Shock Waves In Nitrogen Research Articles

On the evolution of magnetohydrodynamic flow instability in shock-accelerated light bubble

The study investigates the evolution of flow instabilities in a magnetohydrodynamic (MHD) environment involving a shock-accelerated light cylindrical bubble. Numerical simulations were conducted using a cylindrical helium (He) bubble accelerated by a shock wave in nitrogen (N2) gas at various magnetic field strengths. The results highlight the impact of magnetic fields on flow morphology, vorticity generation, and enstrophy. The interaction between incident shock waves and the gas bubble revealed significant differences in flow patterns and interface features when magnetic fields were applied. Key findings include the quantification of shock trajectories and detailed visualizations of the evolving flow structure. The study provides insights into the dynamics of shock–bubble interactions under MHD conditions, contributing to the broader understanding of flow instability mechanisms in such complex environments.

Kinetic modelling of rarefied gas flows with radiation

Two kinetic models are proposed for high-temperature rarefied (or non-equilibrium) gas flows with internal degrees of freedom and radiation. One of the models uses the Boltzmann collision operator to model the translational motion of gas molecules, which has the ability to capture the influence of intermolecular potentials, while the other adopts the relaxation time approximations, which has higher computational efficiency. In our kinetic model equations, not only the transport coefficients such as the shear/bulk viscosity and thermal conductivity but also their underlying relaxation processes are recovered. The non-equilibrium dynamics of gas flow and radiation are tightly coupled, where the transport properties of gas molecules and photons are correlatively dependent. The proposed kinetic models are validated by the direct simulation Monte Carlo method in several non-radiative rarefied gas flows (e.g. the normal shock wave, Fourier flow, Couette flow and the creep flow driven by the Maxwell demon), and the experimental data of planar heat transfer and normal shock waves in nitrogen. Then, the rarefied gas flows with strong radiation are studied based on the kinetic models, not only in the above one-dimensional gas flows, but also in the two-dimensional radiative hypersonic flow passing a cylinder. The characteristics of heat transfer in the tightly coupled fields of gas and radiation are systematically investigated, particularly the influence of the non-equilibrium photon transport and their interactions with gas molecules are revealed. It is found that the radiation makes a profound contribution to the total heat transfer in radiative hypersonic flow at an intermediate photon Knudsen number.

Performance assessment of thermoelectric detector for heat flux measurement behind a reflected shock of low intensity

The study is devoted to assessing the applicability of the manufactured thermoelectric sensor for functioning in shock tubes to measure instantaneous heat fluxes occurring in shock-wave processes. The gas-dynamic parameters of supersonic and hypersonic flows in test sections of such facilities can be quite harsh due to high values of enthalpies. At the same time, the typical operating period in such experiments is several milliseconds, which imposes specific requirements on the instruments used for registering heat fluxes. Thermoelectric heat flux sensors have been constructed in-house. The sensitive element of the sensor is a thin film of artificially anisotropic chromium obtained by oblique deposition on a high-resistance silicon substrate. This technology is used in laser systems to measure the power of laser radiation. The results of experiments on the generation of low-intensity reflected shock waves in nitrogen are presented. The new thermoelectric detector was used to register the heat flux from a hot gas heated by a shock wave reflected from the end of the shock tube. At the same time, the heat flux was measured using a sensor based on anisotropic thermoelements with a known sensitivity. Experiments have shown that the sensor has a high speed (~1 μs), a high signal-to-noise ratio, and a high electrical signal. The results obtained demonstrate the applicability of the sensor for measuring convective heat flux in shock tube experiments.

Master Equation Analysis of Post Normal Shock Waves of Nitrogen

One-dimensional post normal shock flow calculations are carried out using state-of-the-art thermochemical nonequilibrium models. Two-temperature, four-temperature, and electronic master equation coupling models are adopted in the present work. In the four-temperature model, the rotational nonequilibrium is described by Parker and modified Park models. In the electronic master equation coupling model, recently evaluated electron and heavy-particle impacts and radiative transition cross-sections are employed in constructing the system of electronic master equations. In analyzing the shock-tube experiments, the results calculated by the state-of-the-art thermochemical nonequilibrium models are compared with existing shock-tube experimental data. The four-temperature and electronic master equation coupling models with rotational nonequilibrium described by the modified Park model approximately reproduce the measured rotational, vibrational, and electronic temperatures.

