improving gas flow in gas atomization - diva portal

IN DEGREE PROJECT MATERIALS SCIENCE AND ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2021

Improving gas flow in gas atomization

ZHIWEI QIU

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

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Abstract

Gas atomization is a cost-effective processing method to produce fine, spheroidized metal powders. During the process, high velocity jets of gas are sprayed at a molten metal stream to break it into small droplets, which will solidify and form the powder particles. Gas atomized powders usually have a wide size range (1-300 μm), and the range can be up to 500 μm for free-fall gas atomization. Close-coupled gas atomization produces a higher percentage of fine particles and is more attractive to manufacturing applications (-45 μm for MIM, 20-45 μm for SLM, 45-106 μm for EBM). However, compared to the close-coupled process, free-fall type suffers less from the problem that the splashing melt can solidify on gas nozzles. It is believed that by improving the nozzle configuration and arrangement design, the yield and powder particle fineness can be improved. Gas nozzle design is one of the key factors to control gas properties and thus the powder characteristics. Visualization techniques (shadowgraphy and Schlieren imaging) and computational fluid dynamics (CFD) were used to investigate the gas flow from the free-fall atomizer. Schlieren imaging method was used to validate the CFD model, but the results did not match. Potential causes of the discrepancy that affect the CFD model include problems with discretization, input data, boundary conditions and the selection of, and parameters in the turbulence model. A qualitative parametric study was performed using this CFD model to test different designs and study the effect of gas nozzle diameter, angle, distance between melt and gas nozzles. The results showed that a smaller diameter (e.g. decreasing from 1.7 mm to 1.0 mm) resulted in the recirculation intensity(maximum pressure) decreasing from 2.4 bar to 1.9 bar and the gas velocity hitting axis of the melt nozzle increasing from 301m s-1 to 426 m s-1; a smaller angle (e.g. decreasing from 30º to 10º) resulted in a decrease in both recirculation intensity (from 3.5 bar to 2.4 bar) and gas velocity hitting the axis (from 390m s-1to 301 m s-1); a smaller distance between melt and gas nozzles (e.g. reducing 30mm to 13 mm) resulted in an increase in both recirculation intensity (from 1.9 bar to 2.4 bar) and gas velocity hitting the axis (from 254m s-1to 301 m s-1). In addition, a smaller diameter or shorter distance made the flow decay earlier. For example, the transition point between shock units and turbulence occurred 0.301 m downstream of the

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melt nozzle when the gas nozzle diameter was 1.7 mm, but after 0.182 m when the diameter was reduced to 1.0 mm. It was estimated that a smaller diameter combined with larger angle and distance (e.g. ∅1.7mm, 30º, 30mm in this study) will improve gas flow in gas atomization. It was estimated that a smaller gas nozzle diameter combined with a larger angle and distance between the gas nozzles (e.g. ∅1.7mm, 30º, 30mm in this study) will improve gas flow in gas atomization. This combination brought a less intense recirculation zone and relatively high energy in the gas to break the melt in a relatively long flow region.

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Sammanfattning

Gasatomisering är en kostnadseffektiv teknik som framställa små och sfäriskt metallpulver. Under processen, gasstrålar med hög hastighet sprutas mot en ström av flytande metall för att dela den i droppar. Dessa droppar kommer att stelna och förvandlas till pulverpartiklar. Gasatomiserade pulver har ofta en bred storleksdistribution (dvs. 1-300 µm), och distributionen kan vara upp till 500 µm i processen som heter ”free fall” gasatomisering. Den alternativa processen (som heter ”close-coupled” gasatomisering) framställer flera små partiklar och därför är mer attraktivt för pulverbaserade tillverkningsprocesser (t ex. ”metal injection moulding” kräver partiklar som är mindre än 45 µm, ”selective laser melting” kräver partiklar mellan 20 µm och 45 µm och ”electron beam melting” kräver partiklar mellan 45 µm och 106 µm). Problemet med ”close coupled” gasatomisering är att det är lätt för den flytande metallen att stänka och stelna på munstyckena. Problemet är mindre för ”free-fall” gasatomisering. Om munstyckskonfigurationen och arrangemang kan förbättras kan processutbytet ökas och partikelstorleken förminskas samtidigt. Gasmunstyckedesign är en av de mest viktiga faktorerna i processen. Den påverkar gasegenskaper och därför pulveregenskaper. Visualiseringstekniker (dvs. Schlieren-bildbehandling och skuggografi) och ”computational fluid dynamics” (CFD) användas för att undersöka gasflödet från en ”free-fall” gasmunstycke. Schlieren-bildbehandling användas för att validera CFD-modellen men resultaten stämde inte. Möjliga orsaker till avvikelsen som påverkar CFD modellen kan vara diskretiseringen, indata, gränsförhållanden och val av och parametrar i turbulens modellen. En kvalitativ parametrisk studie med användning av CFD-modellen utfördes för att jämföra olika design och studera effekten av gasmunstyckediameter, gasmunstyckevinkel, avståndet mellan gasmunstycken och smältmunstycket. Resultaten visar att en mindre diameter (vid minskning från 1.7 mm till 1.0 mm) gör att intensitet av recirkulering minskas (den högst trycke sjunker från 2.4 bar till 1.9 bar) men hastighet av gas vid smältmunstycks axel ökar från 301 m s-1 till 426 m s-1; en mindre vinkel mellan gasmunstycken gör att både intensiteten av recirkulering och hastighet av gas vid smältmunstycks axel minskas (från 3.5 bar till 2.4 bar respektive från 390 m s-1 till 301 m s-1); ett mindre avstånd mellan smältmunstycket och gas munstycken gör att både intensiteten av recirkulering och hastighet av gas vid

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smältmunstycks axel ökas (från 1.9 bar till 2.4 bar respektive från 254 m s-1 till 301 m s-1). En mindre diameter eller ett mindre avstånd gör att gasflödet sakta ner snabbare. Till exempel är övergångspunkten mellan shockwaves och turbulens 0.301 m nedströms smältmunstycket när gasmunstyckets diameter var 1.7 mm, men efter 0.182 m när diametern reducerades till 1.0 mm. Det uppskattades att en mindre gasmunstyckesdiameter i kombination med en större vinkel och avstånd mellan gasmunstycken kan förbättra gasflödet i gasatomisering (t ex. 1.7 mm diameter, 30° vinkel och 30 mm avstånd i den här studien). Den här kombinationen gör att intensitet av recirkulationen är minskad och det finns mer energi i gasen för att bryta upp smältan i ett relativt långt flödesområde.

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Table of Contents

1. INTRODUCTION ........................................................................................................ 1

GOALS ......................................................................................................................... 2 SCOPE .......................................................................................................................... 2 SUSTAINABILITY .......................................................................................................... 3

2. BACKGROUND ........................................................................................................... 4

2.1 GAS ATOMIZATION ....................................................................................................... 4 2.2 FREE-FALL GAS ATOMIZER ........................................................................................... 5

2.2.1 Cylindrical gas nozzle ......................................................................................... 6 2.2.2 Effects of process parameters on particle characteristics .................................. 8

2.3 COMPUTATIONAL FLUID DYNAMICS ............................................................................ 9 2.3.1 CFD methodology ............................................................................................. 10 2.3.2 Governing equations ......................................................................................... 11 2.3.3 Turbulence modelling ....................................................................................... 13

2.4 SCHLIEREN IMAGING & SHADOWGRAPHY .................................................................. 14

3. METHOD .................................................................................................................... 16

3.1 CFD SIMULATION METHOD ........................................................................................ 16 3.1.1 Geometry ........................................................................................................... 16 3.1.2 Meshing ............................................................................................................. 17 3.1.3 Fluent setup ....................................................................................................... 17 3.1.4 Parametric study ............................................................................................... 21

3.2 EXPERIMENT METHOD ................................................................................................ 22 3.2.1 Assembly and alignment ................................................................................... 22 3.2.2 Experiment procedure ....................................................................................... 23 3.2.3 Post processing ................................................................................................. 24 3.2.4 Safety precautions ............................................................................................. 24

4. RESULTS .................................................................................................................... 25

4.1 CFD SIMULATION FOR EXPERIMENTAL VALIDATION .................................................. 25 4.2 EXPERIMENT RESULTS ............................................................................................... 25

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4.3 QUALITATIVE PARAMETRIC STUDY ............................................................................ 28

5. DISCUSSION .............................................................................................................. 37

5.1 SHADOWGRAPH AND SCHLIEREN IMAGING RESULTS .................................................. 37 5.2 EXPERIMENTAL VERIFICATION OF THE CFD MODEL .................................................. 37 5.3 QUALITATIVE PARAMETRIC STUDY ............................................................................ 39

5.3.1 Effect of gas nozzle diameter ............................................................................ 39 5.3.2 Effect of gas nozzle angle .................................................................................. 41 5.3.3 Effect of distance between melt nozzle and gas nozzles .................................... 41

6. CONCLUSIONS ......................................................................................................... 42

7. FUTURE WORK ........................................................................................................ 44

8. ACKNOWLEDGEMENT .......................................................................................... 45

9. REFERENCES ............................................................................................................ 46

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1. Introduction

Gas atomization is a cost-effective process to produce spherical metal powders by breaking up a continuous molten metal stream with high-velocity gas. As shown in the zoomed part of Figure 1, the atomizer contains two sets of nozzles: the melt nozzle which vertically releases molten metal, and gas nozzles which surround the melt nozzle and eject gas towards the melt. Powders are collected in hoppers at the bottom of the atomization chamber. In this thesis project, the object of interest is a free-fall discrete-jet gas atomizer equipped with cylindrical gas nozzles.

