Tony Midea
Chairman 1F – Process Modeling and Design Committee
Foseco, Inc

What is computer simulation? 
     Computer simulation is the use of computer programs to model actual industrial processes.  There are several types of computer simulations.  The simplest type is “empirical”.  An empirical program is based entirely on experimental results and experience.  Generally, these programs utilize tabularized results obtained from industrial tests and trials.
     Semi-empirical programs are also based upon experimental results, but tend to use some physical relationships and algebraic equations to expand the predictive ability of the program beyond the constraints of the experimental test data.  The physics usually involves correlations and simple, first order relationships.  In some cases, the programs employ simple finite differencing methods that allow the problem to be broken up into many small problems, and thus increase the accuracy of the simulation.  
     First principles programs are derived entirely from the laws of physics, and do not use tables of experimental data, rules or guidelines.  These programs are commonly referred to as “physics-based” programs.  Complex physical relationships and equations are employed to describe the underlying physics of the process.  In this situation, material property data becomes the lifeblood of the programs, and the accuracy of simulation becomes dependent on the accuracy of the material thermal data.  Finite difference or finite element methods are required for this type of analysis because the complexity of the equations to be solved require that the problem be broken into many small problems.
     This paper discusses the details of first principles programs, and shows several examples of how using this type of program results in the optimization of the casting process in iron foundries. 
     First principles programs can model the myriad process steps involved in the making of iron castings.  Mold filling, solidification, metal treatment, heat treatment, metallurgy, etc. can all be analyzed using current tools.  For the purpose of this paper, we will discuss only the mold filling and solidification aspects of computer simulation.
     For filling analyses, the flow equations are referred to as the Navier-Stokes equations.  These equations, in their “full-blown” form, comprise of a 6x6 matrix of flow vector components that must be resolved simultaneously with the continuity, energy and volume of fluid equations to get a solution at any one point in time within the system.  This allows for “6-degreee-of-freedom” movement, which simply means that the flow is calculated in all possible directions.  For each point (volume), at each time step, this matrix of equations must be solved to make progress towards a complete solution.  In many cases, terms can be removed from the equations (e.g. compressibility for molten iron) such that the problem is made simpler.
     To model turbulence, a first principles program uses the k-e equations, which evolved from the aerospace industry.  While not perfect, these equations do an admirable job of predicting the flow behavior of turbulence.    
     Solidification analyses generally use several phenomenological equations.  These equations are based on observation, and are not derived.  However, they have stood the test of time and accurately represent heat flow for most known problems.
     Fourier’s Equation is used to predict heat conduction, while Newton’s Law of Cooling is used for convection.  The Stefan-Boltzmann Law is used to predict radiative heat flow in most analyses. 
     Because the programs are time and temperature based, the calculations are performed just like the physics being modeled.  The program breaks the problem into many small pieces.  Then, the analysis begins by calculating the fluid flow and heat transfer for each of these small pieces at small time steps starting with the initiation of the process.  When the dynamics of the system are quickly changing, the programs take very small time steps to compute the changes taking place in the system.  As the system begins to reach equilibrium (e.g. mold cavity nearly full or solidification of system nearly complete), the programs are able to take larger time steps without sacrificing accuracy.

