Measuring the properties of scattered light is central to many laser-based gas diagnostic techniques, such as filtered Rayleigh scattering (FRS). Alongside the measurements, a model of the scattered light’s spectral lineshape is often used to extract quantitative information about the flow field like pressure, temperature, and velocity. In particular, the Tenti S6 or S7 model are frequently used to model the lineshape of Rayleigh–Brillouin (RB) scattered light. While accurate, it is well attested in the literature that these models can be computationally expensive when evaluated many times, for example, as part of iterative estimation or optimization routines. To overcome this, approximations of these spectral lineshape models can be used instead. In this paper, we develop a method called support vector spectrum approximation (SVSA). This method uses support vector regression and singular value decomposition to create efficient, accurate, and well-conditioned approximations of any existing spectral lineshape model. The SVSA framework improves upon existing approximation methods by allowing quick calculation of spectral lineshapes for arbitrary flow regimes with any number of input parameters over a wide range of values. We demonstrate the efficacy of SVSA in approximating coherent and spontaneous RB scattering spectra. In application, we use SVSA to optimize the design of a filtered Rayleigh scattering experiment of a complex shock-dominated flow. SVSA allows us to comprehensively minimize expected measurement uncertainty of number density and temperature for this experiment. It does this by enabling a high-resolution design of experiments that is otherwise intractable.

Only a few fundamental studies on the dynamics and interactions of supersonic streamwise vortices have been conducted so far despite the recognized potential of these structures to enhance supersonic mixing. In an effort to shed light on this largely unexplored field, multiple experimental campaigns were conducted in a Mach 2.5 flow to probe the dynamics of turbulence decay in complex flows originating from selected modes of supersonic streamwise vortex interaction. The first part of the manuscript presents the detailed study of two vortex interaction scenarios: one selected to obtain merging of co-rotating vortices and the other to prevent vorticity amalgamation. In the second part, data from three additional vortex merging cases are used to substantiate the findings of the first part of the study and characterize the decay of turbulence. Stereoscopic particle image velocimetry was employed to probe the resulting flow fields at different downstream stations. It was found that these complex vortex interactions measurably affect both the morphology and the magnitude of the streamwise vorticity and turbulent kinetic energy as well as the associated decays. Particularly, while the turbulent kinetic energy across each vorticity patch undergoes an initial production before decreasing monotonically in both scenarios, its content in the coalesced structure is roughly double that of the isolated vortices. The manuscript also presents the analysis of the turbulence data from 27 supersonic vortical structures differing in shape, strength and modes of interaction, acquired within a range of vortex Reynolds numbers of almost one order of magnitude. Dimensional analysis was then used to correlate the spatial decay of turbulent kinetic energy with the vortex Reynolds number. For all the cases considered here, where the fluctuating Mach number was found to be subsonic, the form of the resulting law was similar to that reported in previous scholarly publications, despite the complexity of the vortex dynamics considered in this work.

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A peculiar dynamical interaction of two supersonic counter-rotating vortex pairs (CVPs) has been generated by a pair of overlapping expansion ramps mounted on a strut injector in a Mach 2.5 flow. Similar CVP configurations generated by overlapping ramps on the same modular strut injector have previously been studied by the authors and experimentally corroborated the predictions based on the in-house developed reduced order model, VorTx. Two co-rotating vortices at the center of the generated structure have either merged or begun to orbit each other. However, for the case discussed in this work, experiments have revealed an additional structure; in fact, instead of the expected four streamwise vortices in the flowfield consisting of two inner co-rotating vortices and two oppositely rotating external vortices, the formation of a fifth structure, a central vorticity patch, was detected. The manuscript presents a detailed experimental characterization of the flow of interest via the use of stereoscopic particle image velocimetry and a parallel computational effort based on the solution of the Reynolds Averaged Navier-Stokes equations with the ANSYS Fluent CFD Package. The results of the CFD simulations highlight the near injector flowfield, which is unable to be characterized experimentally, in order to focus upon the mechanism that result in the formation and the effects of the central vorticity patch. Nomenclatureh = Ramp height, mm M = Mach number ω = Vorticity, s -1 Subscripts ∞ = Free-stream

Coherent anti‐Stokes Raman Spectroscopy (CARS) is a laser‐based measurement technique widely applied across many science and engineering disciplines to perform non‐intrusive gas diagnostics. CARS is often used to study combustion, where the measured spectra can be used to simultaneously recover multiple flow parameters from the reacting gas such as temperature and relative species mole fractions. This is typically done by using numerical optimization to find the flow parameters for which a theoretical model of the CARS spectra best matches the actual measurements. The most commonly used theoretical model is the CARSFT spectrum calculator. Unfortunately, this CARSFT spectrum generator is computationally expensive, and using it to recover multiple flow parameters can be prohibitively time‐consuming, especially when experiments have hundreds or thousands of measurements distributed over time or space. To overcome these issues, several methods have been developed to approximate CARSFT using a library of pre‐computed theoretical spectra. In this work, we present a new approach that leverages ideas from the machine learning literature to build an adaptively smoothed kernel‐based approximator. In application on a simulated dual‐pump CARS experiment probing a H2/air flame, we show that the approach can use a small number library spectra to quickly and accurately recover temperature and four gas species' mole fractions. The method's flexibility allows fine‐tuned navigation of the trade‐off between speed and accuracy and makes the approach suitable for a wide range of problems and flow regimes.

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