Modelling of electronic excitation and radiation in the Direct Simulation Monte Carlo Macroscopic Chemistry Method

One of the most useful tools for modelling rarefied hypersonic flows is the Direct Simulation Monte Carlo (DSMC) method. Simulator particle movement and collision calculations are combined with statistical procedures to model thermal non-equilibrium flow-fields described by the Boltzmann equation. The Macroscopic Chemistry Method for DSMC simulations was developed to simplify the inclusion of complex thermal non-equilibrium chemistry. The macroscopic approach uses statistical information which is calculated during the DSMC solution process in the modelling procedures. Here it is shown how inclusion of macroscopic information in models of chemical kinetics, electronic excitation, ionization, and radiation can enhance the capabilities of DSMC to model flow-fields where a range of physical processes occur. The approach is applied to the modelling of a 6.4 km/s nitrogen shock wave and results are compared with those from existing shock-tube experiments and continuum calculations. Reasonable agreement between the methods is obtained. The quality of the comparison is highly dependent on the set of vibrational relaxation and chemical kinetic parameters employed.

A Novel Plasma Technique for Surface Treatment: The Plasma Expander

This paper describes a new plasma treatment method: the plasma expander. In this approach, expanding shock waves are generated in a vacuum chamber by pulsed plasmas. Collisions of fast species in the waves modify the properties of solid surfaces exposed to the plasma. The degree of such modification is governed by the energy delivered by the plasma exposure. To confirm the efficacy of this approach, modifications induced in the properties of thin polymer films produced by plasma-enhanced chemical vapor deposition by exposure to nitrogen plasma shock waves were investigated. The films were prepared from benzene radio frequency plasmas and subsequently exposed to different quantities of nitrogen shock waves <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nw</i> . The effects of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nw</i> on the wettability, molecular structure, and mechanical properties of the films were studied. Fourier transform infrared spectroscopy revealed that greater <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nw</i> resulted in the loss of C-H groups and the rupture of benzene aromatic rings observed in the structure of the as-deposited films. Furthermore, the contact angle strongly increased and the hardness, evaluated by nanoindentation, increased up to fourfold with the increase in the intensity of the treatment.

Computer simulation of perturbation of a shock wave in nitrogen by optical radiation

The possibility of a displacement of the front of a shock wave formed in a 1D nitrogen flow to the low gas pressure region (in front of the shock wave) upon absorption of the laser pulse energy in the region of the shock wave front is demonstrated using computer simulation based on the finite difference technique. The low-pressure region formed in the region of the initially high pressure under the action of a light pulse moves in the direction opposite to the direction of propagation of the shock wave front. Analysis is carried out for a typical experimental situation corresponding to the growth of carbon-nitride nanofilms.

Numerical simulation of shock wave structure in nitrogen

The one-dimensional problem of the structure of a stationary shock wave in nitrogen is solved in the frame of the Navier-Stokes (NS) equations. Proper interpretation of the bulk viscosity coefficient included in the shear stress tensor leads to a numerical solution close to the experiment, showing that the NS equations provide more accurate solutions to the problem than supposed previously.

On the theory of bulk viscosity and relaxation pressure

A general theory of bulk viscosity and relaxation pressure, based on the generalized Chapman-Enskog method, is given, and also simple qualitative theories of them. Problems associated with the definition of temperature are discussed. Formulae are given for the bulk viscosity coefficient and the thermal conductivity of a gas possessing rotational degrees of freedom. The influence of bulk viscosity on the absorption and dispersion of sound and on the structure of a shock wave in nitrogen is investigated.