What does computer simulation do for me?  
     Computer simulations should be conducted to optimize the process that is being modeled.  The goal is to improve efficiency, increase productivity and increase profitability.  The optimization process is a means to conduct a cost-effective “what-if” analysis on the computer.  Configurations that show promise can then be trailed in a production environment to prove that the computer optimized design works, as advertised, on the shop floor.
     If properly conducted, this synergistic relationship between computer simulation and production tests can provide a low cost alternative to common trial and error procedures conducted in production environments for generations. 
     In order to determine the “power” or complexity required to accurately model the industrial process in question, one must understand the complexity of the industrial process in question.  
     If the process to be modeled is a simple, repeatable process in which the process variables change only slightly from case to case, then it may be possible to model the configuration using a simple empirical program.  The process could be monitored, process variables recorded, and a simple program could be written to model the process.  An example of this type of program could be the prediction of feeding distance in cast steel.  In this case, a program could be written using the SFSA feeding distance tables as a reference, and feeding distance for a particular case could be predicted quickly and easily.  Several programs exist for exactly this type of process.
     Because programs of this nature are based entirely on experimental data for specific cases, care should be taken so that the user does not attempt to apply the program to cases for which the data is irrelevant.  For the example above, one should not apply a steel feeding distance program to predict the feeding distance in cast iron.  
     If the process to be modeled is well understood, and relatively simple, then a semi-empirical program may suffice.  In this case, the program still fundamentally relies on experimental data, but may also include some functionality to model small changes in the process variables, and may include some simple physics such that the data could be applied slightly beyond the basis of the experimental data.  An example in this case might be a foundry that produces only a few simple steel or iron casting shapes.  Again, the danger in this type of program is that application of the program beyond its experimental dataset could lead to incorrect predictions.
     A first principles program is the best alternative for all processes.  Because the program attempts to model the underlying physics of the process, it can be used to model complex as well as simple processes.  It does not rely on tables of experimental results or guidelines.  As a result, it can be used to model situations in which process variables vary greatly, and can be used to try new ideas and/or processes. 
      A physics based program can perform detailed analyses, including flow and solidification predictions for all metal types.  To be accurate, however, a physics based program must be equipped with accurate thermophysical data for all of the materials to be modeled in the process.
     Ideally, a foundry should be equipped to apply the right tool to the right problem.  For example, a foundry should be equipped to use a simple tool to help rig the casting such that the risers are properly sized, and feeding distance rules are obeyed.  A quick, solidification analysis could then be conducted to verify that the casting is adequately rigged.  At this point, the full physics problem could be modeled to analyze the filling characteristics of the gating system, and the effect on the resultant solidification of the casting.

Other Important Issues
     The previous example illustrates just one example of the analyses made possible by using computer simulation. There are many good case studies recently published that greatly expand on the potential of computer simulation.
     For those considering computer simulation for their foundry, there are several recommendations from the AFS 1F-Process Modeling and Design Committee.  First, success will depend on the expertise of the user.  It is recommended that the user have an engineering degree, or an equivalent amount of actual foundry experience.  Also, expect one year of on-the-job training for the user to get thoroughly familiar with the program, its use, and the calibration of the tool to your specific foundry.  Most users will excel in this area, and be up to speed within 6 months, but plan on one full year to see explicit results in the area of process optimization.
     Dimensionally accurate 3D geometry models are required for all simulations.  Ensure that the user has access to 3D models of the castings, or the technology to electronically model the patterns. 
     Finally, accurate thermal data for all of the materials in the casting process is the lifeblood for physics based programs.  Without this information, it will be impossible to obtain repeatable, accurate predictions.
     Most programs have a baseline set of thermo physical data for metals and mold materials that was obtained from references.  In general, the metal data is quite good.
     The mold material data requires updating, and this is being done presently by the 1F committee via AFS funding.
     Thermo physical data for riser sleeves, hot toppings, etc. can be obtained from your feeding systems vendor. 
     Accurate interfacial heat transfer coefficient data is also critical to the analysis.  Some data is available via AFS, and several research projects are underway to fill in the blanks in this area.

A Final Note
     The filling and solidification of iron castings is difficult to accurately simulate due to the complexity of the process.  For iron simulations, metal chemistry, mold hardness, the inoculation method and quality of inoculant, the nodularity and the nature of the graphitic expansion must all be properly accounted for.  More importantly, these variables change daily in the foundry, so the prudent computer simulation user must calibrate the program to match the variations in the foundry.
     Generally, this means that several simulations must be conducted for each configuration to determine how the foundry process variables will affect the quality of the casting.  Conversely, the user could set up the worst case condition for every configuration, and make this the standard simulation setup.  Nonetheless, attempting to predict the solidification behavior of ductile iron is very complex, and the user cannot expect to get the precise answer for every iteration of every casting configuration.  Experience has taught us to be very conservative in the simulation setup for iron castings.
     In addition, the user should take the time to test the metal and mold material for thermo physical properties, and measure the respective heat transfer coefficients for his respective foundry.  Once this data is obtained, the accuracy of the simulations will increase dramatically, and the results will be very dependable