Thermochemical Nonequilibrium Research Articles

Study on the flow characteristics of double-cone in hypersonic flows

Reusable spacecraft is one of the hot topics in the field of aerospace, attracting wide attention from researchers. Due to the high-Mach-number flight of re-entry, the air near the wall exhibits significant thermochemical nonequilibrium effects. Besides, the existing shock wave/boundary layer interaction (SWBLI) leads to severe aerodynamic heating issues. This study utilizes the two-temperature model to conduct simulations of hypersonic laminar flows around a canonical 25°/55° double-cone with low and high enthalpy. By varying the wall temperature and the aft cone angle, the evolution mechanism of the flow under the high-enthalpy and hypersonic freestream is explored. Our findings illustrate that while the thermodynamic nonequilibrium model closely reflects the separation zone evidenced in the experiments, it habitually overpredicts the peak heat transfer, particularly under high-enthalpy conditions. For the thermochemical nonequilibrium model, the flow field structure appears more uniform, with a reduced standoff distance of the detached shock. An incremental rise in wall temperature correlates with a proportional augmentation of the separation bubble, though its impact on the overall flow field is negligible. Increasing the aft cone angle intensifies the shock/shock interaction (SSI), transitioning from a lower-intensity Type VI to a more intense Type IV shock interplay. The examination reveals that the increase in temperature and cone angle amplifies the interaction between the separation region and shock waves, drastically escalating the peak heat transfer and fostering a secondary peak. The hypersonic flow of the double-cone demonstrates a multifaceted interaction of phenomena, notably SWBLI and SSI, with our analyses providing pivotal insights for the aerodynamic and thermal protection design of the high-Mach-number spacecraft.

Coarse-grained modeling of high-enthalpy air flows based on the updated vibrational state-to-state kinetics

The state-to-state (StS) model can accurately describe high-temperature thermochemical nonequilibrium flows. For the five-species air gas mixture, we develop a comprehensive database for the state-specific rate coefficients for temperatures 300–25 000 K in this paper. The database incorporates recent molecular dynamics simulations (based on the ab initio potential energy surfaces) in the literature, and theoretical methods, including the forced harmonic oscillator model and the Marrone–Treanor model, are employed to complement the rate coefficients that are unavailable from molecular dynamics calculations. The post-shock StS simulations using the present database agree with the experimental NO infrared radiation. Based on this updated StS kinetics database, we investigate the post-shock high-enthalpy air flows by employing both the StS and coarse-grained models (CGM). The CGM, which lumps molecular vibrational states into groups, shows results that align with the StS model, even utilizing only two groups for each molecule. However, the CGM-1G model, with only one group per molecule and belonging to the multi-temperature model (but uses StS kinetics), fails to reproduce the StS results. Analysis of vibrational energy source terms for different kinetic processes and fractions of vibrational groups reveals that the deficiency of the CGM-1G model stems from the overestimation of high-lying vibrational states, leading to higher dissociation rates and increased consumption of vibrational energy in dissociation. Furthermore, the presence of the Zeldovich-exchange processes indirectly facilitates energy transfer in N2 and O2, a phenomenon not observed in binary gas systems. These findings have important implications for developing the reduced-order model based on coarse-grained treatment.

Two-temperature thermochemical nonequilibrium model based on the coarse-grained treatment of molecular vibrational states.

Although the high-fidelity state-to-state (StS) model accurately describes high-temperature thermochemical nonequilibrium flows, its practical application is hindered by the prohibitively high computational cost. In this paper, we develop a reduced-order model that leverages the widelyused two-temperature (2T) framework and a coarse-grained treatment of molecular vibrational states to achieve accuracy comparable to the StS model while ensuring computational efficiency. We observe that the multigroup coarse-grained model (CGM), lumping vibrational energy levels into several groups, yields results close to the StS model for the high-temperature postshock oxygen flows, even using only two groups. However, theone-group CGM (CGM-1G), equivalent to the 2T model but using the StS kinetics, fails to approximate the StS results. Analysis of microscopic group properties reveals that the failure of the CGM-1G stems from the inability to capture the non-Boltzmann effects of mid-to-high vibrational levels, overestimating apparent dissociation rates and vibrational energy loss in the dissociation-dominated region. We then propose an analytical distribution function of vibrational groups by incorporating Treanor-like terms and an additional linear term (addressing the dissociation depletion of high-lying levels). Building upon this algebraic group distribution function and reconstructing vibrational levels within each group using the vibrational temperature, we develop a new 2T model called CG2T, which demonstrates accuracy much closer (than the CGM-1G) to the StS results for the postshock oxygen flows with varying degrees of thermochemical nonequilibrium. Moreover, a fullyconnected neural network is pretrained to substitute the module for the mass and vibrational energy source terms to enhance computational efficiency, achieving about 30-fold speedup in the CG2T model without sacrificing accuracy.

