A new geometry of a sub-boundary-layer vortex generator, which is termed as a slottedramp vortex generator, is proposed here. The geometry of the vortex generator is that of a ramp (triangular wedge) which has a semi-circular groove at its base. The centerplane of the groove or slot, which is basically like a tunnel that runs across the length of the ramp, is located at the spanwise plane of symmetry of the ramp. Preliminary computations of supersonic flow at a free-stream Mach number of 2.5 are conducted over vortex generators 2 mm, 3 mm, and 4 mm high. For each device height h, the flow is simulated for three values of the slot radius -0.2h 0.3h, and 0.4h. The incoming flow profile is based on the experiments conducted by Dr. Babinsky at Cambridge on control of shock/boundarylayer interaction with micro vortex generators at a free-stream Mach number of 2.5. An immersed-boundary technique suitable for high-speed turbulent flows is used for rendering the vortex generators. Comparisons are presented between the different slotted-ramp vortex generators with a standard ramp based vortex generator of the same device height using streamwise velocity profiles at different locations downstream of the device. Velocity plots show that the new device results in higher streamwise velocity along the centerline in the near wake region for the larger sized vortex generators and the effect improves when a higher slot radius is used. Comparisons are also presented with the standard ramp type vortex generator using span-averaged total pressure profiles and momentum-deficit contours at different streamwise locations, and near surface axial velocity contours. Finally, results from computations of an impinging oblique-shock/boundary-layer interaction for a flow turning angle of 7 degrees at Mach 2.5 with and without flow control are presented. To achieve flow control two different cases are considered -one using an array of 3 x 3 mm high slotted-ramp vortex generators and the other using a similar array of the ramp type vortex generator. All the computations done as part of this study solves the Reynoldsaveraged Navier-Stokes equations with Menter's k − ω/k − turbulence model (baseline or SST formulation).Nomenclature h height of vortex generator r slot-radius of vortex generator x streamwise distance measured from the inflow plane of computational domain X streamwise distance measured from the trailing edge of vortex generator y, Y vertical distance measured from lower wall of computational domain Z spanwise distance measured from centerplane of computational domain

Tracking transitional and turbulent flows requires methods other than the classical techniques, which capture coherent structures via locating pressure minima, after the disturbance field has evolved to late-transitional and turbulent flow stages. Keeping it in mind, transition to turbulence of zero pressure gradient flow is studied, following two routes of excitation, by solving the three-dimensional Navier-Stokes equation in derived variable formulation, with vorticity as one of the dependent variables. For such flows, disturbance structures should be traced from the receptivity to the coherent structure stage for the fully developed turbulent flow. The coherent structures in turbulent flows are identified by the Q- and λ2-criteria, based on the occurrence of pressure minima at the vortex cores. In the proposed study here, the zero pressure gradient boundary layer is excited (i) at the wall with a monochromatic source and (ii) causing transition to turbulence, by a convecting vortex in the free stream. The main aim here is to trace the incipient disturbances from the onset to the turbulent state in terms of physical quantities, such as the disturbance mechanical energy introduced by Sengupta et al. [“Vortex-induced instability of an incompressible wall-bounded shear layer,” J. Fluid Mech. 493, 277–286 (2003)] and disturbance enstrophy transport equation, as proposed by Sengupta et al. [“An enstrophy-based linear and nonlinear receptivity theory,” Phys. Fluids 30(5), 054106 (2018)]. Such methods are capable of tracing disturbance structures from the onset to the evolved stage. We compare these methods with Q- and λ2-criteria to trace disturbance evolution.

Three-dimensional (3D) routes of transition affected by the frequency of monochromatic wall excitation started impulsively are studied by performing direct numerical simulation. The computed results for the two frequencies of excitation reported here resemble the experimental setup of Klebanoff et al. [“The three-dimensional nature of boundary-layer instability,” J. Fluid Mech. 12(1), 1–34 (1962)], where a two-dimensional boundary layer is excited using 3D disturbances. Such a monochromatic wall excitation creates three-component disturbance field: a near-field followed by the Tollmien-Schlichting wave-packet and a spatiotemporal wave-front (STWF), which is responsible for eventual transition. It is noted that the case of moderate frequency of excitation shows a complete noninteracting nature of the near-field solution and the STWF. We report another route of transition computationally for a lower frequency of excitation. This case shows an interacting nature of the near-field solution and the STWF. While both frequency of excitations can cause transition for moderate spanwise wavelength (λz) disturbances, dependence of transition on λz is reported here for the first time. It is noted that doubling the spanwise wavenumber leads to the disappearance of STWF and no transition of the flow. We use the recently developed disturbance enstrophy transport equation in Sengupta et al. [“An enstrophy based linear and nonlinear receptivity theory,” Phys. Fluids 30, 054106 (2018)] for a better quantitative method to trace the evolution of disturbance field of the imposed 3D disturbances.

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