arXiv subjects

Blaine Vollmer

Publications and source records attributed to Blaine Vollmer.

5 recordsLinked to original sources

arXiv2026

From Coils to Surface Recession: Multiphysics Simulation of Ablation in ICP Wind Tunnels

This work presents a multi-solver, coupled computational framework for predicting the thermo-chemical material response of thermal protection systems in inductively coupled plasma (ICP) wind tunnels. The framework integrates a high-fidelity Navier-Stokes plasma solver, an electromagnetic field solver, and a discontinuous-Galerkin material response solver using a partitioned coupling strategy. This enables an ab initio, end-to-end simulation of the 350 kW Plasmatron X facility at the University of Illinois Urbana-Champaign (UIUC), including plasma generation, electromagnetic heating, near-wall thermochemistry, and time-accurate material ablation. The model captures key ICP physics such as vortex-mode recirculation, Joule-heating-driven plasma formation, and Lorentz-force-induced flow confinement, and accurately predicts the transition from subsonic to supersonic jet behavior at low pressures. Validation against cold-wall calorimetry shows that predicted stagnation-point cold-wall heat fluxes fall well within experimental uncertainty, while coupled ablation simulations accurately reproduce measured stagnation temperature histories and recession rates with errors below 12% and 10%, respectively. Remaining discrepancies are attributed to uncertainties in power-coupling efficiency, equilibrium ablation modeling, and material property datasets. Sensitivity analyses reveal that a 10% variation in system efficiency can induce changes of up to 11% in steady- state surface temperature and 17% in recession rate, whereas an equivalent variation in material thermal conductivity results in comparatively minor deviations of about 1.5% and 0.5%, respectively. Overall, the framework demonstrates strong predictive capability for ICP wind tunnel environments and provides a foundation for improved design, interpretation, and planning of hypersonic material testing campaigns.

physics.plasm-ph↗

arXiv2026

Resolvent4py: a parallel Python package for analysis, model reduction and control of large-scale linear systems

In this paper, we present resolvent4py, a parallel Python package for the analysis, model reduction and control of large-scale linear systems with millions or billions of degrees of freedom. This package provides the user with a friendly Python-like experience (akin to that of well-established libraries such as numpy and scipy), while enabling MPI-based parallelism through mpi4py, petsc4py and slepc4py. In turn, this allows for the development of streamlined and efficient Python code that can be used to solve several problems in fluid mechanics, solid mechanics, graph theory, molecular dynamics and several other fields.

physics.comp-ph↗

arXiv2025

Surface instabilities in laminar compressible boundary layers with sublimation

Surface patterns on ablating materials are observed in high-speed ground and flight tests, but the mechanisms behind their formation are not known. In this paper, the origin of surface patterns is investigated via a local linear stability analysis of compressible laminar boundary layers over a flat camphor plate. The effects of sublimation and conjugate heat transfer are included both on the baseflow and the linear fluctuations. This framework identifies one mode that fully characterizes the stability of the surface, which becomes unstable when the wall temperature exceeds that of an adiabatic wall, $T_{ad}$. These findings are consistent with experimental observations, where laminar flow conditions at adiabatic wall temperatures are found to be stable. The analysis also reveals that the nature of this surface mode varies as a function of the oblique angle $ψ= \tan^{-1}{β/α}$, where $α$ and $β$ are the streamwise and spanwise wavenumbers. Specifically, for baseflow temperatures below $\approx 1.15~T_{ad}$, the surface mode is most unstable at $ψ= 0$. Conversely, above $\approx 1.15~T_{ad}$ the surface is most unstable near the sonic angle $ψ_s = \cos^{-1}(1/M_e)$, which is the angle at which the normal Mach number equals one. Finally, a critical wavenumber is identified (i.e., one at which the temporal growth rate reaches a maximum) that is in good agreement with available experimental observations of turbulent flows.

physics.flu-dyn↗

arXiv2024

Data-driven model reduction via non-intrusive optimization of projection operators and reduced-order dynamics

Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying systems exhibit large-amplitude transient growth. Although these systems may evolve near a low-dimensional subspace that can be easily identified using standard techniques such as Proper Orthogonal Decomposition (POD), computing accurate models often requires projecting the state onto this subspace via a non-orthogonal projection. While appropriate oblique projection operators can be computed using intrusive techniques that leverage the form of the underlying governing equations, purely data-driven methods currently tend to achieve dimensionality reduction via orthogonal projections, and this can lead to models with poor predictive accuracy. In this paper, we address this issue by introducing a non-intrusive framework designed to simultaneously identify oblique projection operators and reduced-order dynamics. In particular, given training trajectories and assuming reduced-order dynamics of polynomial form, we fit a reduced-order model by solving an optimization problem over the product manifold of a Grassmann manifold, a Stiefel manifold, and several linear spaces (as many as the tensors that define the low-order dynamics). Furthermore, we show that the gradient of the cost function with respect to the optimization parameters can be conveniently written in closed-form, so that there is no need for automatic differentiation. We compare our formulation with state-of-the-art methods on three examples: a three-dimensional system of ordinary differential equations, the complex Ginzburg-Landau (CGL) equation, and a two-dimensional lid-driven cavity flow at Reynolds number Re = 8300.

math-ph↗

arXiv2023

An Extended B' Formulation for Ablating-Surface Boundary Conditions

The B' formulation can be understood as a mass and energy conservation formalism at a reacting singular surface. In hypersonics applications, it is typically used to compute the chemical equilibrium properties of gaseous mixtures at ablating surfaces, and to estimate the recession velocity of the interface. In the first half of the paper, we derive the B' formulation to emphasize first principles. In particular, while we eventually specialize to the commonly considered case of chemical equilibrium boundary layers that satisfy the heat and mass transfer analogy, we first derive a general interface jump condition that lets us highlight all the underlying assumptions of the well-known B' equations. This procedure helps elucidate the nature of the B' formalism and it also allows us to straightforwardly extend the original formulation. Specifically, when applied at the interface between a porous material and a boundary layer (as in thermal protection systems applications), the original formulation assumes unidirectional advective transport of gaseous species from the porous material to the boundary layer (i.e., blowing). However, under conditions that may appear in hypersonic flight or in ground-based wind tunnels, boundary layer gases can enter the porous material due to a favorable pressure gradient. We show that this scenario can be easily handled via a straightforward modification to the B' formalism, and we demonstrate via examples that accounting for gas entering the material can impact the predicted recession velocity of ablating surfaces. In order to facilitate the implementation of the extended B' formulation in existing material response codes, we present a short algorithm in section 5 and we also refer readers to a GitHub repository where the scripts used to generate the modified B' tables are publicly available.

physics.flu-dyn↗