Overview
Computational Fluid Dynamics
Computational Fluid Dynamics: A Virtual Prototyping Tool for Materials Engineering A. Mukhopadhyay, B. Devulapalli, A. Dutta, and E.W. Grald
The use of computational fluid dynamics (CFD) software in many materials processing industries has grown tremendously in recent years. Computational fluid dynamics has been widely utilized for conducting virtual experiments, prototype testing, and parametric studies. Analysis using CFD complements and reduces physical testing, and it can result in a significant time and cost savings. In this article, the application of CFD to a variety of materials-processing problems is presented, with examples taken from the steel, aluminum, glass, semiconductor, and polymer processing fields.
decrease the time and cost associated with new product and process development. Computational fluid dynamics gives insight and provides detailed predictions of operating conditions in lieu of difficult, intrusive, and often expensive experimental methods. It can be used as an aid to scale-up processes from lab or pilot scale to full production. Troubleshooting the performance of existing equipment is often carried out with the help of CFD, as is determining how an existing piece of process equipment will operate under new conditions or with new input materials. The term “materials processing”
INTRODUCTION Computational fluid dynamics (CFD) is the technique of solving the governing equations of fluid motion and other related phenomena using a computer. Computational fluid dynamics software has enjoyed widespread and rapid growth over the last 20 years, starting first in the aerospace and automotive industries. More recently, CFD has also been successfully applied to a great many materials-processing problems. The reasons for this success are many. Using CFD to test design options and reduce the number of physical prototypes can
Mass Fraction of New Grade
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a b Figure 1. (a) The velocity vectors and contours of turbulent kinetic energy in continuous-casting tundish, and (b) outlet stream grade concentration versus time (a comparison between CFD and experimental results; data redrawn with permission from Metallurgical and Materials Transactions).
a b c Figure 2. A flow analysis of the Concept Two Altus tungsten process chamber (courtesy of Novellus Systems): (a) a photograph of the reactor, (b) 3-D solid model, and (c) contours of the tungsten deposition rate across the wafer surface.
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models and numerical algorithms used in CFD software programs. This article illustrates the utility of CFD for solving materials-processing problems via a series of examples from the steel, aluminum, semiconductor, glass, and polymer processing industries. These examples are just a fraction of the universe of problems where CFD is being used everyday. For example, many minerals-processing problems have been tackled, including slurry distributors, rotary kilns, hydrocyclones, and spiral concentrators. The production of nonwoven materials using meltblown, spunbond, hydroentanglement, and other systems has also been analyzed.
covers a diverse array of industrial applications and products. From the continuous casting of steel to the deposition of semiconductor materials atom by atom to the extrusion of molten polymers, materials-processing applications span an incredible range of length scale, process times, pressures, temperatures, and velocities. The material properties (density, viscosity, thermal conductivity, etc.) can be complex functions of temperature, shear rate, chemical composition, and time. In addition, the processing equipment may be very complicated in geometric shape. To overcome these challenges, care must be taken in the choice and design of the
THE STEEL INDUSTRY From building construction to the production of automobiles, steel is one of the most widely used engineering materials. Because of its strength, formability, and adaptability by chemical alteration to suit various applications, worldwide steel consumption is very high today and increasing steadily. More than 90% of the world’s steel is produced using the continuous casting (CC) process. Development of CC technology is driven by the need to increase the production volume and to obtain a higher quality, cleaner product. There are many process parameters that influence final
Temperature (°C)
c d a b Figure 3. The CFD results for a glass furnace simulation: (a) temperature distribution along a plane through the burners, (b) an end-fed batch profile, (c) a side-fed batch profile, and (d) flow pathlines in the glass melt.
1,500 1,400 1,300 1,200 1,100 1,000 0
1 2 3 4 5 6 7 8 Position from the Feed End (m) Figure 4. A temperature profile along a glass-surface centerline.
a b Figure 5. Temperature distributions in two different aluminum extrusion dies show the effect of shear-induced heating: (a) a cut-away through the billet, and (b) a detailed view of material exiting the bearing section.
Figure 6. The CFD simulation of the blow molding of a plastic automotive fuel tank: (a) mold halves and parison, (b) computed thickness distribution, and (c) thickness distribution along a vertical line through the tank (courtesy Mann+Hummel GmbH).
