Direct numerical simulations of temporally evolving compressible mixing layers are performed to study the baroclinic vorticity generation due to the interaction between the intense vorticity structures (IVSs) and the turbulent/non-turbulent interface (TNTI). In order to examine this interaction, the vorticity transport across the TNTI and the IVSs in compressible turbulence are studied. The conditional mean budget of different terms in the transport equation of vorticity with respect to the distance from the TNTI is analyzed in the interface coordinate system. In highly compressible mixing layers, it is shown that in proximity of the TNTI, contribution of the baroclinic torque to the total change of vorticity, compared with the other terms in the transport equation of the vorticity, cannot be ignored. The conditional average of the baroclinic torque in the vorticity transport equation reaches a maximum inside the interface layer, with the thickness of approximately one Taylor length scale, at a distance approximately equal to the radius of the IVS from the TNTI. Flow visualization results show that the intense vorticity structures generate a baroclinic torque as they become close to the turbulent/non-turbulent interface. In order to statistically examine the organized interaction between the TNTI and the IVSs, an algorithm described in the Appendix is developed to detect and to study the intense vorticity structures. It is shown that the IVSs generate a pressure gradient from the core of the vortex, low pressure, towards the region outside of the vortex. As the IVSs interact with the TNTI, the pressure gradient vectors become misaligned with the density gradient vectors, which are aligned with the direction normal to the TNTI, and generate a baroclinic torque. It is also observed that compressibility has a small effect on the structural features of the IVSs in the shear layer.

The local flow topology is studied using the invariants of the velocity gradient tensor in compressible turbulent mixing layer via direct numerical simulation (DNS) data. The topological and dissipating behaviours of the flow are analysed in two different regions: in proximity of the turbulent/non-turbulent interface (TNTI), and inside the turbulent region. It is found that the distribution of various flow topologies in regions close to the TNTI differs from inside the turbulent region, and in these regions the most probable topologies are non-focal. In order to better understand the behaviour of different flow topologies, the probability distributions of vorticity norm, dissipation and rate of stretching are analysed in incompressible, compressed and expanded regions. It is found that the structures undergoing compression-expansion in axial-radial directions have the highest contraction rate in locally compressed regions, and in locally expanded regions the structures undergoing expansion-compression in axial-radial directions have the highest stretching rate. The occurrence probability of different flow topologies conditioned by the dilatation level is presented and it is shown that the structures in the locally compressed regions tend to have stable topologies while in locally expanded regions the unstable topologies are prevalent.

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In this research, an optimal aerodynamic design of an axe-symmetric diffuser is performed via combination of a developed boundary layer numerical code, BSA inverse design Algorithm and genetic optimization algorithm. To do this, developed numerical boundary layer code is incorporated into the genetic algorithm to reach to an optimum pressure distribution on the wall in such a way that the maximum pressure recovery is obtained without separation. To validate the developed boundary layer code, the calculated quantities are compared with Blasius and Howart’s analytical results. Then, the optimized pressure distribution will be the candidate “target pressure distribution” for the inverse design algorithm to find out the relevant optimum geometry. Geometry modification takes place based on the combination of Ball-Spine algorithm and fluent software as the flow field solver. Implementation of this combination is completed through User Defined Function (UDF) feature of Fluent. Fluent advantageous provides the capabilities for extension of the proposed method to turbulent flows, complicated geometries and employment of both structured and unstructured grids. To show the true performance of the proposed method of inverse design, several issues have been investigated for different initial guess. To validate the effect of the presented method, increased pressure coefficient for an optimized diffuser is illustrated.

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