with and without MDT, along axial direction with and without MDT.
Results and Discussions
Mach number measurement along the radial direction at the nozzle exit without MDT and its comparison with experimental values
The figure 5 shows the CD symmetric nozzle that was modeled and meshed using Gambit software. This was used for plotting Mach number along the radial direction at the exit of the nozzle without placing the co-axial MDT inside the nozzle.
[FIGURE 5 OMITTED]
Figure 6 shows the Mach number distribution plot along the radial direction at the exit of the nozzle. In this case, the Mach number decreases along radial direction at the exit of the nozzle towards the nozzle wall.
[FIGURE 6 OMITTED]
From the figure 6 it is clear that, at the nozzle exit, the supersonic Mach number of 2.1 was obtained. Further, at the throat the Mach number was found to be 1 indicating the attainment of sonic condition at the throat. Also there is a development of supersonic velocity in the divergent portion of the nozzle. These observations justify the design methodology that was used for the nozzle.
The figure 7 shows the measurement locations (points) for recording the Mach number in the radial direction at the nozzle exit. 
[FIGURE 7 OMITTED]
The comparison of the Mach number values between the Wind tunnel experiments and the CFD results without placing the co-axial MDT is shown in figure 8. The measurements were taken on one side of the nozzle axis because of symmetry. Mach number was found to be decreasing along the radial direction (from 2.05 to 1.9) in experimental results. It was observed that the Mach number was closest (2.05 Mach) to the designed value at the center and decreased towards periphery . The CFD results indicated a decrease in Mach number along the radial direction (from 2.1 Mach to 1.85 Mach). In both of the cases, the Mach number decreases radially towards the wall at the exit of the nozzle.
[FIGURE 8 OMITTED]
3.2 Mach number measurement along the radial direction with MDT at the nozzle exit and its comparison with experimental values.
The figure 9 shows CD nozzle with a co-axially placed MDT which was modeled and meshed using the Gambit Software and applying the boundary condition as in the previous case. The MDT boundary was considered as a wall.
[FIGURE 9 OMITTED]
Figure 10 shows the Mach number plot which was obtained for CD nozzle when the MDT was placed co-axially placed in the nozzle. Here the Mach number increases (2.2 to 2.3 Mach) and later decreases (2.1 Mach) towards the nozzle wall in the radial direction. Here the desired Mach number of 2.3 is obtained towards the nozzle wall.
[FIGURE 10 OMITTED]
Figure 11 shows the CD nozzle with the co-axially placed MDT and the points where the Mach number was measured along the radial direction at the exit of the nozzle .
[FIGURE 11 OMITTED]
Figure 12 shows Mach number comparison plot for Wind tunnel experiments and CFD trials along the radial direction for a Mach 2.4 nozzle with the presence of MDT. It could be seen that for the Wind tunnel experiments, Mach number was maximum (closest to designed value 2.3 Mach) at the center of the annular region and decreases towards the nozzle periphery. For the CFD trails the same trend (Mach number first increase and decreases later) was observed. In both of the cases, the Mach number first increases and then decreases radially at the exit of the Nozzle.
[FIGURE 12 OMITTED]
3.3 Mach number measurement along axial direction without MDT at the nozzle exit and its comparison with experimental values
Figure 13 shows the CD nozzle without a co-axially placed MDT which was modeled and meshed using Gambit software. For plotting the Mach number; an area at the exit of the nozzle was considered with height more than 2 times the exit diameter of the nozzle (50 mm) and length was taken as 300mm. Hence a chamber like design was considered with PRESSURE-OUTLET boundary condition as the ambient pressure (applied atmospheric pressure of 1 Bar). This was to adopt similar domain as that of wind tunnel experiments.
[FIGURE 13 OMITTED]
Figure 14 shows the Mach number plot for the CD nozzle without placing the co-axial MDT along axial direction. The plot shows the presence of shock waves and the Mach number first increases and reaches to a maximum value (Mach 2) and then decreases along the axis beyond the nozzle exit. The Mach number also varies due to presence of shock waves.
[FIGURE 14 OMITTED]
Figure 15 shows the velocity plot for the CD nozzle without MDT. It shows the presence of shock waves at the exit of the nozzle along the axial direction. During supersonic flow, the velocity of the gas at the exit of the nozzle is maximum (Mach number will also be maximum) and subsequently decreases with the distance.
