Add: new module CT-LIA #991

[AlbertoCuadra]

This pull request introduces the initial components of the upcoming CT-LIA module, aimed at enabling the analysis of shock–turbulence interaction problems using Linear Interaction Analysis (LIA) within the Combustion Toolbox.

The new module, CT-LIA, is intended to extend the capabilities of the Combustion Toolbox by introducing a robust framework for the coupled resolution of Linear Interaction Analysis (LIA) with thermochemical effects. Building on our previous work [1-3], this module aims to capture additional complex phenomena, such as vibrational excitation, dissociation, and ionization, which become significant in high-speed flow environments. Additionaly, compressibility effects are incorporated following our recent research conducted at the Center for Turbulence Research (CTR) Summer Program 2024 at Stanford [4], in addition to Ref. [5].

The implementation reflects the core modeling assumptions of the theoretical framework:

• Upstream turbulence is decomposed into vortical, entropic, and acoustic disturbances using Kovásznay decomposition [6].
• Post-shock fluctuations are computed from the linearized Rankine–Hugoniot relations.
• Thermodynamic properties are evaluated using the Combustion Toolbox equilibrium solvers and databases.
• Compressibility effects are incorporated through explicit dilatational kinetic energy and acoustic mode coupling.
• Turbulence amplification is quantified in terms of streamwise, transverse, and total turbulent kinetic energy (TKE).
• One-dimensional post-shock spectra are computed by integrating single-mode amplification factors over incident wave angles (not-included in this pull request).

New classes

ShockTurbulenceModel (Abstract class)

This abstract class defines the common interface for all shock–turbulence interaction models. It enforces a unified API for:

• Defining the probability density function (PDF) for angular and spectral integration
• Computing turbulence amplification ratios and averaged statistics
• Supporting both 2D and 3D turbulence formulations
• Delegating quadrature to a reusable Integrator object

Each derived class implements a specific physical regime and provides its own formulation for spectral weighting and averaging.

ShockTurbulenceModelVortical

Implements the Linear Interaction Analysis model for purely vortical upstream turbulence following our previous work [3].

• Computes amplification of longitudinal and transverse velocity fluctuations
• Provides turbulent kinetic energy (TKE), enstrophy, and anisotropy metrics

ShockTurbulenceModelVorticalEntropic

Extends the vortical formulation to include entropic disturbances correlated with velocity fluctuations.

• Models correlation between vortical and entropic modes through a tunable parameter chi
• Supports alternative scaling of chi (e.g. normalized by the upstream Mach number)
• Representation of baroclinic vorticity generation at the shock

ShockTurbulenceModelAcoustic

Implements LIA for turbulence comprised of purely acoustic disturbances.

This class models, based on the analytical framework of Huete et al. (2012), the interaction between incident pressure waves and the shock, accounting for the generation of vortical and entropic perturbations downstream and their contribution to turbulence amplification with thermochemical effects.

ShockTurbulenceModelCompressible

Implements a fully compressible turbulence model by combining:

• vortical–entropic contributions
• acoustic contributions

Superposition is controlled through:

• chi: vortical–entropic correlation coefficient
• eta: acoustic-to-vortical TKE ratio

This class represents the most general formulation currently available in CT-LIA and is suitable for broadband turbulence in hypersonic flows.

ShockTurbulenceSolver

Solver class for shock–turbulence interaction problems.

This class provides the main solver interface of the CT-LIA module. It integrates the thermochemical model, the shock-jump solver, and the selected LIA turbulence model into a single workflow.

References:

[1] Cuadra, A. (2023). Development of a wide-spectrum thermochemical code with application to planar reacting and non-reacting shocks. PhD thesis, Universidad Carlos III de Madrid. Available at http://hdl.handle.net/10016/38179.

[2] Cuadra, A., Vera, M., Di Renzo, M. & Huete, C. (2023). Linear Theory of Hypersonic Shocks Interacting with Turbulence in Air. In 2023 AIAA SciTech Forum, National Harbor, USA. doi:10.2514/6.2023-0075.

[3] Huete, C., Cuadra, A., Vera, M., & Urzay, J. (2021). Thermochemical effects on hypersonic shock waves interacting with weak turbulence. Physics of Fluids, 33, 086111. doi:10.1063/5.0059948.

[4] Cuadra, A., Williams, C. T., Di Renzo, M., & Huete, C. (2024). Compressibility and vibrational-excitation effects in hypersonic shock-turbulence interaction. Summer Program Proceedings, Center for Turbulence Research, Stanford University. URL

[5] Cuadra, A., Di Renzo, M., Hoste, J. J. O., Williams, C. T., Vera, M., & Huete, C. (2025).
Review of shock-turbulence interaction with a focus on hypersonic flow. Physics of Fluids, 37(4).
doi:10.1063/5.0255816.

[6] Kovásznay, L. S. (1953). Turbulence in supersonic flow. Journal of the Aeronautical Sciences, 20(10), 657-674. doi:10.2514/8.2793.

[7] Huete, C., Wouchuk, J. G., & Velikovich, A. L. (2012). Analytical linear theory for the interaction of a planar shock wave with a two-or three-dimensional random isotropic acoustic wave field. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 85(2), 026312. doi:10.1103/PhysRevE.85.026312.