Study on the influence of high-temperature thermochemical nonequilibrium effects on the flow field characteristics around shaped wing

With advances in research on hypersonic vehicles, the precise simulation of the effects of thermochemical non-equilibrium has become increasingly important in their design. In light of this, this study explores the influence of high-temperature thermochemical non-equilibrium on the characteristics of the flow field around the hypersonic wings of an aircraft. We initially conducted a numerical simulation by using the model of flow through a cylinder to validate the accuracy and reliability of an 11-species gas model in representing high-enthalpy flow fields. Subsequently, a systematic analysis was conducted on the impact of thermochemical nonequilibrium effects on the temperature, pressure, and enthalpy distribution in the flow field around a symmetric diamond wing under different Mach numbers and angles of attack. The research results indicated that the deeper reason behind the differing thermochemical nonequilibrium effects in the flow field at various Mach numbers lies in the distinct distribution of enthalpy of the air components at different locations, which provided a new perspective for understanding flow field variations from the standpoint of enthalpy. It is disclosed that the thermochemical non-equilibrium significantly altered the characteristics of the flow field, particularly at high Mach numbers and angles of attack, with a significant impact on the aerodynamic parameters of both the windward and the leeward sides of the wing. Through explaining the mechanisms of thermochemical non-equilibrium under flow fields with different structures, this study provides a theoretical foundations for and a fresh perspective on the design of hypersonic vehicles.

Numerical study of shock-induced thermochemical nonequilibrium effects in a high Mach flow field

As Mach number increases, thermochemical nonequilibrium is recognized as potentially affecting the flow field structure, as well as mixing and combustion characteristics, where shock-induced thermochemical nonequilibrium is a common and crucial phenomenon in compressible flow fields. A numerical study of shock-induced thermochemical nonequilibrium effects within a high Mach flow field of the electre vehicle is conducted by employing a two-temperature model-based solver hy2foam. The validation through experimental and simulation data confirms that hy2foam coupled with Park's two-temperature model and Park's five-species mechanism correctly predicts the flow structure and nonequilibrium characteristics. Four regime cases of thermochemical equilibrium, thermal nonequilibrium, chemical nonequilibrium, and thermochemical nonequilibrium are designed for comparison. First, the mechanism of shock-induced nonequilibrium is revealed. The shock induces the thermal nonequilibrium to occur instantly, and then the equilibrium is reestablished by undergoing the relaxation process. However, chemical nonequilibrium works delayed after the shock, and the high temperature induced by the shock motivates deviation from the chemical equilibrium by turning on chemical reactions. Further comparison of the four cases reveals that thermodynamic nonequilibrium significantly affects both shock position and intensity. In contrast, chemical nonequilibrium only significantly affects the distance to the shock detachment. Furthermore, it is found that thermodynamic and chemical nonequilibria behave in a complex coupling relationship after the shock.