Figure 1 Gas atomization process [1].

Gas atomization in general leads to a wide particle size distribution, while Additive Manufacturing technologies usually requires fine particles within a small size range. For example, powder bed systems usually require sizes below 50 μm, electron beam melting and laser metal deposition usually require sizes between 50 μm and 150 μm [2]. Compared to

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close-coupled gas atomization, free-fall gas atomization is less efficient at producing fine powder particles. However, with special design of nozzle configuration and arrangement, it can be improved and yield more relatively fine particles. The gas ejected from nozzles creates turbulence. At relatively high gas pressure and flow rate, the gas will experience repeated expansion and compression downstream the nozzle exit, i.e. the flow becomes compressible. A computational fluid dynamics (CFD) model of the atomizer was created that took into account the turbulence and shockwaves. In order to improve the efficiency of free-fall gas atomization process, the CFD model was then utilized to study the effect of different nozzle parameters. In addition, gas visualization experiments were conducted to validate the CFD model.

Goals A discrete cylindrical gas nozzle set was selected for the thesis project. The planned duration of the project is 22 weeks. The main goals include: l To create a stable and consistent CFD model that provides quantitate information of gas

flows. l To test the accuracy of the model with gas visualization experiments. l To study effects of gas nozzle parameters on flow behaviors through parametric studies. To validate the CFD model, length of the simulated flow structure and its counterpart in experiments will be compared. To investigate effects of parameters, key results of every test should be collected for comparison and analysis.

Scope Due to the time longer than expected for CFD model construction, the project time-limit was extended. Literature research was conducted to get a better understanding of (1) the characteristics of gas flow from a cylindrical gas nozzle; (2) qualitative effects of free-fall gas atomization process parameters, and critical empirical parameters for process evaluation; (3) basic principles and methodologies of gas flow investigation techniques – CFD modelling and Schlieren / Shadowgraph visualization techniques. CFD simulations and visualization experiments were completed. Experiments, including Shadowgraph and Schlieren imaging, used air to prevent asphyxia, so the CFD model for validation also simulated air. For parametric studies, the simulated fluid is nitrogen, the same as in industrial production. The parametric study is qualitative, i.e., it studied the effect of changing parameters, rather than the exact output of parameters. Effects of three key parameters of gas nozzle design (diameter, angle, distance between melt and gas nozzles) were separately compared and analyzed.

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Sustainability This thesis work mainly contributes to goal 9 and 12 of the Sustainable Development Goals by the United Nations (Figure 2). The study of effects of nozzle parameters serves as an initial step for designing a free-fall gas atomization process. Comparing to industrial trials, numerical simulation provides valuable information for process optimization, reduces production and labor costs, thus cuts down waste generation in R&D process and helps combat climate change. The visualization techniques are easy to operate, also are cheap and reliable methods to validate simulation results. Furthermore, an optimized free-fall gas atomization process will decrease the mean size of powders, increase the yield of fine spherical particles, thus improve resource efficiency and development of powder metallurgy products.

Figure 2 Sustainable Development Goals [3].

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2. Background

2.1 Gas atomization Gas atomization is an effective and economic method to produce spherical metallic powder particles in large quantities. The high solidification rate during gas atomization brings particles with attractive material properties and microstructure refinement that are unachievable in conventional ingot casting metallurgy. This is especially beneficial for high-alloyed materials since elemental segregation can be reduced. The fine spherical particles are suitable for applications where good packing and flow properties are wanted, such as Metal Injection Moulding and Additive Manufacturing [4]. The basic principle of gas atomization is to increase the surface area of the melt stream, using high-pressure gas (usually air, nitrogen, helium or argon at 21-55 bar [5]), until it becomes unstable and disintegrates. The kinetic energy of high-velocity gas effectively breaks the continuous melt stream into droplets and push the droplets away from the atomization zone. Gas atomization assemblies can be categorized into two types according to the nozzle configurations that are used: free-fall or close-coupled gas atomization, as shown in Figure 3. Particle size distribution (PSD) of gas atomization usually has a wide range (1-300 μm [6]). It is more difficult to produce fine particles using free-fall gas atomization (mean diameter < 50-60 μm on iron-base materials [7]). While close-coupled type is usually preferred for its higher yield of finer particles thanks to the close configuration of nozzles. However, close-coupled process is more computationally expensive and difficult to model, due to the two-way coupling of the gas and melt flows. The expansion of gas interacts with the nozzle tip and rapidly cools down the area right below the tip – the so-called “freezing” problem. The extensive cooling by expanding gas can create positive or negative pressure below the melt nozzle, thus accelerate or push back the melt flow in the nozzle. Therefore, most development is done empirically or using theory, rather than using computational models. Free-fall type is less problematic in terms of freezing because the melt nozzle and gas nozzles are well separated [4, 6, 8-10].

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Figure 3 Gas atomization assemblies. Left: free-fall type; right: close-coupled type [11].

(Permission to use this image was obtained through Copyright Clearance Center’s RightsLink® service.)

2.2 Free-fall gas atomizer Free-fall gas atomization has lower efficiency producing fine particles (size range up to 500 μm) than the close-coupled type (typically 10-300 μm), but through special design and nozzle arrangements, it can produce relatively fine particles suitable for applications such as hot isostatic pressing [7]. The process can be categorized into annular-slit-die type or discrete-jet-die type, based on the geometry of the gas delivery system. The annular slit die surrounds, and is concentric with the melt nozzle, creating a narrow channel between the die and nozzle, where the gas passes through. While the discrete jet die delivers gas through multiple holes machined into the die or from multiple individual gas nozzles [12]. A discrete jet die arrangement is used in this project. The free-fall discrete-jet atomizer consists of a manifold having several holes for fitting gas jets and gas supply equipment. The holes are positioned at equal circumferential distances and tilted conically, so that their axes intersect at a geometric point on the central axis of the manifold and make an apex angle α. The distance between gas nozzle exits and geometric point is called “focal length” of the atomizer. Apex angle (α), focal length (F), number (N) and diameter (D) of gas nozzles (shown in Figure 4) are critical parameters to consider when designing the atomizer [13].

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Figure 4 Schematic view of a free-fall atomizer [13]. (Permission to use this image was obtained through Copyright Clearance Center’s RightsLink® service.)

The problem of this atomizer is the appearance of a recirculation zone near the nozzles (Figure 5). If the intensity of the recirculation flow is high enough, droplets or ligaments will be transported back to the atomizer instead of falling to the chamber bottom, which may cause clogging of the gas or melt nozzle.

Figure 5 Recirculation zone during free-fall gas atomization [14].

2.2.1 Cylindrical gas nozzle As shown in Figure 6, the gas nozzle internal profile has mainly three types: cylindrical, convergent, convergent-divergent (C-D). Cylindrical gas nozzles are used in this study. Different internal profiles affect the gas flow behavior: for a C-D nozzle, exit gas velocity can be supersonic; for the first two types, when gas pressure is large to an extent, choked flow occurs (i.e. the exit velocity is at maximum Mach 1, the local speed of sound). The flow rate at the exit is fixed and no longer changes with increasing gas pressure. This is because

D

Nozzle

Axis of

melt nozzle

Recirculating

gas

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of the inner flow saturation of Mach number, Reynolds number, and gas velocity inside the nozzle [12, 15].