Burnett's model of the structure of a shock wave in a molecular gas

The Navier-Stokes, Burnett and truncated Burnett systems of equations for a polyatomic gas with a slight exchange of translational and internal energies of the molecules are presented. The establishment method is used to calculate the structure of a shock wave in nitrogen. The results of calculations using these systems of equations are compared with the results of the method of direct statistical modelling. The effect of bulk viscosity and the accuracy of the Eucken approximation in the theory of heat conduction are analysed. The structure of the shock wave in a binary mixture of monatomic gases is calculated using the Navier-Stokes equations and the truncated Burnett equations by numerical upstream integration of a system of ordinary differential equations. The role of thermal diffusion is considered.

Direct simulation of non-equilibrium kinetics under shock conditions in nitrogen

We study the interplay of vibrational kinetics, dissociation, translational and rotational relaxation in a strong shock wave in nitrogen by Direct Simulation Monte Carlo simulation (DSMC). The input data for vibrational and chemical processes are all in the form of cross-sections, mostly determined by molecular physics methods. In particular, we use for the first time very recent Quasi-Classical Trajectory (QCT) results for cross-sections of multi-quantum VT energy exchange and dissociation in N+N 2 collisions. Non-equilibrium distributions are observed and discussed.

Investigation of the nitrogen shock wave structure on the basis of trajectory calculations of the molecular interaction

The shock wave structure in a diatomic gas is investigated using the direct statistical simulation (Monte-Carlo) method. The energy exchange between translational and rotational degrees of freedom (TR-exchange) is calculated by solving the dynamic problem of the interaction between rigid-rotator molecules within the framework of classical mechanics. The density profiles calculated are compared with the experimental data and on this basis the nitrogen rotational relaxation time is estimated. The possibility of using simplified intermolecular interaction models, namely, the variable-diameter sphere model employed together with a phenomenological consideration of the TR-exchange, is studied. Gasdynamic parameter profiles in the shock wave are analyzed. Simple approximations of the velocity gradient and translational and rotational temperature profiles are obtained on the basis of a parametric calculation of the shock wave structure. This makes it possible approximately to describe the gasdynamic parameter profiles in terms of elementary functions.

118 空気及び窒素の強い衝撃波背後の分光計測と数値シミュレーション

118 空気及び窒素の強い衝撃波背後の分光計測と数値シミュレーション

4 Carlo direct simulation of rotational relaxation of diatomic molecules using classical trajectory calculations: Nitrogen shock wave

For accurate and realistic simulations of the rotational relaxation of diatomic molecules, the direct simulation Monte Carlo (DSMC) method is coupled with the classical trajectory calculations (CTC) for full three-dimensional collisions of two rigid diatomic molecules. The CTC-DSMC method with the null-collision technique is examined by simulating the rotational relaxation of nitrogen in an isolated cell over a wide range of temperature using the extended Morse and Lennard-Jones potentials. Although both the potentials yield almost the same results, the extended Morse potential is more efficient than the extended Lennard-Jones potential for use in the CTC-DSMC method. The CTC-DSMC method with the extended Morse potential is applied to the simulation of the rotational relaxation of nitrogen through low and high Mach number shock waves. The CTC-DSMC results obtained using available values of the potential parameters agree well with the experimental results of Robben and Talbot.

A threshold line dissociation model for the direct simulation Monte Carlo method

A new dissociation model for the direct simulation Monte Carlo (DSMC) method is formulated using the threshold line concept. This model considers in some detail the coupling between the vibrational energy distribution of molecules in a gas and the rate of dissociation. For a particular reaction, the new threshold line model only requires determination of a leading multiplicative constant and is therefore significantly less deterministic than existing DSMC chemistry models. The new model is evaluated in a heat bath under equilibrium and nonequilibrium conditions. It is also employed to calculate hypersonic shock waves of nitrogen and air. Comparison of the results generated with the new model is made with existing experimental data and with previous computational results. The more detailed DSMC implementation reveals properties of the threshold line dissociation model not apparent in the previous continuum implementation.

