Degree Of Nonequilibrium Research Articles

Effect of non-equilibrium phase transition on the aero-thermodynamic performance of supercritical carbon dioxide compressors

Phase transition is a prominent issue for the supercritical CO2 compressors operating near the critical region. The non-equilibrium behavior of phase transition makes it difficult to accurately predict performance under these conditions. A non-equilibrium phase transition model is proposed to analyze the aero-thermodynamic performance of supercritical CO2 centrifugal compressors with different inlet conditions. The model examines phase change characteristics and compressor performance under variable operating conditions. The results indicate that this model can effectively predict the aero-thermodynamic performance of compressor near critical conditions, with an average error of less than 2% in the performance curves. The inconsistency between low-temperature and low-pressure regions, along with the increase in liquid phase volume, are typical characteristics of non-equilibrium phase transition in supercritical CO2 compressors. The non-equilibrium effect of phase transition can reduce the leakage loss at high flow rates, but also increases the likelihood of stall at low flow rates. Furthermore, the concept of “non-equilibrium degree” (NED) is introduced to quantify these effects. When NED exceeds 0.2, the isentropic efficiency of the compressor decreases by 15.1% compared to its maximum efficiency. Designing inlet conditions for supercritical CO2 compressors with NED below 0.1 is more suitable because it has a larger inlet flowrate and higher efficiency.

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.

FEATURES OF THE INTERACTION AND FORMATION OF NANOSTRUCTURED CHITOSAN SYSTEMS DURING IONOTROPIC GELATION

Bombyx mori chitosan nanoparticles (ChS NPs) were obtained and the kinetic aspects of their size distribution depending on the degree of nonequilibrium of the synthesis by ionotropic gelation using sodium tripolyphosphate (TPP) were studied. The size of ChS NPs was greatly influenced by the ChS concentration, which varied from 0.5 to 10 mg/ml. The size of the NPs increased from 100 to 300 nm when the ChS concentration increased from 0.5 to 10 mg/ml and while maintaining all other parameters of the reaction. An increase in the ChS to-TPP ratio corresponded to a lower cross-linking density and thus ensured slower kinetics for NP formation alongside the formation of large chitosan/TPP aggregates. There was an almost threefold increase in the particle size when the pH of the medium increased from 3.8 to 4.7; thus, the size of ChS NPs depends on the pH of the solution. There was a slight agglomeration of NPs from 363 to 642 nm with an increase in the NP synthesis time from 4 to 24 h. According to calculations, the maximum interaction energy is 50.4 and 69.4 kcal/mol for deprotonated TPP (P3O105-); after adiabatic transfer of the proton, the value decreases to 32.9–33.5 kcal/mol. The maximum interaction energy is –12.8 kcal/mol for the initially protonated TPP (H4P3O10-).

Forest restoration effects on soil preferential flow in the paleo-periglacial eastern liaoning mountainous regions, China

To provide a practical reference index for the protection of water conservation forests and the establishment of vegetation in different forest restoration areas, we seek to clarify the preferential flow development and its influencing factors under different rainfall events in the forest restoration areas of paleo-periglacial landform in eastern Liaoning Province of China. To quantify the preferential flow development (PFI) in soil profile-scale through soil profile indexes, we carried out dual-tracer experiments with dyeing in two types of forest restoration lands (plantation forest, PF, and natural secondary forest, NSF) in the paleo-periglacial landform forestland to obtain the soil water infiltration trajectories and water-solute transport characteristics. The indexes of preferential flow morphology and pathway diversity (solute migration) were integrated to construct a more complete evaluation system of the PFI. In addition, we explored factors affecting the PFI through soil physical properties and root characteristics. The results showed that: (1) There were obvious preferential flows in both PF and NSF. Compared with NSF, preferential flow in PF diverged earlier, had greater non-equilibrium degree, more paths and higher development degree, and preferential flow was the main infiltration form. (2) Changes in infiltration amount played a key role in altering the PFI, i.e., increasing infiltration amount reduced the PFI, especially in PF (p < 0.05); (3) After water infiltration, the solute Br− diffusion range of the soil profile was wider than that of Brilliant Blue tracer, thus the development of preferential flow was better synthetical reflected by the indexes of water flow morphology and solute distribution characteristics; (4) Differences in the PFI can be explained by variations in clay content, total porosity (TP), and root volume density (RVD), with total path coefficients of 0.824, 0.462, and 0.624, respectively. In addition to establishing different forest restoration types in similar areas, it would be worthwhile to strengthen the prevention and control measures of soil and water loss in NSF, and properly manage PF in a near-natural model to enhance ecologically sustainable development of forest land. The results of this study contribute to the understanding of the hydrological processes of forest ecosystems in paleo-periglacial landforms, and provide theoretical support for the proposed forest management strategies.

