Vortex simulation of a turbulent mixing layer

Abstract

Two-dimensional, turbulent mixing layers are numerically simulated by a vortex blob method. Streaklines of marker particles as well as those of vortices are obtained. The results indicate that not only a vortex pairing process, but also the self-growth of large eddies found by Hernan and Jimenez, play important roles in the development of a mixing layer. Streaklines of marker particles clearly show the entrainment process: non- turbulent fluid particles are entrained into the mixing layer between clusters of vortices because the nonturbulent outer flow acquires a normal velocity that is induced by clusters of vortices via the Biot-Savart law. Fluid par- ticles in the slower-speed flow enter the mixing layer at a shorter downstream distance. Statistical quantities up to the second-order moment show similarity and reasonable agreement with experiments. HE existence of large scale, quasiordered, coherent structures in many types of turbulent flows, especially in the mixing layer, has been well recognized. Observation of the turbulent mixing layer by Brown and Roshko1 and Winant and Browand2 clearly showed that the mixing layer consists of a row of quasi two-dimensional coherent structures. Their work suggests that the amalgamation of the structures into larger ones (vortex pairing) may produce the growth of the mixing layer. These observations suggest that representing turbulence as a superposition of interacting vortices may be a valid and useful idea. Many theoretical and numerical studies based on this idea have been made. They are reviewed by Saffman and Baker,3 Leonard,4 and Aref.5 Readers are also referred to Roshko6 and Cantwell7 for reviews of the mixing layer. Numerical simulation of a turbulent mixing layer by a discrete vortex method is based on this idea. In these studies, the mixing layers are represented as an assembly of two- dimensional, inviscid discrete vortices. It is generally accepted that the Reynolds number effect on the formation and development of large-scale coherent structure is secondary. The assumption of the two-dimensionality of the large-scale structure is supported by many experiments,1'8 although it is not universally accepted when the freestream turbulence level is high or when the boundary layer on the splitter plate is turbulent.9'10 Thus, the simulation of the mixing layer by discrete vortex method is quite reasonable and acceptable. Simulation of the mixing layer by a discrete vortex method can be divided into two different approaches. In the first, the mixing layer is replaced by the time-developing shear layer whose coordinate system is moving with the convection velocity Uc. At an initial instant, vortices distributed in a finite region under periodic boundary conditions are disturbed. Our interest here lies in the time evolution of the distribution of the vortices. Results by this method often give good qualitative agreement with experiment.11'12