Figure 6 Different gas nozzle internal profiles. Three major flow patterns (Figure 7) exist depending on the pressure ratios: l State I: When the ratio between the gas exiting the nozzle and the ambient atmosphere

is 1, the jet is subsonic. It is characterized by a potential core and a mixing region of jet and ambient air surrounding the core. The flow is initially turbulent. Several nozzle diameters downstream of the nozzle tip, the core disappears as the mixing region diffuse inward and spread further downstream. The velocity distribution indicates that the flow becomes laminar.

l State II: When the pressure ratio between the gas exiting the nozzle and the surrounding atmosphere is higher, the exiting gas becomes sonic, shock units appear in the core and gradually decay due to the inward diffusion of the mixing region. Downstream of the core, the mixing region spreads and gas is subsonic. This state is termed “moderately under-expanded”.

l State III: As the pressure ratio increases, the flow reaches a “highly under-expanded” state and a Mach disk forms. The core can be very long and dominated by shock units. The flow velocity decays mainly through oblique shockwaves rather than the mixing region, because the radial diffusion of mixing region is small. Far downstream, usual subsonic decay happens.

In state II and III, the shock waves are one of the main sources to induce turbulence and vortices, thus enhancing the gas/melt mixing during gas atomization. From a macroscopic perspective, the penetration volume and depth of the cone-shape gas flow field are positively correlated to the degree of gas/melt mixing [16-18].

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Figure 7 Flow states of high-pressure gas jet. (Pe: nozzle exit pressure; Pb: ambient

pressure; Pi: nozzle inlet pressure [19]. (Permission to use this image was obtained through Copyright Clearance Center’s RightsLink® service.)

According to a well-known approximation, when Mach number, M > 0.3 (Equation 1, where 𝑢 is local gas flow velocity, 𝑐 is local speed of sound), the flow is considered compressible.

𝑀 = !" (1)

Compressible flow is defined as the case where the gas flows have changing density. The variation of density has significant impact on gas velocity, pressure and temperature [20, 21].

2.2.2 Effects of process parameters on particle characteristics

The disintegration of the melt stream can be described as three stages: primary breakup, secondary breakup and solidification. The first stage happens when the gas jet transfers energy to the melt and breaks it into droplets. The second stage is that the droplets further breakup in the gas stream and form smaller droplets. During the last solidification stage, the droplets undergo cooling and their shape is determined by the solidification and spheroidization time. If spheroidization is faster than solidification, and no surface oxidation happens, the shape will be spherical [22].

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The apex angle, α, affects the particle size and morphology. According to Goudar, et al. [6], increasing apex angle decreases axial velocity and increases the normal component of gas jet velocity, thus facilitates melt disintegration and decrease mean particle diameter. Singh, et al. [13] compared 20◦, 40◦ and 60◦ apex angle and found that the latter two produced more spherical particles, because the ligament after primary breakup is less elongated and takes less time to spherodize. However, when the apex angle is too large, mean particle size increases, and problems include splash back melt and clogging at gas or melt nozzle tip may occur due to a strong recirculation zone. It has been demonstrated by Lubanska [23] that the mean particle size (D50, mass median diameter) of gas-atomized metal powders can be predicted through Equations 2 and 3, where K is an empirical constant (between 40 and 50); d is the melt stream diameter; �̇�L and �̇�G are the mass flow rate of liquid metal and gas; 𝜐L and 𝜐G are the kinematic viscosity of melt and gas; 𝜌L is the melt density; UG is the gas velocity; 𝜎 is the melt surface tension.

𝐷#$ = 𝐾𝑑((1 + %̇!%̇") '!'"()

)*/, (2)

𝑊𝑒 = -!."#/

0 (Weber equation) (3)

Among these parameters, viscosity, density and surface tension are constant at a predetermined melt temperature and melt stream diameter is also constant for an atomizer. Therefore, the mean particle size strongly depends on gas velocity and gas/melt flow rate ratio (G/M ratio, �̇�G/�̇�L) [4, 23, 24]. Bruce See and Johnston [22] found that in a free-fall gas atomization system with four discrete nitrogen jets, the particle sizes of liquid tin and led both become finer as the gas flow rate increases. Besides the popular D50 mass median diameter, different mean diameters that provide different information (e.g. numerical mean diameter, volume mean diameter, etc.) exist and cannot be interrelated unless the particle shape is known [5]. Goudar, et al. [6] produced Al-17Si alloy powder with free-fall atomizer and found that higher G/M ratio leads to an almost linear decrease in volume mean diameter, and significant decrease in Sauter mean diameter, which is the ratio of total droplet volume to total droplet surface area, indicating that there is a higher percentage of spherical particles in the powder.

2.3 Computational Fluid Dynamics Computational Fluid dynamics (CFD) is a computer-based analytical tool that simulates fluid flow behavior. The word “simulate” indicates that it solves numerically the governing laws of flows within/around a material system and produces quantitative predictions of fluid flow behavior. If used correctly, CFD provides information useful information at low costs quickly [25, 26].

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2.3.1 CFD methodology CFD consists of three parts – pre-processing, numerical simulation and post-processing. ANSYS Fluent is a powerful software package that is widely used and trusted. It gives good prediction of single-phase gas flow behavior in gas atomization process that is consistent with experiment results (e.g. Schlieren imaging) [27]. Therefore, in this study ANSYS Fluent will be used. Pre-processing: Firstly, the physical domain (in two or three dimensions) of the engineering problem must be defined, and boundary condition data for the domain should be available. The geometry is then discretized into small cells (the so-called mesh or elements). An adequate number of mesh elements is usually decided by a mesh sensitivity study – the mesh should be refined to a certain level so that the simulation results are independent of the mesh size, thus the simulation solution can be considered to be “convergent” [26]. The process of a mesh sensitivity study is to refine mesh size repeatedly, from a coarse to a fine mesh (usually, the size of the elements is decreased by a factor of 1.5 at each stage [27]), then results are compared. Mesh independence is reached when results stop changing. Boundary conditions are defined in order to determine the flow behavior within the domain. ANSYS Fluent allows various boundary conditions, e.g. velocity inlet and outlet for incompressible flows, pressure/mass inlet and outlet for compressible flows, stationary/moving/(non-)slip wall conditions for walls of a domain [27], etc. In addition, the calculation model and fluid properties are defined. Numerical simulation: The governing equations (conservation of mass, energy and momentum) are discretized and solved for each element iteratively to a steady state. The basic equation discretization approaches are finite volume method, finite element method, finite difference method. In ANSYS Fluent, the finite volume method is used. It solves governing equations over discrete control volumes, then integrates differential forms of governing equations over each control volume [27]. It has a great advantage that it maintains the global conservation of flow equations – the so-called “conservative discretization” [28]. The discretization accuracy depends on the discretization scheme (e.g. upwind scheme which uses the values upstream to calculate the properties of a cell) and order of magnitude (e.g. second order, which means two upstream points are used for the computation) [26]. The integration scheme can be either explicit or implicit. Explicit solution solves each element based on its previous information, while implicit solution solves simultaneous equations for the whole grid for each time step. Implicit scheme is more attractive because it is unconditionally stable and allows large time steps [29]. The convergence of a simulation can be determined based on the following criteria: l the residual values decrease below the criteria value.

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l the solution (e.g. velocity, static pressure, static temperature, mass flow) for a key position in the geometry reaches a steady state after iterations [27, 30].

Post-processing: The simulation results can be visualized by contours and x-y plots. Take Figure 8 as an example, velocity magnitude distribution was demonstrated by the colored contour, while its variation in value along an axis of interest was plotted in the chart below. Based on the visualization methods, one can get a detailed knowledge of the flow, and analyze the effect of parameters associated with the process.

Figure 8 Example of contour and x-y plot.

2.3.2 Governing equations Navier-Stokes equations are a set of time-dependent equations that describes the motion of viscous fluid. For different types of fluid flows, non-conservation and conservation forms of Navier-Stokes equations exist, and the latter one is preferred when the solution of density is discontinuous, e.g. shock waves in compressible flow [31]. The conservation form of Navier-Stocks equations for a two-dimensional compressible flow are listed below (Equation 4-7) [27]:

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Conservation of mass (continuity equation):

1-12+ 1(-!)