[FIGURE 15 OMITTED]
The studies on the gas velocity measurements from a close coupled spray deposition atomizer were done by Bewlay and Cantor and their observation is as follows: The gas velocity decreases with the increasing axial distance from the atomizer. The velocity increases to a maximum value and then decreases along the axial distance towards the substrate. The turbulent mixing of gas flow from the atomizer with the surrounding chamber gas is responsible for this behavior. [20, 21] A verity of theoretical decay profiles of axial gas velocity have been used in numerical models of gas atomization [2, 9, 10, 22, 23, 24, 25, 26, 27]. In each case the results have been approximated to an exponential decay of the axial gas velocity with distance as illustrated in equation 1 [25, 28].
where, ug (z) is the axial gas velocity, uo the initial gas velocity on exit from the atomizer, z the axial distance from the point of atomization, "lamda" the exponential gas velocity decay coefficient, given by equation 2.
[lambda] = [alpha][Square root of [A.sub.e]] (2)
where, a is the empirically determined constant relating to kinematic viscosity of gas and "Ae" the exit area of the atomizer [20, 21]
Figure 16 shows the variation of the gas velocity with respect to axial distance. It shows that the gas velocity is maximum at the exit of the nozzle and decreases axially. At a distance of 300mm, the velocity of the gas is around 360 m/s.  This is nearly equal to the velocity of the gas obtained using CFD plot as shown in figure 15. The Velocity is equivalent to 1.2 Mach which is depicted in figure 14. This matches with the exit velocity as represented in figure 17 which was obtained for CFD trials.
[FIGURE 16 OMITTED]
[FIGURE 17 OMITTED]
Figure 18 shows the presence of shock waves as seen in shadowgraph  which can also be noticed in Velocity plot as shown in figure 15.
[FIGURE 18 OMITTED]
Figure 19 shows the CD nozzle for axial velocity measurement without MDT. Mach number was measured at each 25mm distance .
[FIGURE 19 OMITTED]
Figure 20 shows the experimental Mach number variation along the axial direction as well as CFD trials without placing the MDT. In Experimental results the Mach number at the exit of the nozzle was found to be 2.05 and increased to 2.90 at a distance of 200 mm and became almost constant. Further, the Mach number was increased up to 3 at a distance of 275 mm indicating continued expansion. Even though the nozzle was designed to correctly expanded condition there would be variations from the theoretical values because of machining inaccuracies and experimental errors. . In case of CFD trails, the Mach number decreases as the velocity of the gas decreases as explained in equation :1.
[FIGURE 20 OMITTED]
3.4 Mach number measurement along axial direction with MDT at the nozzle exit and its comparison with experimental values
Figure 21 shows the CD nozzle with a co-axially placed MDT which was modeled meshed and applied boundary conditions using Gambit. This is exactly similar to the nozzle condition as explained in the figure 13 but it has co-axially placed MDT.
[FIGURE 21 OMITTED]
Figure 22 shows the Mach number distribution plot for CD nozzle using CFD with MDT along the axial direction.
The Mach number is maximum the exit of the nozzle (2.3 Mach) at MDT tip which shows supersonic velocity is obtained and then decreases due to decrease in velocity along the axis. This is the similar condition as explained for figure 14.
[FIGURE 22 OMITTED]
Figure 23 shows the shadowgraph illustrating the presence of shock waves in the nozzle when the MDT is placed co axially.
Mach number (velocity of gas) decay after the exit is well accepted (refer equation 1). However during the Pitot tube measurement, Mach number was observed to have increasing trend. It was observed that the Pitot tube started vibrating under the influence of shock waves. This has caused error in the experimental observations.
Theoretically, the nozzle has been designed for correctly expanded condition using the Area-Mach number relationship [7, 12]. Due to some errors in the dimensions as well as inner surface finish and consequent change in the area ratio, the nozzle was found to exhibit under-expanded condition. (Refer figure no. 22).
The figures 24 shows location of points where Mach number was measured for Wind tunnel experimental set up for CD nozzle with MDT .
