Session L03: Supersonic & Hypersonic Flows

Homological Analysis of Schlieren Images of Supersonic Elliptical Jets

This research explores the application of computational homology to the analysis of schlieren photographs of supersonic elliptical jets. In this study, computational homology is used to compute topological invariants called the Betti numbers, which are values associated with the homology groups of a topological space that measure the number of connected components and enclosed regions in the space. To compute the Betti numbers, grayscale schlieren images of supersonic elliptical jets are converted into images that have only black and white pixels. Different threshold values defining black and white regions emphasize different flow structures associated with variations in the fluid density. The schlieren images are for supersonic elliptical jets issuing from a nozzle designed to produce a shock-free jet with a Mach number of 1.52. The jet has an aspect ratio of two with a minor axis length of one inch. Schlieren images are analyzed for both an under-expanded jet and an over-expanded jet with Mach numbers of 1.36 and 1.64 respectively. Both of these off-design jet flows produce complex shock wave phenomena. Computed Betti numbers are discussed in terms of jet aerodynamics as well as the methods used to convert the schlieren images to pictures with only black and white regions.   

Shock oscillations in a supersonic flow due to downstream pressure perturbations

Shock oscillations are observed in various components of a high-speed vehicle, such as supersonic inlets, transonic airfoils, and high-speed compressors. Such unsteadiness of shock waves can lead to engine unstart in supersonic inlets and buffeting on transonic airfoils, while in gas turbine compressors, it can cause severe issues like flutter. Motivated by the above problems, we study in the present work, the response of a normal shock in a supersonic flow subjected to downstream pressure perturbations, generated by rotating a triangular cross-sectional shaft or oscillating a blade, both being downstream of the shock. In both cases, the normal shock is induced and stabilized at a Mach number of 1.3 within a supersonic wind tunnel, and the shock dynamics in response to the downstream pressure perturbations are visualized using high-speed shadowgraphy. Measurements with perturbations from the downstream triangular shaft show large streamwise motions of the shock, with distinct differences in the shock structure and velocity during its upstream and downstream motions. In the other case of pressure perturbations from a heaving blade downstream of a shock, unsteady force measurements have been carried out to understand the influence of shock oscillations on blade flutter.   

Shear layer development and entrainment of a jet in supersonic crossflow

A sonic nitrogen jet is injected into a Mach 1.75 supersonic air crossflow at momentum flux ratios between 1 and 5.5. The jet spreading and shear-layer development is quantified via velocity and scalar concentration measurements using Particle Image Velocimetry and Nano-Particle-Based-Laser-Scattering. Jet penetration, trajectory and spreading is assessed as a function of the momentum flux ratio. Jet spreading is compared to Taylor's classical, incompressible dispersion law. The velocity field is analyzed to obtain the mean and RMS velocity profiles in the jet wake and correlated to the species concentration profiles. These results establish the baseline entrainment characteristics that will be revisited for different gases and reacting flows in the near future.
  

Physics-informed deep learning model for predicting ballistic coefficients of explosively driven fragments

Deep Learning models have the potential for accelerated predictions of physical phenomenon with an acceptable accuracy loss as alternatives to reduced-order models. In this work, we use a Deep Learning network to perform fast and accurate lift and drag predictions of explosively driven fragments traveling at hypersonic velocities. Specifically, we employed a generative adversarial network (GAN) to predict the total force on arbitrary shapes fixed in an external supersonic flow. The loss function of the generator was modified with additional terms based on the physics of the problem, heavily penalizing generated solutions that violated certain physical constraints. We trained our physics-informed network with a large set of flow fields from high fidelity aerodynamics simulations and show that drag was accurately predicted to within 2% average error. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.   

Earliest transition Reynolds number in hypersonic boundary layers

An ensemble-variational algorithm is developed to establish strict bounds on transition Reynolds number in high-speed boundary layers, for specified level of free-stream disturbance energy. The formulation is a constrained optimization where the spectral makeup of the nonlinearly most dangerous disturbance is the control variable, and the constraint is its energy. The optimal amplitudes and phases of the constituent waves cause the earliest possible breakdown to turbulence. Transition is examined in a flat-plate boundary layer at Mach = 4.5, when the energy level is of the same order as that of stratospheric turbulence. The nonlinearly most dangerous disturbance leads to a unique transition mechanism that cannot be categorized as classical fundamental or oblique breakdown. Breakdown to turbulence is initiated due to nonlinear interactions of two acoustic waves and an oblique vorticity wave. The analysis, repeated at different levels of free-stream disturbance energy, provides strict bounds on transition Reynolds numbers.