15+ 1(-6)

17= 0 (4)

Where ρ is density, u, v are velocity in x and y directions respectively, t is time. The mass of the flow is conserved and its rate of change is zero [32]. This equation is also known as the continuity equation. For compressible flow, the density is not constant but varying, hence the density time derivative term is retained. Conservation of energy:

1(-8)12

+ 1(-!8)15

+ 1(-68)17

= 1155𝜆 19

157 + 1

175𝜆 19

177 + 1:

12+ 𝜙 + ST (5)

Where p is pressure, T is temperature, λ is thermal conductivity, ℎ is enthalpy, 𝜙 is an energy dissipation function, ST is an additional source term such as gravity and heat sources. The enthalpy is correlated with the specific energy, E, of a fluid [33]. This equation is derived from the first law of thermodynamics. The left-hand side includes local acceleration (rate of energy change with respect to time) and advection terms (rate of energy change caused by the fluid particle motion). The right-hand side includes diffusion, local pressure time derivative, dissipation and additional source terms. Conservation of momentum:

1(-!)12

+ 1(-!!)15

+ 1(-6!)17

= − 1:15+ 1

155(𝜇 + 𝜇9)

1!157 + 1

175(𝜇 + 𝜇9)

1!177 + 𝑆! (6)

1(-6)12

+ 1(-!6)15

+ 1(-66)17

= − 1:17+ 1

155(𝜇 + 𝜇9)

16157 + 1

175(𝜇 + 𝜇9)

16177 + 𝑆6(7)

Where (𝜇 + 𝜇9) is the diffusion coefficient, 𝑆!, 𝑆6 are potential influences such as gravity. This equation is derived from Newton’s second law of motion. The rate of change of momentum about x and y directions are stated above, they are respectively the sum of the external forces about the axis [33]. The local acceleration and advection terms at the left-hand side, are equal to the pressure gradient, diffusion and source terms at the right-hand side. In the above four equations, five unknown variables (ρ, u, v, p, E) exist. Therefore, equations of state are needed to provide the linkage between the conservation equations [33]. The flow is considered as an ideal gas and follows the ideal gas law (Equation 8).

𝑝 = 𝜌𝑅𝑇 (8)

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Where 𝑅 = ;$<%

, 𝑅! is universal gas constant (8.3145 J mol-1 K-1), 𝜗% is molecular mass of

gas. For compressible flows, pressure contains two parts: pop – operating pressure, p – local static pressure relative to the operating pressure [34]. Density (ρ) and pressure (p) can be evaluated through this equation. Equation 9-11 describe the relation among density (ρ), pressure (p) and specific energy (E), where 𝐶= is the specific heat for a constant volume, k is the heat capacity ratio.

𝐸 = 𝐶=𝑇 (9)

𝐶= =;>?*

(10)

𝑝 = (𝑘 − 1)𝜌𝐸 (11)

2.3.3 Turbulence modelling Turbulent flows are characterized by fluctuating velocity fields and present in gas flow during gas atomization process, as discussed in section 2.2.1. Several numerical methods exist and allow engineers to get a sufficient understanding of turbulence. Reynolds-averaged Navier–Stokes (RANS) models are used in this study. RANS models are highly attractive for industrial simulations because of its balance between computational resources and accuracy. [21] Comparing to other main numerical methods, for example: (1) Direct Numerical Simulation (DNS), which requires very fine mesh throughout the domain to resolve all turbulence scales in space and time. RANS models can be applied to higher Reynolds numbers of flows, large and complex geometry and the CPU reduction is astronomical (1010 or more). This project focuses on understanding the dissipation of kinetic energy instead of resolving the eddies themselves, so RANS models are sufficient. (2) Large Eddy Simulation (LES), which is a scale-resolving method, and its accuracy directly relates to numerical scheme, hence can produce results with narrow error margin. However, for industrial simulations, RANS models offer sufficient accuracy without requiring more investing in additional CPU power like LES. In addition, the Schlieren images reveals that the gas flow near melt nozzle is almost steady state. RANS models are suitable for predicting steady-state flow since small scale turbulent fluctuations are averaged out [27, 35]. The problem with RANS equations is an extra term – Reynolds stress, i.e. there are more unknown variables than equations. The most common solution is the linear eddy viscosity model, which can be further divided into algebraic, one-equation and two-equation models. Two-equation models the most common for complex geometry and flows, and they are known as k-ɛ and k-ω turbulence models (k - turbulent kinetic energy, ɛ - dissipation of turbulent kinetic energy, ω - specific dissipation). The k-ɛ model can describe wall boundary

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layers, when in combination with wall functions. While the k-ω model is considered to provide more accurate and robust modelling for boundary layers. It contains various sub-models and the most popular one is the Shear-Stress-Transport (SST) k-ω model due to its high accuracy [27, 35]. Motaman [27] compared results from two models and no significant differences were found. The SST k-ω model is used in this study.

2.4 Schlieren imaging & shadowgraphy Schlieren imaging and shadowgraphy are visualization techniques to reveal phenomena in fluids and solids with a high-speed camera. The basic principle is to translate invisible light refraction into changes in light intensity, which can be perceived as light and dark by human eyes. Refraction is defined as phase speed changes of light as it passes through a transparent medium. The refractive index of gas, according to the Gladstone-Dale relation (Equation 12), is related to gas density [36].

𝑛 = 𝐾𝜌 + 1 (12)

Where K is the Gladstone-Dale constant, ~ 0.23 cm3/g for air at standard conditions; 𝜌 is the gas density. In gas atomization process, as the high-velocity gas is injected and propagates into the atomization chamber, the compressible flow creates a temperature and pressure gradient, i.e., a gradient in refractive index in the air. In the visualization system, a light ray passing orthogonally through this heterogeneous medium will experience curvatures, and their integral – the ray deflection – is visualized by Schlieren imaging and shadowgraphy. The mirror system can be single-mirror or two-mirror, but the latter one is more common and compelling when two mirrors are available, because the parallel beam between mirrors provides the least ambiguous image and is essential for any quantitative work. The Z-type two-mirror Schlieren system shown in Figure 9 is the most popular method, consisting of a diverging illuminator beam, a converging analyzer beam, a parallel beam between two mirrors. The system captures the jet flow information within the test area (parallel beam) [36].

15

Figure 9 Z-type two-mirror Schlieren system [37].

Shadowgraph technique differs from Schlieren imaging technique mainly in the following three aspects: (1) Schlieren setup includes a knife-edge (cutoff) while Shadowgraph does not. The

orientation of the cutoff affects the image obtained. A simple cutoff only detects ray refractions with components perpendicular to it, e.g. a horizontal cutoff detects vertical refractive index gradient [36];

(2) The percentage of cutoff used determines Schlieren sensitivity, while sensitivity of Shadowgraph depends on optical path length. In general, Schlieren is more sensitive. When the cutoff percentage is too low, the Schlieren effect is very slight, and it resembles shadowgraph. When the cutoff percentage is too high, it results in over-ranging [38], i.e. the brightness is too low and local flow details cannot be observed;

(3) The illuminance level of Schlieren responds to the first derivative of the refractive index (𝜕𝑛/𝜕𝑥), while that of Shadowgraph responds to the second derivative of the refractive index (𝜕,𝑛/𝜕𝑥,) . Although Schlieren has much higher sensitivity in general, Shadowgraph is more sensitive and produces clearer lines in cases where 𝜕,𝑛/𝜕𝑥, is much larger than 𝜕𝑛/𝜕𝑥, for example, gas flows with shockwaves or turbulence [36].

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3. Method

3.1 CFD simulation method For the simulation, ANSYS 2020 R2 Academic for Windows was used. The general procedure to perform a CFD simulation consists of: l Create a geometry. l Discretize the geometry into grid cells, i.e. meshing. l Determine the boundary types of the geometry. l Set up calculation models, boundary conditions, numerical schemes, etc. in ANSYS

Fluent. l Run the calculation until convergence is obtained. l Post-process of the simulation results.

3.1.1 Geometry In order to simplify the problem and to save computational time, the geometries used are 2D axisymmetric models obtained from the normal section of 3D models provided by Uddeholms AB (Hagfors, Sweden). A 2D axisymmetric model is considered to approximate a 3D flow [27]. The geometry (Figure 10) includes a melt nozzle, a cylindrical nozzle configuration and a part of the atomizing chamber. The dashed line is the symmetry axis and the centerline of the atomization chamber. The geometry of the vertical atomization system was rotated 90 degrees counterclockwise, so it is convenient to view on a computer screen and present in a printed report. The limitation of a simplified 2D axisymmetric model is that it assumes the gas jet to be an annular slit die as it rotates around the axis. Therefore, a more advanced method for modelling discrete jets is to use a section of the 3D model with cyclic boundary conditions. However, due to the time limit of the project, 2D axisymmetric model was accepted as an initial investigation method.