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cast quality. For example, liquid steel must be maintained at the proper temperature during various stages of processing. Argon (or in some instances nitrogen) gas is purged into the steel ladles.3–6 This causes a large-scale, recirculating flow and faster mixing, leading to thermal and compositional homogenization. While liquid steel is processed in finite capacity ladles, final casting is a continuous process. Therefore, a buffer vessel called a tundish is used to maintain steady continuous casting while replacing the empty ladle with a fresh one. The tundish plays another significant role in the production of clean, quality steel: tundish designs should allow for flotation and separation of the particulate inclusions in the liquid steel. Inclusions are generally alumina and other metallic oxides that result from de-oxidation and subsequent secondary refinement.7,8
Traditionally, the steel industry has used water models to understand the hydrodynamics of liquid steel flowing in various vessels. The kinematic viscosity of water is very close to that of liquid steel, making it possible to draw hydrodynamic similarity. However, the heat capacities are widely different, so studying the non-isothermal flow configurations in the oxygen steelmaking vessel, ladle, tundish, and CC mold using such similarity-based observations is not strictly valid. These differences are exacerbated in the presence of steel solidification.4,9,10 Moreover, performing the geometric alterations needed for scale-up and repeating the water model experiments is significantly time consuming. Thus, CFD is an attractive alternative, provided that such a tool has the requisite capabilities to accommodate geometrical complexities and changes in process-related parameters.
BACKGROUND Computational fluid dynamics (CFD) involves the numerical solution of the partial differential equations that describe fluid flow, heat transfer, and related phenomenon. These equations include, but are not limited to, the conservation of mass, momentum, and energy. Depending on the problem being solved, other governing equations may be considered. For example, high-temperature problems will require the solution of the appropriate equations for radiation heat transfer. Convection heat transfer in the flowing liquid or gas may be coupled with conduction heat transfer in surrounding solid regions. Turbulent flows necessitate the solution of the turbulence-modeling equations. Flows involving inert or chemically reacting species require the solution of relationships similar to the energy equation for each species. Required in addition to the governing equations is an equation of state, which relates the fluid density to the local temperature, pressure, and/or other conditions. The relations that define the dependence of viscosity, thermal conductivity, and other fluid (and solid) material properties on temperature, shear rate, etc., are also needed. To solve these equations on a computer, they must be converted into discrete, algebraic form. Various discretization techniques, including the finite volume method and the finite element method, are used to accomplish this. The outcome of discretization is a set of coupled, non-linear algebraic equations to be solved. One method of solution is to assemble all of the equations into the form Ax = b and invert the coefficient (A) matrix to obtain values for all the unknowns (x) simultaneously. For a very large number of unknowns, the memory required for this computation can be quite extraordinary. Therefore, so-called segregated methods have been developed, whereby each governing equation (e.g., x-momentum, y-momentum, z-momentum, etc.) is solved for in sequence. For further details on discretization methods, solution algorithms, and other numerical techniques, the reader is referred to one of the many excellent texts on these subjects.1,2 Commercial CFD programs have been developed that incorporate these details. These programs also facilitate the setup and solution of typical problems, which involves the following steps: • Geometry creation—a solid model of the flow problem is built or transferred from a suitable computer-aided design system • Grid generation—the solid model is divided into many small volumes or elements, within which the velocity, pressure, temperature, etc. will be solved • Problem specification—including which equations need to be solved, the operating conditions, and the material properties • Solution—solve the governing equations to obtain the flow solution • Postprocessing—visualization of the results via color contours, velocity vectors, flow pathlines, XY plots, and other qualitative and quantitative means
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The objectives of using a tundish in a plant are to provide a buffer volume of liquid steel between the batch treatment of steel in ladles and continuous casting at the caster, to enhance steel cleanliness by separating oxide inclusion particles from the liquid steel, and to cast different grades of steel that cause significant process variations at times. The steel grade change operation is of great economic significance. The ladles are replenished frequently at high production rates, and the continuous mode of casting unavoidably results in the mixing of two different steel grades. Nevertheless, there are many operational changes by which this mixed-grade volume can be minimized. The tundish response time for a steel-grade change can be estimated using CFD. Figure 1a shows the steel velocity and turbulence distribution predicted by CFD during the fast filling stretch of the grade change operation.7 The turbulent kinetic energy in the entry and exit nozzles ranges from 0.05 m2/s2 to 0.3 m2/s2, but these values drop drastically in the vicinity of the turbostop—it is effectively