Coherent anti-Stokes Raman scattering spectral calculation and vibrational-rotational temperature measurement of non-equilibrium plasma flow field

How to characterize thermodynamic non-equilibrium characteristics of flow field accurately and reliably is the key to solving the thermal and chemical non-equilibrium problem, which is one of the most basic scientific problems in hypersonic aerodynamcis. Based on the principles of coherent anti-Stokes Raman scattering (CARS) and modified exponential gap (MEG) Raman linewidth model, a CARS spectral computation and vib-rotational temperature inversion program is proposed for characterizing the thermodynamic non-equilibrium properties of high-temperature gas flow field. The influence of vibrational temperature and rotational temperature on Raman linewidth and CARS spectral characteristics are studied theoretically. A CARS system is built and the corresponding accuracy in a wide temperature range is verified in a static environment that is established by using a high-temperature tube furnace and a McKenna burner. The results show that the average relative deviation of the vibration temperature &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;v&lt;/sub&gt; and rotational temperature &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;r&lt;/sub&gt; from the equilibrium temperature &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;eq&lt;/sub&gt; are 4.28% and 3.34% respectively in a range of 1000 to 2300 K, and the corresponding average repeatability is 1.95% and 3.03% respectively. These results indicate that the vibrational temperature and rotational temperature obtained by the non-equilibrium program are in good agreement with those obtained from the thermal equilibrium program. Finally, a non-equilibrium microwave plasma flow is built and its vibrational temperature and rotational temperature are obtained by using the developed program. The results show that the microwave plasma is in thermodynamic non-equilibrium, and the vibrational temperature and rotational temperature are proportional to microwave power, while the thermodynamic non-equilibrium degree exhibits an opposite trend. With microwave power increasing from 80 to 180 W, the vibrational temperature of plasma increases from (2201 ± 43) K to (2452 ± 56) K, the rotational temperature increases from (382 ± 20) K to (535 ± 49) K, for which the principal reasons are that the increase in microwave power leads to an increase in electron number density, and neutral particles obtain energy through collision with electrons, resulting in the increase of vibrational temperature, rotational temperature, and translational temperature. The thermodynamic non-equilibrium degree decreases from 0.83 to 0.78 with the microwave power increasing, which is due to the V-T relaxation rate increasing. The molecules in the excited vibrational states lose energy through collision with ground state molecules (i.e. V-T relaxation process), leading the vibrational energy to be converted into translational energy. For N&lt;sub&gt;2&lt;/sub&gt; molecules, the V-T relaxation rate is directly proportional to the temperature, which causes the difference between vibrational temperature and rotational temperature to decrease with microwave power increasing, and non-equilibrium degree to decrease with microwave power increasing as well.

Numerical Study of Hypersonic Near-Continuum Flow by Improved Slip Boundary Condition

Appropriate numerical models and boundary conditions are required to accurately model hypersonic flows involving local nonequilibrium effects, which can be induced by the wall effect and large gradients of flow properties in the flowfield. Considering the strong density gradient near the wall for hypersonic flows, an improved Gökçen slip model is proposed in this paper by introducing a scaled mean free path to the conventional Gökçen’s model. Hypersonic argon flows over a circular cylinder and a blunt plate in the near-continuum regime are simulated by the proposed slip model with the conventional Navier–Stokes–Fourier equations and an extended continuum model, which was recently developed to model the shear nonequilibrium effect in high-speed flows. The accuracy of the new boundary model is evaluated by comparing the results with the direct simulation Monte Carlo method. The effects of Knudsen number, Mach number, and wall temperature on the nonequilibrium degree and aerodynamic predictions are also investigated. The numerical results show that the improved model can well predict the surface friction and heat transfer coefficients, exhibiting much better performance than the existing continuum models.

Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows

This work proposes a new machine learning (ML)-based paradigm aiming to enhance the computational efficiency of non-equilibrium reacting flow simulations while ensuring compliance with the underlying physics. The framework combines dimensionality reduction and neural operators through a hierarchical and adaptive deep learning strategy to learn the solution of multi-scale coarse-grained governing equations for chemical kinetics. The proposed surrogate’s architecture is structured as a tree, with leaf nodes representing separate neural operator blocks where physics is embedded in the form of multiple soft and hard constraints. The hierarchical attribute has two advantages: (i) It allows the simplification of the training phase via transfer learning, starting from the slowest temporal scales; (ii) It accelerates the prediction step by enabling adaptivity as the surrogate’s evaluation is limited to the necessary leaf nodes based on the local degree of non-equilibrium of the gas. The model is applied to the study of chemical kinetics relevant for application to hypersonic flight, and it is tested here on pure oxygen gas mixtures. In 0-textrm{D} scenarios, the proposed ML framework can adaptively predict the dynamics of almost thirty species with a maximum relative error of 4.5% for a wide range of initial conditions. Furthermore, when employed in 1-textrm{D} shock simulations, the approach shows accuracy ranging from 1% to 4.5% and a speedup of one order of magnitude compared to conventional implicit schemes employed in an operator-splitting integration framework. Given the results presented in the paper, this work lays the foundation for constructing an efficient ML-based surrogate coupled with reactive Navier-Stokes solvers for accurately characterizing non-equilibrium phenomena in multi-dimensional computational fluid dynamics simulations.

Properties of the particle distribution in Pb–Pb collisions at sNN=5.02 TeV and sNN=2.76 TeV

Properties of the particle distribution in high energy heavy-ion collisions are important for understanding the particle production. In Tsallis statistics with a multisource production, we study the transverse momentum spectra of D0, D+, D*+, Ds+, J/ψ in Pb–Pb collisions at sNN = 5.02 TeV and charged particles in Pb–Pb collisions at sNN = 2.76 TeV. A good agreement can be observed between the results obtained in the model and the experimental results of ALICE and CMS collaboration. The nuclear modification factor RAA is reproduced. Properties reflected in the multiparticle system are discussed by the parameters provided in the improved model. It is found that the temperature T and the tft/τ increase with the centrality for the same particle due to the excitation degree of the multiparticle system. The non-equilibrium degree at sNN = 5.02 TeV is larger than that at sNN = 2.76 TeV. It shows that the system at the larger collision energy deviates farther from the equilibrium state.

Theoretical modelling of non-equilibrium reaction–diffusion of rarefied gas on a wall with microscale roughness

Heat and mass transports through a rough surface are among the most fundamental and important phenomena in either natural or engineering problems. In this paper, theoretical modelling and direct simulation Monte Carlo method are employed to study the heterogeneous reaction–diffusion features induced by microscale roughness which is comparable to the molecular mean free path of the ambient gas. A quasi-one-dimensional homogeneous model is proposed, and it consists of an external diffusion region outside the roughness elements and an internal reaction–diffusion region which could be equivalent to a smooth surface with an effective chemical property. The external macroscopic diffusion can be characterized by a non-equilibrium criterion – the Damköhler number. The internal diffusion in micro-cavities must be analysed by considering the rarefied gas effects on the diffusivity, and another non-equilibrium criterion, the Thiele number, is introduced to evaluate the effective boundary condition imposed on the external region. Analytical formulae based on these criteria are derived to predict the equivalent surface reaction–diffusion performance, and the predictions compare well with the numerical results of different types of surface reaction, even on the three-dimensional roughness. This reveals that the roughness could either enhance or weaken the apparent reaction rate depending on the non-equilibrium degree. This study could enrich our understanding of the gas–surface interactions on a rough wall, such as the oxidation, catalysis and energy accommodation, and also preliminarily provides a practical method for evaluation of the aerothermochemical performance of coating materials of hypersonic vehicles.

