Stochastic Hypersonics Group

Every time a scientific paper presents a bit of data, it’s accompanied by an error bar – a quiet but insistent reminder that no knowledge is complete or perfect. It’s a calibration of how much we trust what we think we know. - Carl Sagan

The greatest enemy of knowledge is not ignorance; it is the illusion of knowledge. - Stephen Hawking

The study of hypersonic flows has always been a catalyst to answering fundamental questions in fluid mechanics. Challenging technological problems, such as crewed and robotic Space exploration, and future transportation capabilities, further stress the need for a better understanding of complex hypersonic flow phenomena. The scientific underpinnings of the field rest on three fundamental pillars: mathematical models, experiments and numerical simulations. While experimentalists are developing increasingly sophisticated diagnostic tools and measurement techniques, and computational scientists are advancing algorithms to address increasing physical and numerical complexity, a fundamental question remains: how reliable are our models, simulations, and experiments? One of the main bottlenecks in hypersonics today is reaching quantitative agreement about what we know and how confident we can be in it. This is further exacerbated by the fact that each research group analyzes its own data with its own assumptions, reports point estimates without distributions, and leaves to others the challenging task of reconciling disagreement. Bayesian inference and modern uncertainty quantification provide a principled framework for that integration by combining heterogeneous measurements with physical models, propagating uncertainty through to derived quantities, and producing flowfield reconstructions that carry rigorous credible bounds. Recent advances in generative priors, posterior sampling for inverse problems, and experimental design have brought these tools into a regime where they are tractable for dealing with complex flow phenomena.

Our research uses stochastic methods as the basis for advancing our understanding of hypersonic flows. We are particularly interested in three aspects of uncertainty modeling: 1) understanding of complex models and their high-order interactions by functional decompositions and sensitivity analyses; 2) using this information to design more informative experiments for model calibration and validation, leading to better utilization of experimental resources; 3) validation of physico-chemical and fluid dynamics models.

Novel & Scalable UQ methods

The multiphysics and multiscale nature of hypersonic flows naturally pushes the capabilities of current uncertainty quantification methods. Our group works on developing stochastic models tailored to hypersonics to produce reliable uncertainty estimations, model calibrations and validations. In particular, we are investigating the use of latent diffusion models and transport map algorithms to capture complex flow features and accelerate posterior sampling for Bayesian inference problems.

Gas-surface & Gas-phase Thermochemistry

Accurately modeling thermochemistry phenomena for both gas-surface and gas-phase reactions for different atmospheric and material compositions is a pressing research challenge. Due to the tight coupling between physical mechanisms in the flowfield, isolating each relevant thermochemical effect is impossible. In our group, we explore the possibility of exploiting different sources of experimental data for the purpose of statistically inferring both phenomenological and kinetic models for both gas-surface interactions and gas-phase thermochemistry.

Bayesian Design of Experiments

The use of deterministic simulations to identify regions in the flowfield, conditions, and/or geometries that would most discern between candidate models for validation does not offer a complete description of the problem. One could ask the question: can we trust that the experimental data proposed will, in fact, be able to discern between models? And the answer to this question is almost certainly: no. This way of devising new experiments does not account for uncertainty in the experimental data and in the models themselves. Consequently, two simulation outcomes that look different under different models could completely overlap if experimental uncertainty is large and/or model uncertainty can severely affect the outcome. We develop Bayesian design of experiments techniques to help us answer these questions and discover previously unknown physics.

Characterization of Experimental Facilities

Hypersonic shock tunnels serve as critical validation tools in hypersonic vehicle design, code validation, and physics model development. However, shock tunnels themselves are complex systems whose dynamics are not fully understood. Free stream conditions in the test section are a product of many factors, including the species and pressure of the driver and test gas, vacuum pressure in the test section, diaphragm material properties, and nozzle geometry. Recognizing that uniform, steady freestream assumptions are not sufficient to recover freestream conditions in shock tunnels, we develop UQ methodologies for reconstructing freestream fields for shock tunnel tests from onboard sensor data.

High-Speed Boundary Layer Transition

Hypersonic transition is a multiphysics phenomenon that impacts wall heat transfer and skin friction, increasing the drag of the vehicle. Its prediction is a challenging problem dominated by intrinsic uncertainty due to its multiphysics nature. Uncertainty in transition location leads to diminishing vehicle performance. High-temperature effects, body geometry and surface roughness, and overall environment are the general factors that have a great impact on where transition will occur. We are currently focused on developing a stochastic framework that allows us to improve our understanding of transition predictions in hypersonic boundary layers. The ultimate goal is to understand how (and which) wind tunnel tests can inform and improve in-flight probabilistic transition predictions

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