Drag and Thermal Reduction of Spiked Hypersonic Vehicle in Thermochemical Nonequilibrium

This study utilizes the in-house parallel direct simulation Monte Carlo–quantum dynamics method to model the aerodynamic flowfield of a spiked reentry vehicle within a rarefied high-altitude atmosphere. Investigating the flight of spiked aircraft under various flight conditions and spike sizes and considering both the real gas effect and the rarefied gas effect, the aerodynamic characteristic of the aircraft is evaluated. Performance evaluation for effectiveness in drag reduction and thermal protection is based on drag and the maximum stagnation heat flux coefficient at the vehicle’s shoulder. Findings indicate that, in the rarefied atmosphere, the distinction between the characteristic shock intensities of spiked and unspiked vehicles is not pronounced, which results in a drag reduction of approximately 5%, accompanied by a more than 100% increase in thermal effect on the vehicle’s shoulder, obviously poor in effectiveness. Subsequently, this study examines the spiked vehicle equipped with a lateral jet, and this augmented approach achieves a marked reduction in the intensity of the shock wave impacting the vehicle’s shoulder with a drag reduction exceeding 10% and attenuates the thermal impact by over 50% in comparison to the implementation of spiking alone, thereby demonstrating superior performance in terms of effectiveness.

Effect of multi-temperature models on heat transfer and electron behavior in hypersonic flows

In hypersonic computational fluid dynamics, the two-temperature (2-T) model is widely used to simulate thermochemical nonequilibrium. The 2-T model incorporates translational-rotational and electron-electronic-vibrational energies, assuming that the integrated energies have the equivalent temperature. In this study, multi-T models are constructed to accurately predict the effects on heat flux and free electrons due to the separation of energy modes under hypersonic environments. The three-temperature (3-T) model separates the electron-electronic energy from the electron-electronic-vibrational energy of the 2-T model. The 3-T model can accurately predict the distribution and temperature of free electrons by separating the energy of free electrons, which has different characteristics from heavy particles. The four-temperature model treats rotational energy as a nonequilibrium energy mode, distinct from translational-rotational energy. While the rotational temperature reaches equilibrium rapidly at low temperatures, at high-temperature regime rotational temperature shows a relaxation time similar to that of vibrational temperature, which cannot be ignored. To develop multi-T models, electron-vibrational relaxation and translational-rotational relaxation, which are omitted in the 2-T model, are considered. Various flight test and ground facility conditions are analyzed to verify the effects of electron and heat flux under circumstances that include shock, expansion, and shock wave boundary layer interaction. The results of the multi-T models show significant differences in electron temperature and distribution caused by electron-electronic nonequilibrium. Additionally, rotational nonequilibrium increases the shock standoff distance and alters the electron distribution at high altitudes. The heat flux difference across multi-T models is found to be negligible, except in the high degree of ionization condition.

Turbulent Diffuse Molecular Media with Nonideal Magnetohydrodynamics and Consistent Thermochemistry: Numerical Simulations and Dynamic Characteristics

Turbulent diffuse molecular clouds can exhibit complicated morphologies caused by the interactions among radiation, chemistry, fluids, and fields. We performed full 3D simulations for turbulent diffuse molecular interstellar media, featuring time-dependent nonequilibrium thermochemistry coevolved with magnetohydrodynamics (MHD). Simulation results exhibit the relative abundances of key chemical species (e.g., C, CO, OH) vary by more than one order of magnitude for the “premature” epoch of chemical evolution (t ≲ 2 × 105 yr). Various simulations are also conducted to study the impacts of physical parameters. Nonideal MHD effects are essential in shaping the behavior of gases, and strong magnetic fields (∼10 μG) tend to inhibit vigorous compressions and thus reduce the fraction of warm gases (T ≳ 102 K). Thermodynamical and chemical conditions of the gas are sensitive to modulation by dynamic conditions, especially the energy injection by turbulence. Chemical features, including ionization (cosmic ray and diffuse interstellar radiation), would not directly affect the turbulence power spectra. Nonetheless, their effects are prominent in the distribution profiles of temperatures and gas densities. Comprehensive observations are necessary and useful to eliminate the degeneracies of physical parameters and constrain the properties of diffuse molecular clouds with confidence.