Vertical Distribution of Suspended Sediment Concentration in the Unsaturated Jingjiang Reach, Yangtze River, China

The Rouse formula and its variants have been widely used to describe the vertical distribution of the sediment concentration in sediment-laden flows in equilibrium. Han’s formula extends the Rouse formula to non-equilibrium regimes, where the diffusive flux is still assumed to be Fickian. The turbulent flow and suspension regimes downstream of a mega-reservoir, e.g., the Three Gorges Reservoir, usually exhibit fractal and unsaturated properties, respectively. To characterize the non-Fickian dynamics of suspended sediment and the non-equilibrium regime in natural dammed rivers, this study proposes a new formula for the concentration profile of unsaturated sediment based on the Hausdorff fractal derivative advection–dispersion equation. In addition, we find that the order of the Hausdorff fractal derivative is related to the sizes of the sediment and the degrees of non-equilibrium. Compared to Rouse and Han’s formulae, the new formula performs better in describing the sediment concentration profiles in the Jingjiang Reach, approximately 100 km below the Three Gorges Dam.

Sum-of-squares bounds on correlation functions in a minimal model of turbulence.

We suggest a new computer-assisted approach to the development of turbulence theory. It allows one to impose lower and upper bounds on correlation functions using sum-of-squares polynomials. We demonstrate it on the minimal cascade model of two resonantly interacting modes when one is pumped and the other dissipates. We show how to present correlation functions of interest as part of a sum-of-squares polynomial using the stationarity of the statistics. That allows us to find how the moments of the mode amplitudes depend on the degree of nonequilibrium (analog of the Reynolds number), which reveals some properties of marginal statistical distributions. By combining scaling dependence with the results of direct numerical simulations, we obtain the probability densities of both modes in a highly intermittent inverse cascade. As the Reynolds number tends to infinity, we show that the relative phase between modes tends to π/2 and -π/2 in the direct and inverse cascades, respectively, and derive bounds on the phase variance. Our approach combines computer-aided analytical proofs with a numerical algorithm applied to high-degree polynomials.

Interplay of longitudinal and transverse expansion in the kinetic dynamics of heavy-ion collisions

The early dynamics in heavy-ion collisions involves a rapid, far from equilibrium evolution. This early pre-equilibrium stage of the dynamics can be modeled using kinetic equations. The effect of this pre-equilibrium stage on final observables derived from transverse momenta of emitted particles is small. The kinetic equations in the relaxation time approximation for a nonboost invariant system are solved. The asymmetry of the flow with respect to the reaction plane at different rapidities is found to be very sensitive to the degree of nonequilibrium in the evolution. This suggests that the rapidity odd directed flow could be studied to identify the occurrence of nonequilibrium effects and to estimate the asymmetry of the pressure between the longitudinal and transverse directions in the collision.

Controllability of luminescence wavelength from GeSn wires fabricated by laser-induced local liquid phase crystallization on quartz substrates

We examined the effects of the laser scan speed and power on the Sn fraction and crystallinity of GeSn wires of 1 μm width and 1 mm length fabricated by laser-induced local liquid phase crystallization on quartz substrates. The Sn fraction increased from 1% to 3.5% with an increasing scan speed from 5 to 100 μm s−1, corresponding to a luminescence wavelength of 1770–2070 nm. This result can be interpreted as the scan speed dependence of the non-equilibrium degree during crystal growth. The increase in the laser power reduced the Sn fraction and caused a blue shift in the luminescence wavelength. We discuss these phenomena based on the growth kinetics of zone melting.

The connection between dissipative chaos and nonequilibrium

Strong nonequilibrium conditions often give rise to dissipative chaos. However, the underlying connection between dissipative chaos and nonequilibrium remains unclear. Herein, we study this connection from the framework of the nonequilibrium potential-flux landscape. The nonequilibrium system dynamics are determined in part by the potential landscape associated with the steady-state probability distribution. The other part of the driving force for nonequilibrium dynamics comes from the steady-state probability flow, leading to the breaking of detailed balance. We find that dissipative chaos is driven mainly by the nonequilibrium probability flow. Using the Lorenz strange attractor model, we quantitatively demonstrate the close connection between the kinematic measures of the appearance of dissipative chaos and the degree of nonequilibrium. This work reveals the dynamic and thermodynamic origins of dissipative chaos beyond the interpretation based on nonlinearity. This study also provides a new understanding of the phase transitions in nonequilibrium systems.

