Fig 1 - uploaded by César Huete
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Sketch of the interaction of a planar shock wave with an isotropic vorticity field in air, where post-shock high-temperature phenomena is included.
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The interaction between a weakly turbulent free stream of air and a hypersonic shock wave is investigated theoretically by using linear interaction analysis (LIA). The perturbation-free jump conditions across the shock are computed using Combustion Toolbox, an in-house thermochemical code capable of capturing high-temperature phenomena such as diss...
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... is no longer true in hypersonic conditions. Molecular transformations change, among others, the mass compression ratio and the post-shock Mach number, thereby affecting the intensity of The present paper aims to investigate high-temperature effects in the interaction of hypersonic shocks with turbulent air, as depicted in Fig.1. In this respect, this work is a natural extension of Ref. [36] that made use of LIA to study the amplification of turbulence across hypersonic shocks moving in single-species diatomic gases. ...
Citations
... On the theoretical side, we employ a linear interaction analysis framework built on previous works. 47,55,56 This framework enables LIA for multi-component mixtures by using the Combustion Toolbox 57 to incorporate compressible and thermochemical effects. Theoretical (LIA) and numerical (DNS) results are presented across a wide range of Mach numbers to characterize the influence of upstream turbulence compressibility in the hypersonic regime. ...
... The theoretical framework extends LIA. 47,55,56 to multi-component mixtures by incorporating the Combustion Toolbox, 57 accounting for compressible and thermochemical effects. New results across a broad range of Mach numbers characterize the impact of upstream turbulence compressibility in the hypersonic regime, utilizing both LIA and DNS. ...
Hypersonic flight involves a variety of complex flow phenomena that directly impact the aerothermodynamic loading of high-speed vehicles. The turbulence encountered during a typical flight trajectory influences and interacts with the shock waves on and around the surface of a vehicle and its propulsion system, affecting both aerodynamic and power plant performance. These interactions can be studied by isolating a turbulent flow convected through a normal shock, commonly referred to as the canonical shock-turbulence interaction (STI) problem. Scale-resolving computational fluid dynamics (CFD) and linear interaction analysis (LIA) have been crucial in studying this problem and formulating scaling laws that explain the observed behavior. In this work, an extensive review of the theoretical (LIA) and numerical (CFD) work on the canonical STI is presented. The majority of the work conducted to date has focused on calorically perfect gases with constant heat capacities. However, in hypersonic flows, chemical and thermal non-equilibrium effects may alter the nature of the interaction. As a result, relevant LIA and CFD studies addressing high-enthalpy phenomena are also succinctly discussed.
... The specific heat capacity at constant pressure for each of the three species (H 2 O, N 2 , Cs) is modeled here as a temperature-dependent function according to the NASA 9coefficient formulation for thermodynamic properties, keeping only the high-temperature range (from 1000 K to 6000 K) that is of interest in our problem of magnetohydrodynamic direct power extraction [199], [200], [201], [202], [203], [204]. It should be noted that elemental cesium normally vaporizes at a boiling point near 940 K and fuses at a low boiling point of approximately 302 K, which is near ordinary room temperatures [205], [206], [207], [208], [209], [210]. ...
This study explores the suitability of hydrogen-based plasma in direct power extraction (DPE) as a non-conventional electricity generation method. We apply computational modeling and principles in physics and chemistry to estimate different thermal and electric properties of a water-vapor/nitrogen/cesium-vapor (H2O/N2/Cs) gas mixture with different levels of cesium (Cs) at a fixed temperature of 2300 K (2026.85 {\deg}C). This gas mixture and temperature are selected because they resemble the stoichiometric combustion of hydrogen with air, followed by the addition of the alkali metal element cesium to allow ionization, thus converting the gas mixture into electrically conducting plasma. We vary the cesium mole fraction in the gas mixture by two orders of magnitude, from a minute amount of 0.0625% (1/1600) to a major amount of 16% (0.16). We use these results to further estimate the theoretical upper limit of the electric power output from a unit volume of a high-speed magnetohydrodynamic (MHD) channel, with the plasma accelerated inside it to twice the local speed of sound (Mach number 2) while subject to an applied magnetic field of 5 T (5 teslas). We report that there is an optimum cesium mole fraction of 3%, at which the power output is maximized. Per 1 m3 of plasma volume, the estimated theoretical electric power generation at 1 atm (101.325 kPa) pressure of the hydrogen-combustion mixture is extraordinarily high at 360 MW/m3, and the plasma electric conductivity is 17.5 S/m. This estimated power generation even reaches an impressive level of 1.15 GW/m3 (11500 MW/m3) if the absolute pressure can be decreased to 0.0625 atm (6.333 kPa), at which the electric conductivity exceeds 55 S/m (more than 10 times the electric conductivity of seawater).
... Here, the model is extended to account for density (Huete et al. 2011) and pressure (Huete et al. 2012) fluctuations in the upstream flow associated with acoustic, entropic, and vortical fluctuations, as depicted in Figure 1. Furthermore, endothermic effects in the form of vibrational excitation (Cuadra 2023;Cuadra et al. 2023) are also incorporated by solving the perturbation-free jump conditions across the shock using the Combustion Toolbox code (Cuadra et al. 2024). ...