17

Figure 10 Geometry used in this project.

3.1.2 Meshing The geometry was discretized into quadrilateral elements through face sizing. The mesh resolution was divided into two levels. The mesh in the green region in Figure 11 (including gas nozzle, downstream area around the axis) was finer than the gray regions. Its size is half of that of the gray region, 0.35mm and 0.70mm, respectively. This is done because the green region is where the gas jet is supersonic and needs higher resolution and accuracy to calculate shockwaves and turbulence. The growth rate of the mesh is 1.2 as default.

Figure 11 Different mesh regions. The quality of mesh was considered good through monitoring skewness and orthogonal quality. Skewness describes the deviation from the ideal element shape and should be kept at approximately zero. Orthogonal quality describes the closeness of the face normal vector and the vector between two centroids of two adjacent cells and is preferably equal to one. The criteria were met. However, an appropriate number of mesh elements should be decided by a mesh sensitivity study, as discussed in section 2.3.1. Due to the project time limit, the study is listed as a future work.

3.1.3 Fluent setup General A density-based solver was used, in order to take into account the compressibility and density variation in the high-velocity flow [31]. The fluid was set as steady state since the studied

600 mm

150 mm

600 mm

18

object is a fully developed turbulent flow. Gravity was neglected to simplify the problem. Models The energy equation solved by ANSYS Fluent incorporates the coupling between the flow velocity and the static temperature, and should be activated when solving the compressible flow [21]. For the viscous model, SST k-ω model was used. Fluid The fluid was modeled as a compressible ideal gas. Nitrogen was used for the parametric study; air was used for the experimental validation model. The density was obtained through the ideal gas law (Equation 8). The viscosity was computed using Sutherland’s Law using the three coefficients method (Equation 13), which describes the relation between the dynamic viscosity and the temperature of an ideal gas [39].

𝜇 = 𝜇$(99&)@/, 9&AB

9AB (13)

Where μ and μ0 are dynamic and reference viscosity, respectively; T and T0 are static and reference temperature, respectively; S is effective temperature. The gas properties listed in Table 1 were obtained from ANSYS database.

Table 1 Nitrogen and air properties.

Boundary conditions As shown in Figure 12, the boundaries were classified into five different groups, set in the meshing software in advance using the “Named Selection” function. In the next step, different boundary types will be applied to each group.

Properties Nitrogen Air

Specific heat capacity, Cp (J kg-1 K-1) 1040.67 1006.43

Thermal conductivity (W m-1 K-1) 0.0242 0.0242

Reference viscosity, μ0 (kg m-1 s-1) 1.66E-05 1.72E-05

Reference temperature, T0 (K) 273.11 273.11

Effective temperature, S (K) 106.67 110.56

Molecular weight, Mw (kg kmol-1) 28.013 28.966

19

Figure 12 Boundary conditions.

Table 2 shows boundary conditions used for the parametric study. The input values were taken from an industrial trial, measured in the gas pipe before the nozzle set. According to ANSYS Fluent User’s Guide [34], The operating pressure was set as zero so that gauge and absolute pressures are equivalent, according to Equation 14.

pop = pabs – pgauge (14)

At the pressure inlet, Supersonic/Initial Gauge Pressure was irrelevant in this case since the inlet was not supersonic, however, it was set as the inlet gas pressure (e.g. 25 bar) because the solution was initialized based on the pressure-inlet boundary conditions. Gauge Total Pressure was set as a close value (e.g. 25.1 bar) for Fluent to compute initial values of velocity. The pressure at the melt nozzle and downstream outlet was both set as the atomizing chamber pressure, which is atmospheric pressure (1.01 bar). The gas temperature measured was applied to all inlet and outlet boundaries. For the turbulence boundary condition of the fully developed flow, the Intensity and Hydraulic Diameter specification method was used according to ANSYS guidance. Turbulence Intensity can be estimated from Reynolds number using a widely accepted empirical relation suggested in the ANSYS Fluent User’s Guide [34] (Equation 15, in which ReDH is the Reynolds number, given by Equation 16, in which 𝜌 is gas density, UG is gas velocity, DH is hydraulic diameter of the gas pipe, 𝜇 is dynamic viscosity. UG is obtained through Equation 17, where 𝑄6 is volumetric flow rate measured in the pipe.)

𝐼 = 0.16(𝑅𝑒/')?*/C (15)

in which, 𝑅𝑒/' =-."/'

D (Reynolds equation) (16)

𝑈E =F∙H(I∙/'

# (17)

For the industrial trial, the Reynolds number was calculated to be 5.05×106 and the turbulence intensity was 2.3%.

600 mm

20

Table 2 Boundary conditions for the parametric study.

Boundary name Boundary type Boundary conditions

Pressure inlet Pressure inlet

Gauge total pressure: determined from test pressure, 25.1 bar; Supersonic/Initial Gauge Pressure: test pressure, 25 bar; Total temperature: 303 K; Turbulence Intensity: 2.3%; Hydraulic diameter: length of inlet boundary, 0.01 m

Melt nozzle Pressure inlet

Gauge total pressure: ambient pressure, 1.01 bar; Supersonic/Initial Gauge Pressure: 1 bar Total temperature: 303 K; Turbulence Intensity: 2.3%; Hydraulic diameter: 0.003 m (Dmelt nozzle)

Downstream outlet Pressure outlet Gauge pressure: ambient pressure, 1.01 bar; Turbulence Intensity: 2.3%; Hydraulic diameter: 0.3 m (Ddownstream outlet)

Walls of melt nozzle, gas die, chamber;

Upper domain boundary

Wall

Stationary wall No-slip wall Zero heat flux

For the experimental validation model, gas pressure and temperature were set as experimental conditions, while the turbulence boundary condition was calculated based on the flow curve in Figure 13. At the experimental inlet and outlet pressures, the volumetric flow rate exiting gas regulator can be determined. Then gas velocity, Reynolds number and eventually turbulence intensity can be determined. The Reynolds number was calculated to be 3.21×106, and hence the turbulent intensity was 2.5%.

Figure 13 Flow curve of gas regulator before the nozzle set [40]. Solution The implicit second-order upwind scheme was used to solve the governing equations based on the study of Motaman [27]. Detailed settings are listed in Table 3. The density-based

21

implicit scheme is unconditionally stable and allow large time step sizes (Courant number can be 100 or higher [34]). The Courant number describes how far information travels at one time step, in terms of mesh elements. A large Courant number will however be detrimental to accuracy since information travels multiple mesh elements at one time step. The Courant number was set as 1 in this study.

Table 3 Solution methods and controls. Methods Controls

Formulation Implicit Courant number 1

Flux type Roe Flux-Difference Splitting

Turbulent kinetic energy 0.8

Gradient Least Squares Cells Based Turbulent dissipation rate 0.8

Flow Second Order Upwind Turbulent viscosity 1 Turbulent kinetic

energy Second Order Upwind Solid 1

Turbulent dissipation rate Second Order Upwind

The convergence of a solution was determined from the convergence of the continuity equation. The stability was determined by monitoring the plots of variables as the calculation continues: l Vertex maximum of velocity magnitude at nozzle exit; l Vertex maximum of total/static temperature at nozzle exit; l Vertex maximum of static pressure at nozzle exit; l Vertex maximum of density at nozzle exit; The sum of the mass flows at the inlet and outlet was not necessarily zero in this project, due to the presence of reverse flows. Therefore, simulation results were accepted regardless of the flux mismatch.

3.1.4 Parametric study Quantitative parametric study The parametric study aims at investigating effects of different nozzle parameters (gas nozzle diameter, gas nozzle angle, gas and melt nozzle distance) on gas flow behavior. The CFD model for experimental validation was run for approximately 2 ×10F iterations to achieve a stable state of variables at nozzle exit. The calculation was then permitted to continue to iterate in order to reduce the residuals and flux. Following some initial trials, a mismatch between the CFD model and experimental findings from Schlieren imaging was discovered. Since the model does not reflect the experimental findings, it is not necessary to achieve complete precision in the model, as doing so provides no additional useful information. Therefore, the calculation was discontinued at around 8 ×10F iterations. Due to the mismatch and the project time limitation, any quantitative parametric study was discarded.

