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+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6855 +10.21105/joss.06855 + +rgfrosh: A Python package for calculating shock +conditions using real gas equations of state + + + +https://orcid.org/0000-0001-8774-3090 + +Kinney +Cory + + + + + +Vasu +Subith + + + + + +Department of Mechanical and Aerospace Engineering, +University of Central Florida, Orlando, FL USA + + + + +29 +4 +2024 + +9 +99 +6855 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +Python +shock tube +normal shock +frozen shock +ideal gas +real gas + + + + + + Summary +

rgfrosh solves the reflected shock equations + for an arbitrary equation of state, allowing for accurate calculation + of the temperature and pressure behind a reflected shock accounting + for real gas effects. Forward and inverse solvers are provided to + calculate experimental conditions based on measurements and to plan + experiments based on desired conditions, respectively. + rgfrosh is designed to be lightweight and + extensible, with a simple interface for users to utilize existing + thermodynamic libraries.

+ + + Statement of need +

Combustion is a complex process that is influenced by numerous + factors, including temperature, pressure, and chemical composition. + Combustion modeling relies on chemical kinetics mechanisms that detail + how chemical reaction rates – involving many intermediate species – + vary with temperature and pressure. Experimental data is essential for + measuring reaction rates, refining mechanisms, and validating + predictions from these models for certain fuels and conditions.

+

Shock tubes are ideal experimental facilities for performing + fundamental research in combustion because they use shock waves to + impart step changes in temperature and pressure to a test gas mixture. + The gas behind the reflected shock is relatively stagnant, and the + system is considered adiabatic on the relevant time-scales; therefore, + the shock tube closely resembles a constant volume zero-dimensional + reactor, allowing for comparison between experimental measurements and + model predictions. Accurate calculation of the reflected shock + conditions is essential for correctly interpreting experimental + results. This is accomplished by solving the reflected shock equations + under an assumed equation of state using the known initial state of + the gas and the measured shock velocity.

+

Fundamental research into combustion at extremely high-pressure + conditions, such as for rocket engines or direct-fire supercritical + CO2 power cycles + (Kinney, + 2022), requires consideration of real gas effects in + experimental measurements and model simulations.

+ + State of the field +

A shock solver supporting real gas equations of state called + RGFROSH was previously developed in FORTRAN by Davidson & Hanson + (1996); + however, there existed a need for a modernized open-source version, + as the original is not generally available nor would it be readily + compatible with modern tools. The extensive SDToolbox + (Browne + et al., 2021) has functionality for computing the postshock + state for a chemically frozen shock; however, SDToolbox only + supports Cantera + (Goodwin + et al., 2023) for thermodynamic properties and does not + provide a convenient interface to obtain the full solution for a + reflected shock for both the forward and inverse problems. Thus, the + present rgfrosh was developed in Python as a + solution that can utilize any modern thermodynamic library to solve + for the full reflected shock solution for an arbitrary equation of + state to enable further research into high-pressure combustion.

+ + + + Features +

rgfrosh provides a simple interface for + solving the reflected shock equations, allowing the user to obtain the + full solution with a single function call. Two models are provided - + IdealShock for calorically perfect gases, and + FrozenShock for arbitrary equations of state. + The former is primarily included for comparison and validation + purposes, while the latter is the primary focus of the package as it + allows for accurate calculation of the reflected shock conditions for + real gases.

+

To remain as lightweight and extensible as possible, + rgfrosh relies on external packages for the key + thermodynamic functions required by the + FrozenShock solver. The required interface is + defined by the ThermoInterface protocol class, + which was written to provide native support for Cantera + (Goodwin + et al., 2023). Additionally, an interface is provided to wrap + CoolProp + (Bell + et al., 2014), which itself has backend support for NIST + REFPROP + (Lemmon + et al., 2002), for use with the solver. These two compatible + packages enable support for a wide range of equations of state which + should cover the majority of use cases; however, any user-defined + class that implements the simple + ThermoInterface protocol can be used with the + solver.

+

The primary use cases for rgfrosh are + experiment postprocessing and experiment planning. The + solve_incident and + solve_reflected methods implement the + Newton-Raphson solver detailed by Davidson & Hanson + (1996) + for calculating the incident and reflected shock conditions, + respectively, from the initial conditions and the experimentally + measured shock velocity. The solve_initial + method implements the algorithm derived by the author (see + Kinney, + 2022, A.3) for calculating the initial pressure and incident + shock velocity, temperature, and pressure from the initial temperature + and target reflected shock temperature and pressure for an + experiment.

+ + + Future work +

Future work includes the consideration of vibrational + non-equilibrium in the shock solvers. Current solver functionality + would be classified as equilibrium-equilibrium (EE) mode, referring to + the incident and reflected shock, respectively; frozen-equilibrium and + frozen-frozen modes are planned.

+ + + Acknowledgements +

We would like to acknowledge D. F. Davidson and R. K. Hanson for + authoring the original software this work is based on, granting + permission to use the package name, and for providing validation data + for comparison. Additionally, the authors appreciate funding from the + University of Central Florida.

+ + + + + + + + + KinneyCory + + Extreme-pressure ignition studies of methane and natural gas with CO2 with applications in rockets and gas turbines + 2022 + https://stars.library.ucf.edu/etd2020/1033 + + + + + + DavidsonDavid F + HansonRonald K + + Real gas corrections in shock tube studies at high pressures + Israel journal of chemistry + Wiley Online Library + 1996 + 36 + 3 + 10.1002/ijch.199600044 + 321 + 326 + + + + + + BrowneS. + ZieglerJ. + BitterN. + SchmidtB. + LawsonJ. + ShepherdJ. E. + + SDToolbox - numerical tools for shock and detonation wave modeling + California Institute of Technology, Pasadena, CA + 2021 + https://shepherd.caltech.edu/EDL/PublicResources/sdt/ + + + + + + GoodwinDavid G. + MoffatHarry K. + SchoeglIngmar + SpethRaymond L. + WeberBryan W. + + Cantera: An object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes + https://www.cantera.org + 2023 + https://doi.org/10.1002/ijch.199600044 + 10.5281/zenodo.8137090 + + + + + + BellIan H. + WronskiJorrit + QuoilinSylvain + LemortVincent + + Pure and pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library CoolProp + Industrial & Engineering Chemistry Research + 2014 + 53 + 6 + http://pubs.acs.org/doi/abs/10.1021/ie4033999 + 10.1021/ie4033999 + 2498 + 2508 + + + + + + LemmonEric W + HuberMarcia L + McLindenMark O + + NIST reference fluid thermodynamic and transport properties–REFPROP + NIST standard reference database + 2002 + 23 + 2002 + v7 + + + + + +