The interaction of turbulence with shock waves significantly modulates the frequency and amplitude of hydrodynamic fluctuations encountered by aerospace vehicles in low-altitude hypersonic flight. In these high-speed flows, intrinsic compressibility effects emerge together with high-enthalpy phenomena in the form of internal-energy excitation. The present study specifically compares direct numerical simulation (DNS) and linear interaction analysis (LIA) to characterize the impact of density fluctuations and endothermic processes in Mach-5 canonical shock-turbulence interaction (STI). Both the numerical and theoretical approaches reveal that increasing upstream compressibility augments the turbulent kinetic energy (TKE) across the STI for varying turbulent Mach numbers. The effect of endothermicity is likewise assessed in each framework by introducing equilibrium vibrational excitation, which is shown to further amplify the TKE downstream of the shock.
... Despite the deep understanding provided by the latter approach, there are still cases in which a proper physical explanation can not be found based only on numerical results. In these cases, separation of scales may allow to split the problem into simpler ones, where the assumption of chemical equilibrium could be justified in some representative scenarios [45,52,53]. ...
... Combustion Toolbox was conceived with these long-term goals in mind, and is now presented and validated in this work. This MATLAB-GUI thermochemical code represents the core of an ongoing research work and has been used to investigate a series of problems during the last few years [45,52,53,[60][61][62][63][64][65]. Results are in excellent agreement with NASA's CEA code [17], Cantera [66] within Caltech's Shock and Detonation Toolbox (SD-Toolbox) [67,68], and the Thermochemical Equilibrium Abundances (TEA) code [25]. ...
The Combustion Toolbox (CT) is a newly developed open-source thermochemical code designed to solve problems involving chemical equilibrium for both gas- and condensed-phase species. The kernel of the code is based on the theoretical framework set forth by NASA’s computer program CEA (Chemical Equilibrium with Applications) while incorporating new algorithms that significantly improve both convergence rate and robustness. The thermochemical properties are computed under the ideal gas approximation using an up-to-date version of NASA’s 9-coefficient polynomial fits. These fits use the Third Millennium database, which includes the available values from Active Thermochemical Tables. Combustion Toolbox is programmed in MATLAB with an object-oriented architecture composed of three main modules: CT-EQUIL, CT-SD, and CT-ROCKET. The kernel module, CT-EQUIL, minimizes the Gibbs/Helmholtz free energy of the system using the technique of Lagrange multipliers combined with a multidimensional Newton-Raphson method, upon the condition that two state functions are used to define the mixture properties (e.g., enthalpy and pressure). CT-SD solves processes involving strong changes in dynamic pressure, such as steady shock and detonation waves under normal and oblique incidence angles. Finally, CT-ROCKET estimates rocket engine performance under highly idealized conditions. The new tool is equipped with a versatile Graphical User Interface and has been successfully used for teaching and research activities over the last four years. Results are in excellent agreement with CEA, Cantera within Caltech’s Shock and Detonation Toolbox (SD-Toolbox), and the Thermochemical Equilibrium Abundances (TEA) code. CT is available under an open-source GPLv3 license via GitHub https://github.com/CombustionToolbox/combustion_toolbox, and its documentation can be found in https://combustion-toolbox-website.readthedocs.io.
This study explores the suitability of hydrogen-based plasma in direct power extraction (DPE) as a non-conventional electricity generation method. We apply computational modeling and principles in physics and chemistry to estimate different thermal and electric properties of a water-vapor/nitrogen/cesium-vapor (H
2
O/N2/Cs) gas mixture with different levels of cesium (Cs) at a fixed temperature of 2300 K (2026.85 °C). This gas mixture and temperature are selected because they resemble the stoichiometric combustion of hydrogen with air, followed by the addition of the alkali metal element cesium to allow ionization, thus converting the gas mixture into electrically conducting plasma. We vary the cesium mole fraction in the gas mixture by two orders of magnitude, from a minute amount of 0.0625% (1/1600) to a major amount of 16% (0.16). We use these results to further estimate the theoretical upper limit of the electric power output from a unit volume of a high-speed magnetohydrodynamic (MHD) channel, with the plasma accelerated inside it to twice the local speed of sound (Mach number 2) while subject to an applied magnetic field of 5 T (5 teslas). We report that there is an optimum cesium mole fraction of 3%, at which the power output is maximized. Per 1 m
3
of plasma volume, the estimated theoretical electric power generation at 1 atm (101.325 kPa) pressure of the hydrogen-combustion mixture is extraordinarily high at 360 MW/m
3
, and the plasma electric conductivity is 17.5 S/m. This estimated power generation even reaches an impressive level of 1.15 GW/m
3
(11500 MW/m
3
) if the absolute pressure can be decreased to 0.0625 atm (6.333 kPa), at which the electric conductivity exceeds 55 S/m (more than 10 times the electric conductivity of seawater).
