Optimization of Turbulent Mixing Restricted by Linear and Nonlinear Constraints资料.pdfVIP

Optimization of Turbulent Mixing Restricted by Linear and Nonlinear Constraints Sara Delport, Martine Baelmans, and Johan Meyers Mechanical Engineering, Katholieke Universiteit Leuven, Celestijnenlaan 300A, B3001 Leuven, Belgium, sara.delport@mech.kuleuven.be; martine.baelmans@mech.kuleuven.be; johan.meyers@mech.kuleuven.be Abstract The mixing in a temporal mixing layer after a selected simulation time horizon is maximized by optimizing the initial disturbances on the mean velocity field. We concentrate on algorithms which impose the necessary energy and conti- nuity constraints on the initial disturbances. A constrained optimization method is selected and applied to five different cost functionals. 1 Introduction Thanks to the continuing increase of computational resources, it is at present possible to combine optimization techniques with direct numerical simulations or large-eddy simulations for the optimization and control of turbulent-flow features [1, 8]. Important in any problem trying to find an optimum to a de- sired cost functional, are the restrictions imposed by physical, and engineering constraints. In flow optimization, a central relation is posed by the Navier– Stokes equations to which the flow should strictly adhere. On top of that several constraints can enter the problem, and reduce the domain in which the parameter functions one wishes to optimize can freely change. When these constraints are nonlinear, and the parameter space has a large number of di- mensions, such as encountered in turbulent-flow optimization, they are not trivially imposed. In the current study, we focus on the enhancement of turbulent mixing in a temporal mixing layer by optimizing the spatial distribution of initial velocity perturbations φ imposed on a tangent-hyperbolic mean velocity pro- file. Five different cost functionals are considered ba