arresting a majority of the high-energy turbulence. Figure 1b compares the CFD results and experimental data for the concentration of the new grade exiting the tundish—the agreement is quite good. THE SEMICONDUCTOR INDUSTRY The evolution of integrated circuits has powered the phenomenal success of the semiconductor industry. In the past few years, there have been revolutionary changes in semiconductor manufacturing equipment, not only to meet new challenges but also to contain the cost of fabrication facilities. There are numerous areas where CFD modeling can play a critical role in semiconductor manufacturing. One of them is equipment design. Computational modeling tools are used to reduce the number of design iterations and to assist in process optimization, process recipe development, and process troubleshooting. Modeling of semiconductor manufacturing equipment and processes can be classified based on geometric scales (i.e., device scale, feature scale, and reactor scale). Other studies focus on throughput and yield modeling. Reactor modeling, which is of primary JOM • March 2004
interest to both equipment manufacturers and chip makers, starts with fluid dynamics and then draws from such diverse fields as plasma physics/ chemistry, heat and mass transfer, electromagnetics, and fluid-structure interaction. Typical equipment processes include chemical vapor deposition (CVD), physical vapor deposition, electrochemical deposition, dry etch, rapid thermal processing, atomic layer deposition, spin coating, chemical mechanical planarization, lithography, and wet cleaning. As an example, consider the modeling and optimization of a tungsten CVD reactor design. Tungsten CVD is a key process used to fabricate reliable contacts and interconnects in manufacturing semiconductor devices. In the CVD process, tungsten is deposited on the wafer as a planar film and then selectively removed from the surface so that tungsten plugs remain.11 CFD tools provide a fast way to examine the flow patterns, temperature and species distributions, as well as specific quantitative values, such as the tungsten film thickness variation across the wafer. An exclusion ring technique was incorporated in the reactor design shown in Figure 2 to permit the deposition of tungsten within 3 mm of the wafer edge. Computational fluid dynamics simulations were used to quantify the disturbances to uniform flow over the wafer caused by the exclusion ring. Using the CFD model, it was possible to evaluate the effects of introducing a second gas source to enhance the deposition rate near the wafer edge. By performing virtual experiments with the CFD model, it was possible to quickly optimize the geometry of the ring’s gas inlet, without having to test many physical prototypes. THE GLASS INDUSTRY The technical challenges facing the glass industry are great. It is one of the most energy-intensive industries in the world. According to studies conducted by the U.S. Department of Energy Office of Industrial Technologies,12 the glass industry produces 19 million tonnes of consumer goods annually valued at $22 billion consuming 179 trillion kJ, equal to about 15 percent of production costs. Theoretically, glass making requires 2.55 million kJ of energy to melt 1 2004 March • JOM
tonne of glass, but twice that amount is actually used because of inefficiencies and losses. Technological improvements are needed in several areas, including production efficiency, energy efficiency, and conservation, as well as environmental protection and recycling. Key priorities of the industry include development of refractory materials, optimization of oxygen and fuel consumption, and modeling of furnace operations. By 2020, the glass industry hopes to cut production costs by 20% (of 1995 levels), reduce energy use by 50%, reduce air/water emissions by 20%, and recover 100% of available consumer glass. Computer simulation is an effective tool that can assist the glass industry in meeting some of these goals.13 Simulation of melters, refiners, and furnaces can lead to designs and operating procedures that improve heat transfer, thereby reducing energy consumption and optimizing the furnace with a view toward reduced emissions. Modeling glass production and forming (fiber drawing, stretching, and blowing) can help improve product quality, minimize defects, and boost productivity. Computational fluid dynamics can be used to model the entire range of glass processes including melters, furnaces, and refiners; glass flow, mixing, and heat transfer in forehearths and feeder bowls; forming, stretching, and drawing of glass; glass container forming/blowing; and fiber production. As an example, consider the application of CFD to glass furnace simulation. The overall volume and residence time distribution in glass furnaces is significantly larger than equipment encountered in many other industries. The design issues that dictate the furnace parameters are mainly chemical kinetics, product quality, and cleanliness. Other issues that must be taken into account include batch melting, radiation heat transfer through both the semi-transparent glass bath and the foam layer floating on top, and overall thermal coupling between the combustion space, batch blanket, and melting tank. Glass quality is measured by the concentration of undissolved sand grains and gas bubbles. The energy efficiency of these furnaces is strongly dependent on combustion efficiency and control. Over the last two decades,