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Qualitative parametric study A qualitative parametric study was continued. It was decided that 8 ×10F iterations was not necessary since the model already stabilized and converged. Therefore, a smaller iteration number of 7.1 ×10F was selected, which resulted in: l Stability of variables (velocity magnitude, static temperature, static pressure, density) at

nozzle exit. l Stable and relatively small residuals. l A shorter simulation time. In total, six qualitative parametric study simulations were completed. The qualitative parametric study, by comparison of results, reveals the qualitative effect of varying nozzle parameters on flow behavior, instead of real quantitative flow properties of every nozzle design.

3.2 Experiment method

3.2.1 Assembly and alignment The arrangement of the visualization was setup based on the discussion in section 2.4. A Z-type 2-mirror system (Figure 9) and an off-axis single-mirror system (as Figure 14 shows) were both used to visualize the gas flow. It was observed that in the sing-mirror system, when the gas passes through the test area, since the incident and reflected light rays are closely coupled, it will affect the reflected light and have negative impact on the image quality. While in the Z-type 2-mirror system, the test area (parallel beam) can be elongated arbitrarily, so that the gas has less disturbance on the diverging and converging light rays. Therefore, the experiment was proceeded using Z-type 2-mirror system. Shadowgraphy and Schlieren imaging techniques were both attempted to visualize the gas flow.

Figure 14 Diagram of off-axis sing-mirror Schlieren system. The Z-type 2-mirror system (Figure 9) includes the following components: (1) a blue-color

23

point light source; (2) two off-axis parabolic mirrors, for which the off-axis angle is 30º and the focal length is 326.64 mm; (3) a high-speed camera (MotionBLITZ Cube 4 camera), connected to MotionBLITZ software to capture images; (4) a knife-edge to cut off light for Schlieren imaging. The two parallel mirrors were bolted to individual base plates. The plates were placed at two ends of a table while keeping the mirror centers on the centerline. The point light source was placed at an angle of 30º to the centerline and at a distance of approximately 326.6 mm (focal length of the mirror) to the mirror. The point light source, mirror centers and the center of camera lens were kept at the same height. For shadowgraph, the camera was placed at the focal point of the converging beam. For Schlieren imaging, the cutoff was placed at the focal point of the converging beam, and the camera was placed a little behind it. In order to achieve better image quality, (1) horizontal and vertical cutoff were compared to decide the suitable orientation; (2) different cutoff percentages, i.e. different levels of illumination, were attempted to decide the optimal percentage.

3.2.2 Experiment procedure As shown in Figure 15, the experiment setup included a Schlieren imaging system, and a vertical-placed nozzle set connected to a gas regulator and a metal hose. The parameters of nozzle used in the experiment was ∅1.7 mm, 10º, 30 mm. A gas pressure of 23 bar was applied to the nozzle set. A 200 bar pressurized air gas cylinder chained to wall was used to provide the high-pressure gas. The ambient pressure was atmospheric pressure, 1.01 bar. The gas temperature (-10 ℃) was measured at the nozzle exit.

1.5m

Figure 15 Experiment setup.

Due to the inevitable spacing between the gas cylinder and the visualization system, a metal hose and gas regulators were used for gas delivery. Two single-stage gas regulators were used to monitor the pressure – the first one connected to the cylinder, the second one connected to the nozzle set. Two regulators both have a maximum allowed pressure exceeding 200 bar, i.e. both are capable of handling the maximum inlet pressure. The size of the second gas regulator

24

outlet is 1/4’’ NPT. They were connected by a 1 m long metal hose. The intermediate pressure (the outlet of the first regulator / the inlet of the second regulator) was 90 bar. According to the flow curve in Figure 13, the volumetric flow rate was 68.75 Nm3/h. The complete procedure for one test includes: l Setting up the visualization system. l Connecting the nozzle set with the regulators and gas cylinder. l Placing the nozzle set properly so that all discrete nozzles are inside the test area. l Pressurizing the gas regulators before the nozzle set. l Turning on recording and releasing gas. l A steady gas flow quickly establishes and is kept for a few seconds. l Saving captured images as AVI files and image stacks in MotionBLITZ software for

post-process. It was observed that the pressure in the cylinder fell by 10 bar after each test. The results of shadowgraph, Schlieren imaging with varying cutoff positions were collected. After finishing all tests, the gas cylinder was sealed first, then gas inside the metal hose was vented.

3.2.3 Post processing The best-quality images of each test were selected for comparison. Then the optimal one showing the clearest patterns was used for CFD model validation. Which was then imported into ImageJ software. Brightness and contrast were adjusted to highlight the shockwaves.

3.2.4 Safety precautions Experiments were conducted in a lab that could be made completely dark in order to improve the quality of the captured images. The only suitable lab was on a basement level and had poor ventilation. To prevent asphyxiation, compressed air was used and released only when taking images. The operation and handling of the pressurized gas cylinder were done by the supervisor under safety guidelines. Ear defenders were used to prevent noise hazards of releasing gas. Goggles with suitable filters were wore to protect eyes from blue point light source.

25

4. Results

4.1 CFD simulation for experimental validation A density gradient contour of experimental validation model was obtained (Figure 16). Two Mach disks (also called “shock diamonds” according to the shape) are visible in the contour. The distance between the nozzle exit and the second shock diamond is 0.063 m.

Figure 16 Density gradient (𝜕𝜌/𝜕𝑥) contour of experimental validation model.

4.2 Experiment results Shadowgraph and Schlieren imaging techniques were both used to investigate the flow pattern (Figure 17). It was observed that the shadowgraph image was the least clear. While in Schlieren images, shock units can be seen using both cutoff orientations, but horizontal cutoff gave better image regarding to the turbulence zone.

0.063m

Shock diamonds

26

Figure 17 Raw images of gas flow at 23 bar. (a) Shadowgraph;

(b) Schlieren using horizontal knife-edge; (c) Schlieren using vertical knife-edge.

Results of different horizontal cutoff percentage were obtained (Figure 18). Further analysis was made using the cutoff percentage in Figure (b) since it revealed turbulent flow without losing too much brightness.

Figure 18 Raw Schlieren images with increasing (horizontal) cutoff percentage.

(a) (b) (c)

(a) (b) (c)

50 (mm)

0 10

20 30

40

40 20 0

50 (mm) 10 30

Turbulent flow

Flow direction

Flow direction

27

Figure 19 is the edited version of Figure 18 (b). Brightness and contrast were modified to make the flow structure clearer. The distance between nozzle set surface and the second shock diamond is 4.82 mm.

Figure 19 Edited Schlieren imaging result. It should be noted that a distance (3.133 mm, marked in Figure 20) was blocked by the nozzle head in experiments. The actual distance between the nozzle exit and the second shock diamond is the sum of two distances measured, i.e. 7.953 mm.

Figure 20 Engineering drawing of the atomizer used in experiments.

4.82mm

3.133 mm Gas

Observed distance (4.82 mm)

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4.3 Qualitative parametric study The qualitative parametric study investigated six different nozzle designs. Different designs were listed in Table 4 and numbered as 1 to 6. Six simulations were completed to analyze the effect of three nozzle parameters (Figure 21) on the gas flow: (1) gas nozzle diameter; (2) gas nozzle angle; (3) distance between gas and melt nozzle.

Figure 21 Variables in qualitative parametric study.

Table 4 Experiment parameters for parametric study.

Experiment Gas nozzle diameter (mm)

Gas nozzle angle (º)

Gas/melt nozzle distance (mm)

1 1.0 10 13

2 1.0 30 30

3 1.7 30 13

4 1.7 10 30

5 1.0 30 13

6 1.7 10 13

All simulations were performed at gas temperature of 303K, gas pressure of 25 bar, ambient pressure of 1.01 bar. Each was run until the residual value of continuity decreased to approximately 1 × 10-3. Velocity magnitude contours, velocity vector fields near nozzles, and x-y plots were obtained for further analysis and comparison. As shown in Figure 22, in each individual experiment, three critical positions along the symmetry axis were selected and analyzed. The first position characterizes any recirculation zone near nozzles. The second is where the gas flow hits the axis, which is also considered as the initial contact position between gas flow and melt stream. The third is the transition point between the shock units (the “core area” in Figure 7) and subsonic turbulent flow. The exact positions were determined with the help of x-y plots. The plot of static pressure is parallel to that of density and is therefore omitted.

