Using mathematical optimization in the CFD analysis of a continuous quenching process

This paper describes the use of Computational Fluid Dynamics (CFD) and math ematical optimization to determine the optimum operating conditions and geo metry of a continuous quenching process. The pump power as well as the quen ch rate of the steel plate in this process is influenced by many parameters . These include the nozzle and header geometry, plate speed, water flow rat e, etc. Since an experimental approach is time consuming and costly, use is made of numerical techniques. Furthermore, it is sometimes impossible to m easure certain values in this manufacturing process (e.g. the quench rate a t a certain depth in the plate). These quantities can; be obtained by CFD t echniques. Using CFD without optimization on a trial-and-error basis, howev er, does not guarantee optimal solutions. A better approach, that has until recently been too expensive, is to combine CFD with mathematical optimizat ion techniques, thereby incorporating the influence of the variables automa tically. The current study investigates a simplified two-dimensional contin uous quenching process. The first part of the study investigates the operat ing conditions required to quench a plate at a specific quench rate. The se cond part of the study minimizes the pump power to quench a plate at a spec ific quench rate. The CFD simulation uses the STAR-CD code to solve the Rey nolds-Averaged Navier-Stokes equations with the k-epsilon turbulence model. The optimization is carried out by means of Snyman's DYNAMIC-Q method, whi ch is specifically designed to handle constrained problems where the object ive or constraint functions are-expensive to evaluate. The paper illustrate s how this optimization technique can be used to obtain the operating condi tions needed for a manufacturing process with complex flow and heat transfe r phenomena. The paper also illustrates how these techniques can be used in the design phase of such a manufacturing process to determine the optimum geometry and process parameters. Copyright (C) 2000 John Wiley & Sons, Ltd.