Numerical Analysis of Aerodynamic Thermal Properties of Hypersonic Blunt-Nosed Body with Angles of Fire

A hypersonic electromagnetic railgun projectile undergoes severe aero-heating with an increase in altitude. The purpose of this study was to investigate the characteristics of the shock layer flow field as well as the thermal environment of the blunt body wall of a hypersonic electromagnetic railgun projectile at different launching angles. The two-temperature model considers the thermal nonequilibrium effect and is introduced into the Navier–Stokes (N-S) equation, and it is solved using the finite volume method (FVM). The reliability of the calculation model in terms of thermal properties and composition production was verified against a blunted-cone-cylinder–flare (HB-2) test case. The surface temperature of the hypersonic blunt projectile was simulated using a radiation balance wall boundary. The thermal characteristics at the emission angles α = 60° and α = 45° were checked within an altitude range of 0–70 km, including the nonequilibrium effect, reaction heat release, aerodynamic heat flux, and wall temperature. The results show that the translational rotational temperature is higher than the vibrational electronic temperature, and the thermal nonequilibrium effect increases with an increase in altitude. Comparing the two launching angles, the nonequilibrium degree and reaction heat release at α = 60° were higher than those at α = 45°. The rates of exothermic reaction decreased with an increase in altitude. The heat flux along the wall of the generatrix decreased sharply from the stagnation point. With an increase in altitude, the heat flux dropped sharply from 7 MW/m2 at H = 0 km to approximately 2 MW/m2 at H = 70 km. The wall temperature distribution was similar to the heat flux distribution; however, the surface temperature decreased less rapidly than the heat flux.

Исследование динамической прочности мелкозернистого оксида алюминия, полученного методом электроимпульсного плазменного спекания

The results of dynamic compressive testing of alumina samples with different grain sizes sintered from nano and fine α-Al2O3 powders are presented. The ceramics were obtained by spark plasma sintering (SPS). The effect of heating rate (Vh), sintering temperature (Ts), holding time (ts), cooling rate (Vc) on hardness, fracture toughness, dynamic strength stress (σY) of Al2O3 has been studied. An amorphous layer of nanometer thickness was present on the surface of nanopowders in the initial state. After sintering, the grain boundaries of the ceramics had a crystalline structure; no inclusions of the amorphous phase were found. It has been suggested that during the SPS process, an amorphous structure containing an excess free volume is transformed into a crystalline phase with the formation of dislocation-type defects at the grain boundaries, which create long-range internal stress fields. It is shown that nanopores less than 50 – 100 nm in size are present at the grain boundaries of sintered ceramics. It is shown that the nonmonotonic nature of the dependence of σY on the temperature and time of the SPS is due to the simultaneous change in the density, the nonequilibrium state of the grain boundaries, and the grain size of the ceramic. It is shown that a decrease in the degree of nonequilibrium of the grain boundaries of alumina due to an increase in the SPS temperature or an increase in the holding time makes it possible to increase the dynamic strength of alumina. It has been established that an increase in the cooling rate leads to the formation of compressive residual stresses and a slight increase in σY of ceramics. The maximum dynamic strength (σY = 1755 MPa) for alumina ceramics with average grain size 1.6 – 2 µm obtained by SPS (Vh = 50 °С/min, Ts = 1520 °С, ts = 50 min).

Peak heat flux prediction of hypersonic flow over compression ramp under vibrationally excited free-stream condition

In hypersonic shock tunnel experiments, the high-temperature reservoir gas expands and accelerates so rapidly that there is not enough time for vibrational energy relaxation. As a result, thermal nonequilibrium gas flow is frequently encountered in the test section, and this significantly affects the measured heat flux. In this paper, hypersonic compression-ramp flows are studied numerically to investigate the effect of incomplete vibrational energy accommodation on the separation flow structure and peak heat flux in the reattachment region under low-to-medium Reynolds number and high Mach number conditions. Numerical results and theoretical analysis suggest that the vibrational energy accommodation has no noticeable impact on the length scale of the separation zone, but strongly influences the peak heat flux of the separated ramp flows. Decomposing the peak heat flux into translational–rotational energy and vibrational energy components, qtr and qv, respectively, we find that qv/qtr characterizes the nonequilibrium degree of the vibrational energy accommodation. A formula for predicting the peak heat flux is then proposed, taking the effect of incomplete vibrational energy accommodation into consideration. Finally, surface heat flux measurements in a hypersonic shock tunnel indicate that a deviation of up to 13% in total peak heat flux could arise if vibrational energy accommodation is not considered under the vibrationally excited free-stream condition.