29

From the contour and plots in Figure 22, results of Experiment 1 can be obtained: l Point 1: the backflow reaches its maximum velocity (128 m s-1). The maximum static

pressure is 1.9 bar. l Point 2: the gas velocity is 426 m s-1. l Point 3: the transition point is 0.182 m.

Figure 22 CFD results of Experiment 1 (∅1 mm, 10º, 13 mm).

Exp. 1

○1

○1

○2 ○3

700 m s-1

350 m s-1

0 m s-1

30

The results of Experiment 2 are shown in Figure 23. l Point 1: the maximum velocity and pressure are 194 m s-1 and 2.1 bar, respectively. l Point 2: the gas velocity is 425 m s-1. l Point 3: the transition point is 0.314 m.

Figure 23 CFD results of Experiment 2 (∅1 mm, 30º, 30 mm).

Exp. 2

○1

○1

○2 ○3

700 m s-1

350 m s-1

0 m s-1

31


Figure 24 CFD results of Experiment 3 (∅1.7 mm, 30º, 13 mm).

Exp. 3

○1

○1

○2 ○3

700 m s-1

350 m s-1

0 m s-1

32


Figure 25 CFD results of Experiment 4 (∅1.7mm, 10º, 30mm).

○3

Exp. 4

○1

○1

○2

700 m s-1

350 m s-1

0 m s-1

33


Figure 26 CFD results of Experiment 5 (∅1mm, 30º, 13mm).

Exp. 5

○1

○1

○2 ○3

700 m s-1

350 m s-1

0 m s-1

34


Figure 27 CFD results of Experiment 6 (∅1.7mm, 10º, 13mm).

A close examination of the velocity vector fields of recirculation zones reveals the width of the expanding wave and the length of recirculation zone. The results were marked in Figure 28.

Exp. 6

○1

○1

○2 ○3

700 m s-1

350 m s-1

0 m s-1

35

Recirculation length = 0.028 m




0.017 m

0.014 m

0.011 m

0.011 m

Exp. 2

Exp. 3

Exp. 4

Exp. 1 700 m s-1

350 m s-1

0 m s-1

700 m s-1

350 m s-1

0 m s-1

700 m s-1

350 m s-1

0 m s-1

700 m s-1

350 m s-1

0 m s-1

36

Figure 28 Comparison of velocity vector fields of the recirculation zone around nozzles.

The results of six experiments are summarized in Table 5 for comparison and analysis.

Table 5 Results of qualitative parametric studies.

No. Angle (º)

Gas/melt nozzle

distance (mm)

Diameter (mm)

Recirculation zone Gas velocity

reaching axis (m s-1)

Shock units / turbulence transition point (m)

Max. velocity (m s-1)

Max. pressure

(bar)

Length (m)

1 10 13 1.0 128 1.9 0.028 426 0.182

2 30 30 1.0 194 2.1 0.063 425 0.314

3 30 13 1.7 152 3.5 0.017 390 0.326

4 10 30 1.7 196 1.9 0.064 254 0.413

5 30 13 1.0 75 2.3 0.024 550 0.202

6 10 13 1.7 199 2.4 0.020 301 0.301



0.017 m

0.010 m

Exp. 5

Exp. 6

700 m s-1

350 m s-1

0 m s-1

700 m s-1

350 m s-1

0 m s-1

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5. Discussion

5.1 Shadowgraph and Schlieren imaging results In Figure 17, it was observed that although both Shadowgraphy and Schlieren methods revealed shockwaves, but turbulence downstream of the shockwaves could hardly be seen in shadowgraph. This is probably because in the experiment, compressed air was used and the refractive index gradient downstream was too weak to be captured by Shadowgraphy. Schlieren imaging is more sensitive in this case. In addition, horizontal knife-edge produced clearer images of the horizontal flows since the density gradient on vertical direction is more obvious. Besides the orientation of knife-edge, the cutoff percentage also plays an important role in obtaining a clear Schlieren image. In Figure 18. At a lower percentage, the Schlieren sensitivity was low, and the turbulence was unclear in figure (a). At a relatively high cutoff percentage, a significant over-ranging was observed in figure (c), and turbulent flow structure was washed out. The optimum cutoff percentage (approximately 60%), figure (b), was obtained, which was sensitive enough to reveal the turbulent flow without causing severe over-ranging. In addition, spraying argon would also give better contrast, since it will be different to the ambient air.

5.2 Experimental verification of the CFD model The results of the CFD model and Schlieren imaging (section 4.1, 4.2) under the same conditions were compared. A compressible flow with multiple shock units and shock diamonds (Mach disks) were observed in both Figure 16 and Figure 19. The shock diamond is created by the normal shock wave (i.e., a shock wave perpendicular to the flow direction), at where the compressed oblique shock waves are deflected outwards and expand again. Immediately after the shock diamond, pressure rises, and velocity drops rises rapidly. The shock diamond is where a strong density gradient exists. The determination of shock diamonds was based on the brightness in CFD density gradient contour and Schlieren imaging. However, in Figure 16 only two shock diamonds were observed while in the equivalent experiment (Figure 19) four can be seen. And the distance between the nozzle exit

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and the second shock diamond in CFD is almost eight times of that in the experiment result. The mismatches may be resulted from the following sources of error: l Discretization. The flow field was discretized into a finite number of elements (mesh) to

solve the problem. As discussed in section 2.3.1 that at the stage of domain discretization, a mesh sensitivity study should be done in advance to make sure results are independent of mesh fineness. Besides meshing, the numerical scheme also causes a certain order of magnitude of discretization error. For example, second-order upwind scheme used in this project is of second-order accuracy [21]. As shown in Figure 29, it determines the value of a cell surface, 𝜙e, by linear extrapolation from the two upstream cell centers (Equation 18, where 𝜙 and ∇𝜙 are the cell-centered value and its gradient in the upstream cell, 𝑟 is the displacement vector from the upstream cell centroid to the face centroid). Its accuracy is based on Taylor series truncation error [26].

Figure 29 Second-order upwind scheme.

𝜙) = 𝜙 +∇𝜙 ∙ 𝑟 (18)

l Inappropriate input data, such as the flow geometry and fluid properties [26]. As discussed in section 3.1.1, the 2D axisymmetric geometry assumes the gas nozzle to be annular-slit type instead of the actual discrete-jet type. A more accurate way to describe the problem is using a section of 3D model containing a single nozzle. Another source of error should be noted is that, the geometry of gas supply chamber before the gas nozzle was drawn to be a square-shape adopted from the work of Motaman [12], instead of the actual shape. This may affect the inlet gas properties. Although the ideal gas law and Sutherland viscosity law were recommended in previous studies and the ANSYS user’s guide, they have their own limitations. The ideal gas causes errors at extremely low temperatures where intermolecular attraction becomes important so it is acceptable in the project [41]. The Sutherland’s viscosity law has 2% error for air between 170K and 1900K, which includes the current cases [42].

39

l Incorrect boundary conditions. The inlet flow properties applied to the CFD model were

measured in the gas pipe before entering the nozzle set. It can be estimated that pressure and velocity loss exist, hence the input boundary conditions cannot describe the real conditions precisely.

l Modelling error. The turbulence model used was the widely accepted SST k-ω model. It

models the boundary layer near the inner wall of gas nozzle in different ways depending on the value of a parameter called y+, which is computed from the first cell height at the wall y, local flow speed UG, density 𝜌 and dynamic viscosity 𝜇 [43], Equation 19. If the first cell at the wall is large, y+ is large (e.g. y+ ~30 or above), the software will automatically use wall functions to solve boundary layers, which can cause modelling errors. And if the first cell is small, i.e. the mesh resolution near wall is high and y+ is small (e.g. y+ ~1), more meshing and solution time will be required but better prediction will be obtained [44]. The value of y+ was not considered in the project but is an important criterion for future improvements.

𝑦+= 7∙.)∙-D

(19)

Among the above potential sources, domain discretization error and modelling error are most likely to be responsible for the mismatch, since the rest of the settings are based on published papers and produced satisfying results. They can be fixed by improving the mesh quality, for example, conducting a mesh sensitivity study and refining mesh at the inner walls of nozzles.