Quasi-one-dimensional non-equilibrium method for shock tube and stagnation line flows

Shock tube experiments are used to investigate non-equilibrium thermochemistry and radiative processes in reacting gas hypersonic flows. Boundary layer and shock structure are known to influence the spatial variation of the test slug state properties. This work derives and validates a novel method for viscous, quasi-one-dimensional, non-equilibrium flow in a shock tube assuming constant shock speed. The proposed method fully resolves the shock structure. Mirels' estimate for boundary layer growth around the test slug determines the dilation rate at the centerline. This, along with relevant boundary conditions, appropriately models core flow in a shock tube. The flow equations are discretized by finite differences on a staggered grid. The resulting highly non-linear set of algebraic equations is solved by Newton iterations. The Jacobian matrix is block tridiagonal with a Schur complement, allowing efficient inversion. This culminates in a unique and computationally efficient quasi-one-dimensional method offering improved modeling of the physical characteristics of shock tube experiments. Results of a 3 km/s, 66.6 Pa argon test case solved by a viscous, axisymmetric Navier–Stokes solution had agreement with the proposed method in temperature and pressure profiles to within 2% and post-shock velocity to within 15%. Reacting gas shock tube experiments in synthetic air and synthetic Titan atmospheres were analyzed. Radiance values in the non-equilibrium and equilibrium regions were compared under various assumptions for the shock structure and radial velocity distribution. These results highlight the necessity of a dedicated shock tube solver when analyzing shock tube thermochemistry, particularly when determining reaction rates and relaxation parameters.

A thermochemical nonequilibrium model of CO2 plasma for studying flow-field properties of the spacecraft Mars Pathfinder

A thermochemical nonequilibrium model of CO2 plasma for studying flow-field properties of the spacecraft Mars Pathfinder

A three-dimensional thermochemical nonequilibrium model for simulating air plasma flows around an inflatable membrane reentry vehicle

A three-dimensional thermochemical nonequilibrium model for simulating air plasma flows around an inflatable membrane reentry vehicle

Effect of non-equilibrium thermochemistry on Pitot pressure measurements in shock tunnels (or: Is 0.92 really the magic number?)

Pitot pressure is the most common measurement in high total enthalpy shock tunnels for test condition verification. Nozzle calculations using multi-temperature non-equilibrium thermochemistry are needed in conjunction with Pitot measurements to quantify freestream properties. Pitot pressure is typically matched by tuning the boundary layer transition location in these simulations. However, non-equilibrium thermochemistry effects on the Pitot probe are commonly ignored. A computational study was undertaken to estimate the effect of non-equilibrium thermochemistry on Pitot pressure and freestream conditions. The test flow was produced by a Mach 7 nozzle in a reflected shock tunnel for air at a relatively low total enthalpy of 2.67MJ/kg. Three different thermochemical models (equilibrium, finite-rate chemistry and two-temperature thermochemistry) were employed to compute flow variables at the nozzle exit and Pitot probe. Pitot pressures from these simulations were compared against those obtained via experiments. The results show a departure from the commonly utilized C of 0.92 in the reduced Rayleigh-Pitot equation form for high Mach numbers. Additionally, calculations were done with a sweep of free-stream conditions and resulting in values for one- and two-temperature models to use in future shock tunnel studies. Overall, our results show that the influence of finite-rate thermochemistry should be taken into account, even at relatively low flow enthalpies.

The nature of diffuse ionized gas in star-forming galaxies

ABSTRACT We present an analysis of the diffuse ionized gas (DIG) in a high-resolution simulation of an isolated Milky Way-like galaxy, incorporating on-the-fly radiative transfer and non-equilibrium thermochemistry. We utilize the Monte-Carlo radiative transfer code colt to self-consistently obtain ionization states and line emission in post-processing. We find a clear bimodal distribution in the electron densities of ionized gas ($n_{\rm e}$), allowing us to define a threshold of $n_{\rm e}=10\, \mathrm{cm}^{-3}$ to differentiate DIG from ${\rm H\, {\small II}}$ regions. The DIG is primarily ionized by stars aged 5 – 25 Myr, which become exposed directly to low-density gas after ${\rm H\, {\small II}}$ regions have been cleared. Leakage from recently formed stars ($\lt 5$ Myr) is only moderately important for DIG ionization. We forward model local observations and validate our simulated DIG against observed line ratios in [${\rm S\, {\small II}}$]/H$\alpha$, [${\rm N\, {\small II}}$]/H$\alpha$, [${\rm O\, {\small I}}$]/H$\alpha$, and [${\rm O\, {\small III}}$]/H$\beta$ against $\Sigma _{\rm H\alpha }$. The mock observations not only reproduce observed correlations, but also demonstrate that such trends are related to an increasing temperature and hardening ionizing radiation field with decreasing $n_{\rm e}$. The hardening of radiation within the DIG is caused by the gradual transition of the dominant ionizing source with decreasing $n_{\rm e}$ from 0 to 25 Myr stars, which have progressively harder intrinsic ionizing spectra primarily due to the extended Wolf–Rayet phase caused by binary interactions. Consequently, the DIG line ratio trends can be attributed to ongoing star formation, rather than secondary ionization sources, and therefore present a potent test for stellar feedback and stellar population models.

