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

This paper describes the use of Computational Fluid Dynamics (CFD) and mathematical optimization to determine the optimum operating conditions and geometry of a continuous quenching process. The pump power as well as the quench rate of the steel plate in this process is in#uenced by many parameters. These include the nozzle and header geometry, plate speed, water #ow rate, etc. Since an experimental approach is time consuming and costly, use is made of numerical techniques. Furthermore, it is sometimes impossible to measure certain values in this manufacturing process (e.g. the quench rate at a certain depth in the plate). These quantities can be obtained by CFD techniques. Using CFD without optimization on a trial-and-error basis, however, does not guarantee optimal solutions. A better approach, that has until recently been too expensive, is to combine CFD with mathematical optimization techniques, thereby incorporating the in#uence of the variables automatically. The current study investigates a simpli"ed two-dimensional continuous quenching process. The "rst part of the study investigates the operating conditions required to quench a plate at a speci"c quench rate. The second part of the study minimizes the pump power to quench a plate at a speci"c quench rate. The CFD simulation uses the STAR-CD code to solve the Reynolds- Averaged Navier}Stokes equations with the k}e turbulence model. The optimization is carried out by means of Snymanʹs DYNAMIC-Q method, which is speci"cally designed to handle constrained problems where the objective or constraint functions are expensive to evaluate. The paper illustrates how this optimization technique can be used to obtain the operating conditions needed for a manufacturing process with complex #ow and heat transfer 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