[FIGURE 23 OMITTED]
[FIGURE 24 OMITTED]
Figure 25 shows Mach number comparison plot for Wind tunnel experiments as well as CFD trails for axial measurement with MDT. For Wind tunnel experiments, the Mach number increases up to 3 at a distance of 275 mm indicating continued expansion. This is similar to the condition where under expanded flow was observed without MDT also (as explained in fig 20) . Where as in CFD trails, the Mach number decreases along the axial distance as velocity reduces as explained in equation 1.
[FIGURE 25 OMITTED]
To sum up the Wind tunnel results show the increase in the mach number along the axial direction from desired mach number of 2 to 3 and the continues expansion of gas. But the CFD results show that Mach number varies inside the nozzle from subsonic to supersonic (2.35 mach) and decreases with the axial distance (2.25 to 1.55 Mach) due to decrease in velocity.
Analysis of flow parameters (pressure and temperature) for CD nozzle: CFD trails
For CFD trials, it was observed that pressure decreases in the nozzle region (from 3 Bar to 0.35 Bar) and then it attains the atmospheric pressure in the chamber region. This shows that a pressure of 1 bar was obtained in chamber region which was considered for experimental results. The temperature decreases in the nozzle region from 300K to 170K. The temperature decreases along the axial direction at the exit of the nozzle due to the adiabatic expansion of the gas. Also temperature is equal to 300K in the chamber region which is equal to designed ambient temperature.
In the present study, an attempt has been made to analyze the velocity / Mach number variation in a CD nozzle particularly when MDT is placed co-axially in the nozzle. Numerical results using CFD technique was compared with the Wind tunnel/Pitot tube experiments.
Mach number values for the Wind tunnel experiments and the CFD trails without placing the co-axial MDT decreases radially at the exit of the Nozzle. The Mach number plot shows that there is not much difference between the experimental and the numerical values and they are almost close.
The Mach number plot for the Wind tunnel experiments and the CFD trails for CD nozzle with MDT show that the Mach number first increases and then decreases radially at the exit of the Nozzle.
The Mach number for CD nozzle without placing the co-axial MDT for Wind tunnel experiments shows continuous expansion along the axial direction. But in the case of CFD trails, the Mach number increases to a maximum value and later decreases along the axial distance due to decay in the velocity of the gas. The same trend is observed when the MDT is placed co-axially in the CD nozzle for Mach number plot.
The authors thank Management and students of MSRIT--Bangalore, Prof. Prabhu and Prof. Vasudevan of Aerospace Engineering, Indian Institute of Science, Bangalore and JSSATE--Bangalore for the cooperation and encouragement during the present study.
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P. Sanjay (a), N.S. Mahesh (b) and S. Kishore Kumar (c)
(a) Dept. of Mechanical Engineering, JSS Academy of Technical Education, Bangalore--560060
(b) Dept of Mechanical and Automotive Engg, MSR school of Advanced Studies, Bangalore--560054
(c) CFD Group, Gas Turbine Research Establishment, Bangalore--560093, Karnataka, India E-mail: firstname.lastname@example.org
Table 1: CD Nozzle dimensions and Process Parameters. Serial No Nozzle Parameters Values 1 Inlet Diameter 23.35 mm 2 Outlet Diameter 24.12 mm 3 Throat Diameter 16.00 mm 4 Distance between Inlet and nozzle throat 14.78 mm 5 Distance between nozzle throat and outlet 19.71 mm 6 Inlet Pressure 3 Bar 7 Gauge Pressure 1 Bar 8 Exit mach 2.4 Mach 9 Temperature of the gas at inlet 300 K 10 Boundary condition applied at inlet PRESSUE_INLET 11 Boundary condition applied at outlet PRESSURE_OUTLET 12 Boundary condition applied for chamber PRESSURE_OUTLET design 13 Boundary condition applied at axis SYMMETRY 14 Boundary condition applied at the nozzle WALL wall 15 Boundary condition applied for MDT WALL 16 Atomizing gas used Nitrogen 17 Courant number used - Radial 5 CFL measurement 18 Courant number used - Axial 0.1 CFL measurement
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|Author:||Sanjay, P.; Mahesh, N.S.; Kumar, S. Kishore|
|Publication:||International Journal of Dynamics of Fluids|
|Date:||Jun 1, 2009|
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