Thermo-chemical nonequilibrium effects on combustion characteristics of a transverse jet in the scramjet

As the Mach number increases, the local static temperature gradually approaches the characteristic gas vibration/dissociation temperature, and significant thermo-chemical relaxation processes occur. The thermo-chemical nonequilibrium phenomenona could affect the mixing and combustion process and become a factor that must be considered for scramjet design. In this paper, a large eddy simulation solver based on the two-temperature model is developed. The transfer terms between vibrational and trans-rotational energy are modeled by the Landau–Teller formulation and the vibrational-dissociation coupling is considered by adopting the Park model. Three sets of simulations based on the Hyshot Ⅱ engine configuration with different models were performed simultaneously to validate numerical methods and analyze results. The results reveal that the shock, cross-injection of fuel, and Prandtl-Meyer flow induce significant nonequilibrium regions. The vibration relaxation process in the jet mixing region is frozen, the vibration temperature is much higher than the trans-rotational temperature, and the extra energy is converted from the vibration mode to the trans-rotational mode, resulting in the increase of the trans-rotational temperature and the advance of auto-ignition in the nonequilibrium condition. Considering the vibration-dissociation coupling, the higher vibration temperature promotes dissociation. It inhibits the generation of active radicals in the ignition process, weakening the enhancement effect of nonequilibrium on auto-ignition. In the expanded nozzle, the concentrations of molecules and trans-rotational temperature in nonequilibrium cases are slightly lower than those in the equilibrium case due to the enhancement of dissociation.

Mechanism analysis of thermochemical nonequilibrium flow field for re-entry vehicle with magnetohydrodynamic control technology

Mechanism analysis of thermochemical nonequilibrium flow field for re-entry vehicle with magnetohydrodynamic control technology

INFLUENCE OF THERMOCHEMICAL NONEQUILIBRIUM ON CHARACTERISTICS OF BOUNDARY LAYER AT FLIGHT IN THE MARTIAN ATMOSPHERE

In framework on the eN-method, comparative calculations of position beginning zone of laminar-turbulent transition completed for two points on landing trajectory of “Pathfinder” spacecraft on surface of the Mars. The calculations used a three-component model of a thermochemical nonequilibrium mixture CO2=CO=O. The set of frequencies of spatial disturbances is determined along neutral curves for first unstable modes of temporary disturbances. The transition Reynolds number Re T was determined from envelopes of families of the N-factor curves at NT=8. In hypersonic regime at M=12:6, taking into account the developed thermochemical nonequilibrium leads to a significant decrease in the static temperature of gas in the lower part of the boundary layer. As a result, beginning of the zone of laminar-turbulent transition shifts downstream by approximately 9% compared to case of a perfect gas.

Simulations of early structure formation: Properties of halos that host primordial star formation