5.3 Qualitative parametric study As shown in the velocity magnitude contours (Figure 22-27) as well as velocity vector fields (Figure 28), the gas rapidly expands as it leaves the exit, and a recirculation zone can be seen between the nozzles. The expanding and compressing gas formed a shock unit right downward the nozzle exit. Further downstream, the flow meets its twin flow at the symmetry axis. As seen in velocity magnitude contours, between point 2 and 3, repeated expansion and compression formed a series of shock units, which is supported by the fluctuating velocity and density data. After point 3, density decayed continuously, i.e. the flow no longer contracts, therefore point 3 was considered as the end point of the shock units and only subsonic turbulent flow occurred downstream of this point.

5.3.1 Effect of gas nozzle diameter The effect of diameter can be observed by comparing Experiment 1 and 6 (or 3 and 5). As shown in Figure 28, When the gas nozzle diameter was made smaller while other parameters were kept unchanged, the flow expansion became smaller, indicated from the width of the first shock unit. This made the recirculation zone expand slightly and become more elongated.

40

The recirculation was also less intense – the maximum velocity and pressure inside decreased. Effects of diameter on the recirculation zone are shown in Figure 30.

Figure 30 Effects of gas nozzle diameter on the recirculation zone.

Since the flow from a smaller nozzle was thinner, the interaction between the flow and its complementary flow along the symmetry axis was weaker. Take the differences between results of Experiment 3 and 5 for example (diameter of 1.7 mm and 1 mm respectively, Figure 24 and Figure 26), the smaller diameter of Experiment 5 significantly weakened the repeated expansion and compression between point 2 and 3. In order to better contrast the differences, the x-y plots of Mach number are shown in Figure 31. For Experiment 5, the plot has less fluctuation and decays quickly, thus the transition point between shock units and turbulence is closer to the nozzle. Another notable effect of decreasing the diameter is that the gas velocity reaching the symmetry axis increased significantly (from 390 m s-1 to 550 m s-1, Table 5), which might facilitate primary breakup of the melt.

Figure 31 Local Mach number as a function of position along the symmetry axis,

Experiment 3 (∅1.7 mm) and Experiment 5 (∅1 mm).

Transition points

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5.3.2 Effect of gas nozzle angle The effect of gas nozzle angle can be observed by comparing Experiment 3 and 6 (or 1 and 5). The major effect was observed in the recirculation zone. When the angle was larger, the expanding wave was slightly rotated clockwise, which confined the recirculation zone to a smaller region and increased the pressure inside. This might cause a clogging problem at the nozzle exits in practice. On the other hand, a larger angle makes the gas travel less distance to the axis and the gas may have higher velocity to hit the melt. This will aid primary breakup of the melt stream.

5.3.3 Effect of distance between melt nozzle and gas nozzles The effect of distance between gas and melt nozzles can be observed by comparing Experiment 4 and 6 (or 2 and 5). When the distance is smaller, the recirculation zone is compressed to a smaller area by the surrounding expanding gas wave, and its length is cut by more than half (Figure 28). In addition, the pressure inside the recirculation zone becomes higher. The gas velocity hitting the symmetry axis increases, because less energy is lost in the smaller distance that the gas travels before it meets the axis. A smaller distance also makes the transition point between shock units and turbulence closer to the nozzle (Table 5) and the full length of the flow shorter. To make a clearer comparison, x-y plots of turbulent kinetic energy of Experiment 2 and 5 are shown in Figure 32. It is evident that in Experiment 2 where the distance is larger, turbulence is pushed further downstream and the whole flow decays after a longer distance.

Figure 32 Turbulent kinetic energy vs. symmetry axis of Experiment 2 (30 mm) and Experiment 5 (13 mm).

Turbulence downstream

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6. Conclusions

This thesis project has built a 2D axisymmetric CFD model of a free-fall discrete-jet gas atomizer. The CFD model was compared with experimental results, using Schlieren imaging technique, for validation. Then the CFD model was run with different gas nozzle designs, and the results were collected and discussed for a qualitative parametric study. Shadowgraph is theoretically suitable for flows containing turbulence and shockwaves, but Schlieren imaging was more sensitive to the air flow in this project. The use of a horizontal knife-edge was found to be better at differentiating the high velocity gas jet flows from the atmosphere. A knife-edge cutoff percentage of approximately 60% was determined to reveal flow details without causing severe over-ranging. By comparing the Schlieren result and the density gradient contour of the CFD result, mismatches were found in both distance (a difference of eight times) and number of the shock diamonds (four and two, respectively). The most likely causes are errors in domain discretization (meshing) and modelling (large y+ value), which can be fixed by improving mesh quality in future work. Despite the mismatch, a qualitative parametric study was then continued. According to CFD results under the same inlet gas conditions in qualitative parametric studies, the effects of different nozzle parameters were summarized in Table 6. It was found that when other parameters were kept constant: l Decreasing the gas nozzle diameter increases the gas velocity hitting the symmetry axis

significantly; decreases the width of the flow, which makes the recirculation zone expand and pressure inside decrease; weakens the flow interaction along the axis and increases the rate at which the velocity of flow decays. For example, when decreasing the nozzle diameter from 1.7 mm to 1.0 mm, the pressure inside the recirculation zone dropped from 2.4 bar to 1.9 bar; the gas velocity hitting the axis increased from 301 m s-1 to 426 m s-1; the transition point between shock units and subsonic turbulent flow shortened from 0.301 m to 0.182 m.

l The gas nozzle angle mainly affects recirculation: Decreasing the angle expands the recirculation zone and makes it less intense (the maximum pressure inside decreases);

43

decreases the gas velocity hitting the symmetry axis. For example, when decreasing the nozzle angle from 30º to 10º, the pressure inside the recirculation zone decreased from 3.5 bar to 2.4 bar; the gas velocity hitting the axis increased from 390 m s-1 to 301 m s-1.

l Decreasing the distance between melt and gas nozzles increases the pressure inside the recirculation zone and decreases the size of the zone; increases the gas velocity hitting the symmetry axis; increases the rate at which the velocity of the flow decays. For example, when decreasing the distance from 30 mm to 13 mm, the pressure inside the recirculation zone increased from 1.9 bar to 2.4 bar; the gas velocity hitting the axis increased from 254 m s-1 to 301 m s-1; the transition point between shock units and subsonic turbulent flow shortened from 0.413 m to 0.301 m.

Table 6 Effects of gas nozzle parameters.

Diameter ↓ Angle ↓ Distance ↓

Recirculation zone intensity ↓ ↓ ↑

Gas velocity hitting the axis ↑ ↓ ↑

Shock units Weaker interaction, shortened - Shortened

It was found that the best design is a smaller diameter combined with a larger angle and a longer melt/gas nozzle distance. For example, in Experiment 2 (∅1.7mm, 30º, 30mm), the nozzle design leads to a relatively long and less intense recirculation zone, a relatively high velocity to hit the symmetry axis, plus longer lengths of the core area and the whole flow. This is likely to be good for both primary and secondary breakup of the melt, thus producing powders with a smaller mean diameter more efficiently. The main advantage of the gas atomization process is its controllability which can be guided by numerical methods by adjusting the parameters. These simulations serve as a good guidance for further controlled experiments.

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7. Future work

To improve the accuracy of the CFD model, possible future works are listed as follows: l Refine the mesh size at the inner wall of the gas nozzle, in order to reduce y+ value, thus

to produce better prediction. l Perform a mesh sensitivity study on this CFD model, so that the results are independent

of the element/grid number. l Improve the accuracy of CFD model describing reality. For example, make the 2D

geometry in line with the cross section in reality; reduce errors in boundary conditions. l Validate the CFD model and perform quantitative parametric study. l Create a 3D model of a section of the nozzle set (containing one single nozzle) with

cyclic boundary conditions to solve the problem.

Furthermore, a CFD model containing the melt stream is beneficial for directly studying the melt breakup.

45

8. Acknowledgement

I would like to express my sincere gratitude to my supervisors at KTH, Department of Material Science and Engineering (MSE) - Assistant Professor Christopher Hulme, PhD student Arun Kamalasekaran. I would like to thank Chris for giving me this opportunity to do the project and providing me with support and guidance. I would like to thank Arun for your continuous support and encouragement. You have been patient and enthusiastic and guided me through many doubts and troubles. Also, thanks to my colleague Mahsa Darvishghanbar for helping me with setting up the laboratory experiments. I would like to thank my supervisors at Uddeholms AB - Victoria Bergqvist and Giulio Maistro, for offering me this wonderful opportunity and for your trust and support. The project would not have been smooth without your regular and timely feedback.

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