CFD models have developed to the point that today, glass furnace and tank modeling has become a routine activity to assist design optimization, troubleshooting, scale-up, and furnace modification efforts. The hydrodynamics of liquid glass involves laminar, natural convection flow dominated by high Peclet numbers, low Reynolds numbers, and temperature-dependent viscosity and transport properties. The flow in the combustion space above the glass melt is fully turbulent, with large energy source terms arising from the combustion reactions and radiation heat transfer. Since the physics in these two regions (glass melt and combustion space) are so very different, they are typically simulated with two different CFD models. The heat flux from the combustion space is passed to the glass melt model. In return, the glass surface temperature computed in the glass tank model is passed back to the combustion space model. More advanced CFD programs allow these two regions to be coupled into one model. Computational fluid dynamics results for a typical glass furnace simulation14 are shown in Figure 3. Figure 3a shows the flame shape in the furnace as indicated by the temperature contours on a horizontal plane through the burners. Figure 3b and c shows the predicted batch shapes for back feeding and side feeding of the batch into the furnace respectively. Figure 3d shows the flow pathlines in the glass tank with side feeding of the batch. Finally, Figure 4 shows a comparison of measured and computed temperatures on the glass-top surface. While the measurements were few, the match is good. The dip in the temperature at about 2.5 m from the feed end signifies the strongest reaction zone where most of the batch melting occurs. The peak temperature at around 7 m corresponds to the top of the booster electrodes. THE ALUMINUM INDUSTRY Computational fluid dynamics is also widely used in the aluminum industry. Typical applications include aluminum extrusion,15 aluminum furnaces,16 pollution abatement in smelters, increased current efficiency and improved energy efficiency in reduction cells, filling, solidification, and casting. Models of 47
aluminum extrusion may include the aluminum billet, the surrounding die wall, die bearing, and extruded part. The results from the CFD model provide detailed information about the velocity, strain rate, and temperature distribution inside the flowing aluminum, as well as the forces experienced by the die walls and bearing surfaces. This information can be used to design better extrusion dies. An example is shown in Figure 5. One critical area in the die is the weld zone, where the aluminum coming from different portholes is recombined. A good weld zone exhibits steady, planar flow and is located midway between the two ports. In some cases, the CFD results have shown that the weld zone shifted nearer to one of the portholes. Such a flow pattern is likely to cause problems, so the CFD model was used to improve the extrusion die design. Another critical region of the die is the outflow region. If the outflow velocity distribution is non-uniform, the extruded sections may bend or twist. Waves, bending, and twisting can also occur as a result of local stress levels exceeding the yield stress. Computational fluid dynamics has been used to predict these conditions and to evaluate the performance of alternate die designs at minimal cost. Simulation can also provide insights into the mechanical properties of the extrudate. THE POLYMER PROCESSING INDUSTRY Fluid flow and heat transfer problems abound in the field of polymer processing, where the equipment and product design challenges include single- and twin-screw extruders, extrusion dies, injection molding, blow molding, and thermoforming. Computational fluid dynamics has been successfully applied to all of these problems. For example, CFD simulations of the blow-molding process can include all aspects of the extrusion, injection, and injection-stretch blow molding techniques, including single-layer and multi-layer parisons or performs, parison extrusion (including sag), parison pinch-off, inflation, mold contact and heat transfer, moving molds and mandrels, and parison programming.
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While one of the most important outputs is the wall thickness distribution in the blown part, the CFD model also provides details about the temperature distribution and cooling history, product weight, permeability, and weight/volume of the flash (waste). Computational fluid dynamics can be used to determine the initial parison thickness distribution required to minimize the thickness variation in the blown part. Blow molding of fuel tanks is now common in the automotive industry because polymer materials offer lower weight, better corrosion resistance, lower fuel permeability, and easier production of complex shapes compared to metal tanks. The need for a fast, predictive virtual prototyping tool for this application is also driven by stringent new evaporative emissions regulations, the growing number of fuel tank designs, and the increased complexity of these designs. Figure 6 shows a typical automotive fuel tank design and the thickness distribution in the blown part predicted by CFD.17 The results are within 8% to 15% of experimentally measured values. These results can be used to evaluate and improve the thickness distribution in the fuel tank, leading to better mechanical strength and barrier properties. CONCLUSION In the highly competitive materialprocessing-related industries, where relatively small improvements in cost or quality can have a major impact, virtual prototyping tools such as CFD have become indispensable for timely analysis, design, troubleshooting, and scale-up. This article has presented only a brief summary of some typical CFD applications. Two factors will result in even more widespread adoption of such tools by industry in the future. First, the speed and power of computers will continue to increase, even as the cost of these machines rapidly declines. Second, the mathematical models of the complicated physics encountered in materials processing will continue to be refined and developed, thus improving the accuracy, robustness, and ease-of-use of the software programs.