Context. Population III (pop III) stars were born in halos characterised by a pristine gas composition. In such a halo, once the gas density reaches nH ∼ 1 cm−3, molecular cooling leads to the collapse of the gas and the birth of pop III stars. Halo properties, such as the chemical abundances, mass, and angular momentum can affect the collapse of the gas, thereby leading to the pop III initial mass function (IMF) of star formation. Aims. We want to study the properties of primordial halos and how halos that host early star formation differ from other types of halos. The aim of this study is to obtain a representative population of halos at a given redshift hosting a cold and massive gas cloud that enables the birth of the first stars. Methods. We investigated the growth of primordial halos in a ΛCDM Universe in a large cosmological simulation. We used the hydrodynamic code RAMSES and the chemical solver KROME to study halo formation with non-equilibrium thermochemistry. We then identified structures in the dark and baryonic matter fields, thereby linking the presence or absence of dense gas clouds to the mass and the physical properties of the hosting halos. Results. In our simulations, the mass threshold for a halo for hosting a cold dense gas cloud is ≃7 × 105 M⊙ and the threshold in the H2 mass fraction is found to be ≃2 × 10−4. This is in agreement with previous works. We find that the halo history and accretion rate play a minor role. Here, we present halos with higher HD abundances, which are shown to be colder, as the temperature in the range between 102 − 104 cm−3 depends on the HD abundance to a large extent. The higher fraction of HD is linked to the higher spin parameter that is seen for the dense gas.

Navier-Stokes characteristic boundary conditions for high-enthalpy compressible flows in thermochemical non-equilibrium

This fundamental study presents Navier-Stokes characteristic boundary conditions (NSCBCs) for high-enthalpy hypersonic flows in thermochemical non-equilibrium. In particular, the relevant locally one-dimensional inviscid (LODI) relations are derived within a two-temperature framework for high-enthalpy hypersonic flows undergoing finite-rate thermochemical processes, including air dissociation and vibrational relaxation. Using these LODI relations, a set of NSCBCs are proposed and later demonstrated in canonical test cases, including the interaction of homogeneous isotropic turbulence with a shock wave subject to high-enthalpy thermochemical non-equilibrium effects.

Effect of Hyperthermal Hybrid Gas Composition on the Interfacial Oxidation and Nitridation Mechanisms of Graphene Sheet.

Graphene is one of the most promising thermal protection materials for high-speed aircraft due to its lightweight and excellent thermophysical properties. At high Mach numbers, the extremely high postshock temperature would dissociate the surrounding air into a mixture of atomic and molecular components in a highly thermochemical nonequilibrium state, which greatly affects the subsequent thermal chemical reactions of the graphene interface. Through establishing a reactive gas-solid interface model, the reactive molecular dynamics method is employed in this study to reveal the influences of the thermochemical nonequilibrium gas mixture on the thermal oxidation and nitridation mechanisms of graphene sheet. The results show that three distinctive stages can be recognized during bombardment of various nonequilibrium gas components toward the graphene sheet: (i) collision and surface adsorption stage, (ii) gas-solid heterogeneous reaction stage, and (iii) gas phase homogeneous reaction stage. The surface catalysis effect is found to be dominant during the first two stages, which can influence the following ablation behavior of graphene significantly at high-temperature conditions. Moreover, surface catalysis, oxidation, nitridation, and ablation mechanisms between nonequilibrium gas and graphene interface are revealed, which is of high relevance for future interfacial design and application of graphene as a thermal protection material.

Effects of thermochemical non-equilibrium in the boundary layer of an ablative thermal protection system: A state-to-state approach

In the era of space exploration, one of the fundamental goals is the investigation of the atmospheric re-entry of a space vehicle, which undergoes tremendous heat load due to the shock waves forming in front of its thermal shield. In the view of heat mitigation, ablative materials are employed for the design of the Thermal Protection System (TPS) of most of the modern vehicles. Such materials essentially modify the nature of the gas in the boundary layer due to the interaction of the solid and gas phases. Thanks to the material consumption, heat load is mitigated at the expense of ablated species which significantly contaminate the boundary layer gas mixture. In this context, this work aims at characterizing the aerothermodynamics environment around a bluff body in the presence of ablation and thermochemical non-equilibrium. Specifically, a five species neutral air mixture (N2, O2, NO, N, O) is combined to a six ablated species mixture (CO, CN, CO2, C, C2, C3). Two test cases are considered. Firstly, a subsonic pure nitrogen flow past an ablative sample is simulated, which is used as verification study by direct comparison with numerical results. For this reason, a classic multitemperature (mT) approach is employed to handle non-equilibrium. The second test case is a well-known hypersonic air flow past a spherical body used as a benchmark to assess the influence of ablation. In this case, two different kinetics models are used, namely the classical multitemperature and the more sophisticated State-to-State (StS) approach.