Numerical investigation of the effect of rotational relaxation rate on the nitrogen shock wave structure

The nitrogen rotational relaxation process is numerically investigated on the basis of the Monte-Carlo method and the calculation of the classic three-dimensional equations of motion of rigid-rotator molecules. The dependence of the relaxation parameterZ R on the initial values of the translational and rotational temperaturesT t andT R and the asymmetry parameter in the molecular interaction potential is obtained. The problem of the shock wave structure is solved using the Pullin phenomenological model whose parameters are determined on the basis of the solution of the relaxation problem with exact calculation of the molecular interaction. The dependence of the flow fields and the relative thickness of the density profile on the quantityZ R is obtained and the calculated data are compared with the results of experiments. It is shown that the data are in better agreement for larger values of the asymmetry parameter.

Computation of axisymmetric and ionized hypersonic flows using particle and continuum methods

Comparisons between particle and continuum simulations of hypersonic near-continuum flows are presented. The particle approach employs the direct simulation Monte Carlo (DSMC) method, and the continuum approach solves the appropriate equations of fluid flow. Both simulations have thermochemistry models for air implemented including ionization. A new axisymmetric DSMC code that is efficiently vectorized is developed for this study. In this DSMC code, particular attention is paid to matching the relaxation rates employed in the continuum approach. This investigation represents a continuum of a previous study that considered thermochemical relaxation in one-dimensional shock waves of nitrogen. Comparison of the particle and continuum methods is first made for an axisymmetric blunt-body flow of air at 7 km/s. Very good agreement is obtained for the two solutions. The two techniques also compare well for a one-dimensional shock wave in air at 10 km/s. In both applications, the results are found to be sensitive to various aspects of the chemistry model employed.

Direct simulation with vibration-dissociation coupling

The majority of implementations of the Direct Simulation Monte Carlo (DSMC) method of Bird do not account for vibration-dissociation coupling. Haas and Boyd have proposed the vibrationally-favored dissociation model to accomplish this task. This model requires measurements of induction distance to determine model constants. A more general expression has been derived that does not require any experimental input. The model is used to calculate one-dimensional shock waves in nitrogen and the flow past a lunar transfer vehicle (LTV). For the conditions considered in the simulation, the influence of vibration-dissociation coupling on heat transfer in the stagnation region of the LTV can be significant.

Statistical inelastic cross-section model for the Monte Carlo simulation of molecules with continuous internal energy

The statistical inelastic cross-section [SICS(C)] model for the Monte Carlo simulation of molecules with continuous internal energy is derived by modifying the SICS(D) model for discrete internal energy [Phys. Fluids A 4, 1782 (1992)]. The SICS(C) model specified for rotationally inelastic collisions with the use of Parker’s rotational energy gain function is applied to the Monte Carlo simulation of a nitrogen shock wave and compared with the SICS(D) model.

Temperature dependence of rotational relaxation in shock waves of nitrogen

Computations are presented for one-dimensional Shockwaves of diatomic nitrogen. The direct simulation Monte Carlo method (DSMC) is employed. A model which allows the use of the Sutherland viscosity model in the DSMC technique is further developed to include the modelling of rotational relaxation. This is achieved by employing a temperature-dependent expression for the rotational collision number to simulate the rate of relaxation, in contrast to earlier DSMC studies which employed a constant value for the collision number. The behaviour of the new model is first considered for rotational relaxation in a heat bath. Comparison is made with the more traditional DSMC collision model termed the variable hard sphere (VHS) model in which the viscosity has a fixed temperature exponent. These two models are then applied to a number of shock-wave cases for which experimental data exist. These have Mach numbers ranging from 1.5 to 26, yet the enthalpies involved are sufficiently low to allow omission of vibrational relaxation. It is found that both the VHS and Sutherland viscosity models give excellent agreement with the experimental data for shock-wave thickness, and for profiles of density, rotational temperature, and velocity. The most significant finding of the study is that the reciprocal shock thickness varies with the upstream temperature condition. This variation is observed in the experimental data, and is simulated numerically by employing the temperature-dependent expression for the rotational collision number.