Symmetric-hyperbolic quasihydrodynamics

We set up a general framework for systematically building and classifying, in the linear regime, causal and stable dissipative hydrodynamic theories that, alongside with the usual hydrodynamic modes, also allow for an arbitrary number of nonhydrodynamic modes with complex dispersion relation (such theories are often referred to as ``quasihydrodynamic''). To increase the number of nonhydrodynamic modes, one needs to add more effective fields to the model. The system of equations governing this class of quasihydrodynamic theories is symmetric hyperbolic, thermodynamically consistent (i.e., the entropy is a Lyapunov function) and can be derived from an action principle. As a first application of the formalism, we prove that, in the linear regime, the Israel-Stewart theory in the Eckart frame and the Israel-Stewart theory in the Landau frame are exactly the same theory. In addition, with an Onsager-Casimir analysis, we show that in strongly coupled plasmas the nonequilibrium degrees of freedom typically appear in pairs, whose members acquire opposite phase under time reversal. We use this insight to modify Cattaneo's model for diffusion, in a way to make its initial transient consistent with the transient dynamics of holographic plasmas.

Near-surface gas discharge effect on a steady bow shock wave position in a supersonic flow past a cylindrically blunted body in the air

The problem of the bow shock wave control using a near-surface gas discharge in a supersonic flow past a semi-cylindrical body at Mach number M = 4 in the air is investigated experimentally and numerically. The possibility of controlling the position of a steady bow shock wave and the characteristics of a streamlined body by creating a volumetric plasma region using a surface gas discharge organized on the entire front surface of the body is shown. An increase in the stand-off distance of a steady bow shock is experimentally and numerically obtained, which is the greater, the higher the discharge power and the greater the adiabatic index in the plasma region created by the discharge. A comparison of the numerical and experimental data showed good agreement. It is established that the relative value of the steady bow shock stand-off distance increases linearly in the power range from 1.5 × 105 to 2.4 × 105 W at the discharge current from 430 to 670 A, and the adiabatic index in the plasma region can be estimated as 1.3. It is also found that at higher values of the discharge power, the adiabatic index in the plasma region decreases. The average plasma parameters were expressed as functions of the discharge specific power and the adiabatic index. The mechanism of the gas discharge effect on the bow shock wave is established, and it is shown that the plasma parameters in the region created by the discharge, including the degree of ionization and the degree of nonequilibrium, affect the position of the steady bow shock wave.

Numerical simulations of Richtmyer–Meshkov instability of [formula omitted] square bubble in diatomic and polyatomic gases

The Richtmyer–Meshkov instability of a shock-driven SF6 square bubble in monatomic, diatomic, and polyatomic gases is investigated numerically. The focus was placed on presenting more intuitive details of the flow-fields visualizations, vorticity production, degree of thermal non-equilibrium, enstrophy and dissipation rate evolutions, and interface structures. A mixed-type modal discontinuous Galerkin method is employed for solving the two-dimensional system of physical conservation laws derived from the Boltzmann–Curtiss kinetic equation of diatomic and polyatomic gases. For validation, the numerical results were compared with the existing experimental results. The results revealed that diatomic and polyatomic gases provoke considerable changes in the flow-fields, resulting in complex wave patterns, bubble deformation, and outward SF6 jets formation in contrast to monatomic gas. A detailed investigation on the effects of diatomic and polyatomic gases is carried out through the vorticity production, degree of nonequilibrium, and evolution of enstrophy as well as dissipation rate. Moreover, the length and height of the interface structures are investigated quantitatively. Finally, the effects of thermal non-equilibrium parameters, such as inverse power-law index and bulk viscosity ratio are examined. The present work attempts to enhance the understanding of the RM instability studies in monatomic, diatomic, and polyatomic gases.