References 1. S.V. Patankar, Numerical Heat Transfer and Fluid Flow (New York: McGraw-Hill, 1980). 2. A.J. Baker, Finite Element Computational Fluid Mechanics (New York: McGraw-Hill, 1983). 3. A. Mukhopadhyay and J.K-W. Lam, “Role of CFD in Analysis and Optimization of the Continuous Casting Processes” (Paper presented at the 1st MIT Conference on Computational Fluid and Solid Mechanics, Cambridge, MA, June 2000). 4. A. Mukhopadhyay, S.A. Vasquez, and J.K-W. Lam, “Modeling Advancements in Casting” (Paper presented at AISE Annual Convention, Cleveland, OH, 23–26 September 2001). 5. A. Mukhopadhyay et al., “Prediction of Temperature in Secondary Steelmaking: Mathematical Modeling of Fluid Flow and Heat Transfer in Gas Purged Ladle,” Steel Research, 72 (2001), pp. 192–199. 6. P. Deb et al., “Operational Experience with a Mathematical Model for Temperature Prediction in Secondary Steelmaking,” Steel Research, 72 (2001), pp. 200–207. 7. A. Mukhopadhyay et al., “Simulation and Validation of Tundish Flows in Predicting the Grade Change during Continuous Casting of Steel” (Paper presented at 58th Electric Furnace Conference, ISS PTD Forum, Orlando, FL, 2000). 8. A. Mukhopadhyay, H.L. Gilles, and B. Kocatulum, “Study of Inclusion Flotation in Continuous Casting Tundishes” (Paper presented at the 85th Steelmaking Conference, Nashville, TN, 10–13 March 2002). 9. A. Mukhopadhyay, A. Troshko, A. Singh, “Multiphase Modeling of Gas Purging during Continuous Metal Casting” (Paper presented at the TMS Annual Meeting, Seattle, WA, 2002). 10. A. Mukhopadhyay, “Unsteady Mold Flow Analysis in Continuous Casting Processes” (Paper presented at the TMS Annual Meeting, Seattle, WA, 2002). 11. P. Geraghty and J. McInerney, “Using Exclusion Ring Technology to Avoid CVD Tungsten Bevel Contamination,” Micro Magazine, 49 (2000). 12. Glass Technology Roadmap Workshop (Washington, D.C.: Office of Industrial Technology, U.S. DOE, September 1997). 13. M.K. Choudhary, “Modeling Needs of the Glass Industry” (Paper presented at the Modeling for the Glass Industry Workshop, July 1996). 14. C.Q. Jian et al., “Explicit Coupling Between Combustion Space and Glass Tank Simulations for Complete Furnace Analysis” (Paper presented at the First Balkan Conference on Glass Science and Technology, Volos, Greece, October 2000). 15. I. Skauvik et al., “Numerical Simulation in Extrusion Die Design,” Proceedings of the 6th International Aluminum Extrusion Technology Seminar (Wauconda, IL: Aluminum Extruders Council, 1996), pp. 79–82. 16. V.Y. Gershtein, C.E. Baukal, and R.J. Hewertson, “Oxygen-Enrichment of Side Well Aluminum Furnaces, Part I,” Industrial Heating Magazine, 67 (9) (2000), p. 121. 17. E. Grald et al., “Virtual Prototyping of Blow Molded Parts Using a Comprehensive Simulation Tool” (Paper presented at 19th Annual Blow Molding Conference, Society of Plastics Engineers, Troy, MI, October 2003). A. Mukhopadhyay, B. Devulapalli, A. Dutta, and E.W. Grald are with Fluent Inc. in Lebanon, NH. For more information, contact E. Grald, Fluent Inc., 10 Cavendish Court, Lebanon, NH 03766; (603) 643-2600, ext. 215; fax (603) 643-3967; e-mail
[email protected].
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